Understanding the interactions between light and small samples at the diffraction limit is critical for solving inverse problems in microscopy. Several models for light and matter interactions have been proposed, including Born and Rytov approximations, Mie theory, T-matrix, Finite element methods, and coupled wave theory. Coupled wave approaches provide unique advantages for realistic samples by allowing refinement of the sample in the Fourier domain, where many realistic samples are considered sparse. However, this model still relies on computationally intensive operations as the sample and field resolution increases. In this paper, we develop an optimized open-source tool using established coupled-wave theory. This can be computationally efficient for realistic problems, since many practical samples are sparse in the Fourier domain. Then we analyze the computational complexity of the model and optimize the process.
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