Extended capture range for focus-diverse phase retrieval in segmented aperture systems using geometrical optics

Area of Science:

• Optics
• Astronomy
• Image Processing

Background:

• Segmented-aperture systems present unique challenges for wavefront sensing.
• Existing phase retrieval algorithms can suffer from stagnation, limiting their effectiveness.

Purpose of the Study:

• To develop an algorithm for estimating segment tips and tilts in segmented-aperture systems.
• To overcome stagnation issues in nonlinear optimization-based phase retrieval for segmented systems.

Main Methods:

• Utilized multiple point spread functions (PSFs) in different defocused planes.
• Developed novel methods to address stagnation in nonlinear optimization algorithms.
• Combined PSF analysis with advanced optimization techniques.

Main Results:

• Successfully estimated segment tips and tilts from defocused PSFs.
• The developed methods significantly improved the capture range of phase retrieval.
• Achieved a success rate exceeding 98% in Monte Carlo simulations for combined methods.

Conclusions:

• The combined approach effectively solves the capture range problem in focus-diverse phase retrieval for segmented systems.
• This advancement is crucial for improving the performance of large segmented telescopes and optical systems.