Adaptive Optics:basic concepts, principles

and applications

Short course of lectures

Vadim Parfenov

Res.Ctr. “S.I.Vavilov State Optical Institute”Birzhevaya liniay, 14, St.Petersburg, 199034, Russia

vadim@optilas.spb.ru

Contents

Lecture #1

Basic Concepts and Principles

of Adaptive Optics

Lecture #2

Applications of Adaptive Optics.

New Technologies. Future of AO.

Lecture #1

Basic Concepts and Principles of Adaptive

Optics

• Basic Definitions on Optics• Some definitions concerned with Adaptive

Optics• History and basic concepts of Adaptive

Optics• Principles of Linear and Non-linear

Adaptive Optics• Conclusions

Outline

• The energy propagates along the rays.

• A continuous surface orthogonal to all rays is called wavefront. Wavefront can be defined for a non-monochromatic light.

• It can be shown that the phase of monochromatic light is constant on the wavefront surface.

Basic Definitions on Optics

Light

• Wavelengths (color). Optics deals with the range of 10 nm to about 500 m.

• Visible light occupies range of 350 to 700 nm.

• The speed of light is 300000 km/s and depends on the material. Light propagates slower in transparent dielectrics.

Point source

• Point source is an infinitely small source of light.

• Point source produces a bunch of rays.

• As light propagates with the speed C in all directions, we can define a spherical surface indicating the current position of light, emitted at “zero” moment. This surface is a spherical wavefront of light source radiation.

Geometrical optics

1 1n sin = n sin

Refraction and reflection of light rays are treated by geometrical optics:

'

1

n

1n

'

Refraction

Reflection

Imaging optics

F2F

a b

1/ 1/ 1/a b F

Geometrical aberration

An ideal lens transforms a spherical wavefront (WF) into a spherical WF – image of a point is a sharp point.

In case of an aberration, the WF deviates from sphere, resulting in a blurred image of a point source.

Aberrations

• Aberration can be described in terms of ray pointing (homocentric beams).

• Aberration can be described in terms of wavefront shape.

• Only spherical wavefront can form a good image of a point.

Diffraction

/ D

2 /l D

Diffraction limits the resolution of optics !

Beam divergency depends on the beam diameter (area) and on the wavelength.

Another parameter is the far-field distance, defining the applicability of geometrical optics.

2( / ) /D l D l D l

CoherenceFor spatial coherence all waves should be statistically in phase over the cross section of the beam.

For temporal coherence the waves should be statistically in phase over some time delay.

/ D

/l C

Some definitions concerned with Adaptive Optics

A Wavefront is an abstract representation of the phase of a propagating wave. It describes a surface which joins points of equal phase.

A point light source may produce a spherical wavefront which travels outward from the source. A flat (or collimated) wavefront may be focussed down by a telescope or other image-forming device to a diffraction-limited image.

In case of astronomical observations atmospheric turbulence introduces distortions into the wavefront arriving from an astronomical source (guide). Such a distorted wave cannot be focused into a diffraction-limited image unless some sort of phase correction is applied.

r0 is a time-dependent parameter which entirely defines the spatial statistics of phase fluctuations occuring across a telescope aperture. It was originally defined as the maximum diameter of telescope which can support diffraction-limited imaging under the particular conditions of turbulence.

At a good observing site one would expect r0 to vary between about 1 cm and 20 cm, depending on the how strong the turbulence is at the time.

The Diffraction Limit refers to the smallest (angular) size of detail theoretically resolvable by a telescope of a particular size and shape. This is inversely proportional to the diameter (D) of the aperture of the telescope, so a 10m telescope should be able to see details in the science object which are 100 times smaller that a 10 cm telescope can.

In fact, with perfect optics, a telescope should be able to resolve detail which is (wavelength/D) in angular extent.

Unfortunately atmospheric turbulence blurs the image formed in a telescope so that the diffraction limit of that telescope cannot be reached without some sort of correction.

A Reference Star (or guide star) is a light source, which is used to provide a wave whose phase geometry before encountering the atmosphere is known sufficiently well in order to be able to measure distortions introduced by the atmosphere.

It needs to be bright enough so that sufficient photons are collected in order to make a good estimate of the geometry of the wavefront distortions.

A natural guide star (i.e. an astronomical source), or even the science object itself, may be used as a reference star; however, if one is not available close to the science object then a laser beacon may be manufactured.

A Laser Beacon is an artificial reference star which may be manufactured if a sufficiently bright natural star is not available close to the science object. It is made by shining a very high-power laser into a small region of the atmosphere and collecting and observing light which is scattered back to the ground.

The Science Object is the astronomical object which is under study; this may or may not be the same as the reference source used in adaptive optics.

Phase Corrector is used in an adaptive optics system to take out some of the distortions introduced by the atmosphere (or any other similar phenomena). It often consists of a mirror (or other optical element) which can be rapidly deformed to the equivalent shape of the wavefront which must be subtracted out.

A Wavefront Sensor is used to measure the phase distortions introduced by the atmosphere into a reference wave (which are similar to those introduced into the wave arriving from the science object in the case of an adaptive optics system). Such a device may also be used to perform seeing measurements.

Open-loop is the mode of operation of an adaptive optics system in which the phase aberrations are measured but not corrected. In this situation, the wavefront sensor observes the full aberrations introduced by the atmosphere during each cycle. The open-loop frequency is simply the inverse of the time taken to detect the phase distortions, calculate the signals required for correction and drive the phase corrector.

Closed-loop is the mode of operation of an adaptive optics system in which the phase corrector is used to correct measured phase aberrations. Once the loop is closed, the wavefront sensor will only measure residual, or uncorrected, phase distortions, i.e. the difference between the actual phase aberrations and the most recent position of the phase corrector.

A Pupil image is the intensity pattern which is formed on the telescope pupil; in other words it might be what would be observed on a flat screen placed just above the telescope, over a region which corresponds to the shape of the telescope aperture (usually an annular ring). Normally, one might expect the pattern to be uniform, but atmospheric turbulence diffracts the light from a source above the atmosphere and causes fluctuations in the pattern, rather like the ripples seen on the bottom of a swimming pool.

Zernike Polynomials are a convenient set of circular or annular basis functions which may be used to represent an arbitary phase distribution over a telescope pupil in a mathematical form. A sum of a number of polynomials, each with its own weighting, may be used to reconstruct an atmospherically degraded wavefront; the higher the number of polynomials used, the better, in general, will be the fit to the actual physical phase distribution.

History and Basic Concepts of Adaptive Optics

1953 - Horace Babcock, then director of the Mount Wilson and Palomar Observatories, was first who suggested how one can build an astronomical telescope with compensation of atmospheric seeing

(H.Babcock, Publ. Astron.Soc.Pac., 65, 229(1953)).

1957 – Vladimir Linnik, Russian Academician from the Vavilov State Optical Institute, independently described the same concept in Soviet journal Optika i Spektoskopiya( V.Linnik, (USSR), Opt.Spectosk., 3, 401 (1957)).

 Linnik was first who suggested to use an artificial “beacon” to compensate aberrations of optical imaging systems. (He proposed to place a portable light source at 8- to 10-km altitude at the airplane or dirigible to provide the reference wavefront).

In 1950s realization of adaptive optical systems was beyond the technological capabilities…

For this reason… 

…first fully operational adaptive optics system was built and installed by American military scientists only in the mid of 1970s on a surveillance telescope at Haleakala Observatory in Maui, Hawaii, USA, where it imaged satellites launched by the Soviet Union.

1980 – Nick Woolf & Roger Angel

recognized the “polychromatic” nature

of adaptive optics:

Because the atmosphere is only weakly dispersive, natural stars measured at optical wavelengthscan be used to correct wavefront errorsat infrared wavelenghts.

(N.Woolf, R.Angel, in Optical and Infrared Telescopes for the 1980s, A.Hewitt, ed., Kitt Peak Natl. Observarvatory, Tucson, Ariz. (1980), p..1062)

1968 – M.Kogelnik & K.S.Pennington proposed a concept of holographic correction of aberration of optical systems.(M.Kogelnik, K.S.Pennington, JOSA, 58, 273-274 (1968))

1971 – Russian scientists Yu.Denisyuk & S.Soskin carried out first experiments on an aberrated telescope primary mirror holographic correction

(Yu.Denisjuk, S.Soskin (USSR), Optika I Spektroskopiya, 33, 992-993 (1971) ).

Works of M.Kogelnik, K.S.Pennington, Yu.Denisyuk, & S.Soskin –

beginning of Non-linear Adaptive Optics.

1980s – beginning of the era of artificial laser guide stars. 

1983 – Russian scientists V.Lukin & V.Matyukhin,

from the Institute of Atmospheric Optics (Siberian

branch of the Russian Academy of Sciences), renewed

an idea of V.Linnik on the use of reference light beacon

for adaptive image correction

(V.Lukin, Vmatyukhin, (USSR), Kvantovaya elektronika, 10, 2465-2473(1983) )

1985 – French astronomers Renaud Foy & Antonie Laberyie suggested that backscattered light from a laser could be usedto produce what now is called a laser guide star( R.Foy, A.Laberyie, Astron.Astrophys., 152, L29 (1985) ). 1991 – Declassification of the US military research programs concerned with Star Wars –US military research groups stepped forward to announce that they too had been investing in both adaptive optics and laser-guide-star (LGS) researches and independently devised LGS concept approximately four years before Foy and Laberyie, but it was not known in open literature.

TECNOLOGY

ASTRONOMY SYSTEM

LASER GUIDE STARS

THEORY

MERKLE

BECKERS

HUDGIN

LINNIK

FRAED

TYLER

FEINLIEB

HAPPER

FOY&LABEYRIE

GREENWOOD

LUKINBABCOCK

MIT/LL

TTC

ESO/ONERA

UTRC

AOA

ITEC

HUGNES

PERKIN-ELMER

RODDIER

ADAPTIVE OPTICS SYSTEMESO/VLT

Mt.WILSON

SOR (FUGATE)

CFHT

ANGLO-AUSTR. TELESCOPE

MMT

NATIONAL SOLAR OBS.

KECK

SUBARUAEOS

YERKES (U.CHICAGO)

LA PALMA (U.DURHAM)

CIS

Mt.HALEAKATA

GEMINI

What’s now ?

- Era of building a number of large adaptive astronomical telescopes.

- There are a number of non-astronomical applications of adaptive optics

Principles of Adaptive Optics  

An Adaptive optics system is optical system which automatically corrects for light distortions in the medium of transmission in real time.

An adaptive optics system measures the characteristics of the aberrated wavefront of incoming light and corrects for it either by means of a deformable mirror controlled by a computer or by means of nonlinear optics.

Two alternative approaches:

 Linear Adaptive Optics

and

Non-linear Adaptive Optics

What is difference ?

Linear Adaptive Optics

Real-time compensation of wavefront aberrations by means of adjustable optical elements.

Non-linear Adaptive Optics

Compensation of wavefront aberrations by means of non-linear optics phenomena.

Linear Adaptive Opticsdeals with optical systems operating in wide spectral range

(astronomical telescopes, imaging systems, etc.).

Non-linear Adaptive Optics

deals with coherent optical systems

(high-power lasers, laser communication systems, coherent optical imaging systems, etc.).

Principles of Linear Adaptive Optics

  

Linear Adaptive Optics

includes Active and just Adaptive Optics

Active Optics deals with wavefront errors of rather low temporal (less than 0.01 Hz) and spatial frequencies.

Adaptive Optics deals with rapidly varying wavefront distortions (up to 1000 Hz).

GRAVITY THERMAL WIND

FIGURING

ACTIVE OPTICSADAPTIVE OPTICS

LOCAL AIRATMOSPHERE

dc 0.01 0.1 1 10 100 TEMPORAL FREQUENCY (Hz)

10/D

1/D

0.1/D

SP

AT

IAL

FR

EQ

UE

NC

Y

FREQUENCY DOMAIN OF WAVEFRONT ABERRATIONS GENERATED BY VARIOSLY SOURCES.

THE SPATIAL FREQUENCY IS MEASURED IN TERMS OF D, THE DIAMETER OF THE TELESCOPE.

The simplest example for considering principles of Adaptive Optics is case

of astronomical observations through distorted Earth athmosphere…

  

STELLAR OBJECT

PERFECT WAVEFRONT ATMOSPHERIC EFFECTS AND OPTICAL SYSTEM ABERRATIONS

PERTURBED WAVEFRONT

ACTIVE ELEMENT

CONTROL SYSTEM

WAVEFRONT SENSOR

CORRECTEDWAVEFRONT

LIGHT BEAM SPLITTER

ASTRONOMICAL DETECTOR

THE PRINCIPLE OF ACTIVE AND ADAPTIVE OPTICS

Linear Adaptive Optics Systems work in a conceptually very simple manner:

Light arriving from a distant optical source (star or any extended object) is essentially a plane (flat) wave until atmospheric turbulence (or other aberrant medium) deforms the wavefront’s shape or, equivalently, induces local phase delays across the wavefront.

These deformations or phase delays in the wavefront can be monitored by wavefront sensor and compensated by deformable mirror in real time.

Incoming light from an astronomical source reflected off the deformed mirror leaves the mirror’s surface in its original pristine state, as it had never encountered any atmospheric distortions.

Principle 3. Wavefront sensing

The wavefront sensor (WFS) measures the distortions in the wavefront of light incoming into adaptive optical system.

Different approaches:- Hartmann method;

- Interferometric methods (phase-shifting, shearing, two-wavelength

interferometry);

- Curvature sensing;

- Scene-based sensing (WFS operating on image of extended object).

Hartmann Sensor

hartm ann m ask

detecto r p lane

aberra ted w avefron ts

turbu lent m edium

plane w avefron ts

disturbed wavefront

X

Y

The Shack-Hartmann method is the most commonly used approach.

This approach is completely geometric in nature and so has no dependence on the coherence of the sensed optical beam.

The incoming wavefront is broken into an array of spatial samples, called subapertures of the primary aperture, by a two dimensional array of lenslets. The subaperture sampled by each lenslet is brought to a focus at a known distance F behind each array. The lateral position of the focal spot depends on the local tilt of the incoming wavefront; a measurement of all the subaperture spot positions is therefore a measure of the gradient of the incoming wavefront. A two-dimensional integration process called reconstruction can then be used to estimate the shape of the original wavefront, and from there derive the correction signals for the deformable mirror.

imager (CCD, CMOS imager)

limited frame rate

data-reduction algorithm

position-sensitive detector matrix (PSD)

fast readout

direct spot position output

H a rtm a nn m ask

C C D o r C M O S im ag er

im ag epro cessing

w a vefro ntrecon stru ction

un kn ow n w av efron t

b itm a p

spo t p ositio ns

w a vefro nt sha pe

m a tr ix o f P S D 's

lig ht spo ts

Main elements and typical parameters of Shack-Hartmann Wavefront Sensor

Lenslet Array

CCD- Camera

Spectral bandwidth 200-..1600 nmDynamic phase range of the beamaperture

Up to 15m

Accuracy of measurements 0.08mData acquisition and analysis frequency Up to 30 Hz

CCD image input Using Matrix MeteorII/Standardframe grabber

The number of Zernike terms 36

The number of working sub- apertures Up to400

Principle 4. Deformable mirrors and wavefront correctors

Deformable mirrors and wavefront correctors are optical elements which are used to compensate distortions of wavefront.

Two types of deformable mirrors:

- Large-size adjustable mirrors (used to correct slow changes of WF)

- Small-size wavefront correctors (used to compensate fast changes of WF)

Large-size adjustable mirrors

Large primary mirror of astronomical (or imaging telescope) is flexible enough for mechanical devices (so-called actuators) to provide constant adjustment of its figure in accordance with the wavefront measurements.

Three types of adjustable primary mirrors are in the use or under development of present technology:

- Continuous mirrors (which maybe moderately thin menisci);

- Segmented mirrors (typically – structured honeycomb separate mirrors);

- Membrane-type (inflatable) mirrors manufacturing from thin polymer foil.

Segmented mirror

3-meter segmented mirror of adaptive imaging telescope developed at the Vavilov State Optical Institute (St.Petersburg, Russia)

Segmented mirror. General view

1-m prototype of membrane mirror developed at the U.S. Air Force Research Laboratory

MEMBRANE MIRROR

0.3-m prototype of membrane mirror developed at the Vavilov State Optical Institite, St.Peterburg, Russia

Small-size wavefront correctors

Wavefront correctors are small-size deformable mirrors (or other types of adjustable optical elements), which are used for compensation of high-frequency (up to 1000 Hz) distortions of wavefront.

Because of the high bandwidth and the small field, usually wavefront correctors have diameter of 10 to 20 cm and are located within the optical train of the telescope or in separate box behind the focus of the telescope at an image of the pupil.

1. Segmented wavefront corrector 

developed at the Vavilov State Optical Institute (St.Petersburg, Russia) for the space-based NASA/CSA lidar ORACLE

Design of the bimorph mirror

2. Bimorph Mirrors

2. Bimorph mirrors

General view of copper bimorph mirror(developed by the Adaptive Optics group of Russian Academy of Sciences)

3. Micromachined Membrane Deformable Mirrors

The shape of tensed membrane iscontrolled by the electrostatic attraction to the grid of electrodes

(developed by G.Vdovin, Delft Technical University, Netherlands)

4. Liquid-crystal spatial light modulators (LC SLM)

First application of LC SPMs in Adaptive Optics -

D.Es’kov, A.Onokhov, V.Reznichenko, V.Sidorov, the Vavilov State Optical Institute, Russia (reported at the SPIE Symposium on Astronomical Telescopes for 21 century, Hawaii, USA, March, 1994)

Principle 5. Artificial Laser Guide Star

For what Laser Guide Star is needed ?

Not just any star can be used as reference beacon !

1. It must be bright enough, that is, generate enough light to serve as a reference

light source.

When observing at visible wavelengths, astronomers using adaptive optics

require a 5-magnitude star, one that is just bright enough to be seen unaided.

(For near-infrared observations, only a 10-magnitude star is needed, which is 100

times fainter.)

2. Even though there may be hundreds of thousands or even a million stars bright

enough to be guide stars, they only cover a small fraction of the sky.

There just isn't a natural guide star in the area you want to observed !

Creating a Laser Guide Star

First approach (Ralyleigh scattering of laser beam in stratosphere)

The use of focused visible or ultraviolet laser light to reflect off air molecules

in the lower atmosphere from fluctuations (Rayleigh scattering), creating a

star at an altitude of about 10 km.

Second approach (resonant scattering of laser light by mesospheric sodium)

The use of focused yellow laser light which is directed through the

atmosphere to excite sodium atoms at about 90 km, where the laser beam hits

a layer of sodium atoms created by micrometeorites, which vaporize as they

enter the upper atmosphere.

The yellow laser light, tuned to 589 nanometers, excites the sodium atoms,

which then emit this yellow light in all directions, creating a glowing guide

star in the upper atmosphere.

ALFA

ALFA is the Adaptive Optics with a Laser For Astronomy system for the Calar Alto 3.5-m telescope.

This is a joint project between the MPIA in Heidelberg and the MPE, Germany.

ALFA is based on a Shack-Hartmann sensor with a high-speed low-noise CCD camera, a 97-actuator deformable mirror, a tip-tilt sensor (CCD camera), a tip-tilt mirror and a continuous Ar-Ion laser pumped dye laser which generates the laser beacon in the sodium layer of the mesosphere.

 

 

First civil Laser Guide Star System for Astronomy

Lick Observatory of the University of California on Mount Hamilton near San Jose, C.A., U.S.A Laser Guide Star Laser Laser Guide Star Laser Projection Projection

System of the University of System of the University of California's Lick Observatory California's Lick Observatory

Three views of the satellite Seasat from the U.S. Air Force Starfire Optical Range 3.5 m adaptive optical telescope (AF Kirtland Airbase, NM):

(a) through the turbulence, (b) real time correction using adaptive optical system, (c) post-processed with the blind deconvolution algorithm. 

Principle 7. Multi-modular telescopes

The main idea – using the set of separate small-size telescopic modules one can achive the same resolution, which can be obtained with large-aperture primary mirror.

  

 

Design of multi-modular telescopic system:

1,2, 5 – aspherical mirrors; 3,4,6 – flat mirrors; 7 - spherical mirror; 8 – receiver of image

Preliminary conclusions

• Linear AO is applicable to the optical imaging systems and can increase the resolution of its optics;

• Key components of any AO systems include:

- a wavefront sensor to measure the distortions of the wavefront coming from a star or science object;

- a wavefront correction device (deformable mirror or wavefront corrector);

- a control computer, which can be relatively slow for active optics, but must be extremely fast for adaptive optics.

Principles of Non-linear Adaptive Optics

  Compensation of wavefront aberrations by means of non- linear optics phenomena (phase conjugation, four-wave mixing, dynamic holography, etc.)

You have to know everything about it from

course of lectures of Prof. Andreoni !

5 mm 2·10-3 rad

aberrator initial beam aberrated beam restored beam

PHASE CONJUGATION OF CO2 LASER RADIATION DUE TO FOUR-WAVE MIXING IN SF6 (i 1 mcs)

PHASE CONJUGATION OF CO2 LASER RADIATION DUE TO FOUR-WAVE MIXING IN SF6 (i 1 mcs)

[1] R.C. Lind et al.,1979 - FIRST EXPERIMENTS WITH TEA CO2 LASERS

[2] N.G.Basov, V.P.Kovalev et al.,1982 - DEMONSTRATION OF HIGH PC FIDELITY

[3] D.A.Goryachkin, V.P.Kalinin,N.A.Romanov et al.,1983 -PCM REFLECTIVITY 100%

[4] D.A.Goryachkin, V.P.Kalinin, I.M.Kozlovskaya, V.E.Sherstobitov, 1987 - FIRST

EXPERIMENTS WITH SF ON THE P20 LINE - REFLECTED BEAM PULSE ENERGY ABOVE 2.5J

Preliminary conclusions

• Non-linear AO is applicable to the coherent optical systems (including high-power lasers and laser optical communication systems);

• Researches in the field of non-linear AO also include its application in imaging optical systems;

• Non-linear AO technology does not require investments comparable with linear AO (Lower costs) !

Conclusions

• AO is very promising optical technology which can be applicable to the astronomical telescopes and optical imaging systems and can increase the resolution of its optics;

• There are two alternative approaches to compensation of wavefront aberrations based on the use of Linear AO and Non-linear AO;

• AO is a very research-intensive area;

• Huge investments in AO technology are still necessary to get scientific results and to bring financial returns.