Optimal modal fourier-transform wavefront control.

Optimal modal Fourier-transform wavefront control combines the speed of Fourier-transform reconstruction (FTR) with real-time optimization of modal gains to form a fast, adaptive wavefront control scheme. Our modal basis is the real Fourier basis, which allows direct control of specific regions of the point-spread function. We formulate FTR as modal control and show how to measure custom filters. Because the Fourier basis is a tight frame, we can use it on a circular aperture for modal control even though it is not an orthonormal basis. The modal coefficients are available during reconstruction, greatly reducing computational overhead for gain optimization. Simulation results show significant improvements in performance in low-signal-to-noise-ratio situations compared with nonadaptive control. This scheme is computationally efficient enough to be implemented with off-the-shelf technology for a 2.5 kHz, 64 x 64 adaptive optics system.

[1]  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.

[2]  Robert J. Plemmons,et al.  Optimizing closed-loop adaptive-optics performance with use of multiple control bandwidths , 1994 .

[3]  G Rousset,et al.  Optimization of a predictive controller for closed-loop adaptive optics. , 1998, Applied optics.

[4]  B. Macintosh,et al.  Spatially filtered wave-front sensor for high-order adaptive optics. , 2004, Journal of the Optical Society of America. A, Optics, image science, and vision.

[5]  Russell B. Makidon,et al.  The Structure of High Strehl Ratio Point-Spread Functions , 2003 .

[6]  Douglas G MacMartin,et al.  Local, hierarchic, and iterative reconstructors for adaptive optics. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[7]  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.

[8]  Malcolm J. Smith,et al.  Implementation of the Altair optimization processes , 2003, SPIE Astronomical Telescopes + Instrumentation.

[9]  D. Rouan,et al.  Performance of the Canada‐France‐Hawaii Telescope Adaptive Optics Bonnette , 1998 .

[10]  Chris L. Koliopoulos,et al.  Modal estimation of a wave front from difference measurements using the discrete Fourier transform , 1986 .

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

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

[13]  Curtis R Vogel,et al.  Multigrid preconditioned conjugate-gradient method for large-scale wave-front reconstruction. , 2002, Journal of the Optical Society of America. A, Optics, image science, and vision.

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

[15]  Donald T. Gavel,et al.  Simulation of stellar speckle imaging , 1994, Astronomical Telescopes and Instrumentation.

[16]  David Mouillet,et al.  NAOS, the first AO system of the VLT: on-sky performance , 2003, SPIE Astronomical Telescopes + Instrumentation.

[17]  Chris L. Koliopoulos,et al.  Wavefront Reconstruction from Noisy Slope or Difference Data Using the Discrete Fourier Transform , 1986, Other Conferences.

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

[19]  Donald T. Gavel,et al.  Toward Strehl-optimizing adaptive optics controllers , 2003, SPIE Astronomical Telescopes + Instrumentation.

[20]  Jean-Pierre Veran,et al.  Analytical model for Shack-Hartmann-based adaptive optics systems , 1998, Astronomical Telescopes and Instrumentation.

[21]  Fang Shi,et al.  Sparse-matrix wavefront reconstruction: simulations and experiments , 2003, SPIE Astronomical Telescopes + Instrumentation.

[22]  Bruce A. Macintosh,et al.  Speckle Decorrelation and Dynamic Range in Speckle Noise-limited Imaging , 2002 .