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    Area of Science:

    • Optical Metrology
    • 3D Surface Profilometry
    • Image Processing

    Background:

    • Phase-measurement profilometry (PMP) is susceptible to nonlinear phase pattern distortion caused by the gamma effect.
    • Gamma correction is vital for accurate surface profile reconstruction using commercial projectors.
    • Projector defocusing introduces errors in gamma estimation, affecting PMP accuracy.

    Purpose of the Study:

    • To develop a robust gamma calculation method for PMP that accounts for projector defocusing.
    • To improve the accuracy of gamma correction in the presence of nonlinear distortions.
    • To enhance the quality of reconstructed 3D surface profiles.

    Main Methods:

    • Constructing a gamma mapping using duty ratio (DR) to encode simulated distorted phase chord distribution.
    • Considering projector defocusing in the gamma mapping construction.
    • Calculating accurate gamma by applying DR coding to the actual distorted phase under defocusing.

    Main Results:

    • Simulated experiments showed relative errors in calculated gamma less than 3.5% under varying degrees of defocus.
    • The proposed method demonstrated robustness against projector defocusing effects.
    • Gamma correction using the proposed method led to smoother reconstructed surface profiles.

    Conclusions:

    • The developed gamma calculation method effectively addresses projector defocusing in PMP.
    • Accurate gamma estimation is achievable even with optical system imperfections.
    • The method significantly improves the fidelity of 3D surface reconstruction in PMP.