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Related Experiment Video

Updated: Nov 1, 2025

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
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Photon-limited bounds for phase retrieval.

Timothy J Schulz, David J Brady, Chengyu Wang

    Optics Express
    |June 22, 2021
    PubMed
    Summary
    This summary is machine-generated.

    We determined the optimal limit for estimating coherent signals using photon-limited data. This limit is achievable with phase-retrieval systems, even without a reference beam, advancing optical measurement techniques.

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    Area of Science:

    • Optical physics
    • Information theory
    • Signal processing

    Background:

    • Photon-limited measurements pose challenges for coherent signal estimation.
    • The Cramér-Rao lower bound (CRLB) quantifies estimation error.
    • Phase-quadrature holography is a known method for signal estimation.

    Purpose of the Study:

    • To establish the optimal CRLB for coherent signal estimation from intensity measurements.
    • To identify methods that can achieve this optimal bound.
    • To analyze bounds for phase-retrieval and ptychography.

    Main Methods:

    • Theoretical derivation of the Cramér-Rao lower bound for coherent signals.
    • Analysis of phase-quadrature holography performance.
    • Investigation of phase-retrieval systems without a coherent reference.
    • Evaluation of bounds for phase-retrieval and ptychography.

    Main Results:

    • The optimal CRLB is equal to the number of signal elements (or N-1 with unobservable reference phase).
    • Phase-quadrature holography attains this bound.
    • Phase-retrieval systems without a reference beam can also attain the bound.
    • Bounds for phase-retrieval and ptychography were derived.

    Conclusions:

    • Optimal coherent signal estimation is achievable with intensity measurements.
    • Phase-retrieval techniques offer a viable alternative to holography for optimal estimation.
    • Practical coding strategies can approach theoretical performance limits in phase-retrieval methods.