Optical analysis of BISOU: a balloon project to measure the CMB spectral distortions

BISOU (Balloon Interferometer for Spectral Observations of the Universe) is a CNES phase 0 study investigating the feasibility of observing spectral distortion in the CMB signal using a balloon-borne spectrometer, which also will act as a pathfinder for a future space mission dedicated to the measurements of the CMB spectral distortions. The CMB frequency spectrum is an important probe of the cosmological model. In this paper, we describe the optical layout and outline the initial optical analysis of the signal path and the reference beam path. The major challenge outlined is the inclusion of the required optical train in a confined volume of the cryostat. We include a multimoded description of the optical response of the system from the mutimoded pyramidal horn through the optical path containing mirrors and wire grids and predict beam patterns on the sky.