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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 aredoi:10.1364/josaa.9.001072 fatcat:fqagkezhsbbzjiguaw4opsu3eu