Family of detuning-insensitive phase-shifting algorithms

Area of Science:

• Optical metrology
• Interferometry
• Signal processing

Background:

• Phase-shifting algorithms (PSA's) are crucial for quantitative phase measurement in interferometry.
• Existing PSA designs employ various strategies, leading to diverse performance characteristics.

Purpose of the Study:

• To develop a generalized algebraic approach for designing detuning-insensitive PSA's.
• To analyze the behavior of these algorithms under linear phase error using geometric interpretations.
• To derive new criteria and analytic expressions for PSA performance evaluation.

Main Methods:

• Generalized algebraic approach for PSA design.
• Geometric analysis of algorithm behavior under phase error.
• Comparison with Fourier representation of sampling functions.

Main Results:

• A family of detuning-insensitive PSA's was derived.
• New criteria for assessing detuning insensitivity were established.
• Analytic expressions for phase error and novel PSA's with unique properties were achieved.

Conclusions:

• The generalized algebraic approach provides a systematic method for designing robust PSA's.
• The geometric analysis offers insights into PSA performance under detuning.
• The newly derived criteria and algorithms advance the field of phase measurement.