ADAPTIVE OPTICS FOR ESO'S VERY LARGE TELESCOPE (VLT)

PROJECT

Fritz Merkle

European Southern Observatory Karl-Schwarzschild-Str. 2

D-8046 Garching Fed. Rep. Germany

May 1986

VLT REPORT No. 47

ADAPTIVE OPTICS FOR ESO'S VERY LARGE TELESCOPE (VLT)

PROJECT

Fritz Merkle

Abstract

Imaging in ground-based astronomy is limited by the transmission of the light through the turbulent atmosphere. Adaptive optics offers the possibility to overcome these limitations. It employs a real-time phase compensation with a phase shifting optical element, which is usually a deformable mirror. The information for the control of the mirror surface is gained from a wavefront sensor. This report describes the principles of adaptive optics and its application in astronomy. It gives an overview over the major elements like the wavefront correction devices, the wavefront sensors, and control systems. The performance of adaptive systems and the requirements in astronomy are discussed and guidelines for the implementation of this technology in ESO's Very Large Telescope given.

Table of Contents

1 Introduction 1 2 Principles of Adaptive Optics 4 3 Adaptive Optics in Astronomy 9 4 Strategy for Seeing Optimization 10 5 Elements of an Adaptive System 14 5.1 Wavefront Correction Device 14 5.2 Wavefront Sensor 17 5.2.1 Shearing-Interferometer 17 5.2.2 Shack-Hartmann Sensor 19 5.3 Control System 22 6 Performance of an Adaptive System 22 7 Requirements for Adaptive Correction in Astronomy 24 8 Adaptive Optics for the VLT 28 9 Conclusion 31

References 32

1

1 Introduction

A perfect astronomical telescope should have a theoretical angular resolu-tion of

A ~a = 1.22 D (in Radians)

(A: wavelength, D: telescope diameter), where ~a is the radius of the first dark ring of the Airy disc. This would lead to the resolution values dis-played in figure 1 for different telescope diameters. However, in practice the imaging quality of ground-based telescopes is degraded by the transmission of the light from the astronomical object through the turbulent atmosphere of the earth. The reason for this degradation is a random spatial and tem-poral wavefront perturbation induced by the turbulences in the different layers of the atmosphere. In addition to this, also the aberrations of the optical elements of the telescope contribute to the degradation. All these

t c:

,..... u .. III u .. ,. ......

~ 10-2 +.t-.'-+-'1f--.;+-+----+----! ::::I C III QI <-<-tV

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

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

[/Lm] Wavelength -

Figure 1: Angular resolution of an astronomical tf'lpscope in the absence of any atmospheric and instrumental distortion of the light transmission (The angular 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) - iA(r, t)

of the light beam. The real part <P(r, t) represents the phase shift of the wavefront, usually called" seeing" , while the imaginary part A( r, t) is a mea-sure for the intensity fluctuations across the aperture plane, called "scintil-lation". Figure 2 displays the influence of phase distortions on the image quality, which is commonly described with the Strehl ratio S:

S = peak irradiance in the f oeaL pLane

peak irradiance diffraction limited

o t= « ex: 0.5 ...J :I: w ex: ~

VI

O'--------'-----_L---...J o 0.05 01

RMS ERROR [wave~

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

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

-<P(r, t) + iJ.tA(r, t)

OBJECT

WAVEFRONT CONTROL

CONTROL SYSTEM

WAVEFRONT SENSOR

IMAGE

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

3

(J.L : dimensionless intensity scaling factor). For most of the imaging prob-lems, especially with very large telescopes, the phase correction part is sufficient and for technical reasons its realization is much easier than the correction of the intensity fluctuations. The field of adaptive optics is in astronomy often divided [Woolf 1984] in the so-called "active optics': which is used for the figure correction of the telescope optics and the "adaptive optics" for the correction of atmospheric effects. In this definition the field of active optics is just a special case of the general principle of adaptive optics at low spatial and temporal frequencies. However, in optical and control engineering the distinction is different. Here, active optical systems or the active components thereof are capable of reshaping a wavefront by adding a set of controllable path differences. No closed loop servo control that operates on the actual wavefront error information is present. An adaptive optical system includes a closed loop phase error sensor that acts to drive a set of path differences to zero. Therefore, the terminology used in astronomy is in some sens contradictory to the technical definition but useful to identify the different applications, mainly because the ways of their technical realization are quite different. The scope of this paper is the field of adaptive optics for atmospheric turbulence correction.

During the last 10 years the techniques of adaptive optics have been developed, mainly for laser beam transmission through the turbulent at-mosphere. Although most of the developments have been made in the United Sta.tes (at companies like ITEK, Lockheed, United Technologies, AVCO Everett, The Aerospace Corp., AOA, and others), there are some promising 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 not straight forward, mainly because of the very low light levels compared with laser applications and the large apertures of the astronomical telescopes. However, the progress in wavefront-sensor technology and the availability of fast computers to cope with the large number of corrections at large aper-tures has opened the technical feasibility of adaptive optics to astronomy. New ideas came up to overcome the intensity problems, like shooting laser beams to the higher atmosphere to create an artificial star-like reference sources.

The intention of this report is to introduce the techniques of adaptive optics and its implication to astronomy. The chapters 2 and 3 will give an introduction to principles of adaptive optics. Chapter 4 describes correction strategies and chapter 5 the the basic elements of an adaptive system. The performance of an adaptive system is evaluated in chapter 6. Chapter 7 and 8 describe the requirements for the design of an adaptive system in astronomy 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: an optical train and image detector, a wavefront sensor, a servo-control system, and a phase-shifting optical element. The distortion of the received wave-front. is usually compensated by reflecting the light beam on a deformable mirror. The surface of this mirror is adjusted in real-time to compensate the path length aberrations. The information required to deform the mirror is obtained by analyzing the light beam with a wavefront sensor. A map of wavefront errors is then derived at each instant of time. Using this error map. tht> control system determines the signals required to drive the phase shifting optical element and to null the phase aberrations by closing the adaptive loop. The phase correction values can be obtained by expanding the phase-correction function

N

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

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

,.- - '---...--., .. I

[ONTROL SYSTEM

I I ~ I I I I I I l_

LIGHT FROM THE TELESCOPE

WAVEFRONT SENSOR

[LOSED LOOP

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

5

The complexity and design of an adaptive system depends of the aper-ture size D of the telescope, the direction of the optical path specified by the zenith angle, and the atmospheric conditions. The atmospheric condi-tions are usually described with the atmospheric turbulent refractive-index structure constant C~ [see Roddier 19811 which is a function of the height h above the ground. Figure 5 (left) shows a model of the vertical profile of the C~ distribution of as a function of altitude h for day and night time [Fried 1982~ and some measurements of C~ in Europe [Barletti 1976, (right). The resulting seeing conditions are often characterized by the scaling parameter

with

ro = [0.423k 2 ~ C~(h} dh] -3/5

7r k = 2->.

(A: wavelength, R: height of the atmosphere) called atmospheric corre-leation 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/ro.

6 2 PRINCIPLE OF ADAPTIVE OPTICS

" IE-13 10- 1 !1 ,

~ N < U 1£'-1" 10- 1 , '" C~ (Z), W t-W -21] . I: 1~-15 < 10- 1

'" ,

< 0.. w IE-Ie '" :0

1~-17 f 10. 1

t-U :0

'" t-V> 10- 1

"AVG" I. , IIARLETII

h~ ElIROI'~CAY

h ANONICHT "LUCKY"

1

W > H t- 1(-18 U

LO- 1 < '"

L 'L , I~

u. w '" IE-I;

I~I 1~2 1~3 1~5

10- 1

AL TITUDE ABOVE SITE (m) , ". .,

ALTAIOV!5ITI,k.'I.

Figure 5: Model of the vertical distribution of the refractive-index structure constant C~ [Fried 1982] (left) and its distribution measured in continen-tal Europe [Barletti 1976] (right). Model and measurements are in good agreement.

The following expression [Brown 1975] gives then the number of neces-sary subapertures for an ideal adaptive system with a deformable mirror as active element when a certain Strehl ratio S should be achieved by the c lased loop correction:

This expression can be simplified to

N ~ (D)2 TO

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

The temporal development of the wavefront depends on the transit time of the atmospheric perturbations. It is usually described by the so-called correlation 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 assuming a correction result of ..\/10 RMS residual error.

10 o os

06 'Vi' LLJ > 4(

~ "" 0

0.6 01 "" "" LLJ

0 0-;:: Z 4( 0

"" 04 "" u.. .....J

LLJ

:I: > LLJ 4(

"" ~ 0-

02 III 02 III :I:

"" 0

0.5 2 5 10

RELA liVE FREnUENCY

Figure 7: Quality of the corrected image vs the temporal cutoff frequency of the correction system. The theoretical curve is normalized to the frequency 1 for an imagE' quality of ..\ /1 0 RMS residual error.

8 2 PRINCIPLE OF ADAPTIVE OPTICS

where 6v is a measure for the velocity dispersion of the turbulent at-mospheric layers.

The following parameters are usually used to describe the dependencies of an adaptive system from atmospheric properties (ro), wavelength ().), and viewing direction (1: zenith distance):

• The number of degrees of freedom (N) which is given by the number of 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 se-lected subapertures for correction)

~

(d/To)5/6 ).

~ ).0 , ex (cos ,tl/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 aver-age astronomical site are (assuming a telescope diameter of 8 meters):

TABLE]

). 0.5f.1,m 2.2f.1,m 5.0J,Lm i lOf.1,m TO 10cm 60cm 160cm 360cm N 6400 180 12 4 7 6ms I 35ms 95ms 220ms

9

As seen, for an 8m telescope this would lead to approx. 6000 controlled subapertures working at frequencies higher than 170Hz. Therefore, a real-istic aim for an adaptive system within the next few years is a correction at infrared wavelengths (> 4.um) with systems of 40 to 200 subapertures and frequencies of 50 to 100Hz.

For the 8m telescopes of the VLT the wavefront correction range is

tl.z ~ ±12.5.um

and independent of the wavelength.

A perfect adaptive optical system will perform diffraction limited imag-ing on the optical axis. For off-axis parts in the image which have different viewing angles with respect to the optical axis, the correction is limited due to the limited atmospheric correlation length. The angular range wherein the light suffers from the quasi same atmospheric disturbance is called iso-planatic angle

0= [1.45k2 k Z5/3C~(h) dhr3/5 .

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

Table II displays some typical values of the isoplanatic angles at different wavelengths:

TABLE II

>. I 0.5.um 2.2.um i 5.0.um : 10.um

0! 1.8" 10" , 30" ! 70" I ,

3 Adaptive Optics in Astronomy

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

10 4 STRATEGY FOR SEEING OPTIMIZATI01\'

the title: "The possibility of compensating astronomical seeing" [Babcock 1953]. First observatory results of stellar image sharpening were reported in 1977 by Buffington et al. [Buffington 1977] and McCall et al. [McCall 19771·

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

Possibilities for an adaptive compensation of the atmosphere should be integrated in the design of new telescopes and of their instrumentation at a very early stage for optimum operational performance and reliability. The recent technical progress demonstrates its feasibility and indicates the pos-sible success of adaptive optics in astronomy and that it could revolutionize ground-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) using a set of orthogonal whole-aperture modal functions. Analytically, the two systems are equ ivalent in terms of the number of degrees of freedom required to specify a given wavefront to a certain precision. However, there are major practical differences, especially, in the implementation of wavefront sensors and compensation devices. All practical wavefront sensors and most of the deformable mirrors use the zonal approach. With zonal mirrors, the main variable if, t he shape of the influence function of each zone, which determines 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, astigmatism etc. encountered in conventional optical components, may be employed as the spatially dependent function fn(i1 of chapter 2. The strategy of modal correction is already applied at ESO for the active correction of primary mirrors. In this case the quasi-Zernike polynomial IWilson )981 i

describes the low-order abberations as follows (Table III):

TABLE III

Iw ~--

I--I

- I a -

__ 1 +brlcos(4) + 8d

'--I !

t +cr2cos

=_-m'COS(<I> + 0,1 +egr4

+ frG

--- ----r+gr 2cos(2<1> + 8 2)

constant lateral focus (tilt) longitudinal focus decentering coma 3. order sperical aberration 5. order sperical aberration 3. order astigmatism triangular coma I

I I __ -~ i ~_hr5_~os(3~_-+:_ 8 3 ) I

~-- 1 + lT4 cos( 4<1> --+ 8 4 ) I quadratIC astigmatism : i---: "+-.. -.------ I··· ----------! - ______ 1_- _ _ _________ ~_ _ ______________________ '

For turbulence comJH'nsation the Zernike polvnomials seem to be opti-.. mal only for a small number of modes rWang 1 978j. A more general set of functions, the Karhunen-Loeve expansion. can be optimized for turbulence compensation 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.

• Comput.ation of a wavefront map.

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

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

• Conversion of control signals to the required drive signal for the cor-rection device.

12 4 STRATEGY FOR SEEING OPTIMIZATION

In control engineering, modal control can be applied to distributed pa-rameter systems as it is in the case of the wavefront reconstruction, which is distributed in time and in space [Bille 1982, Merkle 1983b]. In principle, a transformation of the system of eigenfunctions of the local differential operator is executed. From the partial differential equat.ions describing the wavefront, a system of decoupled ordinary differential equations is derived. Each of these equations can be treated separately, i. e. control in seperated individual channels (modes). The advantage of modal control is the reduc-tion of the treatment of a complex system to the control of simple separated systems. Figure 8 shows schematically the modal control concept.

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

desired value

4>( r)

4>(r,t)

U(r. t)

synthes

N

L Wn fn(r') , n=l N

L an(t) fn(T) n=l N

L un(t) fn( T) n=l

wave fo----"I front

analysis

u(i1) mirror deflechon un (t)

telescope and atmosphere

wave L...-_______ ---'-________ ---j front

analysis

~(i1)

actual wave front

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

13

As ~ is independent of time the coefficients Wn are constant. In case of an unresolved star, the values of all Wn will be zero, for an extended object at least one Wn #- O. The error signal

is fed into the individual control elements which can be desribed by Lapla-cian transfer functions Rn U1 and have to be determined properly in order to provide loop stability. The control loop, too, is decomposed into sepa-rated channel described by Laplacian transfer functions L n P1 taking into account the loop dynamics for an undisturbed system. The complete sys-tem with distributed parameters is equivalent to an infinite manifold of separated 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) is adjusted to the corresponding coefficient of the t.arget wavefront. ~(r). In this way, the control is distributed over an infinit.e manifold of separated channels.

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

ired des valu e

+ - modal

controller

state and dis turbance observer

dis turbance Zn

+ Un ~ telescope and a. - atmosphere

a.= f (un+z,,)

1- -- .... -------=---f-I 1 ~ model an 1

I -:- +1 1 ~ an= f (un+ i., I 1 I I I I 1 1 in=z.zn

~ I

I i. +K' (a,,-a., I I

a.-a. I L ____________ .1

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

14 5 ELEMENTS OF AN ADAPTIVE SYSTEM

formulated in terms of the time variances of the estimated .expansion co-efficients Ctn(t). The output values of the observer zn(t) are individually superimposed to the controller outputs Un. In the observer like control structure the dynamics of the control loop and the state observer can be sparat,(\d. Calculating ill addition to the state variables Ctn(t) the estimates for the disturbances zn(t) would provide the advantage of feedforward con-trol. If the dynamics of the observer structure is choosen faster than that of the control loop the influence of the disturbances can be compensated more efficiently. In any case, this technique requires a good knowledge of the optical and mechanical model of the optical sytem in case of active optics and, additionally, of the atmospheric model in the case of adaptive optics.

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

5 Elements of an Adaptive System

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

5.1 Wavefront Correction Device

The wavefront can lH' controlled by' either changing the velocity of propa-gation or by changing the opt iral path length. The former is achieved by varying the refraction index of a medium, while the latter is implemented by moving a reflective surface such as a mirror or by generating a grating as in a Bragg cell.

At the pr"esent time, reflective devices are the most successful and widely used as wavefront correctors. The problem with the other devices are mainly the limited range of refraction index change, the spectral absorp-tion, and nonuniform transmission. On the other side mirror coatings are available with high efficiencies over wide spectral ranges, and because the optical 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, the wavefront deformation is a true optical path length change, independent of wavelength. The following scheme gives the basic types of active mirrors which have been developed (see figure 10):

. '

SEGMENTED MIRRORS

Piston actuators Piston+tllt actuators

CONTINUOUS THIN-PLATE MIRRORS

Discrete position ictuators Discrete force actuators

Bending moment actuators

MONOLITHIC MIRROR

MonolithIC pi no multiple electrodes ICtUiltOfS

MEMBRANE MIRROR

Electrostahc 'orce actuators

Figure 10: Different types of deformablt' mirror~.

16 5 £ l"£M£NTS OF AN ADAPTIVE SYSTEM

• Segmenl,ed mirrors

- Pist.on only

- Pist.on only

- Pis t.on and t. ilt

• Cont.inuous t.hi n-p lat.e mirrors

- Disc ret.e pos ition actuat.o rs

Discret.e force act. uators

Bending moment. actuators

• Monolithic mirrors

• Mernbrane or pe ll icle mirrors .

F igure I) shows examples of adaptive mirrors which have been developed in Europe.

Figure] I : Deformable mirrors deve loped in Europe. left: CeE mirror (France) with p iewelec tric act.ua tors (wit.h pe rmission of CGE, DRET). right : Univers it.y of Heidelberg mirror (pRG) with a t.hi n elect.ros t.atica ll y deformable membrane !Merkle ]9821.

5.2 Wavefront Sensor 17

For the correction of atmospheric perturbation in an astronomical tele-scope with adaptive optics the continuous thin-plate mirrors with discrete position actuator or the bending moment actuators seem to be the most favourable ones.

5.2 Wavefront Sensor

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

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

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

3. The wavefront slope of small zones of the wavefront may be mea-sured. This can be achieved by using a shearing interferometer or the Hartmann test.

Each of these three approaches has its own advantages and disadvan-tages. A realization of the first techniques is the so-called multi-dither technique [O'Meara 1977] which requires very bright sources, and is there-fore only applicable for the compensation of high power laser beams. The second technique is excluded also for astronomical application because of the nature of the astronomical light sources. For the application in as-tronomy with the severe int.ensity problems only the third technique has a chance of success. Mainly two approaches seem to be useful and have been tested successfully: the shearing interferometer and the Shack-Hartmann sensor.

5.2.1 Shparing-Interferometer

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

[ i27TW(X,y)]

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

18 5 ELEMENTS OF AN ADAPTH'E SYSTEM

(W{x,y): phase distribution, P(x,y): pupil function) to be measured is amplitude divided into two components which are mutually displaced and recombined with each other to generate an interference pattern. If the path lengths of the two beams are equal, then fringes are generated even with incoh<>renl light. sources, b('cause light. from each element of 1.h(' source in-terferes with a displaced duplicate of itself (see figure 12). Several methods of producing a sheared wavefront are existing, one of the most useful is a moving Ronchi grating located at the focus of the light beam (first Fourier transform). A grating moving in x-direction perpendicular to the lines is given by

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

- vt)]

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

I(x, y, t) 00 00

L L CnCm n=-oo m=-ex:

X exp [£~7r (w ( I - dnAt

, y) - W (x - dmAt

, y) ) ]

X exp [-£27rvt ~m - n)].

Telescope

Rotiting griting

I I I I

I , I , '-f-I

+' order

Zero order

-, order

Figure 12: Principle of the rotating grating lat.eral 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 )..J

.s = d

(J: focal length) and a temporal modulation frequency 271'"v

w=d·

19

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 optical wavefront in the corresponding zone of the aperture. In practice rotating gratings with radial patterns are employed to shear the wavefront in two orthogonal directions to provide two orthogonal sets of slope measurements from which the wavefront itself may be reconstructed. With a radial shear grating a variable-shear interferometer is possible. Low spatial frequency at maximum radius provides a large dynamic range for initial closing of the adaptive loop. High spatial frequency at minimum radius provides a high sensiotivity required to obtain small residual wavefront errors. The grating frE'quency must be set in a way, that only one fringe appears in the interference 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 for checking the figure of large optical elements [Feinleib 1979.Noethe 1984]. Figure 13 shows the schematics of a Shack-Hartmann sensor. The wavefront is 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 of the centroid of each focus is measured in two dimensions by photoelectric device, e.g. a quadrant detector or a CCD camera. Figure 14 displays a typical foci pattern of a Shack-Hartmann lenticular array developed at ESO. The position measurements reveal the mean wavefront slope over each zone. In case of quadrant detectors, one is necessary per subaperture. The tilt angle can then be found from

d0 x = KI(B-+-D) - (A+ Clio

20 5 ELEMENTS OF AN ADAPTIVE SYSTEM

TlI .. eopl

IrrlY I I

olt ctor

-x

/~ .. Sublplrturl I

P pil Imlgl p~nl pllnl

-I~

IndiYldul1 Imlgl Intlnllty dlltribution on d.t.ctor

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

.. " " .. • .. ,. .. .. ..

.. ., • • * • • .. " .. .. .. ..

" .. .. .. .. • * • .. '" .. .. <- .. .. " ..

., • .. .. .. * t .. .. ., .. * • .. ,. .. • ., ..

Figure 14: ~oci pattern of the Shack-Hartmann wavefront sensor developed at ESQ. The lenticular array was developed for ESQ's NTT, and has a total of 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 21

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

where A, B, C, and D are the output signals of the four quadrants and K is a const.ant that. depends on the det.ector responrit.ivity, the shape of the subaperture, and the total optical power distribution. A CCD camera or a Reticon type array can simulate a quadrant detector, but also other sensing 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 wavefront curvature over each zone is not measured, and in fact tends to degrade the signal-to-noise ratio, due to a slight defocus.

The mechanical requirements on the stability of the individual imaging lenses and detector elements are severe. But combining the beam to be analyzed with a (modulated) reference beam, representing, for example a plane wavefront is a possibility to overcome the precise optical alignment requirements (see figure 15) [Feinleib 1979]. At ESO this technique was first implemented around 1979. Such a system can be self-calibrating even during observation.

Hartmann type sensors are unique compared to other systems, such as interferometers with chopper wheels because they collect. and sample virtually 100% of the light entering the optical syst.em. Additionally. the wavefront tilt. over the su bapertures can be measured even when the phase of the light from one side of the su bapert,ure to the other side exceeds 27r. It requires only one det.ector array compared t.o four for a shearing int.er-feromet.er with the same opt.ical effidency. The s~7stcm is limited only by

Aberrated wlYefront '"';:--. (tilt samplldl

Bum splitter

Plane wavefront (from lillerl

Reference bum

Lens Detedor

Figure 15: Principle of the reference beam method for the Shack-Hartmann sensor.

22 6 PERFORMANCE OF AN ADAPTIVE SYSTEM

the size of the detectors. Hartmann-type sensors can also detect wavefront tilts of white light beams because they are independent of wavelength. They measure the tilt angles of wavefronts, and not optical phase differences which makes them robust and well suited for adaptive optical systems. This tilt angle is exactly what is needed to compensate for optical path errors independent of wavelength. Addionally, they do not have the 21T ambiguity problem. They are mechanically less complex than the shearing interferometers, replacing optical and mechanical hardware with electronic processing. Their major disadvantage seems to be their sensitivity to the shape of the source to be corrected, in case of low signal conditions.

5.3 Control System

All slope-measuring wavefront sensors require a reconstruction of the wave-front itself. Normally, two orthogonal wavefront slope measurements are made for each actuator location. In other words there are twice as many measurements as unknowns, so that. a least-squares fit can be performed with beneficial effect on error propagation. Several reconstruction opera-tions have been used or proposed in the literature.

All of these algorithms rf'quir(' very high computation powers in order to meet the t.emporal and spatial requirements of the astronomical appli-cation. With special dedicated hardware or hybrid systems this problem is successfully approachable. At the present time a commercial system is available in the USA (AOA, Cambridge, MA, USA). Other developments are going on. The activities of ONERA (France) are the most advanced in Europe. These systems are based on microprogrammable parallel struc-tures, controlled by a general purpose host processor.

6 Performance of an Adaptive System

The main sources for errors in the model of adaptive optics are wavefront fitting errrors (aF), which depend on how dosely the wavefront corrector can match the actual wavefront error; the det.ection errror (aD)' which is essentially reciprocal to the signal-to-noise ratio of the wavefront sensor output; and the prediction error (ap), which is due to the time delay be-tween the measurement of the wavefront disturbances and their correction.

23

The overall residual error is then given by: 2 2 2 2

(JR = (JF + (JD + (Jp

The wavefront fitting error is d<'scrilwd by

(d) 3/5

(JJ,. = Q -- waves2.

r"

This spatial error is a function of the coherence length r 0, and the size of the interactuator center-to-center spacing d of the active mirror depends on the shape of the wavefront deformation produced by correcting elements. Typical values are given in Figure 16 for different actuator types. Q is the slope for the various cases.

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

0.05

0.04 ,.--, ....."

Q,J > ; 0.03

L......I

N'" o 0.02

0.01

4 5

" Figure] 6: Residual wavefront fitting errors for different. actuat.or types

Th(' detection is described by ..., 0' r 1.' fl an = Ct t~·' wave,';·.

This temporal error is a function of tht' t.ime st.ruct.ure function Ct2 of the

atmosphere and depends on tht' at.mospheric st.ructure and its velocity. ts is the int.egration time.

The prediction error is described by ~ d~

(Jr = (2t~,2 N S2)

24 7 REQUIREMENTS FOR ADAPTIVE CORRECTION IN ASTRONOMY

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

7 Requirements for Adaptive Correction in Astronomy

Any correction is requiring a measurement of the effect to be corrected. This is the major problem in relation to the application of adaptive optics in astronomical observation. The observed sources are in most cases so faint that their light is not sufficient for the correction. A brighter nearby refer-ence source within the same isoplanatic patch is seldom available. Figure 17 gives the density of stars in dependence of its magnitude for the galactic

~ 104~----------~~~,~,~,~ ~ <, ,"""""" CII ~ ~, "" """"" 100 :; -: 103 1--___ ~~~~""--""'b=:.<:90"__i· .~ ~ ~

~ ~ ~ ~ ~

... 102 ~ ~ a. c £ 10' I-A~L------------I 111 "S a. o a.10°1-----------~ ... 111 ....

VI

10 15 magnitude (vis)

20

... 111 ....

VI

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

pole and the galactic equat.or. At the present time a large scanning pro-gram of phot.ographic plates (Mount Palomar Atlas and ESO Southern Sky Atlas) is going on to provide a database for the guide star catalogue of the Bu bble Space Telescope. This listing is of great importance also as a refer-ence source collection for active and adaptive optics. First results indicate [Jenkner 1985 j that the star density is higher than previously described in the literature fAllen 1973].

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

25

at visible wavelengths for any source. Under the assumption that 100 pho-tons per sub aperture are sufficient for a wavefront measurement with an integration time of less than lOms the limiting magnitude mlim would be by far too small. But for infrared wavelengths the situation becomes more favourable because of the increase of the isoplanatic angle as shown in table II.

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

!~ Cent 0"

. " , ~

, ...-"\ I

, \ I

"~j ~N,,"_ ~

, q.

\ I" t ,< ' ;

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

~( Leo 4"

, j~!I' <

'~

ex Cent 21"

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

• I ',~;

..... ' 1,\,/

I" II \\1

1,1' ,

~~

'Y Vel 42"

Figure 18: The one dimensional intensity profiles for double stars with different separations is shown for 5 instantaneous measurements. The upper trace gives the visible (0.5J1m) profile for one component and the lower trace the infrared (2.2J1m) profile for the other component. A certain correJetion up to 21" is obvious.

26 7 REQUIREMENTS FOR ADAPTH'E CORRECTION IN ASTRONOMY

in the visible range and to compensate for infrared wavelengths. It makes adaptive optics in the infrared much easier. The technical realization of a wavefront. sensor in the infrared would be much more complicated and expensive. Table III gives the limit.ation for adaptive optics in the' visible and for selected infrared wavelengths, and t.he' resulting sky coverage at. tlH' galactic pole (C p ) and the galactic equator (CE ):

TABLE III

~-

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

ro I 10em 60em 160em 360cm 7 13 15.5 17 mlsm

Cp I == 0% 0.1% 30% 100% CE I == 0% 0.3% ]00% 100%

Recently, new techniques to overcome the reference source problem even in the visible range have been proposed [Foy 1985]. With a LIDAR like tech-nique an artificial reference source is generated using resonance scattering of yellow laser light in the mesospheric sodium layer (see figure 19). A high power dye laser (rhodamine) pumped with an eximer laser (XeCl) could be an appropriate light source if the future developments will bring up sys-tems with the required power. Another proposal suggests the local heating of the atmospheric ozone layer with an infrared laser pulse. The second way would limit the technique to the infrared. These artificial reference sources have to be generated within the isoplanatic angle of the astronomi-cal source at a repetition rate synchronous to the adaptive correction rate. It would require to gate the astronomical detector during the wavefront. sensing time, which means a small loss compared to the high gain of the adaptive correction. The test of this technique should be included in the further investigations for adaptive optics. If the technique would work re-liably it would revolutionize the astronomical observations by providing diffraction limited observation down to even visible wavelengths.

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

27

STAR BEAM

~~

!"~I SODIUM ~ to • RESONANT SCATTERING

~ n •

- - - -ARTIFICIAL REFERENCE - - - SOURCE

IBEACON)

to

I-I--+-'--+---' on O~ on 100

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

PERTURBED

1 LAYERS ""100KM

==10KM

I

WAVEFRONT ASTRONOMICAL REAL TIME PARALLEL SENSOR INS TRUMENT PROCESSOR

Figure' 19: Schematics of the laser probing principle. A pulsed laser beam is scatterf'd at 1.h(' mesospheric sodium layer. The wavefront of the backscat-l,ered light i~ analyzed and the informat.ion serveI' for the correction with adaptiv(> optic~. The insert shows a plot of a typical density profile.

• Optical figure correction or so-called active optics. In this case the turbulence of the atmosphere is not included. Typical frequencies are 0 to 2H z including possible wind effects on the mirror and structure.

• Image motion stabilization (with a simple tip-tilt mirror, single chan-nel a.da.ptive system).

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

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

28

[I'ml 102

z 0 10' iii 0:: ::;) u )( .... .... laO z 0 0:: u.. .... > <C(

~

8 ADAPTIVE OPTICS FOR THE VLT

Re~ulrements for an active/adaptive system

__ tRA"j:jqNG FOCUSING ___ IMECH VlSR.J SEEING CORRECTION I ' IATMOSPHERIC TURBULENCEI I :

~~;';;;;;';'';';;;';--';'--''-M' _1 •. - , - - t APAPT MIRROR M~2

1-oUII~~~~- TRACKING. H2 - • - TILT MIRROR MC' ______ • __ _ FOCUS I I .-===-~--- 1'12 --:-. .. . I

ACTUATORS I I PIEZO ELECTRIC -----'----;-' -------ELECTRO HECHANICAL -----'----" HYDRAULIC -------'---- - i· .

temporal frequency

Figure 20: Spatial and temporal requirements for an active/adaptive optical system. The correction elements are shown in figure 21. The typical RMS range 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 independent active and adaptive optical systems (see figure 21). The active optics will be used for the figure compensation of the telescope optics. The active ele-ments wiIl be the deformable primary mirror supported by approximately 150 push/pull actuators and the secondary mirror. The latter one is only used for the coma correction, by rotating it around its vertex. For the opti-cal figure corn'ct.ion it is important to measure the wavefront by integrating over the thl;' at lIIospheric fluctuations in order to get only the optical system aberrations due' 10 gravitational, thermal, and wind effects on the telescope optics and struct.ure. A Shack-Hartmann sensor is foreseen as wavefront sensor and located in an image of the primary pupil. Because a phase com-

SECONDARY MIRROR 1M2)

ACTIVE PRIMARY MIRROR IM1)

SCHEMA TICAL DIAGRAM OF THE ACTIVE/ ADAPTIVE OPTICAL SYSTEM

figure control

TlP-TIL T MIRROR IMC 1 )

OFF-AXIS BEAM A SELECTOR OR WAVE-

FRONT SENSOR

- -- ,r BEAM SPLITTER ~

coml, fine tricking

TO INSTRUMENT ON NASMYTH PLA TFORM,IN COUDE LAB OR TO INTERFEROMETRIC COMBINA TION

fOcuf----''--_____ -,

CONTROL SYSTEM

tilt

higher order Iberrltions

29

of the Itmosphere

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

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

30 8 ADAPTIVE OPTICS FOR THE VLT

The atmospheric compensation is foreseen in a separate adaptive opti-cal system which will be installed on the N asmyth platform. A two mir-ror system seems to be favourable; a first mirror to compensate tip-tilt aberrations and a second piezoelectrically actuated deformable mirror to correct all higher order aberrations. As wavefront sensor, again the Shack-Hartmann type, seems to be the most most adequate one. As mentioned above, the active and a.daptive optics will have separate wavefront sensors, due to the different isoplanatic angles and the different time constants for the corrections. At the moment, an adaptive system with 100 to 200 sub-apertures and 50 to 100B z operational frequency is the target for the future investigations.

This adaptive system will serve the instrumentation on the Nasmyth platform and plays an important role for the beam combination modes. The adaptiYc system would offer diffraction limited observation for Nasmyth and Coude images at wavelengths greater than 4J.lm and a partial correction at short.er wavelengths. For long baseline interferometry with the VLT the gain of t he 8m apertures is only given in combination with adaptive optics. Otherwise the signal-to-noise ratio will not be improved compared with int.erferometers with smaller apertures.

It is intended t.o develop within the next two years a. small scale proto-type syst.em with 7 t.o 19 subapert.ures. In a s(>cond step then. a 37 to 61 subaperture adaptive device could serve as the interm<>diat() scale system towards the large units required for the VLT. The experience gained with the planned smaller scale systems is of great importance not only for the realization of the proposed adaptive s}'st.em. but also for the active optical system. Because of the similarity of the control procedure and strategy identical or at least similar algorithms ClJld hardware could be developed and applied. which will improve the performance and reliability of the sys-tems.

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 experi-ence seems to be existing in Europe to perform the necessary developments. Successfully operating adaptive optical systems could become standard tele-scope equipment when the VLT goes into operation and revolutionize the ground based astronomical observation.

32

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