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    This study addresses spatial phase non-uniformity in Fizeau interferometry for spherical surface testing. A novel convolution technique minimizes phase measurement errors caused by algorithm differences.

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    Area of Science:

    • Optical metrology
    • Interferometry
    • Surface testing

    Background:

    • Fizeau interferometry is crucial for high-numerical-aperture spherical surface testing.
    • Spatially nonuniform mechanical phase shifts occur within the observation aperture.
    • Existing methods struggle with phase shift nonlinearity and associated errors.

    Purpose of the Study:

    • To investigate and mitigate phase measurement errors in Fizeau interferometry.
    • To address bias errors at regional boundaries caused by aperture division.
    • To propose and validate a new technique for improving phase measurement accuracy.

    Main Methods:

    • Dividing the observation aperture into annular regions.
    • Calculating object phase using algorithms tailored for different phase shifts.
    • Developing a convolution technique to modify sampling windows and align error coefficients.

    Main Results:

    • Aperture division reduced spatial non-uniformity but introduced boundary bias errors.
    • The proposed convolution technique effectively minimized phase measurement errors.
    • Experimental validation confirmed the technique's efficacy.

    Conclusions:

    • The developed convolution technique offers a robust solution for phase measurement errors in Fizeau interferometry.
    • Accurate testing of high-numerical-aperture spherical surfaces is improved.
    • This method enhances the reliability of optical metrology for complex surfaces.