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    A new least-squares integration (LSI) method accurately reconstructs specular surface shapes from large, quadrilateral gradient data in deflectometry. This enhanced LSI method improves surface reconstruction accuracy for optical metrology applications.

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    Area of Science:

    • Optical Metrology
    • Computational Imaging
    • Surface Metrology

    Background:

    • Deflectometry is crucial for reconstructing specular surface shapes.
    • Traditional least-squares integration (LSI) and radial basis function integration (RBFI) have limitations with large, non-rectangular gradient datasets.
    • Existing methods struggle with the practical challenges of real-world measurement data.

    Purpose of the Study:

    • To develop a novel least-squares integration (LSI) method for accurate specular surface reconstruction.
    • To address the limitations of traditional LSI and RBFI methods when dealing with large, quadrilateral gradient data.
    • To enhance the accuracy and applicability of deflectometry measurements.

    Main Methods:

    • A new LSI method is proposed, approximating normal vector perpendicularity.
    • The method integrates large gradient datasets with quadrilateral grids.
    • A small RBFI-integrated dataset serves as a supplementary constraint.

    Main Results:

    • The proposed LSI method demonstrates effectiveness in simulation and experimental tests.
    • Accurate specular surface shape reconstruction was achieved with challenging datasets.
    • The method overcomes limitations of traditional LSI and RBFI for large-scale measurements.

    Conclusions:

    • The novel LSI method provides an accurate and effective solution for specular surface reconstruction in deflectometry.
    • This approach enhances the capability of optical metrology for complex surface analysis.
    • The findings support the practical application of the proposed method in industrial settings.