emulation of dual-conjugate adaptive optics on an 8-m class telescope

Emulation of dual-conjugate adaptive optics on an 8-m class telescope

Per A Knutsson and Mette Owner-Petersen

Lund Observatory Lund University Box 43 221 00 Lund Sweden perastroluse metteastroluse

Abstract In this article we present a downscaled laboratory setup emulating five natural guide stars a layered static atmosphere and a 75-m aperture telescope equipped with dual-conjugate adaptive optics at a wavelength of 22 microm Three reconstruction alternatives were evaluated conventional adaptive optics field-averaged conventional adaptive optics and dual-conjugate adaptive optics The results were compared with Zemax-simulations of the setup The expected increase of the size of the isoplanatic patch using dual-conjugate adaptive optics was confirmed

copy 2003 Optical Society of America

Ocis codes (3501260) Astronomical optics (0101080) Adaptive optics (0107350) Wave-front sensing

References and links 1 J M Beckers ldquoAdaptive Optics for Astronomy Principles Performance and Applicationsrdquo Annu Rev

Astron Astrophys 31 13-62 (1993) 2 J M Beckers ldquoIncreasing the size of the isoplanatic patch with multiconjugate adaptive opticsrdquo in ESO

symposium on Large Telescopes and Their Instrumentation (European Southern Observatory Garching Germany 1988) 693-703

3 R Foy and A Labeyrie ldquoFeasibility of adaptive telescope with laser proberdquo Astron Astrophys 152 L29-L31 (1985)

4 D C Johnston and B M Welsh ldquoAnalysis of multiconjugate adaptive opticsrdquo J Opt Soc Am A 11 394-408 (1994)

5 B L Ellerbroek ldquoFirst-order performance evaluation of adaptive-optics systems for atmospheric-turbulence compensation in extended-field-of-view astronomical telescopesrdquo J Opt Soc Am A 11 783-805 (1994)

6 R Flicker F Rigaut and B Ellerbroek rdquoComparison of multiconjugate adaptive optics configurations and control algorithms for the Gemini-South 8-m telescoperdquo in Adaptive Optical Systems Technology P Wizinowich ed Proc SPIE 4007 1032-1043 (2000)

7 M Owner-Petersen and A Goncharov ldquoMulticonjugate adaptive optics for large telescopes analytical control of the mirror shapesrdquo J Opt Soc Am A 19 537-548 (2002)

8 T Kelly D F Buscher P Clark C N Dunlop G D Love R M Myers R M Sharples and A Zadrozny ldquoDual-conjugate wavefront generation for adaptive opticsrdquo Opt Express 7 368-374 (2000) httpwwwopticsexpressorgabstractcfmURI=OPEX-7-11-368

9 J W Hardy Adaptive Optics for Astronomical Telescopes (Oxford University Press Oxford UK 1998)

1 Introduction

In order to compensate for the detrimental effects of the turbulent atmosphere at astronomical observatories adaptive optics is used Conventional adaptive optics systems using one deformable mirror (DM) and one guide star (GS) are now present at several astronomical observatories Conventional adaptive optics has its limitations though The single DM can compensate for the cumulative phase distortion in the direction of the GS but since atmospheric turbulence is three-dimensional the corrected field is small The corrected field termed isoplanatic patch is typically a few arc seconds in the visible and NIR [1] This together with the fact that wave-front sensing is restricted to bright GSs implies that the sky coverage for conventional adaptive optics is low

Beckers [2] introduced the concept of multiconjugate adaptive optics (MCAO) to increase the size of the isoplanatic patch The principle of MCAO is to achieve this by optical

(C) 2003 OSA 8 September 2003 Vol 11 No 18 OPTICS EXPRESS 22312760 - $1500 US Received July 18 2003 Revised Septemer 02 2003

conjugation of several DMs to different altitudes in the atmosphere MCAO together with the possibility to produce synthetic reference beacons or laser guide stars [3] has the potential to overcome the limitations of conventional adaptive optics

Analytical studies and numerical simulations of MCAO [4-7] have all shown that the corrected field is increased as compared to conventional AO As of today no practical demonstration of this has been achieved A laboratory AO prototype system emulating a layered atmosphere following Kolmogorov statistics has demonstrated the effect of anisoplanatism when using conventional adaptive optics [8]

The scope of this paper is to practically demonstrate the increase of the isoplanatic patch by using dual-conjugate adaptive optics (MCAO using two DMs) compared to conventional adaptive optics In Section 2 the details of the experiment is given wherein the first subsection contains information about the optical setup the second subsection presents the wave-front reconstruction alternatives used in the experiment and the last subsection gives the obtained results The results from the practical setup are compared with results from a Zemax model of the setup in Section 3 Finally in section 4 some remarks and conclusions are stated and the main conclusion is that the isoplanatic patch was demonstrated to increase using dual-conjugate adaptive optics

2 The Experiment

21 Optical setup

The experiment is a downscaled version of a 75-m aperture telescope equipped with dual-conjugate adaptive optics a four layer atmosphere with an altitude of 16 km and a GS cross (5 on a dice) with an arm length of 45 The setup comprises four different parts a guide star arm an atmosphere also containing the two DMs a telescope and finally a wave-front sensing arm The optical setup is shown in Fig 1

Fig 1 Schematic birds eye view of the optical setup with rays originating from the central GS

Broadband light from the halogen lamp (HL see Fig 1) is focused by L6 and filtered by the green (λ = 550 nm) glass filter (GGF) at a bundle of five optical fibres (FGS) The opposite ends of these fibres constitute the GS cross with an arm length of 25 mm A mask (GSM) is placed in front of the GS cross in order to choose GS The diverging light emanating from the fibres is collimated by L5 (fL5 = +700 mm) This implies that the stars are placed at infinity ie natural GSs are used in the experiment


For simplicity the two DMs are placed directly into the atmosphere not post-focal at optically conjugating planes which would be the case for a real telescope One mirror is placed at ground level and one is placed at an altitude corresponding to 10 km in the parent (scaled-up) version The DMs used in the experiment are micromachined membrane DMs manufactured by OKO Each DM has 37 actuators in a hexagonal pattern with three rings of actuators surrounding the central actuator The membrane of the mirror is grounded and the deflection of the membrane is proportional to the square of the applied actuator voltage A null voltage was applied to all actuators in order to allow bi-directional poking of the membrane The shape of the membrane in this null-position introduces defocus to the wave-front This was compensated for by shifting L5 for DM2 and L1 for DM1 to eliminate the introduced defocus The diameter of the DM is 15 mm In order to allow for a field of view of 15 (in the parent version) and still make use of the entire surfaces of the DMs different scaling of the lower and upper part of the atmosphere is required In addition to fit the setup into the lab different longitudinal and transversal scaling are used to compress the setup The different scaling of the upper and lower part of the atmosphere is allowed by an afocal lens combination ie L3 (fL3 = +200 mm) and L4 (fL4 = -100 mm) The scaling factors relating the laboratory setup to the parent version are given in Table 1

Table 1 Scaling of the atmosphere in the experiment

Lower atmosphere (0-5 km) Upper atmosphere (58-16 km) Transversal scaling ST 1500 11000 Longitudinal scaling SL 14000 116000 Compression factor C 8 16

The compression of the setup gives that angles in the experiment αexp are related by the compression factor C to the angles in the parent version αpar according to

parexp C αα sdot= (1)

The turbulence in the atmosphere is modeled as static layers using four phase screens (PS1-PS4) The phase screens are holographic film exposed by laser speckles and then developed and bleached The result is a screen with varying optical path length which introduces the desired rms phase error Although the spectral content of the phase screen is not known the Kolmogorov-equivalent r0 can be calculated from the variance of the angle of arrival [9]

3531

22 3640

0rD

λσα = (2)

where λ is the wavelength and D is the diameter of the circular aperture Since the angular tilt over each subaperture on the Shack-Hartmann sensor and hence σα

2 can be measured Eq (2) allows r0 to be estimated D is approximated by the width of each square subaperture on the Shack-Hartmann lenset array Each screen was inserted into the setup one at a time The average of ten measurements of the average length of the Hartmann-vectors gave the r0-values presented in Table 2 Apart from r0 characterising the high frequency roll-off a main feature of the phase screen will be the low frequency saturation given by the outer scale L0 Fig 2 gives a sample wave-front plus the structure function of PS2 For this screen L0 is well-defined given by the cut-off at 5 m L0 is in the range 3-6 m for the other phase screens

The entrance pupil of the telescope (P in Fig 1) is emulated by an iris diaphragm placed in front of L2 (fL2 = +350 mm) Wave-front sensing is realised with the collimating lens L1 (fL1 = +100 mm) and the mini-WaveScope Shack-Hartmann sensor The chosen lenslet array has square lenslets with fS-H = +18 mm and width DS-H = 0325 mm allowing 12 subapertures across the pupil The CCD array used is 640times480 with a pixel width of 10 microm The spot size is 2λfS-HDS-H = 61 microm The spot-to-pixel ratio is therefore 61 The centroiding algorithm in the mini-WaveScope software fitting a quadratic surface to the spot area was used All relevant parameters of the experiment are given in Table 2 As seen in Table 2 the field of view (FoV)


of the Shack-Hartmann sensor is larger than the GS-field Since a static atmosphere is emulated the Shack-Hartmann sensor can therefore be used sequentially for all five GSs

Table 2 Key parameters for the experiment and scaled to parent version

Parameter Experiment Parent Parameter Experiment Parent GS field (diagonal)

12 a 15 Actuator spacing S-H FoV (diagonal)

25 a 31 DM1 2 mm 1 m Pupil size 15 mm 75 m DM2 2 mm 2 m Kolmogorov-eq r0 Altitude

PS1 446 mm 223 m DM1 150 mm 06 km PS2 467 mm 233 m PS1 335 mm 13 km PS3 156 mm b 780 m PS2 1090 mm 44 km PS4 173 mm b 863 m DM2 1660 mm 103 km

PS3 1920 mm 144 km PS4 2020 mm 160 km

a In lower part of experiment b Measured inserted in upper atmosphere

The prime goal of this experiment is to investigate the gain in corrected field that can be obtained by using more than one deformable mirror Hence the temporal aspects of AO-correction have not been addressed and the experiment is static

Fig 2 a) Sample of optical path difference from PS2 given in radians with distance r scaled to parent version b) Obtained structure function DΦ from PS2 averaging over 10 measurements (blue) compared to the Kolmogorov structure function DΦ = kr53 (green)

22 Wave-front reconstruction

The actuator commands are given by c = [c1 c2 hellip cN]T where N is the number of actuators The wave-front sensor measurements are given by s = [s1 s2 hellip s2M]T where M is the number of subapertures The vector s gives the average x- and y-gradient of the wave-front over each subaperture These vectors are related according to

cs G= (3)

where the Jacobian matrix G=partspartc is the so-called interaction matrix [6] It is obtained by poking each actuator a unit poke and collecting the corresponding sensor measurements as the columns in G This is done with a flat reference wave-front In this experiment sensor measurements in the directions of the five GSs and actuator commands to the two DMs are used which give a concatenated version of Eq (3)

=

2

1

5

4

3

2

1

c

c

s

s

s

s

s

G where

partpartpartpartpartpartpartpartpartpartpartpartpartpartpartpartpartpartpartpart

=

2515

2414

2313

2212

2111

cscs

cscs

cscs

cscs

cscs

G (4)

0 1 2 3 4 5 6 70

10

20

30

40

OPD rad

rx m r m

r y m

D

Φ

(r)

rad

2

a) b)


The pseudo-inverse of the interaction matrix ie the least-squares solution allows the actuator commands to be calculated from sensor measurements on distorted wave-fronts The pseudo-inverse of the full interaction matrix corresponds to dual-conjugate adaptive optics Conventional adaptive optics is realised by using only the central GS (GS3) and DM1 ie the pseudo-inverse of parts3partc1 Additionally field-averaged conventional adaptive optics is used by using only the left half of the interaction matrix This method uses only DM1 but information from all five GSs is used in the reconstruction procedure

23 Results

Reference Hartmann spots were obtained sequentially for all five GS-directions with phase screens excluded from the setup At the same time poking of the actuators in all directions were executed to obtain the interaction matrix G After inserting the phase screens the three wave-front reconstruction alternatives were implemented based on the Hartmann-vectors (tipamptilt excluded) This corresponds to an open-loop system without servo error and the results presented were obtained after a single iteration Also since the tipamptilt in each of the five wave-fronts were excluded the plate scale modes are excluded from the reconstruction Point spread functions (PSFs) could be extracted with the software mini-WaveScope (AOA) reflecting the relative improvement after correction with the DM(s) The tipamptilt was excluded from the measured wave-fronts Thus the calculated PSFs are centered The PSFs were extracted in each GS direction for the uncorrected case after correction with conventional adaptive optics after correction with field-averaged conventional adaptive optics and after correction with dual-conjugate adaptive optics To obtain a reasonable statistical basis 20 measurements were obtained with phase screens transversely shifted between each measurement The average PSFs were calculated for the cases and directions respectively

Fig 3 Average PSFs from the experiment Case a) is uncorrected b) is corrected with conventional AO c) is field averaged conventional AO and d) is dual-conjugate AO The intensity IN is normalised with the central intensity of the diffraction-limited PSF The axes of the PSFs are the relative coordinates in arc seconds scaled to the parent version


In order to relate the PSFs to the parent version they had to be scaled The obtained PSFs were based upon the size of the pupil as imaged onto the Shack-Hartmann sensor The angular size of the PSF is proportional to λD Taking care of these two facts the angular scaling of the PSFs is given by

exppar

exp

exp

parpar D

D

f

f βλλ

β2L

1L= (4)

where λpar = 22 microm λexp = 550 nm and DexpDpar = 1500 The resulting PSFs presented in Fig 3 have been scaled according to this relationship and thus represent the parent version

The Strehl ratio is equal to the central intensity value normalised with the diffraction-limited intensity Thus the Strehl ratio of the PSFs can be read as the maximum IN-value The calculated seeing angle is λr0eff=032 The calculated diffraction limited angle is 122λD= 0074 The effects on diffraction due to scaling between the parent and experimental version are accounted for by the scaling in Eq (4) It is different from Eq (1) which concerns the scaling of geometrical angles The experiment clearly suffers from more scintillation than the parent version will do but not to a degree where coherent phase maps could not be calculated Hence the change in diffractive effects (Fresnel number) is of no important consequence

3 Zemax-simulations

In order to confirm the experimental results a Zemax model of the setup was made with atmospheric screens generated by Skylight according to Table 2 Relevant global parameters for the parent atmosphere listed in Table 2 are r0eff = 141 m and θi = 175 (isoplanatic angle)

Fig 4 Comparison of the experimental results with a Zemax model of the experiment The black curves depict the Strehl ratio as function of angle α from the central guide star in the parent experiment with error intervals marked in green or blue The red dots are the experimental values including error bars Case a) is uncorrected b) is corrected with conventional AO c) is field averaged conventional AO and d) is dual-conjugate AO The green families resulted from running the optimization routine a single time and the blue family resulted from running it 10 times See text for more explanation

0 20 40 60 80

02

04

06

08

1

0 20 40 60 80

02

04

06

08

1

0 20 40 60 80

02

04

06

08

1

0 20 40 60 80

02

04

06

08

1

SR

SR

SR

SR

α arc seconds α arc seconds


a) b)

c) d)


Ten stochastically independent sets of four phase screens with appropriate values of r0 were generated to obtain reasonable statistics The screens followed Kolmogorov statistics with infinite L0 Adequate wavefront sensing was mimicked by tracing rays in a square pattern comprising 12 rays across the pupil using the ldquoray aiming onrdquo feature in Zemax Figure 4 upper left confirms the screen statistics to be adequate The mirrors were modeled as polynomial phase screens with a certain maximum order which was restricted to four performing conventional AO and comparing to the experiment (Fig 4 upper right shows this to be a bit too optimistic) The field averaged conventional AO and the dual-conjugate AO cases used the above ray and mirror formats when performing optimizations varying the polynomial mirror coefficients and weighting the stars according to the relevant case Only the dual-conjugate case needed more than one iteration to reach saturation

4 Conclusion

It has been demonstrated that the isoplanatic patch is indeed increased using dual-conjugate adaptive optics The improved isoplanatism when going from b) (see Fig 3) to d) is clearly seen The mean Strehl ratio for the peripheral GSs in b) is 011 which is raised to 048 in d) The Strehl ratio for the central guide star is also raised presumably due to the increased number of actuators It can also be observed in Fig 4 d) that the Strehl ratio in the field is higher in the direction of the guide stars already known from [6-7] In spite of the discrepancy regarding the outer scale between the experimental screens and the Skylight screens used in the Zemax model the agreement between the experimental results and the Zemax model is quite good in particular for dual-conjugate AO This reflects the fact that the outer scale mainly affects the low frequency content of the fluctuations which is removed by the mirrors Finally it should be noted that the results are based on calculated PSFs no real images have been obtained

Acknowledgments

The authors have benefited from fruitful discussions at the Research Training Network for Adaptive Optics on Extremely Large Telescopes Thanks are also due to Klas Johnsson and Erik Dalsgaard for their work concerning the phase screens on the project


conjugation of several DMs to different altitudes in the atmosphere MCAO together with the possibility to produce synthetic reference beacons or laser guide stars [3] has the potential to overcome the limitations of conventional adaptive optics

Analytical studies and numerical simulations of MCAO [4-7] have all shown that the corrected field is increased as compared to conventional AO As of today no practical demonstration of this has been achieved A laboratory AO prototype system emulating a layered atmosphere following Kolmogorov statistics has demonstrated the effect of anisoplanatism when using conventional adaptive optics [8]

The scope of this paper is to practically demonstrate the increase of the isoplanatic patch by using dual-conjugate adaptive optics (MCAO using two DMs) compared to conventional adaptive optics In Section 2 the details of the experiment is given wherein the first subsection contains information about the optical setup the second subsection presents the wave-front reconstruction alternatives used in the experiment and the last subsection gives the obtained results The results from the practical setup are compared with results from a Zemax model of the setup in Section 3 Finally in section 4 some remarks and conclusions are stated and the main conclusion is that the isoplanatic patch was demonstrated to increase using dual-conjugate adaptive optics

2 The Experiment

21 Optical setup

The experiment is a downscaled version of a 75-m aperture telescope equipped with dual-conjugate adaptive optics a four layer atmosphere with an altitude of 16 km and a GS cross (5 on a dice) with an arm length of 45 The setup comprises four different parts a guide star arm an atmosphere also containing the two DMs a telescope and finally a wave-front sensing arm The optical setup is shown in Fig 1

Fig 1 Schematic birds eye view of the optical setup with rays originating from the central GS

Broadband light from the halogen lamp (HL see Fig 1) is focused by L6 and filtered by the green (λ = 550 nm) glass filter (GGF) at a bundle of five optical fibres (FGS) The opposite ends of these fibres constitute the GS cross with an arm length of 25 mm A mask (GSM) is placed in front of the GS cross in order to choose GS The diverging light emanating from the fibres is collimated by L5 (fL5 = +700 mm) This implies that the stars are placed at infinity ie natural GSs are used in the experiment








3531

22 3640

0rD

λσα = (2)











PS3 1920 mm 144 km PS4 2020 mm 160 km






cs G= (3)


=

2

1

5

4

3

2

1

c

c

s

s

s

s

s

G where


=

2515

2414

2313

2212

2111

cscs

cscs

cscs

cscs

cscs

G (4)

0 1 2 3 4 5 6 70

10

20

30

40

OPD rad

rx m r m

r y m

D

Φ

(r)

rad

2

a) b)



23 Results





exppar

exp

exp

parpar D

D

f

f βλλ

β2L

1L= (4)



3 Zemax-simulations



0 20 40 60 80

02

04

06

08

1

0 20 40 60 80

02

04

06

08

1

0 20 40 60 80

02

04

06

08

1

0 20 40 60 80

02

04

06

08

1

SR

SR

SR

SR



a) b)

c) d)



4 Conclusion


Acknowledgments









3531

22 3640

0rD

λσα = (2)











PS3 1920 mm 144 km PS4 2020 mm 160 km






cs G= (3)


=

2

1

5

4

3

2

1

c

c

s

s

s

s

s

G where


=

2515

2414

2313

2212

2111

cscs

cscs

cscs

cscs

cscs

G (4)

0 1 2 3 4 5 6 70

10

20

30

40

OPD rad

rx m r m

r y m

D

Φ

(r)

rad

2

a) b)



23 Results





exppar

exp

exp

parpar D

D

f

f βλλ

β2L

1L= (4)



3 Zemax-simulations



0 20 40 60 80

02

04

06

08

1

0 20 40 60 80

02

04

06

08

1

0 20 40 60 80

02

04

06

08

1

0 20 40 60 80

02

04

06

08

1

SR

SR

SR

SR



a) b)

c) d)



4 Conclusion


Acknowledgments









PS3 1920 mm 144 km PS4 2020 mm 160 km






cs G= (3)


=

2

1

5

4

3

2

1

c

c

s

s

s

s

s

G where


=

2515

2414

2313

2212

2111

cscs

cscs

cscs

cscs

cscs

G (4)

0 1 2 3 4 5 6 70

10

20

30

40

OPD rad

rx m r m

r y m

D

Φ

(r)

rad

2

a) b)



23 Results





exppar

exp

exp

parpar D

D

f

f βλλ

β2L

1L= (4)



3 Zemax-simulations



0 20 40 60 80

02

04

06

08

1

0 20 40 60 80

02

04

06

08

1

0 20 40 60 80

02

04

06

08

1

0 20 40 60 80

02

04

06

08

1

SR

SR

SR

SR



a) b)

c) d)



4 Conclusion


Acknowledgments




23 Results





exppar

exp

exp

parpar D

D

f

f βλλ

β2L

1L= (4)



3 Zemax-simulations



0 20 40 60 80

02

04

06

08

1

0 20 40 60 80

02

04

06

08

1

0 20 40 60 80

02

04

06

08

1

0 20 40 60 80

02

04

06

08

1

SR

SR

SR

SR



a) b)

c) d)



4 Conclusion


Acknowledgments




exppar

exp

exp

parpar D

D

f

f βλλ

β2L

1L= (4)



3 Zemax-simulations



0 20 40 60 80

02

04

06

08

1

0 20 40 60 80

02

04

06

08

1

0 20 40 60 80

02

04

06

08

1

0 20 40 60 80

02

04

06

08

1

SR

SR

SR

SR



a) b)

c) d)



4 Conclusion


Acknowledgments




4 Conclusion


Acknowledgments



emulation of dual-conjugate adaptive optics on an 8-m class telescope

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