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Zernike-like Orthogonal Basis Functions for Wavefront Characterization over Sampled, Irregular AperturesFor optical systems with circular apertures, wavefronts are often analyzed using Zernike polynomials, and individual Zernike functions are associated with familiar optical aberrations. For systems with noncircular apertures, or in practical situations in which wavefronts are measured at a limited number of points in the aperture, the Zernike polynomials are no longer an orthogonal basis for the measured data. Although there are an endless number of ways to create a basis for such measured data, a "Zernike-like" basis is useful to connect with our experience with the usual optical aberrations. In this paper, the steps required to identify a Zernike-like basis for wavefronts over sampled, irregular apertures are presented, based on the Gram-Schmidt orthogonalization technique. The benefits of analyzing optical wavefronts using an orthogonal basis specific to an optical system's aperture shape and wavefront sampling, instead of using the traditional Zernike polynomials, are detailed in two examples, from image-based wavefront sensing on a segmented-aperture telescope (the James Webb Space Telescope Testbed Telescope at Ball Aerospace) and from interferometer characterization for surface metrology of a hexagonal mirror segment.
Document ID
20070032106
Acquisition Source
Goddard Space Flight Center
Document Type
Conference Paper
Authors
Aronstein, David L.
(NASA Goddard Space Flight Center Greenbelt, MD, United States)
Dean, Bruce H.
(NASA Goddard Space Flight Center Greenbelt, MD, United States)
Smith, J. Scott
(NASA Goddard Space Flight Center Greenbelt, MD, United States)
Date Acquired
August 23, 2013
Publication Date
August 26, 2007
Subject Category
Optics
Meeting Information
Meeting: SPIE Optics and Photonics
Location: San DIego, CA
Country: United States
Start Date: August 26, 2007
End Date: August 30, 2007
Sponsors: International Society for Optical Engineering
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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