Abstract

An orthonormal hexagonal Zernike basis set is generated from circular Zernike polynomials apodized by a hexagonal mask by use of the Gram–Schmidt orthogonalization technique. Results for the first 15 hexagonal Zernike polynomials are shown. The Gram–Schmidt orthogonalization technique presented can be extended to both apertures of arbitrary shape and other basis functions.

© 2004 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Gram–Schmidt orthonormalization of Zernike polynomials for general aperture shapes

W. Swantner and Weng W. Chow
Appl. Opt. 33(10) 1832-1837 (1994)

Generalization of Zernike polynomials for regular portions of circles and ellipses

Rafael Navarro, José L. López, José A. Díaz, and Ester Pérez Sinusía
Opt. Express 22(18) 21263-21279 (2014)

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

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

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 OSA member, or as an authorized user of your institution.

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

Figures (4)

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

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

Tables (1)

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

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

Equations (9)

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

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

Metrics

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

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