Parallax And Distortion
How to adjust your scope.
I have written about parallax on several occasions in this magazine. Yet, questions still arise, partly because users are seeing other distortions that sometimes make adjusting for parallax confusing. Recognizing these distortions as not belonging to parallax might make the exercise less frustrating.
Parallax is normally described as the image cone entering the objective lens not converging at the reticle. Webster defines parallax as, “An apparent change in the direction of an object, caused by a change in the observational position that provides a new line of sight.” A riflescope may be parallax free at one distance and not another. Riflescopes that have no parallax adjustment are normally set at some range at the factory. It might be at 100 yards or some slightly longer distance. If the riflescope includes a parallax adjustment, you can fiddle with the knob or the front adjusting objective until it is parallax free at any distance desired.
The internal cone of convergence from the objective lens becomes shorter or longer as the image moves closer or farther away. Stated differently, the internal cone is not the same length for images at different distances.
The observer is viewing through the ocular lens from an angled position (above).
Note the position of the crosshair. Also note that there is no color fringing at the
edges of the white board on the black backer. One sign of a superior optic
(a Zeiss ranging riflescope, by the way). Now the observer is looking through
the ocular lens, straight on, with a full view (below). Note the position of the
crosshair is in the exact same spot. The reticle is parallax free at 600 yards.
If it were not, the position of the crosshair would have moved about 1/2
(or more) the width of the white board from one photo to the next.
The telephone post to the left of the target is old and is leaning. However,
from one photo to the next there is no pincushion or barrel distortion.
Note the clarity when the eye is centered (below).
Not A Rangefinder
Some refer to the parallax adjustment knob as the focus knob. In fact some people try to use it for ranging. As an example, suppose a deer is located exactly 600-yards away. You turn the parallax adjustment knob until the deer is perfectly focused and is parallax free and then look at the numbers on the knob. You would expect to see the knob positioned at exactly 600 yards. Voilà! Just dial in your 600-yard dope and have at it. Although that seems perfectly logical, unfortunately, it does not always work that way for several reasons.
Some optical designers and manufactures do an excellent job of securing the objective lens as well as ensuring that moving parts move exactly and then labeling the parallax adjustment knob with great precision. Others, well, not so much. Even so, heat and humidity tend to play games with those dimensions. During competition, it is common to have to tweak the parallax a bit throughout the day. As you might now imagine, some scopes are perfectly parallax free and focused well at 600 yards, but a look at the parallax adjustment knob says almost 700 yards or maybe close to 500 yards. To rely on that for ranging could mean missing the shot.
It also depends on the manufacturer’s method of adjusting parallax. Some do it by adjusting the objective lens, others by a knob located on the left side of the elevation and windage manifold. Some actually use a portion of the ocular housing. On many European style “fast focusing” ocular diopter adjustments, it must be tweaked a bit to obtain the best focus when the image appears to be parallax free. On occasion, you will find a scope where the image is still a bit fuzzy when it is parallax free, or some small amount of parallax when it is perfectly focused. Such situations can drive you nuts.
On occasion, that will be complicated by another phenomenon. There is a small amount of distortion at the edge of the field in most scopes, sometimes referred to as vignetting. Generally, in any riflescope, distortion and field curvature are greater at lower powers. Trimming the field of view would reduce this effect, but that consequence is not considered acceptable since the purpose of lower power is generally to increase field of view.
Another phenomenon is related to field curvature or Petzval curvature. With this condition the image of the target at the reticle is actually curved like a shallow bowl. There are two components of field curvature, horizontal and vertical, where the field may actually curve slightly more in one axis than the other. During the optical design, the designer has the flexibility to minimize field curvature, and also the ability to place more emphasis on the horizontal or vertical components. However, as with any optical aberration, field curvature can’t be completely eliminated.
Optical designers use computers to analyze the optics with the internal erector system tilted as it is at adjustment extremes. They examine the aberrations present at this position and “tweak” the curves and thicknesses of lenses to correct for these flaws. These corrections are possible only with state-of-the-art computer design tools and the skill of experienced optical designers.
Zoom ratios of 4:1 and larger require larger internal lenses to accommodate the extended axial movement of the lenses in the erector system. Leupold, for example, always makes the internal lenses large enough to pass all of the valuable paraxial light produced by the objective; they never restrict the objective aperture with internal lenses at higher powers. They do trim the aperture at low power where the exit pupil would get far beyond the capability of the eye’s pupil to encompass, and image quality is better with this restriction.
Barrel and pincushion distortion can affect a shooter’s ability to find a parallax-free position, thinking it some manifestation of parallax. Rolling distortion may contribute in some rare instances as well.
In some forms of competition and hunting, you do not have the time to fine tune parallax or even mess with the knob. With practice, you can develop a cheekrest that will eliminate parallax. In these instances, you might preset the parallax at some mid-range object because the farther you shoot, the greater the error of point of intention, of a steady hold, and of parallax. But at shorter ranges, the error is reduced and the target has an apparent larger hit zone. A little practice with this problem goes a long way.
By Jacob Gottfredson
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