Recently exact and approximate solutions were presented for focusing of two-dimensional scalar and electromagnetic waves through a slit aperture in a perfectly conducting screen. We present, on the basis of these solutions, numerical comparisons between exact results and approximate Debye and Kirchhoff results for a variety of different focusing geometries. At moderately low Fresnel numbers large discrepancies are found between Debye and Kirchhoff results, and the latter are found to show greater agreement with the exact results. However, at low Fresnel numbers and large angular apertures significant discrepancies are also found between exact and Kirchhoff results, particularly at observation points inside the geometrical focus.
© 1998 Optical Society of America
(050.1220) Diffraction and gratings : Apertures
(220.2560) Optical design and fabrication : Propagating methods
(260.2110) Physical optics : Electromagnetic optics
(350.7420) Other areas of optics : Waves
Hans A. Eide and Jakob J. Stamnes, "Exact and approximate solutions for focusing of two-dimensional waves. II. Numerical comparisons among exact, Debye, and Kirchhoff theories," J. Opt. Soc. Am. A 15, 1292-1307 (1998)