Using exact equations in PSF calculations.

We are interested in calculating precisely the Point Spread Function (PSF) far from its maximum, where the maxima of the irradiance are falling to 1E-06, or less. The first and most used method consist in calculating the Fourier transform of the wavefront using the Fast Fourier Transform algorithm (FFT). Another method is using the Beam Superposition Technique (BST) to decompose the wavefront in Gaussian beams, propagate those beams, and recompose to obtain the result. The third method is to apply the exact equations derived at the end of last century and described in reference books like Born and Wolf or Marechal and Francon. We shall compare the results obtained with the three methods, FFT (CODE V), BST (ASAP) and exact calculation (MATLAB) in the case of a F/3 system working at 4000 nm, in focus and in presence of small defocusing.