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    Area of Science:

    • Optical Engineering
    • Computational Imaging
    • Adaptive Optics

    Background:

    • Single-shot phase retrieval techniques are crucial for efficient optical system analysis.
    • Conventional methods often face limitations in handling complex aberrations and noise.
    • The need for advanced techniques that incorporate both amplitude and phase information is evident.

    Purpose of the Study:

    • To introduce and validate a complex diversity concept for single-shot phase retrieval.
    • To enhance the accuracy of aberration estimation in optical systems.
    • To demonstrate the application of complex diversity in sensorless adaptive optics.

    Main Methods:

    • Designing complex-number pupil filters with amplitude and phase values.
    • Utilizing numerical propagation from computer-generated holograms for multi-image acquisition.
    • Employing a modified Fourier iterative algorithm with area restriction for reconstruction.

    Main Results:

    • Numerical simulations demonstrated superior estimation of extrinsic Kolmogorov aberration compared to conventional single-shot techniques.
    • Experiments successfully achieved sensorless adaptive optics correction using the complex diversity method.
    • The technique effectively mitigates noise amplification during reconstruction.

    Conclusions:

    • Complex diversity offers a robust framework for single-shot phase retrieval, addressing system design and reconstruction challenges.
    • The developed method significantly improves aberration estimation accuracy for distant objects.
    • Complex diversity is a viable technique for real-time adaptive optics correction in optical systems.