Fast and robust two-frame random phase-shifting interferometry without pre-filtering.

Area of Science:

• Optical Metrology
• Interferometry
• Image Processing

Background:

• Phase-shifting interferometry (PSI) is crucial for precise optical measurements.
• Traditional PSI methods often require multiple frames and specific phase-shifting distributions, increasing computation time.
• Existing algorithms may struggle with low fringe counts or varying background intensity.

Purpose of the Study:

• To develop a computationally efficient and accurate phase-shifting algorithm.
• To reduce the number of required interferograms for phase extraction.
• To enhance robustness against noise and variations in interferogram intensity.

Main Methods:

• A novel random phase-shifting algorithm combining Principal Component Analysis (PCA) and Least Squares Iteration (LSI).
• Utilizes only two-frame phase-shifted interferograms without pre-filtering.
• Leverages PCA for efficient phase extraction and LSI for refinement.

Main Results:

• Achieved higher phase accuracy with significantly reduced computation time.
• Successfully extracted phase with high precision even with few fringes.
• Demonstrated robustness against fluctuations in background intensity and modulation amplitude.
• Outperformed other methods under various noise conditions.

Conclusions:

• The proposed PCA&LSI algorithm offers an efficient and accurate solution for phase extraction in interferometry.
• It overcomes limitations of traditional methods, requiring fewer frames and no pre-filtering.
• The algorithm is suitable for complex and noisy interferometric scenarios, enhancing practical applications.