This paper describes the construction of a cryostat and an optical system with a free-space coupling efficiency of 56.5% ± 3.4% to a superconducting nanowire single-photon detector (SNSPD) for infrared quantum communication and spectrum analysis. A 1K pot decreases the base temperature to T = 1.7 K from the 2.9 K reached by the cold head cooled by a pulse-tube cryocooler. The minimum spot size coupled to the detector chip was 6.6 ± 0.11 µm starting from a fiber source at wavelength, λ = 1.55 µm. We demonstrated photon counting on a detector with an 8 × 7.3 µm2 area. We measured a dark count rate of 95 ± 3.35 kcps and a system detection efficiency of 1.64% ± 0.13%. We explain the key steps that are required to improve further the coupling efficiency.