Modified three-step iterative algorithm for phase-shifting interferometry in the presence of vibration

Area of Science:

• Optical Metrology
• Interferometry
• Surface Measurement

Background:

• Phase-shifting interferometry (PSI) is sensitive to mechanical vibrations.
• Vibrations introduce errors like tilt and fringe contrast variations.
• Existing algorithms struggle to fully compensate for these vibration-induced errors.

Purpose of the Study:

• To develop a robust algorithm for suppressing vibration sensitivity in PSI.
• To accurately calculate and compensate for tilt-shifting errors and fringe contrast variations.
• To enhance the precision of surface measurements obtained via interferometry.

Main Methods:

• A modified three-step iteration algorithm (MTIA) was proposed.
• Wavefront phase, x-, and y-directional phase shifts are calculated iteratively.
• Orthogonal decomposition and linear regression are used to solve tilt factors, avoiding nonlinear optimization.

Main Results:

• MTIA accurately calculates and compensates for tilt-shifting error and fringe contrast variation.
• Simulations demonstrated MTIA provides more accurate results than algorithms without contrast compensation.
• Experimental results confirmed MTIA suppresses vibration effects (amplitude > wavelength, wide frequency range) on surface measurements.

Conclusions:

• MTIA effectively suppresses the detrimental effects of mechanical vibration in phase-shifting interferometry.
• The algorithm offers improved accuracy and robustness for surface metrology.
• MTIA shows good insensitivity to increased exposure times, enhancing its practical applicability.