formula for perceived sharpness of fixed-parallax riflescopes?

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There is a standard formula for the worst-case amount of error due to parallax based on the objective size, the magnification, the target distance, and the fixed parallax distance.

Is anyone aware of a similar formula describing how "out of focus" an image will be given the above parameters?
 
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What’s the purpose? Sure there’s a formula to just about everything, but what would it explain? Parallax drift is based on eye position behind the scope. Focus blur would likely be some ratio of parallax distance versus target distance. However there would also have to be an angular dispersion in there as well. Focusing on a target 1km away and another 10km away isn’t a huge difference. Focusing on a target 5 inches away and 6 inches away is significantly more difficult.
 
So, I found that by moving my head side to side (or up and down) behind a scope, it appears that the cross hair moves side to side on the target. I read long time ago that there can only be one distance where parallax is 0 - i.e. you can move your head but crosshair stays still on the target. My Leupold Rimfire scope booklet says it is set parallax free at 60 yards. So, I would expect the same amount of error 30 yards beyond that as with 30 yards closer than that. Many centerfires are set at 150 yards. If you have an adjustable parallax scope, you want to verify were "0" is, regardless of the marks. I have read that for many, especially adjustable objectives, that the numbers shown are mor like suggestions... And, I have never read that parallax is about focus, although no doubt the two are related mechanically in the optic's physics. So, I can adjust my eyepiece to get perfect focus at 30 yards, but will have parallax error; I can have poorly focused (fuzzy image) at 60 yards, but no parallax.
And, as mentioned in the previous posting, you can eliminate parallax completely by having absolute consistent eye placement behind the scope, for every shot. Perfect, consistent cheek weld would be a start.
 
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But you didn't answer the question. :)

You gave the formula for the amount of "aiming error" due to parallax. What I'm looking for is something similar to determine how "out of focus" the image will look in the scope.

Basically I'm trying to pick a fixed-parallax scope and I'm trying to decide between versions of the same scope with parallax set to 60yd, 75yd, or 150yd. I'm trying to get a feel for how much more blurry the one set for 150yd would be than the one set to 75yd both were looking a target at say 35yd.
 
I am just guessing that you may have never set up the focus for yourself on a scope? Best way is to look through it at a blank white wall, or at the sky (infinity) and adjust the eye piece until the crosshairs are absolutely crisp. Don't stare as you do this - look away, adjust, look through scope, repeat. Of the 20 or more scopes I have here, that procedure gives me a clear focus on targets at any distances that I have used the scopes for - note: this is with a fixed 10x as most powerful and 2 1/2x as least powerful, all but two are fixed parallax scopes. I can be corrected, but at this point I believe that "focus" (adjusted on the eyepiece) and "parallax adjustment" (often done on the objective end) are two different, but perhaps related, things.
 
The eyepiece focus adjustment is used to focus the crosshairs, not the image. The parallax adjustment is used to move the plane on which the image is focused, within the scope, to the same plane on which the crosshair exists. Parallax exists when those two items...image and crosshair...are on two different planes, so that if you move your eye away from the perfectly centered position you are looking "around" the crosshairs at the image. The error won't be the same when the target is the same distance in front and behind the "focused" distance, just as 1MOA is a different measurement at 100 yards and at 200 yards.

If you are looking at a target at a distance which differs from the pre-set parallax setting on your scope, you're relying on the scope's depth of field to allow you to see it in focus; since depth of field is much greater with a low-mag scope than with a high-mag one, you can get away with seeing a clear image much closer at low magnifications. This is easy to see by switching a variable scope from its lowest to its highest setting, and observing how close you can be to target and still see it as 'in focus" on both settings.

I once thought that parallax adjustability was worse than useless for 99% of hunting shots, and 95% of all shooting in general. I've changed my mind about that; so many people try to use it as an alibi for their terrible shooting that it obviously has value to them. :)
 
jjohnwm said:
The eyepiece focus adjustment is used to focus the crosshairs, not the image. The parallax adjustment is used to move the plane on which the image is focused, within the scope, to the same plane on which the crosshair exists. Parallax exists when those two items...image and crosshair...are on two different planes, so that if you move your eye away from the perfectly centered position you are looking "around" the crosshairs at the image. The error won't be the same when the target is the same distance in front and behind the "focused" distance, just as 1MOA is a different measurement at 100 yards and at 200 yards.

If you are looking at a target at a distance which differs from the pre-set parallax setting on your scope, you're relying on the scope's depth of field to allow you to see it in focus; since depth of field is much greater with a low-mag scope than with a high-mag one, you can get away with seeing a clear image much closer at low magnifications. This is easy to see by switching a variable scope from its lowest to its highest setting, and observing how close you can be to target and still see it as 'in focus" on both settings.

I once thought that parallax adjustability was worse than useless for 99% of hunting shots, and 95% of all shooting in general. I've changed my mind about that; so many people try to use it as an alibi for their terrible shooting that it obviously has value to them. :)
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Excellent explanation.
 
It is difficult to shoot a 1/4" group with a 1/2" parallax error.

For hunting, the extra 1/2" probably won't matter, unless you are shooting gophers at 400 yards. In which case a AO scope is called for.
 
Ganderite said:
It is difficult to shoot a 1/4" group with a 1/2" parallax error.

For hunting, the extra 1/2" probably won't matter, unless you are shooting gophers at 400 yards. In which case a AO scope is called for.
Click to expand...

That's the 1% of shooting that I wasn't talking about. :)

I use a scope with parallax adjustment if I am looking for every last conceivable minutely fractional scrootch of accuracy possible...but I think it's cheating! If you have parallax, your shooting form is not perfect; your head and eye are not centered behind the objective perfectly each time. The inconsistency in the placement of your eye is what creates the parallax error. It doesn't exist in a scope just sitting on the table; the potential for it is there, to a degree that is determined by the difference between actual target distance and the pre-set parallax-free range. How much, or how little, of that potential error actually manifests itself is entirely the result of shooter skill. I want to improve my own shooting ability and accuracy, not rely on a crutch like an A.O.

In case it isn't obvious...I don't shoot competitively, and usually not even with anybody else around. I've got nobody I need to beat except myself. :)
 
Just to reiterate...I know all about the possible aiming error due to parallax effects. I'm looking for a way to quantify how out-of-focus a target image will be with a given magnification, objective size, parallax distance, and target distance.

It seems to be remarkably difficult to find information on this.
 
Well - Frankly I don't think the information exists. How do you quantify out-of-focus? And how does parallax error correlate to focus error? (ie you can have substantial parallax error and the scope is in focus)
BTW - I'm reiterating what has been pointed out in previous posts. Pick a scope whose parallax setting matches the longest distance you intend to shoot ( in your case 150 y). Confirm the parallax setting by visual confirmation - a lot of scopes are poorly calibrated. Adjust the focus using the ocular bell at the desired distance, and shoot.
 
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Ive got a physics background, so I know this has to be quantifiable, but after some experimentation I've concluded that in practice image blurriness is only a serious issue with high magnification at short range. For my purposes I think I'll be okay just turning the magnification down.
 
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