Adaptive optics for the Euro 50- Design and performance

Adaptive optics for the Euro50: design and performance

Alexander Goncharov a, Mette Owner-Petersen a, Torben Andersen a,Jacques Beckers b, Nicholas Devaney c

a Lund Observatory, Box 43, SE-22100 Lund, Swedenb University of Chicago 100 E. Huron Street, Apt 2404, Chicago, IL 60611

c Instituto de Astrofísica de Canarias, GTC Project, 38200 La Laguna, Tenerife, Spain

ABSTRACT

The optical design for the proposed Euro50 extremely large telescope with integrated adaptive optics (AO)is presented. For atmospheric turbulence correction, we propose using single and dual-conjugate AOsystems working with natural and laser guide stars. The corrective shape of the deformable mirrors (DMs)is derived from an analytical algorithm based on minimization of the sum of the residual power spectra ofthe phase fluctuations seen by guide stars after correction. Predictions for performance of the Euro50 ELTwith Dual-conjugate AO are given for the K band using a seven layer atmospheric model for theatmosphere at the Observatorio del Roque de los Muchachos (ORM) on La Palma. The average Strehl ratiois used to quantify the system performance for different values of actuator pitch and DM conjugationaltitudes. The influence of the outer scale and telescope pointing on the RMS stroke of the DMs ispresented. It is concluded that construction of such a system is feasible and that there is a need fordevelopment of a simulation tool to verify the analytical calculations. Precise knowledge of the outer scaleof the atmosphere at the ORM is needed to establish the dynamical range of the mirrors.

Keywords: Extremely large telescopes, optical design, adaptive optics, multiconjugate adaptive optics.

1. INTRODUCTION

The impact of technology on the manufacture and optical testing of large astronomical mirrors,computer techniques (end-to-end modeling) and adaptive optics (AO) systems have made it possible toachieve near diffraction-limited image quality for the new generation of optical telescopes with primarymirror diameters of 8-10 m. Using a thin, fast primary mirror, the total mass of the telescope is reduced aswell as the size of the telescope mount and the dome. This in turn brings down the total telescope cost.

These principles constitute the basis for the concept of the proposed Euro50 extremely largetelescope having a segmented primary mirror with a diameter of 50 m. The major challenge for successfulrealization of the concept will probably be the right choice of the telescope optical system configuration,which must be cost-effective and optimal in terms of the number of observing modes and the overallsystem complexity. In this case the optical system should have a fast primarymirror and an AO system forimage stabilization and correction of wavefront distortion caused by the atmospheric turbulence. Inprinciple, an AO system allows the effect of the Earth’s turbulent atmosphere to be compensated for a 1-2arcmin field of view (FoV) in the K band. Within such a corrected field the image quality is limited only bythe telescope optics, and therefore the telescope optical system should provide diffraction-limited imagequality unless some telescope intrinsic aberration is compensated by the AO system. Since theminimization of the total number of optical components is of a great importance, the integration of an AOsystem into a telescope design is one of the key features of the Euro50 concept1.

The optical design of the Euro50 consists of two principle parts (see Figure 1). The fast F/0.85elliptical primary mirror M1 and the concave elliptical secondary mirror M2 form the first part, which is anF /13 aplanatic Gregorian (AG) system providing a diffraction-limited FoV of 3 arcmin for observations inthe K band. The second part is a three-mirror relay system designed as an F /20 focal extender providing a1 arcmin FoV for observations in the K band. The relay system has a plane of symmetry containing theGregorian and final foci, which is perpendicular to the optical axis of the primary mirror, M1. The plane ofsymmetry is rotated 90 degrees in Figure 1 for clarity.

Future Giant Telescopes, J. Roger P. Angel, Roberto Gilmozzi, Editors,Proceedings of SPIE Vol. 4840 (2003) © 2003 SPIE · 0277-786X/03/$15.00

36

Downloaded From: http://spiedigitallibrary.org/ on 08/02/2013 Terms of Use: http://spiedl.org/terms

Each part contains its own adaptively controlled mirror for atmospheric turbulence compensation.The first deformable mirror (DM1) is the secondary mirror M2 in the AG system, which is conjugated to aheight of 0.6 km. The second deformable mirror (DM2) conjugated to 10 km height is a flat mirror M4 inthe relay system. A beam splitter B1 situated at the distance of 6 m behind M1 directs the light along thetelescope elevation axis into the three-mirror relay system. B1 is feeding the Gregorian focus, which is 2 mafter B1. The motivation for employing two deformable mirrors will now be discussed.

Figure 1. The Euro50 optical design layout

Atmospheric turbulence severely limits the angular resolution of ground based astronomical telescopes. Toovercome this limitation and to reach the diffraction limit of large telescopes the AO technique is used2.In a conventional AO system for astronomical telescopes the wavefront distortion induced by theatmospheric turbulence is measured by a wavefront sensor (WFS) and corrected by a single adaptiveelement such as a deformable mirror (DM), which is optically conjugated to the entrance pupil or to thenear ground layer. Due to the fact that atmospheric turbulence is a three-dimensional medium withcontinuous structure, a single DM is able to correct turbulence only in the direct path between the referencesource and the telescope. The field angle over which one could obtain effective correction is limited byanisoplanatism3. The latter phenomenon is characterized by the isoplanatic angle, within which the residualvariance of wavefront phase fluctuations after correction is smaller than a given upper value, as a rule it is1 rad2, which corresponds to a Strehl ratio of 0.37. For a good astronomical site the isoplanatic angle can be10-15 arcseconds in the K band. Operation of an AO system using a natural guide star (NGS) in the FoVfor WFS measurements is restricted to a very small fraction of the sky (of the order of 5 to 10 % at Kband). Laser Guide Stars (LGSs) have been proposed to increase the sky coverage for AO system4.Unfortunately, because of the tip-tilt indetermination problem5 this solution does not provide full skycoverage. In addition it introduces the ‘cone’ effect due to the finite height of the LGS. Atmospherictomography6, stiching and butting7 of the wavefront have been suggested to solve the cone effect.

The corrected field of view can be extended by employing several DMs conjugated to differentatmospheric turbulent layers and using several guide stars together with several WFSs conjugated to theDMs or to the telescope pupil. Such a multiconjugate adaptive optics system (MCAO) 8-10 is a keytechnology for the future ELTs.

M1

M2

M3

M4

Gregorian focus F /13

M5

(DM1) (DM2)

B1

Final focus F /20

Proc. of SPIE Vol. 4840 37


M1

M2

M3

M4

(DM2) B1

NasmythFocus f/5

NasmythFocus f/5

2. AO SYSTEM DESCRIPTION

The Euro50 can be operated in one of several modes, using either no AO system, single conjugate AO(SCAO) or dual-conjugate AO systems (DCAO). Seeing limited operation (without AO) within a technicalFoV of 4 arcmin in the AG focus is provided for telescope testing. The image plane can also be transferredoutside the telescope structure to a Nasmyth platform (see Figure 2) by means of a two-mirror relay systemincreasing the focal ratio up to F/5. In that case the telescope can be operated as a conventional, seeinglimited telescope with intrinsic resolution higher than 0.5 arcsec over a 4 arcmin FoV in the V band.

2.1 Single Conjugate AO system for the Euro50Diffraction-limited operation with single- or dual conjugate AO systems requires sufficiently brightreference sources, which are located not too far from the center of the scientific field (within a fewisoplanatic angles), in order to probe the atmospheric turbulence above the telescope. Followingestimations of D. G. Sandler11 and N. Hubin et al.12, sources with a minimum brightness of 12m in the K-band and 8m in the visible are needed for proper wavefront correction.

The star statistics is such that even at the galactic equator13 it is very unlikely to find several NGSsof reasonable magnitude within the scientific FoV of 1-2 arcmin.

Figure 2. The Euro50 with seeing-limited relay optics for Nasmyth focus.

It has been suggested,13 that an ELT with an extremely large aperture (100 meters) may be able towork with NGSs offset by 10-15 arcmin. However, clear demonstration of the feasibility of this scheme hasnot been documented yet. For the classical MCAO concept it would require that the entire optical train,including the adaptive optics relay mirrors, be designed for a field of 10-15 arcminutes, which in practice isclose to impossible. For the EURO50 the maximum allowed offset is only half this large eliminating theNGS option. Thus, LGSs will be needed for the proposed telescope. Since it is not possible to measure theglobal tilt based on LGS measurements, a NGS of magnitude of 20 or brighter will be needed for SCAO tocorrect for global image motion (global tip/tilt). The brightness requirement for field NGSs is relativelyrelaxed due to the fact that the near diffraction limited image provided by the full telescope aperture isused.

38 Proc. of SPIE Vol. 4840


0 10 20 30 40

0.2

0.4

0.6

0.8

1

0 10 20 30 40

0.2

0.4

0.6

0.8

1

It is believed that the secondary mirror can play the role of a tip/tilt mirror because the dynamicalrange of the secondary mirror actuators is 10 µm. For Kolmogorov turbulence, the RMS tip/tilt componentof the wavefront error in rad is 0.424λ/D1/6r05/6, where r0 is Fried’s parameter which characterizes thestrength of atmospheric turbulence. This gives 0.5-µm RMS translation of the edge of the 4-m secondarymirror for tilt correction in the SCAO mode. It might be possible to provide such small translation bymeans of actuator action. In the Euro50 the secondary mirror also defines the exit pupil of the AG systemwhich is favorable for tip/tilt correction and near infrared operation. The effect of image motion is even lesspronounced for atmospheric turbulence with outer scale comparable with the telescope entrance pupildiameter. According to the seven-layer atmospheric model14 for the Observatorio del Roque de losMuchachos (ORM) at La Palma the outer scale is 20 m.

Integration of the AO system into the telescope as a part of the AG system employing thesecondary mirror as DM1 is the best approach for a SCAO configuration since it provides the bestthroughput and the lowest infrared emissivity. The scale at the AG focal plane is such that Nyquistfrequency criterion is fulfilled: f/D=2p/λ, where f/D is telescope focal ratio, p is pixel size and λ iswavelength. The Airy disk full-width at half-maximum (FWHM) is λf /D =29.4 m (9.3 milliarcsec) in theK band, so that sampling of the Airy disk FWHM by 2 pixels implies a pixel size of 15 m in the infrareddetectors. This fulfills the Nyquist criterion for sampling. To also comply with this criterion in the V band,where the Airy disk FWHM is 7 m (2.1 milliarcsec), a 4.5 m pixel CCD camera or an additional focalextender is required.

The operation of the Euro50 in the SCAO mode allows obtaining diffraction limited image qualitywithin an isoplanatic patch, which is approximately 4 arcsec in the V band and 20 arcsec in the K band forthe ORM atmosphere with infinite outer scale, and it becomes 6 arcsec and 30 arcsec respectively for a 20m outer scale. Since the AG system has 3 arcmin diffraction-limited FoV (at K band), the corrected FoV isonly limited by the size of the isoplanatic patch. Performance estimation for the SCAO mode working inthe K band with an on-axis NGS is presented in Figure 3. It shows the Strehl ratio as a function of fieldangle (in arcsec) for two possible regimes; in the first one the number of actuators across the diameterDM1 is 64 (a) and in the second one it is 300 (b). In the latter case the DM1 fitting error associated withfinite size of sensors and correctors is negligibly small. The lower curve in each plot is for the ORMatmosphere with infinite outer scale, and the upper curve corresponds to 20m outer scale.

In order to probe the atmosphere turbulence along the line of sight, a sufficiently bright NGS or aLGS is needed near the scientific object within the isoplanatic patch. In stellar astronomy, many objectshave extended structure with stellar components, which can be used as reference sources for WFSmeasurements. An NGS is also available when searching for faint companions (brown dwarfs and extra-solar planets) around nearby stars.15 For such cases a dedicated WFS, for example a Shack-Hartman sensorwith 128 sub-apertures across the pupil (it is assumed that DM1 has 64 actuators across the diameter), willbe sufficient for SCAO correction. Sampling with twice as many sub-apertures across the diameter asactuators ensures reduction the aliasing effect.

Figure 3. Performance in the SCAO mode for 64 (a) and 300 (b) actuators across the diameter of DM1.

0 10 20 30 40

0.2

0.4

0.6

0.8

1

0 10 20 30 40

0.2

0.4

0.6

0.8

1

(b)(a)

SR SR



In the general case it is highly unlikely to find a bright NGS within the isoplanatic patch aroundthe scientific object. For the 15 arcsec isoplanatic patch the probability of finding a guide star of 12thmagnitude or brighter for arbitrary science objects chosen near the galactic equator is less than 1%.16Since the LGS can be placed at will, the use of LGSs solves the problem of low sky coverage. Howeveranother problem arises because the sodium LGSs are located approximately at 90 km height and not atinfinity. In addition to the resulting cone effect, the LGS for the Euro50 will therefore not be focused at theAG focus but at the laser guide star (LAG) focus, which is 5 m behind the AG focus when the telescope ispointed to the zenith. Several adaptive optics schemes have been suggested to overcome the LGSreimaging problem17. For non-zero zenith distance the LAG focus is closer to AG focus and at a 60 degreezenith angle it is only 2.5 m behind it. Ray tracing has shown that the quality of LGS images formed by theAG system is acceptable and the major aberration is field coma, which does not exceed 1.2 arcsec. UsingAO correction based on nulling the average wavefront error, it can be shown that field coma will becanceled out and it will not contribute to the AO correction for LGSs distributed with circular symmetry(we assume, that the focus term must be determined from an NGS, as is the case for tip-tilt term)Introducing a beam splitter B1 at an appropriate position before the AG focal surface is reached, the lightfrom the science object is transferred sideways perpendicular to the AG optical axis, whereas the LGS lightpropagates along the AG optical axis (see Figure 4). LGS images are focused on individual wavefrontsensors (LGS WFS) mounted on 2.5 meter long translation stage to compensate for the change in the LAGfocus, providing information about high order atmospheric wavefront aberrations. Using a field lens FL inthe AG focus behind B1, as shown in Figure 4, one can obtain a telecentric configuration for the LGSlightbeams, thus eliminating the need to move the LGS wavefront sensors sideways when adjusting themlongitudinally to take account of distance (focus) changes.

In order to achieve near-diffraction limited correction in the V band, it is planned to use a DM1with 300 actuators across the diameter and a classical SH wavefront sensor with 4 sub-apertures peractuator. Marginal LGSs should be positioned about 1 arcmin off the center of the field to assure completeprobing of the atmosphere turbulence along the line of sight to an astronomical target.

B1

M5M3

Gregorian focuswith test source

Final focus

WFSLGS

WFSTS

M4

M1

FLPM

Figure 4. The optical design of the relay system with wavefront sensors.40 Proc. of SPIE Vol. 4840


2.2 Dual Conjugate AO system for the Euro50

One possible solution to the LGS reimaging problem in the DCAO system is to perform the LGSsensing in the intermediate focus (LAG focus), where the AG system forms images of the LGSs withacceptable quality for wavefront sensing, as for the SCAO system, see Figure 4. While sensing at the LAGfocus, the effect of the DM2 shape on the measured wavefronts cannot be seen. Therefore, this approachcalls for an algorithm controlling the two deformable mirrors from the measured LGS wavefront and theinstantaneous shape of the DM2. Based on the known shape of DM2, the measured LGS wavefronts couldbe transformed into “virtual” wavefronts from which the two mirror deformations are estimated using theopen loop correction algorithm (analytical reconstructor).18 A “virtual wavefront” is the LGS wavefront asit would have been measured after passing over DM2. To do the transformation, it is necessary to know theinstantaneous shape of DM2. It is monitored by a dedicated wavefront sensor (TS WFS) working with atest source in the AG focus (see Figure 4), as if the source were at infinite distance. The success of thisapproach depends on the development of an absolute and accurate wavefront sensor, which would allowmeasuring the wavefront distortions over a dynamical range that is large enough to cover the atmosphericand instrumental effects.

The principle of LGS sensing in the intermediate focus and the derivation of correction with theuse of an analytical reconstructor is depicted in the block-diagram in Figure 5. The atmosphericallydistorted wavefronts W1(A,1 ,…, A,q ) from the q LGS’s enter the telescope. After passing the adaptivesecondary mirror DM1 they are partly corrected to W2(A,1+ 1,1,…,,A,q+ 1,q), and measured as W3 bywavefront sensor system WFS1 consisting of q LGS WFSs. From the virtual wavefront sensor q averagewavefronts W4 (A,1+ 1,1+ 2,1 ,…, A,q + 1,q+ 2,q ) are obtained by adding shifted contributions fromDM2. Based on W4 the analytical estimator derives the incremental deformations of DM1 and DM2 as 1and 2 respectively.

LGSs Atmos-phere DM1 WFS1 Estimator

Shift

Control-ler

Conver-sion

Control-ler

Conver-sion DM2 WFS2Control-

ler

W1 W2 W3

1

2 2,c 2,c AC2W4

2,a

AC1

2,a

ACU

1,c

Figure 5. Block-diagram of a DCAO system with LGS sensing performed before DM2.

By means of controllers these deformations are transformed into commanded deformations 1,c and 2,c ofthe DMs. They are in turn converted into the actuator commands AC1 and AC2 leading to accomplishedshapes 1,a (not shown) and 2,a of the DM1 and DM2 respectively (see Figure 5). Controllers may includeintegrators for compensation of low frequency errors.

Since the DM2 does not receive light from LGSs, the real shape of DM2 is controlled by means ofa wavefront control system WFS2 consisting of a test source located at the AG focus and a wavefrontsensor TS WFS, which is placed after the final scientific focus and conjugated to DM2 (see Figure 4). ThisWFS2 system monitors the shape of DM2 and provides the actuator commands for achieving thecommanded shape of DM2. In order to account for the DM2 contribution to the turbulence correction theblock “Shift” in Figure 5 shifts the wavefronts 2, q (r) = 2,a (r + ωq h), where r is the position vector, ωq isthe angular distance of an LGS from the center of FoV, and h is the conjugated altitude of DM2. They arethen added for each LGS q to the incoming real wavefronts measured by WFS1 system. The latterwavefronts contain the implicit information of the real shape 1,a of DM1, accomplished by the actuatorcommands AC1 degraded by some errors. Assuming that the atmosphere changes slower than the timeconstant of the control loop, the virtual wavefront sensor provides the data for the analytical estimator as asum A,q + 1,q+ 2,q for the q’th LGS, based on which the new increments 1 and 2 will be derived.Since there is no simple way to check the shape of DM1 directly, several iterations might be required to



achieve the desired shape of DM1. The analytical estimator distributes the correction of a layer between theDMs in such a way that if the layer is situated on top of a DM, then this DM alone will correct the layer. Ifthere is a deformation error of one of the DMs, this error will act as an atmospheric layer situated on top ofthat DM, and will be corrected by it in the next cycle of the servo loop. Consequently there is no cross talkbetween the DMs and one may safely put an amplification in the controllers for the two loops. Due to thefact that the shape of DMs is driven by the analytical estimator, the number of iterations needed to achievethe desired correction is expected to be small compared to the bootstrapping procedure.19

It is worth noting that the proposed DCAO system corrects the wavefront distortions in the reverseorder, first the lowest layer by DM1 (the secondary mirror) then the higher layer by DM2. This is animportant condition to be satisfied for suppression of scintillation effects in the V band.20

Compared to the SCAO mode, the DCAO mode requires measurements of individual NGS tilts inorder to distribute correction of the quadratic modes among the deformable mirrors.21 At least 3 NGSswithin the FoV will be needed to sense the quadratic modes (defocus and two astigmatic modes) as well asthe global tip-tilt.

3. ANALYTICAL ALGORITHM FOR AOWAVEFRONT CORRECTION

There are two main issues associated with the concept of MCAO: probing of the three-dimensionaldistributed turbulence (sliced into several thin layers) and the optimal conjugation and control of the DMs.Even if the strength of the turbulent layers is known there is still a problem of optimal atmosphericcorrection with the number of DMs smaller than the number of layers. An analytical algorithm has beenproposed18 in order to derive the optimal correction on DMs and to model the performance of the MCAOsystem.

The key idea of the algorithm is to solve the problem of optimal correction in spatial Fourierspace. Assuming that the number of guide stars is q = 1…Q and the number of DMs is m =1…M, theresidual wavefront error at the pupil of the telescope can be expressed as

)L()()( m

M

1mmqq qrrr +ϕ+ϕ=ε

=

where r is the two-dimensional vector position in the pupil, q(r) is the pupil wavefront error for the star q,m(r) the phase-deformation for mirror m, Lm is the altitude of mirror m, q is the two-dimensional angularvector position on the sky (see Figure 2). According to “Big pupil” approximation18, 22 the DMs act asadditional layers at the corresponding conjugate heights in the atmosphere. In two-dimensional spatialFourier space the residual error is

)Li(2exp)()()( m

M

1mmqq qffff ⋅π+=

=

The optimal atmospheric correction is achieved based on the minimization of the sum S(f) of theresidual power spectra for the phase fluctuations seen by the guide stars after correction:

Minimization of the sum S(f) with respect to the DM phase-deformation spectra, Φm(f), will lead to asystem of M linear equations. Its solution gives the DM phase-deformation spectra Φm(f), which aretransformed back to provide the required shape deformations m(r) for the DMs.

Estimating the corrective shapes of the DMs, the algorithm relies only on the measuredatmospheric wavefronts q(r) referred to the telescope pupil. Therefore, no a priori assumption on theatmospheric statistics is invoked. Minimizing these residual power spectra, the images of the guide stars aresharpened up in the best possible way leading to a solution, which is similar to that obtained with othercorrective algorithms based on the principle of least squares. Perhaps the main advantage of this algorithmis the simplicity of analytical evaluation of MCAO performance for ELTs for given atmospheric conditionsand configurations of guide stars and deformable mirrors. It is used here to calculate the performance of theproposed Euro50 ELT with an integrated AO system having two DMs (dual conjugate AO).22-24

Some modification of this algorithm is needed for the case of an AO system with LGSs. In order toapply this algorithm one should generate “synthetic” wavefronts of NGSs using measurements of the LGSwavefronts.25 This concept of synthetic NGS wavefronts is described in a separate paper in thisconference.26

2Q

1qq )()S(

=

= ff



0

(a) (b)DM1

DM2 Lm

q

r

)(aq rϕ

Figure 6. Geometry for phase projections onto the telescope pupil (a), 5 NGS in a regular cross within 20 FoV (b)

4. AO SYSTEM PERFORMANCE ANALYSIS

Performance analysis of future ground-based extremely large telescopes with MCAO systems requires anatmospheric model and a wavefront correction algorithm. The atmospheric model employed here is a 7layer model for the Observatorio del Roque de los Muchachos (ORM) with r0=0.89 m (at K band) and anouter scale of 20 m14,27. Five guide stars at infinite distance are used for probing atmospheric turbulence(we assume here that “synthetic” wavefronts of NGSs are identical to real NGSs). They form a regularcross on the sky as shown in Figure 1 (b). Applying the analytical algorithm for atmospheric correctiondescribed in section 3, the performance of the Euro50 working in the DCAO mode has been analyzed. Forthe proposed Euro50 optical design the conjugation of DM1 is 0.6 km and DM2 is 10 km. As a measure ofperformance, the Strehl ratio corresponding to the residual wavefront variance averaged over the 5 NGSs ischosen. The correction is performed to maximize this value.

In Figure 7 the RMS stroke (m) on DM1 and DM2 are shown as a function of actuator pitchmeasured in r0 units for an outer scale L0=20m (a) and for Kolmogorov turbulence L0= (b). Note thedifference in the scale of the vertical axes. Estimating each point on the curves, we assume identical pitch onboth DMs. It is easily seen that if outer scale size is roughly equivalent to the telescope aperture diameter orsmaller, then the requirement for DM stroke is relaxed significantly compared to the case of infinite outerscale26. Figure 7 also shows that varying the actuator pitch within the useful range (0.4r0…2r0) does notchange the RMS stroke required for the DMs for a given atmosphere and DM conjugation geometry. It hasbeen shown24 that the RMS stroke grows with decrease of DM2 conjugation height, since many turbulentlayers lay outside the conjugation span of DMs.

In modeling the performance of the Euro50 with the dual-conjugate AO system, it is assumed thatthe critical spatial frequencies are filtered out. One can derive the first critical frequency as f0=1/(L1− L2),where L1 and L2 conjugation altitudes of DMs and is the angular separation between neighboring guidestars, see Figure 2 (a). Depending on the guide star separations and DM conjugation altitude differencethere will be critical frequencies (f0 ,2f0 ,…), which must be left uncorrected.

Figure 7. RMS stroke on DMs as a function of pitch size for outer scale L0=20m (a) and L0= (b).

0.25 0.5 0.75 1 1.25 1.5 1.75 20123456

(a) (b)

DM1

DM2DM2

DM1

pitch/r0pitch/r0

RMS stroke (m) RMS stroke (m)

0.25 0.5 0.75 1 1.25 1.5 1.75 20

0.10.20.30.40.50.6



Figure 8 depicts the average Strehl ratio for 5 NGS (2α0 =1 arcmin) as a function of the actuatorpitch measured in r0 units. Two curves are shown; the upper curve (a) corresponds to the case when theactuator pitch on DM1 (pitch1) is equal to that on DM2 (pitch2). The lower curve (b) is for the case whenthe actuator pitch on DM2 is twice as large as on DM1. In the latter case performance is degraded less than10%.

Figure 8. Average Strehl ratio for pitch1=pitch2 (curve a) and pitch2=2pitch1 (curve b).

Telescope pointing imposes additional requirements on the dynamical range of the DMs and limitssystem performance. For a given zenith angle, Z, the spectrum of a turbulent layer n is

where fos,n = 1/L0,n is outer scale contribution. The distances of the layers relative to the primary mirrorbecomes h = h0/cosZ, where h0 is altitude of the layer. The conjugation distances of the DMs remainconstant. Figure 9 shows the dependence of the RMS stroke of the DM’s and the average Strehl ratio onzenith angle for FoV 20=1’. The zenith angle is in the range 0...60 degrees. It is obvious that for largezenith angles the atmosphere becomes thicker along the line of sight. Therefore, the DM strokes requiredfor wavefront correction grow and at Z = 60 degrees it is almost doubled for DM2 and is increased by 50%for DM1 compared with the case of zenith angle Z=0. It is seen in Figure 9 (b) that a significant drop inStrehl ratio occurs for zenith angles larger than 30 degrees.

10 20 30 40 50 600

0.2

0.4

0.6

0.8

1

Figure 9. RMS stroke on DMs (a) and system performance (b) as a function of zenith angle Z.

When pointing the telescope far off zenith, the DMs become mis-conjugated, especially DM2, and theintegrated effect of atmospheric turbulence becomes the dominating factor in degrading systemperformance. Figure 10 shows system performance (average Strehl ratio) as a function of DM2 conjugationheight (km), with the DM1 conjugation height fixed at 0.6 km. There are 4 curves in Figure 10,corresponding to zenith angles Z=0, 30, 45, 60˚ respectively. The number of actuators across the diameterof DM1 and DM2 is 64. The decrease in Strehl ratio with increasing zenith distance is obviously notcaused by the mismatching of conjugate heights but by the increased wavefront distortion. The maximumaverage Strehl ratio is achieved for a conjugate height of 10 km at Z=0˚, 11 km at Z=30˚, 14 km at Z=45˚

10 20 30 40 50 600

0.2

0.4

0.6

0.8

1RMS stroke (m)

DM1

DM2

Z

11/62nos,

25/3no,

n )f(fcosr

0.023(f)P −+=Z

0.25 0.5 0.75 1 1.25 1.5 1.75 20

0.2

0.4

0.6

0.8

1

0.25 0.5 0.75 1 1.25 1.5 1.75 20

0.2

0.4

0.6

0.8

1

a

b

SRav

pitch1/r0

SRav

Z

(a) (b)



and 18 km at Z=60˚. In the latter two cases the variation of Strehl ratio is marginal, when the conjugation ofDM2 is in the range of 10-20 km. Based on the results in Figure 10, one can see that the optimal DM2conjugation height is about 10-12 km. This figure clearly shows that adjustments of DM2 conjugationduring the telescope operation is not necessary for the ORM atmosphere. It is a crucial fact for simplifyingthe telescope optical design.

5 10 15 200

0.2

0.4

0.6

0.8

1

Figure 10. System performance as a function of DM2 conjugation height and zenith angle.

5. CONCLUSIONS

Modeling system performance for the Euro50 working in the DCAO mode has been carried outbased on an analytical corrective algorithm and a 7 layer ORM atmospheric model with a finite outer scale.Estimation of system performance accounts for fitting error and angular anisoplanatism. For a givenatmospheric turbulence model angular anisoplanatism depends only on the size of FoV and number ofDMs. The fitting error is roughly proportional to the DM pitch size, which is limited by technology inmanufacturing adaptively controlled deformable mirrors of large diameter. The requirements for SCAOand DCAO systems have been derived. It has been shown that the optimal conjugation of DM2 is 10-12km. Changing the conjugation altitude of DM2 as a function of zenith angle does not significantly improvesystem performance. For zenith angles exceeding 30 degrees the image quality deteriorates rapidly anddemands larger actuator strokes. Having 2 DMs with 64 actuators across their diameter in the DCAOsystem one would expect to achieve an average Strehl ratio of 0.8-0.4 within the 1 arcmin FoV for zenithdistances in the range 0-60˚.

Some modification of the analytical algorithm is needed for the DCAO system with LGSs. Theconcept of “synthetic” NGS-like wavefronts based on the LGS measurements must be developed andtested.

ACKNOWLEDGEMENTS

This research has benefited from the support of the European Commission RTN program: "Adaptive Opticsfor the Extremely Large Telescopes", contract #HPRN-CT-2000-00147.

REFERENCES

1. T. Andersen, A. Ardeberg, J. Beckers, A. Goncharov, M. Owner-Petersen, H. Riewaldt, R. Snel, D. Walker,”The Euro50 Extremely Large Telescope”, this conference.

2. J. Hardy, J. Lefevbre, and C Koliopoulos, “Real time atmospheric compensation,” J.Opt.Soc.Am. 67(3), pp.360-369, 1977.

3. D. Fried,”Anisoplanatism in adaptive optics”,J.Opt.Soc.Am.72(1),pp.52-61,1982.

SRav

DM2 conj(km)

0˚30˚45˚

60˚



4. R. Foy and A. Labeyrie, “Feasability of adaptive optics telescope with laser probe,” Astron.Astrophys. 152, pp.L29-L31, 1985.

5. F. Rigaut and E.Gendron, “Laser guide star in adaptive optics: the tilt determination problem,” Astron.Astrophs.261, pp. 677-684,1992.

6. R.Ragazzoni, E. Marchetti and F.Rigaut, “Modal tomography for adaptive optics,” Astron.Astrophys 342, pp.53-56,1999.

7. D. Fried,”Focus anisoplanatism in the limit of infinitely many artificial-guide-star reference spots”,J.Op.Soc.Am,A 12, pp.939-949,1995.

8. R.H. Dicke, “Phase-contrast detection of telescope seeing errors and their correction,” Astrophys. J. 198, 605-615, 1975.

9. J. Beckers, “Increasing the Size of the Isoplanatic Patch with Multiconjugate Adaptive Optics” ESO conf. onVery Large Telescopes and their Instrumentation, pp. 693-703, March 1988.

10. J. Beckers, “Detailed Compensation of Atmospheric Seeing using Multiconjugate Adaptive Optics” SPIE vol.114, pp.215-217, 1989.

11. D. G. Sandler, “Adaptive optics with laser beacons,” Part 4 in Adaptive Optics in Astronomy, F. Roddier, Ed., pp.257-261,Cambridge University Press, 1999.

12. N. Hubin, M. Le Louarn, M. Sarazin, A. Tokovinin, E. Viard, “New challenges for adaptive optics: the OWL100m telescope,” Proc. SPIE 4007, pp. 1100-1107, 2000.

13. R. Ragazzoni, “No laser Guide Stars for Adaptive Optics in Giant Telescopes,” Astron& Astrophys SupplementSeries 136, pp.205-209, 1999.

14. N. Devaney, and M. Owner-Petersen, The ORM seven layer standard atmosphere, Technical note, Lund,Sweden, 2001.

15. R. Angel “Ground-Based Imaging of Extrasolar Planets using Adaptive Optics,“ Nature, 368, pp.203-207, 1994.16. J. M. Beckers , and L. E. Goad, "Image Reconstruction Using Adaptive Optics" in Instrumentation for

Ground-Based Optical Astronomy, L. B. Robinson, Ed., pp. 315-336, Springer Verlag (1987).17. A. Gontcharov, M. Owner-Petersen, T. Andersen, J. Beckers, “Adaptive Optics Schemes for Future Extremely

Large Telescopes” Opt.Eng. 41(5), 1065-1072, 2002.18. M. Owner-Petersen, A. Goncharov, “Multi-conjugate Adaptive Optics for Large Telescopes. Analytical Control

of the Mirror Shapes” J.Op.Soc.Am,A 19(3), pp.537-548, 2002.19. R. Ragazzoni, “Adaptive Optics for Giant Telescopes” Proc. of the Bäckaskog Workshop on Extremely Large

Telescopes, 175-180 (1999).20. R. Flicker “Sequence of phase correction in multiconjugate adaptive optics” Optics Letters,26, No.22, pp.1743-

1745.21. F. Rigaut, B. Ellerbroek, R. Flicker “Principles, Limitations and Performance of Multi-Conjugate Adaptive

Optics,” Proc. SPIE 4007, 1022-1031 (2000).22. Gontcharov and M. Owner-Petersen, “Multiconjugate Adaptive Optics for the Swedish ELT” Proc. SPIE 4004,

pp.309-395, 2000.23. T. Andersen, A. Ardeberg, J. Beckers, R. Flicker, A. Gontcharov, N. C. Jessen, E. Mannery and M. Owner-

Petersen, “The proposed 50 m Swedish Extremely Large Telescope,” Proc. of the Bäckaskog Workshop onExtremely Large Telescopes, 72-82, 1999.

24. A. Goncharov and M. Owner-Petersen, “Dual-conjugate AO for the Swedish 50 m ELT Mirror Dynamical Rangeand Actuator Pitch”, Proc. Of the Venice conf. Beyond Conventional Adaptive Optics, May 2001.

25. M. Owner-Petersen and A. Gontcharov, “Multi-conjugate Adaptive Optics for the Swedish ELT. Investigation ofthe Effect of Laser Guide Stars at a finite Distance”, Proc. Of the Venice conf. Beyond Conventional AdaptiveOptics, May 2001. http://www.adaopt.it/venice2001/proceedings/index.html

26. M. Owner-Petersen, T. Andersen, A. Goncharov, “Control strategy for the adaptive optics of the Euro50”, thisconference.

27. M. Owner-Petersen, T. Andersen , A. Goncharov, V. Lukin, “Atmospheric model with outer scale distribution:impact on AO mirrors dynamics”, Tomsk, 2002.



Adaptive optics for the Euro 50- Design and performance

Documents

Transcript of Adaptive optics for the Euro 50- Design and performance