Abstract

Characteristics of the Hubble Space Telescope (HST) that affect image deblurring are described, with emphasis on the phase errors that are determined by phase retrieval algorithms. The aberrations of the HST are determined from the measured point spread functions (PSFs) by phase retrieval algorithms of two types: nonlinear least squares optimization over coefficients of Zernike polynomials and iterative transform algorithms. In either case, accurate and comprehensive optical system models are needed to satisfy stringent requirements on the retrieved phase error, both for the purpose of building appropriate correction optics and for analytic computation of space variant PSFs for image deblurring. This paper describes phase retrieval algorithms incorporating a system model that involves multiple-plane propagation through the system and weighted error metrics that allow for bad CCD pixels to be ignored. Analytic expressions of the gradient of the error metric, with respect to either polynomial coefficients or point-by-point phase maps, are derived that allow for a full gradient calculation to be performed with a small number of fast Fourier transforms (FFTs) independent of the number of parameters. Other system characteristics that hinder image deconvolution are described, including the telescope jitter, the space-variant nature of the system, finite spectral bandwidth, and image undersampling.

© 1991 Optical Society of America