Random two-step phase shifting interferometry based on Lissajous ellipse fitting and least squares technologies

Area of Science:

• Optical metrology
• Interferometry
• Surface analysis

Background:

• Accurate phase distribution extraction is crucial for optical surface testing.
• Phase shift errors in interferometry can lead to inaccurate measurements.
• Existing algorithms may struggle with non-uniform background intensity and modulation amplitude.

Purpose of the Study:

• To develop a robust phase extraction algorithm for optical surfaces.
• To overcome phase shift errors in interferometric measurements.
• To propose a method effective under fluctuating and non-uniform conditions.

Main Methods:

• A random two-step phase shifting algorithm is introduced.
• Lissajous ellipse fitting and least squares iterative phase shifting algorithm (LEF & LSI PSA) are employed.
• The method does not require pre-filtering of interferograms.

Main Results:

• The proposed LEF & LSI PSA achieves relatively accurate phase distribution.
• The algorithm successfully determines unknown phase shift values.
• Simulations and experimental results confirm the algorithm's correctness and feasibility.

Conclusions:

• The LEF & LSI PSA is a viable and accurate method for phase extraction in optical surface testing.
• The algorithm demonstrates robustness against varying background intensities and modulation amplitudes.
• This technique offers an improvement over existing methods by eliminating the need for pre-filtering.