Radio astronomy allows observations of unique objects and phenomena relating to the electric and magnetic fields of celestial objects. Radio astronomy can be preformed at any time of day and is less beholden to atmospheric conditions than optical astronomy. A radio telescope designed to receive radiation at 1.421 GHz, the 21 cm line, needs a resonator designed to maximize the signal to noise ratio at this frequency
Radiation reflected off of the parabolic dish of a radio telescope can be modeled as
diffraction through a circular aperture. This leads to an Airy disk pattern of radiation at the focal plane. An integral describing this pattern was set up and evaluated using the scipy package in python, yielding a description of the Airy disk.
The diameter was determined by noting that the resonator should be large enough to encompass the bulk of the reflected radiation while being as small as possible to limit noise entering from other sources. This compromise is reached by having a diameter that extends to the first zero of the Airy disk pattern, yielding an ideal diameter of 11.235 cm. The ideal length of a resonator for a telescope observing the 21 cm line was found via interference calculations to be [5λ over 4] ≈ 26.38 cm.