6th Feb 2019 – Parallax Error
I first encountered and really grasped the consequences of scope parallax error some years ago while tuning a PP700W air pistol over a number of weeks. The pistol was intended for HFT competition use and was fitted with a fixed focus 4x25 scope. I’d corrected a series of mechanical problems with the pistol and had refined the regulation so that there was much less discrepancy shot to shot. However, at the range, no matter how securely I rested the pistol on the bench rest, the .22 pellets often missed their mark, seemingly randomly by around 5mm on a zero target set at 15 yards.
I’d seen the error in the past and being quite honest had always put it down to either my inability to shoot straight, or a muzzle energy differential in the gun, but this time the chronoscope tended to contradict the muzzle energy differential as the cause. On one particular night I noticed something really odd as I happened to reach for a mug of coffee. With the unloaded and un-cocked pistol propped securely on a bench rest cushion and with a sharply focused reticle set dead centre on a 15 yard “zero” target, I moved my head to one side and noticed that the crosshair came off the target. After a double take I suddenly realised, that unless my head was in precisely the right place when viewing the target through the scope, the crosshair simply wouldn’t sit on the target centre and so it wasn’t possible to accurately zero the gun. I mentioned this to a good range friend (Alan) who suggested it might be a parallax error – something I’d heard of but didn’t fully understand. I suspect that might also apply to quite a few air gunners and so I wrote these notes.
The problem was that the pistol had been fitted with a fixed focus 4x25 scope and unfortunately fixed focus scopes always come with a guarantee of parallax error.
When an image is sharply in focus it is said to be in a particular focal plane. If you were to look across a road, the cars parked closest to you will be in one focal plane while those parked on the other side will be in a more distant focal plane. Your eye actually adjusts to bring both planes into focus as you move your gaze from one side of the road to the other. Technically parallax error occurs in a scope when two images... namely the image of the crosshair or reticle and the second image of the target are displayed on two different focal planes. Under those conditions, movement will be observed between the two images whenever the viewer shifts their eye position. In other words, the crosshairs will move against the target if you move your head
Parallax error is easy to demonstrate using your thumbs as shown in this picture. Align both thumbs with your dominant eye and then move your head gently to the left and note how the thumb closest to your eye appears to move right. This occurs because the two thumbs are not in the same focal plane. If you were to bring your two thumbs together (placing them in the same focal plane and side by side) then the same error won’t occur.
Don’t confuse this with the focus of the reticle (crosshair) which is a separate issue. Generally all scopes (even cheapy ones from fleaBay) have a front focus ring designed solely to bring the reticle into sharp focus. You typically point the scope at some bland but well lit object (for example the sky or a blank white wall) and then turn the dedicated reticle focus control to make the crosshair reticle pin sharp. By doing this, you place the image of the reticle into a focal plane that makes it pin sharp for your particular eye.
For this discussion, let’s assume that that reticle focus is sharp when you view through the scope.
What about focussing the target image... well, unfortunately for fixed focus scopes there isn’t a separate focus control for the target image. Fixed focus scopes are manufactured so that at a single fixed distance (quoted by the manufacturer as the parallax range) a target will be sharply in focus. For example quite a few 4x32 fixed focus scopes quote a parallax range of 100 yards in their specifications and that figure means that if the scope is used to view a target at precisely 100 yards, the focus of that target will be pin sharp in the scope. As the 100 yard target is then correctly focussed and as we know the reticle (crosshair) adjustment has been made to ensure the reticle is sharply focussed then the two images will be in the same focal plane when viewed by the shooter. Any head movement under those circumstances won’t matter, because the crosshair and the target will remain perfectly together. It’s a little like having our two thumbs side by side in the example above.
But what happens when the target is at some other distance than that single parallax range? Well, because the target image won't be in the same focal plane as the reticle then it will either end up in front or behind the reticule image. As the target image and the reticle image are not in the same plane (just like a thumb that’s close to the eye and one that’s more distant in our example) the viewer will see a shift between the reticle image and the target image if they happen to move their head.
Unless the shooters eye is precisely centre aligned with the scopes optical axis, this error is guaranteed to occur when the target isn’t sitting at the parallax range.
In my case the PP700W pistol had a cheap 4x25mm fleaBay Chinese scope fitted... so cheap that the specification from the manufacturer didn’t even bother to quote a parallax range. So let’s assume for arguments sake that the parallax range for this scope is manufactured to be either 50 yards, or 100 yards (we'll work out figures for both):-
On this pistol the diameter of the scopes objective bell (D) was 25mm and we were assuming either a 50 or 100 yard parallax range set by the factory (P) – in which case we got the following errors for targets ranging from 5 to 25 yards in 5 yard increments
The maximum parallax error lies between 6 and 12mm at the target unless the shooters eye is positioned precisely on the centre line of the optical axis of the scope and interestingly that error is considerably worse when the target is closer. The calculated errors closely correlated to the error I experienced on the shooting range at 15 yards.
The only way to accurately resolve the problem is either to use open sights or to use a scope with an adjustable focus for the target image - sometimes referred to as an AO or Adjustable Objective scope or a side wheel focus scope (they both do the same thing, but use a different technique to achieve the effect). This is where the focus is designed to bring the target and the crosshair into the same optical plane eliminating parallax error.
There are four ways to achieve parallax correction in a scope.
REAR (SECOND FOCAL PLANE) CORRECTIVE ADJUSTMENT
This is usually a numbered ring that sits in front of the eyepiece and which is marked in yards from a minimum to infinity. Generally these are only found on fixed power scopes due to their internal construction – normally when the fixed magnification sits between 8x and 20x. The adjustment will be near the shooters eye so it can be reached and as a design it is cheap to make, but in practice it is a coarse adjustment and impossible to make work with variable magnification scopes.
MIDDLE TURRET CORRECTIVE ADJUSTMENT
This design will be familiar to air gunners as the traditional side focus or "wheel" scope. The focus turret is usually on the left side of the bridge of the scope and comes with yardage increments on the wheel. There are two big advantages with this design – firstly the wheel allows the shooter to accurately set the focus so that the parallax error is minimized. Secondly if the wheel is calibrated, it allows the shooter to range check the target.
Accurately being able to tell the target range allows a shooter to determine the hold over or under required to bring the pellet onto the target, based on the known ballistics curve of the pellet. Side focus provides two levels of accuracy and it is also possible to alter the focus while the shooter is in firing position. The disadvantages are that it is more expensive to manufacture because it is more complex (requiring an additional centre lens arrangement) and off course more can go wrong.
FRONT OBJECTIVE LENS CORRECTIVE ADJUSTMENT
The oldest and most proven solution to this problem and arguably still the best way to resolve it is simply to adjust the focus by means of an adjustable objective bell lens, where the bell is usually marked in yards and the thread offset is used to physically move the lens. These are often referred to as adjustable objective or AO scopes. It is by far the cheapest solution to make and the most versatile as it suits any magnification and any lens diameter. It is also mechanically the most robust. The downside is that it’s hard for the shooter to reach or alter when in firing position and it does introduce a risk of water ingress. The Hawke IR scope (shown below) is a particularly good and reliable example of an AO scope.
US OPTICS “ERGO” ADJUSTMENT SYSTEM
FIXED PARALLAX RANGE SCOPES FOR AIR SHOOTING – TECHNIQUE
This is a refinement of the front objective lens system – but where the yardage increments can be seen by the left eye while looking through the scope with the right eye. It’s easily adjusted in the shooting position and has very fine adjustment but the downside is cost. Most US Optics scopes retail for around $2000
There are some techniques that can be used to reduce parallax error if forced to use a fixed focus scope (or for example if you have an adjustable focus scope, but can’t use it due to competition restrictions)
The first is to lock the position of your head and eye by using something like an eye piece. In that way you help lock your eye position in a reproducible way for every shot. A second technique is to take advantage of a narrowed eye relief, where the position of the eye results in the scope cylinder obscuring some of the target view. You can do this by bringing your eye slightly too close to the scope until you can see a dark ring obscuring the outer part of the target view. You then position your eye so that the dark ring is evenly spaced all the way round the boundary of the scope tube – and in that way you go some way to minimising the parallax error leaving your eye on the centre of the optical axis.
The problem with both techniques is that they are highly subjective and really very difficult to make work in practice across multiple shots.
The best way to resolve parallax errors is simply to use open sights or a scope with an adjustable target focus. Once the focus is properly set the parallax error will be almost entirely eliminated.
You can use parallax error as an aid to check that you have correctly and accurately focused your scope – by setting the focus to where you think the target is sharp and then very slightly moving your head. If there is any perceptible movement between the crosshair and the target you know the target is not totally in focus. Readjust and try again
With the target and reticle pin sharp, head movement won’t result in any movement between the crosshair and target.
ADJUSTABLE FOCUS SCOPE SETUP
The proper setup of an adjustable focus scope can be summarised as follows:-
- First determine the eye relief for the scope – which is the distance the eye needs to be from the ocular lens in order to see an image across the whole of the lens. Generally this will be around 2” in order to ensure that the scope remains clear of the eye during recoil
- With the eye relief set, focus the reticle with your eye at that distance. Aim the scope at a constant flat colour with fairly good lighting – but without any high contrast change. For example a white wall or the sky works well. View the ocular lens from the eye relief distance and then turn the reticle focus control so that the reticle is pin sharp. Test the setting by moving your eye away and then back onto the ocular lens to make sure your eye is not compensating unduly. The reticle should be sharp as soon as it comes into your field of view. Lock off the adjustment if possible.
- Point the scope at a zero target, and adjust the focus until the zero target is sharp. You can test that the focus is correct by gently moving your head left/right to make sure the reticle and the zero target remain aligned. At that point you have eliminated parallax error.
- Zero the scope on the zero target by adjusting the windage and elevation turrets to bring pellets on the target centre. It’s always a good idea to test your zero using multiple shots rather than single shots. Use 3 to 5 before adjusting so that you get an average view and rule out those odd shots that tend to spring randomly. Unless you’re very lucky, it is not that common to get pellet on pellet groupings.
Regarding a suitable zero range... well, being honest there simply is no right answer to this common question. Software like Chairgun Pro allows you to
model different zero distances - and takes into account the muzzle energy of the air rifle, the resulting speed (and calibre) of the pellet and its balistic
characteristics. Better still the software provides a means to figure out what zero range will provide the longest distance where the centre of the crosshair
can be used with no extra hold to strike a target. Personally I find that a .177 UK air rifle will zero nicely at around 30 yards resulting in a useful range
between 10 and 50 yards. The slower .22 zero's quite well at around 25 yards. Mind you, that just suits me... and everyone is different.