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    Area of Science:

    • Optics and Photonics
    • Computational Imaging
    • Materials Science

    Background:

    • Optical diffraction tomography (ODT) reconstructs sample properties by solving inverse scattering problems based on the wave equation.
    • Traditional ODT algorithms use linear approximations (Born, Rytov), limiting reconstructions to low-contrast, thin samples due to unaddressed multiple scattering effects.
    • Nonlinear models in ODT enhance reconstruction quality by incorporating multiple scattering and reflections, crucial for complex biological and material samples.

    Purpose of the Study:

    • To develop a more computationally efficient method for nonlinear optical diffraction tomography.
    • To enable high-fidelity imaging of samples with significant refractive index variations and complex structures.
    • To reduce the computational complexity and memory footprint of advanced ODT reconstruction algorithms.

    Main Methods:

    • Derivation of an explicit formula for the Jacobian matrix within the nonlinear Lippmann-Schwinger model.
    • Efficient evaluation of the gradient of the data-fidelity term using the derived Jacobian.
    • Application of efficient optimization methods to solve the inverse problem under sparsity constraints.

    Main Results:

    • The derived explicit Jacobian formula significantly reduces computational complexity and memory requirements for nonlinear ODT.
    • Efficient gradient evaluation facilitates the deployment of advanced optimization techniques for inverse problem solving.
    • The method enables high-quality reconstructions by effectively handling multiple scattering and reflections in complex samples.

    Conclusions:

    • The proposed method offers a computationally feasible approach to nonlinear optical diffraction tomography.
    • This advancement improves the accuracy and applicability of ODT for imaging intricate structures in various scientific fields.
    • The efficient Jacobian calculation is key to unlocking the potential of nonlinear models for robust inverse scattering solutions.