On the foundation of the scalar diffraction theory of optical imaging

Abstract

In this paper the relationship between the rigorous vector theory and the approximate scalar theory is investigated and the usual procedure of calculating the intensity in optical images from a single scalar wave-function is justified. Unlike the earlier discussion of Picht (1925) the present analysis takes fully into account the polarization and amplitude properties which an actual light source and the optical instrument impose upon the radiation field. In the calculations of diffraction images the effect of the non-monochromatic nature of natural light is usually disregarded. We give an estimate for the maximum wave-length spread of the source which will give rise to a diffraction pattern that may be calculated from the single monochromatic wave-function of the scalar theory. We find that one of the main reasons for the validity of the scalar theory for wide class of optical instruments is the fact that each monochromatic component of the spectrum gives rise to E and H fields with the property that at any particular instant of time they are nearly constant over each of the geometrical wave-fronts which are not too close to the source or the image region.