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Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
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Accelerated phase retrieval using adaptive support and statistical fringe processing of phase estimates.

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    Area of Science:

    • Optics and Photonics
    • Computational Imaging
    • Image Reconstruction

    Background:

    • Iterative phase retrieval methods are crucial for reconstructing object wavefronts from intensity measurements.
    • Conventional multiple-plane phase retrieval techniques can suffer from slow convergence and sensitivity to noise.
    • The development of efficient and robust phase retrieval algorithms is an ongoing challenge in optical sciences.

    Purpose of the Study:

    • To demonstrate an accelerated multiple-plane phase retrieval technique using adaptive support.
    • To introduce a novel approach combining phase estimates and statistical metrics for generating noise-robust support masks.
    • To quantify the improvement in convergence speed and data fitting performance compared to conventional methods.

    Main Methods:

    • Development of an adaptive support strategy based on the statistical analysis of phase estimates.
    • Implementation of a novel technique utilizing both phase estimates and a statistical metric for support mask generation.
    • Evaluation of data fitting performance using varying numbers of intensity recordings (two, three, and four or more).

    Main Results:

    • A fourfold improvement in convergence speed was achieved compared to the conventional multiple-plane phase retrieval method.
    • The adaptive support strategy demonstrated noise-robustness in generating support masks.
    • Accurate data fitting was achieved with four or more intensity recordings; three led to overfitting, and two to underfitting.

    Conclusions:

    • The demonstrated adaptive support technique significantly accelerates multiple-plane phase retrieval.
    • The novel combination of phase estimates and statistical metrics provides a robust and efficient method for generating support masks.
    • This adaptive support strategy holds potential for application in various iterative phase retrieval algorithms.