Binocular Vignetting
For less technical instructions on doing tests of vignetting indoors or outdoors outdoors please download the pdf file of length 400 Kb at indoor/outdoor tests. For other tests of vignetting done indoors please visit indoor tests.
This article below is primarily devoted to explaining these tests above using ray diagrams. Vignetting is defined as the blockage of light anywhere between the eyepiece and objective lenses. The suggestion is that if you look from the objective end into the binocular along the edge of the barrel and if you see a "cat's eye" shaped region of light then this necessarily means you have internal aperture vignetting. The purpose of this article is to show how this arises and to identify another type of vignetting due to the eyepiece itself.
In Figure 1A below we see the two dimensional representation of a three dimensional binocular. We also assume that the optical system is axially symmetric about the optic axis and there are no other lenses inside the binocular, that is, only the objective and eyepiece. We also assume the lenses are perfect, thin, and satisfy the laws of geometrical optics. If the exit pupil is square or asymmetrical because of too-small prisms or misalignment then this article does not address this more complicated case. The tests we describe do not require any disassembly of the binocular.
We have in mind a 10 X 80 binocular with the objective FL = 40 cm and the eyepiece FL= 4 cm. The diameter of the objective lens is 80 mm so the maximum diameter of the exit pupil is 8 mm. Light can travel in either direction through the binocular. If light enters from the right side through the exit pupil in a narrow parallel beam then the light leaves the objective lens to the left in a wide parallel beam. On the other hand if the light enters first through the objective in a wide parallel beam then it will leave through the exit pupil in a narrow parallel beam. There are two possible sources of vignetting that we consider. These are the internal aperture stop, or even the prism stops if sufficiently small, and the actual eyepiece lens itself. The eyepiece field stop, and objective lens, are assumed to be given. Figure 1A below identifies the various parts of the binocular and is for an inverted image which is not the case for a real binocular. The region between the two vertical green lines acts as a solid piece of glass and represents the prisms inside the binocular.
Figure 1B below shows an erect image which corresponds to a real binocular. One can imagine the prisms located between the green lines producing an erect image. The actual light rays can be obtained by rotating the portion of the rays after the eyepiece field stop by 180 degrees about the optical axis. So when looking from the objective end you can see only up to the eyepiece field stop and when looking through the eyepiece you can also only see to the eyepiece field stop. We assume that at least the very center of the eyepiece field stop is 100% illuminated. This ensures that the size of the exit pupil is at its maximum. We show you how to tell later in this article.
1) We now begin the simple tests for vignetting. Focus the binoculars for infinity.
2) Our first test is to determine whether there is either aperture or eyepiece vignette or both at the extreme edge of the eyepiece field of view. At night point the binocular at a bright distant light so that the image in the eyepiece appears at the exact edge of the field of view. It would be desirable to mount the binocular on a tripod to hold the binoculars from moving. Slide a piece of cardboard across the front of the objective while looking through the eyepiece at the bright light.
3) In Figure 1D below we show a ray diagram that explains how the aperture vignette is caused by the internal aperture stop. Suppose the light disappears when the last 1 cm of the objective is uncovered. No light reaches the eyepiece in this case because the aperture stop blocks whatever light is not blocked by the cardboard. If the distance AB is zero there is no internal aperture vignette at the extreme edge of the field of view.
4) We now test for vignetting caused by the edge of the eyepiece itself. Again at night point the binocular at a bright distant light so that the image of the light in the eyepiece appears at the extreme upper edge of the field of view. Slide the cardboard up in front of the objective until the light in the eyepiece is extinguished. If this should occur only when the entire objective is covered then there is no eyepiece vignette. On the other hand if it occurs at D as in the figure below then there is eyepiece vignette at the edge of the field of view.
The explanation of eyepiece vignette using ray diagrams is shown in in the Figure 1C below. The light appears to come through at the very top of the eyepiece field stop. While looking through the eyepiece, slide a piece of cardboard in front of the objective, with edge horizontal, from the bottom of the objective upwards until the light in the eyepiece is extinguished. If this occurs only when the objective end is completely covered then there is no vignetting in the eyepiece lens. The reason is that the light ray from the upper edge of the objective misses the internal aperture stop and passes highest through the eyepiece lens. For example if the cardboard covers the lower 7/8 of the objective as in the figure below when the light vanishes in the eyepiece then only 7/8 of the exit pupil or 7 mm emerges. This leaves 1 mm blocked by the edge of the actual eyepiece lens which is shown blackened passing through the exit pupil. The portion of the objective, uncovered still, is shown as CD.
Procedure For Determining The Portion Of The Field Of View Which Is 100% Illuminated.
In Figure 2 below imagine you are looking straight into the horizontal binoculars with the objective end toward you and the eyepiece end away from you. Then the top of Figure 2 will be on your left side of the actual binoculars and the bottom on your right side. The eye is located at about one objective focal length in front of the objective lens. In the diagram you have to imagine that each ray is actually a thin beam of parallel rays so that an image on the retina will be formed consisting of points. When the eye is one focal length in front of the objective then the rays traveling through the binocular are parallel to each other. This helps to visualize the actual sizes of the internal parts but is not essential for this test. Also notice that all rays entering the pupil of the eye come through a single point just in front of the exit pupil. Look into the binocular so that the edge of the internal aperture stop appears at the very left edge of the objective lens. The ray diagram in figure 2 below shows this case since the uppermost ray touches the internal aperture stop and the edge of the objective. ( When the eye distance to the objective is exactly one objective focal length then the rays travel in parallel lines through the binocular.) The center of the eyepiece field stop is on the optic axis marked by an X in Figure 2 below. You will be able to see that portion of the eyepiece field stop between the two short horizontal lines at the focal plane, one above and one below the position X. This is the "cat's eye" that is visible to the eye in a real binocular.
In the figure below we see the actual view from the objective end looking along the edge of the barrel that corresponds to the Figure 2 above. The bright region is a portion of the eyepiece field stop. ( Note that this is not the exit pupil) The symbol X marks the center of the field of the eyepiece stop shown in white just as in Figure 2 above. The two short lines now appear as one white line to the left of X and the black line to the right of X. The small circle with center at X and radius equal to the distance from X to the edge of the objective ( or the short white line) marks the portion of the eyepiece field which is 100% illuminated. In this example, about one-half of the diameter of the eyepiece field is 100% illuminated.
On the other hand, if you can see the entire eyepiece field stop from the edge of the objective and the edge of the aperture stop as in the figure below then the entire eyepiece field of view is 100% illuminated .
If the X appears at the very left edge as in the figure below then only the point at the exact center of the eyepiece field stop is 100% illuminated. ( In this case the radius of the circle is zero)
If the location of X is even further left as in the figure below then no part of eyepiece field is 100% illuminated.
Once again position the eye about one objective focal length in front of the objective lens so that the internal aperture stop is tangent to the edge of the objective lens. If there is no aperture vignette then you see all of the lighted eyepiece field stop as shown in the figure below. However if there is vignetting by the eyepiece then we see a portion of the right side of the eyepiece field stop shaded. Note that eyepiece vignetting occurs on the side of the eyepiece field stop which is opposite that of the vignetting from an aperture stop. Also the boundary of the eyepiece vignetting region in the figure below is much less curved than for aperture vignetting.
When both aperture and eyepiece vignetting occur the view from the edge of the objective will be similar to the figure below.
Eyepiece vignetting does not affect the portion of the eyepiece field stop which is 100% illuminated unless nearly all of the eyepiece stop is fully illuminated. The reason is that if only the central portions of the eyepiece field stop are 100% illuminated then the rays passing through are far from the edge of the eyepiece lens so there is no eyepiece vignetting. Therefore we can mostly assume that the region of 100% illumination is determined entirely by the internal aperture stop. The percent illumination at the edge of the eyepiece field stop however always depends on both whenever they occur.
In Figure 5 below the ray diagram with erect image shows that the light through the portion AB of the objective is blocked by the internal aperture stop whereas the portion CD is blocked by the edge of the eyepiece lens. The blackened portions indicate absence of rays passing through the exit pupil.
Supplementary Topics
Reduced size and new position of exit pupil
When Aperture Vignetting Occurs
The exit pupil is the bright spot of light you see in the eyepiece when you hold the binocular at arm's length from your eyes. Without any internal aperture stops the entrance pupil of the binocular is the objective lens itself and the exit pupil is defined to be the image of the entrance pupil formed by the eyepiece. Even when there is an internal aperture stop the entrance pupil is still the same provided no stop protrudes below the sloping line in the upper portion of the figure below. This line passes from the edge of the objective to the center of the eyepiece field stop. In the diagram below, none of the internal aperture stops will reduce the size of the exit pupil. The exit pupil will remain the same. There can still be a moderate amount of vignetting without any change to the exit pupil. This vignetting will affect the percent illumination at the edge of the eyepiece field stop or field of view.
In this case we can calculate the magnification of the binocular by dividing the diameter of the objective lens by the diameter of the exit pupil. We can also see in the diagram that the very center of the eyepiece field is fully illuminated by the objective lens. ( In this extreme case this is the only point fully illuminated. This reaffirms the statements made earlier that if you can see the edge of the objective lens and the edge of the aperture stop appear at the center of the eyepiece field stop then at least the center of the field of view is fully illuminated and the exit pupil is still the same maximum size). However if the internal aperture stop does protrude below the sloping line as in the lower of the figure below, then the new exit pupil is reduced in size and appears further to the right shown as the short red line next to the old exit pupil. The new exit pupil is now the image of the limiting internal aperture stop. This also indicates severe internal aperture vignetting since even the very center of the eyepiece field of view is not fully illuminated. Thanks to Jean-Charles Bouget for pointing this out. The actual ray diagrams are still correct.
Point B in the lower figure marks the effective edge of the objective lens and determines the percent illumination at the center of the eyepiece field of view. For example, if B is at one-half the radius of the objective then the center of the eyepiece field is only 25% illuminated by the objective lens.
How to Measure the Diameter of the Exit Pupil
As shown in the figure below, only when the eye is far from the eyepiece can we measure the diameter of the exit pupil directly at any position along the beam. Holding the binocular at arm's length while looking at the eyepiece as in the lower portion of the figure below however is not without error since the ruler must be located at a certain position.
To easily and accurately measure the diameter of the exit pupil, hold the binocular on a tripod facing the bright sky and place a sheet of waxed paper behind the eyepiece and move it until you get a sharp outline of the exit pupil on it as in the figure below. Imagine rays enter the eyepiece from the left side and pass through the exit pupil on the right. The red lines are light rays diffusely scattered by the waxed paper and some of these rays will enter the eye. Now the distance of the eye does not affect the measured diameter of the exit pupil. Measure the diameter of this image to get the diameter of the exit pupil. This exit pupil will be the "new" exit pupil when there is severe vignetting. Because the exit pupil is small use great care in measuring its diameter. You should be able to measure to the nearest 1/10 mm.
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