Performances of any system for data processing based on acousto-optical technique are mainly determined by parameters of the acousto-optical cell (AOC) exploited within the schematic arrangement. Here, basic properties of the AOC, involved into a novel processor for precise optical spectrum analysis dedicated to modern astrophysical applications, are considered. Because potential applications of this processor will be focused on investigations in extra-galactic astronomy as well as studies of extra-solar planets, an advanced regime of the non-collinear two-phonon light scattering has been elaborated for spectrum analysis with significantly improved spectral resolution. Under similar uprated requirements, the AOC, based on that specific regime in the calomel (Hg2Cl2) crystal, had been chosen, and its parameters were analyzed theoretically and verified experimentally. Then, the adequate approach to estimating the frequency/spectral bandwidth and spectral resolution had been developed. The bandwidth was calculated and experimentally realized with the additionally involved tilt angle of light incidence, allowing variations for acoustic frequencies. The resolution was characterized taking into account its doubling peculiar to the nonlinear two-phonon mechanism of light scattering. Proof-of-principle experiments were performed with the calomel AOC of 52 mm optical aperture, providing ~94% efficiency in the transmitted light due to the slow-shear acoustic mode of finite amplitude (the acoustic power density ~150 mW/mm2) with the velocity of 0.347×105 cm/s at the radio-wave acoustic frequency ~71 MHz. As a result, we have obtained the spectral resolution <0.235 Å within the spectral bandwidth <290 Å that looks as the best one can mention at the moment in acousto-optics.