Comparison of minimum-norm maximum likelihood and maximum a posteriori wavefront reconstructions for large adaptive optics systems.

The performances of various estimators for wavefront sensing applications such as adaptive optics (AO) are compared. Analytical expressions for the bias and variance terms in the mean squared error (MSE) are derived for the minimum-norm maximum likelihood (MNML) and the maximum a posteriori (MAP) reconstructors. The MAP estimator is analytically demonstrated to yield an optimal trade-off that reduces the MSE, hence leading to a better Strehl ratio. The implications for AO applications are quantified thanks to simulations on 8-m- and 42-m-class telescopes. We show that the MAP estimator can achieve twice as low MSE as MNML methods do. Large AO systems can thus benefit from the high quality of MAP reconstruction in O(n) operations, thanks to the fast fractal iterative method (FrIM) algorithm (Thiébaut and Tallon, submitted to J. Opt. Soc. Am. A).

[1]  R. Lane,et al.  Simulation of a Kolmogorov phase screen , 1992 .

[2]  Lisa A. Poyneer Advanced techniques for Fourier transform wavefront reconstruction , 2003, SPIE Astronomical Telescopes + Instrumentation.

[3]  J. Y. Wang,et al.  Modal compensation of atmospheric turbulence phase distortion , 1978 .

[4]  Michael C. Roggemann,et al.  Optical performance of fully and partially compensated adaptive optics systems using least-squares and minimum variance phase reconstructors , 1992 .

[5]  A. Agabi,et al.  Optical parameters relevant for High Angular Resolution at Paranal from GSM instrument and surface layer contribution , 2000 .

[6]  H. Sorenson Least-squares estimation: from Gauss to Kalman , 1970, IEEE Spectrum.

[7]  J. Herrmann,et al.  Least-squares wave front errors of minimum norm , 1980 .

[8]  David L. Fried,et al.  Least-square fitting a wave-front distortion estimate to an array of phase-difference measurements , 1977 .

[9]  L. Gilles,et al.  Order-N sparse minimum-variance open-loop reconstructor for extreme adaptive optics. , 2003, Optics letters.

[10]  C. Kulcsár,et al.  Optimal control law for classical and multiconjugate adaptive optics. , 2004, Journal of the Optical Society of America. A, Optics, image science, and vision.

[11]  E. P. Wallner Optimal wave-front correction using slope measurements , 1983 .

[12]  Douglas P. Looze Minimum variance control structure for adaptive optics systems , 2006 .

[13]  Brent L Ellerbroek,et al.  Efficient computation of minimum-variance wave-front reconstructors with sparse matrix techniques. , 2002, Journal of the Optical Society of America. A, Optics, image science, and vision.

[14]  Lisa A Poyneer,et al.  Fast wave-front reconstruction in large adaptive optics systems with use of the Fourier transform. , 2002, Journal of the Optical Society of America. A, Optics, image science, and vision.

[15]  Robert J. Noll,et al.  Phase estimates from slope-type wave-front sensors , 1978 .

[16]  Luc Gilles,et al.  Closed-loop stability and performance analysis of least-squares and minimum-variance control algorithms for multiconjugate adaptive optics. , 2005, Applied optics.

[17]  R. Hudgin Wave-front compensation error due to finite corrector-element size , 1977 .

[18]  Mitchell Troy,et al.  Experimental validation of Fourier-transform wave-front reconstruction at the Palomar Observatory. , 2003, Optics letters.

[19]  Gerard Rousset,et al.  Comparison of centroid computation algorithms in a Shack–Hartmann sensor , 2006 .

[20]  G Rousset,et al.  High-order adaptive optics requirements for direct detection of extrasolar planets: Application to the SPHERE instrument. , 2006, Optics express.

[21]  M. le Louarn,et al.  Analysis of modes and behavior of a multiconjugate adaptive optics system. , 2002, Journal of the Optical Society of America. A, Optics, image science, and vision.

[22]  B. Ellerbroek First-order performance evaluation of adaptive optics systems for atmospheric turbulence compensatio , 1994 .

[23]  Robert J. Noll Dynamic Atmospheric Turbulence Corrections , 1976, Other Conferences.