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    This study introduces a novel optical differentiation method for complete 2D field analysis. It overcomes limitations of prior techniques, enabling broader applications in optical computing and image identification.

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    Area of Science:

    • Optics and Photonics
    • Computational Science

    Background:

    • Optical differentiation is crucial for computation due to parallel processing capabilities.
    • Existing optical differential methods yield only partial differential information, limiting their application scope.

    Purpose of the Study:

    • To develop a general optical approach for obtaining complete differentiation of 2D fields.
    • To overcome the limitations of existing methods by enabling separate amplitude and phase differentiation, preserving negative values, and acquiring differentiation in arbitrary directions.

    Main Methods:

    • A novel optical differentiation technique is proposed.
    • The method's capability is demonstrated by measuring the differentiation of a Gaussian beam.
    • Practicality is verified through an experiment identifying the motion direction in a blurred image.

    Main Results:

    • The proposed method successfully obtains complete differentiation, including amplitude and phase components.
    • Negative differentiation values are preserved, and differentiation is achievable in arbitrary directions.
    • The technique proved effective in identifying motion direction in a practical image identification task.

    Conclusions:

    • The developed general optical differentiation approach offers a significant advancement over existing methods.
    • This technique has broad potential applications in intelligent algorithms, image identification, and optical analog computing.