Fast calculation of the line-spread-function by transversal directions decoupling

We propose a simplified method to calculate the optical spread function of a paradigmatic system constituted by a pupil-lens with a line-shaped illumination (line-spread-function). Our approach is based on decoupling the two transversal directions of the beam and treating the propagation by means of the Fourier optics formalism. This requires simpler calculations with respect to the more usual Bessel-function-based method. The model is discussed and compared with standard calculation methods by carrying out computer simulations. The proposed approach is found to be much faster than the Bessel-function-based one (CPU time ≲5% of the standard method), while the results of the two methods present a very good mutual agreement.