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

Radio astronomical measurements of extended emission require knowledge of the beam shape and response because the measurements need correction for quantities such as beam efficiency and beamwidth. We describe a scheme that characterizes the main beam and sidelobe in all Stokes parameters employing parameters 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 beamwidth, ellipticity and its orientation, coma and its orientation, the point-source gain, and the integrated gain (or, equivalently, the main-beam efficiency); for the other Stokes parameters, the beam parameters include beam squint and beam squash. For the first sidelobe ring in Stokes I, the parameters include an eight-term Fourier series describing the height, radius, and radial width; for the other Stokes parameters they include only the sidelobe's fractional polarization. We illustrate the technique by applying it to the Arecibo telescope. The main-beam width is smaller and the sidelobe levels higher than for a uniformly illuminated aperture of the same effective area. These effects are modeled 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 polarized emission, the effects of beam squint (difference in pointing direction between orthogonal polarizations) and squash (difference in beamwidth between orthogonal polarizations) do not correspond to theoretical expectation and are higher than expected; these effects are almost certainly caused by the blockage. The first sidelobe is highly polarized because of blockage. These polarization effects lead to severe contamination of maps of polarized emission by spatial derivatives in brightness temperature.