Efficient computation with special functions like the circle polynomials of Zernike

Philip R. Riera; Geoffrey S. Pankretz; Daniel M. Topa

doi:10.1117/12.481181

4 September 2002 Efficient computation with special functions like the circle polynomials of Zernike

Philip R. Riera, Geoffrey S. Pankretz, Daniel M. Topa

Proceedings Volume 4769, Optical Design and Analysis Software II; (2002) https://doi.org/10.1117/12.481181
Event: International Symposium on Optical Science and Technology, 2002, Seattle, WA, United States

Abstract

The circle polynomials of Zernike play a prominent role in optical analysis. While decompositions of wavefronts into Zernike polynomial series can yield valuable insight, computing with the polynomials themselves is quite inefficient. Here we outline how rational polynomials like those of Zernike, Legendre, Chebyshev and Laguerre can be handled as affine combinations of a Taylor monomial set. We demonstrate how calculations can be performed much more rapidly in the Taylor basis and how to use integer transformations to recover the exact amplitudes in the desired basis. We also explore C++ optimizations for storing the Zernike amplitudes and transforming between Zernike polynomials and Taylor monomials.

Citation Download Citation

Philip R. Riera, Geoffrey S. Pankretz, and Daniel M. Topa "Efficient computation with special functions like the circle polynomials of Zernike", Proc. SPIE 4769, Optical Design and Analysis Software II, (4 September 2002); https://doi.org/10.1117/12.481181

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