The diffraction theory of optical aberrations : Part III: General formulae for small aberrations; experimental verification of the theoretical results

Abstract In extension of the theoretical results obtained before, formulae are given from which the intensity distribution in the diffraction pattern received in a suitably chosen focal plane may be calculated while single third order aberrations are present of such an amount that the maximum deviation of the wavefront from a spherical wave is of the order of λ or less. By way of example some special cases (with larger aberrations than dealt with before) are numerically evaluated. A very simple result is obtained in the case of astigmatism for the intensity at the centre of the pattern situated in the plane midway between the focal lines (the so-called “definition”). The diffraction patterns have also been investigated experimentally by photographing the image of a light source emitting coherent light formed by a lens having single aberrations of known magnitude. Some patterns, in particular those which had been calculated, were evaluated. There is good agreement between the theoretical and experimental results.