Bayesian modeling of microwave radiometer calibration on the example of the Wendelstein 7-X electron cyclotron emission diagnostic.

This paper reports about a novel approach to the absolute intensity calibration of an electron cyclotron emission (ECE) spectroscopy system. Typically, an ECE radiometer consists of tens of separated frequency channels corresponding to different plasma locations. An absolute calibration of the overall diagnostic including near plasma optics and transmission line is achieved with blackbody sources at LN temperature and room temperature via a hot/cold calibration mirror unit. As the thermal emission of the calibration source is typically a few thousand times lower than the receiver noise temperature, coherent averaging over several hours is required to get a sufficient signal to noise ratio. A forward model suitable for any radiometer calibration using the hot/cold method and a periodic switch between them has been developed and used to extract the voltage difference between the hot and cold temperature source via Bayesian analysis. In contrast to the classical analysis which evaluates only the reference temperatures, the forward model takes into account intermediate effective temperatures caused by the finite beam width and thus uses all available data optimally. This allows the evaluation of weak channels where a classical analysis would not be feasible, is statistically rigorous, and provides a measurement of the beam width. By using a variance scaling factor, a model sensitive adaptation of the absolute uncertainties can be implemented, which will be used for the combined diagnostic Bayesian modeling analysis.