The thermal emission from finite-size bodies is directly investigated without resorting to reciprocity. Specifically, an integral equation representing the electromagnetic field distribution on a conductive body under investigation is proposed. The source of the electromagnetic field is classic as it is an extension of Johnson noise sources to volumetric problems. The solution of the integral equation allows one to study the radiometric properties for geometries that are smaller than the investigated wavelengths, and in observation points, both in the near and in the far-field. The limits of validity of the formulation are clarified.

A Volumetric Method of Moments accelerated by means of iterative solvers combined with FFT matrix-vector products has been presented. The method allows analyzing small lens antennas with their integrated feeds efficiently since different structures and geometries can be studied with the same discretization, just by adding the material characteristics in post-processing.