The linear BBSO (i.e. as done by BBSO) method and the modification that operates on logarithmed images can be compared:
A strip, 20 rows wide, across the image was made and the rows of that strip averaged, and the average plotted. Black is the original bias-subtracted image, red is theordinary linear BBSO method and blue is the log-method. We plot the absolute value of the fluxes to avoid problems with log.
Both the linear and the log method does well on the sky at left, but there are differences on the edge-near disk. Tests on synthetic images, where we know the flux to expect on the disk, has shown that the log-method is more accurate than the linear method.
The residual mean (about 2) is unsettling, but has to do with the use of absolute values and the averaging over several rows – inspection of the images reveal values distributed around 0.