Dependence of the focal shift on Fresnel number and f number

TLDR

The study examines axial intensity patterns from diffraction of a uniform converging spherical wave through a circular aperture using boundary‑diffraction wave theory. The aim is to locate the principal intensity maximum and clarify how focal shift depends on Fresnel and f numbers. Analytic and numerical results are compared with Farnell’s microwave experiments. Analytic and numerical calculations reveal the focal shift dependence on Fresnel and f numbers.

Abstract

The behavior along the axis of the intensity arising from the diffraction of a uniform, converging spherical wave at a circular aperture is studied on the basis of the theory of the boundary-diffraction wave. The results are used to determine the location of the principal intensity maximum and to elucidate the dependence of the focal shift both on the Fresnel number and on the f number of the focusing geometry. Analytic as well as numerical results are obtained. Comparison with microwave experiments of Farnell [ Can. J. Phys.36, 935 ( 1958)] is also made.