It has been known for some time that the range and phase normalized far field is proportional to the three‐dimensional spatial Fourier transform of the source distribution, taken on the surface of the Ewald sphere at a fixed frequency. Unfortunately, however, this very useful relationship is neither widely known, nor does there even exist for it a good, short, simple, and direct derivation in the open literature (thus making references to the relationship difficult). The purpose of this paper is to alleviate these difficulties by presenting a brief derivation of the relationship for both the scalar acoustic as well as the vector electromagnetic cases. A brief discussion of the implications of this relationship on the inverse source and inverse scattering problem is also presented.