Numerical correction of reference phases in phase-shifting interferometry by iterative least-squares fitting

Area of Science:

• Optical Metrology
• Computational Physics

Background:

• Phase-shifting interferometry (PSI) is a key technique for precise surface measurement.
• Uncertainty in reference phase values introduces significant errors in PSI measurements.
• Existing methods struggle to fully eliminate errors caused by nonlinear and random phase shifter behavior.

Purpose of the Study:

• To develop a novel computational algorithm for phase-shifting interferometry.
• To eliminate uncertainty errors associated with reference phase determination.
• To enhance the accuracy and robustness of interferometric measurements.

Main Methods:

• A new algorithm treats reference phases as additional unknowns.
• Numerical least-squares technique is employed to determine exact reference phase values.
• Interferograms are analyzed to solve for both phase maps and reference phases simultaneously.

Main Results:

• The algorithm effectively eliminates reference phase uncertainty errors.
• Simulations demonstrate improved measurement accuracy compared to conventional methods.
• The technique shows robustness against nonlinear and random phase shifter errors.

Conclusions:

• The proposed computational algorithm significantly enhances the accuracy of phase-shifting interferometry.
• This method offers a reliable solution for mitigating reference phase errors.
• The algorithm provides a more robust and precise tool for optical metrology applications.