Testing of Lagrange multiplier damped least-squares control algorithm for woofer-tweeter adaptive optics.

A Lagrange multiplier-based damped least-squares control algorithm for woofer-tweeter (W-T) dual deformable-mirror (DM) adaptive optics (AO) is tested with a breadboard system. We show that the algorithm can complementarily command the two DMs to correct wavefront aberrations within a single optimization process: the woofer DM correcting the high-stroke, low-order aberrations, and the tweeter DM correcting the low-stroke, high-order aberrations. The optimal damping factor for a DM is found to be the median of the eigenvalue spectrum of the influence matrix of that DM. Wavefront control accuracy is maximized with the optimized control parameters. For the breadboard system, the residual wavefront error can be controlled to the precision of 0.03 μm in root mean square. The W-T dual-DM AO has applications in both ophthalmology and astronomy.

[1]  Gang Huang,et al.  Improving wavefront boundary condition for in vivo high resolution adaptive optics ophthalmic imaging , 2011, Biomedical optics express.

[2]  Kenneth Levenberg.  A METHOD FOR THE SOLUTION OF CERTAIN NON – LINEAR PROBLEMS IN LEAST SQUARES , 1944 .

[3]  Rodolphe Conan,et al.  Mean-square residual error of a wavefront after propagation through atmospheric turbulence and after correction with Zernike polynomials. , 2008, Journal of the Optical Society of America. A, Optics, image science, and vision.

[4]  D. Coburn,et al.  Characterisation of MEMs mirrors for use in atmospheric and ocular wavefront correction , 2008, SPIE MOEMS-MEMS.

[5]  Robert J Zawadzki,et al.  Adaptive optics-optical coherence tomography: optimizing visualization of microscopic retinal structures in three dimensions. , 2007, Journal of the Optical Society of America. A, Optics, image science, and vision.

[6]  Joseph Meiron,et al.  Damped Least-Squares Method for Automatic Lens Design , 1965 .

[7]  R Conan,et al.  Distributed modal command for a two-deformable-mirror adaptive optics system. , 2007, Applied optics.

[8]  Stephen A. Burns,et al.  Woofer-tweeter adaptive optics scanning laser ophthalmoscopic imaging based on Lagrange-multiplier damped least-squares algorithm , 2011, Biomedical optics express.

[9]  Weiyao Zou.  New phasing algorithm for large segmented telescope mirrors , 2002 .

[10]  E Glatzel,et al.  Adaptive automatic correction in optical design. , 1968, Applied optics.

[11]  Virendra N. Mahajan.  Strehl ratio for primary aberrations in terms of their aberration variance , 1983 .

[12]  David A. Atchison,et al.  Peripheral refraction along the horizontal and vertical visual fields in myopia , 2006, Vision Research.

[13]  Pablo Artal,et al.  Off-axis monochromatic aberrations estimated from double pass measurements in the human eye , 1999, Vision Research.

[14]  C. Dainty,et al.  Correction of ocular and atmospheric wavefronts: a comparison of the performance of various deformable mirrors. , 2008, Applied optics.

[15]  Colin Bradley,et al.  Woofer-Tweeter Adaptive Optics Test Bench , 2006, First NASA/ESA Conference on Adaptive Hardware and Systems (AHS'06).

[16]  Scot S. Olivier,et al.  High-resolution adaptive optics scanning laser ophthalmoscope with dual deformable mirrors for large aberration correction , 2007, SPIE BiOS.

[17]  Jean-Pierre Véran,et al.  Woofer-tweeter control in an adaptive optics system using a Fourier reconstructor. , 2008, Journal of the Optical Society of America. A, Optics, image science, and vision.

[18]  H Matsui,et al.  Determination method of an initial damping factor in the damped-least-squares problem. , 1994, Applied optics.

[19]  Daren Dillon,et al.  Stroke saturation on a MEMS deformable mirror for woofer-tweeter adaptive optics. , 2009, Optics express.

[20]  Chaohong Li,et al.  A correction algorithm to simultaneously control dual deformable mirrors in a woofer-tweeter adaptive optics system , 2010, Optics express.

[21]  C. Dainty,et al.  Woofer-Tweeter Adaptive Optics for Astronomy , 2010 .

[22]  Wenhan Jiang,et al.  Double-deformable-mirror adaptive optics system for phase compensation. , 2006, Applied optics.

[23]  David A Atchison.  Higher order aberrations across the horizontal visual field. , 2006, Journal of biomedical optics.

[24]  Michael C. Roggemann,et al.  Two-Deformable-Mirror Concept for Correcting Scintillation Effects in Laser Beam Projection Through the Turbulent Atmosphere , 1998 .

[25]  Ankit Mathur,et al.  Ocular aberrations in the peripheral visual field. , 2008, Optics letters.

[26]  Y. Wang,et al.  AUTOMATIC CORRECTION OF ABERRATION IN ASTRO-OPTICAL SYSTEMS , 1974 .

[27]  Pablo Artal,et al.  Peripheral optical errors and their change with accommodation differ between emmetropic and myopic eyes. , 2009, Journal of vision.

[28]  Troy A. Rhoadarmer,et al.  Performance of a woofer-tweeter deformable mirror control architecture for high-bandwidth high-spatial resolution adaptive optics , 2006, SPIE Optics + Photonics.

[29]  Jeffrey D Barchers.  Application of the parallel generalized projection algorithm to the control of two finite-resolution deformable mirrors for scintillation compensation. , 2002, Journal of the Optical Society of America. A, Optics, image science, and vision.

[30]  D. Buchele.  Damping factor for the least-squares method of optical design. , 1968, Applied optics.

[31]  Stephen A Burns,et al.  Wavefront-aberration sorting and correction for a dual-deformable-mirror adaptive-optics system. , 2008, Optics letters.

[32]  Barry Cense,et al.  Volumetric retinal imaging with ultrahigh-resolution spectral-domain optical coherence tomography and adaptive optics using two broadband light sources. , 2009, Optics express.

[33]  Xin Wei,et al.  Modeling the eye's optical system by ocular wavefront tomography. , 2008, Optics express.

[34]  D. Williams,et al.  Monochromatic aberrations of the human eye in a large population. , 2001, Journal of the Optical Society of America. A, Optics, image science, and vision.

[35]  Jeffrey D Barchers,et al.  Closed-loop stable control of two deformable mirrors for compensation of amplitude and phase fluctuations. , 2002, Journal of the Optical Society of America. A, Optics, image science, and vision.

[36]  A. Bradley,et al.  Statistical variation of aberration structure and image quality in a normal population of healthy eyes. , 2002, Journal of the Optical Society of America. A, Optics, image science, and vision.

[37]  W N Charman,et al.  Fluctuations in accommodation: a review , 1988, Ophthalmic & physiological optics : the journal of the British College of Ophthalmic Opticians.

[38]  Stephen A Burns,et al.  High-accuracy wavefront control for retinal imaging with Adaptive-Influence-Matrix Adaptive Optics. , 2009, Optics express.