Journal of the European Optical Society - Rapid publications, Vol 5 (2010)

Synthetic modeling of astronomical closed loop adaptive optics

L. Jolissaint

Abstract


We present an analytical model of a single natural guide star astronomical adaptive optics system, in closed loop mode. The model is used to simulate the long exposure system point spread function, using the spatial frequency (or Fourier) approach, and complement an initial open loop model. Applications range from system design, science case analysis and AO data reduction. All the classical phase errors have been included: deformable mirror fitting error, wavefront sensor spatial aliasing, wavefront sensor noise, and the correlated anisoplanatic and servo-lag error. The model includes the deformable mirror spatial transfer function, and the actuator array geometry can be different from the wavefront sensor lenslet array geometry. We also include the dispersion between the sensing and the correction wavelengths. Illustrative examples are given at the end of the paper.

© The Authors. All rights reserved. [DOI: 10.2971/jeos.2010.10055]

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References


F. Roddier, Adaptive Optics in Astronomy (Cambridge University Press, Cambridge, 1999).

M. Carbillet, C. Vrinaud, B. Femenia, A. Riccardi, and L. Fini, "Modelling astronomical adaptive optics: I. The software package CAOS" Mon. Not. R. Astron. Soc. 356, 1263-1275 (2005).

M. Le Louarn, C. Vrinaud, V. Korkiakoski, N. Hubin, and E. Marchetti, "Adaptive optics simulations for the European Extremely Large Telescope" Proc. SPIE 6272, 627234 (2006).

F. Rigaut, J.-P. Vran, and O. Lai, "An analytic model for Shack- Hartmann based adaptive optics systems" Proc. SPIE 3353, 1038- 1048 (1998).

M. Carbillet, G. Desidera, A. Augier, A. La Camera, A. Riccardi, A. Boccaletti, L. Jolissaint, and D. Ab Kabira, "The CAOS problem-solving environment: recent developments" Proc. SPIE 7736,773644-773648 (2010).

L. Jolissaint, J.-P. Vran, and R. Conan, "Analytical Modelling of Adaptive Optics: Foundations of the Phase Spatial Power Spectrum Approach" J. Opt. Soc. Am. A 23, 382-394 (2006).

K. Ogata, Modern Control Engineering (Third Edition, Prentice Hall, USA, 1997).

B. L. Ellerbroek, "Linear systems modeling of adaptive optics in the spatial-frequency domain" J. Opt. Soc. Am. A 22, 310-322 (2005).

F. Rigaut, "Ground-Conjugate Wide Field Adaptive Optics for the ELTs" in Beyond Conventional Adaptive Optics - ESO Conference & Workshop Proceedings, E. Vernet, R. Ragazzoni, S. Esposito, and N. Hubin, eds., 58, 11-16 (2001).

A. Tokovinin, "Seeing Improvement with Ground-Layer Adaptive Optics" Publ. Astron. Soc. Pac. 120, 203-211 (2008).

L. Jolissaint, J.-P. Vran, and J.A. Stoesz, "Wide Field Adaptive Optics Upper Limit Performances" Proc. SPIE 5382, 468-477 (2004).

B. Neichel, T. Fusco, and J.-M. Conan, "Tomographic reconstruction for wide-field adaptive optics systems: Fourier domain analysis and fundamental limitations" J. Opt. Soc. Am. A 26, 219-235 (2008).

J. W. Goodman, Introduction to Fourier Optics (Second Edition, McGraw-Hill, New York, 1996).

F. Roddier, "The effect of atmospheric turbulence in optical astronomy" in Progress in Optics XIX, E. Wolf, ed., 281-376 (North-Holland Publishing Co, Amsterdam, 1981).

V. I. Tatarski, Wave propagation in a turbulent medium, translated by R.A.Silverman (Dover Publications, New York, 1961).

R. J. Hill, S. F. Clifford, and R. S. Lawrence, "Refractive-index and absorption fluctuations in the infrared caused by temperature, humidity, and pressure fluctuations" J. Opt. Soc. Am. 70, 1192- 1205 (1980).

P. E. Ciddor, "Refractive index of air: new equations for the visible and near infrared" Appl. Opt. 35, 1566-1573 (1996).

R. J. Mathar, "Refractive index of humid air in the infrared: model fits" J. Opt. A. Pure Appl. Op. 9, 470-476 (2007).

L. Jolissaint, and S. Kendrew, "Modeling the Chromatic Correction Error in Adaptive Optics: Application to the Case of Mid-Infrared Observations in Dry to Wet Atmospheric Conditions" in Adaptative Optics for Extremely Large Telescopes (EDP Sciences, UK, 2010).

L. Huang, C. Rao, and W. Jiang, "Modified Gaussian influence function of deformable mirror actuators" Opt. Express 16, 108-114 (2008).

M. Azouit, and J. Vernin, "Optical Turbulence Profiling with Balloons Relevant to Astronomy and Atmospheric Physics" Publ. Astron. Soc. Pac. 117, 536-543 (2005).

A. Berdja, and J. Borgnino, "Modelling the optical turbulence boiling and its effect on finite-exposure differential image motion", Mon. Not. R. Astron. Soc. 378, 1177-1186 (2007).

D. M. Winker, "Effect of a finite outer scale on the Zernike decomposition of atmospheric optical turbulence" J. Opt. Soc. Am. A 8, 1568-1573 (1991).

J. Maire, A. Ziad, J. Borgnino, and F. Martin, "Comparison between atmospheric turbulence models by angle-of-arrival covariance measurements" Mon. Not. R. Astron. Soc. 386, 1064-1068 (2008).

D. L. Fried, "Optical resolution through a randomly inhomogeneous medium for very long and very short exposures" J. Opt. Soc. Am 56, 1372-1379 (1966).

M. Demerle, P. Y. Madec, and G. Rousset, "Servo-Loop Analysis for Adaptive Optics" in NATO ASIC Proc. 423: Adaptive Optics for Astronomy 73 (1994).

G. Rousset, "Wavefront Sensing" in NATO ASIC Proc. 423: Adaptive Optics for Astronomy 115 (1994).

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, "Comparison of centroid computation algorithms in a Shack-Hartmann sensor" Mon. Not. R. Astron. Soc. 371, 323-336 (2006).

L. Jolissaint, and J.-P. Vran, "Fast computation and morphologic interpretation of the Adaptive Optics Point Spread Function" in Beyond Conventional Adaptive Optics - ESO Conference & Workshop Proceedings, E. Vernet, R. Ragazzoni, S. Esposito, and N. Hubin, eds., 58, 201-208 (2001).

A. Sivaramakrishnan, P. E. Hodge, R. B. Makidon, M. D. Perrin, J. P. Lloyd, E. E. Bloemhof, and B. R. Oppenheimer, "The adaptive optics point-spread function at moderate and high Strehl ratios" Proc. SPIE 4860, 161-170 (2003).