Emission from the Herschel telescope is the dominant source of radiation for the majority of SPIRE Fourier transform spectrometer (FTS) observations, despite the exceptionally low emissivity of the primary and secondary mirrors. Accurate modelling and removal of the telescope contribution is, therefore, an important and challenging aspect of FTS calibration and data reduction pipeline. A dust-contaminated telescope model with time invariant mirror emissivity was adopted before the Herschel launch. However, measured FTS spectra show a clear evolution of the telescope contribution over the mission and strong need for a correction to the standard telescope model in order to reduce residual background (of up to 7 Jy) in the final data products. Systematic changes in observations of dark sky, taken over the course of the mission, provide a measure of the evolution between observed telescope emission and the telescope model. These dark sky observations have been used to derive a time dependent correction to the telescope emissivity that reduces the systematic error in the continuum of the final FTS spectra to ~0.35 Jy.
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