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

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

c (Bill Ferris) wrote in message ...

Thanks for your clarifying comments. So when using Bartel's ODM
program, discussed in your August 2003 Sky & Telescope article against
a series of low-contrast extended objects, you recommend using the
following brightness numbers, based on local observing-field
conditions:

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

Your article suggested a series of galaxy DSOs to practice with.
Where I got thrown was its suggestion to use 21 or 22 as a default
brightness number for a "good rural sky". (I may not be remembering
your article correctly, not having it immediately in front of me.)

This threw me, since I experience more nightly variation in
light-pollution at my observing location and wanted to fine tune use
of Bartel's program a little further. I am a small aperture observer
and wanted to experiment with brighter objects across more light
polluted skies than the list of galaxy DSOs in good or excellent skies
suggested in your article.

( Bartel's ODM program: http://zebu.uoregon.edu/~mbartels/dnld/odm.zip
)

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.

As to the top end of Schaefer's and Clark's curve being at 24 MPAS,
above the empirically measured sky brightness of 22, I assume that is
because Blackwell was measuring brightness in an artificially-darkened
controlled-laboratory setting. Your brightness table suffices for my
immediate needs and I'll leave for another day the details of how
Schaefer's and Clark's brightness formulae is used internally in their
models.

The inability of beginning amateurs, like myself, to distinguish
between when an extended object might not have been resolved because
light pollution was too high (and viewing the object should be tried
again), and when the object could not be resolved because it is simply
to faint for the aperature and magnification being used, is one of the
more frustrating aspects of getting started in hobbyist observing.

The traditional method of evaluating the visibility of extended
objects, by their integrated magnitude compared to naked eye limiting
field magnitude or to zenithal limiting magnitude (which seems to
emphasize the bright core of an extended object, e.g. the Andromeda
galaxy), verses an object's dispersed-average brightness (in MPAS)
compared to the background sky brightness (which seems to emphasize
the object's average brightness across its entire area) both have
their strengths and weaknesses. Neither method seems to fully capture
the effect of the dispersion of the brightness of an extended object
between its central core and less-bright outlying oval and its effect
on visibility. (This is probably less true with respect to the list of
distant galaxies of small angular size suggested in your article.)

I found the MPAS-ODM based approach to be a useful adjunct to the
traditional approach of using integrated magnitude, when trying to
decide whether an object could never be seen with the current scope or
might be seen in a future session in better skies. It increased my
understanding of and observing skill with respect to an object's size,
its brightness, the background brightness of the sky and the
magnification employed.

Thanks - Kurt

P.S. -

The following is a csv file I threw together that contains the Messier
objects sorted by descending MPAS brightness and that lists the
corresponding traditional integrated magnitude:

http://members.csolutions.net/fisher..._Mag_to_Ba.csv

The object brightness in MPAS was computed using Clark's estimate of:

B_mpas=V_m+2.5*(log(2827*Size_x_arcmin*Size_y_arcm in))

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

Kurt wrote:
Thanks for your clarifying comments. So when using Bartel's ODM
program, discussed in your August 2003 Sky & Telescope article against
a series of low-contrast extended objects, you recommend using the
following brightness numbers, based on local observing-field
conditions:

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 tossed out the above table as a starting place for a discussion of the
relationship between NELM and sky brightness. After reading Tony Flander's
comments, Carlin and rethinking the problem from the perspective of the eye as
a contrast detector, I'm doubtful that the "one mag. change in sky brightness
yields a one mag. change in NELM" relationship would hold for any more than one
step.

What would really be helpful would be an organized effort at several big star
parties to get attendees to make NELM estimates and at least one CCD imager to
take photometry which could be used to determine the zenithal sky brightness.
If we could get some data, we could draw some objective conclustions about that
relationship.

Your article suggested a series of galaxy DSOs to practice with.
Where I got thrown was its suggestion to use 21 or 22 as a default
brightness number for a "good rural sky". (I may not be remembering
your article correctly, not having it immediately in front of me.)

The table in my article lists 14 galaxies ranging in surface brightness from
21.2 MPSA to 22.7, which I culled from an Excel file I use to track objects
I've observed. ODM recommends using 21.0 as the background for a dark country
or rural sky, which is reasonable for many dark sky sites at least 50-miles
from the nearest city. As you experiment with ODM, trying a range of sky
brightness settings with size and magnitude data for objects you've observed,
you may find a sky brightness setting which generally yields results echoing
your real world experience.

This threw me, since I experience more nightly variation in
light-pollution at my observing location and wanted to fine tune use
of Bartel's program a little further. I am a small aperture observer
and wanted to experiment with brighter objects across more light
polluted skies than the list of galaxy DSOs in good or excellent skies
suggested in your article. [snip]

I'll look into culling a list for smaller apertures and post it when ready.

The inability of beginning amateurs, like myself, to distinguish
between when an extended object might not have been resolved because
light pollution was too high (and viewing the object should be tried
again), and when the object could not be resolved because it is simply
to faint for the aperature and magnification being used, is one of the
more frustrating aspects of getting started in hobbyist observing.

This is one area where a local club--if available--can be a real benefit.
Experienced observers who are familiar with the conditions at local sites can
provide the encouragement and support to help novice observers grow in the
hobby without becoming discouraged. In lieux of that, there are a variety of
published resources which can serve a similar purpose. Burnham's Celestial
Handbook is one. I also recommend two David J. Eicher anthologies: "The
Universe From Your Backyard" and "Stars & Galaxies." "Universe" is a survey of
deep-sky objects by constellation. "Stars" is a survey by object type.

The traditional method of evaluating the visibility of extended
objects, by their integrated magnitude compared to naked eye limiting
field magnitude or to zenithal limiting magnitude (which seems to
emphasize the bright core of an extended object, e.g. the Andromeda
galaxy), verses an object's dispersed-average brightness (in MPAS)
compared to the background sky brightness (which seems to emphasize
the object's average brightness across its entire area) both have
their strengths and weaknesses. Neither method seems to fully capture
the effect of the dispersion of the brightness of an extended object
between its central core and less-bright outlying oval and its effect
on visibility. (This is probably less true with respect to the list of
distant galaxies of small angular size suggested in your article.)

I found the MPAS-ODM based approach to be a useful adjunct to the
traditional approach of using integrated magnitude, when trying to
decide whether an object could never be seen with the current scope or
might be seen in a future session in better skies. It increased my
understanding of and observing skill with respect to an object's size,
its brightness, the background brightness of the sky and the
magnification employed.

Thanks - Kurt

I'm glad you found my article and ODM of some help. As you observe more
objects, you'll build a larger collection of real world experiences with which
to compare against the theoretical approaches to the question, under what
conditions is an object observable? We may never have that ellusive perfect
rule of thumb which covers all objects. But as we, as individual observers,
grow in our understanding of how the eye-brain system sees the universe, at
least we gain a better understanding of the obstacles to be overcome and the
methods which can help in that endeavor.

Regards,

Bill Ferris
Flagstaff, Arizona USA

P.S. -

The following is a csv file I threw together that contains the Messier
objects sorted by descending MPAS brightness and that lists the
corresponding traditional integrated magnitude:

http://members.csolutions.net/fisher..._Mag_to_Ba.csv

The object brightness in MPAS was computed using Clark's estimate of:

B_mpas=V_m+2.5*(log(2827*Size_x_arcmin*Size_y_

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

Hi there. You posted:

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.

Much of what we are seeing here is variation in the sensitivity of eyes rather
than the lack of consistency found with "experts". However, there are very
real variations in the quality of sites when it comes to ZLM of the eye. At
my local observing site, the unaided eye ZLM is often in the 6.5 to 6.9 range.
Last week at the Nebraska Star Party, I did a quick star count in and around
the head of Draco and checked the stars visible against the data in Megastar.
One very faint star I detected surprised me, as it turned out to be
magnitude 7.59! I do know that others with better eyes have gone fainter from
that location, and this is documented in various places (the record appears to
be Dave Nash's 8.2 at the 2nd Nebraska Star Party). I can't go fainter than
7.8 even from NSP, but the sky is clearly better than what I get at home.
Clear skies to you.
--
David W. Knisely
Prairie Astronomy Club: http://www.prairieastronomyclub.org
Hyde Memorial Observatory: http://www.hydeobservatory.info/

**********************************************
* Attend the 10th Annual NEBRASKA STAR PARTY *
* July 27-Aug. 1st, 2003, Merritt Reservoir *
* http://www.NebraskaStarParty.org *
**********************************************

"David Knisely" wrote in message
...

Last week at the Nebraska Star Party, I did a quick star count in and
around
the head of Draco and checked the stars visible against the data in
Megastar.
One very faint star I detected surprised me, as it turned out to be
magnitude 7.59!

Hi David,
Would you describe that star as being constantly visible, or as popping in
and out of vision during your count?

-Stephen

c (Bill Ferris) wrote in message ...
Kurt wrote:
I am a small aperture observer and wanted to experiment with brighter
objects across more light polluted skies than the list of galaxy
DSOs in good or excellent skies suggested in your article.
Bill responded:
I'll look into culling a list for smaller apertures and post it when ready.

Thanks, I'll look forward to it, but your list would probably also be
subject to your qualifer to Tony Flanders that:

[T]he eye behaves more photopically under really heavy light
pollution,
which would lead me to expect the relationship between sky brightness
and the 'dark adapted' eye to break down at some point.

The only way to find out is to gather some data.

- Kurt

Bill Ferris wrote:
The basic formula is NELM=7.93-5*log(10^(4.316-(Ba/5))+1), which predicts the
following:

Sky
SB....... NELM
26.0..... 7.66
25.0..... 7.52
24.0..... 7.31
23.0..... 7.02
22.0..... 6.62
21.0..... 6.12
20.0..... 5.49
19.0..... 4.77
18.0..... 3.97

My initial response was that the formula is much too conservative. There
are reliable reports of observers (Curtis, O'Meara, etc.) seeing stars
as faint as mag. 8.4, naked eye. Yet, under a pristine dark sky (22.0
MPSA), the above formula predicts a NELM of just 6.62.

Two observations:

1. Because the log argument is always greater than 1, the NELM value
from this formula is bounded by 7.93.

2. This formula is almost quadratic over the range given, so it can
be approximated as follows: Add 25 to SB to get X. Subtract 25 from
SB to get Y. NELM is then approximately thrice X minus the square
of Y, divided by 20. (Not very handy, I suppose, but an item of
interest to those, like me, interested in arcane rules of thumb.)

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

c (Bill Ferris) wrote in message ...
The basic formula is NELM=7.93-5*log(10^(4.316-(Ba/5))+1), which predicts the
following:
SB....... NELM
26.0..... 7.66 snip
My initial response was that the formula is much too conservative. There are
reliable reports of observers (Curtis, O'Meara, etc.) seeing stars as
faint as mag. 8.4, naked eye. Yet, under a pristine dark sky (22.0 MPSA),
the above formula predicts a NELM of just 6.62.

I think you are getting off track with this approach. The purpose of
having an naked-eye-limiting-magnitude to sky-brightness (NELM-Ba)
scale is to have some observations to plug into Bartel's ODM program.
After your conversations with Olof-Carlin, you have suggested Ba
values as high as:

SB....... NELM
26.0..... 7.66

which is in excess of the maximum Ba of 24 assumed in Clark's ODM
model, based on darkened laboratory conditions that exceed the
brightness of the sky seen at night. These are based on the
Knolls-Schaefer formulae you cite:

NELM=7.93-5*log(10^(4.316-(Ba/5))+1) (1.0)

The Knolls-Schaefer formulae is simply the inverse solution of
Schaefer's original relationship expressing sky brightness as an
dependent variable of NELM, (as modified by Olof-Carlin) or:

Ba = 21.58 - 5 log(10^(1.586-NELM/5)-1) (2.0)

Your proposed better fit to the observation that in the field, the
maximum sky brightness (Ba) is limited to about 22.3:

NELM=8.67-5*LOG(10^(4.316-(Ba/5))+1) (3.0)

can also be turned into an inverse function that represents Ba as the
dependent variable and NELM as the independent variable:

Ba = 21.58 - 5 log(10^(1.734-NELM/5)-1) (4.0)

Math between your and the inverse function is easy to follow. 7.93
and 8.67 in your forumale (equations 1.0 and 3.0), are

7.93 / 5 = 1.586
8.67 / 5 = 1.734

in the corresponding inverse function (equations 2.0 and 4.0).

It would easier to understand if this is looked at graphically. The
Figu

http://members.csolutions.net/fisher...compare002.gif

shows the original Knolls-Schaefer formulae, reversed solved in terms
of Ba (equation 2.0, above), your original proposed simple linear
model, and your current better fit revision (equation 4.0).

Depending on your rating, add a conversion factor to the 7.93 figure
in the formula . . .

You noted that there is an increased ability of experienced observers
to see faint point sources and that this should be taken into account
when determining sky brightness.

But when proposing to apply that factor, by incorporating it into
equation (1.0), your suggestion _increases_ the resulting sky
brightness even further, i.e. where Ex_cf is the experience adjustment
-

NELM=(7.93+Ex_cf)-5*log(10^(4.316-(Ba/5))+1) (5.0)

or stated in terms of an inverse function where sky brightness is the
dependent variable:

Ba = 21.58-5*(LOG(10^((1.586-(NELM+Ex_cf)/5))-1)) (6.0)

The following figure is a graph of equation 6.0 for three levels of
experience:

Exp.....Conv.
0....-.0.25
1......0.00
5......1.50

http://members.csolutions.net/fisher...compare003.gif

Now, we're getting Ba numbers (assuming that I did not screw the math
up) that are off-the-chart in terms of the known limitation that the
night-sky in the field does not exceed 22 MPAS and Clark's assumption
that MPAS has a maximum of 24 under ideal laboratory conditions. An
MPAS of 26 is not useful for entering into Bartel's ODM program.

This is probably an easily fixed conceptual problem.

The original Knolls-Schaefer formulae, equation 2.0 above -

Ba = 21.58 - 5 log(10^(1.586-NELM/5)-1) (2.0)

represents an overstatement of extended area brightness seen under
ideal laboratory conditions as compared to what observers see in
field. That experienced observers can see fainter point stars (i.e.
an 8.4 mag star you mentioned) only further breaks down the
relationship between extended sky brightness and NELM derived by
observing point source stars.

Tony Flanders alluded to this problem in an earlier post when he noted
that diffuse sky brightness might be better compared to another
extended object, like the brightness of the Moon, than a point object,
like a star.

What you really want is some kind of additional function that _lowers_
the Knolls-Schaefer sky brightness estimate under ideal laboratory
conditions with increasing experience, down to the maximum observed
field condition of 22 MPAS, not one that increases sky brightness with
experience to 26 MPAS, and beyond the observered field condition of 22
MPAS.

The following Figure is a graphical illustration, a simple exponential
curve fit between a Ba of 18 and 22.3:

http://members.csolutions.net/fisher...compare004.gif

Schaefer solved an analogous problem for telescopic limiting magnitude
(the faintest star seen by magnification in the eyepiece) by engaging
in a series of complex calculations based on optical performance of
telescopes, and then, as a last step subtracting for the inexperience
of the observer, e.g. -

TLM_mag = All_other_physical_factors - Experience_correcting_magnitude

Olof-Carlin's page, that you cited, at:

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

notes that Schaefer's experience correcting factor, expressed in
magnitudes, was:

Experience_magnitudes=0.16(6-e) (7.0)

The approach I think that might work better here is to look an
equation that would express an analogous experience correcting factor
for sky brightness. Thus, the inverse of the Knolls-Schaefer
equation:

Ba = 21.58 - 5 log(10^(1.586-NELM/5)-1) (2.0)

would be modified with something like:

Ba = 21.58 - 5 log(10^(1.586-NELM/5)-1) - Experience_correcting_MPAS
(2.1)

What the equation would be that models "Experience_correcting_MPAS" is
beyond me.

But I do not think trying to incorporate the experience correcting
factor as you propose yields sky brightness numbers that can be
properly used, with respect to extraordinary skies, within the limits
of the assumptiomn of the Bartel ODM program. After about NELM 6.5,
what most of us would accept as an excellent sky, your proposed
modifications yields sky brightnesses that are inconsistent with
observed experience, e.g. - greater than 23 MPAS.

The Experience_correcting_MPAS function needs to be around zero for
all experience levels in light-polluted skies and then higher in
excellent skies for experienced observers.

Maybe better math minds can help on this point.

Regards - Kurt

P.S. - The "exponential fit" discussed above was:

Ba = 14.091*e^(0.0612*NELM) (8.0)

but is intended to graphically illustrate what an improved equation
would look like, and is not intended for modelling purposes.