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We present a physically-based computational model of the light sheet fluorescence microscope (LSFM). Based on Monte Carlo ray tracing and geometric optics, our method simulates the operational aspects and image formation process of the LSFM. This simulated, in silico LSFM creates synthetic images of digital fluorescent specimens that can resemble those generated by a real LSFM, as opposed to established visualization methods producing visually-plausible images. We also propose an accurate fluorescence rendering model which takes into account the intrinsic characteristics of fluorescent dyes to simulate the light interaction with fluorescent biological specimen.