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In this paper, we investigate the influence of hyperfine splitting on complexspectral lines, with the aim of evaluating canonical abundances by decomposingtheir dependence on hyperfine structures. This is achieved from firstprinciples through deconvolution. We present high spectral resolutionobservations of the rotational ground state transitions of CH near 2 THz seenin absorption toward the strong FIR-continuum sources AGAL010.62$-$00.384,AGAL034.258+00.154, AGAL327.293$-$00.579, AGAL330.954$-$00.182,AGAL332.826$-$00.549, AGAL351.581$-$00.352 and SgrB2(M). These were observedwith the GREAT instrument on board SOFIA. The observed line profiles of CH weredeconvolved from the imprint left by the lines' hyperfine structures using theWiener filter deconvolution, an optimised kernel acting on directdeconvolution. The quantitative analysis of the deconvolved spectra firstentails the computation of CH column densities. Reliable N(CH) values are ofimportance owing to the status of CH as a powerful tracer for H$_2$ in thediffuse regions of the interstellar medium. The N(OH)/N(CH) column densityratio is found to vary within an order of magnitude with values ranging fromone to 10, for the individual sources that are located outside the Galacticcentre. Using CH as a surrogate for H$_2$, we determined the abundance of theOH molecule to be X(OH)=1.09$\times$10$^{-7}$ with respect to H$_2$. The radialdistribution of CH column densities along the sightlines probed in this study,excluding SgrB2(M), showcase a dual peaked distribution peaking between 5 and 7kpc. The similarity between the correspondingly derived column density profileof H$_2$ with that of the CO-dark H$_2$ gas traced by the cold neutral mediumcomponent of [CII] 158$~\mu$m emission across the Galactic plane, furtheremphasises the use of CH as a tracer for H$_2$.

Fingerprinting the effects of hyperfine structure on CH and OH far infrared spectra using Wiener filter deconvolution