Building the analytical response in frequency domain of AC biased   bolometers Application to Planck/HFI
  Context: Bolometers are high sensitivity detector commonly used in Infrared astronomy. The HFI instrument of the Planck satellite makes extensive use of them, but after the satellite launch two electronic related problems revealed critical. First an unexpected excess response of detectors at low optical excitation frequency for {\nu} < 1 Hz, and secondly the Analog To digital Converter (ADC) component had been insufficiently characterized on-ground. These two problems require an exquisite knowledge of detector response. However bolometers have highly nonlinear characteristics, coming from their electrical and thermal coupling making them very difficult to modelize.   Goal: We present a method to build the analytical transfer function in frequency domain which describe the voltage response of an Alternative Current (AC) biased bolometer to optical excitation, based on the standard bolometer model. This model is built using the setup of the Planck/HFI instrument and offers the major improvement of being based on a physical model rather than the currently in use had-hoc model based on Direct Current (DC) bolometer theory.   Method: The analytical transfer function expression will be presented in matrix form. For this purpose, we build linearized versions of the bolometer electro thermal equilibrium. And a custom description of signals in frequency is used to solve the problem with linear algebra. The model performances is validated using time domain simulations.   Results: The provided expression is suitable for calibration and data process- ing. It can also be used to provide constraints for fitting optical transfer function using real data from steady state electronic response and optical response. The accurate description of electronic response can also be used to improve the ADC nonlinearity correction for quickly varying optical signals. 
Alexandre Sauv\'e and Ludovic Montier
astro-ph.IM