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The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

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Numerical simulations of vibration in phase-shifting interferometry.

P J de Groot, L L Deck

|November 19, 2010

Summary

Computer simulations predict measurement errors in phase-shifting interferometers caused by mechanical vibrations. This research helps improve the accuracy of optical measurements in noisy environments.

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.

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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.