A Brief History of Focusing, Finding Range Without a Ruler

Last time we looked at focusing using a ground glass and the problems it presents as frame sizes and view finders get smaller. This time we’ll look at how to find the distance to something with out leaving the camera or using a ruler.

Finding the Range

What’s needed is a way to measure the distance to the subject with enough accuracy to allow for correct focusing. A tape measure would do, but probably isn’t going to work well for photography. Even if it did work, in many ways, it would only be marginally better than guessing with out a guide. Just imaging asking the important public figure you’ve been hired to photograph to hold one end of the tape measure while you setup the camera.

There is, however, another way to measure the distance to an object with out physically extending a measuring stick to the object. This works because of the trigonometric relationship between angles and the lengths of the sides of a triangle. It doesn’t take long to realize that using trigonometery as a base, the distance to the subject could be computer with out ever leaving the camera.

Figure 2: Overview of the formed to determine the range to the subject when using a rifle scope to calculate range.

Figure 3: Measuring the angle by reading the scale in the scope.

Figure 4: The equation for ranging. (d = distance to subject, s = subject size, α = angle)

To make this trigonometric solution work you do need to know one thing ahead of time, the size of the subject. In addition to that you need a way to measure the angle of the subject and a formula to convert that into a distance. One approach, and what’s used in long distance rifle shooting, is to use a scale in an viewfinder or scope to measure the angle the subject covers from your position. The scale is marked at positions that correspond to known angles. Commonly, at least in rifle scopes, these marks are made in milliradians (mils) or minutes of angle (MOA).

If the hypothetical reticle in figure 3 is marked using milliradians then the subject covers an angle of 4 mils¹ and the subject is known to be 6″ tall. Solving the equation shown in figure 4 for the values given, and a distance of 41.6 inches² is calculated.

Whether or not this is more practical than a tape measure is probably up for debate, what isn’t debatable is that this still isn’t practical for photography. Accuracy is dependent on how well you know the size of the subject and how accurate you can measure the scale and the whole thing is predicated on being able to work out an equation on the scene as a table is still problematic because of the errors in subject size. Fortunately for people shooting rifles, an error of a few feet has little impact on a shot that’s covering 100s of feet. However, an 85mm f/1.4 lens used to make a portrait has a total depth of field of only 4.1 inches at 10 feet.

For what it’s worth, I’m not aware of this style of ranging ever being applied to common photographic equipment. It’s certainly not accessible to most people. However it does introduce the trigonometric strategy for calculating distance rather clearly and that’s what all focusing aids based on range finding use one way or another.

The Coincident Image Rangefinder

The solution to the having to solve equations is to cleverly build that into mechanics of the rangefinder and present it to the user in a simple, easy to understand manner. The basis for doing that is to turn the triangle around so that the length of the subject in the previous figure now becomes a fixed length inside the camera/rangefinder.

The ease of use problem is solved by presenting the user with a pair of superimposed images where adjusting the alignment of the images corresponds with setting the focus. This all comes together in a device known as a coincident image rangefinder (CIR).

In a coincident image rangefinder, the user knows they’ve found the correct distance because the two images in the viewfinder are perfectly aligned. Even better, because of the way the CIR works, the user knows (not that it’s strictly necessary in this case³), which way the lens needs to be adjusted to focus the image.

Figure 5: Reversing range finding triangle.

Reversing the range finding triangle presents us with two solvable  problems, measuring the angle and combining the two images. The second problem is addressed by a beam splitter used as a beam combiner. A beam splitter, like most optical elements, it can be used in both directions. That is, when light is fed into two of the sides of the beam splitter, it will superimpose them over each other and send them out a third side.

Figure 6: Parts of a basic coincident image rangefinder focused at infinity

Figure 7: Distance equation

Figure 7: Simplified light paths though a coincident image rangefinder

The second problem, measuring the angle formed between the two rays form the subject. This appears more challenging at first, however even that is relatively straight forward.

The law of reflection states that the angle of incidence is equal to the angle of reflection. From this two things become clear, first that when the mirror is rotated 45° as shown in figure 6, the camera will be focused at infinity. Second, we know that the angle between the two light rays is equal to twice the angle the mirror will rotated.

From the second point, the equation shown in figure 7 can be derived; where d is the distance to the subject, b is the rangefinder’s base length and θ is the angle the mirror is rotated. Further, this makes measuring the angle α (in figure 5) directly unnecessary to calculating the distance as it was done in the previous method.

The final piece of the puzzle is coupling the rotating mirror to the lens’s focusing ring, so the whole system can be driven by the operator simply by adjust the lens. The actual math is hidden from the user in this mechanical coupling.

How it all fits Together

When the lens isn’t focused properly, the reflected light from the mirror isn’t aimed at the center of the beam splitter. Thus the combined image is misaligned, the direction of the misalignment is also a queue to the direction of the focus error. Figure 8 shows an exaggerated schematic of a coincident image rangefinder at various focus positions.

In practice it’s not quite this simple and there are more elements included to insure that both images are right side up and to project framing lines into the viewfinder, but the concept is the same for all coincident image rangefinders. Visual alignment is the key here, and what makes a CIR easily accessible to all users. The complicated math is handled by the people designing and building the cameras.

This system is used in cameras that are collectively called rangefinders. Arguably, the most successful example of this type of camera is Leica’s M series of rangefinder cameras.

Now that rangefinder provides an easy way to determine when the lens is focused it would seem like this should be the solution to all focusing needs. Simply stick a coincident image rangefinder on top of a camera and it’s good to go.

Not so fast…

Problems with a Coincident Image Rangefinder

There are a few issues the coincident image rangefinder presents. First since a rangefinder doesn’t work though the imaging lens, calibration of the lens-mirror link becomes very important. Small errors in mounting distance, lens construction or even rangefinder construction can throw the focus off enough to cause problems and they aren’t visible until after the image is made.

The second, and more fundamental, issue is accuracy. The rangefinder’s base length dictates the angle the mirror has to rotate for a given focus distance, because of that it controls the accuracy of the range finder. To make the measurement more accurate, a longer base length is needed to increase the angle the mirror has to rotate though. To give an idea how much rotation is involved, the mirror in a hypothetical rangefinder with a 60mm base length will rotate just over 0.5° from the infinity position when focusing on a subject 3M away; at 30m it will have been rotated just over 0.05°.

The objective for the rangefinder designer is to choose a rangefinder base length that is sufficiently long to provide enough accuracy with the focal lengths and working distances that will be used with the system. On the other hand the size of the camera places hard limits on the maximum length of the range finder base length. In turn the limits of the rangefinder place limits on the maximum focal length that the system can reasonably support.

This method of range finding works well, in practice, for wide-angle, normal and short-telephoto focal lengths because the depth of field at long distances grows quickly enough to mask errors in focus. However, telephoto and super telephoto focal lengths require much greater accuracy at long distances. That, coupled with the fixed external viewfinder makes long telephot lenses unwieldy at best on this type of camera, and in general they aren’t available for rangefinder systems.

Conclusions

The coincident image rangefinder solves some of the problems of focusing a small format camera but not all of them. This is no slight of the design though. One things a rangefinder camera offers that was impossible to achieve, before digital at least, is a way to build a very compact camera that doesn’t have any large moving parts. In fact when the exposure is being made, the only moving part in a rangefinder camera is the shutter. This makes rangefinder cameras very quite, as well as eliminating mirror slap induced vibration reducing image quality.

Next time we’ll look at how to make a rangefinder thin enough that it can be placed in a through the lens situation as used in an single-lens reflex camera.