Relative Observing Speed of Lens-Coupled Absorber Focal Plane Arrays for Far-IR Imaging and Spectroscopy: A PRIMA Case Study

The PRobe far-Infrared Mission for Astrophysics (PRIMA) is an astrophysics mission concept currently under study. The instrument comprises four focal plane arrays (FPAs), each with over 1,000 pixels, consisting of lens-coupled kinetic inductance detectors (KIDs) designed for ultra-high sensitivity spectroscopy and imaging. PRIMA covers the far-infrared band from 24 to 250 um. This work presents the fundamental properties of lens-coupled absorbers, including aperture efficiency, throughput, and beam patterns. Compared to bare absorbers, lens-coupled absorbers exhibit reduced sensitivity to noise from both the instrument enclosure and the sky background. We analyze FPA sampling strategies in terms of relative observing speed, considering both detector-noise-limited and background-noise-limited scenarios. In the background-noise-limited case, near-maximum-gain sampling is optimal only when the point source spread function (PSF) in the reflector focal plane is aligned with the lens. For arbitrary PSF incidence, a near-Nyquist sampling configuration provides the best average performance. These calculations are based on a computationally efficient quasi-analytical technique and assume a hex-packed array of circular lenses, recently developed for PRIMA.