Analysis of primary aberration with the two-dimension discrete wavelet transform

Jin Yi Sheu, Rong Seng Chang, Ching Huang Lin

Research output: Contribution to journalConference articlepeer-review

1 Scopus citations

Abstract

As is known, Zernike polynomials find broad application for the solution of many problems of computational optics. The well-known Zernike polynomials are particularly attractive for their unique properties over a circular aperture. Zernike circle polynomials are used for describing both classical aberrations in optical systems and aberrations related to atmospheric turbulence. There are several numerical techniques to solve for the value of Zernike coefficients, the least-squares matrix inversion method and the Gram-Schmidt orthogonalization method would become ill-conditioned due to an improper data sampling. In this article, we present the two-dimension discrete wavelet transform (DWT) technique to find the 3rd order spherical and coma aberration coefficients. The method offers great improvement in the accuracy and calculating speed of the fitting aberration coefficients better than the least-squares matrix inversion method and the Gram-Schmidt orthogonalization method. Furthermore, the result of solving coefficients through the two-dimension DWT is independent of the order of the polynomial expansion. So we can find an accurate value from the datum of fitting.

Original languageEnglish
Pages (from-to)372-380
Number of pages9
JournalProceedings of SPIE - The International Society for Optical Engineering
Volume4056
StatePublished - 2000
EventWavelet Applications VII - Orlando, FL, USA
Duration: 26 Apr 200028 Apr 2000

Fingerprint

Dive into the research topics of 'Analysis of primary aberration with the two-dimension discrete wavelet transform'. Together they form a unique fingerprint.

Cite this