# Range Finder

May 12, 2013

Adapted from: The Great Soviet Encyclopedia (1979)

Range Finder

an instrument for measuring distances. It is used extensively in engineering geodesy (in the construction of transportation and communications lines, hydraulic-engineering structures, and electric power transmission lines), topographic surveying, the military (principally for determining distances to targets), navigation, astronomical research, and photography.

A distinction is made between range finders of the geometric and physical types on the basis of their principle of operation. The measurement of distances with range finders of the geometric type is based on the determination of the height h of the isosceles triangle ABC(Figure 1)—for example, from the known side AB = l (the base) and the opposite acute angle β(the so-called angle of parallax). For small β(expressed in radians), h = l/β. One of the quantities l or β is usually constant; the other is variable (the one being measured). On this basis a distinction is made between range finders having a constant angle and range finders having a constant base.

Figure 1. Diagram illustrating the principle of operation of a geometric range finder: AB is the base,β is the angle of parallax, and h is the distance to be measured

A crosshairs range finder with a constant angle is a terrestrial telescope with two parallel hairs in the field of view. A telemeter rod with equidistant divisions serves as a base of the range finder. The distance measured by the range finder to the base is proportional to the number of rod divisions visible through the telescope between the hairs. Many geodetic instruments (such as theodolites and leveling instruments) have a crosshairs range finder. The relative error of a crosshairs range finder is ˜0.3-l .0 percent.

More intricate optical range finders of the geometric type have their own fixed base. They are divided into two groups, monocular and binocular (stereoscopic).

A monocular range finder (Figure 2) is constructed in such a way that the image of the object (target) can be seen in the eyepiece E as formed by two halves divided by a horizontal line; the halves of the image are constructed by rays that pass through the various optical systems of the range finder (01 and O2). In the case of a very remote object, when the rays A1and A2 incident upon the range finder are virtually parallel, both halves of the image are located at the same point on the horizontal dividing line and form the whole image. As the object approaches the range finder, the parallelism of rays A, and A2 is disrupted, and the halves of the image diverge along the dividing line. To measure the distance to the object it is necessary to bring together the displaced halves of the image

Figure 2. Construction of a monocular range finder: B1 and B2 are reflectors placed at the ends of the base, O1 and O2are optical systems that construct the images, C is a special reflector (prism) that brings together both images in a common focal plane F1and Eis the eyepiece. The image visible through the eyepiece before focusing (a) and after focusing (b) is shown in the circles.

by using an optical compensator housed in one of the optical systems. The result of the measurement is read from a special scale. The error of monocular coincidence range finders is ˜0.1 percent at distances up to 1 km.

Monocular range finders with a base of 3–10 cm are widely used as photographic range finders. Photographic range finders are usually combined with the viewfinder of a still or movie camera into one optical system. The light rays from the object being photographed pass into the range finder (Figure 3) through two different optical systems (main and auxiliary). The images constructed by these systems are seen separately in the eyepiece. To focus the lens and produce a clear photograph, the two images are brought together by moving the optical compensator, which is linked to the focusing mechanism of the camera lens.

Figure 3. Photographic range finder: C1 and C2 are prisms, Bis the camera lens, and kis the lever. Before focusing, the eye sees two images (a) In the viewfinder; after focusing —by rotating the lens and moving the lever attached to the prism —just one image (b) remains