Limiting Magnitude in Binoculars

In July 2003, an active discussion took place concerning the topic
"star magnitude and binoculars". This link goes back to the article,
which includes links to many sites and formula that relate to this
topic.

http://groups.google.com/groups?dq=&....astro.amateur

A great deal concerning the subject Limiting Magnitude in Binoculars
has been published by various noted individuals addressing theoretical
LM values that might be reached. Based on previous studies I
performed in July 2002 and again in winter 2003 relative to what can
be seen in binoculars and the influence of magnification and aperture
on various star fields, I questioned some of the results that were
being predicted. After many nights of recording field notes testing
binocular performance, I was not convinced these limiting magnitude
predictive formula were truly representative of results that could be
achieved in the field, at least not under all conditions.

Based on the questions remaining in my mind after this discussion, I
set out to find some answers. But without the proper data and
analysis, I could not clearly see where the differences might be. It
took a lot longer and a lot more work than I thought before I was
convinced I had enough information to answer these questions for
myself.

After the collection of the field data, it took considerable
additional effort to sort it all out and make sense of it. The end
result will soon be a published article on CN addressing Limiting
Magnitude in Binoculars.

Based on testing eight binoculars on many different nights
representing a range of conditions, this is some of what I found:

Binocular Limiting Magnitudes for a given size aperture are
significantly less, nearly one full magnitude lower, than a scope of
equal aperture. This is due, among other reasons, to the inability of
the aperture in binoculars to reach full potential because of low
magnifications in use.

Two-eyed viewing vs. one-eyed viewing contributes only a small
fractional gain in magnitude. There is no 40% gain realized because
you have two apertures of the same size versus a similar sized scope.
gain may be more like 15% to 20%.

Naked Eye Limiting Magnitude does not act linearly on Binocular
Limiting Magnitude. BLM does not increase in step equally as NELM
increases. For the tested range with a variance of 1.5+ mag NELM,
Binocular Limiting Magnitude varied by less than 0.5 mag.

When binocular magnification and binocular aperture are each tested
separately, for various sizes and powers of binoculars, magnification
produces results about twice what Carlin's formula predicts and
aperture produces results about half of what Carlin's formula
predicts.

When binocular magnification and binocular aperture are each tested
separately, by incremental changes in magnification and aperture, it
is found for each equal increment that magnification has approximately
three to four times the influence as aperture on increases in limiting
magnitude.

In binoculars much more limiting magnitude gain is realized from
increases in magnification than from aperture. This is also related
to the fact that aperture is under-utilized in binoculars. Unless
optimum magnification is employed, the abilities of the aperture to
put an image in the focal plane are never fully delivered to the eye.

Based on my results, for commonly used binocular magnifications in mag
6.5+ skies, I approximate the maximum limiting magnitude for a 100mm
binocular at mag 12.0, for a 60mm binocular at mag 11.0 and for a 40mm
binocular about mag 10.0. For mag 5.0 skies, all limits are about
0.5 mag lower.

The ultimate limiting magnitude reached for any given aperture is
significantly dependant on the magnification in use.

The full article that has been submitted should be available within
the next week or two.

edz

edz wrote in message . ..
snip
The full article that has been submitted should be available within
the next week or two.

Great work ed. Glad that you made and took the time to carry through with collecting some field data. Considering the popularity of
binocular observing, it will be an important contribution to amateur observing. Looking forward to seeing what data you
collected. - Kurt

Naked Eye Limiting Magnitude does not act linearly on Binocular
Limiting Magnitude. . . . The ultimate limiting magnitude reached for any given
aperture is significantly dependant on the magnification in use.

Both consistent with central conclusions of Schaeffer and Clark (ODM).

edz wrote:
The end
result will soon be a published article on CN addressing Limiting
Magnitude in Binoculars.

Pardon me, but "CN" has no meaning to me. Is it a journal, a website or
a magazine?

Based on my results, for commonly used binocular magnifications in mag
6.5+ skies, I approximate the maximum limiting magnitude for a 100mm
binocular at mag 12.0, for a 60mm binocular at mag 11.0 and for a 40mm
binocular about mag 10.0.

Am I correct to assume that 50mm binoculars were not included in your
study? If they were, were their performance closer to the 60mm or to
the 40mm instruments? Halfway?

Maybe I should just upgrade from a 50mm to a 60mm and save the money I
would have spent on a 100mm for something else, like a decent focusser
for my Dob! The mag 1 improvement from a 60mm to a 100mm instrument
makes one feel the extra weight and money is not worth it.

The full article that has been submitted should be available within
the next week or two.

I do look forward to your findings!

Pardon me, but "CN" has no meaning to me. Is it a journal, a website or
a magazine?


CN= www.cloudlynights.com
The mag 1 improvement from a 60mm to a 100mm instrument
makes one feel the extra weight and money is not worth it.

1 magnitude improvement, a factor of 2.5, is about what one would expect when
moving from a 6 inch to a 10 inch telescope, proportionally the same change,
obviously a significant increase in capability. In my experience certainly
worth the effort and expense.

Note that going from 40mm binos to 50mm binos is a only a 1/2 magintude
improvement mathamatically but again, the difference is obvious.



jon isaacs

CN= www.cloudlynights.com

Oh yes of course! It should be compulsory reading for everyone on this
newsgroup.

The mag 1 improvement from a 60mm to a 100mm instrument
makes one feel the extra weight and money is not worth it.


1 magnitude improvement, a factor of 2.5, is about what one would expect when
moving from a 6 inch to a 10 inch telescope, proportionally the same change,
obviously a significant increase in capability. In my experience certainly
worth the effort and expense.

Yes, I see what you mean. The difference from a 6" to a 10" puts it all
in perspective.

The 100mm is back on my to-buy list and a 60mm Pentax PCF WP is
tempting, but I must be strong! ;-)

1 magnitude improvement, a factor of 2.5, is about what one would expect

The 100mm is back on my to-buy list and a 60mm Pentax PCF WP is
tempting, but I must be strong! ;-)

The jump from 60mm to 100mm aperture will provide only about 0.3 to
0.4 LM gain.

The jump from 10x to 16x and likewise the jump from 16x to 25x will
provide 0.4 to 0.6 LM gain each.

You will gain more from the magnification than you will from the
aperture. You don't need 100mm lenses in the binoculars to get the
gain.

edz

So if that is true, what would be the difference for me when switching
from a 20x60 oberwerk to a 20x100 miyauchi fluo? Nearly none???? Hard
to believe!

TK



(edz) wrote in message . com...

1 magnitude improvement, a factor of 2.5, is about what one would expect

The 100mm is back on my to-buy list and a 60mm Pentax PCF WP is
tempting, but I must be strong! ;-)

The jump from 60mm to 100mm aperture will provide only about 0.3 to
0.4 LM gain.

The jump from 10x to 16x and likewise the jump from 16x to 25x will
provide 0.4 to 0.6 LM gain each.

You will gain more from the magnification than you will from the
aperture. You don't need 100mm lenses in the binoculars to get the
gain.

edz

Victor wrote in message ...

Pardon me, but "CN" has no meaning to me. Is it a journal, a website or
a magazine?

Am I correct to assume that 50mm binoculars were not included in your
study? If they were, were their performance closer to the 60mm or to
the 40mm instruments? Halfway?


CN is CloudyNights.com, an astronomy website for publishing articles
and equipment reviews. Hundreds of excellent articles there.

I included 10x50s and 12x50s in these tests. I used eight binoculars
from 8x42 up to 20x80. I tested all my binoculars above 50mm also
masked down to 50mm. So, in effect, I've included results for six
differnt 50mm binoculars.

My 60mm binocular was a 16x60. The 10x50 is closer to 8x42. The
12x50 is closer to 16x60. The 12x50 is more difficult to hand hold
than the 10x.

A 10x50 sees 50% more stars than a 8x42. A 16x60 sees nearly twice as
many stars as a 10x50.

Each jump in magnification from 8x to 10x or from 10x to 12x or from
12x to 16x produces far more significant increases in limiting
magnitude than the jumps from 42mm to 50mm or from 50mm to 60mm.

edz

(edz) wrote in message . com...

Based on testing eight binoculars on many different nights
representing a range of conditions, this is some of what I found:

Binocular Limiting Magnitudes for a given size aperture are
significantly less, nearly one full magnitude lower, than a scope of
equal aperture.

Yes, certainly. I would have thought that the difference would be
more than one magnitude. Magnification helps an awful lot, especially
moving from ultra-large exit pupils like 5mm or 7mm down to respectable
exit pupils like 1mm or 2mm.

Two-eyed viewing vs. one-eyed viewing contributes only a small
fractional gain in magnitude.

Yes, that is my experience too. But small is not nothing, and
also the effect may be greater for diffuse objects than for stars.

Naked Eye Limiting Magnitude does not act linearly on Binocular
Limiting Magnitude. BLM does not increase in step equally as NELM
increases. For the tested range with a variance of 1.5+ mag NELM,
Binocular Limiting Magnitude varied by less than 0.5 mag.

That surprises me immensely, although I cannot claim to have studied
the subject rigorously. I have certainly found the limiting mag in
telescopes to track the NELM modestly well, much better than 0.5 for
1.5, and one would expect binoculars to track it even better. It is
hard to imagine a theoretical explanation for this result.

When binocular magnification and binocular aperture are each tested
separately, by incremental changes in magnification and aperture, it
is found for each equal increment that magnification has approximately
three to four times the influence as aperture on increases in limiting
magnitude.

Again, this surprises me greatly, although I suppose it might depend
what range of mag and aperture you tested. I am generally very
sceptical about the results that you report, but I eagerly await
the details.

- Tony Flanders

(Tony Flanders) wrote in message

Binocular Limiting Magnitudes for a given size aperture are
significantly less, nearly one full magnitude lower, than a scope of
equal aperture.

Yes, certainly. I would have thought that the difference would be
more than one magnitude. Magnification helps an awful lot, especially
moving from ultra-large exit pupils like 5mm or 7mm down to respectable
exit pupils like 1mm or 2mm.

The results of this test simply show support for what Sidgwick stated
and what Schaefer showed us ten+ years ago in his graphic
representation. Increases in magnification provide for significantly
better results in a given aperture.

Two-eyed viewing vs. one-eyed viewing contributes only a small
fractional gain in magnitude.

Yes, that is my experience too. But small is not nothing, and
also the effect may be greater for diffuse objects than for stars.

Barry Simon and I have both performed several tests to try and put a
value on this. I agree, there would appear to be more improvement in
brightness than in magnitude limit.


Naked Eye Limiting Magnitude does not act linearly on Binocular
Limiting Magnitude. BLM does not increase in step equally as NELM
increases. For the tested range with a variance of 1.5+ mag NELM,
Binocular Limiting Magnitude varied by less than 0.5 mag.

That surprises me immensely, although I cannot claim to have studied
the subject rigorously. I have certainly found the limiting mag in
telescopes to track the NELM modestly well, much better than 0.5 for
1.5, and one would expect binoculars to track it even better. It is
hard to imagine a theoretical explanation for this result.

This was a difficult measurement. I felt that NELM determination (at
lower values i.e., 4.0, 4.2, 4.5, but not at higher 5.6, 5.8, 6.0) was
so unreliable that I reported a more conservative variance. My
notebooks show wider variances than I reported here. I reduced my
spreads of NELM and increased my variance of LM. This has the affect
of making the overall differences even smaller.

I have no theoretical explanation either, only actual field data to
support it. But I propose this; What if the binoculars, operating at
4D to 6D, and not at optimum of 24D to 30D, are operating so far below
optimum they could never realize the full potential of not only the
aperture but also because they do not utilize the full potential of
the aperture they also do not realize the full affects of NELM.


When binocular magnification and binocular aperture are each tested
separately, by incremental changes in magnification and aperture, it
is found for each equal increment that magnification has approximately
three to four times the influence as aperture on increases in limiting
magnitude.

Again, this surprises me greatly, although I suppose it might depend
what range of mag and aperture you tested.

I believe this can be explained entirely by the fact that operating at
4D to 6D, and not at optimum of 24D to 30D, they are operating (with
the exception of brightness) so far below optimum they could never
realize the full potential of the aperture. Aperture is so
underutilized that there is so much more potential for improvement
from magnification increases. When the two are isolated from each
other it seems to become readily apparent. This is the third time in
the past 18 months I have tested and published similar results. It is
the first time I have measured the limiting magnitudes to put a real
value on it.


I am generally very
sceptical about the results that you report, but I eagerly await
the details.

- Tony Flanders

I hope you find the documentation supports the claim.

edz