We have extracted the mean value of alfa (the parameter that describes how broad the PSF for a given image is) for a given night, and the corresponding value of the extinction coefficient for that night. We have only few nights where the extinction could be determined.
The plot of one vs the other looks like this:
(download and look, etc)
We see that there is a tendency for alfa to be narrowly constrained, and that the extinction has a broader distribution. In general there is no strong relationship between the values, but if we ignore outliers and the effect they have on the regression (plotted as a red line) we see a general tendency for high extinctions and small alfa values to be related: For B it is quite clear. V would be clear but for the outlier, IRCUT also seems to be clear. VE1 and VE2 are all over the place. A broad PSF is given by small values of alfa. We expect broad halos (i.e. broad PSFs) on hazy or turbid nights - nights on which extinction also should be large.
Factors that determine scatter in alfa are things like image focus and how the nonlinear fitting routine determined it should stop. Physical factors include haze and thin cloudyness on the night in question.
Factors influencing the scatter in extinction include the actual regression: we used all nights with more than 3 observations used to determine the airmass vs extinction line, and for which the determinations from 3 regression methods agreed to a S.D. of less than 0.02. The three methods were - ordinary least squares, and two 'robust' methods ("ladfit" and "robust_poly_fit" in IDL). While doing the actual regression it was necessary to eliminate some outliers by hand. Physical factors include haze and cludyness and whether the halo around the Moon was well captured inside the image frame.
The relatively low value of alfa for the VE2 filter is still not understood.