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Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
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Random phase shifting shadow moiré using a one-dimensional minimizer.

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    This study introduces a novel technique for accurate phase demodulation in shadow moiré systems. It effectively addresses the challenge of estimating unknown phase shifts from random fringe patterns, enhancing measurement precision.

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    Area of Science:

    • Optical Metrology
    • Interferometry
    • Image Processing

    Background:

    • Shadow moiré systems benefit from random phase-shifting techniques for improved measurement accuracy.
    • Simultaneously estimating unequal and unknown phase shifts in these systems remains a significant challenge.
    • Existing optical metrology phase-shifting techniques face limitations with random phase shifts.

    Purpose of the Study:

    • To present a novel one-dimensional minimizer-based technique for phase demodulation.
    • To address the ill-posed problem of phase demodulation from random phase-shifting patterns.
    • To enhance accuracy and robustness in optical metrology measurements.

    Main Methods:

    • A one-dimensional minimizer-based technique is proposed.
    • Two new sets of connected fringe patterns are constructed via normalization.
    • A generalized phase-shifting algorithm is developed using modulation factor's standard deviation distribution.

    Main Results:

    • The proposed method successfully addresses the challenge of estimating unequal and unknown phase shifts.
    • Numerical simulations and optical experiments validate the technique's effectiveness.
    • High accuracy and robustness in phase demodulation were demonstrated.

    Conclusions:

    • The developed technique offers a robust solution for phase demodulation in shadow moiré systems with random phase shifts.
    • This method advances optical metrology by enabling precise measurements even with unknown phase shifts.
    • The findings pave the way for more accurate and reliable optical measurement applications.