[SQM] SQM-L Directional Accuracy, and Why It Matters

Tony Flanders tflanders at skyandtelescope.com
Wed May 27 21:28:23 UTC 2009

I posted a query earlier on whether the optical axis of the SQM-L (i.e. the center of the area of highest sensitivity) is aligned with the SQM-L's body. Since then, I've performed some more careful measurements with my two SQM-L units indicating quite clearly that neither unit's optical axis is aligned with the body, and the two unit's optical axes are not parallel to each other. And although my measurements aren't accurate enough to state this conclusively, I also suspect that in addition to having different spatial centers, the two units have somewhat different directional response curves. Or, if you prefer, their "angle of acceptance" is modestly different.

Given the fact that both the sensor and the unit itself have lenses, that the separation between the lenses is only slightly bigger than the lenses themselves, and that neither lens has high optical quality, none of these facts is surprising in the least. Making a unit with truly repeatable directional characteristics would require more expensive optics housed in a much larger, heavier, and more expensive body. I'm not complaining!

Oh, by the way, my measurements also revealed a fact that I should have known a priori. If you take a cross-section of the SQM-L's response curve, it does *not* look anything like the neat bell-shaped curve of the SQM. Instead, response stays nearly constant a long as the main lens's image falls on the sensor, then starts to drop quite suddenly about 10 degrees off-axis.

Why do I care about all of this? This gets to the question of the relative merits of the SQM and the SQM-L. As far as I'm concerned, the SQM-L has three benefits:

 1.  The SQM-L can measure zenithal sky brightness reasonably accurately even if you can only see a fairly narrow piece of sky overhead. The SQM, by contrast, gets "confused" by any significant obstruction - even a tree behind your back that you might be completely unaware of.
 2.  The SQM-L is dramatically less sensitive to streetlights. At any but the darkest sites, any light source less than 20 degrees off the horizon can safely be ignored when measuring the zenith.
 3.  The SQM-L is potentially able to read sky brightness fairly close to the horizon. With an SQM, by contrast, the horizon starts to obtrude into the FOV and affect the readings at any angle lower than 45 degrees.

Benefits #1 and #2 make the SQM-L far superior for measuring skyglow in suburban settings, where both trees and streetlights are common. But at dark sites, the SQM-L's narrow field of view is actually a liability, because it is much more sensitive to the precise placement of the Milky Way - and also, presumably, the zodiacal light.

In any case, measuring the zenith is nearly useless for distinguishing between truly dark sites and fairly dark sites. The measurements done by the National Park Service team (http://www.nature.nps.gov/air/lightscapes/monitorData/index.cfm) clearly show that over much or most of the American West, variations in zenithal sky brightness due to artificial light pollution are swamped by natural variations.

Many people have suggested compensating for natural variations by modelling the Milky Way and zodiacal light and subtracting them from SQM readings. But that would still leave airglow, which is (relatively) huge. And what about variations in extinction? Moreover, subtracting two large quantities to yield a small difference is inherently inaccurate.

The place where differences between good and great sites *are* both visible and measurable is near the horizon, in the direction of the brightest local light source. That's why I'm trying to determine the SQM-L's directional accuracy - to see how close to the horizon one can safely go, and how accurately one can know where the SQM-L's sensor is actually pointed.

I think that the best procedure is probably to take a series of 3 to 5 measurements (as always) using the SQM-L right-side up, then flip it upside-down, take another 3-5 measurements, and average the two results. Since skyglow varies quite continuously, the errors due to the misalignment of the optical axis should pretty much cancel out.
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