Positioning and orienting a static cylindrical radio-reflector for wide field surveys

TL;DR

This paper derives exact mathematical expressions for the transit time of celestial objects through the acceptance lobe of static cylindrical radio reflectors, aiding in their optimal positioning and orientation for wide field surveys.

Contribution

It introduces a stereographic projection-based mathematical approach to optimize the placement and orientation of static cylindrical radio reflectors in radioastronomy.

Findings

Exact formula for transit time within the lobe

Optimization method for reflector positioning

Potential for precise Fourier Transform coefficients

Abstract

Several projects in radioastronomy plan to use large static cylindrical reflectors with an extended lobe sampling a sector of the rotating sky. This study provides the exact mathematical expression of the transit time of a celestial object within the acceptance lobe of such a cylindrical device. The mathematical approach, based on the stereographic projection, allows one to study the optimisation of the position and orientation of the radio-reflector, and should provide exact coefficients for the spatial Fourier Transform of the radio signal along the cylinder axis.