Two different methods are presented for efficient computation of two-dimensional wave fields in focal regions. Both methods are valid for arbitrarily large relative apertures. One method is based on the impulse-response integral and the other on the angular-spectrum representation. The latter method is used to analyze the discrepancy between applying the Kirchhoff or the Debye assumption to obtain an approximation for the field in the aperture. Two cases of idealized incident waves are analyzed in detail. First, we treat the case of a perfect incident wave, i.e., a wave that, in the limit of an infinitely large aperture, would produce a δ-function field distribution on the focal line if account were taken of evanescent waves. Second, the incident wave is taken to be the field radiated by a point source and subsequently focused by a lens that delays the phase of the incoming wave in a perfect manner without influencing its amplitude. The latter wave has the same phase distribution over the aperture as the perfect wave, but a different amplitude distribution.
© 1981 Optical Society of America
Jakob J. Stamnes, "Focusing of two-dimensional waves," J. Opt. Soc. Am. 71, 15-31 (1981)