Calculate farfield performance of a Gaussian beam from a corrugated feedhorn.

When observing, telescopes collect light from a certain patch of sky, which is dependent on the telescope optics. In microwave astronomy, it's often convenient to talk about telescopes in the reverse time sense - as if the pixels in a telescope's camera were actually broadcasting a signal towards a certain patch of sky and not collecting light from that patch. The physics of the system is totally the same whether time is moving forward or backward, so we're free to choose which frame of reference is easier to understand the problem. (In reality, time only moves forward, so we really are receiving light.) In this time-reversed sense, we call the patch of sky to which we're broadcasting power the telescope's beam.

This code calculates the beam coming out of a corrugated feedhorn coupled to detectors sensitive to 150 GHz microwave light in the SPTpol receiver of the South Pole Telescope. (Think of feedhorns like the bell of a trumpet. The gradual flare helps sound traveling down the thin tubing of the trumpet to exit the instrument without reflecting back inward at the end of the tube. Feedhorns do the same thing for light coming into a telescope before it couples to the detectors actually doing the sensing.) The radial profle of the beam changes a lot at first, in the so-called nearfield of the beam, but sufficiently far away the beam illumination pattern is fixed as a function of angle from the center of the beam. This region is the beam farfield.