The linewidth observable refers to the FWHM of the (assumed) Gaussian absorption line profile for the 6173.3 Å line on the surface of the sun. The linewidth (Lw) data is in the DRMS series hmi.Lw_45s and hmi.Lw_720s
All the FITS header keywords that appear in the Linewidth data are explained here. Any combination of FITS header keywords CAMERA and T_REC is unique for the both DRMS series hmi.Lw_45s and hmi.Le_720s Further explanation on WCL keyword descriptions can be found in this paper.
HMI samples the Fe I absorption line at 6173.3 Angstrom at six points. Assuming that the "pure" solar Fe I line profile is a Gaussian and the HMI filter filter transmission profiles are delta functions, the first and second Fourier coefficients of the of the Fe I line can be calculated and an estimate of the linedepth is made. More details can be found here.
The link to the HMI pipeline processing is here. The status of the pipeline processing can be checked here.
Look-up tables and polynomial correction have *NOT* been applied to the Linedepth data.
All the Line-of-Sight Observables show fluctuation in the values with a twenty four hour cadence. This is an instrumental effect.