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In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.
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All-optical uncertainty visualization for ill-posed image restoration tasks.

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    Area of Science:

    • Optics and Photonics
    • Artificial Intelligence
    • Computational Imaging

    Background:

    • Diffractive neural networks (DNNs) offer efficient all-optical visual data processing, reducing computational load.
    • Current DNNs provide single reconstructions for ill-posed imaging problems, failing to represent reconstruction uncertainty.
    • This limitation hinders applications requiring reliable uncertainty quantification.

    Purpose of the Study:

    • To develop a passive all-optical diffractive network capable of outputting multiple plausible reconstructions.
    • To introduce a training loss function that enables simultaneous multi-reconstruction generation.
    • To visualize reconstruction uncertainty in computational imaging tasks.

    Main Methods:

    • Designed a passive all-optical diffractive network architecture.
    • Implemented a dedicated training loss to facilitate multiple outputs.
    • Numerically validated the method on spatial super-resolution and imaging through occlusions.

    Main Results:

    • The proposed diffractive network successfully generated multiple diverse reconstructions for each input.
    • The set of outputs effectively visualized the inherent uncertainty in image reconstruction.
    • Demonstrated efficacy in spatial super-resolution and imaging beyond opaque occluders.

    Conclusions:

    • The developed method provides a crucial first step towards uncertainty-aware all-optical image reconstruction.
    • This approach has potential for scientific and safety-critical computational imaging applications.
    • Passive all-optical processing can be advanced for reliable image reconstruction by quantifying uncertainty.