Fingerprinting the effects of hyperfine structure on CH and OH far
  infrared spectra using Wiener filter deconvolution
  In this paper, we investigate the influence of hyperfine splitting on complex
spectral lines, with the aim of evaluating canonical abundances by decomposing
their dependence on hyperfine structures. This is achieved from first
principles through deconvolution. We present high spectral resolution
observations of the rotational ground state transitions of CH near 2 THz seen
in absorption toward the strong FIR-continuum sources AGAL010.62$-$00.384,
AGAL034.258+00.154, AGAL327.293$-$00.579, AGAL330.954$-$00.182,
AGAL332.826$-$00.549, AGAL351.581$-$00.352 and SgrB2(M). These were observed
with the GREAT instrument on board SOFIA. The observed line profiles of CH were
deconvolved from the imprint left by the lines' hyperfine structures using the
Wiener filter deconvolution, an optimised kernel acting on direct
deconvolution. The quantitative analysis of the deconvolved spectra first
entails the computation of CH column densities. Reliable N(CH) values are of
importance owing to the status of CH as a powerful tracer for H$_2$ in the
diffuse regions of the interstellar medium. The N(OH)/N(CH) column density
ratio is found to vary within an order of magnitude with values ranging from
one to 10, for the individual sources that are located outside the Galactic
centre. Using CH as a surrogate for H$_2$, we determined the abundance of the
OH molecule to be X(OH)=1.09$\times$10$^{-7}$ with respect to H$_2$. The radial
distribution of CH column densities along the sightlines probed in this study,
excluding SgrB2(M), showcase a dual peaked distribution peaking between 5 and 7
kpc. The similarity between the correspondingly derived column density profile
of H$_2$ with that of the CO-dark H$_2$ gas traced by the cold neutral medium
component of [CII] 158$~\mu$m emission across the Galactic plane, further
emphasises the use of CH as a tracer for H$_2$.
