Dark Sky Meter for research

[Jan Hollan <jhollan@amper....muni.cz>]

I am looking forward to get a SQM for our Observatory in Brno too, to play
with it and compare its readings with my measurements of luminance by a
fish-eye converter and and old Nikon 990 Coolpix camera
 (as those at http://amper.ped.muni.cz/light/luminance/tempel/ ).

I'd like to stress that a single measurement of sky luminance, as accurate
as it may be, says not much more than a visual estimate of how faint are
the faintest stars visible at the site. It's a long and not so
easy-to-understand story, so postpone reading it if you are in a hurry.


The reason is that sky luminance changes a lot with the transparency of
the air. I've made a simplified assumption that inside urbanised areas it
is proportional to the so-called zenith extinction (or ``extinction
coefficient''). It holds quite well for Brno. If the zenith extinction
amounts to 0.45 mag, the zenith luminance is about 5 mcd/m2 (corresponding
to a star of 18.3 mag over a square second), if it is just 0.20 mag (a
very clear air), the sky luminance drops to 2 mcd/m2 (equivalent to 19.3
mag star at each square second) over our Observatory.

The extinction coefficient is to be measured as well, if a single sky
luminance measurement is to be interpreted. This achievable with the SQM
itself, as you will see below.

That coefficient can be of course estimated visually -- by finding stars
with the same perceived brightness and very different angular heights. Or
it can be computed from an all-sky image, or from a series of images with
differing angular heights, or even from a single image of low-lying stars
taken by a calibrated camera.

Otherwise, at least an estimate of air transparency (e.g., by reporting
daytime horizontal visibility of distant terrestrial objects) is to be
attached to the single sky luminance measurement.

Anyway, a long series of measurements on a given site, spanning a full
range of air transparencies, will be interesting even with no direct
estimates of transparencies: we can be sure, that if it was no
high-altitude site, the minimum zenith extinction was about 0.20 mag.

HOWEVER,
  you can measure the extinction coefficient very accurately with the
 SQM itself!

I've measured it many times by a luxmeter, comparing the reading with the
computed illumination by the sun, when it was low in the sky. SQM can be
used a similar way.

Take a sheet of white paper facing the sun. Put the SQM into a black box
with just a small opening, so that the sensor ``sees'' just a central part
of the white sheet. Take a pair of measurements at noon: one with the
paper exposed to full light, another one with the paper shadowed from the
direct sunlight (e.g., by another sheet of paper held in a distance). The
difference of these two ``luminances'' (when converted from the reported
logarithmic numbers -- magnitudes to an arbitrary linear scale) is a
measure of the direct sunlight.

Then take further pairs of measurements, as the sun approaches horizon.
The direct sunlight will be fainter, depending on the extinction
coefficient and an ``airmass'' (which is 1 in zenith, 2 at 30 degrees
angular height, 4 at 14.3 degrees, 8 at 6.7 degrees, 16 at 2.5 degrees
unrefracted = 2.75 degrees visible, some 35 when touching the sea).

The transformation from the logarithmic to the linear scale could be
avoided completely, if you would measure direct sunlight only. A long box
enables it: sun shining through a distant opening to the bottom side
of the box, SQM perceiving just this illuminated bottom side. A further
baffle or two within the box would help to eliminate stray light.  Zenith
extinction is the increment in magnitudes divided by the increment in
airmasses.

Once you have the numbers for different airmasses and a given day with
constant weather, you are able to compute a hypothetical reading for 0
airmasses. Write down its difference Sun0 from the nominal -26.8 mag
for the Sun. Any other day, a single measurement of the Sun when it is low
in the sky will suffice, if the same configuration will be used:
  ( Reading - Sun0 ) / airmass  = zenith extinction in magnitudes

How the airmass can be computed...  E.g. by my programme planets,
available online as lun_illum.php, within
  http://amper.ped.muni.cz/jenik/astro/
 -- just give another parameters on the command line:
 c0 zm

You can also give just c0 to demand Sun instead of Moon and compute
illumination of different surfaces by it (or even its brightness,
faintness etc, by using another parameters; e.g., ze30 would set the
zenith extinction to 30 cmag).

I admit it is a lot of labour. But don't give up and try it, if you have a
SQM (and you should have, sooner or later, if not preferring raw-data
imaging by a digital camera).

Having a backup of hard numbers can be helpful for any serious discussions
with the lighting industry in front of the legislators. And even
Pierantonio and Fabio need some good data for verification of their
DMSP-based atlas. Moreover, the Atlas is just a snapshot of the situation
almost a decade ago. No recent values have been published yet. You may be
the first ones to do that. To compare your results with the Atlas,
remember that it was computed for zenith extinction of 0.33 mag, if I
remember correctly, and for the sea level.

And there is another important research field: amounts of light on
overcast nights. They should be lower than on the clear ones. However, in
urbanised areas they are not. This is of course a major disruption of
natural environment, with various probable impacts on wildlife. What's the
sky (or terrain) luminance at your site on non-clear moonless nights? You
can measure it now...

So I wish you cloudy and overcast nights as well,

jenik