Phase retrieval with prior information

Area of Science:

• Optics and Astronomy
• Computational Science

Background:

• Phase retrieval is crucial for imaging systems, but traditional methods struggle with atmospheric turbulence.
• Bayesian statistics offer a probabilistic framework for handling uncertainties in phase estimation.

Purpose of the Study:

• To develop an advanced phase retrieval algorithm using Bayesian statistics and turbulence modeling.
• To address and overcome the challenge of local maxima in phase estimation.

Main Methods:

• Developed a Bayesian algorithm incorporating Kolmogorov turbulence statistics to compute phase screen likelihood.
• Integrated turbulence likelihood with observed data likelihood to form a functional.
• Employed conjugate gradient maximization to optimize the functional, while analyzing phase wrapping artifacts.

Main Results:

• The algorithm significantly improved phase estimate quality compared to standard methods.
• Identified phase wrapping as a primary cause of local maxima in the optimization landscape.
• Demonstrated a new method to increase the probability of converging to the global maximum.

Conclusions:

• Bayesian phase retrieval enhanced with turbulence statistics offers superior performance.
• Understanding and mitigating local maxima due to phase wrapping is key for robust phase estimation.
• The presented method provides a more reliable approach to achieving accurate phase reconstruction.