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    This study introduces a multi-frequency phase merging (MFPM) approach to expand the depth range of binary defocusing systems for 3D measurements. By merging phase maps from different fringe frequencies, it overcomes limitations of the excessive defocusing zone (EDZ).

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    Area of Science:

    • Optics and Photonics
    • Metrology
    • Computer Vision

    Background:

    • Binary defocusing techniques offer high-speed and accuracy in three-dimensional (3D) measurement.
    • A key limitation is the excessive defocusing zone (EDZ), which restricts the measurable depth range.

    Purpose of the Study:

    • To propose and validate a novel multi-frequency phase merging (MFPM) approach.
    • To significantly enhance the large depth range (LDR) capability of binary defocusing systems for 3D surface measurement.

    Main Methods:

    • The MFPM approach leverages the finding that different fringe frequencies yield distinct, non-overlapping EDZs.
    • Phase maps from multiple binary fringes are merged to extend the measurement depth.
    • An optimal fringe frequency combination strategy is developed by analyzing phase error distribution.

    Main Results:

    • The proposed MFPM method effectively expands the measurement depth range.
    • Simulations and experimental results confirm the enhanced depth measurement capability.
    • The strategy for optimal fringe frequency selection proves effective in minimizing phase errors.

    Conclusions:

    • The MFPM approach successfully overcomes the EDZ limitation in binary defocusing systems.
    • This technique enables high-accuracy 3D measurement over a significantly larger depth range.
    • The method is validated for its effectiveness and robustness in practical applications.