The electromagnetic properties of aperture-synthesis telescopes shaped as Reuleaux triangles

Abstract

The electromagnetic properties of aperture-synthesis telescopes in the form of an array of identical antennas sited on the sides of an equilateral Reuleaux triangle are studied in the limit that the number of antennas becomes arbitrarily large. The density of baselines in the uv-plane is derived exactly and is found to be highly irregular: it has seven singularities and 13 finite discontinuities, and is not even approximately circularly symmetric. The response pattern of the synthesized beam is computed numerically and is also found not to be circularly symmetric, although only to a moderate extent. The properties are compared with those of the circular ring array and found to be very similar: the main differences are that the synthesized beam of the Reuleaux triangle is 4 per cent broader than that of the circle with the same diameter whereas the average sidelobe level is 10 per cent lower. The Reuleaux triangle came to attention in a search for the shape of array that gives the most uniform coverage of baselines in the uv-plane, and a discussion is presented whether it really is optimal in this regard.