The point spread function (PSF) is modeled for rapidSTORM purposes as a two-dimensional Gaussian function added to a background signal. This function has the parameters amplitude, background signal, center position and covariance matrix. We can assume the covariance matrix to be constant for any acquisition, and so only the amplitude, the background signal and the center position are fitted by the engine, while the covariance matrix is estimated iteratively by a second fitting process or given a-priori.

While this Gaussian model does not match the point spread functions of real systems exactly, it is a good approximation with easily computed derivatives. Studies such as Thomann et al. have shown that the approximation is good enough for practical purposes.