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Alternative phase-diverse phase retrieval algorithm based on Levenberg-Marquardt nonlinear optimization.

Heng Mao1, Dazun Zhao

  • 1Department of Photo-electronic Engineering, Beijing Institute of Technology, Beijing 100081, China. alexmaomao@bit.edu.cn

Optics Express
|March 19, 2009
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Summary
This summary is machine-generated.

A new Modified Levenberg-Marquardt (MLM) algorithm improves wavefront sensing (WFS) accuracy and repeatability, especially for obstructed pupils. This advanced algorithm overcomes limitations of the Modified G-S (MGS) method.

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Area of Science:

  • Optics and Photonics
  • Wavefront Sensing and Adaptive Optics

Background:

  • Phase-diverse phase retrieval is crucial for wavefront sensing (WFS).
  • Existing methods like the Modified G-S (MGS) algorithm can stagnate in local minima, particularly with obstructed pupils.
  • Accurate wavefront characterization is essential for optical system performance.

Purpose of the Study:

  • To introduce and validate a Modified Levenberg-Marquardt (MLM) algorithm for phase retrieval in WFS.
  • To address the limitations of the MGS algorithm in scenarios with obstructed pupils.
  • To demonstrate superior performance of the MLM algorithm in terms of accuracy and repeatability.

Main Methods:

  • Development of a Modified Levenberg-Marquardt (MLM) algorithm incorporating second derivative information.
  • Application of the MLM algorithm to phase-diverse phase retrieval for wavefront sensing.
  • Experimental validation using a ZYGO interferometer for comparison with the MGS algorithm.

Main Results:

  • The MLM algorithm achieved high WFS accuracy (less than λ/30 RMS) and repeatability (less than λ/200 RMS).
  • The algorithm demonstrated a dynamic range exceeding 7λ PV.
  • Experimental results confirmed the MLM algorithm's superiority over the MGS algorithm in both accuracy and repeatability.

Conclusions:

  • The Modified Levenberg-Marquardt (MLM) algorithm offers a robust solution for phase retrieval in wavefront sensing.
  • MLM effectively mitigates local minimum stagnation issues present in the MGS algorithm, particularly for obstructed pupils.
  • The MLM algorithm provides enhanced accuracy and repeatability, making it a valuable tool for advanced optical metrology.