Spatial Distribution of Thermal Radiation at Microwave Frequencies

Theoretical and experimental radiation patterns are given in spectral form for the thermal radiation from thin slots or heated wires having dimensions of the order of the comparison wavelength. Maxwell's equations and noise theory form the basis of the analyses in which three independent methods are used to predict a spatial distribution which exhibits interference minima and maxima. In the first, the wave equation is solved for a noise-excited transmission line which is suddenly short- and open-circuited at alternate ends. By a study of the trapped noise currents, it is found that the radiation pattern has an interference structure which is smoothed as the loss is increased. Secondly, a formula is derived for the radiation pattern of a heated wire by a computation of its absorption in an isothermal enclosure and by an application of the principle of detailed balancing. Finally, the pattern of a long thin slot is computed directly using the Lpontovich-Rytov distributed source generalization of Nyquist's noise formula. Fraunhofer pattern measurements are taken for a thin slot excited by a gaseous discharge at 10,100 ± 200°K. The pattern measuring apparatus is a Dicke radiometer having the following characteristics: frequency 9200 mc/s, bandwidth to the detector 16 mc/s, modulation frequency 1000 c/s, and residual noise level 0.3 rms°K. The theory and the experiment demonstrate an interference phenomenon even though the source excitation is spatially extended and uncorrelated in time and space. The patterns are not even approximately Lambertian, e.g., a thin slot of 9.5 pi radians length exhibits a pattern having nine relative maxima in 180° with the maximum emission at 63° from the normal.