We describe the measurement of the beam profiles and window functions for the Atacama Cosmology Telescope (ACT), which operated from 2007 to 2010 with kilo-pixel bolometer arrays centered at 148, 218, and 277 GHz. Maps of Saturn are used to measure t
he beam shape in each array and for each season of observations. Radial profiles are transformed to Fourier space in a way that preserves the spatial correlations in the beam uncertainty, to derive window functions relevant for angular power spectrum analysis. Several corrections are applied to the resulting beam transforms, including an empirical correction measured from the final CMB survey maps to account for the effects of mild pointing variation and alignment errors. Observations of Uranus made regularly throughout each observing season are used to measure the effects of atmospheric opacity and to monitor deviations in telescope focus over the season. Using the WMAP-based calibration of the ACT maps to the CMB blackbody, we obtain precise measurements of the brightness temperatures of the Uranus and Saturn disks at effective frequencies of 149 and 219 GHz. For Uranus we obtain thermodynamic brightness temperatures T_U^{149} = 106.7 pm 2.2 K and T_U^{219} = 100.1 pm 3.1 K. For Saturn, we model the effects of the ring opacity and emission using a simple model and obtain resulting (unobscured) disk temperatures of T_S^{149} = 137.3 pm 3.2 K and T_S^{219} = 137.3 pm 4.7 K.
We explore the reconstruction of the gravitational lensing field of the cosmic microwave background in real space showing that very little statistical information is lost when estimators of short range on the celestial sphere are used in place of the
customary estimators in harmonic space, which are nonlocal and in principle require a simultaneous analysis of the entire sky without any cuts or excisions. Because virtually all the information relevant to lensing reconstruction lies on angular scales close to the resolution scale of the sky map, the gravitational lensing dilatation and shear fields (which unlike the deflection field or lensing potential are directly related to the observations in a local manner) may be reconstructed by means of quadratic combinations involving only very closely separated pixels. Even though harmonic space provides a more natural context for understanding lensing reconstruction theoretically, the real space methods developed here have the virtue of being faster to implement and are likely to prove useful for analyzing realistic maps containing a galactic cut and possibly numerous small excisions to exclude point sources that cannot be reliably subtracted.
