Issue |
J. Eur. Opt. Soc.-Rapid Publ.
Volume 6, 2011
|
|
---|---|---|
Article Number | 11028 | |
Number of page(s) | 14 | |
DOI | https://doi.org/10.2971/jeos.2011.11028 | |
Published online | 23 May 2011 |
Regular papers
New analytic results for the Zernike circle polynomials from a basic result in the Nijboer-Zernike diffraction theory
Department EE and EURANDOM, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
Received:
10
December
2010
Several quantities related to the Zernike circle polynomials admit an expression, via the basic identity in the diffraction theory of Nijboer and Zernike, as an infinite integral involving the product of two or three Bessel functions. In this paper these integrals are identified and evaluated explicitly for the cases of (a) the expansion coefficients of scaled-and-shifted circle polynomials, (b) the expansion coefficients of the correlation of two circle polynomials, (c) the Fourier coefficients occurring in the cosine representation of the radial part of the circle polynomials.
Key words: Diffraction / Zernike Polynomals / Scaling / Shifting / Optical Transfer Function
© The Author(s) 2011. All rights reserved.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.