Si:As blocked impurity band detectors have been partially deprocessed and measured by Fourier transform spectroscopy to determine their transmittance and reflectance at cryogenic temperatures over the wavelength range $2\mathrm{\mu m}$ to $40\mathrm{\mu m}$ . A method is presented by which the propagation constants can be extracted from an inversion of the transmittance and reflectance data. The effective propagation constants for the active layer from $2\mathrm{\mu m}$ to $20\mathrm{\mu m}$ were calculated as well as the absorption cross section of arsenic in silicon, which agrees well with previous results from the literature. The infrared absorptance of the full detector was determined, and the analytical method also provides an estimate of absorption in the active layer alone. Infrared absorptance of the active layer is compared to the quantum yield measured by photoelectric means on similar detectors. The optical methods outlined here, in conjunction with standard electronic measurements, could be used to predict the performance of such detectors from measurements of the blanket films from which they are to be fabricated.