Application of Coherence Theory to Modeling of Blackbody Radiation at Close Range

We apply coherence-propagation theory to model the radiation generated by a planar passive thermal source of any state of coherence. Of our particular interest is the blackbody calibration source with partially coherent characteristic that produces the radiant intensity with its angular distribution following Lambert’s cosine law in the far field. A closed-form expression of the Poynting vector of the electromagnetic field is obtained from the theoretical framework. The formulation links the radiation field to the correlation function of the sources in a straightforward manner, though numerical computation of the Poynting vector involves evaluation of a quadruple integral and is difficult to implement directly, especially when the observation of radiation occurs at a close distance from the source. The study of the close-range radiation would, in particular, benefit the microwave remote sensing radiometric calibration that is encountered in terrestrial laboratories and space-borne satellites. To tackle the challenges in numerical calculation, we have made a few mathematical adjustments to develop a feasible scheme for improved computational efficiency, including reformulation in the angle-impact notation and various simplifications of the integration. We apply the theory and numerical techniques to simulate thermal radiation in some illustrative examples such as an isothermal blackbody source, a blackbody misaligned from the on-axis position, and a nonuniformly heated blackbody target. The coherence property of the blackbody source is shown to possess influential impacts on the radiation arising from such a source, especially in the near-field range where most measurements of the radiation take place in a practical system. The theory and technical approaches provide a systematic and reliable way to quantify the Poynting vector radiated by the blackbody source in a microwave remote-sensing radiometer.