Analysis of a cluster feed for the Arecibo trireflector system using forward ray tracing and aperture integration

A cluster feed for the Gregorian dual-reflector feed of the Arecibo radio telescope is studied. The system is analyzed by forward ray tracing from each individual feed horn via the three reflectors to the aperture. The radiation pattern is determined by aperture integration. The analysis method is very time efficient compared with physical optics (PO) integration, the latter being unusable at high frequencies because the computer time increases by a factor proportional to the frequency to the power 4. Results obtained by the ray tracing method and PO integration are in very good agreement at frequencies low enough to be used for PO calculations. A special algorithm is developed to determine the squint and directivity of an individual main beam without computing the radiation pattern. This makes it possible to use the program very efficiently when searching for optimum cluster feed geometries. The computer programs are used to design a seven-element cluster feed for the Arecibo trireflector system