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Fourier ptychography tomography (FPT) is a novel computational technique for coherent imaging in which the sample is numerically reconstructed from images acquired under various illumination directions. FPT is able to provide three-dimensional (3D) reconstructions of the complex sample permittivity with an increased resolution compared to standard microscopy. In this work, FPT is applied to coherent anti-Stokes Raman scattering (CARS) imaging. We show on synthetic data that complex third-order susceptibilities can be reconstructed in 3D from a limited number of widefield CARS images. In addition, we observe that the non-linear interaction increases significantly the potential of CARS-FPT compared to linear FPT in terms of resolution. In particular, with a careful choice of the pump and Stokes beam directions, CARS-FPT is able to provide optical sectioning even in transmission configuration.
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