Direct inversion algorithm for focal plane scanning optical projection tomography

To achieve approximately parallel projection geometry, traditional optical projection tomography (OPT) requires the use of low numerical aperture (NA) objectives, which have a long depth-of-field at the expense of poor lateral resolution. Particularly promising methods to improve spatial resolution include ad-hoc post-processing filters that limit the effect of the system's MTF and focal-plane-scanning OPT (FPS-OPT), an alternative acquisition procedure that allows the use of higher NA objectives by limiting the effect of their shallow depth of field yet still assumes parallel projection rays during reconstruction. Here, we provide a detailed derivation that establishes the existence of a direct inversion formula for FPS-OPT. Based on this formula, we propose a point spread function-aware algorithm that is similar in form and complexity to traditional filtered backprojection (FBP). With simulations, we demonstrate that our point-spread-function aware FBP for FPS-OPT leads to more accurate images than both traditional OPT with deconvolution and FPS-OPT with naive FBP reconstruction. We further illustrate the technique on experimental zebrafish data, which shows that our approach reduces out-of-focus blur compared to a direct FBP reconstruction with FPS-OPT.