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Applied Optics

Applied Optics


  • Vol. 40, Iss. 35 — Dec. 10, 2001
  • pp: 6505–6514

Sparse matrix approximation method for an active optical control system

Timothy P. Murphy, Richard G. Lyon, John E. Dorband, and Jan M. Hollis  »View Author Affiliations

Applied Optics, Vol. 40, Issue 35, pp. 6505-6514 (2001)

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We develop a sparse matrix approximation method to decompose a wave front into a basis set of actuator influence functions for an active optical system consisting of a deformable mirror and a segmented primary mirror. The wave front used is constructed by Zernike polynomials to simulate the output of a phase-retrieval algorithm. Results of a Monte Carlo simulation of the optical control loop are compared with the standard, nonsparse approach in terms of accuracy and precision, as well as computational speed and memory. The sparse matrix approximation method can yield more than a 50-fold increase in the speed and a 20-fold reduction in matrix size and a commensurate decrease in required memory, with less than 10% degradation in solution accuracy. Our method is also shown to be better than when elements are selected for the sparse matrix on a magnitude basis alone. We show that the method developed is a viable alternative to use of the full control matrix in a phase-retrieval-based active optical control system.

© 2001 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(350.1260) Other areas of optics : Astronomical optics
(350.6090) Other areas of optics : Space optics

Original Manuscript: February 15, 2001
Revised Manuscript: July 17, 2001
Published: December 10, 2001

Timothy P. Murphy, Richard G. Lyon, John E. Dorband, and Jan M. Hollis, "Sparse matrix approximation method for an active optical control system," Appl. Opt. 40, 6505-6514 (2001)

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