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.
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.