Cmb Polarization Analysis On Circular Scans

Most cosmic microwave background experiments observe the sky along circular or near-circular scans on the celestial sphere. For such experiments, we show that simple linear systems connect the Fourier spectra of temperature and polarization time-ordered data to the harmonic spectra of T, E and B on the sphere. We also show how this can be used to estimate those spectra directly from data streams by inversion of a linear system that connects Fourier spectra to angular power spectra, offering an easy way to down-weight those modes of observation most contaminated by low-frequency noise, ground pickup, or fluctuations of atmospheric emission on large angular scale. This direct connection between Fourier spectra and harmonic spectra on the sphere can be of interest for the analysis of future CMB data sets, in complement to other approaches that involve map-making as a first analysis step.