Ray-tracing and physical-optics analysis of the aperture efficiency in a radio telescope

The performance of telescope systems working at microwave or visible-IR wavelengths is typically described in terms of different parameters according to the wavelength range. Most commercial ray-tracing packages have been specifically designed for use with visible-IR systems and thus, though very flexible and sophisticated, do not provide the appropriate parameters to fully describe microwave antennas and to compare with specifications. We demonstrate that the Strehl ratio is equal to the phase efficiency when the apodization factor is taken into account. The phase efficiency is the most critical contribution to the aperture efficiency of an antenna and the most difficult parameter to optimize during the telescope design. The equivalence between the Strehl ratio and the phase efficiency gives the designer/user of the telescope the opportunity to use the faster commercial ray-tracing software to optimize the design. We also discuss the results of several tests performed to check the validity of this relationship that we carried out using a ray-tracing software, ZEMAX, and a full Physical Optics software, GRASP9.3, applied to three different telescope designs that span a factor of approximately 10 in terms of D/lambda. The maximum measured discrepancy between phase efficiency and Strehl ratio varies between approximately 0.4% and 1.9% up to an offset angle of >40 beams, depending on the optical configuration, but it is always less than 0.5% where the Strehl ratio is >0.95.