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Visual Accuity

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#1 MikiSJ

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Posted 17 September 2020 - 11:15 PM

The smoke has cleared momentarily from the Santa Clara Valley and I was able to see my personal test of conditions. There is a transmission tower 5.61 miles from my house and if I can see the cables then I know the conditions are likely to be good.

 

Assuming the cable is 1.0" to 1.5" in diameter then, if my arithmetic is good then, roughly, I am able to resolve 9-12 arc seconds. I know this is different than resolving two lines but it works for me.


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#2 Augustus

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Posted 17 September 2020 - 11:48 PM

Resolving a line is easier than resolving a point source. The Cassini division is only 0.65 arcsec wide but we can resolve it with scopes as small as 50-60mm. A 60mm can't resolve a 1-arcsec double.

 

The maximum resolution of the human eye on a non-linear source is 28 arcsec.


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#3 TOMDEY

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Posted 18 September 2020 - 02:03 AM

Resolving a line is easier than resolving a point source. The Cassini division is only 0.65 arcsec wide but we can resolve it with scopes as small as 50-60mm. A 60mm can't resolve a 1-arcsec double.

The maximum resolution of the human eye on a non-linear source is 28 arcsec.

Yep, our resolution of lines is way better than for dots (both presumed to be black features on brightish white surround). The Snellen Standard is kind of a blend of those two extrema...with the letters on the chart comprising short line segments that are one arc-min thick, for nominally-acceptable "20/20 vision" And even there, as most of you have probably noted... certain letters are more apt to get confused: O vs Q vs C vs G, M vs H, P vs F vs E, etc. The retinal-limit acuity is around 20/10 = twice as resolved vs meh 20/20. Note that power lines are not good discriminators of astigmatism. Even with objectionable astigmatism, you may be able to resolve lines, it they happen to be oriented in the clocking direction of your astig. Nother thing that very few people realize >>> If you are myopic, and wear ~distance glasses~ for looking at the starry sky... then your magnitude limit is impaired, because your pupils are rendered smaller, as seen through your glasses, from the outside. e.g. (extreme example) if you are 10D myopic, and your eyeglass lenses are an inch in front of the pupil of your eye, as seen through the cornea... then your functional pupil is only 80% as big as without those glasses = stars 64% as bright. This is why some people get lens implants... naked eye stars look a lot brighter! Far-sighted goes the other way... with glasses rendering stars brighter.

 

I never see this kinda stuff ever discussed among amateur astronomers. Maybe it's just me, but I pretty much notice everything ~optical~ in every-day life... and (thankfully) have developed the habit (and obsessive skills) to derive pretty much everything... from first principles.     Tom


Edited by TOMDEY, 18 September 2020 - 02:06 AM.

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#4 freestar8n

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Posted 18 September 2020 - 02:26 AM

Being able to detect a line in the sky is more a measure of contrast than "resolution" - and things like Dawes' limit don't apply.

 

A good example is a tethered satellite in orbit, where the tether is 1/8" thick and you are viewing it from 100's of miles away.  You can see it clearly as a white line against a black background - even though it is WAY below Dawes' limit.

 

But if you had light pollution and the sky background was bright - it would be harder to see - because of loss of contrast.

 

A black line against a white background is similar.  The black line will make a dip in the profile and that dip will be broadened by optics and diffraction.  But the dip will be there - against a white background - just as a slight bump is there - and visible - against a black background for the tether.

 

For a powerline in the distance - I think haze would be a big factor.  I expect transparency might be more a factor for visibility than steadiness of the seeing.

 

Frank


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#5 BradFran

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Posted 18 September 2020 - 07:45 AM

The Vernier Acuity is much higher, down to 8 arc seconds according to this unsourced Wikipeida entry. Further:

 

The smallest detectable visual angle produced by a single fine dark line against a uniformly illuminated background is also much less than foveal cone size or regular visual acuity. In this case, under optimal conditions, the limit is about 0.5 arc seconds or only about 2% of the diameter of a foveal cone. This produces a contrast of about 1% with the illumination of surrounding cones. The mechanism of detection is the ability to detect such small differences in contrast or illumination, and does not depend on the angular width of the bar, which cannot be discerned. Thus as the line gets finer, it appears to get fainter but not thinner.

I'd like to find the source for this... and

 

After training, observers' threshold has been shown to improve as much as 6 fold.

Source: Stereoscopic acuity for moving retinal images

 

There was a paper written by film experts to determine the finest detail an audience could perceive in a typical movie theater, they also expressed it in lines resolvable rather than angular resolution. The discussion was interesting. If I can find that, I'll link it here.


Edited by BradFran, 18 September 2020 - 07:45 AM.


#6 TOMDEY

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Posted 18 September 2020 - 09:27 AM

The Vernier Acuity is much higher, down to 8 arc seconds according to this unsourced Wikipeida entry. Further:

 

I'd like to find the source for this... and

 

Source: Stereoscopic acuity for moving retinal images

 

There was a paper written by film experts to determine the finest detail an audience could perceive in a typical movie theater, they also expressed it in lines resolvable rather than angular resolution. The discussion was interesting. If I can find that, I'll link it here.

I actually did some work on that stuff for B&L long ago, back when they were aggressively getting into contact lenses. My part was math-modeling of how images interact with the cones and rods. Also did metrologies on the eye's tear layer that is so important twixt contact lens and cornea. Came up with a way to measure that on the fly over the whole pupil and beyond. The tear ducts (at bottom of eye lids) send out this oil that looks like colorful little smoke stacks. ~Dry Eye~ is actually a big problem for some people. I based the tear layer thickness on the color of reflected white light... exactly like the colors we see in soap bubbles. As the layer evaporates, the color follows a voluted parametric trajectory meandering around the IES color map. So, I quantitatively unraveled all of that for the corp and then built the proto instrument to measure and map that. Computers were very slow then, so we had to post-analyze the data. Many of the developmental subjects were --- monkeys cloistered on some island!    Tom

 

Here's an old cartoon of mine showing how lines are hyper-resolvable. As long as our subconscious knows the spatial mapping of each and every cone... an arbitrarily thin line might be resolvable. The ultimate limiter is how good the image is on the retina and of course contrast detection.    Tom

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#7 freestar8n

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Posted 18 September 2020 - 05:44 PM

For a very thin line the width of the image of that line on the retina reaches a limit set by optics and diffraction - and it won't keep getting smaller.  It's the same for stars - and we see them just fine spanning many cones and rods even though the angle they span in the sky is milli-arc-seconds and the corresponding image on the retina would be much smaller than a single cone.

 

For a black "star" against a white sky it's no different - and it isn't the size of that black image on the retina, but its contrast that determines how visible it is.

 

This is all about detection of a single object against a background, as opposed to recognizing details within a given object.

 

Frank


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#8 BradFran

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Posted 19 September 2020 - 07:41 AM

I agree with Frank. We all know that we can't resolve stars, yet we still see them. So it is really two different questions, both interesting. How much contrast is needed to detect a point source (non resolvable)? What is the smallest detail that the human eye can resolve (ie planetary surface details or letters on a wall)?

 

It isn't possible to completely eliminate contrast and only talk about angular resolution. But even if you could, angular resolution seems to be dependent on shape, motion and time observed. If you move your eye position or the object movies, it seems to increase the threshold dramatically. Training seems to increase the threshold dramatically. TomDey's drawing is an interesting way to model the shape part of the question.

 

This isn't talked about by amateurs much beyond the theoretical Dawes' limit for the pupil and the Rayleigh criterion. The retina has the largest role and it and probably isn't completely understood. Look at how image stacking algorithms have advanced CCD photography. Our neurons have a few million years head start.

 

Interesting topic.


Edited by BradFran, 19 September 2020 - 07:41 AM.



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