From: clarke@acme.ucf.edu (Thomas Clarke)
Subject: Re: Binoculars, exit pupil size, etc...
Organization: University of Central Florida
Distribution: na
Date: Tue, 29 Dec 1992 20:58:42 GMT

In article <1992Dec29.144420.1@stsci.edu> gawne@stsci.edu writes:
> Concerning the ongoing discussion of binoculars, image brightness, etc...
> I went to the library and looked at the recent issue of Astronomy which
> included the binocular buyer's guide.  While the guide is overall well
> written it does seem to have suffered from not having been proofread by
> an optics expert.  
> 
> Specifically, the guide claims that larger exit pupils (up to 7 mm)
> produce brighter images.  As someone else has recently pointed out this
> just is not the case.  Image brightness depends only on:
> 
> 	1.  The area of the objective lenses.
> 	2.  The quality of the anti-reflective coatings.
> 	3.  The effective focal ratio of the binoculars.
> 
> The first gathers photons over a given area.  The larger that area the more
> photons gathered.  The second gets as many photons as possible from the
> front of the binoculars to your eyes.  The third factor (focal length) 
> governs how well you'll be able to see dim extended objects, with image
> brightness for extended objects dropping off as f squared.
> ..... 
I beg to differ.  If a film or CCD sensor were located at the binocular
objective's focal plane, then the brightness of extended objects
would depend on the objective focal ratio.  

Binoculars produce virtual images, however, so that the real image 
is formed on the retina of the person looking through the binocular. 
The important focal ratio is thus that of the viewer's eye.  I don't
have exact figures, but this would be something like f/3 or 4 depending
on the individual. This results from the approximately 7 mm entrance
pupil of the eye and the 2-odd cm focal length of the eye.

When using a binocular the focal ratio is determined by the
combination of objective, eyepiece and eye-optics of the viewer.
Maximum brightness is determined by the structure of the individual's
eye.  If the binocular exit pupil fills the eye's pupil, and the
binocular has 100% transmission efficiency, then the brighntess is
at the physiological maximum for extended objects.

For extended objects - there's the rub.  For point objects, the image 
size is to a large extent independent of magnification or anything else,
so that brightness is determined by the effective aperture of the binocular.
That is, it is detemrined by how much light focuses into the eye's
resolution patch.

> BUT if instead of 11x80's you were to use 20x80's with a 5mm exit pupil
> then the person with 6mm dark adapted pupils would see 1.56 times brighter
> images than with the 10x70's!  A person with 5 mm dark adapted pupils would
> see images 2.25x brighter!

Under these conditions extended objects would have equal surface
brightness (I assume you mean 16x80s to get 5mm), although nebulae
would of course be larger in the 16x's.  Stars would be brighter in
the 16x's since the all the light from the objective gets
through to the retina.
> 
> So where is this all going, you ask?  My point is that very few people 
> using binoculars for astronomy have pupils that dilate to 7mm.  You are
> much better off getting binoculars with a 5 or 5.5 mm exit pupil and
> getting ALL the light into your eyes.
> 
Having differed, I nevertheless agree with your conclusions.  The
eyes entrance pupil is maximum only in very dark conditions, so that
exit pupils larger than 5 or so waste light under many conditions.
If the sky is less than perfectly dark, then the contrast of stars
may be increased with a smaller exit pupil.  The brightness of 
the extended sky background is decreased by a smaller exit pupil,
whereas the stellar brightness remains nearly constant.

--
Thomas Clarke
Institute for Simulation and Training, University of Central FL
12424 Research Parkway, Suite 300, Orlando, FL 32826
(407)658-5030, FAX: (407)658-5059, clarke@acme.ucf.edu
Newsgroups: sci.astro