Co-phasing of the segmented mirror and image retrieval based on phase diversity using a modified algorithm.

Area of Science:

• Optics
• Computational Science
• Image Processing

Background:

• Phase diversity (PD) algorithms rely on cost functions to determine wavefront aberrations.
• Conventional optimization methods like Broyden-Fletcher-Goldfarb-Shanno (BFGS) may fail to converge globally for non-convex cost functions.
• Segmented active optics systems require precise wavefront control for optimal performance.

Purpose of the Study:

• To develop a modified BFGS method with guaranteed global convergence for PD algorithms.
• To apply this method to co-phase a segmented active optics system and recover unknown objects.
• To address noise amplification issues in PD problems.

Main Methods:

• A modified BFGS optimization algorithm was developed to handle both convex and non-convex cost functions.
• The modified BFGS method was applied to minimize the PD cost function for a segmented active optics system.
• A novel strategy for estimating the regularization parameter was implemented to mitigate noise amplification.

Main Results:

• The modified BFGS method demonstrated superior global convergence compared to the conventional BFGS method, particularly for non-convex cost functions.
• Accurate wavefront coefficients were recovered, leading to improved object recovery.
• The proposed regularization parameter estimation effectively removed noise amplification effects, enhancing algorithm accuracy under high noise conditions.

Conclusions:

• The modified BFGS method provides a robust solution for phase diversity problems, ensuring convergence to the global minimum.
• This advancement is crucial for the accurate phasing of segmented active optics systems and reliable object recovery.
• The method shows significant potential for applications in various imaging and optical systems, even in noisy environments.