Half-quadratic cost function for computing arbitrary phase shifts and phase: Adaptive out of step phase shifting

Area of Science:

• Optical Metrology
• Image Processing
• Signal Processing

Background:

• Phase shifting algorithms are crucial for quantitative phase imaging.
• Irregular or unknown phase steps introduce significant artifacts in phase reconstruction.
• Existing methods struggle with non-ideal phase step conditions.

Purpose of the Study:

• To develop a robust phase shifting method capable of handling irregular and unknown phase steps.
• To simultaneously compute accurate phase maps and correct arbitrary phase shifts.
• To provide a reliable phase refinement strategy for improved imaging quality.

Main Methods:

• Formulation as a half-quadratic regularized cost function minimization problem.
• Iterative, alternated minimization for phase map correction, outlier rejection, and phase shift correction.
• Utilizes a coarse phase and phase shift estimation as an initial guess for refinement.

Main Results:

• Guaranteed convergence to at least a local minimum.
• Effective correction of artifacts caused by imprecise phase steps.
• Demonstrated superior performance compared to standard filtering and arbitrary phase step detection algorithms.

Conclusions:

• The proposed method offers a robust solution for phase shifting in the presence of unknown or irregular phase steps.
• This technique enhances the accuracy of phase map reconstruction and reduces artifacts.
• The algorithm provides a valuable tool for quantitative phase imaging applications requiring precise phase retrieval.