Modal optical modelling of a test system for ultra-low-noise transition edge sensors for space science

For all high-performance detectors, well-understood optical test systems are needed for precise characterisation and calibration. A cryogenic variable temperature blackbody load has been developed to test the optical efficiencies of ultra-low-noise (NEP ~ 10-19 WHz-1/2) Transition Edge Sensors for space science. The few-mode, partially coherent illumination conditions of the measurement system are engineered to be precisely the same as those of the telescope. We have used a SPICA/SAFARI-like telescope/detector for demonstration purposes. The essential difference between the test system and an equivalent representation of the telescope's optics is that the telescope has a lens of effective focal length f, but the test system does not. A key part of our analysis is to describe behaviour in terms of the optical modes of the test system, as distinct from the optical modes of the detector under test. In the paper we describe the analysis of the test assembly in terms of signal power, background power and photon noise.