Computation of the circle polynomials of Zernike

Phillip R. Riera

doi:10.1117/12.507565

11 December 2003 Computation of the circle polynomials of Zernike

Phillip R. Riera

Proceedings Volume 5162, Advanced Wavefront Control: Methods, Devices, and Applications; (2003) https://doi.org/10.1117/12.507565
Event: Optical Science and Technology, SPIE's 48th Annual Meeting, 2003, San Diego, California, United States

Abstract

The circle polynomials of Zernike are a vital tool in the analysis of optical systems. Decomposition of wavefronts into Zernike polynomials can be insightful. Computation in the Zernike basis, however, is quite cumbersome and inefficient. This paper will address how rational polynomials such as Zernike, Laguerre, Legendre and Chebyshev can be represented as affine combinations of a Taylor monomial set. This paper also demonstrates the efficiency of common routines using a Taylor basis as well as implementation and optimization issues.

Citation Download Citation

Phillip R. Riera "Computation of the circle polynomials of Zernike", Proc. SPIE 5162, Advanced Wavefront Control: Methods, Devices, and Applications, (11 December 2003); https://doi.org/10.1117/12.507565

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available

Members: $17.00

Non-members: $21.00 ADD TO CART

PROCEEDINGS
9 PAGES

DOWNLOAD PAPER SAVE TO MY LIBRARY

GET CITATION

RIGHTS & PERMISSIONS

Get copyright permission Get copyright permission on Copyright Marketplace

KEYWORDS

Zernike polynomials

Wavefronts

C++

Mathematics

Matrices

Matrix multiplication

Wavefront sensors

Show All Keywords

Keywords/Phrases

Search In:

Publication Years