ADAPTIVE OPTICS FOR ESO'SVERY LARGE TELESCOPE (VLT)

PROJECT

Fritz Merkle

European Southern ObservatoryKarl-Schwarzschild-Str. 2

D-8046 GarchingFed. Rep. Germany

May 1986

VLT REPORT No. 47

ADAPTIVE OPTICS FOR ESO'SVERY LARGE TELESCOPE (VLT)

PROJECT

Fritz Merkle

Abstract

Imaging in ground-based astronomy is limited by the transmissionof the light through the turbulent atmosphere. Adaptive optics offersthe possibility to overcome these limitations. It employs a real-timephase compensation with a phase shifting optical element, which isusually a deformable mirror. The information for the control of themirror surface is gained from a wavefront sensor. This report describesthe principles of adaptive optics and its application in astronomy. Itgives an overview over the major elements like the wavefront correctiondevices, the wavefront sensors, and control systems. The performanceof adaptive systems and the requirements in astronomy are discussedand guidelines for the implementation of this technology in ESO'sVery Large Telescope given.

Table of Contents

1 Introduction 12 Principles of Adaptive Optics 43 Adaptive Optics in Astronomy 94 Strategy for Seeing Optimization 105 Elements of an Adaptive System 145.1 Wavefront Correction Device 145.2 Wavefront Sensor 175.2.1 Shearing-Interferometer 175.2.2 Shack-Hartmann Sensor 195.3 Control System 226 Performance of an Adaptive System 227 Requirements for Adaptive Correction in Astronomy 248 Adaptive Optics for the VLT 289 Conclusion 31

References 32

1

1 Introduction

A perfect astronomical telescope should have a theoretical angular resolu­tion of

A~a = 1.22 D (in Radians)

(A: wavelength, D: telescope diameter), where ~a is the radius of the firstdark ring of the Airy disc. This would lead to the resolution values dis­played in figure 1 for different telescope diameters. However, in practice theimaging quality of ground-based telescopes is degraded by the transmissionof the light from the astronomical object through the turbulent atmosphereof the earth. The reason for this degradation is a random spatial and tem­poral wavefront perturbation induced by the turbulences in the differentlayers of the atmosphere. In addition to this, also the aberrations of theoptical elements of the telescope contribute to the degradation. All these

....u..III

u.........

tc:~ 10-2+,t-,'-+-'1f---/+-+----+------l::::JCIIIQI......IV

~ 10-3+--+/-+-----1---+-----(c:IV

10-4L----t---+---t----'0.1 1 10 100 1000

[/Lm]Wavelength -

Figure 1: Angular resolution of an astronomical tf']pscope in the absence ofany atmospheric and instrumental distortion of the light transmission (Theangular resolution is given as radius of the. first dark ring in the Airy disc.)

2 1 INTRODUCTION

wavefront perturbations together result in a complex phase aberration

<P(r, t) - z'A(r, t)

of the light beam. The real part <P(r, t) represents the phase shift of thewavefront, usually called" seeing" , while the imaginary part A(r, t) is a mea­sure for the intensity fluctuations across the aperture plane, called "scintil­lation". Figure 2 displays the influence of phase distortions on the imagequality, which is commonly described with the Strehl ratio S:

S = peak z'rradz'ance z'n the j oeaL pLanepeak z'rradz'ance dz'j jractz'on hm£ted

010.05O'--------I--- L----.J

o

ot=«ex: 0.5...J:I:wex:~

VI

RMS ERROR [wave~

Figure 2: Image quality vs. the RMS wavefront error. The image qualityis given by the Strehl ratio S.

It is possible to correct the phase shift with a technique called adaptiveoptics [Hardy 1978, Pearson 1979, Merkle 1983a). The basic principle ofadaptive optics is to use a phase shifting optical element, which can becontrolled in space and time in order to compensate the atmospheric phaseshift (see fig.ure 3). A correction of the scintillation would require a spatiallyand temporally controllable apodization element. Thus, a system for thefu 11 correction of the aberrations applies a compensation equal to

-<P(r, t) + z'J.tA{r, t)

3

OBJECT

WAVEFRONTCONTROL

WAVEFRONTSENSOR

IMAGE

CONTROLSYSTEM

Figure 3: Principle of active/adaptive optical correction system.

(J.L : dimensionless intensity scaling factor). For most of the imaging prob­lems, especially with very large telescopes, the phase correction part issufficient and for technical reasons its realization is much easier than thecorrection of the intensity fluctuations. The field of adaptive optics is inastronomy often divided [Woolf 1984] in the so-called "active optics': whichis used for the figure correction of the telescope optics and the "adaptiveoptics" for the correction of atmospheric effects. In this definition the fieldof active optics is just a special case of the general principle of adaptiveoptics at low spatial and temporal frequencies. However, in optical andcontrol engineering the distinction is different. Here, active optical systemsor the active components thereof are capable of reshaping a wavefront byadding a set of controllable path differences. No closed loop servo controlthat operates on the actual wavefront error information is present. Anadaptive optical system includes a closed loop phase error sensor that actsto drive a set of path differences to zero. Therefore, the terminology usedin astronomy is in some sens contradictory to the technical definition butuseful to identify the different applications, mainly because the ways oftheir technical realization are quite different. The scope of this paper is thefield of adaptive optics for atmospheric turbulence correction.

During the last 10 years the techniques of adaptive optics have beendeveloped, mainly for laser beam transmission through the turbulent at­mosphere. Although most of the developments have been made in theUnited Sta.tes (at companies like ITEK, Lockheed, United Technologies,AVCO Everett, The Aerospace Corp., AOA, and others), there are somepromising activities in Europe (CGE, ONERA (France), MBB, and Diehl

4 2 PRINCIPLE OF ADAPTIVE OPTICS

(FRG)). The transfer of these techniques to the astronomical field is notstraight forward, mainly because of the very low light levels compared withlaser applications and the large apertures of the astronomical telescopes.However, the progress in wavefront-sensor technology and the availability offast computers to cope with the large number of corrections at large aper­tures has opened the technical feasibility of adaptive optics to astronomy.New ideas came up to overcome the intensity problems, like shooting laserbeams to the higher atmosphere to create an artificial star-like referencesources.

The intention of this report is to introduce the techniques of adaptiveoptics and its implication to astronomy. The chapters 2 and 3 will give anintroduction to principles of adaptive optics. Chapter 4 describes correctionstrategies and chapter 5 the the basic elements of an adaptive system. Theperformance of an adaptive system is evaluated in chapter 6. Chapter 7and 8 describe the requirements for the design of an adaptive system inastronomy and, especially, with respect to ESO's Very Large Telescope(VLT) project.

2 Principle of Adaptive Optics

An adaptive optical system (see figure 4) contains four basic elements: anoptical train and image detector, a wavefront sensor, a servo-control system,and a phase-shifting optical element. The distortion of the received wave­front is usually compensated by reflecting the light beam on a deformablemirror. The surface of this mirror is adjusted in real-time to compensatethe path length aberrations. The information required to deform the mirroris obtained by analyzing the light beam with a wavefront sensor. A map ofwavefront errors is then derived at each instant of time. Using this errormap. the control system determines the signals required to drive the phaseshifting optical element and to null the phase aberrations by closing theadaptive loop. The phase correction values can be obtained by expandingthe phase-correction function

N

<l> (r, t) = L an (t) f n(7'1n=l

in a spatially (fn(r)) and temporally (an(t)) dependent function. The spa­tial functions might represent zones or mode of the aperture, resulting in azonal or modal correction strategy.

5

LIGHT FROM THETELESCOPE

(- ~-t=I""L

ICONTROLSYSTEM

II

~IIIIIIl_ WAVEFRONT

SENSOR

CLOSEDLOOP

Figure 4: Principle of the application of adaptive optics in astronomy.

The complexity and design of an adaptive system depends of the aper­ture size D of the telescope, the direction of the optical path specified bythe zenith angle, and the atmospheric conditions. The atmospheric condi­tions are usually described with the atmospheric turbulent refractive-indexstructure constant C~ [see Roddier 19811 which is a function of the height habove the ground. Figure 5 (left) shows a model of the vertical profile of theC~ distribution of as a function of altitude h for day and night time [Fried1982~ and some measurements of C~ in Europe [Barletti 1976, (right). Theresulting seeing conditions are often characterized by the scaling parameter

TO = [0.423k 2 ~ C~(h) dh] -3/5

with7r

k = 2->.

(A: wavelength, R: height of the atmosphere) called atmospheric corre­leation length or coherence diameter. It was introduced by Fried in 1965[Fried 1965]. The size of the resulting seeing disc is then in the order of

A/TO'

6 2 PRINCIPLE OF ADAPTIVE OPTICS

,

,

,

"AVG" -,,lIARLETII

h~ElIROI'~O,l,Y

hANCNICHT

"LUCKY"1

L l., I~

,00' .,

" IE-13 10- 1::~

N <u 1E-'" 10- 1

Cl:c~ (Z),W

t-W .~2IlI: 1~-15< 10- 1Cl:<0..

w lE-leCl::0

1~-17f10. 1

t-U:0Cl:t-VI 10. 1

W>Ht- lE-I8U

lO·1<Cl:u.w ICl: 1[-1;

IEI 1~2 1~3 1~5

IO~1

AL TITUDE ABOVE SITE (m)ALTAIOV!5ITI,k.'I.

Figure 5: Model of the vertical distribution of the refractive-index structureconstant C~ [Fried 1982] (left) and its distribution measured in continen­tal Europe [Barletti 1976] (right). Model and measurements are in goodagreement.

The following expression [Brown 1975] gives then the number of neces­sary subapertures for an ideal adaptive system with a deformable mirroras active element when a certain Strehl ratio S should be achieved by theclosed loop correction:

This expression can be simplified to

N ~ (D)2TO

A spatial undersampling of the subapertures has a strong impact on theimage quality which is shown in figure 6. An undersampling in the temporaldomain is of similar severity [Greenwood 1977] as shown in figure 7.

The temporal development of the wavefront depends on the transit timeof the atmospheric perturbations. It is usually described by the so-calledcorrelation or life time

7

Figure 6: Quality of the corrected imagE' vs the relative number of actuators.The theoretical curve is normalized to 1 act.uator per su bapNture assuminga correction result of ,\/10 RMS residual error.

10

oosOB 'Vi'

LLJ

>4(

~ et::0

0.6 01 et::et::LLJ

0 I-;::: Z4( 0

et:: 04et::u..

....JLLJ

:I: >LLJ 4(

et:: ~I-

02III 02 III:I:et::

00.5 2 5 10

RELAliVE FREnUENCY

Figure 7: Quality of the corrected image vs the temporal cutoff frequency ofthe correction system. The theoretical curve is normalized to the frequency1 for an imagE' quality of ,\ /l 0 RMS residual error.

8 2 PRINCIPLE OF ADAPTIVE OPTICS

where 6v is a measure for the velocity dispersion of the turbulent at­mospheric layers.

The following parameters are usually used to describe the dependenciesof an adaptive system from atmospheric properties (ro), wavelength ().),and viewing direction (T: zenith distance):

• The number of degrees of freedom (N) which is given by the numberof independent modes or zones to be controlled depends like

~ (~) 2 ,

~ ).12/5,

~ (cos ,tG/5

• The wavefront correction range (6z) depends like (d: size of the se­lected subapertures for correction)

~

(d/To)5/6).

~ ).0 ,ex (cos ,t1

/2

,

• and the temporal frequency (1/7) like

-I~ TO

ex >.-G/f. ,

~ (cos ,(3/5

Typical values of these parameters for different wavelengths at an aver­age astronomical site are (assuming a telescope diameter of 8 meters):

TABLE]

). 0.5f.l,m 2.2J.tm 5.0J.Lm i lOJ.tmTO 10cm 60cm 160cm 360cmN 6400 180 12 47 6ms I 35ms 95ms 220ms

9

As seen, for an Bm telescope this would lead to approx. 6000 controlledsubapertures working at frequencies higher than 170Hz. Therefore, a real­istic aim for an adaptive system within the next few years is a correctionat infrared wavelengths (> 4.um) with systems of 40 to 200 subaperturesand frequencies of 50 to 100Hz.

For the Bm telescopes of the VLT the wavefront correction range is

li.z ~ ±12.5.um

and independent of the wavelength.

A perfect adaptive optical system will perform diffraction limited imag­ing on the optical axis. For off-axis parts in the image which have differentviewing angles with respect to the optical axis, the correction is limited dueto the limited atmospheric correlation length. The angular range whereinthe light suffers from the quasi same atmospheric disturbance is called iso­planatic angle

[ r ]-3/5o = 1.45 k2JR Z5/3 C~(h) dh .

This parameter togE'ther with To completely determines the optical prop­erties of the t.urbulen1 layer at. points on the ground. The expressions forTO and 0 are based on plane and spherical wave theory, respectively. Theydescribe a model for which measurements have shown sufficient evidence.The wavelength dependence of e is given by

Table 11 displays some typical values of the isoplanatic angles at differentwavelengths:

TABLE II

>. I 0.5.um 2.2.um i 5.0.um : 10.um0! 1.8" 10"

,30" ! 70"

I ,

3 Adaptive Optics in Astronomy

The first suggestion$ for the construction of an adaptive optical correctiondevicE' came from astronomy. In 1953, Babcock published his paper with

10 4 STRATEGY FOR SEEING OPTIMIZATI01\"

the title: "The possibility of compensating astronomical seeing" [Babcock1953]. First observatory results of stellar image sharpening were reportedin 1977 by Buffington et al. [Buffington 1977] and McCall et al. IMcCall

19771·

At the present time (begin/1986), there are seven centers where the ap­plication of adaptive optics in astronomy is investigated: NOAO (Tucson),Harward (Cambridge), CFHT (Hawaii), Observatoire de Meudon, and ESOfor stellar observation, and LEST and Sacramento Peak (New Mexico) forsolar observation. NOAO allready started to built adaptive correction sys­tem with 37 subapertures. A cooperation program associating ESO andseveral European scie~tific and industriel groups is being organized. Thegoal of this collaboration is an experimental 19 subaperture adaptive sys­tem which will be available in 1988. The experience with this system underrealistic astronomical observation conditions on La Silla will be an impor­tant input for the' development and final design of the adaptive systems forthe VLT.

Possibilities for an adaptive compensation of the atmosphere should beintegrated in the design of new telescopes and of their instrumentation at avery early stage for optimum operational performance and reliability. Therecent technical progress demonstrates its feasibility and indicates the pos­sible success of adaptive optics in astronomy and that it could revolutionizeground-based observation.

4 Strategy for Seeing Optimization

The shape of an optical wavefront may be represented in two different ways:(1) using an array of independent localized zonal functions. or (2) usinga set of orthogonal whole-aperture modal functions. Analytically, the twosystems are equ ivalent in terms of the number of degrees of freedom requiredto specify a given wavefront to a certain precision. However, there are majorpractical differences, especially, in the implementation of wavefront sensorsand compensation devices. All practical wavefront sensors and most ofthe deformable mirrors use the zonal approach. With zonal mirrors, themain variable if, t he shape of the influence function of each zone, whichdetermines the waVt'front fitting error (see chapter 6).

For modal compensation, the well-known Zernike polynomials, which

11

correspond to systematic optical aberrations such as defocus, astigmatismetc. encountered in conventional optical components, may be employed asthe spatiaJly dependent function fn(i1 of chapter 2. The strategy of modalcorrection is already applied at ESO for the active correction of primarymirrors. In this case the quasi-Zernike polynomial IWilson 1981 i

describes the low-qrder abberations as follows (Table HI):

TABLE III

= I a constant__ 1 +brlcos(4) + 8d lateral focus (tilt)t+cr2cos longitudinal focus

=_-m'COS(<(> + 0,1 decentering coma+egr4 3. order sperical aberration+ fr G 5. order sperical aberration

--- -----r+gr2cos(2<l> + 8 2) 3. order astigmatism__-~ i ~_hr5_~os(3~_-+:__83) triangular coma IIII

i-­

I'-­I

!

For turbulence comJH'nsation the Zernike polvnomials seem to be opti-..mal only for a small number of modes rWang 1978j. A more general set offunctions, the Karhunen-Loeve expansion. can be optimized for turbulencecompensation of systems of any size.

In a modal concept single st.eps in the feedback procedure are:

• Measurement of the local slope of the wavefront.

• Computation of a wavefront map.

• Computation of the modal coefficients (e.g. Zernike coefficients).

• Computation of the control signals for the wavefront correction de-vIce.

• Conversion of control signals to the required drive signal for the cor­rection device.

12 4 STRATEGY FOR SEEING OPTIMIZATION

In control engineering, modal control can be applied to distributed pa­rameter systems as it is in the case of the wavefront reconstruction, whichis distributed in time and in space [Bille 1982, Merkle 1983bJ. In principle,a transformation of the system of eigenfunctions of the local differentialoperator is executed. From the partial differential equat.ions describing thewavefront, a system of decoupled ordinary differential equations is derived.Each of these equations can be treated separately, i. e. control in seperatedindividual channels (modes). The advantage of modal control is the reduc­tion of the treatment of a complex system to the control of simple separatedsystems. Figure 8 shows schematically the modal control concept.

The modal decomposition of the wavefront control loop is based on aseries expansion for the desired target wavefront 4> (r'), the actual measuredwavefront 4>(r,t), and the momentary controller output u(r,t):

N

4>( r) L W n fn(r') ,n=lN

4>(r,t) L an(t) fn(T)n=lN

U(r. t) L un(t) fn( T)n=l

syntheswave

~--''-J frontanalysis

desiredvalue

uli11mirror deflechon un It)

telescope and atmosphere

waveL...-----------'------------l frontanalysis

~(i1)

actualwavefront

Figure 8: Modal control concept for a.daptive optical phase compensation

13

As ~ is independent of time the coefficients W n are constant. In case of anunresolved star, the values of all W n will be zero, for an extended object atleast one W n #- O. The error signal

is fed into the individual control elements which can be desribed by Lapla­cian transfer functions Rn U1 and have to be determined properly in orderto provide loop stability. The control loop, too, is decomposed into sepa­rated channel described by Laplacian transfer functions L n (i1 taking intoaccount the loop dynamics for an undisturbed system. The complete sys­tem with distributed parameters is equivalent to an infinite manifold ofseparated control loops with concentrated parameters as shown in figure 9.In each loop only one mode of the wavefront ~(T, t) described by an(t) isadjusted to the corresponding coefficient of the target wavefront ~(r). Inthis way, the control is distributed over an infinite manifold of separatedchannels.

The wavefront disturbances caused by the telescope and atmosphere canbe taken into account by extending the control loop to a "state observer"structure as shown in figure 9. The model of the disturbances has to be

dis turbance Zn

+ + Un ~ telescope and anmodal- controller - atmosphereired an= f (un+z,,)e

1- -- .... -------=---- .....11~ model an

1I -:- +1I ~ an= f (un+Zn) II II I

I I1 Zn=Z'Zn

~I

state and I Zn +K' (a,,-an) Idisturbance I

an-an Iobserver L ____________ ..!

desvalu

Figure 9: Control loop for a single coefficient of the wavefront expansionseries including state and disturbance o~server

14 5 ELEMENTS OF AN ADAPTIVE SYSTEM

formulated in terms of the time variances of the estimated .expansion co­efficients Ctn(t). The output values of the observer zn(t) are individuallysuperimposed to the controller outputs Un' In the observer like controlstructure the dynamics of the control loop and the state observer can besparat,(\d. Calculating in addition to the state variables Ctn(t) the estimatesfor the disturbances zn(t) would provide the advantage of feedforward con­trol. If the dynamics of the observer structure is choosen faster than thatof the control loop the influence of the disturbances can be compensatedmore efficiently. In any case, this technique requires a good knowledge ofthe optical and mechanical model of the optical sytem in case of activeoptics and, additionally, of the atmospheric model in the case of adaptiveoptics.

If the modal approach is used rather than a zonal decomposition, imageimprovement is possible even with a limited number of modes. This is oneof the essential advantages of the modal correction strategy. The goal forthe future investigations is to determine the optimum algorithms for theadaptive correction with large telescopes in astronomy.

5 Elements of an Adaptive System

The main elements of an adaptive optical system are the wavefront correc­tion device, the wavefront sensor, and the control computer.

5.1 Wavefront Correction Device

The wavefront can lH' controlled b:v' either changing the velocity of propa­gation or by changing the opt ical path length. The former is achieved byvarying the refraction index of a medium, while the latter is implementedby moving a reflective surface such as a mirror or by generating a gratingas in a Bragg cell.

At the pr'esent time, reflective devices are the most successful and widelyused as wavefront correctors. The problem with the other devices aremainly the limited range of refraction index change. the spectral absorp­tion, and nonuniform transmission. On the other side mirror coatings areavailable with high efficiencies over wide spectral ranges, and because theoptical path is confined on one side of the mirror surface, a great variety of

5.1 Wavefront Correction Device 15

substrates and methods of deforming the mirrors are available. Finally, thewavefront deformation is a true optical path length change, independent ofwavelength. The following scheme gives the basic types of active mirrorswhich have been developed (see figure 10):

SEGMENTED MIRRORS

Piston actuators Piston. tilt actuators

. '

CONTINUOUS THIN-PLATE MIRRORS

Discrete position ictuators Discrete force actuators

Bending moment actuators

MONOLITHIC MIRROR

-MonolithIC plUO multipleelectrodes ICtUiltOfS

MEMBRANE MIRROR

Eleetrostohe force oetuotors

Figure 10: Different types of deformablt> mirror~.

16 5 ELEMENTS OF AN ADAPTIVE SYSTEM

• Segmented mirrors

- Piston only

- Piston only

- Piston and tilt

• Continuous thin-plate mirrors

- Discrete position actuators

Discrete force actuators

Bending moment actuators

• Monolithic mirrors

• Membrane or pellicle mirrors.

figure 11 shows examples of adaptive mirrors which have been developedin Europe.

Figure 11: Deformable mIrrors developed in Europe. left: CGE mIrror(France) with piezoelectric actuators (with permission of CGE, DRET),right: University of Heidelberg mirror (FRG) with a thin electrostaticallydeformable membrane !Merkle 1982].

5.2 Wavefront Sensor 17

For the correction of atmospheric perturbation in an astronomical tele­scope with adaptive optics the continuous thin-plate mirrors with discreteposition actuator or the bending moment actuators seem to be the mostfavourable ones.

5.2 Wavefront Sensor

It is not. possible to measure directly the phase of an optical wavefront,as no existing detector will respond to the temporal frequencies involved.Three techniques are commonly used to overcome this problem:

1. Measurements can be made on the intensity distribution of the imageproduced by the entire wavefront.

2. A referencE' wavefront of the same or slightly different wavelengthcombined with the wavefront to be measured to produce interferencE'fringes.

3. The wavefront slope of small zones of the wavefront may be mea­sured. This can be achieved by using a shearing interferometer or theHartmann test.

Each of these three approaches has its own advantages and disadvan­tages. A realization of the first techniques is the so-called multi-dithertechnique [O'Meara 1977] which requires very bright sources, and is there­fore only applicable for the compensation of high power laser beams. Thesecond technique is excluded also for astronomical application because ofthe nature of the astronomical light sources. For the application in as­tronomy with the severe intensity problems only the third technique has achance of success. Mainly two approaches seem to be useful and have beentested successfully: the shearing interferometer and the Shack-Hartmannsensor.

5.2.1 Shparing-Interferometer

In a shearing interferometer [Koliopoulos 1980~ Wyant 1974 and 1975], thewavefront

[i27TW(X,y)]

U(x, y) = P(x, y) exp . A

18 5 ELEMENTS OF AN ADAPT/\'E SYSTEM

(W(x,y): phase distribution, P(x,y): pupil function) to be measured isamplitude divided into two components which are mutually displaced andrecombined with each other to generate an interference pattern. If the pathlengths of the two beams are equal, then fringes are generated even withincoh<'renl light. sources. b('cause light from each element of th(' source in­terferes with a displaced duplicate of itself (see figure 12). Several methodsof producing a sheared wavefront are existing, one of the most useful is amoving Ronchi grating located at the focus of the light beam (first Fouriertransform). A grating moving in x-direction perpendicular to the lines isgiven by

G(x, y) = nJ;oo Cn exp [i27r (xd

- vt)]

(v: speed, d: grating period). After a second Fourier transform the intensityin the detector plane is

I(x, y, t)00 00

L L CnCmn=-oo m=-ex:

X exp [i~7r (w (I - dnAt

, y) _ W (x - dmAt

, y) ) ]

X exp [-i27rvt~m - n)] .

Telescope

Rotitinggriting

IIII

III

I

'-f­I

+' order

Zero order

-1 order

Figure 12: Principle of the rotating grating lateral shear interferometer.

5.2 Wavefront Sensor

A sine grating with only the +/ - 1. diffraction order generates

I(x,y,t) = ~ [1 + cos (2; (W (x - s,y) - W (x + s,y)) + 2wt)]

with the shear distance

19

)..JS = d

(I: focal length) and a temporal modulation frequency

271'"vw=d'

The intensity in a single subaperture is modulated with the frequency 2w.The phase shift (modulo 271'") compared with a reference phase signal is

271'">: [W (x - ,<;,y) - W (x + s,y)].

The phase of this electrical signal is proportional to the slope of the opticalwavefront in the corresponding zone of the aperture. In practice rotatinggratings with radial patterns are employed to shear the wavefront in twoorthogonal directions to provide two orthogonal sets of slope measurementsfrom which the wavefront itself may be reconstructed. With a radial sheargrating a variable-shear interferometer is possible. Low spatial frequencyat maximum radius provides a large dynamic range for initial closing ofthe adaptive loop. High spatial frequency at minimum radius provides ahigh sensiotivity required to obtain small residual wavefront errors. Thegrating frE'quency must be set in a way, that only one fringe appears in theinterference pattern. Without this the solution is not unique.

5.2.2 Shack-Hartmann sensor

The Shack-Hartmann sensor is based on the well-known Hartmann test forchecking the figure of large optical elements [Feinleib 1979.Noethe 1984].Figure 13 shows the schematics of a Shack-Hartmann sensor. The wavefrontis divided into a number of zones, usually contiguous and of equal size.The light from each zone is brought to a seperate focus and the position ofthe centroid of each focus is measured in two dimensions by photoelectricdevice, e.g. a quadrant detector or a CCD camera. Figure 14 displaysa typical foci pattern of a Shack-Hartmann lenticular array developed atESQ. The position measurements reveal the mean wavefront slope over eachzone. In case of quadrant detectors, one is necessary per subaperture. Thetilt angle can then be found from

d0 x = KI(B-+-D) - (A+ C)i.

20 5 ELEMENTS OF AN ADAPTIVE SYSTEM

hln,opl

___~~h'"//"

/LlnsIrrlY

I Dot etort

-x

-I~

x'

/~ ..Sublplrturl I

P pi! Imlglp~nl pllnl

IndiYldul1,mlgo intlnlltydIStributionon d.t.ctor

Figure 13: Principle of the Shack-Hartmann wavefront sensor.

.. " " .. 4> " .. .. .. ..

.. ., .. .. .. .. • ..

".. .. .. ..

.. " .. " .... .. • .. .... .. .. .. .. " ..

• • .... .. .. .. .. ..

" .. .. .. .. .. ..• .. ..

Figure 14: ~oci pattern of the Shack-Hartmann wavefront sensor developedat ESQ. The lenticular array was developed for ESQ's NTT, and has a totalof 40 by 40 lenses at a 1mm raster with appproximately 170mm focal length.A section for 10 by 10 subaperture wavefront sensor is shown.

5.2 Wavefront Sensor

and

21

dell = K [( A + B) - (C + D) 1,

where A, B, C, and D are the output signals of the four quadrants andK is a constant that. depends on the detector responrit.ivity, the shape ofthe subaperture, and the total optical power distribution. A CCD cameraor a Reticon type array can simulate a quadrant detector, but also othersensing schemes are useful to determine the position of the individual foci,e.g. calculating the center of gravity within a subarray of the detector array.In this case typically 10 by 10 elements are used. The residual wavefrontcurvature over each zone is not measured, and in fact tends to degrade thesignal-to-noise ratio, due to a slight defocus.

The mechanical requirements on the stability of the individual imaginglenses and detector elements are severe. But combining the beam to beanalyzed with a (modulated) reference beam, representing, for example aplane wavefront is a possibility to overcome the precise optical alignmentrequirements (see figure 15) [Feinleib 1979]. At ESO this technique wasfirst implemented around 1979. Such a system can be self-calibrating evenduring observation.

Hartmann type sensors are unique compared to other systems, suchas interferometers with chopper wheels because they collect. and samplevirtually 100% of the light entering the optical syst.em. Additionally. thewavefront tilt. over the su bapertures can be measured even when the phaseof the light from one side of the su bapert.ure t.o the other side exceeds 21r.It requires only one detector array compared to four for a shearing inter­ferometer with the same opt.ical effidency. The s~7st.cm is limited only by

Ab,rrat,dwlY,front '"';:--.!tilt sampledl

Detectorarray

Referencebum

Planeway,front(from lillerl

figure 15: Principle of the reference beam method for the Shack-Hartmannsensor.

22 6 PERFORMANCE OF AN ADAPTIVE SYSTEM

the size of the detectors. Hartmann-type sensors can also detect wavefronttilts of white light beams because they are independent of wavelength. Theymeasure the tilt angles of wavefronts, and not optical phase differenceswhich makes them robust and wel1 suited for adaptive optical systems.This tilt angle is exactly what is needed to compensate for optical patherrors independent of wavelength. Addionally, they do not have the 21Tambiguity problem. They are mechanical1y less complex than the shearinginterferometers, replacing optical and mechanical hardware with electronicprocessing. Their major disadvantage seems to be their sensitivity to theshape of the source to be corrected, in case of low signal conditions.

5.3 Control System

Al1 slope-measuring wavefront sensors require a reconstruction of the wave­front itself. Normal1y, two orthogonal wavefront slope measurements aremade for each actuator location. In other words there are twice as manymeasurements as unknowns, so that a least-squares fit can be performedwith beneficial effect on error propagation. Several reconstruction opera­tions have been used or proposed in the literature.

All of these algorithms rt>quir(' very high computation powers in orderto meet the temporal and spatial requirements of the astronomical appli­cation. With special dedicated hardware or hybrid systems this problemis successful1y approachable. At the present time a commercial system isavailable in the USA (AOA, Cambridge, MA, USA). Other developmentsare going on. The activities of ONERA (France) are the most advancedin Europe. These systems are based on microprogrammable paral1el struc­tures, control1ed by a general purpose host processor.

6 Performance of an Adaptive System

The main sources for errors in the model of adaptive optics are wavefrontfitting errrors (OF), which depend on how dosely the wavefront correctorcan match the actual wavefront error; the det.ection errror (OD)' which isessential1y reciprocal to the signal-to-noise ratio of the wavefront sensoroutput; and the prediction error (op), which is due to the time delay be­tween the measurement of the wavefront disturbances and their correction.

23

The overall residual error is then given by:

2 2 2 2OR = OF + OD + Op

The wave/ront fitting error is d<'scrilwd by

(d) 3/5

0;" = Q -- waves2.r"

This spatial error is a function of the coherence length r0, and the size ofthe interactuator center-to-center spacing d of the active mirror depends onthe shape of the wavefront deformation produced by correcting elements.Typical values are given in Figure 16 for different actuator types. Q is theslope for the various cases.

54

0.01

,.--,

"'1nQl

>; 0.03.........

N'"o 0.02

0.06 ,....---------r------------.,

0.04

0.05

" Figure] 6: Residual wavefront fitting errors for different actuator types

Th<> detection is described byo"l 0' r I·' 01an = et t~" wave,';·.

This temporal error is a function of tht> time structure function Ct2 of the

atmosphere and depends on tht> at.mospheric structure and its velocity. isis the integration time.

The prediction error is described by

~ d~

op = (2t~,2N S2)

24 7 REQUIREMENTS FOR ADAPTIVECORRECTION IN ASTRONOMY

This photon error is a function of the fringe contrast 1 , the number ofphotons per measurement N, and in case the wavefront is measured witha shearing interferometer the shear distance s.

7 Requirements for Adaptive Correction inAstronomy

Any correction is requiring a measurement of the effect to be corrected.This is the major problem in relation to the application of adaptive opticsin astronomical observation. The observed sources are in most cases so faintthat their light is not sufficient for the correction. A brighter nearby refer­ence source within the same isoplanatic patch is seldom available. Figure17 gives the density of stars in dependence of its magnitude for the galactic

ClI....::::Jc'EClI

10" ..."'::::JCl"Oil

10-2 ...ClICl.

C0

:0:

"'"SCl.0Cl.

..."'....

VI

2010 15magnitude (vis)

ClI 104 r--------....,...,~"t"<"<"'~~ClI...enClI

"1:l

ClI 103 I-----~~~~""---"="_l...IV::::JCl"Oil... 1021---~~~------IClICl.

c£ 10' I-A~L.------------lIV"SCl.oCl. 10°1------------1...IV....VI

Figure 17: Star density for the galactic poles and equator [Alien 1973].

pole and the galactic equator. At the present time a large scanning pro­gram of photographic plates (Mount Palomar Atlas and ESO Southern SkyAtlas) is going on to provide a database for the guide star catalogue of theHu bble Space Telescope. This listing is of great importance also as a refer­ence source collection for active and adaptive optics. First results indicateIJenkner 1985 j that the star density is higher than previously described inthe literature [Alien 1973].

Although, the coverage with reference stars seems to be denser thanassumed, it is by far not sufficient to operate an adaptive optical system

25

at visible wavelengths for any source. Under the assumption that 100 pho­tons per subaperture are sufficient for a wavefront measurement with anintegration time of less than lOms the limiting magnitude mlim would beby far too small. But for infrared wavelengths the situation becomes morefavourable because of the increase of the isoplanatic angle as shown in table11.

Theoretically there is a correlation between the atmospheric MTF atvisible and infrared wavelengths. First measurements on La Silla [Lena andMerkle (additional measurements will follow)] indicate that the low spatialfrequencies in the visible MTF are correlated with the infrared MTF (seefigure 18). This correlation opens the possibility to measure the wavefront

!~ Cent0"

."

, ~

, ....... \ I

, \ I

"~j ~N,,"_~

,".\ I" t

,< • ;

~\ ,f\.J\ '!'r~f~

~( Leo4"

,

j~!I' <

'~

ex Cent21"

\,,, ," , : I: 1<

. I'll;

..... ' 1,\)

I"11 \'1

l,p ,

~~

"y Vel42"

Figure 18: The one dimensional intensity profiles for double stars withdifferent separations is shown for 5 instantaneous measurements. The uppertrace gives the visible (0.5j1m) profile for one component and the lower tracethe infrared (2.2j1m) profile for the other component. A certain correletionup to 21" is obvious.

26 7 REQUIREMENTS FOR ADAPTl\'ECORRECTION IN ASTRONOMY

in the visible range and to compensate for infrared wavelengths. It makesadaptive optics in the infrared much easier. The technical realization ofa wavefront sensor in the infrared would be much more complicated andexpensive. Table III gives the limit.ation for adaptive optics in the' visibleand for selected infrared wavelengths, and t.he' resulting sky coverage at. tlwgalactic pole (Gp) and the galactic equator (GE ):

TABLE III

~-

I O.5j.lm>. 2.2j.lm 5.0j.lm lOj.lm

~~60cm 160cm 360cm

mlsm 7 13 15.5 17Gp I == 0% 0.1% 30% 100%CE ! == 0% 0.3% 100% 100%

Recently, new techniques to overcome the reference source problem evenin the visible range have been proposed [Foy 1985]. With a LIDAR like tech­nique an artificial reference source is generated using resonance scatteringof yellow laser light in the mesospheric sodium layer (see figure 19). A highpower dye laser (rhodamine) pumped with an eximer laser (XeCl) could bean appropriate light source if the future developments will bring up sys­tems with the required power. Another proposal suggests the local heatingof the atmospheric ozone layer with an infrared laser pulse. The secondway would limit the technique to the infrared. These artificial referencesources have to be generated within the isoplanatic angle of the astronomi­cal source at a repetition rate synchronous to the adaptive correction rate.It would require to gate the astronomical detector during the wavefrontsensing time, which means a small loss compared to the high gain of theadaptive correction. The test of this technique should be included in thefurther investigations for adaptive optics. If the technique would work re­liably it would revolutionize the astronomical observations by providingdiffraction limited observation down to even visible wavelengths.

Depending on the future progress in the developments for adaptive op­tics different levels of correction can be approached for the adaptive cor­rection of the atmospheric disturbances and aberrations of the telescopeoptics (i. e: including active optics) (see figure 20):

27

~~

!"~I SODIUM~ to • RESONANT SCATTERING

~ n •

1-1--...._-+---'on O~ on 100

A'ONIC; SODIUM O(HSlfY t nil 1110' I

PERTURBED 1LAYERS

==10KM

I

STAR BEAM

- - - -ARTIFICIAL REFERENCE- - - SOURCE

(BEACON)

== 100KM

WAVEFRONT ASTRONOMICAL REAL TIME PARALLELSENSOR INSTRUMENT PROCESSOR

Figure' 19: Schematics of the laser probing principle. A pulsed laser beam isscatterf'd at 1.h(' mesospheric sodium layer. The wavefront of the backscat­l.ered light i~ analyzed and the information serveI' for the correction withadaptiv(> optic~. The insert shows a plot of a typical density profile.

• Optical figure correction or so-called active optics. In this case theturbulence of the atmosphere is not included. Typical frequencies are 0 to2H z including possible wind effects on the mirror and structure.

• Image motion stabilization (with a simple tip-tilt mirror, single chan­nel a.daptive system).

• Partial wavefront correction (with less subapertures and frequencyrange than turbulence sampling requires).

• Full wavefront correction (with full sampling of the aperture and tem­poral variations for a given wavelength).

28

["ml

8 ADAPTIVE OPTICS FOR THE VLT

Re~ulrements for anactive/adaptive system

IIIIIIIII

__tRA"j:jqNG FOCUSING • __IMECH VlSll.J SEEING CORRECTIONI I (ATMOSPHERIC TURBULENCEJ

I :~~;';;;;;';'';';;;';--';'--'-M' _I... ,

- - t ApAPT MIRROR M~2

1-.ulI~I:::lllI.lllIlOo~- TRACKING. H2 - - - ••FOCUS I TILT MIRROR 1'1[1- - - - - - - - - -.-===-~--- 1'12 --+ .. _. I

I IACTUATORS I I

PIEZO ELECTRIC :ELECTRO MECHANICAL I

HYDRAULIC ------'---- • i - -

temporal frequency

Figure 20: Spatial and temporal requirements for an active/adaptive opticalsystem. The correction elements are shown in figure 21. The typical RMSrange of correction and possible types of actuators are indicated.

8 Adaptive Optics for the VLT

It is considered to equip each indivldual VLT telescope with independentactive and adaptive optical systems (see figure 21). The active optics willbe used for the figure compensation of the telescope optics. The active ele­ments will be the deformable primary mirror supported by approximately150 push/pull actuators and the secondary mirror. The latter one is onlyused for the coma correction, by rotating it around its vertex. For the opti­cal figure corn',tion it is important to measure the wavefront by integratingover the thl;' at lIIospheric fluctuations in order to get only the optical systemaberrations due 10 gravitational, thermal, and wind effects on the telescopeoptics and structure. A Shack-Hartmann sensor is foreseen as wavefrontsensor and located in an image of the primary pupil. Because a phase com-

29

T1P-TILTMIRROR (MC 1 )

OFF-AXIS BEAMA SELECTOR OR

- -- ,r BEAM SPUTTER

~TO INSTRUMENTON NASMYTHPLATFORM,INCOUDE LABORTO INTERFEROMETRICCOMBINATION

WAVE­FRONTSENSOR

comil,finetrilckingfOcuf----''-- -,

SCHEMATICALDIAGRAM OF THEACTIVE/ADAPTIVEOPTICAL SYSTEM

ACTIVEPRIMARYMIRRORIM1)

SECONDARYMIRROR 1M2)

tilt

figurecontrol

CONTROLSYSTEM

higher orderilberriltionsof the iltmosphere

Figure 21: Schematic diagram of the active/adaptice system for the VLT.

pensation with the primary mirror is limited for mechanical reasons to lowtemporal frequencies in the range of a few Hertz, the atmospheric compen­sation needs a separate correction system. The wavefront sensor for theactive optics has to be arranged on a scanning system in order to set it ona suitable reference source. There is basically no isoplanicity problem forthis active optical system. Also the wavefront computation problems arerelaxed because of the low temporal frequencies.

30 8 ADAPTIVE OPTICS FOR THE VLT

The atmospheric compensation is foreseen in a separate adaptive opti­cal system which will be installed on the Nasmyth platform. A two mir­ror system seems to be favourable; a first mirror to compensate tip-tiltaberrations and a second piezoelectrically actuated deformable mirror tocorrect all higher order aberrations. As wavefront sensor, again the Shack­Hartmann type, seems to be the most most adequate one. As mentionedabove, the active and adaptive optics will have separate wavefront sensors,due to the different isoplanatic angles and the different time constants forthe corrections. At the moment, an adaptive system with 100 to 200 sub­apertures and 50 to 100B z operational frequency is the target for the futureinvestigations.

This adaptive system will serve the instrumentation on the Nasmythplatform and plays an important role for the beam combination modes. TheadaptiYc system would offer diffraction limited observation for Nasmyth andCoude images at wavelengths greater than 4J.lm and a partial correction atshort.er wavelengths. For long baseline interferometry with the VLT thegain of the 8m apertures is only given in combination with adaptive optics.Otherwise the signal-to-noise ratio will not be improved compared withinterferometers with smaller apertures.

It is intended to develop within the next two years a small scale proto­type system with 7 to 19 subapertures. ]n a sc>cond step then. a 37 to 61subaperture adaptive device could serve as the interm<>diat() scale systemtowards the large units required for the VLT. The experience gained withthe planned smaller scale systems is of great importance not only for therealization of the proposed adaptive s}'stem. but also for the active opticalsystem. Because of the similarity of the control procedure and strategyidentical or at least similar algorithms ClJld hardware could be developedand applied. which will improve the performance and reliability of the sys­tems.

31

9 Conclusion

This report has given a brief summary of the principles of adaptive optics,the hardware and software of its applications, its possibilities in astronomy,and the impacts of adaptive optics for the VLT project. Sufficient experi­ence seems to be existing in Europe to perform the necessary developments.Successfully operating adaptive optical systems could become standard tele­scope equipment when the VLT goes into operation and revolutionize theground based astronomical observation.

32

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