Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group

Orthonormal polynomials in wavefront analysis: error analysis

Not Accessible

Your library or personal account may give you access

Abstract

Zernike circle polynomials are in widespread use for wavefront analysis because of their orthogonality over a circular pupil and their representation of balanced classical aberrations. However, they are not appropriate for noncircular pupils, such as annular, hexagonal, elliptical, rectangular, and square pupils, due to their lack of orthogonality over such pupils. We emphasize the use of orthonormal polynomials for such pupils, but we show how to obtain the Zernike coefficients correctly. We illustrate that the wavefront fitting with a set of orthonormal polynomials is identical to the fitting with a corresponding set of Zernike polynomials. This is a consequence of the fact that each orthonormal polynomial is a linear combination of the Zernike polynomials. However, since the Zernike polynomials do not represent balanced aberrations for a noncircular pupil, the Zernike coefficients lack the physical significance that the orthonormal coefficients provide. We also analyze the error that arises if Zernike polynomials are used for noncircular pupils by treating them as circular pupils and illustrate it with numerical examples.

© 2008 Optical Society of America

Full Article  |  PDF Article
More Like This
Orthonormal polynomials in wavefront analysis: analytical solution

Virendra N. Mahajan and Guang-ming Dai
J. Opt. Soc. Am. A 24(9) 2994-3016 (2007)

Systematic comparison of the use of annular and Zernike circle polynomials for annular wavefronts

Virendra N. Mahajan and Maham Aftab
Appl. Opt. 49(33) 6489-6501 (2010)

Orthonormal aberration polynomials for optical systems with circular and annular sector pupils

José Antonio Díaz and Virendra N. Mahajan
Appl. Opt. 52(6) 1136-1147 (2013)

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (9)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (7)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (34)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Select as filters


Select Topics Cancel
© Copyright 2024 | Optica Publishing Group. All Rights Reserved