Accurate and fast two-step phase shifting algorithm based on principle component analysis and Lissajous ellipse...

Area of Science:

• Optical Metrology
• Interferometry
• Phase Measurement

Background:

• Phase shifting interferometry (PSI) is crucial for accurate optical measurements.
• Traditional PSI methods often require multiple phase-shifted interferograms and significant computational time.
• Existing algorithms can be sensitive to noise and variations in intensity and modulation.

Purpose of the Study:

• To develop a novel random phase-shifting algorithm for enhanced measurement accuracy and reduced computational load in interferometry.
• To propose a method that minimizes pre-filtering requirements and is adaptable to various experimental conditions.

Main Methods:

• A new algorithm combining Principal Component Analysis (PCA) and Lissajous Ellipse Fitting (LEF) is introduced.
• The PCA&LEF algorithm processes only two phase-shifted interferograms.
• It is designed to be effective without pre-filtering and robust against noise and non-uniform intensity/modulation.

Main Results:

• The PCA&LEF algorithm achieves relatively accurate phase distribution with minimal computational time.
• It demonstrates suitability for diverse background intensity, modulation amplitude distributions, and noise levels.
• The method can yield absolutely accurate results under ideal conditions and partially suppresses imperfections.

Conclusions:

• The proposed PCA&LEF algorithm offers a computationally efficient and accurate solution for phase measurement in interferometry.
• It overcomes limitations of traditional PCA methods, such as the need for more than three interferograms.
• Simulations and experimental results confirm the correctness and feasibility of the PCA&LEF approach.