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

TLDR: In this article, a general Bayesian approach for the joint estimation problem of fixed aberrations, dynamic aberrants, and the object from phase-diverse speckle data that leads to a maximum a posteriori estimator is presented.

Abstract: In phase-diverse speckle imaging one collects a time series of phase-diversity image sets that are used to jointly estimate the object and each of the phase-aberration functions. Current approaches model the total phase aberration in some deterministic parametric fashion. For many imaging schemes, however, additional information can be exploited. Specifically, the total aberration function consists of the fixed aberrations combined with dynamic (time-varying), turbulence-induced aberrations, about whose stochastic behavior we often have some knowledge. One important example is that in which the wave-front phase error corresponds to Kolmogorov turbulence. In this context using the extra statistical information available may be a powerful aid in the joint aberration/object estimation. In addition, such a framework provides an attractive method for calibrating fixed aberrations in an imaging system. The discipline of Bayesian statistical inference provides a natural framework for using the stochastic information regarding the wave fronts. Here one imposes an a priori probability distribution on the turbulence-induced wave fronts. We present the general Bayesian approach for the joint-estimation problem of fixed aberrations, dynamic aberrations, and the object from phase-diverse speckle data that leads to a maximum a posteriori estimator. We also present results based on simulated data, which show that the Bayesian approach provides an increase in accuracy and robustness for this joint estimation.