Atmospheric extinction is caused by absorbtion and scattering of light.
Usually photometry is performed on images of sources by collecting the flux from an area near the source and relating it to the airmass of that particular observing moment. In a Langley plot the relationship between magnitudes and airmass will be an (almost) straight line, and the extinction coefficient is the slope of that line.
As light passes through more and more atmosphere there will be more absorbtion as well as more scattering. Both remove intensity from the direct beam. Absorbtion just takes the light away (at least at optical wavelengths) while scattering redistributes the light near the source. If the method of measuring light from the source therefore allows re-capture of the light scattered – for instance by allowing for large collection areas in the image – then the effect of scattering will be reduced and a smaller extinction coefficient should resultr, as compared to the extinction calculated when scattering is allowed to remnove light from the calculation.
Thus, when considering an extended source like the Moon we have an opportunity to test the magnitude of scattering vs absorbtion by explicitly collecting all light near the Moon (for instance, by summing the flux in the whole image frame) and comparing to what we find when light is collected only from a small patch on the lunar bright side.
We have done this for 5 wavelength bands and a score of observing nights where conditions were right. We measured flux in each image in two ways – either as the total flux in the image frame or as the flux inside a small patch on the lunar brightside defined by selenographic longitude and latitude. Langley plots were constructed and slopes measured using regression, along with error estimates of the slopes.
Results are plotted here:
Langley extinction for whole-image fluxes plotted against extinctions determined from a small bright-side patch in each image.
If the image is rotated and inspected (sorry about that) we see that for the five filters extinction determinations often agree, despite the expectation that extinction determined from the small patch (allowin scattered light to escape) would be larger than the extinction determined from whole image. Only a few points deviate significantly from the diagonal line.
This implies that scattering at MLO was very low, compared to absorbtion – as scattering includes Rayleigh scattering thge plot for B should be considered carefully.
In a few cases the plots allows us to identify ‘bad nights’ when the extinction determinations do not follow the diagonal.