Numerical model of a multiple-grating interferometer

A numerical model of a multiple-grating interferometer is presented. The foundation of the model is an efficient algorithm that computes the propagation of a wave governed by the Helmholtz equation between two parallel planes in O(N log N) time, where N is the number of transverse sample points. The algorithm provides a large improvement in computational time over O(N²) brute-force approaches and has the advantage that the computational time increases linearly with the number of planes in the interferometer. The model is applied to a three-grating atom interferometer to calculate the loss of contrast in the interference signal as a function of longitudinal grating misposition and to investigate the effects of wide beam-collimating slits.