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Related Experiment Video

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Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
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Amplitude and phase retrieval with simultaneous diversity estimation using expectation maximization.

Joyce Fang, Dmitry Savransky

    Journal of the Optical Society of America. A, Optics, Image Science, and Vision
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    Summary
    This summary is machine-generated.

    This study introduces a new method using expectation-maximization and Kalman smoothing to accurately reconstruct wavefronts and lens positions from intensity images, improving accuracy by reducing errors.

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    Area of Science:

    • Optical metrology
    • Wavefront sensing
    • Computational imaging

    Background:

    • Iterative algorithms accurately reconstruct wavefronts from intensity measurements when system parameters are known.
    • Moving a lens to create phase diversity can introduce position errors, degrading reconstruction.
    • Accurate wavefront reconstruction is crucial in various optical applications.

    Purpose of the Study:

    • To develop a method for simultaneously recovering complex wavefronts and lens position from intensity images.
    • To improve the accuracy of wavefront reconstruction in the presence of lens position errors.
    • To address the limitations of existing iterative amplitude and phase retrieval algorithms.

    Main Methods:

    • Utilizing an expectation-maximization algorithm combined with Kalman smoothing.
    • Processing a stack of intensity images with induced phase diversity.
    • Employing nonlinear least-squares optimization for lens position estimation.

    Main Results:

    • Successfully recovered both the complex field (wavefront) and the moving lens position.
    • Demonstrated a significant reduction in the mean-squared-error of the estimated wavefront compared to methods without position error estimation.
    • Validated the effectiveness of the Kalman smoother and nonlinear least-squares optimization for lens position recovery.

    Conclusions:

    • The proposed expectation-maximization algorithm with Kalman smoothing offers a robust solution for accurate wavefront and lens position recovery.
    • This method enhances the reliability of phase retrieval in optical systems with moving components.
    • The findings have implications for improving imaging quality and system calibration in optical metrology.