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    This study introduces two efficient methods to correct nonlinear errors in 3D measurements using fringe projection profilometry (FPP). These techniques improve accuracy and boost measurement efficiency by 34% compared to existing methods.

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    Area of Science:

    • Optics and Photonics
    • Metrology and Measurement Science
    • Computer Vision and Image Processing

    Background:

    • Nonlinear projector response in Fringe Projection Profilometry (FPP) significantly impacts 3D measurement accuracy.
    • The Double N-Step Phase-Shifting Method (DNPSM) corrects nonlinear errors but reduces measurement efficiency due to increased fringe patterns.
    • Existing methods struggle to balance accuracy improvement with efficient 3D data acquisition.

    Purpose of the Study:

    • To propose and evaluate two novel Nonlinear-Induced Phase Error Correction (NIPEC) methods for FPP.
    • To enhance the efficiency of 3D measurement while maintaining high accuracy.
    • To address the trade-off between accuracy and speed in FPP.

    Main Methods:

    • Optimizing the DNPSM by strategically adding fringe patterns in high-frequency regions, reducing the total count from 18 to 12.
    • Introducing a Hilbert transform-based three-step phase-shifting algorithm (PSA) that synthesizes phase-shifted patterns without additional projections.
    • Implementing and comparing the proposed NIPEC methods against traditional DNPSM.

    Main Results:

    • Both proposed NIPEC methods effectively suppress periodic ripple phase errors.
    • The optimized DNPSM reduced fringe patterns from 18 to 12, enhancing efficiency.
    • The Hilbert transform-based PSA achieved comparable error correction without extra fringe patterns.
    • Overall measurement efficiency improved by 34% compared to the traditional DNPSM.

    Conclusions:

    • The developed NIPEC methods offer a significant improvement in both accuracy and efficiency for FPP systems.
    • The Hilbert transform-based approach presents a particularly efficient solution by eliminating the need for additional fringe patterns.
    • These advancements contribute to more practical and faster 3D measurement applications.