Abstract

The classical Lommel intensity distribution in the vicinity of the focus of a uniform spherical wave diffracted by a circular aperture is found to be in error in large f/No. systems. In particular, the point of maximum intensity is not found at the geometrical focus but is shifted toward the aperture. We consider the more general problem of a uniform spherical wave which is diffracted by a circular aperture and then focused by a lens. The Huygens-Fresnel integral is solved to obtain the axial intensity distribution following the lens. The result is where G (z) is the geometrical intensity (obtained in the absence of diffraction) and F (z) is the number of Fresnel half-period zones at z. The migration of the intensity maximum from the geometrical focus, known as the focal shift, is found to be dependent on the aperture–lens separation. Defining this separation to be z₀ and the focal length to be f, we find that, for z₀ < f, the focal shift is toward the lens and, for z₀ > f, it is away from the lens. When z₀ = f there is no focal shift even for small aperture radii, and the classical result is retrieved.

© 1986 Optical Society of America