Analytical correction for direct detection in the retrieval of gas spectral lines measured with superconducting hot-electron bolometer mixer

We present a method by which the direct detection effect in superconducting hot-electron bolometer mixers can be analytically accounted for with sufficient practical accuracy. This is achieved by means of the advanced uniform, non-linear two-temperature model that considers the effective temperatures of electrons and phonons alongside established material parameters. We demonstrate the efficacy of this approach for the ex situ correction of the radiance of the emission line of atomic oxygen under conditions when the direct detection causes a 30% error in the line magnitude. The correction was applied to data collected by a balloon-borne heterodyne receiver operating in the upper atmosphere of Earth. The corrected line shape and magnitude are in reasonable agreement with the predictions of atmospheric radiation transfer models.