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