Gradient flipping algorithm: introducing non-convex constraints in wavefront reconstructions with the transport of...

Area of Science:

• Optics and Photonics
• Computational Imaging
• Wavefront Sensing

Background:

• The transport of intensity equation (TIE) is crucial for wavefront recovery using intensity measurements.
• Solving TIE is often ill-posed due to unspecified boundary conditions or noisy data, necessitating additional constraints.

Purpose of the Study:

• To address the limitations of convex constraints in TIE solutions, specifically low-frequency artifacts.
• To introduce and validate a non-convex constraint approach for more robust wavefront recovery.

Main Methods:

• Implementation of a novel gradient flipping algorithm for TIE.
• Comparison of non-convex constraints against traditional total variation minimization (a convex approach).
• Validation using simulated and experimental data.

Main Results:

• Non-convex constraints effectively mitigate low-frequency artifacts common in convex TIE solutions.
• The gradient flipping algorithm demonstrates superior performance over total variation minimization.
• Accurate wavefront recovery was achieved even with challenging data.

Conclusions:

• Non-convex constraints are essential for overcoming specific artifacts in TIE-based wavefront recovery.
• The gradient flipping algorithm offers a significant advancement for TIE solutions, particularly in practical scenarios with imperfect data.