Two image reconstruction methods for 3D lens-based intensity diffraction tomography (I-DT) are developed that account for the effects of a focusing lens placed between the object and the detector. One reconstruction method is a generalization of the original I-DT method and requires measurement of the transmitted wavefield intensity on two detector planes behind the object at each tomographic view angle. The second method employs a data-acquisition strategy in which the two intensity measurements are acquired, in turn, on a fixed detector plane, corresponding to distinct forms of lens aberration. Preliminary computer-simulation studies are conducted to demonstrate the numerical implementation of both methods and corroborate their mathematical correctness.
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