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Phase retrieval with prior information.

R Irwan1, R G Lane

  • 1Department of Electrical and Electronic Engineering, University of Canterbury, Christchurch, New Zealand.

Journal of the Optical Society of America. A, Optics and Image Science
|August 12, 2008
PubMed
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This study introduces a Bayesian algorithm for phase retrieval, improving estimates by incorporating Kolmogorov turbulence statistics. A novel method addresses local maxima to enhance convergence to the global maximum.

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.

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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.