Radiometric analysis of diffraction

Abstract

A description of Fresnel and Fraunhofer diffraction of quasi‐homogenous optical fields in any state of spatial coherence is presented, which clearly differs from the classical formalism. Instead of the propagation of the cross‐spectral density from the diffracting aperture to the observation plane, the diffracting aperture is regarded as a planar quasi‐homogeneous source, whose generalised radiance is carried by the spatial coherence wavelets, and the power distribution at the observation plane is expressed in terms of the generalised radiant intensity. It allows interpreting the negative values of the generalised radiance as “negative energies” emitted along specific directions and subjected to the achievement of the conservation law of energy. This interpretation is not evident in the classical formalism. Consequently, interference can be thought as resulting of energy transfer over a given wavefront, due to the addition of equal amounts of “positive” and “negative” energies, along specific directions, to the contributions provided by the individual radiators of the radiant source. In this sense, the radiant flux from the source, which is provided only by the individual contributions, is redistributed depending on the spatial coherence properties of the field. This redistribution characterises the diffraction phenomenon. It is also shown that the supports of the complex degree of spatial coherence near the aperture edge are vignetted by the edge. This feature is a cause for the generalised radiance providing “negative energies”, and constitutes the actual effect of the edge on diffraction. The approach is validated by the close concordance between the numerical and the experimental results, which should be regarded as a proof of the physical existence of the spatial coherence wavelets.