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In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
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Model-independent nonlinearity rectification algorithm using a phase-probability-equalization-based look-up table.

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    This study introduces a new nonlinear rectification algorithm for fringe projection systems. It effectively corrects phase errors and artifacts, improving accuracy and efficiency in 3D measurements.

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    Area of Science:

    • Optics and Photonics
    • Metrology
    • Computer Vision

    Background:

    • Fringe projection systems are susceptible to nonlinearities causing artifacts like gamma effect and phase-shifting errors.
    • Existing methods often address only specific nonlinearity models and struggle with coupled nonlinearities.

    Purpose of the Study:

    • To propose a model-independent nonlinear rectification algorithm for fringe projection systems.
    • To enhance the accuracy and robustness of 3D measurements in the presence of nonlinearities.

    Main Methods:

    • Developed a model-independent nonlinear rectification algorithm using phase probability equalization (PPE).
    • Constructed a lookup table (LUT) correlating phase error with wrapped phase on flat areas.
    • Retrieved accurate phase by subtracting a searched phase error.

    Main Results:

    • The proposed algorithm demonstrates robustness to object height variations.
    • Achieved superior rectification performance on incomplete fringe periods compared to traditional full-field PPE.
    • Exhibited higher efficiency due to local processing and non-iterative nature.

    Conclusions:

    • The novel algorithm effectively rectifies nonlinearities in fringe projection systems.
    • Offers improved accuracy, robustness, and efficiency for 3D measurement applications.
    • Presents a significant advancement over existing nonlinearity correction techniques.