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Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

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Design of algorithms for phase shifting interferometry using self-convolution of the rectangle window.

Zhenguang Shi¹, Jian Zhang, Yongxin Sui

¹State Key Laboratory of Applied Optics, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun, Jilin 130033, China. shizg@ciomp.ac.cn

|September 22, 2011

Summary

This study introduces novel phase shifting algorithms designed to resist errors from nonlinearities in phase-shift errors and detectors. The new algorithms demonstrate improved error resistance compared to existing methods.

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Area of Science:

Optical Engineering
Signal Processing

Background:

Phase shifting algorithms are crucial for optical metrology.
Nonlinearities in phase-shift errors and detectors limit algorithm accuracy.
Existing algorithms struggle with simultaneous nonlinearities.

Purpose of the Study:

To design novel phase shifting algorithms resistant to simultaneous nonlinearities.
To enhance error-resistance capabilities of phase shifting techniques.
To improve accuracy in optical measurements despite detector and phase errors.

Main Methods:

Proposed a construction approach based on self-convolution of a rectangle window.
Designed algorithms with perfect zero point distribution in their Fourier transform.
Utilized theoretical analysis and numerical simulations for validation.

Main Results:

Developed algorithms with enhanced error-resistant capabilities.
Demonstrated superior performance against CCD-caused harmonics and PZT ramping nonlinearity.
Validated the approach through comparison with a commercial 13-frame algorithm.

Conclusions:

The proposed self-convolution approach effectively designs error-resistant phase shifting algorithms.
The new algorithms offer improved robustness against common sources of optical measurement error.
This method provides a pathway for more accurate optical measurements in the presence of nonlinearities.