Phase-shifting algorithms for a finite number of harmonics: first-order analysis by solving linear systems

Area of Science:

• Optical metrology
• Signal processing

Background:

• Phase-shifting algorithms are crucial for optical metrology.
• Existing algorithms can be sensitive to harmonic components and frequency detuning.
• Robust phase retrieval methods are needed for accurate measurements.

Purpose of the Study:

• To develop a generalized linear system analysis for phase-shifting algorithms.
• To design algorithms that are insensitive to harmonic components in fringe patterns.
• To achieve insensitivity to detuning of the fundamental frequency.

Main Methods:

• Analysis of generalized phase-shifting equations.
• Linear system modeling for equally and nonequally spaced phase shifts.
• Fourier domain analysis of the wrapped phase equation.
• Incorporation of finite harmonic components and detuning effects.

Main Results:

• Development of phase-shifting algorithms with inherent insensitivity to harmonics.
• Demonstration of insensitivity to fundamental frequency detuning.
• Linear systems effectively compensate for linear phase shift errors.
• Fourier analysis provides insights into algorithm performance.

Conclusions:

• The proposed linear system analysis offers a robust framework for phase-shifting algorithms.
• The developed algorithms enhance measurement accuracy in optical metrology.
• This approach provides a method for creating phase-shifting techniques with improved insensitivity properties.