Optical Systems, Singularity Functions, Complex Hankel Transforms

Two-dimensional singularity functions are discussed and used to determine the point spread of an optical system from its line spread. Certain properties of Fourier, Hankel and Hilbert transforms are developed and applied in the study of two-dimensional systems.The notion of the complex Hankel transform is introduced in terms of the Struve function, defined as the Hilbert transform of the Bessel function. As an application, a simple derivation of the Schlömilch series is given.