W. Ferris article in Sky and Telescope August 2003 article on ODM

c (Bill Ferris) wrote in message ...
At best, I suspect such a conversion would get an observer in the ballpark,
perhaps to within 0.5 magnitude. Here's a table I'll throw out for commentary.
I'd be interested in hearing how well this reflects the real life experiences
of other observers:

NELM.(+/- 0.5)..===..Sky Brightness (mag./sq. arc sec.)
.......8.0............22.0
.......7.0............21.0
.......6.0............20.0
.......5.0............19.0
.......4.0............18.0

I believe that I have read somewhere that NELM scales roughly
as the 2/3 power of sky brightness, not directly proportional.
In other words, every extra 3 mag of sky brightness decreases
the NELM roughly 2 mag. Sorry I cannot cite the source.
Certainly, playing around with the program the Schaefer
published in S+T some while back indicates that NELM varies
much more slowly than sky brightness.

That accords with my own intuition, which is that light pollution
hurts the visibility of diffuse sources much more than it hurts
the visibility of stars. Also, I can see mag 4.0 stars fairly
easily in Manhattan, and the sky there sure *seems* more than
16 times as bright as a dark sky where I can see mag 7.0 stars.
But that is pure hunch, of course.

I would also expect NELM to vary more slowly than sky brightness
on theoretical grounds, for two reasons. First, stars to the
naked eye are effectively point sources, with (theoretically)
infinite contrast against the background. In practice, of
course, defects in your eye blur that theoretical point source.

Second, even for diffuse sources, the surface brightness of an
object at the edge of visibility must vary more slowly than
the sky brightness. That is because invisibility has two
components, one due to lack of contrast against the background
and one due to sheer faintness. As you can easily determine
by experiment inside a house at night with shades drawn, there
is some threshold surface brightness below which a light
source becomes completely invisible even against a perfectly
dark background -- a situation in which the contrast is,
again, theoretically infinite. Put another way, there are
some astronomical objects that the human eye simply can't see,
not even if you were in outer space, not even if there were no
zodiacal light.

- Tony Flanders

Tony Flanders wrote:

Certainly, playing around with the program the Schaefer
published in S+T some while back indicates that NELM varies
much more slowly than sky brightness.


Yes.

Nils-Olof Carlin has written a web page about Schaefer´s paper at
http://w1.411.telia.com/~u41105032/visual/Schaefer.htm
If you scroll down a little, you will find a table giving the
limiting magnitude for different sky backgrounds, both according to
Knoll/Schaefer and Blackwell/Clark. Behold.

Cheers -- Harald

Harald Lang wrote in message ...

To summarize -

Naked-eye-limiting-magnitude to background brightness
conversion table

=================================
Backgrd
brightns Limiting magnitude
Ba Knoll/Schaefer Blackwell/Clark

18.4 4.30
19 4.77 5.80
20 5.49 5.81
21 6.12 6.56
22 6.62 7.17
23 7.02 7.59
24 7.31 7.83
25 7.52 7.95

.. . .

Given the visual limit, the apparent background brightness Ba can be
had from the inverse of the formula above:

Ba = 21.58 - 5 log(10^(1.586-lim_mag/5) - 1)

==================================

Excerpt from Nils Olof Carlin internet page Schaefer's paper at:

http://w1.411.telia.com/~u41105032/visual/Schaefer.htm

(PrisNo6) wrote in message . com...

To summarize -
Backgrd
brightns Limiting magnitude
Ba Knoll/Schaefer Blackwell/Clark

18.4 4.30
19 4.77 5.80
20 5.49 5.81
21 6.12 6.56
22 6.62 7.17

...

Charming, isn't it, how wildly the experts vary? Let's say that
the dream sky, which can be approached but never equalled on Earth,
is mag 22 per square arcsecond. Knoll/Schaefer places the NELM
for that sky at 6.6, Blackwell/Clark at 7.2, and Ferris at 8.0.
FWIW, under my customary decent rural skies -- surely no better
than mag 21 per square arcsecond, if that -- I have seen stars
to mag 6.8 or 6.9, but I have done no better at all under far
darker and clearer skies out West.

And estimates of NELM under heavy light pollution vary even more,
if possible, although I suspect for somewhat different reasons.

Oh how I long for a cheap, widely available device to give an
objective measure of sky brightness! As things stand, we are
like the people building the tower of Babel, all talking at
cross-purposes to each other.

- Tony Flannders

(Tony Flanders) wrote in message ...

Oh how I long for a cheap, widely available device to give an
objective measure of sky brightness!

I'll second that request for a simple device that would measure
naked-eye and through the scope sky brightness. Until then, a good
rule-of-thumb is useful.

Bill Ferris, whose record as an observer in the extraordinary skies of
Flagstaff is without comparision (see
http://members.aol.com/billferris/h400.html ), proposed a simplified
linear rule-of-thumb for relating naked-eye-limiting magnitude to sky
brightness in magnitudes per arcseconds. Boiled down, his rule is sky
brightness (Ba) = naked-eye-limiting-magnitude + 14. Ferris requested
comments on the reasonableness of his proposed rule-of-thumb. Harold
Lang commented that Schaefer's exponential model of sky brightness was
not linear and therefore Ferris's proposed rule may not work.

The following is a comparision of the Schaefer brightness model to
Ferris's proposed simplified rule:

Ferris
Schaefer simplified
Olof-Carlin rule-of-
rule thumb Diff.
NELM Ba
4.0 18.0 18.0 +0.0
4.5 18.7 18.5 +0.2
5.0 19.3 19.0 +0.3
5.5 20.0 19.5 +0.5
6.0 20.8 20.0 +0.8
6.5 21.7 20.5 +1.2
7.0 22.9 21.0 +1.9
7.5 24.9 21.5 +3.4

Schaefer revised by Olof-Carlin
Ba = 21.58 - 5 log(10^(1.586-lim_mag/5)-1)
Ferris proposed simplified rule of thumb
Ba = lim_mag + 14

Ba = sky brightness measured in
magnitude per square arcsecond (MPSA)
NELM = naked-eye limiting magnitude in field of
observation

A graphical representation of the above table is available on my
personal web page at:

http://members.csolutions.net/fisher...le_compare.gif

From the table and graph, is appears that Harold is right, after
leaving a light-polluted sky for extraordinary skies, the Ferris's
proposed simplified rule breaks down. (Although overall the
coeffiecient of correlation for the Schaefer to Ferris rules is .98.)

Conversely, most beginning amateurs, like myself, cannot measure
naked-eye limiting magnitude or zenith limiting magnitude to an
accuracy of under .5 mags. We also live in semi-light-polluted areas
under mag 6.5. So, for most people of moderate skill using the
simplified rule, they probably can use Ferris's simplified rule.
(This would not apply to advanced amateurs like yourself and Ferris.)

The purpose of all of this talk about ODM is to improve your
observing. Olof-Carlin summarizes Clark's optimum detection
magnification concept with following easily remembered rule-of-thumb:

"To detect a faint object, you can increase magnification till the sky
is so dark that you have difficulty seeing the field stop, or till the
object has an apparent size of 1 degree, whichever comes first."

and

"The thresholds here (using the ODM algorithm-program) are for
catching barely visible faint objects. If an object is brighter than
that, it may be possible to see detail by increasing the magnification
even further."

See http://zebu.uoregon.edu/~mbartels/vi.../blackwel.html
(accessed August 2003).

Charming, isn't it, how wildly the experts vary? . . . .
And estimates of NELM under heavy light pollution vary even more,
if possible, although I suspect for somewhat different reasons.

Olof-Carlin's web page discussion pointed out that the Blackwell/Clark
estimate of sky-brightness contained some implementation errors.
Therefore, Carlin concluded that the Schaefer formulae probably better
modeled what is observered in the sky. This was based on Olof-Carlin
detecting an err in the Clark's ODM algorithm, to which Harold has
referred a couple of times. See -

http://zebu.uoregon.edu/~mbartels/vi.../blackwel.html
(Olof-Carlin states that "[t]o my surprise, my results did not quite
match Clark's' and goes on to described Clark's 'double-fault' in
implementing his algorithm.)

Bartel's ODM program, discussed in the Ferris' article in the August
Sky & Telescope, corrects Clark's error in implementation, (but does
not change Clark's important underlying insight).

Let's say that the dream sky, which can be approached but
never equalled on Earth, is mag 22 per square arcsecond.
. . . FWIW, under my customary decent rural skies --
surely no better than mag 21 per square arcsecond, if that
-- I have seen stars to mag 6.8 or 6.9, but I have done no
better at all under far darker and clearer skies out West.

For most of us living in semi-light-polluted skies, Ferris's
simplified rule would be useful. (Ba = NELM + 14 up to mag. 6.5) For
personal purposes, I'll probably use the Schaefer brightness rule
table I restated in this post, when using Bartel's ODM program
(discussed in the August 2003 Sky & Telescope). (But if I happen to
leave the table at home, "NELM + 14" is easy to remember. - .)

For the rare luckly few of us, like Bill Ferris, an expanded rule for
extraordinary skies might still be useful. Extraordinary skies (above
mag 6.9) occur in Ferris's Flagstaff, Arizona observing location near
the Lowell Observatory, and according to some reports of varying
dispute, on rare occasions exceeds an MPAS of 22. Ferris is a
beneficiary of Flagstaff's Lighting Code, first begun in 1958, to
protect dark skies around the Lowell Observatory.

As you suggest, having a simple device that amateurs could use to
objectively quantify sky brightness would aid in training the amateur
observing eye and in improving their observing technique.

A simple, cheap device that amateurs could use to objectively quantify
sky brightness would also be a positive step in collecting local site
specific data to lobby local government to adopt ordinances similar to
Flagstaff's Lighting Code. If local government is to adopt
regulations, usually it should be based on some objective measurement
of the evil to be remedied, to assure fairness to all. In this case,
the measurement is objective data about the light pollution of a
common public resource - dark skies - that is not dependent on
subjective interpretations of light by interested persons - amateur
astronomers. If you cannot measure it; you cannot regulate it.

Regards - Kurt

References:

W. D. Ferris. Dark Skies Rule. Sky and Telescope. 106(2):62 (August
2003).

Schaefer, Bradley E. 1990. Telescopic limiting Magnitudes
Pub. ASP 102:212-229.

Clark, Roger N. 1991. Visual Astronomy of the Deep Sky. Cambridge
Univ. Press.

Olof Carlin, Nils. About Bradley E. Schaefer: Telescopic limiting
Magnitudes . . . . Web page discussion of brightness in Schaefer
(1990) and Clark (1994) at:
http://w1.411.telia.com/~u41105032/visual/Schaefer.htm (accessed
7/2003)

Olof Carlin, Nils. 1997. Another interpretation of the data from
Blackwell . . . Web page at
http://zebu.uoregon.edu/~mbartels/vi.../blackwel.html (accessed
8/2003)

Flagstaff Lighting Code.
http://c3po.cochise.cc.az.us/astro/pollution06p.htm (accessed 8/2003)

Kurt wrote:
Ferris
Schaefer simplified
Olof-Carlin rule-of-
rule thumb Diff.
NELM Ba
4.0 18.0 18.0 +0.0
4.5 18.7 18.5 +0.2
5.0 19.3 19.0 +0.3
5.5 20.0 19.5 +0.5
6.0 20.8 20.0 +0.8
6.5 21.7 20.5 +1.2
7.0 22.9 21.0 +1.9
7.5 24.9 21.5 +3.4

Schaefer revised by Olof-Carlin
Ba = 21.58 - 5 log(10^(1.586-lim_mag/5)-1)
Ferris proposed simplified rule of thumb
Ba = lim_mag + 14

You might try, as an intermediate rule of thumb, if you can juggle
figures with reasonable facility: Halve the NELM, subtract 1, square,
and add 17. I understand that for most people, this won't seem like
much fun (sorry!), but it yields the following values of Ba:

NELM Ba Diff
4.0 18.0 +0.0
4.5 18.6 -0.1
5.0 19.3 +0.0
5.5 20.1 +0.1
6.0 21.0 +0.2
6.5 22.1 +0.4
7.0 23.3 +0.4
7.5 24.6 -0.3

I'm mostly with Tony; I'm dubious as to how useful this will be
in practice. But I did find it an interesting mental exercise to
find a reasonably simple fit.

Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.txt

(PrisNo6) wrote in message . com...

The purpose of all of this talk about ODM is to improve your
observing. Olof-Carlin summarizes Clark's optimum detection
magnification concept with following easily remembered rule-of-thumb:

"To detect a faint object, you can increase magnification till the sky
is so dark that you have difficulty seeing the field stop, or till the
object has an apparent size of 1 degree, whichever comes first."

and

"The thresholds here (using the ODM algorithm-program) are for
catching barely visible faint objects. If an object is brighter than
that, it may be possible to see detail by increasing the magnification
even further."

Certainly useful advice. Even better advice is from Jay Reynolds
Freeman, which I will paraphrase rather than quote.

Don't have preconceptions; experiment! If one magnification
doesn't work, try another. Often, different magnifications
will show different aspects of the same object. Small changes
in magnification can have surprisingly large effects on what
you see.

I have half a dozen rules of thumb w.r.t. magnification stashed in
my mind. For instance, in most cases, the greater the sky brightness,
the higher the optimal magnification for a given object. But every
rule has plenty of exceptions; there are cases where I have found
exactly the opposite to be true.

- Tony Flanders

PrisNo6 wrote:
(Tony Flanders) wrote in message ...


Oh how I long for a cheap, widely available device to give an
objective measure of sky brightness!


I'll second that request for a simple device that would measure
naked-eye and through the scope sky brightness. Until then, a good
rule-of-thumb is useful.


How about the "Dark Sky Meter" Sky & Telescope, Feb 2001. Build one,
do some experimentation on converting it's reading to limiting mag and
you're off to the races.


Cheers,
JH

Tony Flanders wrote:
Charming, isn't it, how wildly the experts vary? Let's say that
the dream sky, which can be approached but never equalled on Earth,
is mag 22 per square arcsecond. Knoll/Schaefer places the NELM
for that sky at 6.6, Blackwell/Clark at 7.2, and Ferris at 8.0.
FWIW, under my customary decent rural skies -- surely no better
than mag 21 per square arcsecond, if that -- I have seen stars
to mag 6.8 or 6.9, but I have done no better at all under far
darker and clearer skies out West.

I suspect much of the difference in NELM numbers can be resolved by taking a
closer look at the way the data were obtained. With respect to the 8.0 (+/-
0.5-mag.) number I use, this is based on reliable reports from observers such
as Heber Curtis, Stephen James O'Meara, Brian Skiff and others who've made
repeated NELM observations within that range. These are observers with acute
vision, access to dark skies and experience.

The Blackwell data, which is foundational in Clark's work, is taken from
experiments in which novices were given 15-seconds or less to detect light
stimuli against backgrounds of varying brightnesses. This methodology provides
a clue as to why NELM estimates based on Blackwell's data are relatively
conservative. The Blackwell data could be said to indicate what the average
person would see, while I'm relying on observations made by top observers.

Also, it should be pointed out that there really is no controversy over the
surface brightness of the darkest sites on Earth. That limit is 22.0 MPSA (+/-
0.1-mag.), which has been derived from photometric data taken over decades from
sites all over the planet.

And estimates of NELM under heavy light pollution vary even more,
if possible, although I suspect for somewhat different reasons.

Oh how I long for a cheap, widely available device to give an
objective measure of sky brightness! As things stand, we are
like the people building the tower of Babel, all talking at
cross-purposes to each other.

I'd say Clark, Schaefer, Carlin, Bartels and other have done an excellent job
of speaking in the same language. And they share similar motivations and goals:
to help us better understand how we see under low-light conditions and what our
limits of vision under those conditions are. And they've had some significant
success.

Clark showed us how to talk about the eye as a contrast detector in a
quantifiable manner. Schaefer opened the door for the integration of difficult
to quantify variables, such as observer experience, when predicting limiting
magnitudes. Carlin and Bartels have furthered the evolution of our
understanding in this area by building a bridge between the the theoretical and
amateur communities: Carlin through his analysis and Bartels through his ODM
program.

Regards,

Bill Ferris
"Cosmic Voyage: The Online Resource for Amateur Astronomers"
URL: http://www.cosmic-voyage.net
=============
Email: Remove "ic" from .comic above to respond

I said:

Oh how I long for a cheap, widely available device to give an
objective measure of sky brightness! As things stand, we are
like the people building the tower of Babel, all talking at
cross-purposes to each other.

Bill Ferris responded:

I'd say Clark, Schaefer, Carlin, Bartels and other have done an
excellent job of speaking in the same language. And they share
similar motivations and goals: to help us better understand how
we see under low-light conditions and what our limits of vision
under those conditions are. And they've had some significant
success.

Yes, I would agree. And as for your own chart of NELM - sky brightness,
I am sure that your 22.0 mag per square arcsecond figure is quite
reliable, since it is totally objective except for some possible
quibbles about spectral distribution. And I am sure that *some*
people can see mag 8.0 stars under such circumstances. I doubt
that I could see much fainter than mag 7.0, however, so that isn't
much help for me. For me, NELM seems to stop being a useful
measuring device for any skies much darker than 20.5 mag per
square arcsecond; after that, my NELM bottoms out. I get much
more useful results by seeing what diffuse objects are visible,
which does *not* bottom out. But it also isn't quantitative.

Moreover, although I am happy to accept your 8.0 - 22.0
correspondence for an important set of experienced observers,
I suggest that this does *not* extrapolate to 7.0 - 21.0,
6.0 - 20.0, etc. Instead, I suggest a curve more like this:

8.0 - 22.0
7.0 - 20.5
6.0 - 19.0
...

The only way to tell for sure is to take one highly conscientious
observer and get NELM estimates under various conditions, with
a good photometric device at hand to get simultaneous measurements
of sky brightness. Actually, this should probably be tried for
multiple observers; there is no reason that the shape of the
curve should be the same for all.

Thanks to the Moon, it should actually be quite easy to get
measurements under various conditions of sky brightness.
Starting at a dark site, you don't have to travel anywhere;
just wait for different Moon phases.

But even if you can derive such a curve, it isn't necessarily
helpful for the average moderately experienced amateur, whose
NELM estimate may be quite different from, say, O'Meara's.
That is why, in response to the question "what should I expect
to see under my skies", the best I can usually say is that
you can see what you can see, and probably more if you try
harder.

The closest I have come to an objective measure of light
pollution is to observe the skies at various Moon phases.
If the sky is very little worse at full Moon than at new,
then you have very bad light pollution. If the sky is
blatantly worse when a 5-day-old Moon is up than at new
Moon, then you have pretty decent skies. But that is
an exceedingly crude measure.

- Tony Flanders