Abstract

The joint estimation of an object and the aberrations of an incoherent imaging system from multiple images incorporating phase diversity is investigated. Maximum-likelihood estimation is considered under additive Gaussian and Poisson noise models. Expressions for an aberration-only objective function that accommodates an arbitrary number of diversity images and its gradient are derived for the case of a Gaussian noise model. Expressions for the log-likelihood function and its gradient are presented for the case of Poisson noise. An expectation-maximization algorithm that enforces a nonnegativity constraint in a natural fashion is constructed for use in the Poisson noise case.

© 1992 Optical Society of America

Maximum a posteriori estimation of fixed aberrations, dynamic aberrations, and the object from phase-diverse speckle data

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