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

How do you measure sky brightness in magnitudes per square arcsecond
(MPSA)? Is there some way to relate this measurement to the more
typical zenith limiting magnitude or limiting magnitude of the
observing field?

Bill Ferris' article in this month's Sky and Telescope on Optical
Detection Magnitude (ODM) provides a reference to Bartel's c-code
software to compute the ODM. (
http://www.efn.org/~mbartels/aa/visual.html )

One of the input parameters for this model for the visibility of
extended objects is the background brightness of the sky measured in
magnitude per square arcsecond (MPSA).

I am unable to relate this parameter to my existing knowledge of the
limiting magnitude of the observing field, so I can make estimates of
the MPSA during my observing sessions.

Some of the background internet references related to the article
suggest values like:

Mount Wilson 19.8
Palomar Mountain 21.5
Lick Obs. 20.7
Mount Lemmon 21.5 (near Tucson)
Lowell (Mars Hill) 20.5
Van Vleck 18.7 (Connecticut)
David Dunlap 18.4 (Toronto)
Haute Provence 21.8 (southern France)

Any help on how to estimate the MPSA during my local observing
sessions would be appreciated.

Thanks - Kurt

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

Brian Skiff. How dark can the sky get. Internet article.
http://www.astropix.com/HTML/L_STORY/SKYBRITE.HTM accessed July 2003
(2001)

fisherka wrote:
How do you measure sky brightness in magnitudes per square arcsecond
(MPSA)? Is there some way to relate this measurement to the more
typical zenith limiting magnitude or limiting magnitude of the
observing field?

Bill Ferris' article in this month's Sky and Telescope on Optical
Detection Magnitude (ODM) provides a reference to Bartel's c-code
software to compute the ODM. (
http://www.efn.org/~mbartels/aa/visual.html )

One of the input parameters for this model for the visibility of
extended objects is the background brightness of the sky measured in
magnitude per square arcsecond (MPSA).

I am unable to relate this parameter to my existing knowledge of the
limiting magnitude of the observing field, so I can make estimates of
the MPSA during my observing sessions.

Some of the background internet references related to the article
suggest values like:

Mount Wilson 19.8
Palomar Mountain 21.5
Lick Obs. 20.7
Mount Lemmon 21.5 (near Tucson)
Lowell (Mars Hill) 20.5
Van Vleck 18.7 (Connecticut)
David Dunlap 18.4 (Toronto)
Haute Provence 21.8 (southern France)

Any help on how to estimate the MPSA during my local observing
sessions would be appreciated.

One of the challenges I've been mulling over is finding a way to convert a
naked eye limiting magnitude estimate to a sky surface brightness value. It's a
challenge because, even among a group of experienced observers, naked eye
limiting magnitude estimates can vary significantly. See Bradley Schaefer's
1990 PASP paper for an illustration of this:

http://adsbit.harvard.edu/cgi-bin/np...=1990PASP..102
...212S&db_key=AST&page_ind=0&plate_select=NO&data _type=GIF&type=SCREEN_GIF

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

The scale assumes a naked eye limiting magnitude of 8.0 (+/- 0.5) under a dark
country sky and a logarithmic relationship between sky brightness and NELM: for
every full magnitude change in sky brightness, there is a full magnitude change
in NELM.

The faint limit is actually well-established. The darkest the sky gets anywhere
on the planet is 22.0 mag. per sq. arc second. Observers with acute vision have
been known to go as faint as about 8.0 mag. (+/- 0.5 mag., depending on the
observer) under such conditions. Hence, the choice of an NELM of 8.0 with a +/-
0.5 magnitude range for a truly pristine sky.

The sky surface brightness over Mars Hill on the west side of Flagstaff,
Arizona, has been measured by Brian Skiff at 20.3 magnitude per square arc
second on a moonless, clear night. His NELM from this site is about 6.4
magnitude. It's only one data point but it falls within the NELM range for a
sky brightness of 20.0 mag. per sq. arc second.

A sky brightness of 18.0 mag. per sq. arc second corresponds to conditions at
Mars Hill during full Moon. From my home in north-central Flagstaff, about 3
miles east of Mars Hill, I can still see most of the stars in the Little Dipper
asterism under a full Moon. Also from home, I've seen M44 (3.1 mag, 95'
diameter) with the full Moon just 25-degrees away in Leo. A naked eye limit 4.0
magnitude (+/- 0.5) seems a reasonable choice for a bright sky with an 18.0
mag. per sq. arc second surface brightness.

You can also use Bartels' ODM program to explore this. Go back through your
observing records and find the most difficult visual detections of galaxies.
You can go to the NASA/IPAC Extragalactic Database (NED:
http://nedwww.ipac.caltech.edu/ ) to find magnitude and size data for the
galaxy. Enter those numbers and the aperture of your telescope in ODM. Then,
experiment with a range of sky surface brightness numbers to see where the
cutoff is for detection.

Keep in mind that an object at the very threshhold of detection may be visible
only 30% of the time or so with averted vision. In other words, if the objects
you're using to test ODM were visible with direct vision pretty much all the
time, then the LCD (Log Contrast Difference) will probably be 0.25 or greater.

Here's a recent example from my observations. MCG +7-34-50 is a 14.8 magnitude
galaxy near NGC 6166. I observed this object about three weeks ago from a true
dark sky site with my 10-inch Newtonian. Its small size, about 0.4'x0.4',
yields a quite reasonable surface brightness of 21.6 MPSA. At high
magnification, this little stinker was visible with averted vision about 40% of
the time.

Using the above numbers and a sky brightness of 22.0 MPSA, ODM predicts an
object of this type would be visible with an LCD of 0.09. Increasing the sky
brightness to 21.5 MPSA, the LCD drops to 0.02, indicating an object at the
very threshhold of visibility. The site I use is probably not perfect but,
taking into consideration photometry for the Lowell research site several miles
to the north, should fall somewhere around 21.8 MPSA.

I'd cite this as an observation which tends to confirm ODM's efficacy as a tool
for testing your observing site.

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

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

Bill, thank you for the post. I'll add an empirical test of the
relationship using Bartel's ODM program and your proposed table for
magnitude per square arcsecond (MPAS) to my observing list of
things-to-do for the summer season.

Regards - Kurt

P.S. references -

Bartel's version of Clark's ODM program:
http://www.efn.org/~mbartels/aa/visual.html
http://zebu.uoregon.edu/~mbartels/dnld/odm.zip

P.P.S. -

Your proposed table is the simplest to use. Perhaps a direct
relationship equation for MPAS to NELM can be teased out of equations
17 and 18 in Schaefer's 1990 paper (PASP 102:212 at 215), using
simplifying assumptions of observer visual acuity (F_s) = 1.0 and the
extinction coefficient to its mid-point of 0.25 in a range of 0.2 to
0.3? But the math is beyond me.

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