Numerical simulations of vibration in phase-shifting interferometry.

Area of Science:

• Optical Metrology
• Computational Physics

Background:

• Phase-shifting interferometry is a key technique for precise surface measurement.
• Mechanical vibrations can introduce significant errors in interferometric measurements.
• Understanding and mitigating vibration effects is crucial for reliable optical metrology.

Purpose of the Study:

• To predict the root-mean-square (RMS) measurement error in phase-shifting interferometers due to mechanical vibrations.
• To evaluate the performance of different phase-shift algorithms under vibrational conditions.
• To validate a numerical model for vibration-induced errors.

Main Methods:

• Developed and numerically solved a nonlinear mathematical model of a phase-shifting interferometer.
• Performed computer simulations across various vibrational frequencies and amplitudes.
• Utilized three distinct phase-shift algorithms in the simulations.
• Conducted experimental validation using an interference microscope.
• Compared simulation results with analytical solutions.

Main Results:

• The study successfully predicted RMS measurement errors for different vibration parameters.
• The impact of vibrational frequencies and amplitudes on measurement error was quantified.
• The performance variations among the three phase-shift algorithms under vibration were identified.
• Experimental and analytical comparisons confirmed the accuracy of the numerical model.

Conclusions:

• Computer simulations provide an effective tool for predicting vibration-induced errors in phase-shifting interferometry.
• The validated model can guide the selection of appropriate phase-shift algorithms for specific vibration conditions.
• This work contributes to enhancing the robustness and accuracy of optical measurement systems.