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Resolution of binoculars

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#1 edcannon


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Posted 26 January 2004 - 03:49 AM

This one needs "resolving" (ahem). EdZ wrote:

"I'm not aware of any fixed power binocular on the market today, at any
magnification, that is capable of achieving 3.5 arcseconds of resoltion.

"Well, possibly a 60mm or 70mm high end binocular with interchangable
eyepieces that maybe gets 40x to 50x magnification at a minimum."

Brock pointed out a couple of BVD links talking about such high

I don't know at all, but I just Googled a few things on the

This one says the resolution of a 7x50 is about 12 arc seconds --

This one says an 8x40 and 10x50 yield 8 and 6 arc seconds respectively--

And this seemingly almost identical one says the same thing
about some ITE binoculars (which must be same as Newcon?):

This one says resolution of a certain image-stabilized 16x50
is "seconds of arc, 5.3 max":


Al Nagler wrote in 1991 that a traditional resolution "guideline"
developed by Dawes, who "found that he could just distinguish
the components of faint double stars of equal magnitude when
their separation was equal to 4.56 arc seconds divided by the
aperture in inches", and Nagler wrote, "if the naked-eye
resolution is 1 arc minute (for people with the best
eyesight)..." --


The following one says the Moon is 1800 arc seconds, so 18 would be 1/100
diameter of the Moon; says best naked-eye resolution is about 240 arc
seconds [1/7.5 of the Moon's diameter] but that twice that is "more
practical for comfortable viewing" [1/4 of Moon's diameter]. Would a
10x50 make that theoretically 10 times better, i.e., 24 arc seconds?

The next one appears to be a government contract soliciation with
specifications for 8x23 compact binoculars and says, "The on-axis,
high contrast (100 percent) resolution of the binocular through
each individual telescope shall not be greater than 15.46 arc
seconds per cycle (or arc seconds per line-pair). The resolution
of the human eye is taken as 120 arc seconds per cycle" [twice as
good as the asterism.org statements above] --

This seems like it might be worth a thread. As I don't know
optics and am still learning, when I've seen resolution numbers
cited for binoculars, I haven't known what to think of them.
Above is the first time I've thought of the size of the Moon
in arc seconds.

Ed Cannon - ecannon@mail.utexas.edu - Austin, Texas, USA

#2 EdZ


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Posted 26 January 2004 - 06:51 AM

In another thread, it was mentioned there is a published table shwing a pair of 8x42 binoculars has a reolution of 3.5 arcseconds.

In a word


As an example at the BVD site, Ingraham,s chart shows an 8x42 binocular with a resolution of 3.5 arcseconds. Now mind you we're talking binoculars here.

First, dispell any ideas of using Dawes limit for determining resolution. That's not what Dawes is for. Dawes is used to indicate the point at which two double stars of equal magnitude, can first be noticed as not being a single component. This is not a measure that should be used to state the resolution of optics, even though it is widely done.

Rayleigh Criterion, the formula which states the laws of physics for diffraction limited optics is 5.45/D or 138/Dmm. But it is only true for diffraction limited optics at optimum magnification, for two equally bright double stars of moderate brightness.

For a 42mm diffraction limited lens, R.L. is 138/42 = 3.28 arcsec. That would be possible in astronomical applications if you could use that lens at appoximately 24D to 30D, or magnifications of 30x to 50x, and only for a diffraction limited system.

For bright daylight conditions, optimum magnification can be closer to 12D, or for that 42mm diffraction limited lens (not a binocular), a magnification of 20x.

Fixed power binoculars are not diffraction limited. There are just to many things in the way for the lens to be performing at optimum potential that nothing other than the laws of diffraction are going to limit its performance. Resolution limits, just on that basis might be expected to be twice stated above, but there is more.

For anything less than optimum magnification, resolution delivered is dramatically reduced. Let's not get into a match about the resolution is in the focal plane. The question is, "What does the system deliver?" especially in a fixed power binocular, as there is no possible way to observe the resolution in the focal plane without using the whole system. Your 8x42 BEST binocular may be capable of 10 to 12 arcsec, and a 16x70 Fujinon is capable of about 7 to 8 arcsec, by the best observers.

The other thing is this statement "eye is capable of 1 arcmin resolution". I'm surprised Al Nagler is quoting this one. Humans are not capable of 1 arcmin resultion in astronomical viewing applications. This value represents the absolutely very best vision, (think O'Meara here), observing a black line on a white ground (think the power line example), in the very best optimum lighting conditions (think black line against blue sky on a bright sunny day with no glare). This is a totally unrealistic staged situation, not likely to ever occur or be applicable.

There are no other conditions that are as easily seen as the above example. Every other condition is more difficult.

This one says an 8x40 and 10x50 yield 8 and 6 arc seconds respectively-

This link is a perfect example of how misinformation is diseminated by the internet. A lot of people are reading this stuff and believing it. The uneducated amateur wouldn't know if this is right or wrong. But You will see by the tests provided below this is very very far from true and accurate information.

8-22-05 this link is added here because it is an accurate summary of measures for various binoculars using a USAF Line Pairs Resolution Chart. It may answer the questions of some of the expectations for resolution in binoculars. You will see from the Line Pairs resolution that all the values stated in all the above links are completely misleading. Included in this summary are values for limits of observation of point source resolution. Binocular Resolution Testing w/USAF Charts

Even Sidgwick's publication in the early 70s "Amatuer Astronomer's Handbook", referencing studies by Pickering showed that above mentioned special case of extended object resolution (black line on a white ground) is 3 to 5 times better than a white dot on a black ground (point sources). Also, any number of publications report tests that show that a better than average human is capable at best of 2 arcmin and for very good and normally 3 arcmin or less of resolution when viewing point sources under subdued light conditions (astronomy).

So both Inghram's site and Al Nagler are misusing and misrepresent information and both are providing a misleading result. Both should make an attempt to very clearly explain the basis of their position to the public. In Ingrahram's case to birding public, Al Nagler to the astronomy community. Statistics such as these should not be published in such a way as to be so misleading. They should be clearly represented, basis stated and conclusions described in terms that are realisticly achieved.

Those statistics at the BVD site are not achievable by anyone with common fixed power binoculars, and most humans cannot achieve 1 arcmin resolution in nearly any application, let alone astronomical applications.

Nearly two months ago I submitted a full length comprehensive article on the topic of resolution to CN. It should answer any and all questions you might have. I anxiously await it's publication.

In the meantime you can visit the Double Star Forum, where I have published excerpts on Resolution that might help you understand more of the specifics.
Rayleigh Limit / Dawes Limit

Read this thread and the results of twenty or so CN observer's. It is a good representation of the black line example of resolution in an astronomy application with diffarction limited optics. Keep in mind the black line example is indicitve of R/3 to R/5, where R represents the resolution of the diffraction limited system.
What’s your Lowest power to see Cassini division?

Also, read the threads here in the binocular forum and doubles forum on acuity.
Testing for Visual Acuity
Epsilon Lyrae


#3 brocknroller


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Posted 26 January 2004 - 08:07 PM


It's not just BVD, here's an ad for a Russian BPO 10X42 that states its resolution as 4.29 arc seconds.

but here's some support for the "poppycock theory":
A nice triple star. 39 Draconis A and C can be separated with binoculars, being of about fifth and eight magnitudes respectively, and about 90 arc seconds apart. A and B are much closer, about 3.5 arc seconds apart. 39 Draconis C is quite dim, at magnitude 8.7. Quite high magnification will be required to separate all three stars.

i'm going to ask steve at BVD if he'll tell us how he derived those resolution #'s on his site. i'm sure he just didn't make them up.

#4 brocknroller


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Posted 26 January 2004 - 08:08 PM


It's not just BVD, here's an ad for a Russian BPO 10X42 that states its resolution as 4.29 arc seconds.

but here's some support for the "poppycock theory":
A nice triple star. 39 Draconis A and C can be separated with binoculars, being of about fifth and eight magnitudes respectively, and about 90 arc seconds apart. A and B are much closer, about 3.5 arc seconds apart. 39 Draconis C is quite dim, at magnitude 8.7. Quite high magnification will be required to separate all three stars.

i'm going to ask steve at BVD if he'll tell us how he derived those resolution #'s on his site.

#5 edcannon


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Posted 26 January 2004 - 10:19 PM

Hi EdZ,

My purpose was just to get clarification. I don't know optics. I don't have a telescope. I had just seen those types of resolutions claims for binoculars, and having no knowledge with which to evaluate them just noted them. And more recently I've seen you question them -- with no replies, so I thought I'd dig up some of the claims that are out there just as examples of what optics novices such as I are exposed to as we're searching around reading about things we're interested in.

So anyway, in the other article I think I understand that the general human-eye range is 3 to 5 arc-min or 180 to 300 arc-sec (1/10 to 1/6 the Moon's diameter).

In a very general sense, is it fair to infer that "if a binocular in theory moves me n times closer to the target, then the resolution will be n times better"? I.e., 10x would get 18 to 30 arc-sec? Something like that would enable people as naive as I am about optics with a rule of thumb by which to evaluate claims that are out there.

One other consideration might be something like the gasoline usage numbers cited by manufacturers, "This car gets n miles per gallon using such-and-such a test method." With binoculars, is it okay to infer that if the same theoretical formula is used, even if it is unrealistic, there could be some value in terms of relative comparisons, even if not in terms of absolute numbers in the real world? I really don't know and am just after more solid information to have in mind when I'm reading about binoculars -- especially advertising.

Thank you very much for sharing your knowledge and research results with those of us at or near the beginning of the learning curve!

Ed Cannon - Austin, Texas, USA

#6 edcannon


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Posted 26 January 2004 - 10:21 PM

Oh, I meant to say that the Al Nagler article was originally published in Sky & Telescope in 1991, and I wonder if there wasn't some follow-up, at least a letter or two to the editor. I only go back to about 1999 on S&T.
That article now resides on the Televue web site, which may or may not mean a lot, I assume.

Ed Cannon - Austin, Texas, USA

#7 EdZ


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Posted 27 January 2004 - 06:25 AM

Ed and Brock,

I recognize that the collection of links you provided was a sampling. I had read Al N's web article long ago. There are other articles and quite a few books that discuss the acuity of the human eye. Some others also refer to the 1 arcmin resolution limit of the eye. But I have found, just like articles and books presenting diffraction theory and the formula for the Airy disk, few ever explain the values they use and many are incorrect, some just because they didn't explain the basis, but some are just plain incorrect.

Ed, you identified a website of formulas posted by some fellow from AAI Instrument verification (Asterism). There are four formulas in the middle of that page that have to do with the Airy disk and resolution. They are incorrect either in form or explanation. His formula for the Airy disk is incorrect. His definition of the Dawes Limit is incorrect.

I've been to many websites, some by very well known web-posters and some by authors in our present day astronomy community. About half of them have the formula for the calculation of Rayleigh Limit (the Airy disk formula) incorrect. Almost none of them show the proper corellation between The Airy disk formula and Rayleigh Limit. Some have even gone so far as to relate the Airy disk formula to Dawes!

I had one fellow respond to me once, why am I quoting Rayleigh limit when discussing binoculars, that's used for determining splitting of double stars!!!

Rayleigh Limit IS the determinant according to the laws of physics for the resolution of a lens, any lens. The criteria to be used is two point sources at infinity. Any other test that might be devised for the testing of resolution should be described in terms of R, the resolution as determined by Rayleigh Limit.

Going back to Sidgwick for a moment, he does a very fine job of presenting the collected results of resolution testing for many types of conditions, point sources and extended, from some of the finest experts, and he presents those results in a manner clearly explaining the relationship of expected resolutions for various conditions, all in terms of R.

Brock, I'm sure the answer Steve would give is binoculars are tested by using a resolution line chart. If so, that should be stated as the basis for the resolution test, as it will produce results approximatly 3x finer than physics would dictate is possible for a given system. Now there's a useful value! It is not likely a result that will ever be achieved under any normal viewing circumstances.

Likewise, Al Nagler's use of the value that humans can see resolution of 1 arcmin. That value simple has no place in any discussion related to astronomy, under any circumstances. A thorough reading of the literature clearly represents the 1 arcmin achievement is related to very high contrast targets, (but not point sources) in bright daylight. Whereas, there are few people on this Earth that can achieve unaided resolution in dark skies of 2 arcmin and 95% or better may fall into a range at or below 150 arcsec to 240 arcsec. And that in perfect conditions.

Ed, you are correct to state that as magnification increases we get to resolve easier. For example, an individual with 150 arcsec acuity can use 10x binoculars to resolve a 15 arcsec double star. However, the same person with 150 arcsec acuity would not be able to see a 1" arcsec double resolved if magnified only to 150x. It would take more like 200x or 250x or more. As objects get closer to the Rayleigh limit, resolution becomes far more difficult and a much higher magnification is need.

In general it is a reasonable assumption to estimate that an observer with above average acuity of 150 arcsec would require magnification at least 1.5x objective diameter to resolve a double star at the limit of resolution for any given size objective. As examples, a 42mm (diffraction limited) lens has a Rayleigh limit of 5.45/(42/25.4)= 3.3arcsec. While our observer (with 150 arcsec acuity) might use that 42mm objective at 10x to see a 15 arcsec double, the same observer would need approx 60x magnification to see a 3.3 arcsec double with that 42mm objective. Another example: I have acuity near 150 arcsec. I can see near 10" doubles in my 15x70 binoculars. My 6" scope can resolve doubles to 5.45/6=0.9 arcsec. However, for me to see 0.9 arcsec in my 6" scope, I use magnification of about 250x to 300x.

In another example, viewing two stars with widely varying magnitudes such as a close (1 arcsec) pair with components of mag4 and mag8, might require 220x to 250x or more for the same person (who has 150 arcsec acuity) to see. Or as another example, a double star with one or both of the components being red, may require 25% greater magnification to resolve, while a double with both components being blue may require 25% less magnification to resolve.

Although not my argument concerning the criteria used by some to publish values for resolution, every single variable that can possibly change when viewing any object thru optics has an impact on resolution. Overall brightness, differnece in brightness, color, shape, contrast and magnification all affect resolution to a far greater degree than almost anyone ever mentions. These same criteria apply to terrestrial viewing of bright objects, dim, varying brightness between subjects, high contrast, shape and color all affect resolution.

Not to mention the size of the exit pupil vs. the size of the eye's pupil. A 50mm lens with a 5mm exit pupil (10x50 binos), if used in daylight by a person who's eye pupil has contracted to 3mm, is delivering light and resolution to the eye as if it were from a 30mm lens. This is the whole basis of the argument against the use of a 7mm exit pupil for astronomy by individuals with 5mm eye pupil.

All of these things mentioned is why any statement of values for resolution should always be clearly identified with a basis, so the reader might begin to understand what those values represent and whether they may ever be achieved in real use.


#8 KennyJ


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Posted 27 January 2004 - 03:12 PM

I'm the first to admit that when it comes to advanced calculations of the scientific variety ,the complex physics and mathematical equations involved in optical theory, and talk of arc seconds and limiting magnitude , I might as well be reading the whole discussion in a totally foreign language.

What I DO know is that to be able to resolve ANYTHING , whether it be through naked eye or magnifying instrument , I need LIGHT.

In terrestrial applications I can see absolutely NOTHING in pitch darkness through ANY telescope or binoculars.

On a typical dark , dreary , damp and cloudy day I can barely see the hill half a mile from my house, and when it is foggy I can't even see the end of our road.

On the other hand ,on some days , sometimes even when it is quite cloudy and windy with rain about and odd patches of blue sky , I can clearly "resolve" fell tops in the English Lake District 60 miles away by naked eye.

On such days ,even with 10 x 50 binoculars I can clearly "resolve" details such as old stone trigonometry points on the highest points of hills 17 miles away.

Whilst such detailed resolution may not come anywhere remotely close to approaching the kind of "limits" defined by Dawes , Rayleigh , Sidgwick or Brocknroller,what I can say is that without certain "seeing conditions" I would not be able to confirm the presence of the hills, let alone the trig. point.

Surely LIGHT itself , whether natural or artificial ( such as via searchlights )is the MAIN factor in achieving RESOLUTION.

The apparant absence of any mention of this all -important commodity in any article I've ever read about terrestrial resolution testing surprises me to say the very least.

I'll say another thing too.

If when looking at that trig.point through my 10 x 50s I then mask my binoculars down to 25mm. the image of the trig.point can become so dull and vague that to say it were truly "resolved" would in all honesty represent a misrepresentation of the term "resolved".

I have no means of measuring my eyes' entrance pupils, and often wonder how so many people so eager to defend their chosen "theories" always seem to "know" there own pupil dilation in any given circumstances as if they had some kind of magical micrometric measuring device wired to their brain with a speaking gauge -counter.

In spite of all the so called "indisputable evidence" supporting this notion that a human eye pupil dilation of only 3mm will render a 10 x 50 binocular as being capable only of resolving exactly the same as would a 10 x 30 binocular in that given situation , I have "proved" to myself through more experimentation than has been good for my reputation amongst my neighbours, that this is NOT always the case.Not to MY eyes at any rate.

If anyone doubts me about this rather controversial assertion , until you get to read the "paper" I have forwarded to the administrator for consideration for future publication on the CN article section, you can try this.

Make or find yourself an objective "mask" with a perfectly central opening of 25mm.

Attach this "mask" to any of the two objective lenses of any binocular you have to hand that has objective lenses of at least 42mm. (50mm ,60mm or 70mm might even illustrate my point better )

If you are using a 10 x 50 binocular for example , you will now effectively be in possession of two "monoculars" or mini -spotting scopes in one instrument.

Through one set of prisms you have a 10 x 50 configuration and through the other a 10 x 25 system.

Get yourself in the BRIGHTEST possible surroundings you can and allow your eyes time to "close down the pupils" to their minimum millimetre diameters , whatever that might or might not be , given the presumed absence of the "magical pupil measuring device".

According to all the "experts" this measurement ought to be less than 2.5mm. and especially if you are over 50 years of age as I was at the time of all my tests last autumn.

Now select an object that you wish to view --any object at any distance will suffice -- but the more distant it is and the smaller it is the more it seems to prove my point , which is quite interesting in itself . I wonder WHY ?.

Anyway , whatever you decide upon , first focus the binoculars , not in the usual "way" , but just focus the right side with the diopter adjustment and the left side with the central focusser , then re -check each individually, but DO NOT carry out the usual final"fine tweaking of the central focusser " as you normally would , otherwise the foccusing will tend to be "unbalanced" in favour of the side of the binocular your weakest eye normally looks through .

Using the 10 x 25 as a monocular using your "best" eye ,take a good look at the object. Now quickly move the binocular so you are looking at the same object through the unaltered 10 x 50 side.

Keep swapping and changing quickly from one to the other and take VERY careful notice of what you are seeing through each one.

Now BE HONEST with yourself ! -- not easy if you go into this little experiment with any pre -conceived ideas of what the outcome should or should not be.

Better still , if you can , without "cheating" -- get your partner or assistant to place the eyepieces in turn in front of your eye whils shielding the objectives from view , so you don't actually "know" which one you are looking through.

Of course if al this "optical theory" is correct , it should not matter which one you are looking through because "in theory" there ought not to be ANY discernible difference between the two.

Try it for yourselves and see what you think.

I must say now that I have asked members of another forum to try this for themselves before -- and what REALLY intrigued me was the fact that certain people who were prepared to spend HOURS searching libraries and internet archives for grains of evidence to the contrary , not to mention many hours sitting at their PCs typing away thousands of words in defence of their chosen creed , were apparantly unwilling to spend even the 10 minutes or so required to carry out this little experiment just to give it a try.

One particularly interested "neutral" observer would DID at least have a sufficiently "open mind" to give it a try , happens to be far more knowledgable ,qualified and technically proficient than I am in the field of optics, and indeed it is he, indeed inspired solely by the sheer persistence of myself ,who has carried out the painstaking work that produced the "paper" I so dearly hope finds it's way through the current "backlog" of forewarded articles to this , my favourite internet site , before we all perish !

Regards -- Kenny.

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