All-Stokes parameterization of the main beam and first sidelobe for the Arecibo radio telescope

Radio astronomical measurements of extended emission require knowledge of t he beam shape and response because the measurements need correction for qua ntities such as beam efficiency and beamwidth. We describe a scheme that ch aracterizes the main beam and sidelobe in all Stokes parameters employing p arameters that allow reconstruction of the complete beam patterns and, also , afford an easy way to see how the beam changes with azimuth, zenith angle , and time. For the main beam in Stokes I, the parameters include the beamw idth, ellipticity and its orientation, coma and its orientation, the point- source gain, and the integrated gain (or, equivalently, the main-beam effic iency); for the other Stokes parameters, the beam parameters include beam s quint and beam squash. For the first sidelobe ring in Stokes I, the paramet ers include an eight-term Fourier series describing the height, radius, and radial width; for the other Stokes parameters they include only the sidelo be's fractional polarization. We illustrate the technique by applying it to the Arecibo telescope. The ma in-beam width is smaller and the sidelobe levels higher than for a uniforml y illuminated aperture of the same effective area. These effects are modele d modestly well by a blocked aperture, with the blocked area equal to about 10% of the effective area (this corresponds to 5% physical blockage). In p olarized emission, the effects of beam squint (difference in pointing direc tion between orthogonal polarizations) and squash (difference in beamwidth between orthogonal polarizations) do not correspond to theoretical expectat ion and are higher than expected; these effects are almost certainly caused by the blockage. The first sidelobe is highly polarized because of blockag e. These polarization effects lead to severe contamination of maps of polar ized emission by spatial derivatives in brightness temperature.