Table of Contents
Last updated: 23 November, 2011
doDeconvolution is the post-Level 2 task that separates (or unfolds) double sideband (DSB) data that is inherently produced by HIFI's heterodyne process into a single sideband (SSB) result. Figure 11.1 shows an example of how the spectral ranges of the upper and lower sidebands of HIFI are folded together during an observation, causing the spectra to overlap and add, causing features to blend. Also notice that the continuum doubles.
Fluxes (F_DSB) in the DSB spectrum can be expressed in terms of the LO frequency and the IF frequency (where, for bands 1-5, the IF frequency goes from 4 to 8 GHz):
F_DSB(IF) = 2 * usbGain * F_sky(LO+IF) + 2 * lsbGain * F_sky(LO-IF)
Here F_sky are the true input fluxes from the sky and 2 * usbGain and 2 * lsbGain are the sideband gain (imbalance) factors, typically close to 1.0. The deconvolution is usually used to reduce HIFI Spectral Scans, which are collections of overlapping observations taken at many LO settings. But, in principle, any set of spectra taken at differing nearby LO settings, such that the frequency coverage of each overlaps with the next, may be together deconvolved. Observations taken at multiple LO settings serve to constrain the SSB solution. Given the observed F_DSB fluxes at multiple LO settings, the deconvolution solves for the unique F_sky solution that best models the observed multiple F_DSB observations through iterative chi-square minimization using the Conjugate Gradient Method (Comito and Schilke 2002, A&A, 395, 357). The method can also be used to simultaneously solve for the usbGain and lsbGain gain factors, as described below. No detailed knowledge of the algorithm is required by you in order to operate the deconvolution task. With good input data, as few as 3 DSB spectra may be sideband-deconvolved, as shown in an example in Figure 11.2.