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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 23, Iss. 10 — Oct. 1, 2006
  • pp: 2629–2638

Quantifications of error propagation in slope-based wavefront estimations

Weiyao Zou and Jannick P. Rolland  »View Author Affiliations

JOSA A, Vol. 23, Issue 10, pp. 2629-2638 (2006)

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We discuss error propagation in the slope-based and the difference-based wavefront estimations. The error propagation coefficient can be expressed as a function of the eigenvalues of the wavefront-estimation-related matrices, and we establish such functions for each of the basic geometries with the serial numbering scheme with which a square sampling grid array is sequentially indexed row by row. We first show that for the wavefront estimation with the wavefront piston value determined, the odd-number grid sizes yield better error propagators than the even-number grid sizes for all geometries. We further show that for both slope-based and difference-based wavefront estimations, the Southwell geometry offers the best error propagators with the minimum-norm least-squares solutions. Noll's theoretical result, which was extensively used as a reference in the previous literature for error propagation estimates, corresponds to the Southwell geometry with an odd-number grid size. Typically the Fried geometry is not preferred in slope-based optical testing because it either allows subsize wavefront estimations within the testing domain or yields a two-rank deficient estimations matrix, which usually suffers from high error propagation and the waffle mode problem. The Southwell geometry, with an odd-number grid size if a zero point is assigned for the wavefront, is usually recommended in optical testing because it provides the lowest-error propagation for both slope-based and difference-based wavefront estimations.

© 2006 Optical Society of America

OCIS Codes
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
(080.2720) Geometric optics : Mathematical methods (general)
(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure
(220.4840) Optical design and fabrication : Testing

Original Manuscript: November 28, 2005
Revised Manuscript: March 31, 2006
Manuscript Accepted: April 7, 2006

Weiyao Zou and Jannick P. Rolland, "Quantifications of error propagation in slope-based wavefront estimations," J. Opt. Soc. Am. A 23, 2629-2638 (2006)

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