The following properties of the spheroidal wave functions of zero order important for diffraction optics are considered: invariance with respect to the Fourier transform, immunity to diaphragm adjusting in optical systems, and self-reproducibility at a certain distance in a free space. The effect of the size of a diaphragm on the accuracy of signal transmitting matched with prolate spheroidal functions by lens systems is studied. A comparison with the Gaussian and Hermitian functions is carried out.
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