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    Image:Optical Theodolite.jpg|right|thumb|Diagram of an Optical Theodolite
    A theodolite (am "transit") is an instrument for measuring both horizontal and vertical angles as used in triangulation networks It consists of a telescope mounted movably within two perpendicular axes the horizontal or trunnion axis and the vertical axis These 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
    Both axes of a theodolite are equipped with graduated circles that can be read out through microscopes The vertical circle (the one associated with the horizontal axis!) should read 90° or 100 gon when the sight axis is horizontal(or 270° 300 gon when the instrument is in its second position "turned over") If not we call half of the difference with 300 gon index 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 mounted on a tripod by means of a forced centering plate or tribrach containing 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 -- levelling The former is done using a plumb the latter using a spirit level Fast and accurate procedures for doing both have been developed


    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 thenused 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

    Triangulation as invented by Gemma Frisius around 1533 consists of making such direction plots of the surrounding landscape from two separate standpointsAfter 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, eg 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

    Modern theodolites

    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 eg 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
    Today's theodolites are usually equipped with integrated electro-optical distance measuring devices allowing the measurement in one go of complete three-dimensional vector -- 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

    See also