Orthonormal polynomials in wavefront analysis: error analysis
Applied Optics, Vol. 47, Issue 19, pp. 3433-3445 (2008)
http://dx.doi.org/10.1364/AO.47.003433
Enhanced HTML 
Acrobat PDF (3238 KB)
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
OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
(220.0220) Optical design and fabrication : Optical design and fabrication
(220.1010) Optical design and fabrication : Aberrations (global)
(330.4460) Vision, color, and visual optics : Ophthalmic optics and devices
ToC Category:
Wave-front Sensing
History
Original Manuscript: April 4, 2008
Manuscript Accepted: May 23, 2008
Published: June 23, 2008
Virtual Issues
Vol. 3, Iss. 8 Virtual Journal for Biomedical Optics
Citation
Guang-ming Dai and Virendra N. Mahajan, "Orthonormal polynomials in wavefront analysis: error analysis," Appl. Opt. 47, 3433-3445 (2008)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-47-19-3433
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
Log in to access OSA Member Subscription
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
Log in to access OSA Member Subscription
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
Log in to access OSA Member Subscription
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
Log in to access OSA Member Subscription
Related Journal Articles 
- Analysis of imaging properties of a vibrating thin flat mirror (JOSAA)
- Zernike aberration coefficients transformed to and from Fourier series coefficients for wavefront representation (OL)
- Orthonormal polynomials in wavefront analysis: analytical solution (JOSAA)
- Bilinear wavefront transformation (JOSAA)
- Systematic comparison of the use of annular and Zernike circle polynomials for annular wavefronts (AO)
Related Conference Papers
- Linear Systems Modeling and Evaluation of Adaptive Optics in the Spatial Frequency Domain
- A Software Framework for Fast Adaptive Optics Control with Atmospheric Tomography
- Optimization of the Pre-Compensation of Non-Common Path Aberrations for Adaptive Optics Systems
- Aberrations Induced by Laser Guide Stars in Adaptive Optics
- AO System Design for Direct Exo-Planet Detection on the VLT
« Previous Article | Next Article »
OSA is a member of 