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    Area of Science:

    • Optical metrology
    • Surface characterization
    • Non-destructive testing

    Background:

    • Accurate measurement of transparent planar elements is crucial for high-accuracy optical systems.
    • Existing Fourier-based methods face challenges with closely spaced frequencies and spectral leakage, limiting surface-reconstruction accuracy.
    • Short data records exacerbate frequency separation issues in traditional algorithms.

    Purpose of the Study:

    • To develop an advanced phase measuring deflectometry method for high-precision measurement of transparent planar elements.
    • To overcome the limitations of Fourier-based algorithms in frequency resolution and spectral overlap.
    • To enable non-destructive, in-situ surface reconstruction of transparent components.

    Main Methods:

    • Combines the Root-Multiple Signal Classification (Root-MUSIC) algorithm with the Non-dominated Sorting Genetic Algorithm II (NSGA-II).
    • Utilizes eigenvalue analysis of intensity sequence covariance matrices to estimate noise subspace and initial reflection coordinates.
    • Employs a nonlinear optimization framework with NSGA-II to minimize mean square error for iterative convergence.

    Main Results:

    • Numerical simulations achieved a root mean square (RMS) reconstruction error of 5 nm for a 10 mm-thick glass element.
    • Experimental tests on a 55 mm-diameter window glass yielded an RMS error of 59 nm compared to interferometry.
    • Root-MUSIC demonstrated enhanced frequency resolution over multi-frequency methods, with parallel computation improving efficiency.

    Conclusions:

    • The proposed Root-MUSIC and NSGA-II combined method offers superior frequency resolution and accuracy for transparent element measurement.
    • This technique provides a non-destructive and high-precision solution for in-situ metrology of optical components.
    • The approach effectively addresses spectral leakage and overlap issues inherent in traditional Fourier-based algorithms.