The BINGO Project III. Optical design and optimization of the focal plane

Context. The Baryon Acoustic Oscillations from Integrated Neutral Gas Observations (BINGO) telescope was designed to measure the fluctuations of the 21 cm radiation arising from the hyperfine transition of neutral hydrogen. It is also aimed at measuring the baryon acoustic oscillations (BAO) from such fluctuations, thereby serving as a pathfinder to future, deeper intensity mapping surveys. The requirements for the Phase 1 of the projects consider a large reflector system (two 40 m-class dishes in a crossed-Dragone configuration) illuminating a focal plane with 28 horns to measure the sky, with two circular polarizations in a drift scan mode to produce measurements of the radiation in intensity (I) as well as the circular (V) polarization. Aims. In this paper, we present the optical design for the instrument. We describe the optical arrangement of the horns in the focal plane to produce a homogeneous and well-sampled map after the end of Phase 1, as well as the intensity and polarization properties of the beams. Our analysis provides an optimal model for the location of the horns in the focal plane, producing a homogeneous and Nyquist-sampled map after the nominal survey time. Methods. We used the GRASP package to model the focal plane arrangement and performed several optimization tasks to arrive at the current configuration, including an estimation of the sidelobes corresponding to the diffraction patterns of the two mirrors. The final model for the focal plane was defined through a combination of neural network and other direct optimization methods. Results. We arrived at an optimal configuration for the optical system that includes the focal plane positioning and the beam behavior of the instrument. We present an estimate of the expected sidelobes both for intensity and polarization, as well as the effect of band averaging on the final sidelobes, as well as an estimation of the cross-polarization leakage for the final configuration. Conclusions. We conclude that the chosen optical design meets the requirements for the project in terms of polarization purity and area coverage as well as a homogeneity of coverage so that BINGO can perform a successful BAO experiment. We further conclude that the requirements on the placement and rms error on the mirrors are also achievable so that a successful experiment can be conducted.