Suppression of fundamental-frequency phase errors in phase-shifting interferometry

Area of Science:

• Optical metrology
• Interferometry
• Phase-shifting techniques

Background:

• Fizeau interferometers are crucial for precise optical measurements.
• Phase-shift miscalibrations introduce errors in interferometric measurements.
• High numerical aperture (NA) spherical cavities present unique challenges for interferometry.

Purpose of the Study:

• To develop and experimentally validate novel phase-shifting formulas for Fizeau interferometers.
• To investigate and compensate for phase-shift errors, particularly in high-NA spherical cavities.
• To enhance the accuracy of phase reconstruction in interferometric measurements.

Main Methods:

• Development of new phase-shifting algorithms tailored for Fizeau interferometry.
• Experimental testing using a high-NA spherical cavity to induce and analyze phase errors.
• Application of characteristic polynomial theory and modified averaging methods for error compensation.

Main Results:

• Identified residual phase oscillations at 1 and 3 times the fringe frequency after initial error removal.
• Demonstrated that 3f oscillations are addressable by characteristic polynomial theory.
• Showcased that 1f oscillations can be mitigated using modified averaging methods, enabling empirical optimization.

Conclusions:

• The new phase-shifting formulas effectively compensate for miscalibrations in Fizeau interferometers.
• A combination of characteristic polynomials and averaging methods successfully reduces phase errors.
• Empirical optimization based on these methods significantly improves phase reconstruction performance.