In the framework of this MSc thesis, the analysis and design guidelines for part of the quasi-optical system of a proposed astronomical instrument, called TIFUUN, are presented. The TIFUUN instrument is an imaging spectrometer, planned to be placed in the ASTE telescope to perform ground-based astronomical observations in the mm-submm wavelength regime. Part of the instrument development involves the design of the quasi-optical system coupling the radiation from the telescope’s main dish to the spectrometer array. In this thesis, the focal plane array of antennas, as well as the first component of the quasi-optical chain are analyzed and two different design approaches are presented, as candidate geometries. Each of them satisfies the requirements of different science surveys targeted by TIFUUN. The first examined architecture is comprised of a focal plane array of on-chip feeding elements under a single hyper-hemispherical lens, which is then coupled geometrically to a hyperbolic lens. The second geometry is instead comprised of an array of integrated elliptical lenses, with a single on-chip feeding element per lens, diffractively coupled to a hyperbolic lens. The methodologies to efficiently analyze these kinds of geometries are Geometrical Optics (GO) combined with analysis in reception for the first design approach and Coherent Fourier Optics (CFO) for the second one. During the design process, the performance of both architectures is optimized throughout the field of view, using methodologies to correct for phase aberrations, such as feed displacement inside the lenses and symmetric shaping of dielectric surfaces. The design guidelines provided and insights obtained during this MSc project will be utilized to develop the quasi-optical system of the TIFUUN instrument, within the limited space of its cryostat.