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What the human eye really sees

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Post by shootingsight on 1/13/2021, 10:58 pm

Last weekend I finally completed a task that I set my mind to do 10 years ago.

For years I have been preaching about the optics of shooting: where should your eye be focused for optimal sight picture, railing against people who say you should focus on the sights, using an aperture to improve your depth of field, etc.  Well, I can finally show what I mean.

The human eye is about 1 inch in diameter, so around 25mm.  So I got a 24mm lens (close enough), and put it on my Nikon DSLR, so the camera is seeing about what my eye sees.  I then hung a target 50 feet away, I put the slide of a 1911 longslide on a tripod, aiming at the target, and I positioned my camera about 24" behind the rear sight, which is about how far my eye is from the rear sight.  I then set the camera aperture from about 3/8" diameter to about 1/8" diameter, which is about the size range of the human pupil.  I also included smaller apertures, which represent looking through openings on something like a Merit Disk.  These different apertures provide differing depths of field.  I took pictures with the camera focused on the target, and at a point between the rear and front sight, and at several positions in between, in steps of 0.25 diopters, which is the increment in power you get from eyeglasses.

Then I cropped the pictures to show just the sights and target, and assembled them in a grid, so for any setup, you can track up/down to compare focal points, or track left/right to compare aperture sizes.

And phooey, I just realized I cannot link to a pdf, but I don't want to retype this message.  So I'm going to post it as a teaser, and will return tomorrow to add a link to the pdf.  It's good.  I promise.

Added it below, before thinking to simply edit the original post, so I'll put it in both places: [url=https://www.dropbox.com/s/3cvu289yir12j8c/DOF3.01 comparison.pdf?dl=0]https://www.dropbox.com/s/3cvu289yir12j8c/DOF3.01%20Comparison.pdf?dl=0[/url]


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Post by Jon Eulette on 1/13/2021, 11:18 pm

So does our eyes pupil dilation size change the focal length like your camera lens aperture? I don’t believe it does. I know when I use different iron sighted pistols with varying barrel lengths the clarity of front sight focus is easier to see when farther away (longer barrels) for my old eyes.
Sight alignment is much more important that target focus because when we apply the fundamental of accepting the hold the target is irrelevant to to sight alignment as long as we’re close to the aiming point on the target; thus 10 ring hold equal to 10 ring hold. 
So I’m curious to see your witchcraft lol.
Jon
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Post by shootingsight on 1/14/2021, 12:30 am

No, you are confusing focal length with f:ratio.

The human eye and a camera lens are subtely different, though it is not important to this case.  A camera lens has a fixed focal length, and you achieve focus by varying the distance between the lens and the film plane (retina).  The eye has a fixed distance between the lens and the retina, but varies the lens focal length to achieve focus.  But it does not matter.  The human eye is about a 25mm lens, and the change in focal length from focusing on the target to focusing on the sights is about 0.5mm.

Focal length affects where the eye is focused.  Pupil size (f:ratio) determines how big the depth of field is, centered around that focal point.

Ignore geometry, and consider focal distance as diopters.  With the relaxed eye, the target is at 0 diopters, the rear sight is at about 1.5 diopters. 

If you focus on the target, you have a 1.5 diopter error to the sight.  If your aperture is so small, that you have a depth of field of +/- 1.5 diopters, you will see the target and sight in great clarity, but practice says that is not real.  Further, it is wasteful, because it means you also have 1.5 diopters of focus beyond the target, which is wasted.

Similarly, if you focus on the rear sight, you would need +/- 1.5 diopters to also see the target clearly, which is difficult, and it wastes the depth of field closer than the rear sight.

Best would be to focus at +0.75 diopters.  Now you only need a depth of field of +/- 0.75 diopters to see both the target and the rear sight clearly as your focal point of 0.75 plus the 0.75 depth of field gives you 1.5, so the sights are clear, and the focal of 0.75 minus the 0.75 depth of field gives you 0, which makes the target clear.  Since your distance to the FRONT sight is less than 0.75 diopters from your focal point, the rear and target will be acceptable, and the front sight will be even clearer.  In photography, this is referred to as hyperfocal distance.  Since you only need 1/2 the diopter error (+/- 0.75 versus +/- 1.50), your aperture can be 2x as big, which means it lets in 4x as much light!

So the best solution for low light is a +0.75 diopter focal position, to balance your focus between sights and target, and get maximum utility from your depth of field.  Many shooters like a +0.75 lens for shooting, they find the degree of blur on the target to be acceptable.

However, if you have extra light, and can tolerate a smaller aperture, and bigger depth of field (say a +/- 1.0 diopter depth of field), if you now focus at 0.75, you would now have a target and sights that are sharper than the 'minimum acceptable' because your target is 0.75 diopters away, while your depth of field goes all the way to 1.0 diopters away).  This is generally good.

A better solution might be to pull your focus in slightly.  If you focus at 1.0 diopter instead of 0.75 diopters, with a +/- 1.0 diopter depth of field, your target will still be in acceptable focus, but your sights at 1.5 diopters would only have a 0.5 diopter error from your focal point - way less than 'minimum acceptable'.  So you would have an acceptable target, and sights that are sharper.  The limitation being that a +/- 1.0 diopter depth of field requires a smaller aperture, which lets in less light.

If you are shooting outdoors, you might go a step further, and use an aperture small enough that you can achieve a +/- 1.25 diopter depth of field.  Now you could focus at 1.25 diopters.  your target would still be acceptable, falling inside your depth of field (barely), but your sights would be near perfect, with only 0.25 diopters of error to the rear sight, and less than that to the front sight - indeed diopter errors of less than 1/8 diopter are below the eye's threshold, so your front sight might be optically perfect.


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Post by Jon Eulette on 1/14/2021, 12:35 am

Oops I think I was meaning to say depth of field not focal length.
I normally use +0.75, maybe I need to try +1.0 & +1.25 to bring my 50 yard target into better focus. 25 yds is fine, but 50 is too blurred.
Jon
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Post by radjag on 1/14/2021, 12:41 am

Eagerly awaiting the PDF!

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Post by shootingsight on 1/14/2021, 8:40 am

https://www.dropbox.com/s/3cvu289yir12j8c/DOF3.01%20Comparison.pdf?dl=0

Several pages long, and the same set of images are shown over and over, but with comments on them to explain what you are seeing.

Final page is the images with no comments.

Art

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Post by shootingsight on 1/14/2021, 9:05 am

Jon Eulette wrote:Oops I think I was meaning to say depth of field not focal length.
I normally use +0.75, maybe I need to try +1.0 & +1.25 to bring my 50 yard target into better focus. 25 yds is fine, but 50 is too blurred.
Jon
No, you are going the wrong way.  Increasing your lens power will move your focus closer to you, improving the sights at the expense of the target.

The two things you can do to improve target clarity are either to reduce your lens power to +0.50, or to reduce your aperture, giving you a greater depth of field.

Note that the recommendation of +0.75 is based on the assumption that your unaided eye is 20/20 and requires +0 diopters to see the target perfectly.  If you have a vision error in your eye of +0.25 diopters, that might be slight enough that you never know you have it, but if you then add +0.75 in a lens, you would be shooting with vision of +1.00 total (lens diopters simply add up), so your lens could be biasing you to the sights.

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Post by radjag on 1/14/2021, 9:16 am

Excellent presentation! Thank you very much for sharing. It all makes logical sense to me now, but I did not have the understanding of optics and stuff anyway, so could never have reached these conclusions without your excellent assistance.

I had Lasik surgery some 15 years ago when it first became widely available (I was about 50 at the time and had worn glasses or contacts since my mid-teens). On the advice of the surgeon I chose "mono-vision" where my right (Master) eye was corrected for distance and my left eye for reading, etc. It worked very well. I went back to the same surgeon a year or so ago for a check-up. He was very pleased to see me and found that whilst my left eye had deteriorated slightly with age, my right eye was still very close to where he corrected it. Good.

I have spectacles with the left eye corrected to distance vision, originally only used them for driving at night. But when I got back into shotgun shooting a few years ago I found that I needed them to see clearly when shooting with both eyes open.

I have experimented with many different types of shooting glasses for Bullseye. Tried a Merit, then an Eyepal, but eventually plumped for Champion/Knobloch frames with all of the "gubbins". 

With a red dot in outdoor bright conditions I use a plain lens and an Iris (variable aperture) just to help me to concentrate my vision. And a blinder on my left eye. I do not shoot indoors or in very low light outdoor conditions very often, but at one range in particular I have experienced difficulties with vision, tried winding down the iris, but then the light level is too low to see clearly. I now realise from the PDF that what I actually need to do is add a corrective lens and use a larger aperture. I will need to do some experimentation, but hopefully I now have some better direction to follow. Excellent!

For iron sights in bright outdoor conditions I am currently using a +0.25 corrective lens and an Iris. But I have struggled to achieve a consistent sight picture with different guns at different ranges in variable light conditions. Once again I now realise that a "one size fits all" solution is not working and I need to be prepared to make changes as and when conditions vary significantly. Very interesting.

With the introduction of the new CMP rules regarding safety glasses I am right now in the process of creating a pair of "Hybrid" glasses based on a high clarity set of wrap around safety glasses with the "scaffolding" for the Knobloch attachments mounted on to the frames. With this new to me PDF knowledge I need to definitely make provision to readily swap out corrective lens. These frames will primarily be used for CMP iron sight events and I really need to optimise my vision.

Thanks again.

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Post by CR10X on 1/14/2021, 9:24 am

Radjag:

Keep an eye out (sorry for the pun) for any ClearSight sets you see in the classifieds or elsewhere.  The are clip on lens with +.5, .75, etc. lenses that clip onto standard glasses.  I use these for CMP. 

https://www.bullseyeforum.net/t5047-solvedclearsight-complete-shooting-optic


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Post by SteveT on 1/14/2021, 9:25 am

Interesting experiment and good pictures, but that's not what it looks like to me. Indoor my sight picture looks more like F11 and outdoor is more like F16.

I don't know what the difference is. I am no optics expert. Maybe 24mm isn't the correct lens length, maybe my eye actually has a smaller aperture, maybe the brain is doing some additional processing so I think it is clearer than it is. I am pretty sure my focus is not jumping back and forth.
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Post by chopper on 1/14/2021, 9:32 am

Art, how would lens implants affect all of this? I had cataract surgery with distant focus only, since they are fixed and cannot change?
 Stan

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Post by Jon Eulette on 1/14/2021, 10:00 am

shootingsight wrote:
Jon Eulette wrote:Oops I think I was meaning to say depth of field not focal length.
I normally use +0.75, maybe I need to try +1.0 & +1.25 to bring my 50 yard target into better focus. 25 yds is fine, but 50 is too blurred.
Jon
No, you are going the wrong way.  Increasing your lens power will move your focus closer to you, improving the sights at the expense of the target.

The two things you can do to improve target clarity are either to reduce your lens power to +0.50, or to reduce your aperture, giving you a greater depth of field.

Note that the recommendation of +0.75 is based on the assumption that your unaided eye is 20/20 and requires +0 diopters to see the target perfectly.  If you have a vision error in your eye of +0.25 diopters, that might be slight enough that you never know you have it, but if you then add +0.75 in a lens, you would be shooting with vision of +1.00 total (lens diopters simply add up), so your lens could be biasing you to the sights.
My vision is 20/20 correctible. I use both +0.50 & +0.70 diopters now in my shooting glasses frames. Sights and target at 25 yds looks great, but 50 yards sucks. Target is just a blob.
Jon
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Post by shootingsight on 1/14/2021, 10:21 am

chopper wrote:Art, how would lens implants affect all of this? I had cataract surgery with distant focus only, since they are fixed and cannot change?
 Stan
All the diopter values I talk about are diopters that are added to someone who has perfect distance vision, or are added to your eyeglasses that correct your distance vision.

Diopters are inverse focal lengths, which make no logical sense, but they are used as a unit of measure for lenses, because they make lens math very simple.  At the end of the day, lenses add.  0 diopters focuses you at infinity, which is distance vision.  This is where the human eye will focus if the eye muscle is relaxed, which is what you want for shooting.

If your eye has a built in +1.00 diopter error (you are near sighted), your distance glasses will have a -1.00 diopter lens, so when your eye looks through the lens, it is a zero diopter.  So eg, for this person, when I say shoot with a +0.75 correction over your distance vision, they would want a lens that is -1.00 +0.75 = -0.25.  When they stack the -0.25 lens on their eye that has a +1.00 error, the result is a +0.75 correction while their eye is relaxed.

So if you had cateract implants that are fixed at infinity (0 diopter), you would simply use a +0.75 lens to shoot.  This is why I make safety glasses that have +0.75 molded right in to the lens.

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Post by shootingsight on 1/14/2021, 10:27 am

SteveT wrote:Interesting experiment and good pictures, but that's not what it looks like to me. Indoor my sight picture looks more like F11 and outdoor is more like F16.

I don't know what the difference is. I am no optics expert. Maybe 24mm isn't the correct lens length, maybe my eye actually has a smaller aperture, maybe the brain is doing some additional processing so I think it is clearer than it is. I am pretty sure my focus is not jumping back and forth.
 You are correct, I'm using mid-values.  Medical data suggests human eyes are between 20 and 25mm.  You occasionally meet people with very big pupils or very small pupils.  Based on autopsies, the density of photoreceptors on the retina can span almost 2x across people.  And of course, you hit the nail on the head that there is some brain processing that is going on which I do not account for.

I am highly confident that for most shooters, focus does not jump back/forth, rather your brain will settle in to achieve best overall focus, which is around the hyperfocal distance of +0.75.  Normally, your eye/brain will focus on an object, but in this case, your eye is focusing on the image, which ends up placing your focal point between two images.

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Post by PhotoEscape on 1/14/2021, 10:51 am

I've been watching this topic with great deal of interest.  And reasons are the obvious - Aperture rings were designed around same idea as presented by OP.  However aperture rings are specific to red dot sights.  Understanding the difference is very important.  Red dot sight provides for single plane focusing, while irons are two planes.  Introducing aperture to iron sights is even more important because of that.  Here is something I experimented with:

What the human eye really sees Img_5110

Front sight ID is sized for 25Y.  It is about 2mm, and of course specific to my corrected eyesight.

I agree with OP that +0.75 is optimal for most people to correct distance vision.  To aid answering question for each individual - check your prescription's Cylinder value, then add correction so result comes out to +0.75.  Keep in mind that prescription values most likely will be different for left / right eyes. 

This is a great post!

AP
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Post by Wobbley on 1/14/2021, 11:33 am

When I shoot irons indoors I really struggle with the dim light.  Groups all over the black and bigger groups in general.  Now I see why.  Outdoors I still struggle with focusing on the front sight.  I have a +.25 diopter in my outdoor shooting lenses.  They are ‘orange’ tinted.
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Post by shootingsight on 1/14/2021, 12:27 pm

PhotoEscape wrote:I've been watching this topic with great deal of interest.  And reasons are the obvious - Aperture rings were designed around same idea as presented by OP.  However aperture rings are specific to red dot sights.  Understanding the difference is very important.  Red dot sight provides for single plane focusing, while irons are two planes.  Introducing aperture to iron sights is even more important because of that.  Here is something I experimented with:



Front sight ID is sized for 25Y.  It is about 2mm, and of course specific to my corrected eyesight.

I agree with OP that +0.75 is optimal for most people to correct distance vision.  To aid answering question for each individual - check your prescription's Cylinder value, then add correction so result comes out to +0.75.  Keep in mind that prescription values most likely will be different for left / right eyes. 

This is a great post!

AP
Irons in pistol are actually 3 planes: rear sight, front sight, and target.  I am not a pistol shooter, I shoot high power, where the rear aperture sight is so close to you, you never consider focusing on it, so that is a 2 plane setup with front sight and target, so the most reasonable setup is to balance 50/50 between the two.

In pistol, this is more complex.  The much smaller distance between the front and rear sights makes sight alignment much more important than sight/target alignment, so in pistol, you want to bias focus towards the sights.  Unfortunately, I have not yet come up with the optical math to justify how much you want to bias toward the sights.  I suspect I can come up with a justification, but at the end of the day, personal preference will still dominate.

One final comment - when looking at your prescription, it is the sphere value you want to add +0.75 to.  Cylinder value and axis should remain unchanged.

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Post by shootingsight on 1/14/2021, 12:29 pm

Wobbley wrote:When I shoot irons indoors I really struggle with the dim light.  Groups all over the black and bigger groups in general.  Now I see why.  Outdoors I still struggle with focusing on the front sight.  I have a +.25 diopter in my outdoor shooting lenses.  They are ‘orange’ tinted.

Focal point is not impacted by brightness, so you probably want a +0.75 lens for all conditions, indoor, or out.

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Post by sharkdoctor on 1/14/2021, 2:53 pm

The OP provided good info and pictures to help us think about the optics of a good sight picture and what might be required.  Nearly all representations of a sight picture in literature show (for pistol) a sharp rear, sharp front and sharp target - not going to happen, except under rare and likey unobtainable conditions (very bright and pinhole aperture to yield maximal depth of field).  So we need to consider what we can do.

Try different diopters to focus simultaneously on the front and rear.  Try +0.75, but our eyes (and arms and guns) vary and so do focal requirements.  Age is a compounding factor.  Most of us have lost the ability to accommodate (adjust) to different distances re: focusing.  My prescription is -3.0 sphere and I use that for a dot, but add +0.5 or +0.75 (= -2.5 to -2.25) for irons.  The 50 yd bull is a gray blob, but center hold works well for me since gun sight alignment is critical.

Small apertures increase depth of field.  The iris adjusts: a smaller pupil is better.  If you wear sunglasses, maybe you shouldn't (lens colors and polarization are another discussion).  Merit irises can help.  I spoke of occluders in another thread.  They shouldn't block light due to a contralateral effect for pupil dilation, which reduces acuity.  Use translucent.

I'll stop now but will note that the eye and vision is exceeding complex.  Consider that since the eye is a simple lens, the retinal image we process is upside down and backwards - it is amazing we can function at all😜!

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Post by shootingsight on 1/14/2021, 3:10 pm

What happens with 'old eyes' is that the human lens is surrounded by the cilary muscle.  In the relaxed state, the lens is big and relatively flat, so you focus at infinity.  To focus up close, the eye muscle exerts and squeezes the lens making it smaller and fatter.  This adds diopter to your eye.  When you are young, the lens is flexible enough that you can usually add about +4.0 diopters to your relaxed focal point, so for kids shooting, adding +0.75 is no problem, they can do that all day long.

Once you pass about 43 years old, +/- about 3 years, the lens starts to lose its flexibility, so the muscle has to work harder to add diopters, indeed, you can no longer add +4, you get to +3, then +2, and so on.  +2 is about what you need to read.  So many of you can still add +0.75 to shoot, but reality is that while you can do it, the eye muscle is straining to hold it there.  In a slow-fire string, you might see the sights fine for the first few shots, but then the muscle tires and you cannot see the sights by the end of the string.

So by adding a positive lens, you can now achieve close focus without your eye muscle making the effort, so the muscle stays relaxed, even if you stare at the sights for 10 minutes.  Net, with no lens, your eye struggles.  With a 0.25 lens, you might still see the sights, but your eye is doing less work, and won't tire as fast.  With a +0.50 lens, your eye isn't doing much work at all to just add the extra 0.25 that your brain wants.  By using a 0.75 lens, your eye stays totally relaxed.

However, there is no opposing muscle to drive your focus out.  So if you use a lens that is too strong, your eye cannot subtract power.  If you overdo the lens, the only way to regain target clarity is by reducing aperture.

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Post by PhotoEscape on 1/15/2021, 7:03 pm

shootingsight wrote:
Irons in pistol are actually 3 planes: rear sight, front sight, and target.  I am not a pistol shooter, I shoot high power, where the rear aperture sight is so close to you, you never consider focusing on it, so that is a 2 plane setup with front sight and target, so the most reasonable setup is to balance 50/50 between the two.

In pistol, this is more complex.  The much smaller distance between the front and rear sights makes sight alignment much more important than sight/target alignment, so in pistol, you want to bias focus towards the sights.  Unfortunately, I have not yet come up with the optical math to justify how much you want to bias toward the sights.  I suspect I can come up with a justification, but at the end of the day, personal preference will still dominate.

One final comment - when looking at your prescription, it is the sphere value you want to add +0.75 to.  Cylinder value and axis should remain unchanged.
I respectfully disagree here.  Even with 10" sight radius the distance isn't sufficient to consider front and rear sight as two different planes.  You pictures prove this as same f-stop (i.e. f4) with focus on front sight provides with enough clarity of the rear sight.  At the same time target is definitely in different plane.  If you look at older manual photo lenses, you'll see focusing ring providing with visual aid for focusing distances, and on most lenses there is very little of the rotation needed between 2.5 and 3 feet marks.  That is the most common distance range from cornea to front sight in most shooters arm.  

One phenomena might be helpful when you are talking about finding justification.  And very specifically, - human eye has ability to refocus ("accommodation" is the term for it) very quickly, 30-60 frames per second in average.  And it is a trainable quality.  I would argue that precision pistol shooters can refocus faster than average person.  Refocusing process is much faster than shooter's wobble, and top shooters have incredible ability to hold pistol pretty much motionless for much longer then time needed to refocus from target to front sight.  I suspect, and would be very interested to get confirmation from M-HM level shooters, that there are "multiple check" of the sights alignment versus target.  In simple terms, there are multiple refocusing processes while trigger is moving to breaking point.   

With that said, you've done fantastic job, IMHO, explaining and illustrating what we see when we shoot irons.  Your conclusion that introduction of apertures would enhance the process of shooting is the same as what I came up with while experimenting with aperture rings for dot sights.  There are couple of more beneficial levels in addition to increasing depth of field.  Aperture provides for narrowing field of view, which in turn eliminates destruction from peripherals.  Dr. Norman Wong calls it "visual noise".  Lastly if aperture device has sufficient thickness, it can help shooters with astigmatism by forcing "seeing roundness" of the aperture.  I don't pretend that my thoughts are 100% accurate and complete, - I'm sure there is more to it.  Oh... I shoot while wearing prescription glasses with +0.75 resulting correction.

AP
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Post by radjag on 1/15/2021, 9:37 pm

[quote="sharkdoctor"]I spoke of occluders in another thread.  They shouldn't block light due to a contralateral effect for pupil dilation, which reduces acuity.  Use translucent.[/quote]

I have not yet found Sharkdoctor's other thread re' occluder's, but I must say that I have a better feeling with an opaque (dark grey) occluder, and I prefer the Champion/Knobloch wide occluder with the hinged flap. I've experimented quite a bit with occluders and blinders - for me there is certainly an optimum degree of coverage - go too far and I start to sway because of lack of peripheral vision keys.

IMHO (and possibly only in my personal case) the primary advantage of wide occluders is to block out all kinds of light/visual distractions - thus allowing me to concentrate better on the sights. YMMV!

This is a fantastic thread!

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Post by sharkdoctor on 1/15/2021, 10:12 pm

Radjag,

To demonstrate the phenomenon I described, stand in front of a mirror, and note pupil size in your shooting eye. Cover the other eye with your hand, and observe.  The result should be "eye-opening"!  If you want to experiment, you might try the same with and without your occluder.

Regarding speed of accommodation, it is not very fast.  A research paper I recall noted ca. 250 ms for people in their 20's and 400+ms for those in their 60's to shift from distance to close. The practical aspect for us is that if one is old like me, and lets focus drift to the target, it is going to take some time to get back to the iron sights.  That can eat up a lot of time in a rapid string. On the other hand, distance vision is the relaxed state and can be used to rest the eye if time is available. Close focus is work, and lens correction can help to reduce fatigue.

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Post by shootingsight on 1/16/2021, 9:57 am

The brain does not have the ability to voluntarily dilate both eyes differently, so both are dilated the same amount.  This is the experiment being described above, looking in a mirror, and covering one eye will cause the other to dilate.  If one eye sees light, and the other sees dark, both eyes will dilate to an average value of light and dark.  So if you occlude one eye with an opaque occluder, your aiming eye will dilate to an opening larger that ideal, robbing you of depth of field.

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Post by shootingsight on 1/16/2021, 10:21 am

PhotoEscape wrote:
shootingsight wrote:
Irons in pistol are actually 3 planes: rear sight, front sight, and target. 
I respectfully disagree here. 

AP
Rear and front sights are definitely in different planes.

Diopters are inverse focal lengths, measured in meters.  So a 2 diopter lens will focus at 1/2 meter.  Due to distance being the denominator in the equation, distances become dominant when you are focusing close up.

In my example, the rear sight is 24" from my eye, which is 0.61 meters away, requiring a 1/0.61 = 1.6 diopter lens to exactly focus on the rear sight.  With a 9" sight radius, the front sight is 33" away.  This is 0.84 meters, requiring a 1.2 diopter to see it, so 0.4 diopters difference between the rear and front sight.  This is visible to the human eye, which can detect diopter changes as low as 0.125.

This inverse relationship is also why target distance is not important.  Not being able to distinguish diopter shifts of less than 1/8 diopter means that to the human eye, there is no difference in focus from 8 meters out to infinity, hence anything beyond 8 meters is referred to as 'optical infinity'.

When using diopters, it also becomes easy to calculate the hyperfocal distance by simply averaging two diopter values.  The target at 10 meters has a diopter value of 0.1 (close enough to zero that it can be ignored, but we'll use it for the math example).  The rear sight has a diopter value of 1.6.  So if I average 1.6 and 0.1, I get a hyperfocal value of 0.85.  Since your eye can add power, but not subtract it, to achieve 0.85, you would use a 0.75 lens, with your eye adding 0.1.

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