Applications of Fast Convolution on the Sphere

TL;DR

This paper demonstrates the versatile applications of the spherical fast convolution method in telescope design, data analysis, and filter construction, highlighting its effectiveness in improving astronomical observations and data interpretation.

Contribution

It introduces the use of spherical fast convolution for diverse applications in telescope analysis, background contamination assessment, and filter design, showcasing its broad utility.

Findings

Sidelobe contamination in CALISTO telescope designs can be minimized to < 0.1 MJy/sr.

Fast convolution impacts the accuracy of the Planck temperature power spectrum recovery.

A class of orientable filters on the sphere is specified and demonstrated.

Abstract

We present several diverse applications of the spherical fast convolution method suggested by Wandelt and Gorski (2001), which is useful for studies of telescope optical properties and for construction of shaped filters for analysis of all-sky data. We study sidelobe pickup in three design concepts for the CALISTO infrared telescope. The beam convolution allows for direct comparison of the performance of each telescope design. At 100 microns, the best of these designs limits sidelobe contamination from Galactic dust emission to < 0.1 MJy/sr for most of the sky with |b| > 25 deg. With the fast convolution method, we illustrate the impact of asymmetric primary beams on the recovery of the temperature power spectrum for the Planck microwave background mission. Finally, we use the fast convolution method to specify a class of orientable filters on the sphere, working through a pedagogical example.