Theodolite

About Theodolite

An optical theodolite, manufactured in the Soviet Union in 1958 and used for topographic surveying.

Diagram of an Optical Theodolite.

A 'theodolite' is an instrument for measuring both horizontal and vertical angles, as used in triangulation networks. It is a key tool in surveying and engineering work, but theodolites have been adapted for other specialized purposes in fields like meteorology and rocket launch technology. A theodolite consists of a telescope mounted movably within two perpendicular axes, the horizontal or trunnion axis, and the vertical axis. When the telescope is pointed at a desired object, the angle of each of these axes can be measured with great precision, typically on the scale of arcseconds.
The 'transit' refers to a specialized type of theodolite that was developed in the early 19th century. It featured a telescope that could "flop over" ("transit the scope") to allow easy back-sighting and doubling of angles for error reduction. Some transit instruments were capable of reading angles directly to thirty arc-seconds. In the middle of the 20th century, transits came to be known as a simple form of theodolite with less precision, lacking features such as scale magnification and mechanical meters. The importance of transits is waning since compact, accurate electronic theodolites have become widespread tools, but transits still find use as a lightweight tool for construction sites. Some transits do not measure vertical angles.
The builder's level is often mistaken for a transit, but is actually a type of inclinometer. It measures neither horizontal nor vertical angles. It simply combines a spirit level and telescope to allow the user to visually establish a line of sight along a level plane.

Contents
Concept of operation
History
Using theodolites in surveying
Modern theodolites
Gyrotheodolites
References
See also

Concept of operation


The axes and circles of a theodolite.

Both axes of a theodolite are equipped with graduated circles that can be read out through magnifying lenses. The vertical circle (the one associated with the horizontal axis) should read 90° or 100 grad when the sight axis is horizontal (or 270°, 300 grad, when the instrument is in its second position, "turned over" or "plunged"). If not, we call half of the difference with 300 grad index error.
The horizontal and vertical axes of a theodolite must be mutually perpendicular. The condition where they deviate from perpendicularity (and the amount by which) is referred to as horizontal axis error. The optical axis of the telescope, called sight axis and defined by the optical center of the objective and the center of the cross-hairs in its focal plane, must similarly be perpendicular to the horizontal axis. If not, we call the deviation from perpendicularity collimation error.
Horizontal axis error, collimation error and index error are regularly determined by calibration, and removed by mechanical adjustment at the factory in case they grow overly large. Their existence is taken into account in the choice of measurement procedure in order to eliminate their effect on the measurement results.
A theodolite is a mounted tripod by means of a forced centering plate or tribrach, containing four thumbscrews (or in some modern theodolites three thumbscrews) for rapid levelling. Before use, a theodolite must be placed precisely and vertically over the point to be measured — centering — and its vertical axis aligned with local gravity — leveling. The former is done using a plumb, the latter using a spirit level. Fast and accurate procedures for doing both have been developed.

History


The history of theodolites goes back to so-called plane table alhidades, devices allowing the graphical mapping of the terrain. These devices consisted of a plane table and a telescope mounted in a fork-like contraption or alhidade, allowing it to be aimed out of the horizontal plane. The whole assembly rested on a plane table, onto which graphing paper was attached; a ruler connected to the alhidade in such a way as to be always pointing in the same horizontal direction as the telescope, was then
used to plot the direction to the target.
The first description of a theodolite, or 'theodelitus', is found in the surveying textbook ''Pantometria'' (1571) by Thomas Digges, son of Leonard Digges who is widely credited with the invention. He also invented the name, but its origin is unclear.

Using theodolites in surveying


U.S. National Geodetic Survey technicians observing with a 0.2 arcsecond resolution Wild T-3 theodolite mounted on an observing stand. Photo was taken during an Arctic field party (circa 1950). Credit: NOAA.

Triangulation, as invented by Gemma Frisius around 1533, consists of making such direction plots of the surrounding landscape from two separate standpoints.
After that, the two graphing papers are superimposed, providing a scale model of the landscape, or rather the targets in it. The true scale can be obtained by just measuring ''one'' distance both in the real terrain and in the graphical representation.
Modern triangulation as, e.g., practiced by Snellius, is the same procedure executed by numerical means. Photogrammetric block adjustment of stereo pairs of aerial photographs is a modern, three-dimensional variant.
In the late 1780s Jesse Ramsden, a Yorkshireman from Halifax, England who had developed the technique of dividing angular scales accurately to within a second of arc, was commissioned to build a new instrument for the British Ordnance Survey. The Ramsden theodolite was used over the next few years to map the whole of southern Britain by triangulation.
In network measurement, the use of forced centering speeds up operations while maintaining the highest precision. The theodolite or the target can be rapidly removed from, or socketed into, the forced centering plate with sub-mm precision. Nowadays GPS antennas used for geodetic positioning use a similar mounting system. The height of the reference point of the theodolite -- or the target -- above the ground bench mark must be measured precisely.
The American transit gained popularity during the 19th century with American railroad engineers pushing west. The transit replaced the railroad compass, sextant and octant and was distinguished by having a telescope shorter than the base arms, allowing the telescope to be vertically rotated past straight down. The transit had the ability to 'flop' over on its vertical circle and easily show the exact 180 degree sight to the user. This facilitated the viewing of long straight lines, such as when surveying the American Wild West. Previously the user rotated the telescope on its horizontal circle to 180 and had to carefully check his angle when turning 180 degree turns.

Modern theodolites


Modern theodolite Nikon DTM-520

In today's theodolites, the reading out of the horizontal and vertical circles is usually done electronically. The readout is done by a rotary encoder, which can be absolute, e.g. using Gray codes, or incremental, using equidistant light and dark radial bands. In the latter case the circles spin rapidly, reducing angle measurement to electronic measurement of time differences. Additionally, lately CCD sensors have been added to the focal plane of the telescope allowing both auto-targeting and the automated measurement of residual target offset. All this is implemented in embedded software.
Also, many modern theodolites are equipped with integrated electro-optical distance measuring devices, allowing the measurement in one go of complete three-dimensional vectors -- albeit in instrument-defined polar co-ordinates -- which can then be transformed to a pre-existing co-ordinate system in the area by means of a sufficient number of control points. The technique is called free station position surveying and is widely used in mapping surveying. The instruments, "intelligent" theodolites called self-registering tachometers or "total stations", perform the necessary operations, saving data into internal registering units, or into external data storage devices. Typically, ruggedized laptops or PDAs are used for this purpose.

Gyrotheodolites


The 'gyrotheodolite' is a special type of theodolite used for surveys which do not have sky visibility (mining, underground survey). This instrument gives the orientation of true north (the direction of Earth's rotational axis), which is set as a reference for future underground observations.[1]
The gyro-theodolite is composed of a theodolite with a gyroscope on it. True north is stored in the gyroscope for future use by orienting the theodolite approximately to the north (within a few minutes of arc); this minimizes losses when the directionality is later read. A power supply activates the rotation of the gyro spinner, which maintains orientation as the theodolite is transported. To read, the theodolite is set at rest. The gyro will then oscillate through the north meridian until reaching the direction of true north; this is a point of minimum potential energy, similar to the bottom point of a pendulum. When the gyro has stabilized, the reading on the horizontal circle of the theodolite is equivalent to true north, and can therefore be used as a reference point.

References


1. http://www.geodesy.hu/gyrotheodolites.html

See also



★ Tacheometry

★ clinometer

★ Surveying

★ Rankine's method

★ Dumpy level

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