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    Area of Science:

    • Optical metrology
    • Image processing
    • Phase demodulation

    Background:

    • Fringe pattern analysis is crucial for optical metrology.
    • Existing methods struggle with unknown, non-uniform phase shifts (tilt-shift error).
    • Accurate phase demodulation is essential for reliable measurements.

    Purpose of the Study:

    • To develop a robust algorithm for fringe pattern phase demodulation.
    • To address and correct for unknown, linearly non-uniform phase shifts (tilt-shift error).
    • To provide a method effective for both small and large tilt angles.

    Main Methods:

    • Intensity-based filtration to isolate the tilt-shift component.
    • A two-step nonlinear error functional minimization process.
    • Validation using both simulated and experimental fringe pattern data.

    Main Results:

    • The algorithm successfully performs phase demodulation with high accuracy.
    • Demonstrated robustness against varying degrees of tilt-shift error.
    • The method exhibits good numerical properties and stability.

    Conclusions:

    • The presented algorithm offers a reliable solution for phase demodulation under tilt-shift error.
    • It provides accurate results for a wide range of tilt magnitudes.
    • The availability of numerical codes facilitates practical application and further research.