Maximum-likelihood estimation of parameterized wavefronts from multifocal data.

Area of Science:

• Optical Engineering
• Wavefront Sensing
• Computational Optics

Background:

• Accurate pupil phase distribution is critical for optical system performance.
• Traditional wavefront sensing methods can be limited by aberrations or computational complexity.
• Estimating wavefronts from irradiance data requires robust algorithms.

Purpose of the Study:

• To demonstrate a new method for determining pupil phase distribution.
• To estimate wavefront expansion coefficients using likelihood methods.
• To validate the method through simulation and experimental data.

Main Methods:

• Utilized likelihood methods for estimating wavefront coefficients from near-focus irradiance patterns.
• Employed simulated annealing to address local extrema in the likelihood function for Maximum Likelihood (ML) estimates.
• Investigated Fisher information matrices and Cramér-Rao bounds.
• Applied rapid processing techniques to enhance computational efficiency.

Main Results:

• Proof-of-principle results were achieved in both simulated and experimental setups.
• The method demonstrated capability in handling large-aberration wavefronts numerically.
• Nuisance parameters were effectively managed in the experimental phase.
• ML estimates were successfully obtained despite complex likelihood surfaces.

Conclusions:

• The demonstrated method provides a viable approach for pupil phase distribution determination.
• The technique is robust and applicable to systems with significant aberrations.
• Computational efficiency was improved through rapid processing techniques.