Phase differences in the far field of a coherently illuminated object are used to estimate the two-dimensional phase in the measurement plane of an imaging system. A previously derived phase-correlation function is used in a minimum-variance phase-estimation algorithm to map phase-difference measurements optimally to estimates of the phase on a grid of points in the measurement plane. Theoretical and computer-simulation comparisons between the minimum-variance phase estimator and conventional least-squares estimators are made. The minimum-variance phase estimator produces a lower aperture-averaged mean-square phase error for all values of a sampling parameter β.
© 1998 Optical Society of America
(030.6600) Coherence and statistical optics : Statistical optics
(100.0100) Image processing : Image processing
(100.3010) Image processing : Image reconstruction techniques
(110.1650) Imaging systems : Coherence imaging
William W. Arrasmith, Michael Roggemann, and Byron Welsh, "Optimal Wave-front Reconstruction for a Coherent Diffracted Field," Appl. Opt. 37, 4457-4467 (1998)