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Progress in Aerospace Sciences 41 (2005) 93–142

www.elsevier.com/locate/paerosci

Property measurement utilizing atomic/molecularfilter-based diagnostics

M. Boguszko, G.S. Elliott�

Department of Aerospace Engineering, University of Illinois Urbana Champaign, 306 Tabolt Laboratory, 104 South Wright Street,

Urbana, IL 61801-2935, USA

Abstract

A variety of atomic/molecular filter diagnostic techniques have been under development for qualitative and

quantitative flow diagnostic tools since their introduction in the early 1990s. This class of techniques utilizes an atomic

or molecular filter, which is basically a glass cell containing selected vapor-phase species (e.g., I2, Hg, K, Rb). In filtered

Rayleigh scattering (FRS), and techniques derived from it, the atomic/molecular filter is placed in front of the detector

to modify the frequency spectrum of radiation scattered by flow-field constituents (i.e., molecules/atoms and/or

particles) when they are illuminated by a narrow linewidth laser. The light transmitted through the filter is then focused

on a detector, typically a CCD camera or photomultiplier tube. The atomic/molecular filter can be used simply to

suppress background surface/particle scattering, and thereby enhance flow visualizations, or to make quantitative

measurements of thermodynamic properties. FRS techniques have been developed to measure individual flow

properties, such as velocity (when the scattered light is from particles) or temperature (when the scattered light is from

molecules), and measure multiple flow properties simultaneously such as pressure, density, temperature, and velocity.

This manuscript summarizes the background needed to understand FRS techniques, and gives example measurements

that have been used to develop FRS, demonstrate its capabilities, and investigate flow fields (both non-reacting and

combustion) of research interest utilizing the unique capabilities of FRS. In addition, FRS has been used in conjunction

with other diagnostics to improve the technique or measure properties simultaneously such as temperature and velocity

(measured with PIV), or temperature and species concentration (measured by Raman scattering or laser-induced

fluorescence). Also, a brief discussion is given of similar techniques being developed which utilize atomic/molecular

filters and Thomson scattering from electrons to measure the electron number density and electron temperatures in

plasmas.

r 2005 Elsevier Ltd. All rights reserved.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

1.1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

1.2. Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

1.3. General description of molecular/atomic filter-based techniques for property measurement . . . . . . . . . 96

e front matter r 2005 Elsevier Ltd. All rights reserved.

erosci.2005.03.001

ing author. Tel.: +1217 265 9211; fax: +1 217 265 0720.

ess: elliottg@uiuc.edu (G.S. Elliott).

ARTICLE IN PRESS

Nomenclature

a polarizability

B background calibration coefficient

c speed of light

cp specific heat at constant pressure

cv specific heat at constant volume

C dark current and offset constant

E radiant energy

gðy;T ; nÞ scattering spectral distribution based on

Gaussian model

gðnÞ absorption line shape (assumed Gaussian)

h Planck’s constant

I transmitted radiant intensity through the

filter

I0 incident radiant intensity to the filter cell

k Boltzmann’s constant

kl laser propagation direction unit vector

ks scattering direction unit vector

K energy-to-grayscale conversion constant

l filter cell optical path length

L optical path imaged at detection element

m molecular mass

n index of refraction

N fluid number density

Npe number of photo-electrons

p pressure

r(y) Rayleigh scattering spectral distribution

(Cabannes line)

RðfÞ Rayleigh scattering calibration coefficient

S grayscale value (counts)

tðnÞ filter absorption function

T temperature

u, v, w Cartesian velocity components

uk velocity component along j vector

V velocity vector

x non-dimensional frequency

Xj mole fraction of gas species j

y order parameter

Greek letters

aj scattering angle with respect to horizontal

plane

b background scattering cross section

g anisotropy

Gj integrated absorption coefficient for ab-

sorption transition j

DnD optical frequency Doppler shift

DnT FWHM of the Rayleigh scattering spec-

trum

Dnj FWHM of absorption line j

DO scattering solid angle

� optical efficiency constant

z frequency function

Z fluid shear viscosity

y scattering angle w.r.t. the laser propaga-

tion direction

j scattering wave vector

l laser wavelength

r degree of polarization

s Rayleigh scattering cross section

ds=dO differential scattering cross section

n optical frequency (GHz)

n0 laser central optical frequency

n frequency wave number (in cm�1)

nj frequency line center of absorption transi-

tion j (in cm�1)

f angle relative to the incident laser polar-

ization

c angle between incident and detected polar-

ization vectors

Subscripts

cam camera filter cell

e electron

i incident quantity

iso isotropic

j running index for multiple quantities

f filtered

p polarization-sensitive quantity

pe photo-induced electrons

photon relative to a photon

ref reference condition

s scattered quantity

stp standard temperature and pressure

u unfiltered quantity

0 polarization-insensitive quantity

1 undisturbed flow quantity

Superscripts

c spectral central line alone

M total number of absorption transitions

Acronyms

ASE amplified spontaneous emission

BBO beta barium borate crystal

BUT buildup time

CARS coherent anti-stokes Raman scattering

CCD charged coupled device

CW constant wave

CMOS complimentary metal oxide semiconductor

DC direct current

DGV Doppler global velocimetry

FARRS filtered angularly resolved Rayleigh scat-

tering

FRS filtered Rayleigh scattering

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–14294

ARTICLE IN PRESS

FM-FRS frequency-modulated FRS

FWHM frequency width at half-maximum

HSRL spectral high-resolution LIDAR

ICCD intensified CCD

KTP potassium titanyl phosphate crystal

LIDAR light detection and ranging

MFRS modulated FRS

Nd:YAG neodymium-doped yttrium aluminum gar-

net crystal

Nd:YVO4 neodymium-doped orthovanadate crystal

PD photodiode

PDV planar Doppler velocimetry

PIV particle image velocimetry

PLIF planar laser-induced fluorescence

PMT photomultiplier tube

QE quantum efficiency

RF radio frequency

SBS stimulated Brillouin scattering

STP standard temperature and pressure

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 95

2. Rayleigh scattering from atomic and molecular species . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

2.1. Intensity characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

2.2. Spectral characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

3. Atomic/molecular absorption filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

4. The FRS signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

5. Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

5.1. Typical atomic/molecular filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

5.2. Illuminating lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

5.3. Laser frequency monitoring. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

6. FRS flow visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

7. Single property measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

7.1. FRS velocimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

7.2. Frequency-modulated filtered Rayleigh scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

7.3. FRS thermometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

8. Multiple property measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

8.1. Average measurements (FRS frequency scanning technique) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

8.2. Instantaneous measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

9. Combined techniques and future trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

10. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

1. Introduction

1.1. Motivation

Recent advances in sensor and laser technologies have

led many flow diagnostics previously utilized only in the

development laboratory to gain widespread use as ‘‘off-

the-shelf’’ diagnostics. Techniques such as particle image

velocimetry (PIV) and spectroscopy are now more

widely available due to advances in camera, laser,

computer, and sensor technologies and are common-

place due to reduced costs and software integration

making them more ‘‘user friendly’’. This has led to a

more complete understanding of many thermal/fluid

systems and the ability to verify computer models of

complex flows. As these techniques are more universally

applied to problems of research interest, there is still a

need, however, to develop techniques that measure

properties non-intrusively without introducing artificial

particles or substances into the flow being measured. In

addition, it is desirable to enhance current capabilities so

that multiple properties can be measured simultaneously

and in more than one spatial dimension. The perfect

technique might be thought of as one that allows the

measurement of all the properties, everywhere, at all

times. For example, properties in a compressible flow

may vary significantly throughout the flow field (i.e.,

through shock and expansion waves) and compressible

turbulence quantities such as Reynolds stresses have

terms that involve multiple fluctuating variables that

must be measured simultaneously and independently.

The number of properties we desire to measure becomes

even larger and more complex as we consider reacting

flows and turbulent flames. Although as the subject of

the current review article, atomic/molecular filter-based

techniques do not reach all these goals, they do provide

a unique means of measuring flow properties that few

other techniques can achieve as effectively.

1.2. Background

As an introduction to molecular/atomic filter-based

techniques we consider first how these techniques came

to be utilized by the scientific research community. In

ARTICLE IN PRESSM. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–14296

1983, Shimizu et al. [1] proposed the use of atomic and

molecular vapor filters for high spectral resolution

LIDAR (HSRL). The purpose of the atomic and

molecular vapor filter was to eliminate the interference

of particles and aerosols in atmospheric Rayleigh

scattering measurements. Shimizu and colleagues pro-

posed that since the particle/aerosol spectrum has a

bandwidth on the order of 100MHz (due to the radial

wind velocities) and the Rayleigh scattering from

molecules, although much weaker, has a broader line-

width (�2GHz for visible wavelengths due to Doppler

broadening), an atomic/molecular filter may be able to

block the particle scattering, while passing much of the

Rayleigh scattering signal [1]. In their groundbreaking

paper, they presented fundamental calculations demon-

strating how the temperature (and backscatter ratio)

could be measured using HSRL and atomic/molecular

vapor filters used in conjunction with the appropriate

laser to an accuracy of 71K if the signal-to-noise ratio

is 300. Later, utilizing a pulsed Nd:YAG laser and

iodine-vapor filter, Hair et al. [2] developed an HSRL

system which measured the atmospheric temperature

over an average time span of about 6 h, and an altitude

range of 2–5 km for eleven nights, yielding values

accurate to within 72.0 K of balloon soundings. The

authors also discussed the use of different molecular/

atomic filters and the upper limit of temperature

sensitivity with the technique.

From Shimizu’s initial LIDAR application, two

research groups applied similar types of filters to the

area of fluid mechanics. Komine, Brosnan and Meyers

[3,4] introduced atomic/molecular filters to fluid me-

chanics research in the 1990s to measure the velocity in a

seeded flow in a technique they termed Doppler global

velocimetry (DGV). With DGV (which also has been

termed planar Doppler velocimetry, PDV, by some

investigators [5–7]) one records laser radiation scattered

from particles, when the laser optical frequency is tuned

to a gradual sloping edge of the filter absorption profile.

The shifts in frequency are thus detected as changes in

iodine cell transmission, while rationing filtered and

unfiltered images (taken simultaneously) removes seed-

ing non-uniformities. The Doppler shift, and therefore

the velocity, can be determined by converting the

measured cell transmission to frequency. Of course,

since these initial efforts, much development has taken

place, as summarized by Elliott and Beutner [8], and

Samimy and Wernet [9].

At approximately the same time period Miles and

Lempert [10,11] introduced another atomic/molecular

filter technique termed filtered Rayleigh scattering

(FRS) based on the scattered light from atoms/

molecules (or even small condensation particles in the

Rayleigh scattering regime, in which case the technique

becomes similar to PDV without artificial seeding). In

FRS Miles and colleagues illuminated the flow field with

a sheet of laser light from a frequency-doubled injection-

seeded Nd:YAG laser and modified the spectrum of the

scattered light from the flow field using an iodine vapor

filter placed in front of the detector. By tuning the

narrow linewidth laser to an absorption line of iodine,

the scattering passing through the filter is spectrally

modified. FRS was first demonstrated by Miles and

Lempert to improve flow visualizations by blocking

strong background scattering from walls and windows,

and later with Forkey the technique was developed to

measure flow quantities [10–14]. From these initial

studies several investigators have further developed

FRS techniques and applied them to study various flow

fields. This article will review the development and

application of FRS, as well as techniques that utilize

similar technologies for flow property measurement. In

particular, we will highlight the applications of FRS

where molecules or particles small enough to be

considered in the Rayleigh scattering regime have been

utilized

1.3. General description of molecular/atomic filter-based

techniques for property measurement

In most FRS techniques, the laser beam is either

focused to a small volume or formed into a sheet that

interrogates the flow field to be measured. As the

incident light encounters the particles or the gas

molecules in the flow field, a portion of the light is

scattered. Whether from small particles or molecules in

the flow field, the scattering intensity and spectral profile

contain information about the fluid properties. The

scattering from particles will be shifted in frequency due

to the Doppler effect (which will be presented shortly),

and the magnitude of the shift is a function of the

velocity and observation direction. Since particles are

generally not affected as much by the microscopic

thermal motion (due to their relatively high mass

compared to molecules) they generally have a spectral

linewidth approximately equal to that of the radiation

source, which is on the order of tens of megahertz when

narrow-bandwidth lasers are used; this is represented in

Fig. 1(a). It should be noted that if the particles were

uniformly distributed within the interrogation volume

the total scattered intensity would be also proportional

to the density, but often the process is affected by

varying particle size, agglomeration, and formation/

evaporation processes. If the scattered light is from gas

molecules, as shown in Fig. 1(b), the shape of the

molecular Rayleigh scattering spectrum is related to

other flow properties in addition to the velocity-induced

Doppler shift. As will be shown in detail in Subsection

2.1, the total intensity of the scattered light is related to

the density, the width of the spectrum is related to the

temperature, and the spectral line shape is related to

both pressure and temperature. Therefore, the molecular

ARTICLE IN PRESS

Camera or Detector

Atomic/MolecularFilter

Laser Sheet

Polarizer

Interference filter

Fig. 2. General FRS optical arrangement.

0.0

0.2

0.4

0.6

–3 –2 –1 0 1 2 3Optical Frequency ν

–3 –2 –1 0 1 2 3Optical Frequency ν

y (T, p)

0.8

1.0

∆ν (T )T

I (N )

Inte

nsity

(a.

u.)

Inte

nsity

(a.

u.)

Molecular Rayleighscattering spectrum

Laserspectrum

0.0

0.2

0.4

0.6

0.8

1.0

∆ν (V)D

∆ν (V)D

Particle scatteringspectrum

Laserspectrum

(a)

(b)

Fig. 1. Characteristics of the spectral intensity profile from

particle (a) and molecular (b) scattering.

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 97

Rayleigh scattering spectral intensity profile contains

information about the properties of the fluid (pressure,

density, temperature, and velocity) and a measurement

of these properties can be made if their contributions are

separated. To accomplish this, FRS employs a mole-

cular or atomic filter, which acts as a spectral absorption

notch. The filter is simply a glass cell that contains a

species in vapor form with absorption lines that are

accessible in frequency by the interrogating laser. The

scattered radiant energy is collected by a detector [e.g.,

photomultiplier tube (PMT), photodiode (PD), etalon]

or imaged by a CCD camera through the atomic/

molecular filter, which is placed in front of it. Fig. 2

illustrates the general optical experimental arrangement,

consisting of the three major components. By utilizing

this frequency notch filter, researchers have been able to:

reduce background scattering from walls and windows

in flow visualizations, measure individual flow proper-

ties such as velocity and temperature, or deduce multiple

flow field properties simultaneously. The remainder of

this paper will describe the background needed to

understand FRS, and by extension, other diagnostic

techniques that are based on similar principles.

2. Rayleigh scattering from atomic and molecular species

2.1. Intensity characteristics

The process of light scattering by air molecules was

presented by Lord Rayleigh [15] utilizing a simple

mechanical model. This model consists of a positively

charged nucleus containing the majority of the mass

surrounded by a negative shell of electrons. The binding

forces between the nucleus and electrons are represented

by ideal springs. The system is assumed to be in

electrical equilibrium (i.e., non-ionized), with the nega-

tive charge spherically distributed concentric to the

nucleus (i.e., non-polar). The binding forces are assumed

to be linear and with the same spring constant in all

directions (i.e., isotropic system obeying Hooke’s law).

When the system is subjected to an electromagnetic

field it will experience a redistribution of its electric

charges bringing the negative and positive charges to a

new equilibrium position, creating an induced dipole.

The dipole, based on the assumption of isotropy will

align itself with the electric field and will try to

counteract its action, according to Lenz’s law. In the

case of an electromagnetic wave, the induced dipole will

follow the time-varying electric field with the same

frequency, producing a secondary wave propagating

outwardly from the dipole. In general, scattering is

considered to be in the Rayleigh regime when the

particle size is less than 1/10 of the wavelength of the

incident wave [16]. In this regime the electric field of the

primary wave can be safely considered uniform across

the particle. Since visible light ranges between approxi-

mately 400 and 700 nm, molecules (such as those

comprising air) are generally considered to be in the

Rayleigh scattering regime.

The ratio of the total scattered intensity to incident

irradiance is a measure of how much energy is being

taken away from the primary wave and radiated in all

ARTICLE IN PRESSM. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–14298

directions, and is known as the scattering cross section,

generally denoted in the literature as s. A very clear and

intuitive derivation of this quantity using the Rayleigh

mechanical spherical model is presented by McCartney

[16]. Detectors usually receive a fraction of the total

scattering over a limited solid angle DO, so a more useful

quantity is the differential scattering cross section

ds=dOU The latter is defined as the intensity per unit

irradiance per unit solid angle, scattered at an angle fwith respect to the incident polarization direction, and

for a perfectly isotropic gas it is expressed as

dsiso

dO¼

4p2ðnstp � 1Þ2

N2stpl

4sin2 f, (1)

where nstp and Nstp are the index of refraction and

number density respectively, measured at STP (standard

temperature defined at 273.15 K), l is the wavelength of

the incident radiation, and the subscript iso indicates the

condition of isotropy. The scattering in this case is fully

polarized in the same direction as that of the incident

radiation and can be observed in monatomic gases such

as helium, argon, etc, or spherical-top molecules such as

methane, carbon fluoride, etc. The cross section depends

on the substance (through the index of refraction) and is

inversely proportional to the fourth power of the

incident laser wavelength. The scattered light intensity

has a toroidal spatial distribution as seen in Fig. 3. For

this reason, it is always preferable to align the

polarization direction perpendicularly to the measuring

direction (on the x2y plane in Fig. 3) so that the

detected signal is strongest.

More generally, gases such as air or many combustion

byproducts are not isotropic, and therefore their

polarizability tensor is not spherical. The incident

radiation induces changes in vibrational and rotational

states of the molecules, and thus gives rise to vibrational

Polarization direction

x y

z

Fig. 3. Spatial distribution of the differential angular Rayleigh

scattering cross-section.

and rotational Raman scattering, both of which reach

the detector as well. The vibrational manifold intensity is

spectrally well separated (on the order of 103 cm�1) from

the incident frequency and contains less than 0.1% the

total signal and thus can be neglected in most cases. The

rotational manifold is composed by the Stokes and anti-

Stokes bands (lines appearing at lower and higher

frequency, respectively), and Q-branch (same frequency

as the incident energy). All of these components are

incoherent due to the random orientation of the

molecules, which are averaged within the interrogation

volume, and so, their scattering signal is partially or

fully depolarized.

The polarizability tensor was expressed by Placzek

[17] in terms of an isotropic part and an anisotropic part.

Placzek introduced two invariant scalar quantities

derived from them that completely characterize the

system, namely the polarizability a (equal to the trace of

the isotropic tensor) and the anisotropy g (equal to the

second invariant of the polarizability tensor). With this

concept, the central portion (unshifted) molecular

scattering can be thought of as originating from

perfectly spherical imaginary molecules (now referred

to as the Placzek trace component [18]), and from Q-

branch rotational Raman. These two occur at the same

frequency as that of the incident wave and are referred

to as the Cabannes line [18], which will be described in

further detail in the next sub-section. The frequency-

shifted bands (Stokes and anti-Stokes rotational Ra-

man) fall only a few cm�1 away from the Cabannes line

and are also referred to by many authors as the wings of

the scattering profile [21]. If the scattering medium is air

and one uses linearly polarized incident light and

polarization-insensitive detector, the wings contribute

approximately 2.5% of the total scattering intensity (see

[2,21]), and because they are so close to the Cabannes

line their contribution is often not negligible. Young [19]

points out that ‘‘Rayleigh scattering consists of rota-

tional Raman lines and the central Cabannes line’’. He

discourages the use of the term Rayleigh or Rayleigh–

Brillouin line when referring to the central feature, and

instead favors the term Cabannes line to avoid any

confusion. This terminology has been recently adopted

by Miles et al. [20], and Hair et al. [2] among others.

The degree of depolarization of the detected scatter-

ing, usually expressed in the literature with the symbol r,

is defined as the ratio of observed scattering with

polarization perpendicular and parallel to the incident

radiation vector. The depolarization takes different

values depending on how it is measured. Kattawar et

al. [21] tabulated relative scattering intensities, which

provides the necessary information for the investigation

of polarization effects in all circumstances. For instance,

let us assume that the incident radiation propagates

horizontally along the x-axis of a Cartesian coordinate

system and the detector is on the horizontal plane in the

ARTICLE IN PRESS

Polarizationdirection

x

y

z

Propagationdirection

Observationdirection

π/2

Fig. 4. Schematic representation of the polarization, propaga-

tion and observation directions.

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 99

y direction (see Fig. 4) then the depolarization is

rp ¼3g2

45a2 þ 4g2; r0 ¼

6g2

45a2 þ 7g2and so r0 ¼

2rp

1þ rp

,

(2)

where the subscript p and 0 indicate polarized (in the z

direction) and unpolarized incident radiation, respec-

tively. Note that in this case the total Rayleigh scattering

(Cabannes+wings) is detected. If the wings are spec-

trally removed, for instance by means of an narrow-

band filter (e.g., a spectrometer) before reaching the

detector, only the Cabannes portion will be captured;

then the depolarization becomes

rcp ¼

3g2

180a2 þ 4g2; rc

0 ¼6g2

180a2 þ 7g2and rc

0 ¼2rc

p

1þ rcp

,

(3)

where the superscript c makes it explicit that the

Cabannes line is the only contribution. However, except

for H2, which is very light and thus has the rotational

bands spectrally separated, it is difficult to remove the

rotational Raman with ordinary interference filters,

where 1 nm FWHM is considered very narrow.

In typical laboratory Rayleigh scattering experiments

the incident radiation is polarized, as it comes from a

laser source, and the total Rayleigh scattering is

collected, and therefore rp is normally used. In atmo-

spheric studies, however, r0 is preferred (as the source,

sun light, is unpolarized). Different research groups have

published data for both quantities. For example,

Fielding [22] reports values of rp for different species,

while Bates [23] gives values of r0 for air. Also, it is

worth noting that Bridge and Buckingham [24] pub-

lished values of rp of different gases using a helium–

neon laser, but they chose to represent the results with

the symbol r0. This shows that the terminology used is

not consistent across the literature and may possibly

lead to bias errors as noted by Young [25]. An

interesting technique that takes advantage of the

different depolarization ratios was introduced by Field-

ing et al. [22]. With it, they measured temperature,

mixture fraction and species in flames, where the species

are determined by detecting the depolarized Rayleigh

signal. Although the intensity of the latter is about 10�2

with respect to the total Rayleigh scattering they point

out that it still represents a gain in signal strength by a

factor of about 10 as compared with vibrational Raman

scattering methods.

The differential Rayleigh cross section from an

anisotropic gas is presented by Penney [26] from the

quantum mechanical formulation. Its value can be

expressed in an equivalent but slightly different, form as

dsdO

� �p

¼4p2ðnspt � 1Þ2

N2sptl

4

3

3� 4rp

!½rp þ ð1� rpÞ cos2 c,

(4)

dsdO

� �0

¼4p2ðnspt � 1Þ2

N2sptl

4

3

3� 4rp

!

½2rp þ ð1� rpÞ cos2 c, ð5Þ

where subscripts p and 0 on the left-hand side indicate a

polarization-sensitive or polarization-insensitive detec-

tion, respectively; c is the angle between the incident

and detected polarization vectors. The only difference

between the detection scheme of Eqs. (4) and (5) is the

use of a polarizer or a beam-splitting cube in front of the

detector. According to this definition we have cos c ¼sinf; and so, for an isotropic gas, Eqs. (4) and (5) reduce

to Eq. (1). Equivalent expressions have been derived and

presented by Miles et al. [20] in terms of r0. Using the

index of refraction formula given by Birch [27] at STP,

ðn� 1Þs 108 ¼ 8342:54þ 2; 406; 147½130� nðmm�1Þ�1

þ 15; 998½38:9� nðmm�1Þ�1 ð6Þ

and Fielding’s data for rp in air [22], we obtain a

differential Rayleigh cross section of

dsdO

� �p

ðair; l ¼ 532 nm; STP;c ¼ 0Þ

¼ 5:986 10�28 cm2=steradian: ð7Þ

The factor 3=ð324rpÞ in Eqs. (4) and (5) is a result of

assuming that the total Rayleigh scattering is detected,

including Q, S, and O branches of rotational Raman. As

was mentioned above, in general it is difficult to exclude

the S and O branches for all but very light molecules

such as H2 (where rotational side bands are widely

separated) without significantly reducing the intensity of

the Cabannes line. In fact, one can use a molecular/

atomic filter to block the latter and thus resolve the

ARTICLE IN PRESS

Velocity (V)Particle

IncidentLaser Radiation

ObservedScattered Radiation

(ks – kl) ~ κ

ˆ

(ks)ˆ (kl)ˆ

ˆ

Fig. 5. Geometry of velocity and light wave unit vectors for the

Doppler shift equation.

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142100

Stokes and anti-Stokes bands, as was done by Finkel-

stein et al. [28]. In FRS thermometry (as will be

explained in Section 7) the scattering signal is reduced

as the temperature increases. Also, the Cabannes line is

significantly attenuated by the absorption filter. How-

ever, the Stokes and anti-Stokes wings remain present,

and may become important enough to impact the

results.

The energy reaching the detector, scattered through a

solid angle DO can be expressed as

Es ¼ �NLEi

Xj

X j

ZDO

dsj

dOdO, (8)

where Es is the scattered energy, Ei is the incident energy

on the probe volume, whose integration optical path

along the viewing direction is L; N is the gas number

density, Xj is the mole fraction of species j, � is the

optical efficiency constant, and dsj=dO is the appro-

priate differential Rayleigh scattering cross section of

species j. If the differential cross section variation over

the solid angle is negligible (as is typical), Eq. (8) can be

approximated as

Es � �NLEiDOX

j

X j

dsj

dO. (9)

The scattered energy is equal to the number of

scattered photons times the energy of the photon,

Es ¼ Nphc=l. Due to the finite efficiency of the detector,

the number of photo-electrons (those created by the

scattered photons when they reach the detector) is going

to be Npe ¼ �Np, where e is the efficiency stemming from

the quantum efficiency QE and transmission through the

lens system and other minor losses. Then, in terms of

photo-electrons, Eq. (9) can be written as [29]

Npe ¼�NLlEiDO

hc

Xj

X j

dsj

dO. (10)

The significance of this is that detectors such as PMTs

and CCDs respond to the number of photons striking

them (not, as such, to the energy or power reaching

them). If one substitutes in Eq. (10) the value for the

differential scattering cross section, it becomes apparent

that the detected signal (in counts, for example) is

proportional to l�3. This strong wavelength dependence

makes it attractive to work in the ultraviolet regime,

where the scattering signal is greatly enhanced. How-

ever, additional problems are encountered at ultraviolet

wavelengths, such as higher cost of equipment and

optics, diminished detector efficiencies, and possible

fluorescence interferences. Due to these problems that

many times outweigh the benefits of working in UV, a

large part of Rayleigh scattering investigations is done

in the visible range. In the next section, we will

further describe the spectral structure and position of

the central Cabannes line as a function of thermo-

dynamic properties.

2.2. Spectral characteristics

In the previous section, we focused our attention on

the fact that a molecule scatters light at the same

frequency as that of the irradiating wave. As we

carefully analyze in more detail, however, we will

show that the Rayleigh scattering central frequency

can be Doppler shifted, and second, we will discuss

that the characteristics of the Cabannes line spectral

profile are determined by the thermodynamic state of

the gas.

It is well known that when there is a relative motion

between the source and the receiver the wave suffers

a shift in frequency that depends upon the frame

of reference in consideration. For our present Rayleigh

scattering discussion we consider a moving particle

that encounters incident light and scatters a portion

of it, which is observed at a given direction as

shown in Fig. 5. In this case the Doppler shift is given

by [30]

DnD ¼1

lV � ðks � klÞ, (11)

where V is the velocity vector of the particle (or

molecule), ks is the observation unit vector (defined

from the scatterer to the observer), and kl is the incident

light unit vector defined from the laser to the scatterer.

Often it is convenient to define a quantity called the

scattering wave vector as

j ¼2plðks � klÞ, (12)

which has a magnitude

k ¼4pl

siny2, (13)

where y is the angle between the incident and observa-

tion vectors as shown in Fig. 5. Therefore, another way

ARTICLE IN PRESSM. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 101

of expressing the Doppler shift is

DnD ¼1

2pV � j (14)

or in scalar form

DnD ¼k2p

uk, (15)

where uk is the velocity component along j (see Fig. 5).

With this arrangement it is possible to measure the

velocity component along the sensitivity direction j.

From Eq. (13) it can be seen that the system is highly

dependent on the observation angle, being zero at y ¼ 0

and maximum at y ¼ p. It would be ideal to observe the

flow at an angle as close to y ¼ p as possible (back-

scatter arrangement). However, most of the work

presented here was performed on planar fields, making

the laser beam into a thin sheet of light. In order to

avoid image distortions the preferred observation

direction is generally close to y ¼ p/2. The Doppler

shift does not only play a roll in determining the

frequency shift of the center of the Rayleigh scattered

spectrum, but, is also used to describe the broadening of

the scattered spectrum. Also it is noted that the Doppler

frequency shift affects both particles and molecules by

changing the center of their respective spectral profiles

with respect to that of the incident beam.

Now that the major source of frequency shift has been

presented, we also need to determine the spectral profile

of the Rayleigh scattered light. Owing to the fact it is

difficult to model the Raman scattering lines and that

their contribution is relatively small, we will neglect

them, and only consider that the Rayleigh scattering line

shape is that of the Cabannes line.

Let us assume the radiation is scattered by molecules

from monochromatic and linearly polarized incident

light. In addition to the Doppler frequency shift due to

the bulk fluid motion, the shape of the molecular

scattering spectral intensity profile is also affected by the

molecular thermal motion, which can be related to the

thermodynamic properties (i.e., pressure, temperature,

density) of the medium. On an atomic scale, the light

scattered by each molecule is going to experience a

Doppler shift due to its motion with respect to the

source and the observer, also governed by Eq. (11). The

macroscopic result of the thermal motion is a frequency

broadening of the scattering profile, which is referred to

as thermal broadening. At a low gas density (or high

temperature) the Rayleigh scattering spectral profile is

Gaussian and is given by [20]

gðy;T ; nÞ ¼2

DnT

ffiffiffiffiffiffiffiffiln 2

p

rexp �4 ln 2

n� n0

DnT

� �2" #

, (16)

where (n2n0) is the relative frequency from that of the

irradiating beam (n0), and DnT is the full-width at half-

maximum (FWHM) of the thermally broadened profile

which is given by

DnT ¼k2p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi8kT ln 2

m

r¼

2 sinðy=2Þl

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi8kT ln 2

m

r, (17)

where k is the Boltzmann constant, m is the molecular

mass, T is the temperature, and k the magnitude of the

wave vector, which was previously defined in Eq. (13).

The FWHM of the Gaussian distribution as defined here

grows asffiffiffiffiTp

. It should be noted that the distribution is

not only dependent on the thermodynamic properties

of the gas, but also dependent on the angle between

the incident and observation light vectors, y, through the

magnitude of the wave vector (k factor). This is the

distribution observed at low densities, when the mean

free path is large with respect to the wavelength, and is

referred to as the Knudsen regime.

At the opposite extreme, when gas density is very

high, the mean free path becomes small compared to the

wavelength. In this regime, referred to as the hydro-

dynamic regime, the motion of a molecule is not

random, but correlated to the motion of the rest of the

molecules in its vicinity. The spectral distribution is

governed by the density fluctuations in the fluid [31].

This phenomenon, which is specifically related to

adiabatic sound disturbances propagating in the med-

ium, [32] produces two symmetrically displaced wings

from the incident frequency n0 (the Mandel’shtam–Bril-

louin doublet). Kattawar et al. [21] and Young [19] point

out that the Brillouin doublet can be thought of as the

translational Raman lines, while the central peak should

be called the Gross line. Additionally, a central peak

occurs at the same frequency as that of the incident

wave, which is due to the thermal diffusion [33,34]. It is

known that the ratio of the central peak to the displaced

peaks is equal to ðcp2cvÞ=cv [35]. The reader is referred

to Crosignani [33] who presents the derivation of the

spectral profile for a continuous liquid medium.

For the intermediate regime, which corresponds to

standard atmospheric pressures and temperatures, the

continuum assumption cannot be made, since the

wavelength is of the order of the molecular mean free

path. A number of kinetic models have been developed

to overcome this difficulty over the last 50 years. The

most significant works related to the study of the

Rayleigh scattering spectrum were put forth between

1966 and 1974 by Yip, Nelkin and co-workers [34–38],

Hanson and Morse [39,40], and Tenti et al. [41]. All

these works are based on the study of the double Fourier

transform of the density–density correlation function.

The S6 model developed by Tenti [41] is generally

utilized by researchers to describe the Rayleigh scatter-

ing distribution for diatomic molecules such as nitrogen.

It should be noted that the S6 model has also been

verified for a variety of atomic, diatomic, and polya-

tomic molecules [42]. Various curves using this model

are presented in Fig. 6. The Rayleigh scattering

ARTICLE IN PRESS

0.0

0.2

0.4

0.6

–3 –2 –1 0 1 2 3

x

r (x

,y)

0.8

1.0

y = 0.01

y = 0.50

y = 1.00

y = 2.00

y = 4.00

Fig. 6. Cabannes line in the over a range of y-parameters.

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142102

distribution (only Cabannes line modeled, wings are

neglected) rðx; yÞ is generally expressed asZ 1�1

rðx; yÞdn ¼Z 1�1

rðn� n0; p;T ; yÞdn ¼ 1, (18)

which is a normalized distribution defined so that the

integral over all frequencies is equal to one. The profile

is written in terms of two dimensionless parameters used

in the analysis, which are sufficient to describe the

spectrum and are given by Tenti [41] as

x ¼2pðn� n0Þ

km

2kT

� �1=2¼ðn� n0Þl2sinðy=2Þ

m

2kT

� �1=2, (19)

y ¼p

kZm

2kT

� �1=2¼

lp

4pZ sinðy=2Þm

2kT

� �1=2, (20)

where p is the pressure in the medium, Z is the shear

viscosity. The variable x is referred to as the dimension-

less frequency and the variable y is referred to as the

order parameter or simply as the y-parameter. The latter

is the ratio of the effective wavelength (given by the

inverse of the scattering wave vector) and the mean free

path. Utilizing empirical Sutherlan’s formula for visc-

osity [1] the y-parameter for air is given by

y ¼ 0:2308TðKÞ þ 110:4

T2ðKÞ

pðatmÞlðnmÞ

sinðy=2Þ. (21)

It can be observed from Fig. 6 that the shape of the

Rayleigh scattered spectrum depends upon the y-

parameter, which in turn, depends upon the thermo-

dynamic properties p and T. The width of the scattering,

namely the FWHM grows with the square root of

temperature. Additionally, both x and y depend upon

the angle between the incident and observation direc-

tions through k. Also, the kinetic model satisfies, as is

expected, both Knudsen and hydrodynamic regimes at

the two ends of its range of applicability. As observed

for y51 the spectral profile is essentially Gaussian and

the scattering can be considered to be in the Knudsen

regime, but as y increases the profile tends toward the

hydrodynamic regime as evidenced by the three distinct

peaks described previously. One can now consider that

since the shape of the scattering spectral distribution is

governed by the thermodynamic properties of the gas,

it may be possible to obtain their values from the

scattered light.

3. Atomic/molecular absorption filter

In order to improve flow visualizations or obtain

thermodynamic properties of the fluid flow, it is

necessary to spectrally modify the shape of the Rayleigh

scattering spectrum. In FRS, this is accomplished with

an atomic or molecular absorption filter. The absorption

filter is created by introducing a gas of an atomic or

molecular species in a glass cell, which is placed in front

of the detector (camera or photomultiplier tube) to

modify the scattered light collected from the flow field.

In general, the absorption lines that are used in FRS

may be from single or multiple transitions (i.e., from

hyperfine splitting) merged by Doppler or collisional

broadening. The transmission profile for the atomic/

molecular filter is generally derived from Beer’s law

applied to each line making up the profile and is

represented by Forkey et al. [43,44] for an iodine

molecular filter as

tðnÞ ¼IðnÞI0ðnÞ

¼ exp lXMj¼1

½�GjgjðnÞ

( ), (22)

where l is the length of the absorption cell, j is the

individual absorption line out of all those (M) relevant

to the absorption process (i.e., an absorption line within

the frequency range of interest), n is the optical

frequency wave number (usually in units of cm�1), Gj

is the integrated absorption coefficient for each applic-

able absorption line, and gjðnÞ is the normalized line

shape. The latter is determined by the broadening

process governed by the conditions of the absorption

cell with generally three considered to be significant;

natural broadening due to the lifetime of the excited

energy state, pressure (collisional) broadening due to

collisions between species which cause dephasing of the

wave function, and temperature broadening due to the

random motion of the molecules as they absorb incident

light. In general, temperature broadening is considered

to be the most significant from order-of-magnitude

estimates of the lifetimes of the excited states and

because the absorption filters are normally operated at

ARTICLE IN PRESSM. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 103

low pressure, rendering collisional broadening small.

Therefore, in the absorption model developed by Forkey

et al. [43,44] for iodine (which has been used by several

investigators) the normalized line shape is represented as

a Gaussian profile given by

gjðnÞ ¼2

Dnj

ffiffiffiffiffiffiffiffiln 2

p

rexp �4 ln 2

n� nj

Dnj

� �2" #

, (23)

where Dnj is the FWHM linewidth due to thermal

broadening, which given for the absorption process as

Dnj ¼ nj

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi8kT ln 2

m

r, (24)

where m is the molecular mass, nj is the central frequency

wavenumber of transition j (in cm�1), T is the

temperature of the gas, and k is the Boltzmann constant.

There are three primary characteristics that the

atomic/molecular filter must meet in order for it to be

utilized in FRS experiments. First, the atoms or

molecules must have absorption lines within the

wavelength range of the laser utilized to interrogate

the flow field. There are several different laser and

atomic/molecular filter combinations that have been

utilized in FRS as listed in several previous articles,

[1,8,13] the most common of which will be discussed

shortly. Although as discussed earlier, the signal grows

proportionally to l�3, which makes it attractive to work

in or near the uv range, other characteristics about the

operation and efficiencies of the detector and laser often

determine the wavelength to be utilized. For instance,

the lasers typically have less energy per pulse, losses

through windows and collection optics are higher, and

efficiencies of the detector are lower, particularly if CCD

detectors are utilized. Secondly, the absorption line

utilized should have as sharp frequency cut-off edges as

possible, in a range significantly narrower than the

Rayleigh scattering linewidth. This enables the greatest

frequency selectivity and highest frequency profile

resolution. Since one of the objectives of the technique

is to produce velocity and property measurements, a

cutoff edge with a gradual slope would require larger

variations in the measurement quantities to be registered

as intensity changes by the detector. As a first-order

approximation, the slope of the absorption line can be

shown to be inversely proportional to the absorption

thermal linewidth given in Eq. (24) above [12].

Additionally, the filter transmission outside of the filter

should be close to unity, to prevent signal attenuation,

while inside it should be low to achieve a good extinction

ratio. Exactly how low depends on the particular

application, so it is convenient that the extinction ratio

can be variable to adapt the filter to a variety of

conditions. High extinction ratios (deep absorption

lines) are desirable when it is necessary to block strong

background reflections as is the case of flows near

surfaces. Also, from a data processing point of view, it is

convenient to have lines utilized in the measurement

relatively separated from other absorption lines so that

more of the signal outside of the absorption line passes

through the absorption filter and is recorded. It should

be noted that many of these same attributes are desirable

for other molecular filter velocimetry techniques, but the

main difference here is the desire to have sharp edges on

the profile whereas DGV and PDV velocity techniques

may favor gradual slopes for a higher bandwidth in

velocity measurements.

4. The FRS signal

Now that the characteristics of Rayleigh scattering

and the absorption filter have been described, we

consider the signal that would reach a detector viewing

the molecular Rayleigh scattering from a flow field

through an atomic/molecular filter as shown in Fig. 2.

The equations for FRS data interpretation are presented

as developed in detail by Forkey [43]. When the

scattering from the narrow-bandwidth laser is collected

by the camera through the absorption filter, the process

can be summarized as illustrated in Fig. 7. There are

essentially two sources of signal, which will be convolved

with the absorption profile as a portion of the light

is transmitted through the atomic/molecular filter; the

Rayleigh scattering from the flow, and background

scattering from walls and windows. The intensity

of the transmitted light is then integrated in frequency

when it is imaged by the camera (since each camera pixel

will sum the intensity spectrum over its range of

wavelength sensitivity). Following the expressions given

by Forkey et al. [13,43], we consider the portion of

radiant energy due to Rayleigh scattering from air

(considered as a single species) that reaches the camera

through the absorption filter from molecules in the flow

field [43] as

ERayleigh scattering

¼ NLdsdOðfÞDOEi

Z þ1�1

tðnÞ � rðn� n0 � nD; p;T ; yÞdn;

ð25Þ

where N is the fluid number density, ds=dOðfÞ is the

appropriate differential scattering cross section, Ei is the

laser radiant energy, DO (steradian) is the solid angle

subtended by the illumination region to the camera lens

or detector, and tðnÞ is the filter transmission at the

optical frequency n. Recall that the integralR

r dn ¼ 1,

so the filter produces a decrease in the energy collected

which is dependent on the relative position of the

Rayleigh scattering (Doppler shift), shape of the

spectrum (thermodynamic properties) and viewing

angle.

ARTICLE IN PRESS

Spec

tral

inte

nsity

Backgroundscattering Molecular

Rayleighscattering

ν0

∆νD

Absorptionspectrum

Tra

nsm

issi

on

Frequency Frequency

Inte

nsity

× T

rans

mis

sion

EFRS

EBG

Frequency

× =

Fig. 7. Illustration of the FRS signal created from molecular Rayleigh scattering and background scattering (from walls and/or

windows). The figure on the left is the background and molecular Rayleigh scattering spectra, the middle plot is the transmission

profile of the atomic/molecular filter, and to the right is an illustration of the convolution of the scattered light spectrum and

transmission profile resulting in the FRS signal.

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142104

Additionally, background scattering due to wall

reflections will be imaged by the detector. The spectral

distribution of the background scattering is not broa-

dened and has a spectral profile similar to that of the

incident laser. The energy due to background scatter-

ing reaching the camera through the filter is therefore

given by

EBackground ¼ bEi

ZtðnÞlðn� n0Þdn, (26)

where b is the analogous to the Rayleigh differential

cross section, that is, how much of the primary wave is

scattered [43].

As the radiation passes through the camera lens

and reaches the detector (e.g., CCD array) losses

occur from optical transmission and CCD quantum

efficiency. The latter is the number of photoelec-

trons produced per photon. In intensified cameras

(ICCD), the photons reach a photocathode and produce

the release of electrons, which are accelerated through

microchannels where by collisions on the walls release

thousands other electrons, and each of those releases

thousands more in subsequent collisions, an effect

known as cascaded secondary emission. At the end

of the intensifier the electrons hit a phosphor-coated

screen where they are converted back to photons

and are finally detected by the CCD array. In this

way, very weak signals are dramatically strengthened

although quantum efficiency is much lower. The

photoelectrons created in one sensing element over the

entire duration of the frame exposure are collected at

readout, amplified and digitized and sent to the

computer for storage as an image file. Each image

pixel is represented by an integer whose value is

proportional to the energy collected at that resolution

element. It is usual to find that the camera produces

a non-zero output even in the absence of light due

to dark current and offset. The signal recorded is

therefore given by [43]

Sðn0;DnD; p;T ;N; y;fÞ

¼ KNLdsdOðfÞDOEi

Z þ1�1

tðnÞrðn� n0 � nD; p;T ; yÞdn

þ KbEi

ZtðnÞlðn� n0Þdnþ C, ð27Þ

where K is the conversion constant from energy to

grayscale, including camera and lens efficiencies, and C

is the pedestal value due to dark current and signal

offset. In general it can be assumed that the signal

follows a linear relationship with energy, but this should

always be confirmed experimentally in the normal range

of operation of the camera. The constant C is easily

measured by taking images with the camera covered, so

it will be removed from the analysis and we will assume

that it has been subtracted out. For convenience, all the

variables that multiply the integrals of the first and

second term are grouped into two optics calibration

parameters [43]

RðfÞ ¼ KLdsdOðfÞDOEi, (28)

B ¼ KbEi (29)

yielding the equation for the recoded signal given by [44]

Sðn0;DnD; p;T ;N; y;fÞ

¼ RN

Z þ1�1

tðnÞrðn� n0 � DnD; p;T ; yÞdn

þ B

Z þ1�1

tðnÞlðn� n0Þdn. ð30Þ

This equation represents the value of the signal at a

single resolution element (pixel) in the image, which we

will refer to as the FRS signal in our discussions to

follow. The same process occurs at all the other elements

of the CCD and it is assumed that each one of them is

ARTICLE IN PRESS

0.7

0.8

0.9

Tcell = 373 KTcell = 393 KTcell = 413 K

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 105

independent. It should be noted that the formalism of

this derivation is credited to Miles, Lempert, and Forkey

who were the initial developers of FRS with the

nomenclature presented following Forkey’s dissertation

where additional details are given [13,43].

(b)

Tra

nsm

issi

on

-2 -1 0 1 20.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0TI2 = 308 KTI2 = 313 KTI2 = 318 KTI2 = 323 KTI2 = 328 K

(a)

Tra

nsm

issi

on

-2 -1 0 1 2

Relative Frequency (GHz)

Relative Frequency (GHz)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Fig. 9. Experimentally obtained iodine absorption profile

(centered around a wave number of 18789.28 cm�1) as a

function of cell-wall temperature (a) and side-arm temperature

(b). From Mosedale et al. [7] reprinted with permission.

5. Equipment

Before discussing applications of FRS, we note that

there is variety of equipment (i.e., cameras, detectors,

lasers, etc.) with characteristics that may be somewhat

unique to FRS techniques. The equipment and their

attributes relevant to FRS include: experimental char-

acteristics of the atomic/molecular vapor filter, unique

characteristics of the illuminating laser, and methodol-

ogies for monitoring the laser frequency accurately. It

should be noted that slightly more emphasis is placed on

the equipment utilizing the iodine molecular filter and

Nd:YAG laser since this is the most common filter/laser

combination utilized to date.

5.1. Typical atomic/molecular filter

At the heart of any FRS system is the atomic/

molecular vapor filter. Fig. 8 gives a schematic of a

typical filter cell utilized in various FRS experiments. It

is basically a glass cylinder with flat optical-quality

windows generally welded on each end. A stopcock on

the top of the cell allows it to be evacuated. Since many

of the species utilized in FRS are liquid or solid at room

temperatures and pressures, the cell is generally operated

under vacuum and wrapped with heating tape main-

taining it an elevated temperature. The side wall

temperature prevents the crystallization of the species

on the cell walls and windows which are also heated by

conduction, or may have a multiple pane design so that

the temperature of the inner window is elevated.

Elevating the temperature of the cell walls (assuming

that only atomic/molecular vapor is present in the cell)

Cell bodyTemperature ( )Tcel

Iodine Side-ArmTemperature ( )TI2

Fig. 8. Schematic of a typical atomic/molecular filter. From

Boguszko and Elliott [106]; reprinted by permission of the

American Institute of Aeronautics and Astronautics, Inc.

increases the temperature of the species, which will

change the thermal broadening of the absorption lines

and therefore should be regulated. Fig. 9a gives an

example of the effect of cell-wall temperature for

an iodine molecular vapor cell (length ¼ 22 cm, nj ¼

18789:28 cm�1, sidearm temperature ¼ 313 K). As ob-

served, the effect of cell wall temperature is not

significant since it governs the thermal broadening

process only. In most atomic/molecular cell designs, a

side-arm contains the liquid or solid species, which is

maintained at a lower temperature than the cell body.

Often the temperature is maintained by a temperature-

controlled water bath since it generally requires a more

constant temperature. This arrangement allows the

partial pressure (i.e., number density) of the filter species

to be regulated since it will deposit as a liquid/solid at

the coldest point of the cell. Fig. 9b gives an example of

the effect of the sidearm temperature for the iodine

ARTICLE IN PRESSM. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142106

molecular filter described previously. As observed, the

sidearm temperature has a much greater effect on

the absorption profile. Often for a given species

the temperature/partial pressure relationship is avail-

able. For example the relationship for iodine is given

by [43,44]

log10 pðTorrÞ ¼ 9:75715�2867:028

T I2ð�CÞ þ 254:180

, (31)

where TI2is the cold point temperature of the sidearm.

Since the latter must be controlled more accurately, and

may lead to uncertainties in the FRS measurement,

some cell designs incorporate a valve to isolate the

liquid/solid species from the cell body. This ensures that

the density (or partial pressure) of the species remains

constant, and is therefore termed a starved vapor cell

design. Although it is generally more desirable to have

an absorption profile with sharp sloping edges, non-

absorbing species may be added to the absorption cell to

provide pressure broadening resulting in a convolution

of Gaussian and Lorentzian profile, which is equivalent

to the real part of the complex error functional and

is also known as the Voigt function. The addition of the

non-absorbing species is found to greatly decrease

the slope of the absorption line and thus greatly increase

the FWHM. This is also why one must ensure that the

cell is free of contaminants that may vaporize, so that

the most optimum controllable profile can be realized.

5.2. Illuminating lasers

Several different atomic/molecular filter and laser

combinations have been proposed or actually used in

FRS measurement techniques as will be seen shortly

[1,8,20]. An applicable system generally is a combination

of a laser, which is relatively available and well

characterized by industry, with an atomic/molecular

species, which is easily handled, has characterized

absorption properties, and has lines which are sharp

and form relatively isolated absorption profiles simulat-

ing a frequency notch filter. Due to their common use in

FRS applications to be described shortly, there are three

absorption species and laser combinations discussed in

some detail here.

The most utilized filter species/laser combination is

the iodine molecular filter, generally used in conjunction

with a Nd:YAG pulsed laser (although it is noted that

iodine also has absorption lines accessible by cw argon-

ion lasers). At ambient temperature and pressure, iodine

is a solid substance of a dark blue/black color and

sublimates forming a violet color diatomic gas. Spectro-

scopic studies of the iodine molecule [43–51] show that

in the visual range absorption lines occur due to

electronic transitions with associated rotational and

vibrational states. In the literature it is recognized that

only two of these transitions affect the visual range,

namely the bound-bound Bð3Pþ0uÞ X ð1Sþ0gÞ and the

bound-unbound 1P1u X ð1Sþ0gÞ states [45]. At room

temperatures there are approximately 150 rotational

levels and 3 vibrational levels populated [47]. Absorp-

tion lines will occur only when the molecule is excited

with the exact energy to produce a transition to a higher

energy level allowed by the ro-vibrational selection rules.

As noted by Hiller and Hanson [47], there are

approximately 50 higher possible energy levels, which

give rise to approximately 45,000 absorption lines

between 500 and 650 nm. For the unbound state, the

equilibrium inter-nuclear distance of the molecule

requires a higher energy than that of dissociation. A

transition to this state produces the brake-up of the

molecule where there are no longer rotational or

vibrational states, thus producing continuum absorption

at all frequencies [45].

The absorption lines of interest are those near the

laser emission wavelength, which is produced by a

frequency-doubled, injection seeded Nd:YAG laser at

532 nm. There are several manufactures of injection-

seeded Nd:YAG laser systems, which is one of the

reasons this filter species/laser combination is so widely

used. The laser is tuned in frequency by applying a bias

voltage to the injection seeder temperature control

circuit. This changes the temperature and index of

refraction of the Nd:YAG (or Nd:YVO4) crystal which

slightly varies the output frequency (over approximately

80GHz). The injection seeder laser beam is then

introduced into the Nd:YAG host laser cavity where it

is amplified over spontaneous noise emission if it is

within the bandwidth of the longitudinal mode of the

host laser [52]. In order to optimize the output, the host

resonator is mechanically translated by mounting the

rear mirror on a piezoelectric tuning element which is

dithered to provide a feed back signal to produce the

frequency overlap with the seed laser frequency. This

typically results in slow frequency changes to prevent the

laser from unlocking. One indicator of how well the

frequency of the host laser overlaps with the injection

seeder is to monitor the Q-switch Build-up Time (BUT),

which is a voltage output proportional to the time

between the firing of the Q-switch and the occurrence of

the laser pulse. The BUT is minimized for optimized

frequency overlap indicating that most of the energy is

going into the frequency associated with the seed laser

and not spontaneous emission. Generally the resulting

linewidth is quoted as having a frequency linewidth on

the order of 150MHz. The downside of utilizing

injection seeding is that the laser is typically susceptible

to vibrations, and may unlock (support multiple cavity

modes, thus becoming broadband) unexpectedly. For-

tunately, the BUT can be monitored so that data is not

taken when the laser is not seeded. Another practical

aspect to the laser is that it has been observed to have

frequency variations across the beam of up to 100 MHz

ARTICLE IN PRESS

λ /2

λ /2

λ /2

λ /2

FastPockelCells

λ /4

CWLaser

λ /2

λ /4

PCAsse

Amp Optical Isolator

Polarizer

Fig. 11. Schematic of a Nd:YAG pulse-burst laser utilize

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

0

Tra

nsm

issi

on

18787 18788 18789 18790 18791 18792

Wavenumber (cm–1)

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25

Frequency [GHz]

Tra

nsm

issi

on

Experiment

Theory

(a)

(b)

Fig. 10. Portion of the iodine absorption spectra within the

frequency tuning range of a Nd:YAG laser (a) and comparison

of modeled (using the model provided by Forkey et al. [44])

and measured profiles in the vicinity of the feature at

18789.28 cm�1 (b).

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 107

[53] sometimes termed a frequency chirp. This has been

reported to be due to manufacturing limitations in the

Nd:YAG rods and may be fairly stable, but can be

reduced by limiting the useable portion of the laser to

the center of the beam [53,54].

Fig. 10a shows a portion of the absorption spectrum

as modeled by Forkey [13,44], corresponding to the

vicinity of the tunable range of the Nd:YAG laser (it

should be noted that this model does not include the

unbound state). The absorption lines are calculated

from published data of ro-vibrational transitions of the

B2X system. As can be observed, there are several

optically thick absorption features within the tunable

frequency range of the Nd:YAG laser that have the

characteristics mentioned previously and thus can be

utilized for FRS. The absorption feature located near

18789.28 cm�1 is often chosen as the filter band used for

FRS experiments, since it satisfies requirements stated

above. Fig. 10 shows a comparison between the iodine

absorption lines modeled and the absorption profile

experimentally measured in the vicinity of this absorp-

tion feature. As demonstrated here the agreement

between the model and measured profiles is very good

with almost all the features having similar magnitudes

and positions.

Another pulsed laser system which utilizes iodine

molecular filters in FRS techniques is the pulse-burst

laser, first proposed and developed by Lempert et al. and

Wu et al. [55,56]. Fig. 11 gives a general schematic of the

system developed and utilized by Thurow et al. [57] in

their PDV studies and is similar in concept to those

utilized by the other researchers [57,58]. The goal of this

Telescope λ /4

Telescope

λ /4

λ /2

Mmbly

Telescope

FocusingLens

ToApplication

(532 nm)

HarmonicCrystal

Waveplate

Mirror

Focal / Expanding Lens

d by Thurow et al. [57], Reprinted with permission.

ARTICLE IN PRESS

Burst Repitition Rate5 to 10 Hz (0.2 to 0.1 sec.)

Micro-pulses1 to 100 µs pulse separation

Burst1 to 99 Pulses

Time

Fig. 12. Illustration of the output of a pulse-burst laser.

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142108

laser is to provide relatively low frequency (5–10 Hz)

bursts of packets of micro-pulses at a higher frequency

(�1 MHz) as illustrated in Fig. 12. This allows the

micro-pulses to have much higher individual pulse

energy than if the laser were continually pulsed at the

high frequency. The laser is initiated with a CW

Nd:YAG ring laser which serves as the primary

amplifier. Next the beam is double-passed through a

flash-lamp pumped preamplifier. The 200-ms pulse is

then chopped into a predetermined number of micro-

pulses using a Pockels cell pulse slicer. Generally, the

pulse slicer allows micro-pulse spacing of 1 to 100ms

with the number of pulses determined by how many can

be fit into the 200 ms manifold of the Nd:YAG

amplification. This micro-pulse train is then passed

through multiple Nd:YAG flash lamp amplification

stages (some with a double pass configuration) to

increase the energy of the resulting beam. The individual

pulse energies are made relatively equal by adjusting the

energy and delay of each amplification stage, as well as

the transmission through the Pockels cell pulse slicer.

Spatial filters and telescope optics are generally used at

one or more locations in the pulse-burst laser system to

improve the beam profile, and optical Faraday isolators

are utilized to prevent feedback. In addition, a phase-

conjugate mirror is added to the system to reduce the

amplified spontaneous emission and eliminate the DC

pedestal, which decreases the energy available in each

micro-pulse [57]. Before the laser beam exit, a potassium

titanyl phosphate (KTP) crystal doubles the frequency

resulting in a wavelength of 532 nm that can be tuned in

frequency to the iodine absorption features described

previously. The pulse burst laser is tuned in a similar

manner to the injection seed laser by adjusting the

temperature of the Nd:YAG crystal in the CW ring

laser. The advantage of the pulse-burst laser design is

that it does not require injection seeding to the host laser

which results in a much more stable frequency without a

need to lock onto a host laser cavity mode using a

dithered mirror. The frequency linewidth of the pulse-

burst laser has been reported by Thurow et al. [59] to be

approximately 65 MHz before frequency doubling. The

energy of each micro-pulse varies depending on such

quantities as the leakage through the pulse slicer,

number of amplifiers in the system, and number, and

distribution of pulses, as well as other factors, but

typically ranges from 10 to 100mJ/pulse.

A second laser and filter combination that has been

utilized by researchers is the cavity-locked, injection-

seeded titanium:sapphire (Ti:Al2O3) laser and mercury

vapor cells. Application to flow diagnostics with this

combination was first introduced by Finkelstein et al.

[60]. Their Ti:Al2O3 laser which was operated in the

ultraviolet range based on the system described by Rines

and Moulton [61]. Considering the Rayleigh scattering

cross section, it is apparent that utilizing ultraviolet

wavelengths will result in more scattering signal

compared to the visible wavelengths described pre-

viously. It should be kept in mind, however, that the

gain actually achieved may not be as great due to optical

and sensor efficiencies and available laser energies at

ultraviolet wavelengths [62]. The pulsed, injection-

seeded laser developed by Finkelstein et al. [60] consists

of two Ti:Al2O3 crystals pumped by a frequency-

doubled Nd:YAG laser operating at 10Hz. The laser

is cavity-locked to its seed source which is a CW

Ti:sapphire (modified Schwartz Electro-Optics titan CW

ring laser) which is pumped by the 514 nm line of an

argon-ion laser and tunable over a range from 680 to

1100 nm. For FRS measurements utilizing mercury, the

seeded laser is tuned to 761 nm and introduced into the

unstable resonator cavity of the host laser. The pulsed

cavity’s high reflector is mounted on a custom piezo-

electric transducer with a unique ‘‘Ramp and Lock’’

methodology to allow the laser frequency to be rapidly

scanned and the frequency to be locked between the seed

and pulsed laser before every pulse [60]. In order to

attain the ultraviolet wavelengths, the near infrared

output is frequency-tripled by passing the single-mode

pulsed beam through a pair of beta barium borate

ARTICLE IN PRESS

Fig. 13. Mercury absorption profiles over a range of vapor cell

partial pressures accessible by a tirsapphire laser operating at a

wavelength of 253.7 nm. From Yalin and Miles [62]; reprinted

by permission of the American Institute of Aeronautics and

Astronautics, Inc.

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 109

(BBO) crystals. This laser developed for FRS had a

temporal linewidth of 22.5 ns and frequency linewidth of

approximately 20 MHz. It should be noted that, other

than the mercury absorption lines described below, the

seed laser has been used in conjunction with potassium

absorption cells in frequency-modulated studies which

will be described shortly [63].

Fig. 13 shows the mercury lines in the vicinity of

253.7 nm, accessible by the Ti:sapphire laser utilized in

FRS studies by Yalin et al. [62]. The transmission

profiles using the CW seed laser are shown for a cell

length of 5 cm evacuated to minimize collisional broad-

ening. The cell wall body temperature is set slightly

above the cold side-arm temperature which is varied

from 20 to 200 1C in the scan shown resulting in vapor

pressures of 0.003, 0.48 and 2.89 Torr. The transmission

profiles shown are from the 3P-1S mercury transition

with the absorption features due to the naturally

occurring isotopes of mercury [60]. Aside from the

advantages provided to the Rayleigh scattered signal by

ultraviolet illumination, several features of mercury

filters make them an excellent choice for FRS applica-

tions [62]. First is the fact that the absorption profiles

have steeply sloping edges due to the relatively high

atomic weight of mercury. The low melting point allows

the vapor pressure to be attained at reasonable

temperatures. As shown in Fig. 13 the absorption

profile changes greatly due to the increase in mercury

vapor density and collisional broadening that combines

the individual lines into a single feature by 2.89Torr.

Probably the greatest advantage of using mercury vapor

filters, however, is the fact that mercury has much

deeper absorption features than iodine and does not

suffer the continuum absorption from unbound transi-

tions as the number density is increased. Instead, away

from the absorption features, the mercury filter has a

transmission of almost unity with losses due only to

windows and broadening from the adjacent lines.

Although the previously described laser systems

utilized in FRS have all been solid-state lasers, another

laser system utilized in FRS technologies described

below are diode lasers. These can be much less expensive

than the systems previously discussed and can have a

modest cw output with a rapid and continuous tuning

capability within their operational range [64]. Due to

their lower intensities leading to weaker Rayleigh

scattering, however, diode lasers are more commonly

utilized in frequency-modulated FRS techniques [63,64]

that incorporate lock-in amplifiers so that the low signal

levels can be measured. One diode laser and atomic filter

combination utilized in modulated FRS techniques is a

GaAlAs diode operated at a wavelength of 794 and

780 nm to access the D1 and D2 lines of a rubidium

vapor filter [64]. In order to be utilized in FRS these

diode lasers typically require ultra-low current sources,

cooled thermoelectric temperature controllers and, as

reported by Mach and Varghese, must be placed in a dry

nitrogen environment so that excessive condensation is

avoided on the diode [64].

5.3. Laser frequency monitoring

Another equipment item that is somewhat special to

FRS systems is motivated by the need to monitor (and

adjust) the pulse-to-pulse laser frequency. There are two

methods that are commonly employed to monitor the

laser frequency. The first method, illustrated in the

schematic of Fig. 14, has been used by a variety of

research groups for FRS and PDV measurements that

employs a second atomic/molecular filter sometimes

termed the reference filter [6,7,65–69]. As seen in Fig. 14,

a portion of the laser beam is directed to the laser

frequency monitoring system (or wavemeter) with an

optical wedge and divided again to be directed to

multiple photodiode locations. Generally, at least three

measurement locations are utilized, one to measure the

intensity directly, one to measure the transmission

through the iodine reference filter, and a third location

used to calibrate other filters used in the experiment.

Before passing the light through the filters, the beam is

generally expanded and collimated to a larger diameter

(�28mm). After emerging from the filters, the beams

were refocused onto diffusing elements before being

collected by the photodiodes. This allowed for the

highest intensity to be sent through the filter without

saturating the transition. To ascertain whether or not

the transition is saturated, measurements could be

ARTICLE IN PRESS

testsection

Mach 2nozzle

pulsedNd:YAGlaser

portion ofseed beam M

reference CWNd:YAG laser

KTPcrystal

BS

BD

frequencycounter stabilized

referenceiodine cell

1064nm

HBS

iodinecell lock-in

amplifierand feed backcircuitry

computer -A/D board andframe grabber

intensifiedCCD camera PD

532nm

Fig. 15. Optical heterodyne beat frequency detection utilized

for FRS laser frequency measurement. From Forkey et al. [13];

reprinted by permission of the American Institute of Aero-

nautics and Astronautics, Inc.

Injection-seededNd:YAG laser

M

M

W

RC

BSBS

BI

PD1

PD2 PD3

CLBI

CLFMSFCMNDRCSW

BS: Boxcar Integrator: Beam splitter: : :

: Shutter

Collimating lensesFreq. Monitoring systemIodine filter cell

: Mirror: Neutral density filter: Reference iodine cell

: Wedge

ND

FMS

ND S

Computer FC

To flow field

Fig. 14. Reference filter based FRS frequency monitoring system.

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142110

compared with a neutral density filter inserted in the

beam path in front and behind the filter. If the former

measurement showed greater attenuation than the latter,

the filter was saturated and the irradiance of the beam

needed to be reduced. Boxcar Integrators sampled the

photodiode signals over the 10 ns duration of the laser

pulse and transferred their signals to a personal

computer. The ratio of the outputs from the integrators

is a measure of the transmission of the incident light

through the filter and, with the use of a calibrated filter/

frequency profile can establish the laser frequency. A

shutter is sometimes added to the system, which is

capable of closing and obtaining a background reference

any time the filters are calibrated or the reference

frequency is measured. Additionally the seeder BUT

voltage is measured with each pulse to ensure that the

laser is locked to single-mode operation. Generally, the

laser frequency offset voltage, photodiode values, BUT,

are recorded for each camera image and stored in a log

file. Successful operation of the frequency monitoring

system has been shown to have an ability to accurately

measure the laser frequency within 4MHz [7]. Improved

reference filter frequency monitoring systems (utilizing

fiber optics, and energy meters instead of Boxcar

Integrators) are now commercially available.

The second method of monitoring the laser frequency

utilized in a variety of FRS applications is to incorpo-

rate a heterodyne technique, combining the beam of the

laser interrogating the flow field with a second laser

which is frequency stabilized.

Fig. 15 illustrates the system, first utilized by Forkey

et al. [13]. The system starts by redirecting a small

portion of the CW injection seed laser, which sets the

frequency of the Nd:YAG pulsed laser. This portion of

the CW seed laser beam is sent through a single mode

polarization-preserving optical fiber passing onto a high-

speed detector. A second CW Nd:YAG laser (termed the

reference laser) is frequency stabilized onto the mini-

mum of an optically thin absorption feature of a

controlled reference cell (iodine in the present case).

This is accomplished by frequency doubling the beam

through a KTP crystal, passing it through the absorp-

tion cell, and focusing it on an amplified photodiode.

The signal from the photodiode is used to lock the laser

frequency using a first-derivative nulling technique. A

portion of the CW reference laser beam (before

frequency doubling) is also sent through the fiber optic

overlapping the beam from the injection seed laser. The

interference of the two beams generates a heterodyne

beat signal, which is measured by a microwave

frequency counter. The system developed by Forkey et

al. [13] is quoted to allow frequency measurements over

80GHz with an accuracy of 72 MHz. It should be

noted that similar heterodyne methodologies in FRS

techniques have been used by other researchers who

ARTICLE IN PRESSM. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 111

employ other types of CW lasers (e.g., diode lasers,

Ti:sapphire lasers).

6. FRS flow visualization

One of the first utilizations of FRS in fluid dynamics

research was to improve qualitative flow visualizations.

There are two distinct advantages of FRS when applied

to flow visualizations depending on the characteristics of

the scattered light, as illustrated in Fig. 16. First, if the

source of the scattered light is from solid particles seeded

or naturally occurring (i.e., condensation from CO2,

water, or ethanol) in the flow, the linewidth of the

particulate Rayleigh scattered light will experience little

broadening, often being approximately the same as the

interrogating laser beam. However, if the particles are

moving with the fluid and the incident and observation

directions are set appropriately [according to the

Doppler shift, given in Eq. (11)] the scattered light from

the moving particles will be shifted in frequency. The

scattered light from walls or windows in the test section

will also have a narrow linewidth similar to the

illuminating laser, but it will observe no shift in

frequency. Therefore, when a sharp atomic/molecular

filter is placed in front of the camera and the laser is

adjusted in frequency to be in the absorption well of the

atomic/molecular filter, the unshifted background scat-

tering from the walls and windows is strongly absorbed,

while the Doppler shifted light from the flow field is

transmitted and imaged by the camera. For Nd:YAG

laser and iodine filter combinations the extinction ratio

has been improved when an etalon has been added to the

oscillator cavity [70], and extinction ratios over 5 orders

of magnitude are reported for Ti:sapphire lasers and

AbsorptionProfile

BackgroundSignal TransmittedThrough Filter

BackgroundSignal

Doppler ShiftedScattering FromParticles

Spec

tral

Int

ensi

ty a

nd T

rans

mis

sion

∆νD Freq

Fig. 16. Illustration of the scattered spectra and transmission

profile for FRS particulate-based flow visualizations.

mercury filters. In general, the reason that only

qualitative flow visualizations are accomplished is due

to the fact that the number density of the scattered

particles is unknown (or not measured separately) and

therefore the transmission ratio is unknown, which

could be used to measure the velocity in techniques

discussed shortly.

Miles and Lempert [11] were the first to employ FRS

to flow visualizations in studying a Mach 2.0 supersonic

jet and supersonic boundary layers [12,71]. The scattered

light from the supersonic boundary layer images was

from condensation particles (estimated to be on the

order of 30 nm in diameter), which mark the cold

supersonic free stream and evaporate in the warmer

boundary layer near the wall. This method of seeding for

flow visualizations is sometimes referred to as passive

scalar seeding or vapor screen technique. Additionally,

the free stream provides sufficient Doppler shift to move

the frequency of the condensation outside of the

absorption filter. The resulting signal effectively marks

the free-stream fluid separately from the boundary layer,

which has a significantly lower or no signal at all. The

advantage of FRS for boundary layer flow visualizations

is clearly evident in that almost all of the surface

scattering is absorbed by the filter, which would

otherwise saturate the detector and obscure the flow

features.

Extensive FRS flow visualizations of Mach 3.0

supersonic boundary layers were also conducted by

Samimy et al. [72] and Arnette et al. [73,74] to

characterize the large scale structures. Since FRS allows

measurements to be made close to surfaces, they were

able to characterize the presence of streamwise long-

itudinal structures present in planar views. Also, Arnette

et al. [73,74] attained FRS flow visualizations of the

large-scale structures for a Mach 3.0 boundary layer.

They compared the flat plate boundary layer with

that formed after passing through a centered expansion.

Fig. 17 shows the FRS flow visualizations from water

condensation obtained in those works, where a Mach

3.0 supersonic boundary layer on a flat plate, on a 71,

and on a 141 centered expansion are shown. The large-

scale structures are clearly observed as the signal is

reduced due to the lower Doppler shift and the

evaporation of the seeding existing in the warmer

boundary layer. After analyzing several instantaneous

images, it was found that as large-scale structures pass

through the expansion wave, they increase in scale and

angular orientation. Quite striking, however, is the fact

that the laser sheet, which is directly hitting the surface

visualized, does not saturate the Rayleigh scattering

signal. This is one of the main advantages of using FRS

in flow visualizations.

FRS flow visualizations have also been utilized in

investigations on shock/shock boundary layer interac-

tions in a Mach 3.0 flow by Forkey et al. [75]. Forkey

ARTICLE IN PRESS

Fig. 17. FRS flow visualizations of a Mach 3.0 boundary layer formed on a flat plate (a), and as it propagates through a 71 (b) and 141

(c) expansion as presented by Arnette et al. [74]. The flow direction is from right to left. Reprinted with the permission of Cambridge

University Press.

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142112

and colleagues were not only able to conduct planar

FRS measurements, but they where able to construct a

volumetric FRS flow visualization image by combining

multiple planes together of averaged images. Again FRS

was necessary to minimize the overwhelming scattering

from the walls, near where the images of the flow field

were desired. Also the shock waves were clearly visible

as a discrete increase in the intensity due to the density

increase across the shock or total elimination of the

signal as the droplets evaporated due to the significant

temperature rise across stronger shock interactions.

Elliott et al. [76] have also utilized FRS to investigate

the formation of large scale structures in supersonic

shear layers and their change in characteristics as the

compressibility is increased. Also, Finkelstein et al. [60]

utilized Mercury atomic vapor filters and a Ti:Sapphire

laser to demonstrate the utility of this system for UV

flow visualizations.

Aside from single-shot condensation-based FRS flow

visualizations, investigators have also utilized multiple

laser pulses to investigate the temporal evolution of

large-scale structures in supersonic boundary layers.

Baumgartner et al. and Erbland et al. investigated a

Mach 8 supersonic boundary layer using what they

ARTICLE IN PRESSM. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 113

termed CO2-enhanced FRS imaging [77–79]. Liquid

CO2 was introduced into the stagnation chamber of the

blowdown wind tunnel which initially vaporizes at the

stagnation conditions, but later forms small particles

(cited in their paper to be less than �100 nm, although

no standard deviation is given) as the flow cools and is

expanded through the converging diverging nozzle.

Initially, single-shot instantaneous FRS flow visualiza-

tions were taken [77,78], but later tests incorporated a

double Q-switched Nd:YAG pulsed laser and two

cameras so that images could be taken at two successive

times varying from 15 to 200ms [79]. This allowed

qualitative information about the evolution of the large-

scale structures to be calculated from spatial correlations

between successive frames to determine the size,

coherence, and convective velocity of the large-scale

structures. Erbland reported that structures convect with

the free-stream velocity at the top of the boundary layer,

decreasing to approximately 95% to 98% inside the

boundary layer for the Mach 8 flow studies [79].

With the advent of Nd:YAG pulsed burst-lasers

described previously and high framing rate (at or

exceeding 1MHz) CCD and CMOS cameras, FRS

temporal flow visualizations are possible, allowing ten

to thirty images to be taken in sequence. Utilizing the

Nd:YAG pulse-burst laser with iodine molecular filters

to reduce surface scattering, Lempert et al. [80] and Wu

et al. [56] presented FRS time-sequenced flow visualiza-

tions of a Mach 2.5 boundary layer over a 141 centered

Fig. 18. Volumetric reconstruction (from 28 spanwise images taken at

Mach 8 freestream. The X0-axis is scaled using the convective velocit

Reynolds number of 1.57 l06. From Huntley et al. [81]; reprinted

Astronautics, Inc.

compression (again utilizing CO2 condensation to

enhance the Rayleigh scattering signal). The images

show the temporal evolution of the large-scale structures

and their clear interaction with the oblique shock wave

formed from the compression process. Also, they

demonstrated that the flow visualizations in different

regions of the flow field can be enhanced by tuning the

frequency of the laser to overlap different regions of the

iodine absorption feature utilized in their study.

Additionally, Huntley et al. [81] conducted several

experiments on an elliptic cone placed in a Mach 8 flow

to investigate boundary layer transition using mega-

hertz- rate imaging FRS and a pulse-burst laser. By

taking temporal span-wise images at 500 kHz, Huntley

and colleagues were able to construct volumetric images

indicating the shape of the boundary layer/free-stream

interface (as represented by the CO2 sublimation).

Fig. 18 shows the volumetric FRS flow visualizations

created from span-wise plane imaging with a Reynolds

number (based on the stream-wise distance from the

cone tip) of 1.53 106 for a 4:1 cone. The x0-axis in the

volumetric image is constructed assuming the average

convective velocity measured by plan-view images and

calculating the distance, based on the time separation

between sequential images. The frozen-field hypothesis

was then investigated for a range of conditions by taking

simultaneous plan-view images and determining if the

structures could be identified in the volumetric image.

For the upstream location, the large-scale structure is

500kHz) of the centerline region of a 4:1 elliptic cone placed in a

y and the streamwise location of the imaging plane results in a

by permission of the American Institute of Aeronautics and

ARTICLE IN PRESSM. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142114

characterized by a hemispherical bulge followed by pairs

of smaller-scale ‘‘arms’’ which wrap around either side.

The train of characteristic structures may represent

hairpin vortices as observed in subsonic boundary layers.

Other images taken further downstream indicate that

the structures become smaller and their evolution is

more pronounced. Structures of the boundary layer for

a 2:1 elliptic cone show similar results [81].

The second type of flow visualization that can be

enhanced by FRS is illustrated in Fig. 19. Again, if the

Fig. 20. Instantaneous (a) and average (b) molecular FRS flow visualiz

of 2.0. The flow is from left to right as depicted in the setup shown t

BackgroundSignal TransmittedThrough Filter

AbsorptionProfile

BackgroundSignal

Doppler ShiftedThermally BroadenedScattering FromMolecules

Spec

tral

Int

ensi

ty a

nd T

rans

mis

sion

∆νD Freq

Fig. 19. Illustration of the molecular Rayleigh scattering

spectra and transmission profile for FRS molecular based flow

visualizations.

scattered light is from molecular scattering, it may be

Doppler shifted, but more importantly, is broadened

due to the thermal motions of the molecules present in

the flow field. Therefore, background scattering from

walls and windows are again strongly suppressed, since

the linewidth of the scattering is narrow and unshifted in

frequency. One might consider why only qualitative flow

visualizations are obtained, until Eq. (30) is fully

considered and it is observed that there are many

thermodynamic and optical arrangement variables

which govern the intensity of the scattered light taken.

If these quantities are not measured, can be assumed to

be negligible, or are not modeled, then there will be more

unknowns than equations or measurements to solve

them and only qualitative measurements can be made.

Even though quantitative measurements are not possi-

ble, qualitative flow visualizations still serve a useful

purpose having led to many discoveries and descriptions

of flow phenomena.

As an example of molecular FRS flow visualizations,

Fig. 20 shows instantaneous and averaged images of an

underexpanded jet formed from a converging nozzle

operated at an equivalent Mach number (Mach number

realized if the flow was expanded isentropically from

stagnation conditions) of Me ¼ 2:0 as presented by

Elliott et al. [82]. The laser sheet and camera are oriented

for a stream-wise view of the jet as shown so that the

Doppler shift due to the dominant velocity component is

minimized and the intensity changes are more represen-

tative of density variations. As observed, the shock/

expansion diamonds and Mach disk are clearly visible

ation of an underexpanded jet with an equivalent Mach number

o the right [82].

ARTICLE IN PRESS

Fig. 21. Molecular FRS image of the evolution of a laser induced spark from a 200mJ Nd:YAG laser interacting with a Mach disk

formed from a Mach 2.0 underexpanded jet (From Adelgren et al. [83] reprinted with permission).

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 115

and well defined from the change in the density/

pressure/temperature to the scattering profile. Also the

instantaneous image clearly illustrates the presence and

character of the turbulence in the shear layer created

between the jet core and ambient air. In this experiment

the jet was slightly heated so as to avoid condensation.

The effect of velocity is reduced by orientation of the

laser sheet and camera 901 to the major (streamwise)

velocity direction. Therefore, to a first-order approx-

imation, the flow visualization represents the density

changes in the flow. Secondly, it is noted that the effect

of particles present in the ambient air is negligible, since

they have a narrow linewidth and remain in the

absorption profile of the filter. In similar measurements,

Miles et al. [71] utilized molecular FRS flow visualiza-

tion technique in an over-expanded Mach 5 jet to

compare the use of iodine filters to decrease the

background scattering with unfiltered images taken at

lower (266 nm) wavelengths. Also, investigations have

been conducted by Adelgren et al. [83] and Yan et al.

[84] to investigated the flow resulting from laser-induced

optical breakdown in air using FRS. They were able to

characterize the formation of the ringed vortex and

induced jet in the heated region, and also to provide

time-sequenced visualizations of the resulting blast

wave. In addition, Adelgren et al. [83] characterized

the effect and evolution of laser induced breakdown on

the Mach disk formed in an under-expanded jet with an

equivalent Mach number of 1.7 using molecular FRS

flow visualization. By taking images at successive time

delays from the initiation of the laser-induced spark, the

evolution of the heated region and shock interaction can

be characterized as shown in Fig. 21. As observed, the

distortion of the Mach disk (normal shock) due to the

initial blast wave is minimal (t ¼ 8ms), but as the heated

region interacts with the Mach disk (t ¼ 12–16ms) it

distorts upstream in a process sometimes referred to as

thermal lensing. At later times, a vortex ring is formed,

consistent with the interaction of density variations with

the induced curvature of the shock wave.

7. Single property measurement

Returning to Eq. (28), it is clearly evident that the

scattered signal is a function of optical quantities, and

the thermodynamics properties and species concentra-

tion (through the Rayleigh scattering cross section), and

flow velocity. One can imagine that the optical

quantities can be eliminated by normalizing the signal

by that from known conditions (e.g., ambient condi-

tions) and the effect of the background scattering can be

eliminated through calibration (so long as the latter is

not so high as to overwhelm the Rayleigh signal). As

ARTICLE IN PRESSM. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142116

observed in Eq. (30), however, the thermodynamic

quantities are still unknowns. Before describing how to

resolve all the thermodynamic properties using FRS we

will first demonstrate that individual quantities can be

resolved through a combination of assumptions, model-

ing the quantities’ interaction, or through careful

arrangement of the optics. Following is a description

of the methodologies and applications of various

research groups to measure single or a reduced set of

flow properties utilizing FRS.

7.1. FRS velocimetry

Similar to FRS flow visualizations from particulate-

based scattering discussed previously, velocity measure-

ments can be obtained from condensation particles,

which generally place the scattering in or near the

Rayleigh scattering regime. Although previous review

articles have been written on utilizing molecular filters to

measure velocity [8,9], our emphasis will be on reviewing

recent work where Rayleigh scattering was employed.

When utilizing FRS for velocity measurements from

condensation particles there are two differences from the

molecular Rayleigh scattering. First, the scattered signal

from particles is not greatly broadened due to thermal

motions of the gas and therefore we can assume it has a

constant linewidth determined by the spectral linewidth

of the laser used to illuminate the flow field. Secondly,

when utilizing FRS for velocity measurements based on

condensation particles an absorption filter with more

gradual sloping profile is sometimes needed, so that the

Doppler shift does not move the scattered signal entirely

out of the filter profile. This can be accomplished by

introducing a non-absorbing gas into the atomic/

molecular filter. This will pressure-broaden the absorp-

tion profile [7].

Fig. 22 gives a general arrangement of the laser,

cameras and atomic/molecular filter when making FRS

velocimetry measurements. This technique is also

commonly referred to as DGV, or PDV although the

MolecularFilter

Filteredcamera

Referencecamera

Beam SplitterCube

Polarizer

ImagingRegion

LaserSheet

Fig. 22. Schematic of the dual camera configuration for FRS

velocimetry (also termed DGV or PDV) measurements made

from condensation particles.

term FRS velocimetry would also be accurate since the

cases to be presented here collect the scattered light from

particles at or near the Rayleigh scattering regime. As

illustrated, the laser sheet is imaged by one camera,

which views the illuminated plane through the atomic/

molecular filter, termed the signal camera (or signal

image), and a second camera which views the light sheet

without a filter, termed the reference camera (or

reference image). A polarizer is placed before the beam

splitter to insure that there are no polarization-

dependent optical distortions between the signal and

reference images. Also, a neutral density filter is utilized

in the reference camera leg so that the two cameras have

approximately the same intensity range. The atomic/

molecular filter is similar to those described previously

containing an atomic or molecular species having an

absorption line in the frequency tuning range of the

illuminating laser, but as mentioned, the slope of the

absorption profile may be broadened with the addition

of a non-absorbing species. This results in a filter that

has a transmission profile with finite sloping edges, as

shown in Fig. 23a. The term In=I0 is the spectral

transmission of the molecular filter, with I n; defined as

the spectral intensity (intensity at frequency n) after the

cell, and I0 defined as the spectral intensity before

entering the cell. The spectral intensity of the light

passing through the molecular filter is the integral of the

product of the scattered spectral intensity from the

particles illuminated in the flow field, and the absorption

profile of the atomic/molecular filter as illustrated. As an

example, consider a case where the laser frequency, n0, is

tuned to the midpoint of the transmission profile. The

scattered light experiences a change in frequency, due to

the Doppler shift [Eq. (11)], causing the transmission

from the scattered light to either increase or decrease

depending on whether the frequency increases or

decreases. Note, also, that there is no ambiguity in the

direction of the shift: positive and negative frequency

shifts are distinguished by the increase or decrease in

transmission, respectively. The pixels of the signal

camera CCD array, record the integrated spectral

intensity transmitted through the molecular filter’s

absorption profile and is given by I. The second

reference camera (or a separate portion of the same

camera) images the flow field without the molecular filter

and is used to account for intensity fluctuations due to

laser energy variations (and/or sheet energy distribution)

or seed-concentration variations. The reference camera

records the integrated spectral intensity of the unfiltered

light I0.

After appropriately calibrating the reference and

signal camera images so that they have the same

intensity scale and spatial position on a pixel-to-pixel

basis, the integrated transmission through the cell is

obtained by dividing the intensities of the signal (I) and

reference (I0) cameras at corresponding pixels. Several

ARTICLE IN PRESS

Spec

tral

Int

ensi

ty a

nd T

rans

mis

sion

∆νD

Frequency

∆νD

Transmission ratio

Freq

uenc

y fu

nctio

n ζ c

am (G

hz)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0

0.1

0.2

0.3

0.4

0.5

–0.1

–0.2

–0.3

–0.4

–0.5

(a)

(b)

Fig. 23. Illustration of the transmission profile and particle

scattering for FRS velocimetry measurements (a) and resulting

Doppler shift frequency function (b) used to determine the

velocity from the transmission ratio measured by the calibrated

signal (filtered) and reference (unfiltered) cameras.

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 117

works have been published where the details of this

calibration process are described [5,6,7,85,86]. The trans-

mission profile is transformed so that the integrated

transmission is the independent variable and the frequency

shift is the dependent variable as shown in Fig. 23b. In an

FRS velocimetry experiment, once the integrated trans-

mission is determined from the two cameras at each

corresponding pixel, the Doppler shift can be found using

the frequency function (Fig. 23b). This process may be

represented by the equation

DnD ¼ zcamðS=Sref Þ � n0 (32)

where DnD is the Doppler shift, zcamm is the frequency

function of the filter placed in front of the signal camera,

S=Sreff is the transmission calculated at a given camera

pixel after proper calibration, and n0 is the relative

frequency of the laser, measured by the wavemeter. The

velocity is then calculated at each pixel of the image

using this measured Doppler shift in accordance with

vector relationships given in Eq. (10). As may be noted,

the measured Doppler shift is dependent on the

difference between the illumination and observation

directions, respectively. This fact may be exploited in

order to make multi-component velocity measurements

either by viewing the flow field from more than one

direction (changing the direction of the observed vector),

or by illuminating the flow field from multiple directions

(changing the direction of the incident light wave vector)

[87]. In addition, it has been shown that the laser and

camera vectors can be optimized to minimize effects on

laser frequency fluctuations and accuracy of the velocity

components [88,89]. Several works provide the details of

molecular filtered velocimetry (or DGV, PDV) systems

[5–7,85,90], detailed error analysis [86,90,91] and many

practical considerations in implementing a system

[92–94]. Utilizing FRS velocimetry offers two advan-

tages. First, particles are small, and therefore more

accurately track the flow, particularly in turbulent

regions and flows around shock waves where there can

be abrupt changes in velocity. Gustavsson and Segal [95]

theorized that for their axisymmetric supersonic Mach

2.2 jet studies, the decay time of 10 to 100 nm particles

were 2.6 ns and 55 ns respectively, clearly illustrating the

advantages of utilizing smaller particles to more

accurately measure the velocity of the gas. Second, the

scattering characteristics in the Rayleigh scattering

regime from polarized coherent light sources are more

uniform, lacking the intensity lobes characteristic of

larger particles. The latter may cause uncertainties

through the optical train particularly if beam splitters

are utilized or the optics of the signal and reference

cameras are different.

Previously, investigators have utilized condensation

particles in the Rayleigh scattering regime to make velo-

city measurements in supersonic flows [12,71], super-

sonic shear layers [91], supersonic jets [6,7,90,94,95], and

supersonic boundary layers [96]. Since the publication of

a review article on molecular filtered based velocimetry

techniques of Elliott and Beutner [8] several studies have

utilized Rayleigh scattering from condensation particles

to obtain velocity measurements.

Crafton et al. [97] applied PDV (or FRS velocimetry)

to measure three velocity components in a small-scale

supersonic Mach 1.36 jet. Fig. 24 shows the experi-

mental arrangement used for the jet study. The arrange-

ment utilizes two-camera systems and two laser light

positions so that all three velocity components could

be resolved. In order to obtain three mean velocity

components from two camera systems, two orientations

of the incident laser directions were used in the study.

The camera positions were kept the same for both

laser sheet arrangements. The combination of these data

results in three independent system sensitivity vectors.

The jet was seeded with ethanol vapor, which condensed

ARTICLE IN PRESS

Fig. 25. Three components of velocity measured using FRS velocimetry (PDV) in a Mach 1.34 jet with laser excitation at 170 and

220ms. The convective velocity (200m/s) has been subtracted from the velocity vectors (based on date reported by Crafton et al. [97]).

Laser SheetPosition #1

Laser SheetPosition #2

Molecular Filter

Molecular Filter

Excitation LaserBeam

MirrorX

Z

Y

Mirror

SignalCamera

PDVComponent #1

PDVComponent #2

Jet

SignalCamera

ReferenceCamera

ReferenceCamera

Polarizer

Polarizer

BeamSplitterCube

BeamSplitterCube

Fig. 24. FRS velocimetry (PDV) arrangement utilized by Crafton et al. [97] to measure multiple velocity components of a Mach 1.34

supersonic jet force using laser energy deposition.

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142118

in the free stream, forming small particles, which could

accurately follow the flow features. The jet was operated

at Mach 1.34 with a stagnation temperature and exit

velocity (based on isentropic theory) of 300K and

399 m/s, respectively. In addition to measuring the

perfectly expanding supersonic jet using the three

component PDV system, measurements were also taken

of the large-scale structures induced in the supersonic

shear layer using laser energy perturbation (see Fig. 25).

This is accomplished by focusing a second laser beam to

perturb the shear layer at the exit of the nozzle with

approximately 30mJ in a 10 ns pulse from a second

Nd:YAG laser. The interrogation laser beam is then

delayed (by 170 and 220 ms) from the perturbation pulse.

This allows the formation of a large-scale structure in

the shear layer that can be phase-averaged. The figure

shows the resulting three-component velocity measure-

ments obtained in this manner. This not only is a good

laboratory-scale experiment to test the FRS velocimetry

system and data reduction routines, but also is an

ARTICLE IN PRESSM. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 119

interesting flow field to quantify the evolution of the

large-scale structure as it convects downstream. The

color contours indicate the out-of-plane velocity com-

ponent while the vectors indicate streamwise and

spanwise velocity components (with the convection

velocity subtracted from the streamwise component).

Clearly visible is the large-scale structure that is formed

on the shear layer shown to the right. The PDV

technique had the required sensitivity to capture the

change in the core velocity due to the growing structure.

Additionally, one can observe the change in the

spanwise component of velocity, which indicates that a

vortical structure is present. For the later time, the

velocity field shows the effect of the large-scale structure

as it convects downstream and grows as it encompasses

more fluid from the jet core and atmosphere. An

uncertainty analysis was conducted indicating that the

random plus total uncertainty for the three-component

test was 17m/s. This uncertainty is dominated by

speckle noise, with an uncertainty in the mean measure-

ments reduced by about 10 m/s from this level. The error

reported in the mean measurements compared to

isentropic theory was approximately 7.2m/s, which is

less than 2% of the jet core velocity [97].

One recent work which again took advantage of the

naturally occurring condensation particles in the Ray-

leigh scattering regime to measure the velocity using

atomic/molecular filters was conducted by Sethuram et

al. [98]. They used an FRS velocimetry technique (PDV)

to measure the velocity field in supersonic micro flows.

Sethuram and colleagues constructed a Mach 2 rectan-

Fig. 26. Movie of the velocity field of the shear layer and large-scale

measured using pulse-burst laser based PDV. The scattered signal is co

250 kHz with the high-speed jet core at the top of the images and am

permission). The flow direction is from left to right.

gular jet with an exit height of just 1 mm and aspect ratio

of 5 to investigate the ability of PDV to measure the

velocity at small scales. FRS velocimetry techniques

have a great advantage in micro-flows over PIV

techniques since individual particles need not be

resolved, and so the particles mark the fluid continu-

ously instead of at discrete points. Although previously

researchers had been able to combine signal and

reference images on a single camera, after several optical

arrangements were attempted they found that separate

signal and reference cameras were needed to prevent

significant cross-talk (light from the signal and reference

images overlapping) between images. Similar to other

studies an injection seeded frequency-doubled Nd:YAG

laser was used in conjunction with a pressure-broadened

iodine vapor cell. With a dual camera arrangement they

were able to construct a system which had a spatial

resolution of as little as 20 mm and measured a single

component of the velocity within 15% of theoretical

isentropic values in the micro jet core [98].

Going beyond MHz-rate FRS flow visualizations and

single-shot velocity measurements, Thurow et al. have

utilized a Nd:YAG pulse-burst laser (described pre-

viously) to obtain temporally resolved FRS velocimetry

(or PDV) measurements from condensation particles in

the Rayleigh regime [57,59]. They used two high-speed

CCD cameras at framing rates of 250 kHz with

accuracies in measuring the velocity reported to be

within 16–24 m/s for single- (combined signal and

reference images on a single camera) and two-camera

systems, respectively. Fig. 26 presents a sequence of 21

structures created by a Mach 2 jet issuing into ambient air and

llected from condensation particle and the data was acquired at

bient air at the bottom (From Thurow et al. [59] reprinted with

ARTICLE IN PRESS

Fig. 28. Direct and first-harmonic FM absorption spectra of a

potassium vapor filter (Dl absorption line of potassium 39

occurring at 769.9 nm) as measured by Grinstead et al. [100].

Reprinted with permission by the Optical Society of America.

Fig. 27. Frequency-modulated laser spectrum (100MHz mod-

ulation frequency) for a titanium:sapphire laser operating at

770 nm. From Grinstead et al. [99]; reprinted with permission.

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142120

frames taken at 4ms time intervals for the shear layer

created by a Mach 2.0 supersonic jet issuing into

ambient air [59]. The high-speed supersonic core of the

jet is at the top of the image with the ambient air at the

bottom. The images capture the details of a large-scale

structure starting at the left of the first image and the

evolution of the structure and the resulting velocity field

as it is entrained and stretched by the faster moving

fluid. The velocity measured was reported to be within

5% of the expected value in the supersonic core of the

jet. This represents the first time in which the temporal

evolution of the compressible turbulence could be

quantified through velocity measurements at rates high

enough to track the spatial velocity field changes due to

individual turbulent structures at supersonic speeds.

7.2. Frequency-modulated filtered Rayleigh scattering

As utilized by the FRS velocimetry techniques

presented here, the frequency of the scattered light

collected from particles in the flow is changed by the

Doppler shift. Instead of a direct measurement of the

transmission profile to deduce the velocity, as described

above, Grinstead et al. [63,99,100] proposed and

developed a technique they termed frequency-modulated

filtered Rayleigh scattering (FM-FRS). In FM-FRS the

Doppler shift is determined utilizing frequency-modu-

lated absorption spectroscopy. Similar frequency-modu-

lated FRS techniques have been developed by Mach and

Varghese [101] and Jagodzinski and Varghese [102,103]

who investigated the feasibility of utilizing single diode

lasers, as will be described shortly.

As a first step in FM-FRS, Grinstead et al. utilized a

narrow-frequency linewidth CW titanium:sapphire la-

ser, which was modulated using a resonant electro-optic

modulator driven at 100MHz by a phased-lock oscilla-

tor [63,99,100]. The resulting laser beam has a power

spectrum, which is reproduced in Fig. 27. Side bands

representing the first harmonic (at the modulation

frequency) and second harmonic (at twice the modula-

tion frequency) appear symmetrically to the central line.

These side bands are equal, but 1801 out of phase and at

a reduced intensity from the center frequency [99].

Grinstead and colleagues utilized absorption lines of

potassium in their atomic vapor filter (at wavelengths

around 770 nm), which had a Gaussian transmission

profile. When the modulated laser profile (shown in

Fig. 27) is scanned through the filter, the direct

absorption spectrum is also Gaussian. However, if the

transmitted laser light is detected at the modulation

frequency (100MHz in the present case), the spectrum

obtained, referred to as FM absorption spectrum, is

approximately proportional to the first derivative of the

filter transmission profile. For a detailed mathematical

treatment of the FM spectrum the reader is referred to

the work by Hils and Hall [104].

Fig. 28 shows the direct and FM absorption spectra of

the D1 absorption line of potassium 39 occurring at

769.9 nm as modeled and measured by Grinstead et al.,

utilizing a CW Ti:Sapphire laser [100]. Even a qualita-

tive comparison of the direct and FM absorption

profiles reveals that the FM absorption profile is

representative of the first derivative or slope of the

direct absorption profile. As part of the FM-FRS

system, Grinstead and colleagues utilized the FM

absorption signal to form a closed-loop feedback

controller, locking the laser frequency to the cross-over

point of the FM absorption profile. If the laser

ARTICLE IN PRESS

high-speed photodiode

vapor filter

E/O modulator

feedback

phase-sensitivedetector/amplifier

referencelaser

Reference laser frequency

optical heterodyne/high-speed photodiode

frequencycounter

Real-time Doppler shiftmeasurement

flow facility

vapor filter

photomultipliertube

E/O modulator

feedback

probelaser

phase-sensitivedetector/amplifier

Probe laser frequency

Fig. 29. Schematic of the FM-FRS to measure velocity in real time. The FM-FRS system shown here utilizes two titanium: sapphire

lasers one locked directly to the potassium FM absorption line and one locking the Doppler shifted scattering from the flow field to the

FM absorption line. The frequency difference between the two lasers represents the Doppler shift, which is measured using an optical

heterodyne technique. From Grinstead et al. [99]; reprinted with permission.

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 121

frequency drifts to either side of the zero-crossing

frequency of the FM absorption spectra the closed-loop

controller was developed to return the laser frequency to

the zero-crossing frequency (a complete description of

the details of the innovative closed-loop controller is

given by Grinstead et al. [99]).

In order to make velocity measurements using FM-

FRS, Grinstead and colleagues demonstrated that not

only could the modulated laser light be obtained from

the laser directly, but also it can be obtained from the

scattering signal, as the modulated signal is preserved

when scattered light is collected from particles (CO2

condensation particles) seeded into a flow field. If the

flow is moving, however, the modulated laser light will

be Doppler-shifted in frequency [Eq. (9)] due to the

optical arrangement and flow velocity. In FM-FRS the

scattered light from the flow field is collected at the

modulation frequency using a high-speed photodetector

viewing the light through a potassium absorption filter.

Similar to using the direct laser light described above,

the scattering based FM absorption signal can be

utilized in a closed-loop control system to lock the

scattered signal (which represents the laser frequency

plus the Doppler shift frequency) onto the cross-over

point of the FM absorption spectra. The advantage of

utilizing this signal detection at RF is that the noise is

minimized making detection at low light levels possible

[99]. Originally, Grinstead et al. developed a system

utilizing two separate Ti:sapphire laser systems; one

laser was directly frequency-locked onto the potassium

FM absorption profile and the second laser was adjusted

in frequency until the Doppler shifted signal from the

flow field was locked onto an identical potassium FM

absorption profile. A schematic of the FM-FRS system

developed by Grinstead et al. is illustrated in Fig. 29

[99]. The frequency difference between the two lasers

therefore represented the Doppler shift frequency, which

could be used to calculate the velocity from Eq. (11).

Ginstead et al. utilized an optical heterodyne technique

(similar to that employed by Forkey) to measure the

frequency difference (and therefore the Doppler shift)

between the two lasers. In their initial work, they

constructed the mathematical model to analyze the

measurement capabilities and uncertainty of the system.

They also performed rotating disk velocity measure-

ments obtaining a Doppler shift of 164.472.1 MHz, in

very good agreement with the 16573MHz measured by

a conventional system. Also, they evaluated the bias

error introduced in the measurements by background

scattering (not Doppler shifted), and proposed methods

to account for or eliminate this error. Grinstead et al.

[63,100] also demonstrated that a single titanium:sap-

phire laser could be utilized by obtaining the reference

frequency from direct absorption measurement of a

second potassium reference cell instead of utilizing a

second laser and the optical heterodyne technique

(which was unavailable at the time of the test). They

performed experiments in an underexpanded supersonic

ARTICLE IN PRESS

Fig. 30. Real-time velocity measurement in a supersonic jet taken using FM-FRS. The FM-FRS system is locks the Doppler shifted

scattering from the jet to the potassium FM absorption feature and monitors the frequency with a second reference filter. The regions

indicated by B, C, and D represent the measurement as the stagnation pressure (i.e. exit velocity) is changed. From Grinstead et al.

[100]; reprinted by permission of the Optical Society of America.

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142122

jet collecting the scattered light from condensation

particles of CO2 seeded into the flow. Fig. 30 demon-

strates the ability of the single laser FM-FRS system to

measure the flow velocity in real time as the jet

stagnation pressure (and therefore exit velocity) was

varied. Fig. 30 shows the relative laser frequency (which

was locked to the Doppler shifted signal from the flow

field) measured by the potassium reference cell as the

stagnation pressure of the jet was changed as indicated

at the top of the graph. This plot clearly indicates that

the velocity can be measured in real time with an

estimated error of less than 3% in a 10-Hz bandwidth.

Mach and Varghese [101] proposed an alternative

system composed of a single GaAlAs diode laser tuned

in frequency to the absorption lines of Rb isotopes

(either the D1 or D2 lines at 794 and 780, respectively) to

produce and detect modulated filtered Rayleigh scatter-

ing (MFRS). They highlighted the low-cost, reliability,

and ruggedness of diode lasers, which are beneficial for

use in flight instrumentation and industrial applications.

The arrangement modulated the laser at 50 MHz

sinusoidally and detected the second harmonic (see

Fig. 27) of the scattering. In this way, the signal detected

through a Rubidium cell is approximately proportional

to the second derivative of the absorption spectrum. The

spectrum was realized by mounting a second modulation

of a 10-Hz ramp current to the laser tuning circuit,

which caused the laser to scan linearly in optical

frequency over 10.5GHz. In their experiments, the

authors obtained the Doppler shift by comparing the

peaks of the second-harmonic FM scans from the flow

scattering to that from a reference cell. A jet of CO2 gas

operating at high pressure was utilized to test their

system, forming condensation particles when expanding

into the atmosphere. The core velocity of the jet was

measured to be 280725m/s using their laser diode

based MFRS system and sources of uncertainties were

evaluated. Jagodzinski and Varghese later extended

MFRS to measure the velocity in unseeded flows [102],

and improved the temporal resolution of the MFRS

velocimeter [103].

7.3. FRS thermometry

Another thermodynamic property measurement, which

has been measured using FRS is temperature. To begin

our discussion let us consider again the FRS signal

equation [Eq. (28)]. In general, there are three assumptions,

that are needed to reduce the number of unknowns so that

the collected signal is only a function of temperature:

1.

The Doppler frequency shift (DnD) due to the flow

velocity is negligible. As observed in Eq. (11), this can

be accomplished when the flow velocity is negligible

or by aligning the laser and camera directions so that

they do not have a sensitivity to major (e.g., stream-

wise) velocity directions.

2.

The scattered light is from a single species whose

concentration is constant. This allows us to assume

that the Rayleigh scattering cross section [found in

the R calibration parameter; Eq. (30)] is constant and

known at every camera sensing element.

3.

The pressure is relatively constant, which for an ideal

gas allows the temperature and density to be directly

related.

With these assumptions, and the ideal gas law

given by

p ¼ NkT . (33)

ARTICLE IN PRESSM. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 123

Eq. (30) can be represented as

Sðn0; p;T ; y;fÞ

¼ RðfÞp=kT

Z þ1�1

tðnÞrðn� n0; p;T ; yÞdn

þ SBackðn0Þ, ð34Þ

where SBackk is the background signal which includes

any scattered light transmitted through the cell in

addition to the dark-current signal of the camera [term

C in Eq. (27)]. Although the signal is represented as

function of multiple parameters, it is noted that many of

these are optical parameters such as the angle between

the incident and observation direction, y, the polariza-

tion direction, f, and laser set-point frequency, n0. These

can be assumed constant, are known, or can be

measured separately for a given experimental arrange-

ment. If we tune the laser frequency to a specific

frequency in the absorption line of the atomic/molecular

filter (which is known) and also by knowing the

pressure, the FRS signal is only a function of the

temperature and optical calibration parameters R and

SBackk. Therefore, if we can measure these two optical

calibration parameters, the signal is only a function of

the unknown temperature of the flow (since the pressure

is assumed to be known). The method of solution is

realized by considering that the FRS signal (S) given in

Eq. (32) not only can be measured experimentally, but

can also be computationally modeled. The computation

of the FRS signal utilizes a model of the Rayleigh

scattering spectral profile [r: found by Tenti’s six-

moment model, or assuming a Gaussian distribution at

low densities, Eq. (16)] overlapped with the measured

transmission profile of the atomic/molecular filter (t)

and then integrated as shown in Eq. (32). Therefore the

temperature is found by comparing the measured signal

with the modeled signal (using values for the optical

constants, pressure, and laser frequency from the

experimental arrangement), which is computed over a

range of temperatures. When the modeled and experi-

mentally determined FRS signals agree, the temperature

of the flow is found. To use this method of solution,

however, R and SBack must be known at each camera

sensing element (i.e., pixel).

There are various methods for determining R and

SBack. One method is to measure SBack directly by

eliminating all Rayleigh scattering. This can be done by

evacuating the test region or filling it with a gas of small

Rayleigh scattering cross section [13,105]. R can then be

solved by collecting the signal at a known laser

frequency and thermodynamic flow condition (e.g.,

ambient conditions). Another method is to scan the

laser frequency through several locations in the absorp-

tion line for known flow field thermodynamic conditions

and use a curve-fitting routine to solve for the only

unknowns R and SBack [106,107]. This has the advantage

of simplifying the setup and also has the added benefit of

incorporating slight variations that may occur in the

computational model into the calibration coefficients.

The last method and most simplified way to calibrate the

FRS thermometry system is to assume that the back-

ground signal SBack is small compared to the Rayleigh

scattered signal or is constant and can be subtracted

from the collected signal. At first this may seem

unrealistic, but since the background scattering from

solid objects has a narrow spectral linewidth (on the

order of the laser) it will be significantly absorbed when

the laser is tuned near the center of the absorption line of

the atomic/molecular filter. With this simplifying

assumption Equation (32) can now be written as

Sðn0; p;T ; y;fÞ ¼ RðfÞp=kT

Z þ1�1

tðnÞrðn� n0; p;T ; yÞdn,

(35)

where SBack has been neglected or is a constant

subtracted from the collected signal at each pixel.

Therefore, we can now normalize the signal from the

flow at test conditions we wish to measure with the

signal at known thermodynamic condition and laser

frequency. The equation results in the form of

Sðn0;TÞ

Sref ðn0;T ref Þ¼

T ref

Rþ1�1

tðnÞrðn� n0; p;T ; yÞdn

TRþ1�1

tðnÞrðn� n0; pref ;T ref ; yÞdn

¼T ref f ðTÞ

Tf ðT ref Þ, ð36Þ

where Sref, Tref, and pref are, respectively, the signal,

temperature and pressure at the known flow reference

condition. For the form of the equation shown on the

right-hand side, the pressure has been assumed to be

approximately constant with the flow at test and

reference conditions identical. By normalizing the signal

in this fashion the optical calibration does not need to be

found explicitly since it is divided out in the normal-

ization procedure. This method of solving for the

temperature from a FRS signal has been used by

various investigators, but it should be kept in mind that

even a slight amount of background scattering passing

through the filter can lead to large measurement

uncertainties [105,107].

Fig. 31a gives the measured temperature as a function

of the normalized FRS signal as represented in Eq. (34)

for a range of laser set-point frequencies. These curves

were created using Tenti’s six-moment model of the

spectral Rayleigh scattering profile of nitrogen at

atmospheric pressure assuming the detector is located

901 to the incident light direction. An iodine molecular

filter and a frequency-doubled injection-seeded Nd:-

YAG laser were utilized in these simulations. Fig. 3b

represents the location of the laser set-point relative to

the line center of the iodine absorption filter. As can be

observed from these curves the shape of the temperature

ARTICLE IN PRESS

0

0.2

0.4

0.6

0.8

1

1.2

-5 -4 -3 -2 -1 0 2 41 3 5

Frequency [GHz]

Tra

nsm

issi

on

0

0.2

0.4

0.6

0.8

1

1.2

200 400 600 800 1000 1200 1400

Temperature [K]

No

rmal

ized

FR

S S

ign

al [

S/S

ref]

ν1=0.30ν2=0.0ν3=0.30ν4=0.75ν5=1.19ν6=1.74

Fig. 31. Normalized FRS signal versus flow temperature curves (shown on the left) for a range of laser set-point frequencies relative to

an iodine absorption filter (shown on the right).

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142124

FRS signal curve is greatly affected by the laser set-point

and as shown here can become double-valued for some

absorption lines (due to the varying width and weaker

neighboring lines) if the laser frequency is not carefully

selected. This obviously creates a problem if the flow

being evaluated approaches these double-valued tem-

peratures and should be avoided. It should be noted,

however, that other absorption profiles do not show this

problem.

Also, it can be seen in Fig. 31a that as temperature

increases the FRS normalized signal decreases. At high

temperatures it is approximately proportional to T�1.

Thus, when the temperature range is large the decrease

in signal strength with T produces a proportionally

higher measurement uncertainty than at near ambient

temperatures. The technique loses sensitivity as the

temperature increases because the density decreases and

p ¼ const. This makes it difficult to measure high-

temperature flows or flames, and it is usually replaced by

emission spectroscopy or filtered Thomson scattering.

As an example of the utilization of FRS thermometry,

Fig. 32 gives representative images of the temperature

field resulting from laser-induced breakdown in air as

presented by Boguszko and Elliott [106,114]. The laser-

induced breakdown creates a plasma, formed by focusing

the second harmonic of a 200mJ/pulse Nd:YAG laser

using a lens with a focal length of 50mm. After the

plasma forms, a blast wave propagates from the center of

the laser spark, and by 30ms computations and experi-

ments indicate that the pressure remains constant [67].

Therefore, the resulting temperature field can be

measured by FRS using the assumption 3, as outlined

previously. Observed in Fig. 32 is a sequence of FRS

temperature images taken at successive delay times

measured from the instant of the excitation pulse.

Clearly shown is the formation of a vortex ring and

induced jet, which propagates in a direction opposite to

the excitation laser beam. Also, one can observe the

decrease in temperature as the flow field convects and

mixes with the cooler ambient air. Temperature mea-

surements have also been made by Boguszko and Elliott

in natural convection above a heated cylinder [82],

natural convection from heated bars placed between two

insulated flat plates [114] relevant to electrical compo-

nent heat transfer studies. In addition, Kearney et al.

[105] demonstrated the use of FRS in measuring the

thermal development of a forced heated jet. Again, they

utilized the iodine filter with a Nd:YAG laser and were

able to capture average and instantaneous measurements

of the heated air jet as it entrained cooler ambient air.

They report uncertainties on the order of 20K in their

measurements of the 800K heated jet.

In addition, several investigators have utilized FRS to

measure the temperature field in flames. For flame

temperature measurements, Eq. (32) and the assump-

tions associated with it are still applied. Again, one can

generally assume that the pressure is constant, and the

effect of the velocity leading to a Doppler shift is

negligible (due to velocities encountered in the flow or

the direction of the incident and observation directions

selected). A slightly more difficult assumption in making

measurements in flames, however, is that the Rayleigh

differential cross section and molecular mass are

constant (which is a similar problem encountered when

utilizing unfiltered Rayleigh scattering in flames). For

example the Rayleigh scattering cross section of a fuel

such as methane is over twice that of air. Therefore, in

non-premixed flames, regions dominated by fuel lead to

measurement inaccuracies if not corrected. Unknown

species concentrations affects the thermal broadening

and the y-parameter which governs the spectral shape of

the Rayleigh scattering.

The most simple method of minimizing this problem

is to apply FRS thermometry in premixed fuel-air flames

ARTICLE IN PRESS

Fig. 32. FRS temperature measurements of the flow field created from a Nd:YAG laser beam (net energy of 145mJ) focused in

quiescent air taken at four delay times from the initiation of the laser spark. The focused laser beam is propagating from the top to

bottom of each image From Boguszko and Elliott [106]; reprinted by permission of the American Institute of Aeronautics and

Astronautics, Inc.

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 125

or in non-premixed flames, where the Rayleigh scatter-

ing cross section is nearly equal between fuel and air,

and thus may be assumed to be relatively constant. This

method was employed by Hoffman et al. [108] who first

utilized FRS to make temperature measurements in

premixed methane-air flames. They were even able to

extend the FRS temperature measurements to slightly

sooting flames, since the scattering from soot particles

has a narrow linewidth and is absorbed by the iodine

molecular filter. In their experiments, they compared

results from kinetic and hydrodynamic models of the

Rayleigh scattering spectra and were able to make

average measurements with a standard deviation of

7150K in the hot regions of the flame.

Elliott et al. [109] investigated the premixed methane/

air and hydrogen/air flames created above various

burners (i.e., holed array, McKenna, and Hencken

burners) and were able to resolve instantaneous and

average temperature fields in buoyancy-driven flames

and very near the burner surface (within 0.3mm) in

some cases. Again, a Nd:YAG laser and iodine filter

were utilized in these studies. Uncertainties were

evaluated assuming equilibrium species concentrations.

For the premixed methane/air experiments the uncer-

tainty in temperature for the reactants region of the

flame zone was approximately 11–34% depending on

the equivalence ratio (the higher the equivalence ratio

the higher the uncertainty) due to the high Rayleigh

scattering cross section of methane present in the flow.

In reacting regions of the flame, however, the uncer-

tainty reduced to 2.5–4.4% since the molecular mass and

Rayleigh scattering cross section of species were more

consistent. In general, in the flames investigated by

Elliott et al. [109] there was significantly less uncertainty

in the reacting regions of the premixed flames studied.

Even when a fuel such as hydrogen is utilized in a

Hencken burner configuration, the measured tempera-

ture can be relatively accurate in the product region,

which was verified by comparisons of temperature

profiles with CARS measurements. The CARS and

ARTICLE IN PRESS

Fig. 33. Average (a) and instantaneous (b & c) temperature field measurements using FRS of a methane/air stagnation-flame. From

Elliott et al. [110]; reprinted by permission of IOP Publishing Limited.

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142126

FRS measured temperatures almost completely overlap,

but do deviate slightly as the equivalence ratio is

increased.

Additionally, Elliott et al. [110] utilized FRS to make

measurements near surfaces in studying the flow field

of a stagnation flame created below a cooled substrate.

Fig. 33 shows a premixed methane-air stagnation flame

and associated instantaneous and average temperature

fields for an equivalence ratio of 1.08. It is clear that the

instantaneous flames show the temperature fluctuations

due to the vortices rolling up on the edge of the flame.

Also, one can see that due to the elimination of near-

surface scattering, temperature measurements were

possible very near the cold substrate. The study not

only investigated variations in flame conditions, separa-

tion distance, and substrate diameter, but also compared

results with a computation. An uncertainty analysis was

conducted utilizing the computational model that

indicated uncertainties of less than 5% for average

measurements and 6.5% for instantaneous measure-

ments shown in the products region of the flames

studied. Axial profiles were compared to computations

using a one-dimensional detailed chemistry model (GRI-

Mech 1.2 model with 32 species, 177 reactions) showing

generally good agreement. It should be noted that in all

the studies listed above, the mix of species was assumed

to be dominated by nitrogen in the measurement

regions.

Kearney et al. [42,105] utilized FRS to measure

temperature fields in a heated calibration jet, premixed

flat flame, and acoustically forced diffusion flame (which

will be discussed shortly). Similar to the previous

studies, Kearney utilized a Nd:YAG laser and iodine

filter for the FRS experiments. A Hencken burner

geometry was utilized in this study with a methane/air

flame created over a range of equivalence ratios. For this

controlled experiment, Kearney and colleagues studied a

variety of assumptions to correct for scattering varia-

tions from the multiple species found in the product

region of the flame. They compared three approaches to

correct the FRS signal analysis for multiple species

which included: (1) utilizing a NASA equilibrium code

to obtain species concentration, (2) using the species

concentrations at stoichiometric conditions, and (3)

assuming that all of the Rayleigh scattering is from

nitrogen. Fig. 34 shows the results of these tests with

comparisons with CARS measurements and the adia-

batic flame temperature. As observed utilizing the

computational model the FRS results are within 50K

of the CARS measurements. Assuming that the scatter-

ing is only from nitrogen, the measured temperature

using FRS can be up to 150K lower as shown in

Fig. 34b. If even a simple species correction is utilized

assuming stoichiometric conditions, the temperatures

can be measured by FRS to within 50 K. It was

suggested that much of the bias due to the ‘‘nitrogen-

only’’ assumption can be corrected by adding the

contribution of CO2 to the FRS scattering signal since

it has a Rayleigh scattering cross section 2.2 times

greater than that of nitrogen [105].

In addition, FRS has also been utilized to measure the

temperature field in plasmas. Yalin and Miles utilized

ultraviolet FRS to measure the temperature in a weakly

ionized discharge [62,111,112]. Unlike the Nd:YAG

laser and iodine molecular filter combination, which has

been employed in the previous studies, Yalin and Miles

utilized a mercury filter and a Ti:saphire laser system,

described previously [60], operating at a wavelength of

253.7 nm.Although there is significant signal improve-

ment in the UV stemming from the higher Rayleigh

scattering cross section, they also evaluated other

benefits and weaknesses of using the lower wavelength

in this study (i.e., quantum efficiency of the detector,

available energy in lower wavelength sources, tempera-

ture measurement sensitivity of mercury versus iodine

vapor cells). Although in many ways the temperature

ARTICLE IN PRESS

Fig. 34. Comparison of FRS- and CARS-measured flame

temperatures from the Hencken burner and the calculated

equilibrium product temperature for varying fuel-air stoichio-

metries as measured by Kearney et al. Part (a) shows the FRS

temperatures deduced by using the calculated major product

compositions. Part (b) shows FRS temperatures calculated

assuming a stoichiometric mixture (solid symbols) and assum-

ing that all scattering arises from nitrogen (open triangles).

From Kearney et al. [105]; reprinted by permission of the

American Institute of Aeronautics and Astronautics, Inc.

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 127

sensitivity of iodine and mercury filters was similar,

Yalin and Miles indicated that the optical depth of the

latter is much greater (over 105) without the background

continuum absorption observed with iodine. In their

initial study, they presented FRS point measurements in

a 50Torr, 20mA weakly ionized (o10�6 ionization

fraction) argon glow-discharge with unfiltered Rayleigh

scattering data having an uncertainty of 3–4%. In later

experiments they measured the two-dimensional tem-

perature fields in diffuse and contracted discharges using

FRS thermometry [111]. Fig. 35 gives an example of the

temperature field of a diffuse discharge (50Torr) in

argon (20 mA) and in argon plus 1% nitrogen; the small

amount of Nitrogen causes a decrease in temperature

even though the mixture is at a higher current. An

uncertainty analysis indicated that the temperature field

could be measured in these glow discharges within 5%.

In general, flames occur at low velocity and the

orientation of the interrogating beam is such that the

measurement error due to velocity Doppler shift in the

sensitivity direction is negligible. However, when the

velocity is important, such as in highly turbulent flows,

supersonic combustion, or plasma jets, the investigation

of temperature by FRS must include an error analysis in

which Doppler shift is included as a source of bias error.

Some knowledge (or estimation) of the largest velocity

in the flow is necessary so that the error based on some

DV is computed. This error can be calculated by finding

the derivative of the total signal with respect to a change

in velocity and using the customary laws of error

propagation.

8. Multiple property measurements

8.1. Average measurements (FRS frequency scanning

technique)

In the previous sections we have reviewed studies

indicating that single properties (i.e., velocity or

temperature) can be measured using FRS. Now we

would like to investigate and review the research

extending FRS to simultaneously measure multiple

properties. In order to solve for the pressure, density,

temperature, and velocity it is necessary to resolve their

individual effects on the characteristics of the Rayleigh

scattering line shape. Miles et al. [12,71] and Forkey et

al. [13,14,43,112] developed a method from which the

convolution of the Rayleigh spectrum and the absorp-

tion filter can be used to obtain these unknown

properties. Again, the setup is similar to Fig. 2, with a

narrow linewidth laser formed into a sheet passing

through the flow field to be investigated. The Rayleigh

scattering from molecules in the flow is collected with a

detector (generally a CCD or ICCD camera) viewing the

light through an atomic or molecular vapor filter. In the

FRS frequency scanning method, the FRS is recorded

over a range of laser frequencies as the latter is tuned

across an absorption line, as illustrated in Fig. 36a. The

camera then collects the transmitted light integrated

over all the frequencies, within the range of the detectors

sensitivity. This results in a convolution of the Cabannes

line and the filter function, described by Eq. (30).

Note that various thermodynamic properties are

clearly evident in the FRS convolution profile as

illustrated in Fig. 36b [43]. First, the density is directly

proportional to the signal collected when the laser is

tuned outside of the filter since the Rayleigh scattered

intensity is not modified spectrally. The lowest point in

the convolution curve of Fig. 36(b) is an indication of

the shape of the Rayleigh scattering profile which is a

function of pressure (through the y parameter) and

temperature. As the temperature increases, the thermal

broadening will increase, causing a greater portion of

the spectrum to be transmitted. Forkey [43] also

ARTICLE IN PRESS

Fig. 35. The temperature field of a diffuse discharge (50Torr)

in argon (20mA) (a) and in argon plus 1% nitrogen (b)

measured using a mercury filter and ultra-violet FRS. From

Yalin and Miles [62]; reprinted by permission of the Optical

Society of America.

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142128

suggested that the side slopes of the FRS profile can also

be used to determine shape, which is also a function of

pressure and temperature. In addition, the frequency

shift of the minimum relative to the peak absorption is a

measure of the Doppler shift of the profile. Even

utilizing only these general characteristics, the thermo-

dynamic properties can be measured [82], but not as

effectively as the method described below utilizing

curve-fitting algorithms that employ more points to fit

the FRS spectral profile.

As observed in Eq. (30) the convolution of the

Rayleigh scattering spectrum with the absorption

feature chosen depends upon such quantities as the

thermodynamic properties of the gas (p,T,N), viewing

angle (y), angle of polarization (f), laser frequency (n0)

and the Doppler shift DnD, which is proportional to the

flow velocity as defined by Eq. (9). Note that the

constant C has been eliminated since this background is

assumed to be already subtracted from the signal.

Similar to single-property measurement techniques,

from a knowledge of the optical geometry, y and f are

known, and if the frequency is measured using the

methods described previously the laser frequency n0 is

also known. Therefore, the unknowns are the flow

properties (pressure, temperature, number density, and

velocity) and the calibration parameters (R and B),

which must be found for each pixel, similarly to the

temperature measurements. In addition (as described

previously in Section 8.2) R and B can also be obtained

by performing a frequency scan with the flow off at a

known thermodynamic reference condition (ambient).

Generally, several instantaneous images are averaged

together at each laser frequency to obtain the FRS

spectral profile. For the reference condition the signal is

then given by

Sref ðn0;DnD; pref ;T ref ;Nref ; y;fÞ

¼ RðfÞNref

Z þ1�1

tðnÞrðn� n0 � DnD; pref ;T ref ; yÞdn

þ Btðn0Þ, ð37Þ

where Nref, pref, Tref, are the known thermodynamic

conditions, and therefore DnD is also known (since the

velocity is zero). All other parameters are known except

R and B. After experimentally measuring the FRS

spectral profile at the reference condition, the reference

signal expressed in Eq. (35) is calculated at each probed

laser frequency n0 using a computer model of the

Rayleigh scattering (r: calculated using Tenti’s S6

model) at the reference conditions, multiplied by the

absorption filter profile tðnÞ, and integrated over the

frequency domain. R and B are determined using a

curve-fitting routine (e.g., Levenberg–Marquardt algo-

rithm [113]) and adjusting these two quantities until the

error between the computational model and the

measured FRS spectral profile is minimized. Note that

R and B must be determined for each pixel.

Once measurements have been made to determine the

calibration parameters, the laser is again tuned in

frequency through the absorption profile of the atom-

ic/molecular filter, but this time the flow is on. Several

instantaneous images are taken at each laser frequency

and averaged together resulting in an FRS spectral

profile for ‘‘flow-on’’ conditions. Again, the FRS

spectral profile is calculated using the computational

model of the Cabannes line convolved with the

absorption filter, as is described by Eq. (28). In a similar

manner, the computational model of the FRS spectrum

is fit to the function determined experimentally using the

non-linear Levenberg-Marquardt algorithm [113]. With

the calibration factors and geometry known, the only

unknowns are the pressure, temperature, density, and

Doppler shift (i.e., flow velocity), which become the

fitting parameters to the algorithm. Note that the ideal

gas law [Eq. (31)] is also used to reduce the number of

thermodynamic unknowns by solving the density from

the pressure and temperature. The thermodynamic

properties and velocity are determined by their values

ARTICLE IN PRESS

0–1–2 1 2

2000

00

1000

3000

4000

5000

6000

7000

8000

0 1 2

T = 150KT = 200KT = 250KT = 300KT = 350K

~ρ

~T

I

I

I

I

I

S (ν

0,∆ν

D,p

,T,θ

,φ)ν0

ν0

ν0

ν0

ν0

(GHz)ν0

ν

ν

ν

ν

ν

–1–2

∼∆ν D

Fig. 36. Illustration of the FRS frequency scanning technique developed by Forkey et al. [13] and utilized to measure multiple flow

properties (i.e. temperature, density, pressure, and velocity) simultaneously. The illustration on the right depicts the resulting FRS

signal when scanning the Rayleigh spectral profile from a flow field through the iodine absorption feature.

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 129

when the quantities minimize the error between the

computed and experimentally obtained FRS spectral

profile.

Fig. 37 gives a sample experimental and computed

FRS spectra from a free-jet experiment for reference and

‘‘flow-on’’ conditions at a single camera pixel. The

symbols indicate the grayscale values obtained experi-

mentally, and the solid lines are the computationally

modeled profiles obtained by solving the properties

using the curve fitting algorithm of the FRS spectral

profile. As shown, the agreement between the modeled

and experimental profiles is quite good, and the shift in

frequency due to the velocity is clearly quantified.

Unlike the temperature FRS measurement, the fre-

quency scanning technique is especially susceptible to

stray light and particle scattering. Reflections from

surfaces and large particle scattering may be orders of

magnitude larger than Rayleigh scattering. These

sources may mask the Rayleigh signal, particularly

when the scattering frequency is outside of the absorp-

tion line. If the flow field investigated is near walls, has

naturally occurring particles such as soot, a solution

may be to reduce the scanning range only to the region

where the absorption band sufficiently attenuates these

contributions, or use multiple absorption lines with

different characteristics. Of course, whenever possible

one should filter out particles upstream of the inter-

rogation region and block strong wall reflections.

Forkey et al. [13,14] was the first to utilize the FRS

frequency scanning methodology to obtain multiple

thermodynamic properties and the velocity field of a

Mach 2 jet. A Nd:YAG laser and iodine filter combina-

tion was utilized in their study. It should be noted that

their iodine absorption model has been used by a great

number of researchers. In order to measure the

frequency of the Nd:YAG laser, Forkey and colleagues

utilized the optical heterodyne beat signal with a second

frequency stabilized CW Nd:YAG laser described

previously. Additionally, they were able to evacuate

the test chamber to determine the calibration factors R

and B by direct measurement. The velocity measured

within the Mach 2 jet was within an uncertainty of

approximately 75 m/s (out of a measured velocity

between 192 and 221m/s in the direction of system

sensitivity. Pressure measurements were within expected

levels for this initial study, but the temperature had a

variation of 717 K across the jet, but the average of

142K was within 1K from the theoretical isentropic

value. In a later study, Forkey and colleagues conducted

a detailed uncertainty analysis of the FRS system [14].

They reported the uncertainty of the velocity, tempera-

ture, and pressure to be 72 to 73%, 72%, and 74 to

ARTICLE IN PRESSM. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142130

75%, respectively. Evaluating several sources of error,

they determined that significant uncertainties were due

to frequency variations across the laser sheet, long-term

drift of the reference laser frequency, and the measured

scattering angle [13,14,112].

–1–2

.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 1 2 3–3ν (GHz)

Tra

nsm

issi

on

Filter cell

Reference condition

Model fit 1pTu

===

1 atm291.65 K0 m/s

Flow condition

pTu

===

1.62 atm338.76 K373.7 m/s

Model fit 2

Fig. 37. Experimental and modeled FRS spectral profile from

frequency scanning measurements of ambient air and an

underexpanded jet (Me ¼ 1:5) at a single pixel element. The

symbols indicate the grayscale values obtained experimentally,

and the solid lines are the computationally modeled profiles

obtained with properties solved for by the non-linear Leven-

berg–Marquardt algorithm.

Fig. 38. Pressure, temperature, and velocity fields of an underexpand

technique. The flow direction is oriented from the bottom to the top of

permission of Springer Verlag.

Boguszko and Elliott also utilized the FRS frequency

scanning technique to investigate the flow field created

by a converging nozzle operated at subsonic and

underexpanded supersonic conditions [108,114]. The

FRS setup is presented in Fig. 38. A laser sheet from a

Nd:YAG laser (532 nm, 10 ns pulse length) was used to

illuminate the measurement region along the jet axis.

Perpendicular to the sheet an ICCD camera captured

the scattered radiation through the molecular iodine

filter cell. A co-flow of clean dry air was used to prevent

particles from reaching the test section. The viewing

region started 10mm (or about 1.5 diameters) down-

stream to avoid surface scattering from the nozzle exit.

Since the experiments were performed in ambient air, it

was not possible to use evacuation techniques to

determine the calibration factors R and B. Instead, the

FRS frequency scanning technique was applied to a

reference condition (ambient with zero velocity) and R

and B were solved for at each camera pixel using the

non-linear curve fitting algorithm as described pre-

viously. The reference condition was taken by acquiring

images while performing a 120-point scan through the

absorption line, each point being an ensemble average of

50 instantaneous frames. After acquiring the calibration

parameters, the FRS spectral profile is measured again

by tuning the laser across the iodine absorption line

(120-points), but now with the flow on. Fig. 38 shows

the properties measured using FRS with the jet operated

with a stagnation pressure of 364 kPa. For these

conditions the converging nozzle produced an under-

expanded jet with an equivalent Mach number of

Me ¼ 1:5. The shock-expansion diamond patterns char-

acteristic of an underexpanded jet are apparent in the

figure. As the flow propagates downstream, pressure and

temperature decrease as the velocity increases. The

oblique shocks cause a rapid increase in thermodynamic

ed jet (Me ¼ 1:5) measured using the FRS frequency scanning

the image. From Boguszko and Elliott [114] figures reprinted by

ARTICLE IN PRESSM. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 131

properties and a reduction of flow velocity. Several

other flow conditions were studied using FRS rang-

ing from subsonic to supersonic Mach numbers. A

detailed uncertainty analysis conducted indicated that

the pressure, temperature, and velocity had uncertain-

ties on the order of 70.07 atm, 74.1 K, and 77m/s

respectively, which was in general agreement with

measured errors of known (subsonic and sonic) flow

fields.

The FRS frequency scanning technique has also been

applied to study the flow field created by laser induced

optical breakdown by Boguszko and Elliott [106] and

Yan et al. [67], using a similar experimental arrangement

as given in Fig. 38. Although the emission prevented the

measurement of the thermodynamic properties at early

times in the region of the formation of the laser spark,

Boguszko and Elliott were able to capture the property

changes across the blast wave. Fig. 39 shows curves

of flow properties in the radial direction (tempera-

ture, density, and pressure) and velocity behind the

resulting blast wave in air 20ms after a laser induced

optical breakdown event. The initiating laser beam

(Ei ¼ 18373mJ) is focused by a lens with a focal length

of 50 mm. The property changes due to the blast wave

are clearly recorded and are characterized by an increase

in density, pressure, temperature, and induced velocity

1.4

1.3

1.2

1.1

1

0.9

0.8

p/p ∞

0 10 15 20 25r/R0

0 10 15 20 25r/R0

5

5

1.125

1.1

1.075

1.05

1.025

1

0.975

0.95

T/T

∞

ExperimentSimulation

ExperimentSimulation

(a)

(c)

Fig. 39. Comparison between the properties measured using FRS and

deposition in quiescent air with a net energy absorption of 14572 m

Reprinted with permission.

in a discrete region after the shock. Comparisons

between the FRS result and those from a computational

model developed by Yan et al. are also shown in Fig. 39.

The experimental results show good agreement and have

been used to refine the model (in the way the initial

energy is deposited into the flow and the time and

grid scale of the problem), to use in more complex

flow geometries [115]. Comparing the property changes

with the expected changes which would occur across

a moving normal shock, the density change was within

5%, temperature change was within 1%, and the

velocity induced by the shock was within 75m/s of

expected values.

8.2. Instantaneous measurements

The FRS frequency-scanning method is suitable for

fluid flows, which are statistically steady or are

repeatable so that phase-sampling is possible. Therefore,

the method does not capture fluctuating quantities or

inherently unsteady flows, but only the average of the

fluctuating properties. Early in the development of

FRS however, Miles and Lempert [11] proposed that

multiple filters adjusted to have slightly different

absorption profiles could be used to measure the FRS

signal simultaneously on multiple detectors and the

∞ρ/

ρ

0 10 15 20 25r/R0

0

5

5 10 15 20 25r/R0

1.3

1.2

1.1

1

0.9

0.8

0.25

0.2

0.15

0.1

0.05

0

–0.05

–0.1

u/a

ExperimentSimulation

ExperimentSimulation

(b)

(d)

simulated for the flow field resulting from laser-induced energy

J taken 20ms after the discharge as reported by Yan et al. [67].

ARTICLE IN PRESSM. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142132

instantaneous property measurements could be realized.

Boguszko [116] proposed the use of multiple viewing

angles of synchronized detectors so that turbulence or

unsteady flow measurements of multiple properties

could be achieved. So far, however, none of these

techniques has been successfully used to conduct

measurements.

Another possible arrangement for measuring proper-

ties and velocity instantaneously takes advantage of the

angular variation of the scattering spectrum and was

introduced by Shirley and Winter in 1993 [117]. They

proposed an anamorphic optical arrangement utilizing a

low f-number lens to collect rays from different

scattering angles and record them separately in a linear

array of pixels on a CCD camera. Each individual

resolution element provides the intensity from a point in

space as viewed from a different angle. Therefore, as

governed by Eq. (11), the Doppler shift frequency is

slightly different for each pixel (or viewing angle). In

essence, the different viewing angles represent the

intensity from the Rayleigh scattering transmitted

through the atomic/molecular filter at different frequen-

cies due to the different Doppler shift components.

Originally Shirley and Winter proposed this pointwise

technique to measure mass flux distributions. Elliott and

Samimy [118,119] in 1996 further developed this idea,

which they termed filtered angularly resolved Rayleigh

scattering (FARRS) and demonstrated that with addi-

tional cameras the average and instantaneous flow

properties of velocity, density, temperature, and pres-

sure could be measured. Furthermore, Boguszko and

Elliott [116] extended this system to measure the mean

and turbulence quantities of the core flow and shear

layer created by a Mach 1.36 perfectly expanded jet.

The anamorphic optical arrangement used in their

study is illustrated in Fig. 40. The system starts with a

low f-number lens (f/1.2), which is placed relatively

close to the point focused on by the lens of the laser used

to interrogate the flow (the second harmonic of an

injection-seeded Nd:YAG laser). The collection lens

is followed by a field stop, which limits the size

2

Filter

Cylindricallens

Sphericallens

1

50-50Mirror

Fieldstop

Fig. 40. FARRS optic

of interrogation region. This is followed by a spherical

and a cylindrical lens, which allow the light to be

imaged onto the detector so that different pixel elements

in the vertical direction represent a point on the laser

beam waist viewed from different angles. The lenses are

also arranged so that different pixels horizontally

represent different horizontal points along the beam

waist. After passing through the lenses the light is divided

by a beam splitter and imaged with a signal camera,

recording the light passing through an iodine molecular

filter, and a second reference camera, which is unfiltered.

In order to make preliminary measurements of

fluctuating quantities and demonstrate the concept of

FARRS, Boguszko [116] assumed that the Doppler shift

from the flow velocity was predominantly in the

streamwise direction, the background scattering was

negligible, and considered imaging to occur from only

the vertical column in the center of the lens (it should be

noted that in processing the actual data this assumption

is not needed, but greatly simplifies the explanation of

how the technique works). Defining aj , as the viewing

angle for each pixel j located in the vertical center of the

lens, two main equations can be formulated, one for the

filtered (Sf) and one unfiltered (Su) camera pixels that

are given by

Sf ½n0;DnDðaÞ; p;T ;N ;f; aj

¼ Rf ðajÞN

Z þ1�1

tðnÞr½n� n0 � DnDðajÞ; p;T ; aj dn,

ð38Þ

SuðN ; ajÞ ¼ RuðajÞN, (39)

where Rf and Ru are optical calibration factors and aj is

the observation direction of the jth camera pixel in the

imaged column (from the previous equation y is now

replaced by a function of aj). The Doppler shift equation

at each viewing angle can then be written for the

assumptions given previously as

DnDðajÞ ¼1

l½u cosðp=2� ajÞ. (40)

Cameralens

Flow

Á

Laserpolarizationdirection

Laser beampropagation(into page)

o s

al arrangement.

ARTICLE IN PRESS

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

–20 –10 100 20

–20 –10 100 20

0.50.60.70.80.91.01.11.21.31.41.51.61.7

α (degrees)

S (

φ)u

(

(φ))

S u

ref

α (degrees)

Reference case Flow-on caseExper.Model

Exper.Model

ρ = 1.20±0.008 kg/m3ref

ρ = 1.52±0.015 kg/m3

u = 1.80±3.47 m/sref

u = 234.3±39.5 m/s

T = 300.8±0.7 Kref

T = 229.1±5.0 K

r/D = 0

S

S/(

)f

fre

f

N/N

ref

(a)

(b)

Fig. 41. Normalized FARRS signal over the range of viewing

angles for ambient reference conditions and conditions with the

jet running. Experimentally obtained (open symbols) and

computationally modeled (solid symbols) profiles are shown

with the calculated properties from the least-squares curve fit:

(a) density calculation; (b) temperature and velocity calculation.

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 133

The first parameter that can be solved for using

FARRS is the density, which is readily obtained by

dividing Su by a reference condition (flow off)

SuðN; ajÞ

Su ref ðNref ; ajÞ¼

N

Nref(41)

in this way, the calibration constant is eliminated. Now,

normalizing the filtered camera by the same no-flow

condition, the filtered calibration factor is also elimi-

nated and the signal is given by

Snorm½DnDðaÞ; p;T ;N; aj ¼Sf

Sfref

¼NRþ1�1

tðnÞr½n� n0 � DnDðajÞ; p;T ; aj dn

Nref

Rþ1�1

tðnÞr½n� n0 � DnDðajÞ; pref ;T ref ; aj dn. ð42Þ

In Eq. (40) the unknowns are T, p, and DnD (or the u

velocity after the Doppler shift equation is applied)

where it is assumed that N has been calculated from the

normalized unfiltered camera and Eq. (39). The number

of unknowns is further reduced since in general the ideal

gas law can be applied and the pressure can be written as

a function of temperature and density. Since we are

obtaining the normalized signal at each resolution

element, the number of known intensities and equations,

which can be written far exceeds the number of

unknowns. The solution must be evaluated to ensure

the values are not ill-defined (e.g., negative pressure),

which can occur when a stray dust particle is imaged or

when the algorithm fails to converge. Similar to the FRS

frequency scanning technique, the experimental FARRS

signal-observation angle profile can be compared to the

profile calculated from the computational model con-

structed for the experiment using the Tenti model of the

Cabannes line and knowing the absorption profile,

angles, laser frequency, density (from the direct mea-

surement of the unfiltered signal), and ideal gas law

relating the pressure and temperature. The Levenberg-

Marquardt algorithm [113] was again used with the

computational model of the FARRS signal with u, T,

(the pressure is found knowing the temperature and

density using the ideal gas law) as fitting parameters.

More details of this procedure can be found in the works

of Elliott et al. and Boguszko [82,116,118,119].

To evaluate the capability of FARRS to measure

instantaneous flow properties, a preliminary experiment

was conducted on a pressure-matched free jet with exit

diameter of D ¼ 12.7mm, running at an exit Mach

number of Me ¼ 1:36 by Boguszko [116]. The inter-

rogation point was located at a distance x=D ¼ 5

downstream and data was collected at thirteen radial

locations from the centerline r=D ¼ 0 to r=D ¼ 1:4.

Instantaneous values of the properties and stream-wise

velocity were found and used to calculate mean and

fluctuating turbulence profiles for every laser pulse. In

Fig. 41 are sample data of an instantaneous realization

of the FARRS-observation angle profile for the

unfiltered (Fig. 42a) and filtered (Fig. 42b) cameras,

with the flow off (ambient) and flow on conditions. The

experimentally obtained profiles are shown with the

computed profiles and properties that were solved using

the procedure outlined above. As can be observed in

these graphs, the agreement between the experimental

and computational profiles is quite good indicating that

the model captures the relevant physics of the scattering

process. In order to resolve the turbulence profiles in the

jet, seven hundred instantaneous images were taken at

each radial position, from which average and fluctuating

quantities were calculated. Fig. 42 shows the streamwise

velocity, temperature, and density obtained from

FARRS. As expected, the mean profiles show an

increase in velocity and density in the jet core and

decrease in temperature with properties returning to

ambient levels as the interrogation point is moved

ARTICLE IN PRESS

r/D r/D r/D

r/D r/D r/D–2.5 –1.5 –0.5 0.5 1.5 2.50

RM

S V

eloc

ity

(m/s

)

10

20

30

40

50

60

70

80

–2.5 –1.5 –0.5 0.5 1.5 2.50

Mea

n V

eloc

ity

(m/s

ec)

–104090

140190240290340390440

LDVFARRS

0

000.5 1.50 1.0

0.5 1.50 1.0

0.5 1.50 1.0

00.5 1.50 1.0

50

100

150

200

250

300

Mea

n Te

mpe

ratu

re (

K)

5

10

15

20

25

30

RM

S Te

mpe

ratu

re (

K)

0.20.40.60.8

11.21.41.61.8

Mea

n D

ensi

ty (

kg/m

)3

0.05

0.1

0.15

RM

S D

ensi

ty (

kg/m

)3

x D/ =4.0

Fig. 42. Mean and RMS profiles of streamwise velocity, temperature, and density as a function of radius through the shear layer of a

Mach 1.36 axisymmetric jet measured using FARRS. Velocity results are compared to those from previous obtained by LDV.

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142134

radially outward. The RMS fluctuations in all properties

are shown to increase in the shear layer region as

expected. The velocities were compared to LDV

measurements reported by Mosedale [7]. While the

average values seem to agree well, there is a discrepancy

of about 25% in the maximum RMS velocity, most

likely due to the simplifying assumption that all the

Doppler shift is due to streamwise velocity only.

The uncertainty of the results for u, r, and T are

estimated to 7%, 3%, and 6%, respectively using this

technique.

9. Combined techniques and future trends

Now that various FRS techniques have been pre-

sented, it is noted that many of these arrangements can

be used in conjunction with other methods to improve

the accuracy of the property measurement or measure

additional properties (such as species concentration or

velocity) simultaneously. One of the combined techni-

ques utilizing FRS was demonstrated by Elliott et al.

[110,120] to measure the temperature field while

simultaneously measuring the velocity field with PIV.

This was accomplished by seeding small particles into

the flow field, which could be utilized for the PIV

measurement; particle scattering was greatly attenuated

when the laser is tuned in frequency near the peak

absorption of the filter. The Rayleigh scattered signal

from molecules, however, is thermally broadened and a

portion of the scattered light is transmitted through the

filter and imaged by the camera. Utilizing the tempera-

ture measurement technique described previously (Sec-

tion 7.3), the laser does not need to be scanned;

instantaneous measurements of velocity and instanta-

neous measurements of temperature are possible. In

these preliminary experiments an injection-seeded

Nd:YAG laser and iodine absorption filter were used,

and the FRS was imaged with an intensified CCD

camera. The PIV measurements utilized a second

double-pulse Nd:YAG laser synchronized to give two

pulses slightly delayed from the FRS laser pulse. An

interline transfer camera (with the same field of view as

the ICCD camera used in FRS) recorded the two images

of the particle scattering separately. Using cross-

correlation algorithms, particle shifts between the two

images are determined and the velocity field can be

calculated. Elliott et al. [110,120] presented preliminary

results of the PIV/FRS technique for premixed stagna-

tion-flow flames showing the simultaneous instanta-

neous velocity and temperature field even near the

cooled substrate.

The simultaneous FRS/PIV technique was also

demonstrated by Most and Leipertz [121] who measured

the instantaneous temperature and velocity field above a

wire stabilized premixed methane-air V-shaped flame.

Instead of utilizing a double-pulse Nd:YAG laser for the

PIV measurement, however, they were able to use the

FRS laser as the initial pulse needed for PIV and use a

second Nd:YAG laser for the second PIV pulse.

ARTICLE IN PRESS

Fig. 43. Instantaneous temperature and velocity fields in a lean premixed methane-air flame measured using simultaneous FRS and

PIV. The dot in the bottom center of each image represents the position of the flame stabilization wire. From Most and Leipertz [121];

reprinted by permission of the Optical Society of America.

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 135

Additionally, they showed that for temperatures above

600 K, the Rayleigh scattering is in the kinetic regime,

which greatly simplifies the spectral profile calculation

since it is represented by a Gaussian distribution.

Additionally Most and Leipertz utilized the CHEMKIN

combustion code to account for various species con-

centrations and their effect on the FRS signal due to

variable molecular mass and Rayleigh scattering cross

section. Fig. 43 shows instantaneous images of the

simultaneous temperature and velocity field that they

obtained with this combined FRS/PIV technique. As

shown, the local flame structure is clearly evident

revealing characteristics of the temperature and velocity

fields and their interaction in the turbulent flame. An

uncertainty analysis indicated that the velocity could be

measured within 0.2m/s, but the temperature may have

a maximum deviation of 23% in the worst case; this

uncertainty seems to be quite conservative, however,

since comparisons with the adiabatic flame temperature

show a discrepancy of only 4% and a deviation from

ambient temperatures of 9% [121]. Most and Leipertz

[122] also published a paper with some improvements

over the original work by Hoffman.

Another combined technique utilizing FRS for

temperature measurements was proposed by Kearney

et al. [68,105]. Their goal was to solve uncertainties

associated with varying Rayleigh cross sections when

making FRS temperature measurements in non-pre-

mixed flames with unknown species concentrations.

Previously, investigators used premixed flames and

assumed that a majority of the Rayleigh scattering was

from a single species (i.e., nitrogen) or utilized combus-

tion models to adjust the molecular mass and Rayleigh

scattering cross sections in the model used to deduce the

temperature from the Rayleigh scattered signal. Kearney

first proposed that Raman imaging of the fuel could be

used to correct for the Rayleigh scattering cross section

variation using a flamelet-based model. Utilizing an

injection-seeded Nd:YAG laser with an iodine vapor

filter, Kearney et al. [68] made joint FRS/Raman

measurements (shown in Fig. 44) in a methane-

nitrogen-air Wolfhard–Parker slot diffusion flame per-

iodically forced at 90Hz. Since the structure of the flame

could be phased-locked, 100 FRS and 200 Raman

images were averaged at each delay time taken relative

to the acoustic forcing. The Raman images were

obtained by replacing the iodine filter with an appro-

priate interference filter and recording the CH4 vibra-

tional Raman shift, occurring at �2917 cm�1 relative to

the incidence radiation. From the FRS signal and fuel

concentrations measured with the Raman signal, other

major product species were determined using the model

in an iterative procedure so that the species dependent

Rayleigh scattering cross section variations could be

corrected. Fig. 44 shows the temperature and simulta-

neous CH4 mole fraction at various delay times (phase

angles) from the periodic forcing of the slot flame using

the joint FRS/Raman imaging technique. The evolution

of the temperature and fuel mole fraction fields is clearly

observed as the vortices interact to produce a strain-

induced extinction event. Measurements in a laminar

diffusion flame indicate that the FRS corrected tem-

peratures are within 5% of point-wise measurements

made using CARS [68].

Another method of measuring species concentration

with temperature was demonstrated by Jacobsen et al.

[123] and Boguszko [116]. They utilized FRS to measure

the temperature field and laser-induced fluorescence

(instead of Raman imaging) to measure species con-

centration. Jacobsen et al. [123] demonstrated the

combined FRS/PLIF technique to measure the tem-

perature and nitric oxide fluorescence in a DC plasma-

torch. Again the Nd:YAG laser and iodine filter were

utilized at a wavelength of 532 nm for the temperature

ARTICLE IN PRESS

Fig. 44. Joint FRS/Raman scattering measurements of temperature (color) and CH4 mole fraction (line contours) from a CH4–N2–air

Wolfhard–Parker slot flame that is periodically forced at 90Hz. Measurements were taken at successive phase time delays synchronized

to the forcing. From Kearney et al. [42]; reprinted with permission.

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142136

measurements. Relative species concentrations were

measured of nitric oxide utilizing a second Nd:YAG-

pumped dye laser operating at a wavelength of 573 nm,

which was frequency-doubled through a KDP crystal

and combined with the residual 1064 beam in a second

crystal to produce an output beam near 226.1 nm to

access the NO fluorescence lines. Using the FRS

temperature and NO fluorescence system, Jacobsen et

al. [123] and Boguszko [116] were able to obtain

instantaneous temperature relative NO fluorescence

intensity measurements in the plasma torch over a range

of gas flow rates and plasma arc discharge powers.

Fig. 45 shows an instantaneous image of the tempera-

ture (taken using FRS) and NO fluorescence intensity

fields (taken using PLIF) in a plasma jet. Visible is the

increase in the NO fluorescence intensity, and gas

temperature, in the high temperature regions of the

heated gas. Although instantaneous temperature mea-

surements are possible using fluorescence signals (which

are several orders of magnitude greater than the Raman

signal), the extra complexity of the system and data

processing may make it more difficult to implement,

since it requires an additional camera and dye laser and

the fluorescence process is non-linear.

Before concluding our review of FRS, it is worth

mentioning that similar methodologies are being utilized

to measure properties from electrons instead of mole-

cules. Thomson scattering is the scattering of radiation

by free electrons. In plasma flows such as those observed

in high-speed fluid dynamics, there is an interest in being

able to measure key parameters such as the electron

number density and electron temperature. Analogous to

Rayleigh scattering, the electromagnetic wave intro-

duces an oscillating motion to the electrons, which

reradiate the energy at the same frequency. Thomson

scattering has a much larger linewidth than Rayleigh

scattering but is extremely weak and therefore is usually

masked by background scattering. Similar to FRS

investigations, an atomic filter with a spectrally narrow

absorption line is incorporated to block the unwanted

sources of scattering, while allowing a portion of the

Thomson radiation to be detected [124–129].

In essence, electron temperature Te, and number

density Ne are obtained by spectrally resolving the

filtered Thomson scattering spectrum and measuring its

intensity. Its spectral width is sufficiently large that

commercial spectrometers have sufficient resolution for

this application. A Thompson scattering model is used

ARTICLE IN PRESS

Fig. 45. Instantaneous images of relative NO concentration and temperature fields measured with LIF and FRS, respectively, in a

2 kW plasma torch igniter. From Jacobsen et al. [123]; reprinted with permission.

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 137

to fit the spectrum line shape and intensity with Te and

Ne as fitting parameters. Generally, prior calibration is

needed to determine quantitative values, which is usually

done by performing rotational Raman scattering on a

known species, such as N2. The rotational transition

strengths of the reference substance are used to find the

detector sensitivity, probe region length, solid angle

captured, and optical efficiency [124].

There are several difficulties in obtaining successful

quantitative measurements with filtered Thomson scat-

tering technique. The most important is the interference

with elastic scattering, which is circumvented by the high

rejection ratio (�1:105) that can be achieved with the

atomic filter. Another important problem is the residual

broadband spontaneous emission of the laser, usually

referred to as amplified spontaneous emission (ASE).

When the laser does not have a high level of spectral

purity due to ASE, it can induce unwanted fluorescence

in the plasma, which masks the Thomson signal. To

solve this problem Bakker et al. [124,130] proposed an

ASE spectral filter consisting of a sequence of 20

dispersion prisms with a pinhole field stop at each end.

The system achieved a reduction in spectral impurity of

seven orders of magnitude, and has been widely

adopted. The interference with the luminescence from

the plasma also can cause measurement problems when

its spectrum falls near the measurement wavelength.

Care must be taken to choose an interrogation

frequency sufficiently separate from plasma emission.

In recent works a number of different combinations of

lasers and filters have been tested to measure the

Thomson scattering. Bakker et al. [124] utilized an

excimer dye laser emitting at 589 nm and a sodium vapor

absorption cell (exciting its D2 transition at 589.0 nm) to

obtain measurements of electron density and electron

temperature on a fluorescent lamp. They also presented

a thorough description of the filter cell construction,

given that sodium is a highly reducing agent that may

react with the cell materials, including the glass

windows. The spectrometer captured the radiation from

the plasma luminescence and stray and filtered Thomson

scattering combined. The first two were removed by

taking a measurement with the laser off, and subtracting

it from the data. The remaining is a product of the

Thomson spectrum with the absorption filter profile,

convolved with the instrument resolution. The filtered

scattering model was applied and the solution was

reached when it best fit the data [124].

Zaidi et al. [126] utilized a Ti:Sapphire laser at 780 nm,

combined with a rubidium atomic filter to measure

electron density and temperature from Thomson back-

scatter in an argon plasma at atmospheric pressure.

They described the construction and operation of the

rubidium filter, which was capable of producing a

rubidium density gradient in one direction. This was

achieved by diffusion of the metal through He (buffer

gas) between the heated lower surface (source) and the

cooled upper surface (trap). In an earlier work [125],

they demonstrated the dispersion capabilities of this

filter near the D2 absorption line and obtained rotational

Raman spectra of CO2. Using the filter as a notch filter,

in conjunction with a CW Ti:Sapphire seeded laser in a

cavity-locked arrangement, and a 20-prism dispersion

filter (ASE filter) they measured an electron density of

Ne ¼ (1.6170.05) 1016 cm�3 and electron temperature

of T e ¼ 0:82� 0:06 eV (T ¼ 9500� 700K) in an atmo-

spheric pressure argon plasma [126].

Lee and Lempert [127–129] constructed a system

consisting of a diode laser injection-seeded, narrow

spectral bandwidth Ti:Sapphire laser at 780.24 nm and a

rubidium vapor filter for Raman/Thomson scattering

measurements in weakly ionized argon DC discharge

plasmas. Their contribution was significant in demon-

strating how to improve the spectral purity of the

laser with the objective of measuring lower electron

density and electron temperatures. They demonstrated

ARTICLE IN PRESSM. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142138

improvements progressively: First, by using a config-

uration of injection seeding alone, then by coupling the

seed laser through the cavity output using a Faraday

rotation optical isolator, then by using the 20-prism

dispersion monochromator (ASE filter), and lastly by

the addition of a stimulated Brillouin scattering phase-

conjugate cell (SBS cell) [131]. The latter reduced the

residual elastic scattering present after the filter due to

an unlocked component of the output intensity. Using

this system they successfully measured an electron

density and electron temperature of (3.770.08)

1013 cm�3 and 0.6370.025 eV (T ¼ 7300� 290K), re-

spectively, in a 100-mA, 30-torr argon DC constricted

glow discharge [130]. In a following work they incorpo-

rated a feed-back loop between the Ti:sapphire laser

cavity and the CW seed laser increasing the laser spectral

purity to above 0.99999 [128]. This allowed them to

operate the rubidium absorption cell at a lower

temperature (270 1C) resulting in a much narrower

absorption line. In this way a narrower Thomson

scattering spectrum (product of a lower electron

temperature) was resolved. Measurements using this

system yielded Ne ¼ (6.7570.04) 1013 cm�3 with an

electron temperature of T e ¼ 0:27� 0:036 eV (T ¼ 3100

�420K) in the same argon discharge described pre-

viously [128]. It should be noted that although Thomson

scattering represents a different regime than that of the

Rayleigh filtered techniques presented in the majority of

this review article it represents the next step in applying

atomic/molecular filtered-based techniques to measure

the properties of a species making up a fluid medium.

The reader is referred to the book chapter by Lempert

[132] for an in-depth treatment of plasmas and Thomson

scattering.

10. Conclusion

Several applications of FRS have been presented

demonstrating the capabilities of atomic/molecular filter

based techniques. A comprehensive description of the

theoretical and mathematical basis of the scattering/

absorption processes governing FRS and derivate

techniques is presented. The model equations including

particle and molecular scattering, absorption spectro-

scopy, and detection methods are also illustrated

qualitatively with figures so that a reader unfamiliar

with these techniques can comprehend the fundamental

concepts. The mathematical model is explained with

each application so that the method of solution is clearly

understood.

When the scattered light is based on condensation

particles, atomic/molecular filters can be utilized to

improve flow visualizations so that boundary layer

characteristics can be described and multi-component

velocity field measurements are possible. A number of

works were reviewed that utilized particle scattering in

the Rayleigh regime for flow visualizations by leading-

edge research groups. These investigations include

volumetric visualizations, turbulent compressible flows

at MHz rates, and boundary layer imaging. In

quantitative velocity measurements a technique called

DGV or PDV was described with filters of absorbing

species and also with mixtures of absorbing/non-

absorbing species. The literature reviewed describes the

study of single and multiple velocity components based

on the Doppler shift in environments ranging from

large-scale flows to microflows, and studies of accuracy

limits of this velocimetry technique.

In addition to utilizing direct absorption, researchers

have also demonstrated frequency- modulated FRS

techniques (utilizing first or second harmonic absorption

spectra). The basis of the technique is that when the

scattering is demodulated at the frequency of the nth

harmonic, the absorption spectrum recovered corre-

sponds approximately to that of the nth derivative of the

filter absorption function. This allows the system to be

locked into a reference frequency via a closed-loop

controller, having the FM absorption spectrum as the

error signal. The advantages of the method are

discussed, such as velocity measurements in real time,

even at low scattered light intensities.

If the scattered light collected from the flow field

originates from molecules, other thermodynamic prop-

erties can be measured by determining their individual

effect on the FRS signal. FRS-based temperature

measurements have been demonstrated for flows rele-

vant to heat transfer studies, and has even been extended

to make instantaneous measurements in flames and

plasmas with uncertainties less than 75%. Also, FRS

techniques have been extended to measure multiple

properties (pressure, density, temperature, and velocity)

simultaneously by scanning the laser in frequency across

the filter absorption profile, or utilizing anamorphic

optical systems, which allow detection over a range of

angles resulting in a different Doppler shift at each

image element. Uncertainties in making measurements

of velocity, temperature, and pressure have been

reported to be as low as a few percent. FRS can be

combined with other techniques to measure additional

properties (velocity or species concentration) or improve

the accuracy of the FRS measurement.

Going beyond the utilization of Rayleigh scattering,

research groups have also demonstrated the use of

similar atomic/molecular filter technologies utilizing

Thomson scattering from electrons to make measure-

ments of electron temperature and electron number

density. In essence, the filtered Thomson scattering

technique is not much different from FRS thermometry,

except the fact that signals are much weaker, and the

line width of the scattering is much broader. A very

large rejection ratio is needed for the elastic scattering,

ARTICLE IN PRESSM. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 139

thus sodium, potassium, or mercury filters are normally

used.

FRS techniques have been proven to provide a

powerful tool in investigating fluid flow fields and

obtaining quantitative properties from it. As the

technology progresses, they are becoming more and

more widely used and will continue to evolve and they

will likely become commercially available as an off-the-

shelf product in the near future.

Acknowledgements

The authors would like to thank Dr. Campbell Carter,

Prof. Walter Lempert, and Prof. Doyle Knight for

reviewing this manuscript. Their valuable comments

greatly improved this article. In addition we would like

to thank the many researchers and publishers who gave

us permission to reproduce their figures. Also we would

like to thank the National Science Foundation (CTS 03-

14402) and Air Force Research Laboratory at Wright

Patterson Air Force Base for their support of our

research of various molecular filtered based diagnostics

over the years.

References

[1] Shimizu H, Lee S, She C. High spectral resolution lidar

system with atomic blocking filters for measuring atmo-

spheric parameters. Appl Opt 1983;22:1373–81.

[2] Hair JW, Caldwell LM, Krueger DA, She C. High-

spectral-resolution lidar with iodine-vapor filters: mea-

surement of atmospheric-state and aerosol profiles. Appl

Opt 2001;40(30):5280–94.

[3] Komine H, Brosnan SJ. Instantaneous three-component

doppler global velocimetry. Laser Anem 1991;1:273–7.

[4] Meyers JF, Komine H. Doppler global velocimetry: a

new way to look at velocity. Laser Anem 1991;1:289–96.

[5] McKenzie RL. Measurement capabilities of planar

Doppler velocimetry using pulsed lasers. Appl Opt 1996;

35:948–64.

[6] Clancy PS, Samimy M. Two component planar Doppler

velocimetry in high speed flows. AIAA J 1997;35:

1729–38.

[7] Mosedale A, Elliott GS, Carter CD, Beutner TJ. Planar

Doppler velocimetry in a large-scale facility. AIAA J

2000;38(6):1010–24.

[8] Elliott GS, Beutner TJ. A review of recent advancements

in molecular filter based planar Doppler velocimetry

systems. Prog Aerospace Sci 1999;35:799–845.

[9] Samimy M, Wernet M. A review of planar multiple-

component velocimetry in high speed flows. AIAA J

2000;38:515.

[10] Miles RB, Lempert WR. Two-dimensional measurement

of density, velocity and temperature in turbulent high-

speed air flows by UV Rayleigh scattering. Appl Phys B

1990;51:1–7.

[11] Miles RB, Lempert WR. Flow diagnostics in unseeded

air. Paper 90-0624, AIAA, January 1990.

[12] Miles RB, Lempert WR, Forkey JN. Instantaneous

velocity fields and background suppression by filtered

Rayleigh scattering. Paper 91-0357, AIAA, January 1991.

[13] Forkey JN, Finkelstein ND, Lempert WR, Miles RB.

Demonstration and characterization of filtered Rayleigh

scattering for planar velocity measurements. AIAA J

1996;34:442–8.

[14] Forkey JN, Lempert WR, Miles RB. Accuracy limits for

planar measurements of flow field velocity, temperature

and pressure using filtered Rayleigh scattering. Exp

Fluids 1998;24:151–62.

[15] Lord Rayleigh (Strutt JW). On the light from the sky, its

polarization and color. Philos Mag 1871;41:107–20,

274–9 (Also, In: The Scientific Papers of Lord Rayleigh.

New York: Dover; 1964).

[16] McCartney E. Optics of the atmosphere: scattering by

molecules and particles. New York: Wiley; 1976.

[17] Placzek G. In: Marx E, editor. Handbuch der radiologie

IV, vol. 2. Leipzig: Akademische Verlagsgesellschaft;

1934. p. 205–374.

[18] Young AT. Rayleigh scattering. Phys Today 1982; 42.

[19] Young AT. Rayleigh scattering. Appl Opt 1981;20(4):

533–5.

[20] Miles RB, Lempert WR, Forkey JN. Laser Rayleigh

scattering. Meas Sci Technol 2001;12:R33–51.

[21] Kattawar GW, Young AT, Humphreys TJ. Inelastic

scattering in planetary atmospheres. I. The ring effect,

without aerosols. Astrophys J 1981;243:1049–57.

[22] Fielding J, Frank JH, Kaiser SA, Smooke MD, Long

MB. Polarized/depolarized Rayleigh scattering for deter-

mining fuel concentration in flames. Proc Comb Inst

2002;29:2703–9.

[23] Bates RR. Rayleigh scattering by air. Planet Space Sci

1984;32(6):785–90.

[24] Bridge NJ, Buckingham AD. The polarization of laser

light scattered by gases. Proc R Soc Lond A 1966;

59(1442):34–42.

[25] Young AT. Revised depolarization corrections for atmo-

spheric extinction. Appl Opt 1980;19(20):3427–8.

[26] Penney CM. Light scattering in terms of oscillator

strengths and refractive indices. J Opt Soc Am 1969;

59(1):34–42.

[27] Birch KP, Downs MJ. Revised Edlen formula for air

index of refraction at STP conditions. Metrologia 1994;

31:315–6.

[28] Finkelstein ND, Yalin AP, Lempert WR, Miles RB.

Dispersion filter for spectral and spatial resolution of

pure rotational Raman scattering. Appl Opt 1998;23(20):

1615–7.

[29] Seasholtz RG, Buggele AE, Reeder MF. Flow measure-

ments based on Rayleigh scattering and Fabry–Perot

interferometer. Opt Lasers Eng 1997;27:543–70.

[30] Drain LE. The Laser Doppler Tech. New York: Wiley;

1980.

[31] Sugawara A, Yip S. Kinetic model analysis of light

scattering by molecular gases. Phys Fluids 1967;10(9):

1911–21.

[32] Lock JA, Seasholtz RG, John WT. Rayleigh–Brillouin

scattering to determine one dimensional temperature and

ARTICLE IN PRESSM. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142140

number density profiles of a gas flow field. Appl Opt

1992;31(15):2839–48.

[33] Crosignani B, Porto PD, Bertolotti M. Statistical proper-

ties of scattered light. New York: Academic Press; 1975.

[34] Yip S, Nelkin M. Application of a kinetic model to time-

dependent density correlations in fluids. Phys Rev A

1964;135(5):1241–7.

[35] Ranganathan S, Yip S. Time-dependent correlations in a

Maxwell gas. Phys Fluids 1966;9(2):372–9.

[36] Nelkin M, Yip S. Brillouin scattering by gases as a test of

the Boltzmann equation. Phys Fluids 1966;9(2):380–1.

[37] Sugawara A, Yip S. Kinetic model analysis of light

scattering by molecular gases. Phys Fluids 1967;10(9):

1911–21.

[38] Sugawara A, Yip S. Spectrum of density fluctuations in

gases. Phys Fluids 1968;11(5):925–32.

[39] Hanson FB, Morse TF. Kinetic models for a gas with

internal structure. Phys Fluids 1967;10(2):345–53.

[40] Hanson FB, Morse TF. Kinetic description of the

propagation of plane sound waves in a diatomic gas.

Phys Fluids 1969;12(1):84–95.

[41] Tenti G, Boley C, Desai R. On the kinetic model

description of Rayleigh–Brillouin scattering from mole-

cular gases. Can J Phys 1974;52:285–90.

[42] Kearney SP, Beresh SJ, Grasser TW, Schefer RW.

Filtered Rayleigh scattering thermometry in vortex-

strained and sooting flames. Paper 2004–1358, AIAA,

January 2004.

[43] Forkey JN. Development and demonstration of filtered

Rayleigh scattering. A laser based flow diagnostic for

planar measurement of velocity, temperature and pres-

sure. Ph.D. thesis, Princeton University, New Jersey,

1996.

[44] Forkey JN, Lempert WR, Miles RB. Corrected and

calibrated I2 absorption model at frequency-doubled

Nd:YAG laser wavelengths. Appl Opt 1997;36(27):

6729–38.

[45] Tellinghuisen J. Resolution of the visible-infrared absorp-

tion spectrum of I2 into three contributing transitions.

J Chem Phys 1973;58(7):2821–35.

[46] Tellinghuisen J. Insensity factors for the I2 B–X band

system. Quant Spectr Rad Transf 1978;19:149–61.

[47] Hiller B, Hanson RK. Properties of the iodine molecule

relevant to laser-induced fluorescence experiments in gas

flows. Exp Fluids 1990;10:1–11.

[48] Kroll M, Innes KK. Molecular electronic spectroscopy by

Fabry-Perot interferometry. Effect of nuclear quadrupole

interactions on the linewidths of the B3P+0 2X1P+

g

transition of the I2 molecule. J Mol Spectrosc 1970;

36:295–309.

[49] Robinson GW, Cornwell CD. The interaction with

molecular rotation of the nuclear electric quadrupole

moments of two nuclei having spins 3/2. J Chem Phys

1953;10(9):1–11.

[50] Luc P. Molecular constants and Dunham expansion

parameters describing the B–X system of the iodine

molecule. J Mol Spectrosc 1980;8:41.

[51] Gerstenkorn S, Luc P. Identification des Transitions du

Systeme (B–X) de la Molecule d’Iode et Facteurs de

Franck–Condon 14000–15600 cm–1. Orsay, France: La-

boratoire Aime-Cotton CNRS II 91405; 1986.

[52] Injection seeder model 6300/6350 instruction manual,

Spectra-Physics Lasers, Inc., 1994.

[53] Forkey JN, Lempert WR, Miles RB. Observation

of a 100-MHz frequency variation across the output

of a frequency-doubled injection-seeded unstable-resona-

tor Q-switched Nd:YAG laser. Opt Lett 1997;22(4):

230–2.

[54] Clancy PS, Samimy M. Two-component planar Doppler

velocimetry in high-speed flows. AIAA J 1997;35(11):

1729–38.

[55] Lempert WR, Wu PF, Shang B, Miles RB, Lowarance

JL, Mastrocola V, Kosonocky WF. Pulse-Burst laser

system for high-speed flow diagnostics. Paper 96-0179,

AIAA, January 1996.

[56] Wu P, Lempert WR, Miles RB. Megahertz pulse-burst

laser and visualization of shock-wave/boundary-layer

interaction. AIAA J 2000;38(4):672–9.

[57] Thurow B, Hileman J, Samimy M, Lempert W. Narrow

linewidth megahertz rate pulse burst laser for high-speed

flow diagnostics. Appl Opt 2004;43(26):5064–73.

[58] Kastengren AL, Dutton JC, Elliott GS. Time-correlated

visualizations of a three-dimensional supersonic base

flow, Paper accepted to Aerospace Sciences Meeting and

Exhibit, AIAA, January 2005.

[59] Thurow B, Jiang N, Lempert W, Samimy M. Develop-

ment of megahertz rate planar Doppler velocimetry for

high speed flows. AIAA J 2005;43(3):500–11.

[60] Finkelstein ND, Lempert WR, Miles RB, Finch A, Rines

GA. Cavity locked, injection seeded, titanium:sapphire

laser and application to ultraviolet flow diagnostics.

Paper 96-0177, AIAA, January 1996.

[61] Rines GA, Moulton PF. Performance of gain-switched

Ti:Al2O3 unstable-resonator lasers. Opt Lett 1990;15(8):

434–6.

[62] Yalin AP, Ionikh YZ, Miles RB. Gas temperature

measurements in weakly ionized glow discharges with

filtered Rayleigh scattering. Appl Opt 2002;41(18):

3753–62.

[63] Grinstead JH, Finkelstein ND, Lempert WR. Doppler

velocimetry in a supersonic jet by use of frequency-

modulated filtered light scattering. Opt Lett 1997;22(5):

331–3.

[64] Mach J, Varghese PL. Velocity measurements by

modulated filtered Rayleigh scattering using diode lasers.

AIAA J 1999;37(6):695–9.

[65] Elliott GS, Glumac N, Carter CD, Nejad AS. Two-

Dimensional temperature field measurements using a

molecular filter based technique. Comb Sci Tech 1997;

125:351–69.

[66] Crafton J, Carter CD, Elliott GS. Three-component

phase-averaged velocity measurements of an optically

perturbed supersonic jet using multi-component planar

Doppler velocimetry. Meas Sci Technol 2001;12(4):

409–19.

[67] Yan H, Adelgren R, Boguszko M, Elliott GS, Knight D.

Laser energy deposition in quiescent air. AIAA J 2003;

41(10):1988–95.

[68] Kearney SP, Beresh SJ, Grasser TW, Schefer RW.

Filtered Rayleigh scattering thermometry in vortex-

strained and sooting flames. Paper 2004-1358, AIAA,

January 2004.

ARTICLE IN PRESSM. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 141

[69] Roehle I, Schodl R, Voigt P, Willert C. Recent

developments and applications of quantitative laser light

sheet measuring techniques in turbomachinery compo-

nents. Meas Sci Technol 2000;11(7):1023–35.

[70] Seasholtz RG, Buggele AE. Improvement in suppression

of pulsed Nd:YAG laser light with iodine absorption cells

for filtered Rayleigh scattering measurements. NASA

Technical Memorandum 113177. Cleveland: Lewis Re-

search Center; 1997.

[71] Miles RB, Forkey JN, Lempert WR. Filtered Rayleigh

scattering measurements in supersonic/hypersonic facil-

ities. Paper 92-3894, AIAA, July 1992.

[72] Samimy M, Arnette SA, Elliott GS. Streamwise struc-

tures in a turbulent supersonic boundary layer. Phys

Fluids 1994;6(3):1081–3.

[73] Arnette SA, Samimy M, Elliott GS. Expansion effects on

supersonic turbulent boundary layers. AIAA J 1995;

33(4):430–8.

[74] Arnette SA, Samimy M, Elliott GS. The effects of

expansion regions on the turbulence structure of a

supersonic boundary layer. J Fluid Mech 1998;367:

67–105.

[75] Forkey JN, Lempert WR, Bogdaonoff SM, Miles RB,

Russell G. Volumetric imaging of supersonic boun-

dary layers using filtered Rayleigh scattering back-

ground suppression. Paper 94-0491, AIAA, January

1994.

[76] Elliott GS, Samimy M, Arnette SA. Study of compres-

sible mixing layers using filtered Rayleigh scattering

based visualizations. AIAA J 1992;30(10):2567–9.

[77] Erbland PJ, Baumgartner ML, Yalin AP, Etz MR,

Muzas B, Lempert WR, Smits AJ, Miles RB. Develop-

ment of planar diagnostics for imaging Mach 8 flowfields

using carbon dioxide and sodium seeding. Paper 97-0154,

AIAA, January 1997.

[78] Baumgartner ML, Erbland PJ, Etz MR, Yalin A, Muzas

BK, Smits AJ, Lempert WR, Miles RB. Structure of a

Mach 8 turbulent boundary layer. Paper 97-0765, AIAA,

January 1997.

[79] Erbland PJ, Murray R, Etz MR, Huntley M, Miles RB.

Imaging the evolution of turbulent structures in a

hypersonic boundary layer. Paper 99-0769, AIAA,

January 1999.

[80] Lempert WR, Wu PF, Miles RB. Filtered Rayleigh

scattering measurements using a MHz rate pulse-burst

laser system. Paper 97-0500, AIAA, January 1997.

[81] Huntley MB, Wu P, Miles RB, Smits AJ. MHz rate

imaging of boundary layer transition on elliptic cones at

Mach 8. Paper 2000-0379, AIAA, January 2000.

[82] Elliott GS, Boguszko M, Carter C. Filtered Rayleigh

scattering: Toward multiple property measurements.

Paper 2001-0301, AIAA, January 2001.

[83] Adelgren RG, Elliott GS, Knight DD. Energy deposition

in supersonic flows. Paper 2001-0885, AIAA, January

2001.

[84] Yan H, Adelgren R, Boguszko M, Elliott GS, Knight

DD. Laser energy deposition in quiescent air. AIAA

Paper 2003-1051.

[85] Meyers JF. Development of Doppler global velocimetry

as a flow diagnostic tool. Meas Sci Technol 1995;6:

769–83.

[86] Meyers JF, Lee JW, Schwartz RJ. Characterization of

measurement error sources in Doppler global velocime-

try. Meas Sci Technol 2001;12(4):357–68.

[87] Roehle I, Willert CE. Extension of Doppler global

velocimetry to periodic flows. Meas Sci Technol 2001;

12:420–31.

[88] Clancy PS. Development and application of three-

component planar Doppler velocimetry for high speed

flows. Ph.D. dissertation, The Ohio State University,

Columbus, 1997.

[89] Elliott GS, Crafton J, Baust H, Beutner T, Carter CD,

Tyler C. Evaluation and Optimization of a Multi-

component planar Doppler velocimetry system. Paper

accepted to the Aerospace Sciences Meeting and Exhibit,

AIAA, January 2005.

[90] Clancy P, Samimy M, Erskine W. Planar Doppler

velocimetry: three-component velocimetry in supersonic

jets. AIAA J 1999;37:700–7.

[91] Elliott GS, Samimy M, Arnette SA. A molecular filter

based velocimetry technique for high speed flows. Exp

Fluids 1994;18:107–18.

[92] Kuhlman J, Naylor S, James K, Ramanath S. Accuracy

study of a 2-component point Doppler velocimeter. Paper

98-2607, AIAA, January 1998.

[93] Beutner T, Elliott G, Williams G, Baust H, Crafton J,

Carter CD. Forebody and leading edge vortex measure-

ments using planar Doppler velocimetry. Meas Sci

Technol 2001;12:378–94.

[94] Beresh SJ, Kearney SP, Bourdon CJ, Grasser TW.

Development of a Doppler global velocimeter for high-

overexpanded supersonic jet. Paper 2003-0915, AIAA,

January 2003.

[95] Gustavsson JPR, Segal C. Filtered Rayleigh scatter-

ing velocimetry-accuracy investigation in a M ¼ 2.22

axisymmetric jet. Paper 2004-0021, AIAA, January

2004.

[96] Arnette SA, Samimy M, Elliott GS. Two component

planar Doppler velocimetry in the compressible turbulent

boundary layer. Exp Fluids 1998;14:232–332.

[97] Crafton J, Carter CD, Elliott GS. Three-component

phase-averaged velocity measurements of an optically

perturbed supersonic jet using multi-component planar

Doppler velocimetry. Meas Sci Technol 2001;12(4):

409–19.

[98] Sethuram S, Samimy M, Lempert W. Planar Doppler

Velocimetry in supersonic micro flows. Paper 2002-0690,

AIAA, January 2002.

[99] Grinstead JH, Finkelstein, ND, Lempert WR, Miles RB.

Frequency-modulated filtered Rayeigh scattering (FM-

FRS): a new technique for real-time velocimetry. Paper

96-0302, AIAA, January 1996.

[100] Grinstead JH, Finkelstein ND, Lempert WR. Frequency-

locked light scattering: real-time Doppler velocimetry

with closed-loop feedback control. Appl Opt 1998;37(9):

1617–25.

[101] Mach J, Varghese PL. Velocity measurements by

modulated filtered Rayleigh scattering using diode lasers.

AIAA J 1999;37(6):695–9.

[102] Jagodzinski J, Varghese PL. Diode laser velocity mea-

surements in unseeded flows using modulated filtered

Rayleigh scattering. Paper 2000-2297, AIAA, June 2000.

ARTICLE IN PRESSM. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142142

[103] Jagodzinski J, Varghese PL. Velocity measurements by

modulated filtered Rayleigh scattering using diode lasers.

Paper 2001-0848, AIAA, January 2001.

[104] Hils D, Hall JL. Response of a Fabry–Perot cavity to

phase modulated light. Rev Sci Instruments 1987;58:

1406–12.

[105] Kearney SP, Beresh SJ, Grasser TW, Schefer RW,

Schrader PE, Farrow RL. A filtered Rayleigh scattering

apparatus for gas-phase and combustion temperature

imaging. Paper 2003-0584, AIAA, January 2003.

[106] Boguszko M, Elliott GS. Measurements in fluid flows

using molecular filter-based techniques. Paper 2004-0018,

AIAA, January 2004.

[107] Boguszko M, Elliott GS, Carter CD. Filtered Rayleigh

scattering for fluid/thermal systems. Paper 2002-3233,

AIAA, June 2002.

[108] Hoffman D, Munch KU, Leipertz A. Two-dimensional

temperature determination in sooting flames by filtered

Rayleigh scattering. Opt Lett 1996;21(7):525–7.

[109] Elliott GS, Glumac N, Carter CD, Nejad AS. Two-

dimensional temperature field measurements using a

molecular filter based technique. Comb Sci Tech 1997;

125:351–69.

[110] Elliott GS, Glumac N, Carter CD. Molecular filtered

Rayleigh scattering applied to combustion. Meas Sci

Technol 2001;12(4):452–66.

[111] Yalin AP, Ionikh Y, Mechchanov A, Miles R. 2-D

temperature fields in glow discharges measured with ultra

violet filtered Rayleigh scattering. Paper 2000-0375,

AIAA, January 2000.

[112] Forkey JN, Lempert WR, Miles RB. Accuracy limits for

planar measurements of flow field velocity, temperature

and pressure using filtered Rayleigh scattering. Exp

Fluids 1998;24:151–62.

[113] Marquardt DW. An algorithm for least-squares estima-

tion of nonlinear parameters. J Soc Ind Appl Math

1963;11:431–41.

[114] Boguszko M, Elliott GS. On the use of filtered Rayleigh

scattering for measurements in compressible flows and

thermal fields. Exp Fluids 2005;38(1):33–49.

[115] Yan H, Knight D, Candler G, Kandala R, Elliott G,

Glumac N. Control of normal shock in Mach 2 flow by

pulsed laser energy. Paper AIAA 2005-785, AIAA,

January 2005.

[116] Boguszko MG. Measurements in fluid flows using filtered

Rayleigh scattering. Ph.D. dissertation, Rutgers Univer-

sity, October 2003.

[117] Shirley JA, Winter M. Air-mass flux measurement system

using Doppler-shifted filtered Rayleigh scattering. Paper

93–0513, AIAA, January 1993.

[118] Elliott GS, Samimy M. A molecular filter based tech-

nique for simultaneous measurements of velocity and

thermodynamic properties. Paper 96-0304, AIAA, Jan-

uary 1996.

[119] Elliott GS, Samimy M. A Rayleigh scattering technique

for simultaneous measurements of velocity and thermo-

dynamic properties. AIAA J 1996;34(11):2346–52.

[120] Elliott GS, Glumac N, Carter CD. Molecular Rayleigh

scattering applied to combustion and turbulence. Paper

99-0643, AIAA, January 1999.

[121] Most D, Leipertz A. Simultaneous two-dimensional flow

velocity and gas temperature measurements by use

of a combined particle image velocimetry and filtered

Rayleigh scattering technique. Appl Opt 2001;40(30):

5379–87.

[122] Most D, Dinkelacker F, Leipertz A. Direct determina-

tion of the turbulent flux by simultaneous application

of filtered Rayleigh scattering thermometry and

particle image velocimetry. Proc Comb Inst 2002;29:

2669–77.

[123] Jacobsen LS, Carter CD, Jackson TA, Schetz JA, O’Brien

WF, Elliott GS, Boguszko M, Crafton JM. An experi-

mental investigation of a DC plasma-torch igniter. Paper

2002-5228, AIAA, 2002.

[124] Bakker LP, Freriks JM, de Hoog FJ, Kroesen GMW.

Thomson scattering using an atomic notch filter. Rev Sci

Instr 2000;71(5):2007–14.

[125] Tang Z, Zaidi SH, Miles RB. Density gradient rubidium

dispersive absorption filter for low wavenumber Raman

and Thomson scattering. Paper 2000-0644, AIAA,

January 2000.

[126] Zaidi SH, Tang Z, Yalin AP, Barker P, Miles RB.

Filtered Thomson scattering in an argon plasma. AIAA J

2002;40(6):1087–93.

[127] Lee W, Lempert WR. Rubidium vapor filter spectrally

filtered Raman/Thomson scattering. Paper 2002–0394,

AIAA, January 2002.

[128] Lee W, Lempert WR. Rubidium vapor filter spectrally

filtered Thomson scattering. Paper 2002–3236, AIAA,

June 2002.

[129] Lee W, Lempert WR. Spectrally filtered Raman/Thom-

son scattering using a rubidium vapor filter. AIAA J

2002;40(12):2504–10.

[130] Bakker LP, Freriks JM, Kroesen GMW. A new ASE

filter: the 20-fold prism monochromator. Meas Sci

Technol 1999;10:L25–8.

[131] Ni CK, Kung AH. Effective suppression of amplified

spontaneous emission by stimulated Brillouin scattering

phase conjugation. Opt Lett 1996;21(20):1673–5.

[132] Lempert W. Non-equilibrium air plasmas at atmospheric

pressure. In: Becker K, Kogelschatz U, Schoenbach KH,

editors. Plasma Diagnostics. Series in Plasma Physics.

Bristol, UK: Inst. of Physics Pub. Inc.; November 2004

[Chapter 8, ISBN 0750309628].