Suppressing ripple distortions and spurious pistons in phase-shifting interferometry

Area of Science:

• Optical Metrology
• Interferometry
• Signal Processing

Background:

• Phase-shifting interferometry (PSI) is susceptible to phase errors like ripple distortions and spurious pistons.
• These errors occur when PSI processes interferograms with non-uniform phase shifts using algorithms assuming uniform shifts.

Purpose of the Study:

• To develop novel phase-shifting algorithms (PSAs) that effectively suppress ripple distortions and spurious pistons.
• To provide a systematic approach for designing robust PSAs based on frequency transfer function (FTF) analysis.

Main Methods:

• Modeling non-uniform phase shifts as a polynomial of the unperturbed phase-shift value.
• Analyzing the mth derivative of the PSA's frequency transfer function (FTF) to establish conditions for error elimination.
• Developing and presenting four new PSA formulas.

Main Results:

• Demonstrated that specific derivatives of the FTF are key to eliminating ripple distortion and spurious pistons.
• Introduced a robust algorithm design methodology grounded in FTF formalism.
• Presented four practical PSA formulas for implementation.

Conclusions:

• The proposed PSAs effectively suppress phase errors in interferometry.
• The FTF-based design approach offers a robust method for developing accurate phase-shifting algorithms.
• Computer simulations validate the efficacy of the presented algorithms and methodology.