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Area of Science:

Optics
Image Processing
Computational Science

Background:

Wave aberration is crucial for understanding optical system performance.
Retrieving wave aberration from point-spread functions is a challenging inverse problem.
Existing methods may struggle with large aberrations or require initial estimates.

Purpose of the Study:

To present a new procedure for retrieving wave aberration from point-spread functions.
To develop a robust method that avoids local minima and accelerates convergence.
To validate the procedure using simulated large aberrations without initial estimates.

Main Methods:

The study employs the Levenberg-Marquardt optimization algorithm.
A mutiresolution pyramidal scheme is utilized for efficient processing.
The method is tested on simulated point-spread functions with significant aberrations.

Main Results:

The proposed procedure successfully retrieves wave aberration.
The mutiresolution scheme accelerates the convergence of the optimization.
The method demonstrates robustness by avoiding stagnation in local minima, even without initial guesses.
Effective handling of large aberrations was confirmed.

Conclusions:

A new, effective, and robust procedure for wave aberration retrieval from point-spread functions has been developed.
The combination of Levenberg-Marquardt optimization and a mutiresolution pyramidal approach offers significant advantages.
This method provides a valuable tool for optical system analysis and aberration correction.