Brightness Temperature Calculation and Uncertainty Propagation for Conical Microwave Blackbody Targets

We discuss the analytical derivation of the absolute brightness temperature uncertainty of a hollow conical blackbody source for radiometer calibration. We introduce a Monte Carlo uncertainty propagation analysis method to quantify uncertainty contributions from nonideal emissivity, physical temperature, and antenna pattern, which are the three major factors contributing to the uncertainty of the brightness temperature radiation from the source. The low reflectance of the hollow conical geometry depends on multiple bounces on the absorber surface. To quantify total brightness temperature over a nonuniform temperature surface, each individual bounce must be considered. We derive a recursive analytical relationship to quantify this multiple-bounce effect as a function of a view angle. The resulting effective blackbody brightness temperature uncertainty is a function of frequency, temperature, antenna pattern, measurement distance, and the measurement environment. We also propagate the uncertainty to the antenna flange of a radiometer viewing the conical blackbody. This includes additional effects, such as spillover, illumination efficiency, and antenna efficiency. We demonstrate the propagation method with an example case. We use fictional input values to investigate the response of the uncertainty to input variables and distance. We find that as the distance between antenna and blackbody increases, the uncertainty due to spillover dominates, but at close distances, the dominant uncertainty contributor is linked to the physical temperature of the absorber.