The main result: 1 count on average in the empty region per 2x10**9 total counts on the whole image.

The procedure used, i.e., explanation of the figure.

In the top left I show median flux in the empty region as a function of the total flux in the image. The line is the linear fit to the points with flux above 0.5x10**9. I excluded low flux points as they skew the result. The discrepancy between different arc lamps is because they use different exposure times and we do not control that absouletly perfectly. The panels on the right show the result if we don't use darks in reduction, where the ``extra flux'' is then dominated by exposure time.
In the bottom left we can see that dependence of median flux in the empty region is not strongly dependent on exposure time if we detrend with darks (although Neon is behaving somewhat oddly at exposure times of several hundred seconds.)

As such, I conclude that darks are of sufficient quality that the main effect seen in the top left panel is due to scattered light, and I report the value shown in gray dotted lines.