New algorithms for reconstructing wavefront from slopes data are developed, which exhibit high accuracy over broad spatial-frequency bandwidth. Analyzing wavefront reconstructors in the frequency domain lends new insight into ways to improve frequency response and to understand noise propagation. The mathematical tools required to analyze the frequency domain are first developed for discrete band-limited signals. These tools are shown to improve frequency response in either spatial-or frequency-domain reconstruction algorithms. A new spatial-domain iterative reconstruction algorithm based on the Simpson rule is presented. The local phase estimate is averaged over 8 neighboring points whereas the traditional reconstructors use 4 points. Analytic results and numerical simulations show that the Simpson-rule–based reconstructor provides high accuracy up to 85% of the bandwidth. The previously developed rectangular-geometry band-limited algorithm in frequency domain is adapted to hexagonal geometry, which adds flexibility when applying frequency-domain algorithms. Finally, a generalized analytic expression for error propagation coefficient is found for different reconstructors and compared with numerical simulations.
© 2011 OSA
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
Instrumentation, Measurement, and Metrology
Original Manuscript: May 16, 2011
Revised Manuscript: July 28, 2011
Manuscript Accepted: August 16, 2011
Published: September 15, 2011
, "Highly accurate wavefront reconstruction algorithms over broad spatial-frequency bandwidth," Opt. Express 19, 18997-19014 (2011)
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