Parts Of The Scope

In this tutorial, we focus on sporting optics that contain telescopes: rifle scopes, spotting scopes, binoculars, and laser rangefinders. This section covers riflescopes. Sections covering other sport optics will be added later. The major parts of the riflescope are shown in Figure 1. The drawing shows the reticle in the second focal plane (SFP). The reticle may also be located in the first focal plane (FFP).

Figure 1. Parts of a rifle scope.

Optical Design

The optical design of a rifle scope can be considered to have four parts: the objective, reticle, erector and eyepiece (see Figure 2). The objective forms an inverted image at the first focal plane (FFP) position. Together, the objective lens and the eyepiece form an “afocal” telescope (i.e., the telescope produces a focused image at infinity). The erector lenses form a focal telescope that provides additional magnification, creates an erect image at the second focal plane (SFP), and provides reticle adjustments (windage and elevation). Without the erector lenses, the objective and eyepiece lenses would otherwise have a small magnification of about 3X, and the image would be upside down.

The reticle can either be mounted to the erector tube at the FFP, as shown in Figure 2, or mounted to the erector at the SFP, which is after the erector lenses. The windage and elevation adjustments move the FFP reticle by tilting the tube containing the erector lenses (see Figure 6). The windage and elevation adjustments do not move the SFP reticle, however, but instead just tilt the erector tube it is held in. The FFP reticle is magnified by the erector tube along with the objects in the scene. Because it is located after the erector tube, the SFP reticle is a constant size, regardless of erector tube magnification.

The objective lens determines the overall field of view and image quality, especially when large reticle adjustments are made. Image features in the center of the field of view are called “on-axis”, while those away from the center of the field of view are called “off-axis”. A large fraction of the optics cost is in the objective lens. A field lens located between the FFP and the erector tube prevents loss of light for off-axis objects (near the edge of the field of view). The lenses in the erector tube also effect image quality. Because they are small, however, their cost is relatively low.

Figure 2. Rifle scope optics.

Optical Performance

Resolution and Contrast:

A telescope is also called a “visual optic”, because it operates as an aid to the human eye. Unlike a digital camera, which has an image forming lens and image sensor, a telescope needs to be viewed by a person to function. This makes testing visual optics a challenge, because each person judges image quality differently.

Figure 3.Consider the Target – Atmosphere – Scope – Eye as an integrated optical system. One of them usually limits resolution, and it’s not always the scope. In many situations, the atmosphere determines image resolution and contrast, not the scope.

The human eye is a complex optical instrument. The lens in the eye forms an image of an object, or target, on the retina. The photodetectors in the eye, called rods and cones, convert that image to electrical signals, and the brain processes those signals to form what we perceive to be a color image of the target. Image features have a maximum and minimum brightness level, and ratio of the highest to the lowest brightness is called the “contrast.” To varying degrees, the human eye always degrades the contrast of the target.

Resolution is the smallest size image feature that can be distinguished, or “resolved.” This image feature must have a minimum contrast to be resolved. When we say the eye has a certain resolution, what we really mean is that the image has the minimum acceptable contrast at that resolution. Remember, this “image” is something perceived by the brain. For a high contrast, target in direct sunlight, the human eye has a resolution of about 1 arc minute, or 1 minute of angle (1 MOA).

The eye’s contrast depends on the illumination level. This means that in bright light (direct sunlight, etc.) the eye has the best resolution, while in low light (dawn or dusk, dark shade, etc.,) the eye has degraded resolution. By “degraded”, we mean that the minimum acceptable contrast occurs at a larger feature size. At each illumination level the eye trades contrast for resolution in this way to extract the most information from the scene.

We can improve the eye’s image resolution by using a telescope as a visual aid to make the target features appear to have a larger size. For example, a 10X magnification telescope makes target features appear 10 times larger. The aided eye’s resolution is therefore improved by a factor of 10 (i.e., 0.1 MOA for sunlit targets, compared to 1 MOA for the naked eye).

The purpose of the telescope, therefore, is to magnify the target so that it appears larger, or nearer, to the eye. Variety for reasons, the telescope also degrades resolution and contrast (discussed in detail below).

Contrast and Glare:

No riflescope is perfect and two effects in particular can severely degrade image contrast: glare and diffraction. Glare is probably the least understood of all telescope performance parameters, but is one of the primary factors contributing to a clear or “brilliant” image. Glare degrades the image because “stray” light that does not come from the target scene scatters off interior scope surfaces and ends up falling within the image of the scene. This effect is called “veiling glare” and it degrades the contrast of the image. Contrast is the ratio of highest to the lowest possible intensity of an image of a black and white target. Glare is reduced by the use of light baffling apertures inside the riflescope that block stray light, and flat black coatings on the lens edges and interior metal surfaces.

When you look through a good scope and the image seems to “pop” out at you, it’s the absence of scattered light that gives the image such high contrast. There are other sources of scattered light, but glare is often the largest. It’s usually the dominant effect that limits image contrast when the target is marginally illuminated and is surrounded by higher illumination terrain or sky – very common in big game hunting.

Glare performance is one of the differences between good German optics, for example, and lower quality optics. German optical designers minimize glare by adding light baffles (“glare stops”), applying a flat black coating to interior metal surfaces, and using lenses with blackened edges, for example. They test scopes using an integrating sphere to insure they blocked all major sources of glare. These features increase cost.

Generally speaking, glare increases with increasing objective size and magnification. The higher the magnification range of the scope, the higher the glare at all magnification settings. Also, as the magnification range increases, often so does the objective size, leading to a compound effect that significantly increases glare for higher magnification range scopes. Finally, glare seems to increase dramatically at the edge of the exit pupil, making glare much more of a problem for high magnification scopes, in which the eye pupil is larger than the exit pupil and catches all this glare.

For spot and stalk and long range big game hunting, glare performance should be a high priority when selecting a scope. Target contrast and illumination are usually low, making animals difficult to see even with the best optics. Atmospheric turbulence is usually low as well, which minimizes a primary source of blur that would otherwise limit image quality.

Glare performance is not a deal breaker for all applications. For prairie dog and ground squirrel hunting and target shooting at a range, for example, glare is not so important because another effect, called atmospheric turbulence (see below), limits image contrast. Also, target contrast and illumination tend to be good. Sun shades are effective at reducing glare. If you can use one at the range, they are recommended.

Figure 4. Effect of veiling glare on image contrast.

Diffraction:

Diffraction is the second effect that can significantly degrade contrast. The optical resolution of any telescope is fundamentally limited by diffraction. Diffraction occurs whenever light is passes through an aperture (such as the objective lens). The fundamental “diffraction limited” resolution is rarely achieved in consumer optics, because optical aberrations are present. Aberrations are another topic. Here we are concerned mainly with the effect of diffraction on image contrast.

Lens optical surfaces are formed by grinding and polishing glass material. For a lens to have “power” it must have at least one spherical surface. This surface is not perfectly spherical, however, because of minor flaws in the fabrication process. Lens fabricators use a term called “surface figure” to describe the degree to which a lens surface is perfectly spherical – that is, without flaws.

A process called diffraction occurs whenever light passes through any optic whose optical surface is not perfectly spherical. When light is “diffracted” it is diverted away from an image point. The primary effect of diffraction in visual optics is to reduce image contrast.

Somewhere between five and twelve lenses are used in a riflescope, and each one contributes to diffraction. Increasing the polishing time improves the surface figure of the lens and thereby reduces diffraction. Increasing the optical polishing time increases fabrication cost. The use of high quality polishing processes is another reason that German optics have a reputation for providing a brilliantly clear (that is, high contrast) image.

Atmospheric Turbulence:

The atmosphere between the target and the telescope almost always degrades image resolution. Whenever there are temperature variations in the air, light rays don’t actually travel in a straight line, but rather are bent, or “refracted”, a tiny amount as they pass through the air. There are always temperature variations in the air between you and an object that is far enough away that a telescope is useful. This effect causes the image to lose resolution and contrast (Figure 5), and is called turbulence-induced blur.

Figure 5.Turbulence-induced blur.

Most shooters are familiar with “mirage”, which has the appearance of wavy lines moving across the target image. This effect is due to the turbulent air moving across the field of view. Turbulence-induced blur is a somewhat different effect.

The amount of turbulence-induced blur is determined by the length of the optical path (i.e., the range to target), the “strength” of the turbulence, and the size of the aperture. Therefore, turbulence-induced blur is worse for:

• Longer ranges
• Larger scope apertures
• Hotter ground temperatures
• Flatter terrain (light rays closer to ground)
• Target or observer close to the ground.

High turbulence environments are typically those in which the target is small and the terrain in front of the target is flat and in direct sunlight. Typical examples include prairie dog and ground squirrel hunting, and target shooting at a firing range.

Low turbulence environments are typically where the target is surrounded by shade and elevated above the terrain in front of the target (i.e., on a hillside) and/or the air temperature is low. Typical examples include big game hunting in hilly terrain, at dawn and dusk, or under overcast skies, especially in fall and winter when the sun is low in the sky.

The main point is that the image seen when looking through a scope at targets at a firing range is usually blurred due to turbulence, not due to the optics in one scope vs another. Any difference in image “quality” between two side-by-side scopes under these conditions is probably due to the scopes having different effective aperture sizes. It would be much easier to see differences in optical resolution in a side-by-side test if you looked through the scopes at a target across a small valley or canyon on a cool day under an overcast sky.

Magnification and Exit Pupil:

Telescopic magnification allows the shooter to resolve target features at long distances. As magnification increases, however, the field of view decreases, which reduces the shooter’s situational awareness. It also reduces the exit pupil size. In most telescopes the exit pupil is equal to the entrance pupil (i.e., objective diameter) divided by the magnification:

Exit Pupil = Objective Diameter / Magnification

For low magnification variable scopes (M=3 or less), however, the exit pupil is often smaller than this equation would indicate. That is because an aperture stop somewhere in the erector tube limits the effective pupil at low magnification settings.

The human eye protects the retina from overload by automatically adjusting its pupil size in response to illumination levels. The minimum pupil diameter is about 1.5 mm. The eye has the best resolution at a pupil size of 2-4 mm. The maximum pupil size during dawn and dusk is about 5 mm. After long periods of near total darkness, the pupil can increase to about 7 mm, but only for relatively young people. People over about 50 years of age have a maximum pupil size of about 5 mm.

If the eye can accept all the light in the exit pupil, the telescope image is nearly as bright as the image seen by the unaided eye. When the exit pupil becomes smaller than the eye’s pupil, however, the image brightness starts to decrease. This reduction in brightness can be significant. A small exit pupil is also more difficult to align with the shooter’s eye. As we discussed earlier, glare is worse for such small exit pupils.

At low illumination (before dawn and after dusk) there is an optimum scope magnification that produces an exit pupil size equal to the eye pupil. This optimum magnification increases with the objective diameter. A magnification below this value reduces the target size. A higher magnification reduces the pupil size, reducing image brightness and contrast. The size of the scope tube has nothing to do with image brightness.

For big game hunting, we recommend only buying as much magnification as you really need, and no more. A good rule of thumb is 1.5X magnification for every 100yds of range. At a range of 600 yds a magnification of 9X or 10X is usually adequate. Even at 1,000 yds a magnification of 14X to 16X is fine for big game hunting.

In terms of target angles, the size of a typical reticle line is roughly 0.1 MOA, and the size of a reticle dot is 0.125 MOA (fine target dot) to 0.9 MOA (USMC mildot). The vital zone diameter is about 8 inches on most big game. At a range of 1,000 yds, an 8 inch diameter subtends 0.80 MOA. At 15X magnification, the vital zone is magnified to 12 MOA.

This means that the shooter must position the reticle crosshair or dot on a 12 MOA aim point. Recall that the eye has a resolution of about 1 MOA. The angular dimensions of the vital zone is ten times the resolution limit of the eye. The animal’s chest is at about 24” tall, which equals about 36 MOA at 15X magnification, or 36 times the resolution of the eye. This aiming task is fairly easy for an experienced shooter to perform.

Increasing the magnification from 15X to 24X makes the entire sight picture appear 60% larger, but doesn’t make the aiming challenge fundamentally easier. Increasing the upper magnification limit from 15X to 24X, however, significantly increases glare at all magnification settings. For a 50 mm objective, the exit pupil decreases from 3.3 mm to 2.1 mm, reducing both image brightness and eyebox size, and increasing glare for larger eye pupils.

High magnification is useful when the shooter has vision acuity problems that are not corrected. Many shooters cannot wear corrective lenses when they shoot. The scope diopter adjustment will correct for myopia or hyperopia. Astigmatism, however, cannot be corrected using the dioptier adjustment. In this case, higher magnification will improve image resolution, but at the same time degrade contrast (as discussed above).