A simple determination approach for zero-padding of FFT method in focal spot calculation

FFT is a widely utilized method to calculate focal spot, in which zero padding is needed to adjust the sampling interval on the focal plane. This work is to apply Abbe limit of resolution to determining of the number of padded zeros when sampling interval on focal plane is given. We specifically investigate the correlation of digitized Fraunhofer diffraction and discrete Fourier transform (DFT) in a lens model. The theoretical support for zero padding on the back focal plane (BFP) is illustrated based on a hypothesis of lens with finite numerical aperture. The proposed hypothesis and the zero padding approach are verified by focal spots calculation, where lights polarized linearly and radially are used as samples.