Re: sky brightness measures

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

> your method
> (http://amper.ped.muni.cz/jenik/letters/public/msg00188.html)  is quite
> interesting. It should be used as often as possible when SQM measures
> are to be made. Of course the atmospheric condition should be quite
> stable and not change from the day to night time.

> Fabio

Fabio, shortly after I sent the message, I realized that
 direct measurements of extinction
 can be made by SQM if there is Moon low in the sky
(its brightness -- lm/m2 -- or faintness -- mag -- can be computed by my
programme planet, e.g. in its online version through lun_illum.php at
  http://amper.ped.muni.cz/jenik/astro/ ).
 Moon has an advantage to be faint enough to be measured directly by this
instrument. (My programme underestimates Moon's brightness when it is very
close to the to anti-solar point, just missing the Earth semishadow -- the
formula lacks the opposition surge making the Moon up to 12 per cent
brighter, i.e. 0.12 mag less faint.)

When using the Sun,
    evening _and_ morning (or at least next evening) measurements
 are of course preferable, to notice the possible change of the
transparency.

Direct measurements of the Sun, simply measuring the full light and
subtracting another reading made with a small shadow falling onto the
sensor, are of course easier, if you have any luxmeter tolerating these
amounts of light. I hold the cover lid of the sensor at the rope length
from it, to cast the shadow.  Then I shift it just a bit down, to cover a
neighbouring part of the sky, to have the ``full light'' affected by the
lid in a similar way (as the lid blocks not just the sun, but also some
solid angle of the sky). Measuring the Moon by the SQM should be done this
way too.

With Sun/Moon at 11 degrees (five airmasses) or lower, the uncertainty of
their above-atmospheric brightness and of the luxmeter or SQM are no large
problem. Even 0.2 mag uncertainty at these heights translates to 0.04 mag
or less for the uncertainty of zenith extinction.

Another idea came to me now: luminance values for the sky, however they
are expressed, are no values easy to understand. Ratios to the natural
ones are preferable. However, full moon sky is no very good comparison, as
its luminance changes a lot with air transparency (as does that of the
daytime sky). The natural clear deep-night sky having ``a quarter of a
millinit'' is much better choice, as used in the Atlas.

Still better, however, might be to speak about ground illuminance, the
true ``sky brightness'' (brightness: flux density caused by the object).
One millilux (meaning sky brightness of 1 mlm/m2), that's a natural value
easy to remember, for clear nights.  Tenth of that for very cloudy, or
even 1/30 of that (3E-5 lx) for heavily overcast nights. The light comes
from the sky of course -- when it produces these values, then we can speak
about DARK SKY.

It can be measured directly by SQM, pointing it down to a sheet of white
paper (or to snow). Take some 0.87 as its albedo. Of course, if an
overcast sky has a uniform luminance, and you are in a rather open space,
it is sufficient to measure just the sky. (As we photometrists know, then
the illuminance of the horizontal ground is 3.14 times larger than the sky
luminance (3.14 mlx for each 1 mcd/m2), paper luminance is the sky
luminance times albedo of the paper.)

Moon is then a good match for very polluted environments: take 0.1 lx for
the full and 0.01 lx for the half-moon as typical horizontal
illuminanances by them (or maximally 2.5x these amounts when they are high
in the sky, the air is very clear and the moon is not just round, but
really within half a day from the full one).

In Brno, far from any lights, we have half-moon on the clear nights, and
more than full moon on overcast ones. With snow however, it is up to
1 lx everywhere (if not in a dense non-deciduous forest).

jenik