Lenses and apertures
Posted: Sun Feb 13, 2011 8:20 pm
Brand new to the site, so I thought I should introduce myself. My name is Art Neergaard, I never shot cowboy anything, but I am a Service Rifle shooter.
I am not a doctor. I am a mechanical engineer, photographer, I know optical physics some. 50 years old, presbiopic, can't see the front post anymore, so I studied the optics of apertures and lenses to figure out what a rear sight ought to do, and developed a couple of products to help shooters see better, and aim better. I started a small company, ShootingSight LLC to sell these for Service Rifle use.
Recently, a cowboy silhouette shooter contacted me about fitting some of my products to a Williams sight for his rifle, which I did, so I figured I would poke around on the forum and see if any of the lessons from Service Rifle shooting apply, and I'd like to ask your help. I'll give a description of what I know about shooting vision, and end up with some specific questions, and then look to you for general input to see if it is worth anything to your discipline.
Rifle shooting is 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 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. Furthermore, there are certain things you can do to minimize the blur on something that is theoretically not in perfect focus, like reducing the aperture size.
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). 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, and you can calculate it quite simply because the math works out to 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 ciliary 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 20 or 30 shots, the muscle can’t hold, and starts to slip or tremble, and your focus goes away. I’m sure at my age I can still do a snappy pullup. But he second one will be slow, the 5th one might not happen, and the 20th attempt will be not much more than slight muscle twitch as I hang on the bar.
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, 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.
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. 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 will focus you at 32” – it does not seem like much error, but in fact it will give you a really sharp front sight, but the target will be gone in a blur.
If you wear 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.
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 that is displaced from your focal point 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 0.060” diameter aperture will cut the amount of blur by half.
The dark side of apertures (no pun intended) is that the total open area of the aperture limits how much light reaches your eye. As you make the aperture smaller, less light reaches your eye. 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.
There is a subnote on apertures, which bears on my products: apertures focus in an axis, 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, 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 side/side 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.
My questions to you:
What is the barrel length you typically shoot?
What type of front sight do you usually use (bead, post, etc)?
Do you shoot a center of mass, or a 6 o’clock hold?
Are lever actions the only class that commonly shoot iron sights? Seems from reading around, most of the small bore and HP guys use scopes.
Thanks,
Art Neergaard
ShootingSight LLC
http://www.shootingsight.com
email: [email protected]
I am not a doctor. I am a mechanical engineer, photographer, I know optical physics some. 50 years old, presbiopic, can't see the front post anymore, so I studied the optics of apertures and lenses to figure out what a rear sight ought to do, and developed a couple of products to help shooters see better, and aim better. I started a small company, ShootingSight LLC to sell these for Service Rifle use.
Recently, a cowboy silhouette shooter contacted me about fitting some of my products to a Williams sight for his rifle, which I did, so I figured I would poke around on the forum and see if any of the lessons from Service Rifle shooting apply, and I'd like to ask your help. I'll give a description of what I know about shooting vision, and end up with some specific questions, and then look to you for general input to see if it is worth anything to your discipline.
Rifle shooting is 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 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. Furthermore, there are certain things you can do to minimize the blur on something that is theoretically not in perfect focus, like reducing the aperture size.
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). 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, and you can calculate it quite simply because the math works out to 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 ciliary 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 20 or 30 shots, the muscle can’t hold, and starts to slip or tremble, and your focus goes away. I’m sure at my age I can still do a snappy pullup. But he second one will be slow, the 5th one might not happen, and the 20th attempt will be not much more than slight muscle twitch as I hang on the bar.
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, 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.
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. 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 will focus you at 32” – it does not seem like much error, but in fact it will give you a really sharp front sight, but the target will be gone in a blur.
If you wear 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.
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 that is displaced from your focal point 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 0.060” diameter aperture will cut the amount of blur by half.
The dark side of apertures (no pun intended) is that the total open area of the aperture limits how much light reaches your eye. As you make the aperture smaller, less light reaches your eye. 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.
There is a subnote on apertures, which bears on my products: apertures focus in an axis, 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, 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 side/side 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.
My questions to you:
What is the barrel length you typically shoot?
What type of front sight do you usually use (bead, post, etc)?
Do you shoot a center of mass, or a 6 o’clock hold?
Are lever actions the only class that commonly shoot iron sights? Seems from reading around, most of the small bore and HP guys use scopes.
Thanks,
Art Neergaard
ShootingSight LLC
http://www.shootingsight.com
email: [email protected]
