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

Optics Express, Vol. 11, Issue 18, pp. 2231-2237 (2003)

http://dx.doi.org/10.1364/OE.11.002231

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### Abstract

In this article we present a downscaled laboratory setup emulating five natural guide stars, a layered static atmosphere and a 7.5-m aperture telescope equipped with dual-conjugate adaptive optics at a wavelength of 2.2 µm. 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.

© 2003 Optical Society of America

## 1. Introduction

1. J. M. Beckers, “Adaptive Optics for Astronomy: Principles, Performance and Applications,” Annu. Rev. Astron. Astrophys. **31**, 13–62 (1993). [CrossRef]

4. D. C. Johnston and B. M. Welsh, “Analysis of multiconjugate adaptive optics,” J. Opt. Soc. Am. A **11**, 394–408 (1994). [CrossRef]

7. M. Owner-Petersen and A. Goncharov, “Multiconjugate adaptive optics for large telescopes: analytical control of the mirror shapes,” J. Opt. Soc. Am. A **19**, 537–548 (2002). [CrossRef]

8. T. Kelly, D. F. Buscher, P. Clark, C. N. Dunlop, G. D. Love, R. M. Myers, R. M. Sharples, and A. Zadrozny, “Dual-conjugate wavefront generation for adaptive optics,” Opt. Express **7**, 368–374 (2000), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-7-11-368. [CrossRef] [PubMed]

## 2. The Experiment

### 2.1 Optical setup

*f*

_{L5}=+700 mm). This implies that the stars are placed at infinity, i.e. natural GSs are used in the experiment.

*f*

_{L3}=+200 mm) and L4 (

*f*

_{L4}=-100 mm). The scaling factors relating the laboratory setup to the parent version are given in Table 1.

*r*

_{0}can be calculated from the variance of the angle of arrival [9]:

*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

*r*

_{0}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

*r*

_{0}-values presented in Table 2. Apart from

*r*

_{0}characterising the high frequency roll-off, a main feature of the phase screen will be the low frequency saturation given by the outer scale

*L*

_{0}. Fig. 2 gives a sample wave-front plus the structure function of PS2. For this screen

*L*

_{0}is well-defined given by the cut-off at 5 m.

*L*

_{0}is in the range 3–6 m for the other phase screens.

*f*

_{L2}=+350 mm). Wave-front sensing is realised with the collimating lens L1 (

*f*

_{L1}=+100 mm) and the mini-WaveScope Shack-Hartmann sensor. The chosen lenslet array has square lenslets with

*f*

_{S-H}=+18 mm and width

*D*

_{S-H}=0.325 mm, allowing 12 subapertures across the pupil. The CCD array used is 640×480 with a pixel width of 10 µm. The spot size is 2

*λf*

_{S-H}/

*D*

_{S-H}=61 µm. The spot-to-pixel ratio is therefore 6.1. 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.

### 2.2 Wave-front reconstruction

*G*=∂

**s**/∂

**c**is the so-called interaction matrix [6

6. R. Flicker, F. Rigaut, and B. Ellerbroek, “Comparison of multiconjugate adaptive optics configurations and control algorithms for the Gemini-South 8-m telescope,” in *Adaptive Optical Systems Technology*, P. Wizinowich, ed., Proc. SPIE4007, 1032–1043 (2000). [CrossRef]

*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):

**s**

_{3}/∂

**c**

_{1}. 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.

### 2.3 Results

*G*. After inserting the phase screens the three wave-front reconstruction alternatives were implemented, based on the Hartmann-vectors (tip&tilt excluded). This corresponds to an open-loop system without servo error, and the results presented were obtained after a single iteration. Also, since the tip&tilt 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 tip&tilt 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.

*λ*/

*D*. Taking care of these two facts, the angular scaling of the PSFs is given by:

*λ*

_{par}=2.2 µm,

*λ*

_{exp}=550 nm and

*D*

_{exp}/

*D*

_{par}=1/500. The resulting PSFs, presented in Fig. 3, have been scaled according to this relationship and thus represent the parent version.

_{N}-value. The calculated seeing angle is

*λ/r*

_{0,eff}=0.32″. The calculated diffraction limited angle is 1.22

*λ/D*=0.074″. 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

*r*

_{0,eff}=1.41 m and

*θ*

_{i}=17.5″ (isoplanatic angle).

*r*

_{0}were generated to obtain reasonable statistics. The screens followed Kolmogorov statistics, with infinite

*L*

_{0}. Adequate wavefront sensing was mimicked by tracing rays in a square pattern comprising 12 rays across the pupil using the “ray aiming on” 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

6. R. Flicker, F. Rigaut, and B. Ellerbroek, “Comparison of multiconjugate adaptive optics configurations and control algorithms for the Gemini-South 8-m telescope,” in *Adaptive Optical Systems Technology*, P. Wizinowich, ed., Proc. SPIE4007, 1032–1043 (2000). [CrossRef]

7. M. Owner-Petersen and A. Goncharov, “Multiconjugate adaptive optics for large telescopes: analytical control of the mirror shapes,” J. Opt. Soc. Am. A **19**, 537–548 (2002). [CrossRef]

## Acknowledgments

## References and links

1. | J. M. Beckers, “Adaptive Optics for Astronomy: Principles, Performance and Applications,” Annu. Rev. Astron. Astrophys. |

2. | J. M. Beckers, “Increasing the size of the isoplanatic patch with multiconjugate adaptive optics,” in |

3. | R. Foy and A. Labeyrie, “Feasibility of adaptive telescope with laser probe,” Astron. Astrophys. |

4. | D. C. Johnston and B. M. Welsh, “Analysis of multiconjugate adaptive optics,” J. Opt. Soc. Am. A |

5. | B. L. Ellerbroek, “First-order performance evaluation of adaptive-optics systems for atmosphericturbulence compensation in extended-field-of-view astronomical telescopes,” J. Opt. Soc. Am. A |

6. | R. Flicker, F. Rigaut, and B. Ellerbroek, “Comparison of multiconjugate adaptive optics configurations and control algorithms for the Gemini-South 8-m telescope,” in |

7. | M. Owner-Petersen and A. Goncharov, “Multiconjugate adaptive optics for large telescopes: analytical control of the mirror shapes,” J. Opt. Soc. Am. A |

8. | T. Kelly, D. F. Buscher, P. Clark, C. N. Dunlop, G. D. Love, R. M. Myers, R. M. Sharples, and A. Zadrozny, “Dual-conjugate wavefront generation for adaptive optics,” Opt. Express |

9. | J. W. Hardy, |

**OCIS Codes**

(010.1080) Atmospheric and oceanic optics : Active or adaptive optics

(010.7350) Atmospheric and oceanic optics : Wave-front sensing

(350.1260) Other areas of optics : Astronomical optics

**ToC Category:**

Research Papers

**History**

Original Manuscript: July 18, 2003

Revised Manuscript: August 28, 2003

Published: September 8, 2003

**Citation**

Per Knutsson and Mette Owner-Petersen, "Emulation of dual-conjugate adaptive optics on an 8-m class telescope," Opt. Express **11**, 2231-2237 (2003)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-18-2231

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### References

- J. M. Beckers, �??Adaptive Optics for Astronomy: Principles, Performance and Applications,�?? Annu. Rev. Astron. Astrophys. 31, 13-62 (1993). [CrossRef]
- J. M. Beckers, �??Increasing the size of the isoplanatic patch with multiconjugate adaptive optics,�?? in ESO symposium on Large Telescopes and Their Instrumentation (European Southern Observatory, Garching, Germany, 1988), 693-703.
- R. Foy and A. Labeyrie, �??Feasibility of adaptive telescope with laser probe,�?? Astron. Astrophys. 152, L29-L31 (1985).
- D. C. Johnston and B. M. Welsh, �??Analysis of multiconjugate adaptive optics,�?? J. Opt. Soc. Am. A 11, 394-408 (1994). [CrossRef]
- B. L. Ellerbroek, �??First-order performance evaluation of adaptive-optics systems for atmospheric-turbulence compensation in extended-field-of-view astronomical telescopes,�?? J. Opt. Soc. Am. A 11, 783-805 (1994). [CrossRef]
- R. Flicker, F. Rigaut and B. Ellerbroek, �??Comparison of multiconjugate adaptive optics configurations and control algorithms for the Gemini-South 8-m telescope,�?? in Adaptive Optical Systems Technology, P. Wizinowich, ed., Proc. SPIE 4007, 1032-1043 (2000). [CrossRef]
- M. Owner-Petersen and A. Goncharov, �??Multiconjugate adaptive optics for large telescopes: analytical control of the mirror shapes,�?? J. Opt. Soc. Am. A 19, 537-548 (2002). [CrossRef]
- T. Kelly, D. F. Buscher, P. Clark, C. N. Dunlop, G. D. Love, R. M. Myers, R. M. Sharples and A. Zadrozny, �??Dual-conjugate wavefront generation for adaptive optics,�?? Opt. Express 7, 368-374 (2000), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-7-11-368">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-7-11-368</a> [CrossRef] [PubMed]
- J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford University Press, Oxford, UK, 1998).

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