Zernike integrated partial phase error reduction algorithm

Abstract

A modification to the error reduction algorithm is reported in this paper for determining the prescription of an imaging system in terms of Zernike polynomials. The technique estimates the Zernike coefficients of the optical prescription as part of a modified Gerchberg-Saxton iteration combined with a new gradient-based phase unwrapping algorithm. Zernike coefficients are updated gradually as the error reduction algorithm converges by recovering the partial pupil phase that differed from the last known pupil phase estimate. In this way the wrapped phase emerging during each iteration of the error reduction algorithm does not represent the entire wrapped phase of the pupil electric field and can be unwrapped with greater ease.The algorithm is tested in conjunction with a blind deconvolution algorithm using measured laboratory data with a known optical prescription and is compared to a baseline approach utilizing a combination of the error reduction algorithm and a least-squares phase unwrapper previously reported in the literature. The combination of the modified error reduction algorithm and the new least-squares Zernike phase unwrapper is shown to produce superior performance for an application where it is desirable that Zernike coefficients be estimated during each iteration of the blind deconvolution procedure.

Keywords

• Phase retrieval
• Zernike polynomials
• Blind deconvolution