Residuals image of Moon minus model of BS and its halo, fitted to the sky (i.e. the EFM method). The green and blue colors are a few tenths on both sides of 0. The mask used covers the image except the disk of the Moon.
In this application of the EFM to an observed image of high quality we see that the residual sky is not even. Particularly on the BS (to the right) there are some streaks. A blob at the bottom also shows unevenness, as does the striations to the left of the DS.
This illustrates a shortcoming of the EFM. Since the PSF used is rotationally symmetric it is possible that the unevenness seen above are in the observed image – perhaps some sort of reflection effects in the optics. The EFM is a global method seeking to subtract all the scattered light with one model. The BBSO method is essentially local – it estimates the scattered light in a wedge off the disk. On the other hand the BBSO linear method almost certainly removes too little of the halo as you get nearer to the BS. The EFM method attempts to model all parts of the halo.