Generalized phase-shifting algorithms: error analysis and minimization of noise propagation

Area of Science:

• Optics and Photonics
• Interferometry
• Phase Retrieval Techniques

Background:

• Phase shifting is a crucial interferometric technique for phase retrieval.
• Accurate phase retrieval depends on precise phase step control and noise reduction.

Purpose of the Study:

• To develop a novel method for generating phase-shifting algorithms with arbitrary phase step spacing.
• To investigate conditions for minimizing phase retrieval errors caused by phase-shift miscalibration.
• To analyze phase extraction from noisy interferograms and identify error minimization strategies.

Main Methods:

• Development of generalized phase-shifting algorithms.
• Mathematical analysis of phase-shift miscalibration effects.
• Study of additive random noise impact on phase extraction.
• Simulations of algorithms with unevenly spaced steps under linear errors and Gaussian noise.

Main Results:

• A new method for creating phase-shifting algorithms with flexible phase step intervals.
• Identification of conditions to minimize phase retrieval errors from calibration inaccuracies.
• Formulation of criteria for reducing phase retrieval errors in the presence of Gaussian noise.

Conclusions:

• The presented methods offer improved robustness in phase retrieval.
• Optimized algorithms can mitigate errors from both phase-shift miscalibration and noise.
• This work advances phase retrieval accuracy in optical metrology.