TargetTalk

Brand new to the site, so I thought I should introduce myself. My name is Art Neergaard, I never shot competitive pistol, but I am a Service Rifle shooter, so I’m not a novice to the concepts of sight alignment.

I'm a mechanical engineer, photographer, I studied optical physics as part of my engineering degree, but never really worked in the field as a profession. Over 50 years old, presbiopic, can't see the front sight anymore, so I looked at the optics of apertures and lenses to figure out what the optics in your eye ought to do, and why they don’t anymore. Eventually, I developed a couple of products to help shooters see better, and aim better, and started a small company that I run in the evenings and weekends, ShootingSight LLC, to sell these for Service Rifle use. To be clear: I am not an eye doctor. I know nothing of eye diseases, and I cannot diagnose. But I do know optical physics, and I understand lenses from a mathematical formula perspective, so I can offer insights that sometimes an eye doctor cannot.

Shooting is all about focus and depth of field, because you are trying to juxtapose a nearby object (the front sight) and a far object (the target). People who prefer to memorize quips, rather than actually understanding a subject like to throw out "the eye can only focus at one distance at a time". This comment is at best shallow, and under certain circumstances is downright wrong. Yes, in a theoretical sense, a lens has only one focal length, but when the image sensor (your retina) has a maximum resolution, degrees of blur which are less than your maximum resolution will still be perceived to be perfectly in focus. So, there is a range of distance that you can move an object slightly closer than your focal point, or slightly further than your focal point, where the amount of blur will be invisible. There is an even bigger range of distance where the amount of blur is so small that the image is good enough for your brain to use. This range over which an object appears to be in perfect or nearly perfect focus is called your depth of field. It ranges from some point closer than your focal point, and extends out to some range beyond your focal point.

The optics of shooting are all about:
a) Getting your focal point in the right place, so your depth of field is spread evenly between the front sight and the target, and
b) Getting your depth of field to be as big as possible, so you can see both front sight and target at the same time without your eye having to refocus between them.

In order to get the best vision of both a front sight and target, the first thing you want to do is focus your eye on a point between the front sight and the target, so that while the eye is relaxed, the amount of blur on the front sight (because it is closer than your focal point) is equal to the amount of blur you see on the target (because it is further away than your focal point). When you see the same amount of blur on near objects as on far objects, it means your depth of field is centered between them.

This focal distance which exactly divides your depth of field between the front sight and infinity is known to photographers as the ‘hyperfocal’ distance of the front sight. You can calculate the distance quite simply because the math works out to be exactly 2x the distance from your eye to the front sight. When I shoot an AR-15, the sight radius is 20” and there are usually 2” between the rear sight and my eye, so eye to FS is 22”. That means my hyperfocal distance is 44”.

Next question is how do you focus at 44”? In the relaxed state, a healthy human eye will focus at infinity. The cilary muscle around the lens can then exert itself to squeeze the lens to make it focus up close. When you are young, and the eye lens is soft, you can focus as close as about 10”, so making only a slight shift from infinity back to 44” is a breeze (it is not zero effort, but most young people ignore it).

As you get older (usually around 40), the lens starts to get harder, and the eye muscle can only focus up close with great effort, or else can’t focus up close at all. You can still focus at distance fine, but need reading glasses (or longer arms). These people lose the front sight, especially at the end of the day, where they have forced the eye muscle to maximum exertion all day long, and then tried to get the muscle to hold still in that exerted state while they aim. After a few shots, the muscle can’t hold, and starts to slip or tremble, and your focus fades. I’m sure at my age I can still do a snappy pullup. But he second one will be slow, the 3rd one might not happen. Same thing for forcing your eye to try and focus up close. As a sidenote here, I have seen claims about nutrition or exercise programs to get your eye back in shape. I think they are a scam. Yes, if you exercise a muscle, you might build it up, but even if this were true for the eye, you have at best created a compensation; you have not fixed the underlying problem that the lens in your eye is hard, and does not focus as well.

If the eye muscle can’t exert to get your eye to your hyperfocal point for the rifle, the other solution is to add a lens. Positive diopter lenses will shift your focal point closer, so you can see up close without the eye muscle having to make the effort. This is what reading glasses do. Difference is that reading glasses shift your focus way close, to arm’s length for reading, which is much too close for shooting. To shoot, you need only a mild corrective lens to shift your focus from infinity to the hyperfocal point. To be clear, older shooters might NEED this correction to see, but young shooters can benefit from a lens as well - it will give them the same image they see with their unaided eye, but they will see it while the eye muscle remains relaxed, rather than having to hold the eye muscle still in the flexed state. This is why almost every Olympic shooter wears a lens.

What lens to use? Lens math for this is pretty simple. Lens power (measured in diopters) is simply the inverse of the focal length, in meters. A 2.0 diopter lens in reading glasses will focus at ½ meters. A 3.0 will focus at 1/3 meters, and a 1.5 diopter will focus at 1/1.5 = 0.66 meters.

You can easily work the math backwards – if you know the distance you want to focus at, convert it to meters, invert the value, and that is the lens you would want. Using the AR example, if you want to focus at 44”, that is 1.12 meters, and would require a +0.9 diopter lens (1/1.12 = 0.9) to shift your eye’s relaxed focus from infinity to the hyperfocal point. Since lenses typically come in ¼ diopter increments, you would round this to a +0.75 diopter. (I won’t go into why you always want to round down, but you do). Unfortunately, reading glasses from the drugstore usually start at +1.25 diopters, which is much too strong – these would give you a really sharp front sight, but the target will be gone in a blur.

If you wear daily glasses for corrective purposes, the good news is that diopters simply add, so if you are farsighted and need a +1.00 sphere to see distance, you would simply take the +1.00 in your prescription and add the +0.75 we worked in the above example, and your ideal shooting lens would be a +1.75. You do have to beware of signs. If you are nearsighted, and need a -1.00 to correct for distance, adding +0.75 to the -1.00 value would net you a -0.25 lens.

Now, there is an addendum to all of this for pistol shooters. In rifle, the rear sight drops out of the equation, and logically you balance focus between the front sight and the target. In pistol, the rear sight does not drop out of the equation, so there is a subtle shift in the logic. In my gut, I think you want to balance your focus between the rear sight and the target, not the front sight and the target. The difference is subtle, but it is not zero, so it is worth figuring out. I’m still gathering information on this, and welcome input from shooters.

After you have achieved focus at the hyperfocal distance, the next step is to reduce blur across the whole range of distances, and this is done by reducing your aperture size. The amount of blur you see on an object is linear with aperture diameter. Your eye naturally has an aperture (the pupil) of about 0.125” on a bright day. If you try and aim without a rear aperture (ie using notch sights), you will see considerable blur on the front sight and the target, even if your eye is at the hyperfocal distance. Using a 0.0625” diameter aperture will cut the amount of blur by half.

The ‘dark side’ of apertures (pun intended) is that the total open area of the aperture limits how much light reaches your eye. As you make the aperture smaller, the image gets dim. In theory, if you used a 0.012” aperture, the focus on the front sight and the target would both be at the resolving limit of the eye, and would be in perfect focus. Unfortunately, most people need about 10x as much light as this to see a good image, so a 0.040” aperture is about as small as most people can tolerate in an AR-15.

In pistol, you have the option to put an aperture on your lens, since you do not form a cheek weld to the rifle stock, and can thus move your head slightly to get proper alignment. These small apertures will do a huge amount of good in crisping up the focus on sights and on the target at the same time.

There is a subnote on apertures, which bears on my products: apertures focus is a particular direction, based on how big they are in that direction. In other words, a horizontal line has its vertical blur limited by how tall the aperture is, while a vertical line can blur side/side based on how wide an aperture is. If you look at a front sight post through a standard round aperture, it will exhibit the same amount of blur on horizontal and vertical edges. However if you keep the total area constant, but make the aperture wider and shorter, so it becomes oval or rectangular, you will improve focus on horizontal lines, and give up focus on vertical lines, even though you have not given up any brightness. For a post shooter, this is a benefit. Windage aiming, and elevation aiming are two different things for your brain. In windage, you are judging the symmetry of the target to the front sight. Centering a target between two sharp vertical edges of the sight, and centering it between two fuzzy edges is the same thing, so focus is not important for windage estimation. Elevation, however, requires determining exactly where the top edge of your sight is, and for this you need sharp focus. Net, a slit shaped opening will bias your focus on the top horizontal edge, giving you improved focus ion elevation, without any sacrifice in windage aiming.

Remembering that most AR shooters find that an 0.040” diameter is as small as they want to go, a rectangular aperture of 0.025” tall x 0.050” wide has the same open area, so the same image brightness as the 0.040” round aperture, however since blur is linear with aperture dimension, dropping the vertical opening from .040” to .025” will reduce blur on the top edge of the post by about 30%.

Bottom line: for pistol shooters, if you do not wear glasses to see far, you would benefit from a +0.50 or +0.75 lens. If you do wear glasses, adding +0.75 to your distance prescription will do the same thing for you.

In the interests of full disclosure, I do sell the products I am discussing here, so apply the appropriate skepticism to my recommendations. But I developed these products in accordance with the laws of physics, I am not trying to ‘spin’ the laws of physics to justify my products, so you will find many shooters who insist they work.
I do sell safety glasses that have +0.50 or +0.75 lens inserts in them.
I cut custom round lenses for shooters to fit into Knobloch and similar shooting glasses, including prescriptions for astigmatism.
I am working on making self adhesive foil apertures. I have 0.042” and 0.054” apertures. These are in the range of sizes rifle shooters use for outdoor light. I’ll give some of these away to any pistol shooter who buys a lens, just to get feedback on if these sizes work for indoor lighting. If you want a set for free, send me a self-addressed stamped envelope by July 1, and I’ll send a pair out.

Art Neergaard
ShootingSight LLC
607 Redna Terr., Suite 600
Cincinnati, OH 45215
http://www.shootingsight.com
email: shootingsight@nuvox.net

First, I would like to start with the proposition that the target is the only thing in sight allignment and the aiming area that does not move. Next is the fact thar any error in front to rear sight allignment is multiplyed by the number of times it is repeated by the distanse to the target. It would seem that simply using a longer sight radius would be advantagious but the apparent increase in movement is difficult to accept and continue the steadily increasing pressure that in so necessary to delivering consistantly good shots. I advise the shooter to not only establish perfect point focus on the front sight and have a short enough sight radius so as to have the rear sight as near to perfect as can be achieved. Without very good vision on both sights you may not be able to have suffecient perfection in allignment to produce the desired results. You should be shooting tens my friends Good Shooting Bill Horton

Art,
I experimented with your idea a bit. Your .040 wide by .025 tall is obviously to large to attach to shooting glasses for pistol because of the distance from the eye. When I tried just scaling it down proportionally it didn't work for me. For the lighting conditions that I have it worked better at about .075 wide by .017 tall. Although in the end I did not see an advantage over a round hole. Of course I didn't put anywhere near the time into it that you have so all I have stated was opinion not fact. Also my lens is made to provide focus at the front sight. I would like to try your idea having the focal point beyond. I think that sounds like a good idea.

Dan

Dan,

The dimensions of the aperture are not strongly driven by distance from the eye. What affects the 'entrance pupil', which is what actually drives depth of field, is the projection of the aperture from your focal point to the front surface of your cornea. An inch more or less will not matter.

As to trying the idea, do this: get a set of calipers, and hold them in front of your eye, so the gap between the jaws is horizontal. Hold them about eyeglass distance from you, and look through the tips of the blades, where they are ground thin. With your other hand, either hold a pistol, or just hold up a finger. As you roll the wheel to increase/decrease the gap between the blades, you will notice that the blur on the edge of your finger is greater than the blur on the top of your finger. At some point, as you set the jaws too narrow, the image will go dim, so then you can just read out on the calipers what gap that was. This experiment is light sensitive, so if you do it outdoors in bright light, you can tolerate a narrower gap than indoors, but it gives you an idea.

If you want to mock this up, just lay two horizontal strips of electrical tape on your glasses. If you are careful you can eyeball a gap of about 0.025 to 0.030. Add two more vertical strips to create the sides, though frankly, these are not sensitive, just make sure the gap is less than 1/8".

Also note, the effect of the rectangular aperture is real, but it is not huge. To see it, you would need to shoot 10 rounds with a round aperture, then 10 with the rectangular, and actually plot the score. I did this with several shooters on a military team, and plotted the results here:

http://neergaard.org/shootingsight/pdf/6ochresults.pdf[/url]

Art,
Some interesting theories. Just trying to work out how to create the rectangular aperture to easily fit to my Knoblock glasses.
At present I have my iris aperture almost stopped down completely to prevent the forsight from "blurring" out.
The next really interesting development would be the adjustable rectangular aperture, although I suspect that the physical construction is going to somewhat complex to achieve.

ShootingSight wrote:http://neergaard.org/shootingsight/pdf/6ochresults.pdf[/url]

Interesting, did you perform any t-tests? You mentioned that the significance is open for debate in the conclusion but I can't see any p-values.

I did mention in the method discussion that I calculated group size based on the probability that 95% of shots would be within that diameter for any one shooter, which is +/-2.81 standard deviations.

However, the percentage improvement used the same method both times, that is unaffected by the confidence interval.

What I do not remember, and I would need to dig out the original data, is that I think I actually calculated x standard deviation, and y standard deviation separately, then calculated varience,and added the two variences to calculate the overall standard deviation, so I went in with the assumption that windage and elevation SD might not be the same, but I did this over 3 years ago, and my memory is not backing me up ....

Art

I did see the CI calculations and I must say you did a great job with the data. Most people wouldn't take it this far. I just wished there were some p-values as well to back it up.
Do you remember if there actually were any differences between vertical and horizontal SD's? did you perform any calculations based on group center and spread from this? (to see whether results holds up)

Anyway, this is just me being curious, don't answer in case you don't remember (or are not interested). Thanks for the reply!

I just skimmed the wall of text in the OP, but in pistol the whole point is to have the front sight crisp and the target blurry. This is why many shooters (myself included) have a + diopter on their shooting glasses vs. regular prescription, and most coaches eschew the use of an iris.

Dr. Norman Wong has a series of articles in SSUSA and on starreloaders.com addressing this in much more scientific detail than I can provide.

I'm not sure why you would eshew apertures - why would you ever NOT accept a free improvement in focus? I will agree that if you only have the relatively small depth of field afforded by your pupil, you will be forced to chose between seeing the front sight, or seeing the target, because the difference in focus between them is just too great. In this case, I would agree that focusing on the front sight makes more sense. However if you can see both clearly at the same time, that has to be better.

The other part of my hypothesis is that there are two places your eye can focus consistently, and it is consistency you need. The first is if you focus on an object like the front sight, the other is if you can leave your eye totally relaxed. So, the concept of trying to focus between the front sight and the target without using a lens will likely not work, because you cannot consistently get your focus to the same spot. But with the right lens and an aperture, you will leave your eye relaxed and see both sight and target clearly together.

Net, a sharp front sight and a blurry target is not the best solution. It is simply the least bad, if you accept that you are shooting with a poor depth of field.

E-J,

To begin with, I made an error in my previous post - I looked up a single sided error of 0.25% in the Z table, rather than 2.5% when I calculated in my report. THe correct answer is that for an error range of +/- 2SD, the included data set will cover 95% of observed values, so when you consider that an error can occur on the high or the low side, this means 2.5% will be higher than the range, and 2.5% will be lower than the range. Since the data covers 95%, that means 5% will fall outside the predicted range, so your p value will be 0.05.

As for the calculations, the rectangular aperture did, as predicted, have a greater impact on vertical distribution than horizontal. In general, vertical distribution improved, and horizontal did not suffer.

Below is the data. These are SD in inches for targets fired at 100 yards, so it also represents MOA.

Shooter 1 horizontal SD went from .68 to .52
Shooter 1 vertical SD went from .86 to .65

Shooter 2 horizontal SD went from .57 to .70
Shooter 2 vertical SD went from .65 to .48

Shooter 3 horizontal SD went from .37 to .43
Shooter 3 vertical SD went from .43 to .23

Averages were not calculated, because in all cases the shooters were instructed to not adjust their sights during the string of fire, nor were they given feedback during the fire.

Base size is small. All three reduced vertical dispersion by a consistent 0.2 MOA, which is what I had predicted. Horizontal was less consistent, but on average represented a zero change.

ShootingSight wrote:I'm not sure why you would eshew apertures - why would you ever NOT accept a free improvement in focus? I will agree that if you only have the relatively small depth of field afforded by your pupil, you will be forced to chose between seeing the front sight, or seeing the target, because the difference in focus between them is just too great. In this case, I would agree that focusing on the front sight makes more sense. However if you can see both clearly at the same time, that has to be better.<snip>

The reason an iris is not ideal, is because it cuts down the light entereing the eye. As I'm sure you're aware this is less than ideal and will cause eye strain and lead to sub-optimal performance

Net, a sharp front sight and a blurry target is not the best solution. It is simply the least bad, if you accept that you are shooting with a poor depth of field.

I disagree. Why do you need a sharp target ? You can align the gun (foresight) as easily on a blurry bull as you can a crisp one.

It is also easier to maintain concentration on the most important part of the gun, i.e. the foresight and it's relationship to the rearsight. A sharp bull is an unnecessary distraction.

Rob.

While as a novice I'm hardly in a position to make extravagant claims from my own shooting experience, I will say that in my first try today with a 0.030" x 0.075" slot in a piece of thin steel was rather interesting. Having ground down a diamond-coated file to be thin enough to smooth the faces of the slot after drilling it with a tiny bit, .030" was as small as I could manage, not quite the suggested 0.025" but close enough I think. Focus on the upper flat of the front sight is almost automatic, though my lens is ground for focus at 10 metres, which is my preference. The verticals of the front sight are showing with this slot about the same as with the round iris, or perhaps a little less clear, but it's close.

Unfortunately I suffered a back spasm a week ago - struggling with my kid's car seat - and am only just beginning to recover from that nonsense, so my shooting isn't quite at the 94% I was doing last week. My groups today went from average 91 scores spread evenly in all directions with a normal iris, to 93 spread horizontally in a line just over the diameter of the 10 ring. This slot gave me the same apparent brightness level I've been seeing with my iris stopped down to where I like it, the white rings in the black of the target still visible.

I've never enjoyed aiming at a blurry target. The results no matter how I set up my sight blade/slot widths just don't seem to get any more accurate beyond a certain point. On a very good eye day (I'm 50, and there are not-so-good days for seeing now and then) I'm able to see vertical alignment quite well. The combination of focusing clearly on the target and being able to see the upper flat of the front sight clearly placed on the centre of that target is very reassuring for me. I don't quite get this oft-repeated mantra that clear focus is the cause of chicken finger. For me lately it seems quite the opposite, that the more clear I'm able to make both target and the front sight at the same time, the more confident I become, and therefore the more easily I am able to pull the trigger. It's when I'm second guessing alignment because the target and/or sight are blurry that I hesitate to the point of holding much too long, then either abort of take a wild shot which usually ends up an 8 or worse. Knowing with certainty that the hold is at the right height is a big part of the battle won.

So thanks ShootingSight, this is an interesting innovation. I'll try it for the rest of the week and see if it sticks.

Art,

This is really interesting but for me in a different sense. I have an astigmatism in my eye so already the focusing ability of my eye is different for horizontal vs. vertical axes. How do you think your rectangular apertures might affect this situation? Is there a way I could try them? Do I need to buy a pair of your glasses or do I just send you an envelope?

Rob,

If you are shooting center of mass, some amount of blur on the target is not critical. However I think rifle shooters have figured out that a 6 oclock hold is better than COM, as long as you can see well enough to see the target and post together clearly. If your vision cannot see the target clearly, then COM is the best way to go. So if this applies to pistol or not is TBD. I know this is a radical departure from what national champions have been preaching for years, so it will take some time before enough people try it to get a good read on if it makes sense. When I started pitching the hyperfocal concept on the rifle forums, I got a lot of resistance from people who had always preached 'focus on the front sight'. Now, after 4 years, there are lots of people right up to the HM level who are using the word hyperfocal.

As to apertures, indoor smallbore shooters all use apertures, so the amount of light coming in to the eye can be reduced without loss of image clarity. Obviously, you do not want the aperture so small that there is a perceived dimming of the image, but there is some range which is smaller than the pupil, and yet still large enough for adequate vision. Eye strain does not come from inadequate light, eye strain comes from an overexertion of the ciliary muscle, which is the muscle used to focus. The reason eye strain is associated with low light is because people who are presbiopic, like me, cannot focus up close, but as long as the light is bright, so our pupils are constricted, we get sufficient depth of field that if I consider my minimum focus distance, and then add my near side depth of field, I can still function. If you then put me in dim light, my pupil dilates, I lose depth of field, and I can no longer see as close, so the ciliary muscle is straining to help me see.

Gerard, thanks for trying these - let me play around this week, I might be able to laser cut some self adhesive foil disks for you.

vHoff, interestingly, rectangular apertures were used in the olden days by eye doctors to diagnose astigmatism. They would put a slit in front of your eye, and have you rotate it till focus cleared up. There, they did not align the slit horizontally to give you the best depth of field on the top horizontal edge of the post, but they aligned it to give you the best focus in the axis of your astigmatism, where you needed the most help.

However for you - why don't you just get a shooting lens that has the astigmatism cylinder correction in it? That should take care of the differential focus. For Knobloch, etc style of round lenses, I can make you a cylinder corrected lens that has the extra power in it for shooting for $40.

Art

No need to make me any foil disc apertures, really. I'm happy enough experimenting on my own, and the thin piece of spring steel strapping I softened and slotted now has little tabs on the corners to it snaps onto my Champion iris module very nearly, easily rotated until it's perfectly horizontal. It aligns perfectly with the iris, so should I wish to stop that down even further the smallest aperture lines up with the slot (though so far I've never shot in that bright a light).

In an aside; my old Varga glasses came with a lens with cylindrical distortion, completely unusable for me as it caused flaring of the target in one dimension. I thought that was just a very cheaply made lens, now your explanation about astigmatism clears that up, thanks. The previous owner must have suffered from that.

An astigmatism is when you have a bulge in your lens, or in the cornea, so rather than the lens being spherical, shaped like a basketball, it is football shaped, with two different radii in two perpendicular axes.

Lens diopters are pure additive - if I stack a +2 lens on another +2 lens, I effectively have a +4 lens, so the solution to correct an astigmatism is to make another football shaped lens, and put it in your glasses, but rotati it 90 degrees from the astigmatism in your eye. Now, when you add lens powers, everyplace your eye is fat, the lens is thin, and everyplace your eye is thin, the lens is fat, so it neutralizes the bulge.

They call it a clyinder correction, because in geometry, if you blend a sphere and a cylinder, you end up with a football.

Net, a lens prescription consists of a spherical number, which is how much the lens corrects, then a cylinder value, which telly you the difference between the two axes, and it ends with an axis value that tells you how to align the cylinder part relative to your eye.

Seems you know about these things:

What's the relationshio between the gel inside the eyeball, lens and cornea etc. regarding refractive index? No air inside the eye, but a mix of different materials and shapes......

Re. astigmatism:
At age 62 I've got it in the plane that makes the top of rearsight fuzzy; I've known about the aperture "slit" trick for a long time and sometimes use it for reading small print. I imagine some animals with slishaped pupils get a similar effect? And some indigenous peoples in the arctic have made sunglasses in a similar way for ages......

I compromise when focusing a rifle scope ocular to make the horizontal and vertical crosshairs equally sharp/fuzzy. This is quite useful.

Is astigmatism in the other plane less common?
I would imagine that fuzzy vertical lines are less of a problem since you can rely on sideways symmetry quite a bit with open sights?

BTW
drugstore reading glasses are available in +1.0 here in Norway :-)
I've actually used them for DIY bow scope lenses.

Here is the best lens model I have ever found, giving aproximate radii and refractive index of the various eye components:
http://hyperphysics.phy-astr.gsu.edu/hb ... escal.html

Yes, I believe cats have slit shaped pupils, because the prey they hunt lives in a world of grass and other growth that all has vertical edges, so they bias thei focus to see vertical edges more.

For your riflescope problem, I believe I can make a lens that you attach to the riflescope that will compensate for your astigmatism. I have not ever actually tried this, and since I do not have an astigmatism, I cannot experiment on myself, but if you are interested in trying some ideas, I think we can arrange something.

I cannot say in what axes astigmatism is most common, but agree with your conclusion that fuzzy sides (ie fuzzy vertical lines) are less of a problem, because ultimately you have two sides, so even fuzzy, your eye can judge the symmetry to estimate if the target is centered.

I have on rare occasion fount +1.0 reading glasses in the US, but typically they start at 1.25.

Send me your prescription at shootingsight@nuvox.net, and let's talk about how to make a lens for your scope. THe crudest test is to make the lens the same diameter as the objective, and you can simply place it on the end and use tape to attach it.

The link to eye "data" was quite interesting, straight to the point stuff!

Regarding crosshair focusing, I find the compromise solution works quite well. I guess part of the trick is realising that eyesight has to be rather bad before it becomes the limiting factor in shooting precision.

Thus I still shoot AP without glasses although the top of the rear sight appears a bit fuzzy. Shot execution is the limiting factor, and when a shot feels right, it's normally a ten.
I guess there are many like me at different ages needing glasses with a lower power than +1.0. Sitting in front of the PC screen using a pair of +1.0 drugstore reading glasses, I find the optimum distance to the screen in rather dim light and late in the day is about 50 cm. This achieves the same trick as when adjusting a rifle scope: horizontal and vertical lines are equally sharp/fuzzy. Of course I get a better result with my prescription computer glasses with a cylindrical correction.


BTW, you can find the Bowscope nomogram and som other info here:

http://forums.mathewsinc.com/archery-4/ ... ion-47721/