Phase-shifting algorithms with known and unknown phase shifts: comparison and hybrid

Area of Science:

• Optical metrology
• Interferometry
• Precision measurement

Background:

• Phase-shifting interferometry (PSI) is crucial for precision measurements, requiring robust phase-shifting algorithms (PSAs) to mitigate errors like phase-shift inaccuracies, intensity harmonics, and noise.
• Existing research extensively covers known phase-shifting algorithms (kPSAs) but lacks thorough evaluation of unknown phase-shifting algorithms (uPSAs), leaving their prerequisites and performance unclear.

Purpose of the Study:

• To comprehensively evaluate the prerequisites and performance of four representative uPSAs.
• To compare the performance of uPSAs against twelve benchmarking kPSAs.
• To clarify the selection criteria for kPSAs and showcase the potential of uPSAs.

Main Methods:

• Evaluation of four uPSAs: advanced iterative algorithm, general iterative algorithm (GIA), principal component analysis-based algorithm, and VU factorization-based algorithm.
• Comparative analysis of uPSAs against twelve established kPSAs.
• Development of a hybrid kPSA-GIA algorithm.

Main Results:

• Identified limitations and performance characteristics of different uPSAs.
• Demonstrated the need for careful kPSA selection and highlighted the attractive performance and fewer restrictions of uPSAs.
• The general iterative algorithm (GIA) showed outstanding performance.

Conclusions:

• uPSAs offer significant advantages in precision measurement, with the GIA being particularly effective.
• A novel hybrid kPSA-GIA algorithm is proposed to enhance kPSA performance and overcome GIA's fringe density limitations.
• This work provides a clearer understanding of PSA selection for demanding metrology applications.