We have some images of the SKE inserted in the ray path of our telescope, during Moon observations. We also have some images of the same from the BBSO telescope, kindly lent to us by Phil Goode.
BBSO images om two separate periods about a week apart. Top row shows histogram equalized imges of the BS (left and the DS (right) with SKE superimposed over the BS. Lower row shows the same - BS short exposure on left and DS long exposure with SKE on right.
Histogram-equalized image of the Moon with SKE inserted from our own telescope. SKE runs from upper left to lower right and is opaque above that line.
Our image shows a halo around the Moon that stretches behind the SKE - hence we know that halo is formed to a large degree in the secondary optics! On the BBSO images we do not see this as clearly - either because the BBSO telescope is of a different design or because the exposures with SKE (right column of images) covers much more of the BS. Assuming the latter we understand why there is no halo behind the BBSO SKE - the BS was effectively blocked and no bright light entered the secondary optics and could not cause a halo. On our image the SKE is inserted experimentally only, leaving a large part of the BS to shine into the secondary optics.
So, we learn that the halo is not from atmosphere or primary optics alone - apparently a large fraction of it comes from the secondary optics!
We also see the importance of having an SKE. While the BBSO group uses the 'linear BBSO method' to remove scattered light over the DS they have a much smaller problem than us because the halo from the BS is nowhere near as strong as ours is!
We now see how terribly important the SKE is.