Re: Conversion from mg/arcsec^2 to cd/m^2

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

> calculated data. I understand the reference is defined somewhere as
> standard between cd and mg such as 1cd/m^2 = 12.59mg/arcsec^2 or at some
> other point. I want to use constant of 2.51 instead of 2.5 since it
> gives a little better resolution.

Shigemi,

there are two numbers which are close, but are not the same. They are
close just accidentally.

2.511886... = 10^2/5 is the brightness ratio of two stars differing by
1 mag.

2.5 _exactly_ is the coefficient to get faitness difference (in
magnitudes) from the decadic logarithm of brightness ratio (neglecting the
sign).

2.5 log(10^0.4) is identical to 1 log(10), i.e. to 1.

2.5 log(2.51) is almost equal to 1.

In fact, 2.51 is quite close to 2.72 (e) as well.  The consequence is that
if two stars differ by 0.1 mag, then one star is about 10 % brighter than
the other one. 2 dmag correspond to some twenty per cent more brightness.

Another theme, an example of real luminances:

I've processed three images of Brno sky, made in past days. One of them at
an exceptionally clear night, the other ones at a usual one on June 3,
when I tried to find comet Tempel. I could not see it. No wonder, as the
sky luminance was six millicandles per square metre (6 mnt, six
millinits), and the comet sized some 2' had some 10 mag or more, i.e.
luminance of just one millinit or less. The images with tabelled and
colour-coded luminances are within
  http://amper.ped.muni.cz/light/luminance/tempel/
 (colour coding is explained in the parent directory; magenta is centered
at 0.01 cd/m2, with steps equal to 0.5 mag -- five steps comprise 2.5 mag
or luminance ratio 10).

(The extinction made the comet still 1 mag fainter in Brno at
seventeen degrees over horizon, so the attempt was completely hopeless).

jenik