A method to design tunable quadrature filters in phase shifting interferometry

Area of Science:

• Optical Engineering
• Metrology
• Signal Processing

Background:

• Phase shifting interferometry (PSI) is a key technique for high-precision optical metrology.
• Designing robust quadrature filters in PSI is crucial for accurate phase extraction.
• Existing methods may lack flexibility or require complex calibration.

Purpose of the Study:

• To present a novel method for designing tunable quadrature filters in phase shifting interferometry.
• To provide a systematic approach for filter design based on generalized Fourier transforms.
• To demonstrate the method's capability in generating adaptable and accurate PSI algorithms.

Main Methods:

• A generalized Fourier transform of symmetrical quadrature filters is employed.
• Detuning phase shift error and bias modulation are represented as geometrical conditions.
• The filter design problem is formulated as a set of solvable linear equations.

Main Results:

• The proposed method successfully designs tunable quadrature filters.
• Several general tunable filters, including three- and four-frame algorithms, were derived.
• Particular symmetrical four-frame algorithms from existing literature were reproduced, validating the method.

Conclusions:

• The presented method offers a systematic and flexible approach to designing tunable quadrature filters for PSI.
• This formalism simplifies the design process by translating error considerations into solvable linear equations.
• The derived filters demonstrate high accuracy and adaptability for various phase shifting interferometry applications.