The Effect of the Detector Response Time on Bolometric Cosmic Microwave Background Anisotropy Experiments

We analyze the effects of the detector response time on bolometric measurements of the anisotropy of the cosmic microwave background (CMB). We quantify the effect in terms of a single dimensionless parameter $L$ defined as the ratio between the time the beam sweeps its own size and the bolometer response time. As $L$ decreases below $\sim 2.5$ the point source response of the experiment becomes elongated. We introduce a window function matrix based on the timestream data to assess the effects of the elongated beam. We find that the values of the window function matrix elements decrease slowly as a function $L$. Our analysis and results apply to other cases of beam asymmetry. For the High Frequency Instrument on board the Planck Surveyor satellite we show that for a broad range of $L$ the ability of the experiment to extract the cosmological parameters is not degraded. Our analysis enhances the flexibility in tuning the design parameters of CMB anisotropy experiments.