Triangulation (measurement technology)
Triangulation is a geometric method of optical distance measurement through precise angle measurement within triangles. The calculation is carried out using trigonometric functions . In simplified terms, one could also say that angle measurements are made from two points whose distance is known to any other point in space in order to clearly identify their position.
The special procedures for land surveying and mapping are described in the article Triangulation (Geodesy) .
principle
The basic principle of triangulation is shown in simplified form in the figure on the right for the two-dimensional case.
The object point to be determined is targeted from two different stations at positions and . The two angles and are obtained with the accuracy and . Knowing the base length , one can then determine the coordinates of relative to the coordinate origin. The measurement volume of the overall system is the intersection volume of the measurement volumes of the individual measurement systems.
Special features in three dimensions
In the three-dimensional case it should be noted that the two lines of sight of the two base stations normally do not intersect mathematically exactly, but are skewed . If one considers the linear system of equations for determining the point coordinate , then this can be solved unambiguously in the two-dimensional case, but overdetermined in the three-dimensional case and therefore no longer uniquely solvable. This means that the equations contain additional information that can be used, for example, to estimate the measurement error from the distance between the crooked lines.
Conversely, it is also possible to reduce the number of observations. Instead of measuring two directional angles for both base stations, it is sufficient to do this for only one station. At the second station, only the angle component in the plane of the will , and is spanned determined. The graphical solution of the intersection equation no longer contains two straight lines, but a plane and a straight line and can therefore always be solved unambiguously with physically meaningful observations. A technical implementation of this principle can be found in the stripe projection .
Technical implementation
In the classic technical implementation, a theodolite is used to determine the angle. The method is still state of the art in land surveying and high-precision measurement of individual points.
Active methods use a light source, usually a laser , which illuminates the object whose surface is to be measured at an angle . An electronic image sensor, usually a CCD - or CMOS - camera or a PSD , registered the scattered light. If the direction of the beam and the distance between the camera and the light source are known, the distance from the object to the camera can be determined. The connection between the camera and the light source as well as the two rays from and to the object form a triangle , hence the name triangulation . If the process is carried out in a grid-like or continuously moving manner, the surface relief can be determined with great accuracy, with commercially available sensors up to 0.01 millimeters. If a pattern is projected, for example a line or a striped pattern, the distance information to all points of the pattern can be calculated with a single camera image. A line is also called a light section , stripe patterns are used in the stripe projection.
This measuring technique is used in three-dimensional space, among other things, for the subsequent determination of the trajectory of meteorites with the help of the fireball network (in order to be able to estimate the impact location).