Telescope Reviews: Resolution and Visual Acuity

Here's a link to resolution tests that may help put to sleep the many posts on the internet that display data (not listed as test results, just posted as unqualified data) that states to the effect that a 10x binocular can achieve 6 arcseconds resolution or even an 8x binocular that can resolve 4 arcseconds.
Binocular Resolution Testing w/USAF Charts

The amateur astronomer should know the Rayleigh Limit of a lens determines it's resolving limit, however, the resolving limit can only be achieved at magnifications on the order of 25x per inch of aperture. Sure a 50mm lens has a rayleigh Limit of 138/50 = 2.76 arcseconds, but you have no hope of ever seeing that in a binocular.

Also for astonomical use in dark skies (scotoptic light) the human eye is capable of only achieving 2x to 3x less resolution than in daylight (photoptic light). A retailer that is reporting a resolution of 60 arcseconds for the human eye and 3 arcseconds for a 50mm binocular or 6 arcseconds for any 10x binocular is giving grossly misleading information.

Also the amateur should be aware that the USAF Line Pairs Chart is testing resolution in daylight on high contrast line pairs. The results would be much better than anything that could possibly be achieved in astronomical use due to the ability to see certain kinds of resolution (line pars versus point sources) differently. No binocular can reach the same results on point source resolution under dark skies.

Other Resolution Questions

Below is a series of questions and answers that have been culled from various posts here. There are a number of valuable links that will allow you to godd read some important discussion concerning resolution.

Q There's a strong chance that I will be purchasing Oberwerks' 22 x 100 giant binoculars or something very similar. I just want to know if the 22x to 25x magnification found on most giant binocs is enough to resolve globular clusters? and I mean resolve not grainy...

A I would be surprised if 22X binos could resolve globular clusters. I can't resolve stars in even M13 before about 100x with my 8in reflector.

My 150mm refractor needs 200x to resolve M13 to 60 stars. With my 20x80s I cannot resolve any globulars, although I look at a lot and still enjoy the view.

Q These (25x100mm) bino’s have a good solid build. ...M22 had a mottled look, and it was very easy to see that it was a globular cluster even though there was no way of resolving it at 25x.

A For anything less than optimum magnification, resolution delivered is dramatically reduced. ... 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. For astronomy, you cannot achieve those results.

A ...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.

Resolution of binoculars

Q Being as I struggle to come to terms with measurements such as "arcseconds", I wondered how close to these miniscular measurements comes a top "E" first guitar string ,measuring precisely 0.3 millimetres, being "clearly resolved" through 10 x 50 binoculars from a distance of 100 metres in very unfavourable lighting ?

A 0.6 arcseconds. That would be near the equivalent of seeing the Cassini Division with those binoculars. That falls within the realm defined for extended objects of line shape.

What happens when the thin line you've selected reflects light? Two very important conditions conspire to allow you to see this thin reflective wire.

First, It becomes similar to a long line of point sources. The light from a point source can be seen even if it has imperceptible width.

Second, A lens is not capable of showing any object smaller than it's limit of resolution. What it will do is make anything smaller than the Airy disk appear as the same size as the Airy disk. Your lens has actually fattened up the image of the line...

Resolution and contrast are related. The lower the contrast of the target, the lower the resolution of the optical system. Brighter stars are easier to resolve. Shiney wires are the same. Most resolution tests are done with high-contrast targets not only because they are easier, but also they give better numbers.

Resolving a thin wire

Visual Acuity is a limiting factor in the eye’s ability to achieve resolution and magnification is employed to make an image large enough for the eye to perceive. If your visual acuity is 200 arcseconds, you need 12x mag to see a 17” double or 20x mag to see a 10” double.

Acuity can be measured as the apparent separation results for a range of varying doubles recorded with one or more pieces of equipment. The results will fall into a fairly narrow range. This would be the observer's acuity range.

Measuring visual acuity is not the same as measuring the resolving ability of your instrument. Resolving is the closest components that can be detected. Acuity is the apparent separation results for a range of varying width doubles measured with various equipment, or even measured with one piece of equipment on various targets. It is surprising how the apparent separation results for a variety of doubles will fall into a fairly narrow range. This would be the observer's acuity range.

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).

...any number of publications report tests that show that a better than average human is capable at best of 2 arcmin acuity, ...and normally 3 arcmin or less of resolution when viewing point sources under subdued light conditions (astronomy).

Testing for Visual Acuity

Q Are large aperture binoculars providing greater resolution?

A 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. However, without sufficient magnification, the eye will not see what has been resolved.

...even a 50mm (2") objective is capable of resolving two stars 3" apart. But it would be resolved only if you magnified it large enough for the eye to see it. There is not a common fixed power binocular on the market today that will allow you to see the split in a 3" double, even the 25x150s. But if those lowly 50mm binoculars had 60x or 70x magnification you would be able to see that 3" double as split.

This thread discusses some of the reasons for large aperture binocs
Are large aperture, low mag binoculars pointless

Here you will find explanations for some of the terms used to define resolution
Rayleigh Limit / Dawes Limit

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Edited by EdZ (08/23/05 12:46 PM)

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