Confocal Backscatter Laser Velocimeter with On-AxisSensitivity

Kenneth L. Orloff and Samuel E. Logan

A confocal backscatter laser Doppler velocimeter (LDV) that measures two velocity components has beendeveloped. This device requires only two incident beams polarized normally to one another. Moreover,the velocity components sensed are nearly orthogonal. The velocimeter employs a combined dual-scat-ter, local oscillator arrangement to obtain the bidirectional sensitivity. Two photodetectors are used,each sensing only one Doppler frequency proportional to one of the very nearly orthogonal velocity com-ponents. In addition, a single Bragg cell serves to frequency bias both velocity components in order toeliminate directional ambiguity. A differencing technique has also been incorporated to enhance thedual-scatter Doppler signal corresponding to the transverse velocity.

Introduction

The confocal backscatter laser velocimeter, utiliz-ing a common lens system for both transmitting andreceiving, is becoming increasingly popular becauseof its practicality in many flow situations. In thedual-scatter configuration, any velocity componentin a plane normal to the transmitting axis can beeasily measured. However, obtaining the velocitycomponent parallel to the transmitting axis (the on-axis component) in a confocal backscatter systempresents a more difficult problem.

Previous attempts to develop LDV systems withsensitivity in both the transverse and on-axis direc-tions have suffered from various drawbacks. Anearly three-dimensional local oscillator system byFridman et al.1 used three nearly on-axis detectors,resulting in a system. of three equations from whicheach of the orthogonal velocity components could beextracted. This system gives an uncertainty in eachvelocity component approximately three times thatinvolved in each frequency measurement. Further-more, high sensitivity is not achieved in thetransverse direction, but only on-axis.

A proposal by Farmer 2 utilizing two rotationallydisplaced, two-orthogonal component LDV systemsto deduce the on-axis component required numerousincident beams and solution of a complex matrix.

A relative performance analysis given by Farmeret al.3 for local oscillator and dual-scatter LDV sys-

When this work was done, both authors were with NASA AmesResearch Center, Moffett Field, California 94035; S. E. Logan ispresently at the UC School of Medicine, Los Angeles, California90024.

Received 19 January 1973.

tems is appropriate to the combination system whichis the subject of the present paper. The addition ofvelocity component isolation (such as describedherein) to the system, which they show schematical-ly, does not affect the conclusions regarding the per-formance analysis. However, the use of such com-bined dual-scatter, local oscillator systems withoutcomponent isolation suffers from the problem of hav-ing more than one Doppler frequency appearing onone or more of the detectors. Since neither the mag-nitude nor the direction of the velocity vector isknown a priori, such a system cannot be effectivelyused with standard wideband frequency trackers andother electronic processors.

A technique to obtain two near-orthogonal velocitycomponents (one nearly on-axis) in a confocal back-scatter instrument without the previous drawbackshas been developed. The instrument uses only twooutgoing beams polarized normally to each other,and one and only one independent frequency compo-nent is obtained on each of two photomultipliers inthe receiving optics yielding totally isolated velocitycomponents, thus eliminating the need for a matrixof equations. Directional sensitivity is realized inboth components using only one Bragg cell. In ad-dition, an optional differencing technique analagousto those of Goethert4 and Bossel et al.5 can be em-ployed to enhance the transverse dual-scatter Dop-pler signal.

Doppler Signal with Normally Polarized Beams

It has been shown by several authors indepen-dently6 -8 that in the intersection region of two mono-chromatic laser beams in a dual-scatter LDV system,fringes can be observed, and the Doppler signals ob-tained can be thought of as being generated by par-ticles passing through these fringes. However, if the

October 1973 / Vol. 12, No. 10 APPLIED OPTICS 2477

900 POLARIZATION ROTATOR

Fig. 1. Confocal backscatter differential polarization technique.

two incident beams are polarized normally to eachother, no fringes are seen in the intersection regionwhen the observation is made parallel to either ofthe incident polarizations. These observations aremade by viewing a magnified image of the intersec-tion volume when a polarizer is placed before thescreen with its transmission axis at some specifiedangle with respect to the incident beam polariza-tions. Fringes of maximum contrast are observed ateither +45° or -45° with respect to either of the inci-dent beam polarization directions. In addition,these fringes observed at 450 are displaced fromeach other by exactly one-half of the fringe spacing.This implies that Doppler signals generated by eachof these sets of fringes will be phase shifted fromeach other by r. This property has been indepen-dently applied by Goethert4 and Bossel et al.

5 in dif-ferencing techniques to enhance the Doppler signalby eliminating unwanted signals common to bothdetectors, such as the pedestal in Goethert's sin-gle particle LDV system and amplitude fluctuationsin Bossel's multiple particle LDV arrangement.

Application of the signal enhancing polarizationtechnique to a confocal backscatter LDV system uti-lizing a 4-W argon laser is diagramed in Fig. 1. For

the experiment reported herein, the laser output wasless than 100 mW. A Wollastrom prism is used toseparate the scattered light into 45 componentswhich is imaged onto two photomultipliers (EMI9558). The outputs of the two PM tubes were equa-lized by adjusting the individual high voltagesupplies until both signal and noise were as similaras possible (as observed on the spectrum analyzer).The differencing is done on an oscilloscope and thedifference signal fed into a Hewlett-Packard model8552/8553 spectrum analyzer. Signal enhancementwas demonstrated in backscatter from both a rotat-ing lucite wheel and from a low velocity smoky jet.SNR improvements as much as 4-5 dB were ob-served. Figure 2 shows Doppler signals obtainedfrom the smoky jet, illustrating the two individualsignals and their difference. When the sum of thetwo signals is taken, a marked decrease in SNR isobtained, verifying that the two Doppler signals areout of phase with each other. That trace E is notzero does not imply that the phase shift is other than7r, but is rather due to the slightly different charac-teristics of the photomultiplier tubes and the diffi-culty in equalizing both signal and noise simulta-neously.

Although signal enhancement is potentially quiteuseful for LDV work, the primary interest in the nor-mal polarization technique for this application is thepossibility of independently obtaining a nearly on-axis velocity component described in the next sec-tion.

On-axis Velocity Measurement

As mentioned earlier, with normal polarization ofthe two incident beams, fringes of maximum con-trast are observed at E450, and no fringes are ob-served at either 0 or 900 (the directions of incidentbeam polarizations). Thus, the two beams are effec-tively distinguishable from each other, and observa-tion of the scattered radiation at a polarization ofeither 0 or 900 will only allow light scattered fromone beam or the other to be seen since the scattered

Fig. 2. Signal enhancement inconfocal backscatter using dif-ferential polarization technique,low velocity smokeflow: (a) in-dividual signal el and differenceof el and e2: (b) individual sig-

nal e2 and sum of el and e2.

A (e1 - e2) B e1 C 375 kHz D e2 E (e1 + e2 ) F 375 kHz

(a) (b)

2478 APPLIED OPTICS / Vol. 12, No. 10 / October 1973

VI

A0 L ,! -- V2

G

I ~~~~~~~~~V2L

+45o 45

A ARGON LASER WITH ETALON I COLLECTING LENS, DIAMETER= 5cmB BEAM SPLITTER (AM20cM

2)

C POLARIZATION ROTATOR J LOCAL OSCILLATOR MIRROR,D BRAGG CELL FOR DIRECTIONAL DIAMETER= 0.45Cm (A016Cm

2)

SENSITIVITY, UN=37.20 MHZ K PHOTOMULTIPLIERE FRONT-SURFACED MIRROR L WOLLASTROM PRISMF RECEIVING LENSG NEUTRAL DENSITY FILTERH TRANSPARENT GLASS SLIDE * OPTIONAL PHOTOMULTIPLIER, REQUIRED FOR DWH TRNpArcenREFGLA SLIDE, SCATTER SIGNAL ENHANCEMENT DIFFERENCING

4 percent REFLECTION TECHNIQUE

Fig. 3. Two-dimensional confocal backscatter LDV system withon-axis sensitivity, directional sensitivity, and optional dual-

scatter signal enhancement.

light is linearly polarized when the plane of observa-tion is parallel or perpendicular to the primary vi-brations (of the incident light).9 Utilizing these twofacts, an optical system (Fig. 3) was designed that.could simultaneously detect two nearly orthogonalvelocity components, one very nearly along the LDVaxis and the other transverse to the axis. As in Fig.1, the dual-scatter signal is retrieved with a Wollas-trom prism by observing the scattered radiation ateither +450 or 45. (The differencing technique isoptional and may or may not be used, as desired.)

The nearly on-axis velocity component is obtainedwith a local oscillator arrangement that utilizes onlythe scattered radiation from the vertically polarizedincident beam. The reference beam is obtained as aspurious reflection from the splitter cube and alignedwith the returning scattered radiation as indicated inFig. 3. The use of an intercavity etalon for singlefrequency operation allows such a system to workeven with large pathlength differences between thescattered and reference beams.

Originally, a vertical Polaroid was placed in frontof the local oscillator phototube, but it was experi-mentally verified that only scattered light from thevertically polarized outgoing beam heterodyned withthe (vertically polarized) local oscillator beam.Only a small fraction of the collected backscatteredlight (0.20 cm2 out of 25 cm2 on the receiving lens) isneeded to obtain a strong local oscillator Dopplersignal. Utilization of such a small fraction of thescattered light for the on-axis component has the ad-vantages that most of the scattered radiation stillcontributes to the dual scatter signal, and the aper-ture broadening of the local oscillator system is min-imal. In particular, it is only that portion of scat-tered radiation that passes through the transparentglass slide and is parallel10 with the local oscillatorbeam at the focus of the collecting lens that givesrise to a heterodyne signal. Hence, the local oscilla-tor mirror need not be any larger than necessary in

order to minimize shot noise from an increased over-all dc level.

Figure 4 diagrams the two measured velocity com-ponents. They are not exactly orthogonal, but -areseparated by (/2 + 0/4). Since 0 is typically quitesmall, usually a few degrees, 0/4 is much less thanIr/2, and the two components are orthogonal for all

practical purposes. However, the measurement di-rections are well defined, and for two-dimensionalflow,1 the exactly on-axis velocity component canbe computed from axia = V2 sec0/2 + vl tan0/4,where the independent velocity components v andV2 are computed from the measured Dopplerfrequencies

P, = (2nv,/X0) sin(0/2),

V2 = (2nV2/\ 0 ) cos(0/4).

As evident from Fig. 3, frequency shifting the ver-tically polarized beam with a single Bragg cell willgive both components directional sensitivity, a vitalfeature if the velocity vector direction is not known apriori. Frequency shifting one of the laser beams (byamount vi) in either a dual scatter or a reference orlocal oscillator system will bias the Doppler signal VDso that it is added to, or subtracted from, vm, de-pending upon flow direction [i.e., if flow in one direc-tion gives v + VD, flow in the opposite direction(1800) at the same speed will give vm - VD]. Thus,with the Bragg cell in the system (. = 37.20 MHz),the spectrum analyzer will display vm P vi and vin +V2 from the two tubes, respectively, depending on theabsolute directions of the velocity components v andV2.

Experimental Verification

The two-dimensional concept has been verified inscattering from both a rotating lucite wheel and froma smoky, low-velocity jet. Independence of the twosignals and directional sensitivity have been verified.Figure 5 shows dual scatter and local oscillatorsignals simultaneously displayed on the Hewlett-Packard model 8552/8553 spectrum analyzer. Inorder to illustrate directional sensitivity, the localvelocity vectors for both the lucite wheel and thesmoky jet have been chosen so that the local- oscilla-tor and dual-scatter signals lie on the left and right

VI

COLLECTED 8SCATTEREDRADIATION

Fig. 4. Velocity component sensitivity (vi dual-scatter compo-nent, V2 local oscillator component).

October 1973 / Vol. 12, No. 10 / APPLIED OPTICS 2479

JAL

(a) LUCITE WHEEL

Fig. 5. Simultaneous spectrum.analyzer display of the two Dop-pler signals from (a) a lucitewheel and (b) smoky jet. Veloc-ity vectors for both (a) and' (b)oriented in the same direction.The two photomultiplier out-puts are added at the spectrum

analyzer input.

A LOCAL OSCILLATOR, 36.52 MHz D LOCAL OSCILLATOR, 36.20 MHz

B DUAL SCATTER, 38.00 MHz E DUAL SCATTER, 37.72 MHz

C BRAGG CELL 37.20 MHz F BRAGG CELL 37.20 MHz

(a) LOCAL OSCILLATOR b) DUAL SCATTER

Fig. 6. Individual photomulti-plier Doppler signals illustratingcomplete separation of the twovelocity components in the twodetectors, lucite wheel: (a) sig-nal from local oscillator photo-multiplier tube alone, 36.52MHz; (b) signal from dual-scat-ter photomultiplier alone, 38.00

MHz, no differencing.

sides, respectively, of the biasing Bragg cell frequen-cy of 37.20 MHz. Changing the direction of thelocal velocity vector changes the relative positions ofthe two signals relative to the Bragg cell biasing fre-quency, and directional sensitivity can easily be veri-fied. (The small frequency component at the Braggcell driving frequency is pickup resulting from in-complete shielding of the Bragg cell generator. Thiscomponent could have been eliminated, but was leftin the present investigation as a convenient referencefor the Doppler signals.)

Since the acoustooptic modulator (Bragg cell) isfound to be only about 90% efficient in the transferof energy to the first shifted order, equal intensitiesof the outgoing beams must be reestablished throughadjustment of the beam splitter B so as to maintainthe quality of the dual scatter signal. Furthermore,this first-order shifted beam is rendered again paral-lel (to the beam that has been rotated in polariza-tion) by using a wedgelike water-filled cell that is in-serted after the Bragg cell. The unused beams oflower intensity emerging from the Bragg cell neednot be blocked out since they do not intersect the ro-tated polarization beam to form a scattering volume.Also, the spatial resolution obtained by aperturing atthe photodetector precludes reception of scatteredlight from these beams.

2480 APPLIED OPTICS / Vol. 12, No. 10 / October 1973

Figure 6 shows (for the lucite wheel) the outputs ofthe two photomultipliers sequentially illustrating theexcellent separation of the two Doppler signals.12

This complete isolation of the two signals is one ofthe most important features of the present systemand distinguishes it from previous proposals to ob-tain the on-axis velocity component simultaneouslywith the transverse components that suffer frommultiple frequency components emerging from eachphototube. Figure 7 illustrates this multiple fre-quency problem encountered by systems that do notutilize the polarization technique for incident beamisolation. The optics are identical to Fig. 3 exceptthat the polarization rotator has been removed sothat all beams have vertical polarization. On theexpanded frequency scale (0-50 MHz) in Fig. 7,three distinct frequency signals are seen to be pres-ent at the output of the local oscillator photodetec-tor-the desired directionally sensitive local oscilla-tor and dual-scatter signals of Fig. 6, as well as a lowfrequency local oscillator signal resulting from heter-odyne mixing with the unshifted, unrotated beamthat had previously been rotated in polarization.The extraneous dual-scatter and low-frequencylocal oscillator signals (which would make utilizationof a wide band frequency tracker impossible) are ab-sent when the polarization rotator is employed.

Wb SMOKE JET

A L.O. FROM UNSHIFTED BEAM (1.46 MHz) DB L.O. FROM SHIFTED BEAM (36.52 MHz) EC DUAL SCATTER SIGNAL (38.00 MHz) F

Conclusion

The possibility of easily obtaining two-dimensionalvelocity measurements, with one component on theLDV axis, has been demonstrated. Previous prob-lems inherent in LDV systems attempting to mea-sure simultaneously the transverse and on-axis ve-locity components have been overcome. Most sig-nificantly, using the polarization technique, only oneDoppler frequency component is detected on thelocal oscillator photomultiplier tube, whereas with-out orthogonal polarization of the two beams, multi-ple frequency components are obtained. Alignmentdifficulty and aperture broadening were found to beminimal in the local oscillator system.

The normal polarization technique can also derivedirectional sensitivity in both independent velocitycomponents with the use of only one Bragg cell. Adifferencing technique for signal enhancement of thetransverse dual-scatter velocity component was alsopresented.

The technique is designed to be retrofit into an ex-isting two-dimensional confocal backscatter instru-ment at the Ames Research Center, NASA.13Transverse orthogonal two dimensionality is ob-tained by using the two dominant colors from anargon-ion laser (both in the dual-scatter configura-tion) focused at the same spot. Fitting the two-di-mensional polarization technique into one of the col-ors will give three-dimensional, near-orthogonal ve-locity sensitivity.

Fig. 7. Local oscillator (L. 0.)photomultiplier signal demon-strating multiple frequency com-ponents when polarization rota-I l - tor is removed.

ZEROLASER NOISEBRAGG CELL (37.20 MHz)

K. L. Orloff is a National Research Council Asso-ciate.

References1. J. D. Fridman, R. M. Huffaker, and R. F. Kinnard, Laser

Focus 4, 34 (1968).2. W. M. Farmer, Appl. Opt. 11, 770 (1972).3. W. M. Farmer, J. 0. Hornkohl, and D. B. Brayton, Opt. Eng.

11, 24 (1972).4. W. H. Goethert, AEDC-TR-71-70 (1971).5. H. H. Bossel, W. J. Hiller, and G. E. A. Meier, J. Phys. E. 5,

895 (1972).6. D. B. Brayton, and W. H. Goethert, AEDC-TR-70-205 (1970).7. M. K. Mazumder, NASA CR-2031 (1972).8. C. M. Penny, IEEE J. Quantum Electron. QE-5, 318 (1969).9. M. Born, and E. Wolf, Principles of Optics (Pergamon, New

York, 1970), p. 652.10. Actually, any ray within an angular misalignment solid angle

of Q < X2/AR will give rise to Doppler signal according to theantenna theorem for heterodyne receivers.

11. For three-dimensional flow the exactly on-axis component canagain be computed by including the measured value for V3 (ina three-dimensional instrument), where V3 is a transversedual-scatter component orthogonal to both vi and V2. When-ever V3 = 0, the two-dimensional equation is valid.)

12. The very small dual scatter component on the local oscillatorsignal is believed to result from incomplete polarization rota-tion of the horizontally polarized beam and also the fact thatthe laser has approximately 1% horizontal polarization.

13. G. R. Grant and K. L. Orloff, NASA TM X-62, 254 (1973).

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