Accurate reconstruction methods are needed to extend the reach of quantitative 3D microscopy to diverse samples in biology with illumination in an arbitrary states of spatial and temporal coherence. Recent research in optical diffraction tomography (ODT) reconstruction has incorporated non-invertible physics-based forward models, such as beam propagation or the Lippman-Schwinger equation, to overcome these effects. However, partially coherent methods have yet to incorporate more accurate physical models, as these artifacts are reduced by the incoherence of the illumination and require heavy computation. Here we leverage the sparsity of the 3D Green’s function solution to the Helmholtz equation in k-space to reduce the problem’s dimensionality to rapidly compute a partially coherent forward model, allowing for a gradient descent-type iterative solver to reconstruct 3D thick biological samples in a variety of illuminations, including broadband light.
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