Quantifications of error propagation in slope-based wavefront estimations

    Authors

    W. Y. Zou;J. P. Rolland

    Comments

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    Abbreviated Journal Title

    J. Opt. Soc. Am. A-Opt. Image Sci. Vis.

    Keywords

    DIFFERENCE MEASUREMENTS; RECONSTRUCTION; ALGORITHM; Optics

    Abstract

    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. (c) 2006 Optical Society of America.

    Journal Title

    Journal of the Optical Society of America a-Optics Image Science and Vision

    Volume

    23

    Issue/Number

    10

    Publication Date

    1-1-2006

    Document Type

    Article

    Language

    English

    First Page

    2629

    Last Page

    2638

    WOS Identifier

    WOS:000240858500026

    ISSN

    1084-7529

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