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    This study introduces an analytical method for single-pixel ptychography (SPP) reconstruction, offering a unique and determined solution. This approach simplifies complex-field imaging by avoiding iterative methods and enhancing understanding of optical parameters.

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    Area of Science:

    • Optics and Photonics
    • Computational Imaging

    Background:

    • Single-pixel ptychography (SPP) enables non-interferometric complex-field imaging.
    • Conventional SPP reconstruction methods are iterative and nondeterministic, hindering the understanding of optical parameters.

    Purpose of the Study:

    • To develop an analytical approach for unique SPP reconstruction.
    • To provide a theoretical foundation for SPP reconstruction uniqueness.
    • To offer an alternative to iterative reconstruction techniques.

    Main Methods:

    • Conceptualizing SPP as a system of linear equations in the frequency domain.
    • Involving both the object and modulated illumination in the equation system.
    • Solving the equation system to determine the complex object.

    Main Results:

    • Validated the uniqueness of SPP reconstruction through simulations.
    • Demonstrated an analytical solution for complex-field imaging.
    • Identified key properties influencing reconstruction accuracy.

    Conclusions:

    • The proposed analytical method provides a unique and determined solution for SPP reconstruction.
    • This approach offers a valuable alternative to traditional iterative methods.
    • Enhanced understanding of SPP and its optical parameters is achieved.