Telescope Reviews: Aperture / Magnification relationship

Aperture / Magnification relationship in binocs

Most recently, this discussion took place touching on all aspects of the above mentioned topic. This thread may be best read in it's entirety.

Comment about Exit Pupil Size

Numerous other threads have discussion related to the same topics.

Are large aperture, low mag binoculars pointless?

See the following comments from some of our forum participants:

It seems that large aperture, low mag. binoculars are wasteful. What is the reason for their creation if the extra aperture serves virtually no purpose?
(Would I be better off using my brother's 15x45 binos... or at least be just as well served by a pair of 11x50's because the other 20mm of aperture are wasted?)... Please explain this to me...

I’ve have come to the conclusion that with binoculars, like everything else in life, it all boils down to compromise. From my …experience I’d have to say that large aperture/low mag binocs are most definitely NOT pointless, they just fill another niche. ... it depends on what your going to use them for.

whilst neither low mag nor large aperture binoculars are remotely "pointless" both categories DEFINITELY have their place in the pleasures of astronomy, unless you are viewing from an exceptionally desirable, non light polluted site, then the combination of LARGE (70mm +) AND LOW power (<12x) would seem to make little sense to me.

when you increase the magnification the image gets a little dimmer so if you are looking at some of the larger nebulae in dark skies the 11x is probably more appropriate.

See the complete comments at this location
Are large aperture, low mag binoculars pointless?!

Masking a Binocular Aperture
Does aperture rule in bino land?
masking is one way to see the effects of aperture vs magnification. This post has a discussion related to some of those effects.
Also refer to the article
How to Understand Binocular Performance

Binoculars that provide very large exit pupils (large aperture-low mag) are designed with maximum brightness in mind. That is, they will deliver the maximum bright image of faint diffuse objects. This is a benefit when viewing faint diffuse nebula or large comet tails or the extended arms of galaxies like M31, M33 and M101, things of that nature.

For almost all objects other than faint diffuse objects, magnification provides greater benefit. It allows you to see deeper in magnitude, putting more stars in the field. This is a benefit in open clusters and star fields like the M24 star cloud or even scanning the Milky Way.

Magnification also provides larger image scale that allows you to see objects that otherwise would have been to small for the eyes to perceive.

Most people will argue that the size of the objective lens is what determines the resolution, and yes this is true. But how much of that resolution the eye can see is dependant on how large the resolved image is magnified. Just about every binocular objective size provides more than enough resolution for the eyes. Without sufficient magnification, the eye will not see what has been resolved.

Take an example of an observer with acuity that allows seeing objects as separated when they are magnified to an apparent size of 150 arcseconds. When viewing an object like M36 using 15x binocs, stars that are as close to each other as 10 arcsec will be seen as separate objects. The same observer using 11x binocs will not be able to see stars only 10 arcsec apart as separate objects, they will appear as one. Hence, 11x will not resolve as many stars in M36.

Remember, a larger objective gathers more light, allowing you to see faint extended objects. A larger exit pupil delivers a brighter image to the eye, again helpful for faint extended objects. Magnification is what allows you to see most small detail.

Also, increases in magnification show more stars. If you used 10x, 12x and 15x binoculars on the same star field, you would see 25-50% more stars with the 12x and another 25-50% more again with the 15x. If you tried to get the same star magnitude gains by increasing aperture and keeping power constant, the size increases over 50mm would quickly make the aperture diameter prohibitive.

Whether large aperture low power binoculars are the right choice in binoculars depends very much on what you intend to use them for.

Relation: aperture-mag when view extended objects

In my 15x70mm Binoculars I know that I can see more stars than a smaller pair, but what about things other than stars?

Suppose I'm looking at M42 with my 15x70's. I assume that magnification doesn't matter too much as it's already pretty big, aperture big enough to match the magnification is more important. I will rate the 'brightness' of M42 through this pair of binoculars as 1.

Now suppose I use a pair of 7x50's. I had thought that these couldn't compare to the 15x70mm's, but now I'm not so sure. If I was to look at M42, it would look smaller, but also stand out more, right? I'm only getting half as much light as I was with the 70mm lenses, but I'm also only magnifying it to have an area about 1/4 the area of the 15x70's. So I would give these a brightness rating of 2. Which is twice as good as the 15x70's.

I know that the bigger image scale does make up for the dimmer view somewhat, but how much does this matter?

There's a lot of factors that determine whether an object will stand out more in a lower power larger aperture binocular.

The larger aperture has greater light gathering ability.

Image scale has a lot to do with whether you can see detail in an object or not.

Extended objects, especially faint diffuse objects benefit from greater aperture.

In binoculars, even globular clusters and dense open clusters can be considered extended objects. These will benefit much more from larger image scale provided by magnification.

I've seen the North America nebula with my 15x70s. I've never seen it with my 10x50s. Assume viewing a 1 arcminute square. If you consider the amount of light gathered spread over the area of the magnified image, then the 15x70s vs 10x50s gather 1.96x the light (70x70=4900 vs 50x50=2500, so 4900/2500=1.96) and they spread it over an area 2.25x as large (15x15=225 vs 10x10=100, so 225sqarcmin/100sqarcmin=2.25x). If 1.96x the light is spread over 2.25x the area, you would think the 15x70s would make it more difficult to see, but that is not the case. Larger image scale can sometimes make it easier to see faint light.

edz

Read the full response at this post
Relation: aperture-mag when view extended objects?

EXIT PUPILS

I wanted to test the difference between two perfectly matched binoculars, but with one variable, exit pupil. I tested 16x70 Fujinons and it's twin, the Fujinon 10x70. Not identical twins, but sure from the same family. These two binoculars share exactly the same everything except the eyepieces. So, only power, and hence exit pupil, are different (and fov, but not important here).

Think of the sky as the backdrop in a portrait. Your subject must stand out from the backdrop to be seen. Consider it to be a grey scale. You all understand the affect of dark sky background. Higher magnification in a telescope reduces the extended light of the background until it approaches a completely dark sky, to the point you can no longer see the field stop. Lower magnification with a larger exit pupil delivers more light, not only from your subject, but also from the background. This can be beneficial or detrimental, depends on the condition. Generally, this makes it much more difficult to see the subject, unless you are viewing under very dark skies.

In moderate 4.5-5.5 skies, 10x70s show a background about three or 4 shades brighter on the grey scale than what is delivered by 16x70s. With a 7mm exit pupil, there is so much light coming into the eyes from the extended sky background, it makes it more difficult to see anything and everything. The 16x70s provide such a contrasty view against the darker backdrop, the contrast gain from the higher magnification of the 16x70s was far reaching and unmistakable. These are exactly the same binocular, so the only improvement in grey scale background most definitely comes only from the increase in magnification, and hence a smaller exit pupil.

But on one night, I did get both binocs out under mag6+ skies. Since the sky was already so dark, the backdrop in the 10x70s did not appear so much brighter than the 16x70s. Much more could be seen with the 10x70s in a darker sky than in the bright sky. Faint nebula stood out now that they were being used in their productive element. On this night the difference between the two was not nearly as great. The 16x70s still see more, but on the faintest nebula, the 10x70s did very well.

My point is not to say one is better than the other. For me, in most conditions, the 16x70s will perform better. But those 10x70s, under the darkest skies I can get to, would be just the tool to observe extended objects and deliver that "finishing" light to my eyes. They have their place. But used in the wrong circumstances, they are no match for the right tool.

Every tool has it's purpose.

edz

Exit Pupil, Large or Small

sure...more magnification means more diffusion of the extended object's light, but I'm asking about the explicit relationship between exit pupil and brightness, not magnification and brightness per se. yes, these are related, but they're not the same thing (keep in mind that two different scopes/binos can give you a different exit pupil for the same magnification...or the same exit pupil with different magnifications).

If we were looking at a white diffuse surface with equal instruments except for exit pupil diameters, the one with the larger exit pupils would have a brighter image. One of the big issues with large exit pupils is that under light-polluted skies they transmit the light pollution as well as the celestial objects. The claim is that smaller exit pupils yield more contrast by reducing the impact of the light pollution

In order to determine the brightness of a view through a binocular you not only need to know the exit pupil size, but also the AFoV. A binocular with a larger exit pupil doesn't *always* give more light to the observer.

Well, not according to the official definitions I've read.

AFOV has nothing to do with image brightness. You are confusing the image formed in your eye with the exit pupil. The exit pupil is simply the image of the effective aperture of the system.

How much light a system transmits is related to its effective focal ratio. If you change the magnification of a system, you also change the effective focal ratio. This has nothing to do with spreading light - sky glow has the same luminance value whether you measure a tiny area or a whole slab.

Lets see how this works. We will use telescopes because we can change the eyepice. The OTA has a printed focal ratio. The brightness of the aerial image formed is dictated by the focal ratio of the scope. An eyepiece will be used to make an image we can see - in astrophotography this is known as afocal projection but using a camera rather than an eye.

The effective focal ratio of the system = OTA focal ratio X eyepice projection magnification.

The eyepiece projection magnification = the eye's focal length / eyepiece focal length.

As you can see, the magnification increases as the eyepiece focal length deceases. And with the first equation, the systems focal ratio increases with the magnification. Using shorter focal length eyepieces increases the effective focal ratio of the system and makes darker images. As the focal ratio increases, the exit pupil deceases.

Light output is not controlled by field of view. If I use an eyepiece in my scope that produces a 3mm exit pupil, it doesn't matter if that eyepiece has a 50° Afov or a 68° Afov, the light output is exactly the same. I just get the same light output over a wider area.

So in effect the view is being dimmed by having a wider AFoV? If you were to somehow block off the edge in the 68 degree AFoV so that all I see is 50 degrees I would assume light output is decreased so that it is less than the orginal 50 degree view?

Again, Light output is not controlled by Field of View.

What is "image brightness"? Can anyone give a clear definition?

several links to sites

One definition of "Image Brightness"

The apparent luminance of the image as seen through an optical system. This brightness is determined by the brightness of the object, the transmittance and the diameter of the exit pupil of the system.

Take a specific magnification, say
10. Then in relation to that, the larger objectives (gathering
more light) yield larger exit pupils:

10x30 = 3
10x50 = 5
10x70 = 7

So the brightness is directly expressed by the exit pupil: the
ratio of light-gathering to magnification.

In terms of the brightness, the largest exit pupils can only be
fully used by dark-adapted younger folks on moonless nights
under dark skies, because the sky background is very dark in
that situation. But under moonlight and light pollution, then
having a lower ratio of gathered light in relation to
magnification yields more contrast, which makes fainter stars
easier to see, since the background is darker.

Brightness in Exit Pupil
Why some exit pupils appear brighter than others of equal size.

Ray Diagrams
All the rays from the cone passing thru the objective to the focal point will pass thru the eyepiece. No rays will be lost. The cone of rays from the objective focal point to the eyepiece exit pupil has a different angle cone for every eyepiece. The shape of the cone of rays gets narrower or wider depending on the eyepiece focal length. That's what focal length is all about. Focal length of a lens creates a cone of light with an angle from the apex at the focal length to the base at the lens. A ray diagram showing a cone of light from the focal length of the objective, once the rays pass the focal point, will show rays at the angle of the eyepiece focal length. Of course F obj / F ep = Mag.

Focal length of a lens

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