Conditions for the validity of the Debye integral representation of focused fields

Abstract A very simple sufficiency condition is obtained, under which the Debye diffraction integral may be expected to give a good approximation to the solution of a boundary value problem that is generally taken to represent a field in the region of focus. When the angular aperture of the focusing system is sufficiently small, the condition reduces to the requirement that the Fresnel number of the diffracting aperture, when viewed from the geometrical focus, is large compared to unity.