First-year Wilkinson Microwave Anisotropy Probe (WMAP) observations:: Beam profiles and window functions

Knowledge of the beam profiles is of critical importance for interpreting data from cosmic microwave background experiments. In this paper, we present the characterization of the in-flight optical response of the WMAP satellite. The main-beam intensities have been mapped to less than or equal to-30 dB of their peak values by observing Jupiter with the satellite in the same observing mode as for CMB observations. The beam patterns closely follow the prelaunch expectations. The full width at half-maximum is a function of frequency and ranges from 0.degrees82 at 23 GHz to 0.degrees21 at 94 GHz; however, the beams are not Gaussian. We present (a) the beam patterns for all 10 differential radiometers, showing that the patterns are substantially independent of polarization in all but the 23 GHz channel; (b) the effective symmetrized beam patterns that result from WMAP's compound spin observing pattern; (c) the effective window functions for all radiometers and the formalism for propagating the window function uncertainty; and (d) the conversion factor from point-source flux to antenna temperature. A summary of the systematic uncertainties, which currently dominate our knowledge of the beams, is also presented. The constancy of Jupiter's temperature within a frequency band is an essential check of the optical system. The tests enable us to report a calibration of Jupiter to 1%-3% accuracy relative to the CMB dipole.