Optimization approach to the suppression of vibration errors in phase-shifting interferometry.

Area of Science:

• Optical Metrology
• Signal Processing
• Vibration Analysis

Background:

• Phase-shifting interferometry (PSI) is sensitive to environmental vibrations, which introduce significant errors.
• Vibration-induced errors can compromise the accuracy of phase measurements in optical systems.
• Existing methods may not fully address the complex effects of vibration across a range of frequencies.

Purpose of the Study:

• To develop an optimization-based strategy for suppressing vibration errors in PSI algorithms.
• To establish a systematic approach for mitigating the impact of vibrations on phase measurements.
• To analyze the relationship between vibration frequency and error magnitude.

Main Methods:

• An optimization procedure based on a norm-square integral criterion of error as a function of vibration frequency.
• Analytical solutions for specific problem classes.
• Numerical algorithms for cases where analytical solutions are not feasible.
• Simulations for validation and efficacy demonstration.

Main Results:

• An effective optimization strategy for vibration error suppression in PSI was developed.
• Analytical and numerical methods were employed to solve the optimization problem.
• It was demonstrated that averaging measurements reduces the impact of vibration-induced errors on time-averaged phase estimates.
• Simulations confirmed the analytical findings and the overall effectiveness of the proposed approach.

Conclusions:

• The proposed optimization strategy significantly suppresses vibration errors in phase-shifting interferometry.
• Measurement averaging is a viable technique to diminish vibration-induced phase estimation errors.
• The developed methodology offers a robust solution for improving the accuracy of optical measurements in the presence of vibrations.