Re: Sky Quality Meter - Light Pollution Map Correlation

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

> Jan, Anthony Tekatch [anthony@unihedron...] updated the conversion page
> that converts SQM readings to ucd/m2:
> http://unihedron.com/projects/darksky/magconv.php
>
> Using this, his page converts 21.31 to 323.16 ucd/m2 and 21.30 to 326.15
> ucd/m2.  I wanted to double check with you that his math is sound.  So
> hitting 325 is somewhere between these numbers.

Robert, I use the same conversion as Anthony, based on the conventional
assumption that 0 mag means 2.54e-6 lm/m2. This constant is _at least_ one
per cent uncertain. And it will remain so, due to impossibility to define
any accurate non-monochromatic conversion of watts to lumens. So, 325 and
328 (ucd/m2) difference is sure below one sigma!

Demanding that 21.30 is the limiting acceptable reading for NNSB*1.30
(having 250 ucd/m2 as NNSB) would be OK. Of course it could be argued that
21.29 as a mean value for several readings is entirely compatible with the
1.3*NNSB limit (within the uncertainties). Or even 21.28 mag. Actually,
two centimagnitudes never matter (also due to uncertainty of SQM itself).

-----

On the past letters:

As for the luminance limits you wrote down, they are correct and sound. Go
on with them!

As for the number of visible stars, the reduction of their number with
increasing sky luminance is somehow included in the Pierantonio's
algorithms -- this is, however, the most uncertain kind of his maps. The
problem is the luminance as depending on the zenith distance. Obviously,
if the distant pollution sources are discrete, this is even more
complicated (skyglow over them uneven around horizon). My old graphs
within
  http://amper.ped.muni.cz/light/luminance/radial/
 (e.g., the logarithmic plot
  http://amper.ped.muni.cz/light/luminance/radial/all_log.png )
are averaged over the azimuth.

Even the dependence of the limit (how faint stars are visible) on the sky
luminance in some spot (like zenith) is not quite simple, for people who
use rod vision for detecting the faintest stars. When the luminance is
above 10 NNSB, cone (fovea centralis) detection might work better even for
them. Star counting campaigns together with SQM measurements might reveal
the dependence for ``average observer''.

However, within the 1 to 2 NNSB interval, the dependence might be fairly
simple. 0.75 mag brighter sky (2 NNSB) would then give 6.4-0.75 mag, or
some 5.6 mag as a zenith limit of star visibility, and about 2.3 times
less stars in zenith. Due to the larger luminance of polluted sky near to
horizon, the total reduction over the hemisphere might be by factor 4 (my
very crude guess; perhaps I have something on it in my old correspondence
with Pierantonio, as the formula he uses.) I'd guess that factor 5 is
perhaps too much.

Definitely, for 1.3*NNSB, the reduction of star visibility limit within
some 40 degrees from zenith is not almost 1 mag, but merely those 0.3 mag.
Still, quite appreciable. No beautiful sky any more.

--------

Last, terminology proposals.

Let's use brightness for the light flux density caused by the object -- so
if it is the brightness of the whole sky, it is the same number as
horizontal ground illuminance (1.0 mlm/m2, or 1.0 mlx in clear-sky moonless
night nature, slightly more than 250 ucd/m2 times pi steradians, due to
the sky being brighter close to horizon). Maybe, this would be the easiest
measure of the state of the night environment, understandable by most
people: one millilux is natural, more than that means pollution. The only
problem is the real range of natural values (0.9 mlx to 1.3 mlx? I don't
know any reliable data on that). And there is no standard method of
measuring it...

And let's use ``luminance'' for quantities expressed in cd/m2. This is the
word in SI and all technical literature.

Lighting people don't use ``brightness'' as anything well-defined. I've
insisted that in astronomy, a simple and useful definition (even if it is
then something different from what lighting engineers mean by brightness)
would be useful. I have written some text on it in 1999,
     http://astro.sci.muni.cz/pub/hollan/a_papers/english/magnitud.pdf

So, the proper short for ``your'' quantity would be NNSL. And for the
(related, via the ``luminance - zenith distance'' function) luminous flux
density from the sky, NNSB. With flat horizon (or just pitch black
obstacles around), this is the same as NNHI, natural clear night
horizontal illuminance.


sorry for the very delayed reaction; fortunately, there was nothing more
to correct...
  jenik