Theodolite

The theodolite is a angle measuring instrument for measuring horizontal directions and zenith or vertical angles is used in geodesy ( surveying ). For this purpose, it is placed vertically by means of a tripod over a point. A special version is the Hängetheodolit, which is used mainly in mining.

A theodolite consists essentially of a telescopic sight, a vertical and a horizontal circle and several dragonflies. The latter are used to the vertical orientation of the device ( leveling ).

In the riflescope a reticle is integrated with the target is sighted. Usually, the case set angle in the unit Gon be displayed and / or stored (100 gon = 90 °) from the device.

Etymology

The origin of the term is unclear.

Engelberg appears in his thesis contribute to the development history of the theodolite in 1969, as recently Peters in his contribution to the history and meaning of the word theodolite, to the conclusion that the word theodolite comes from the Greek and of the Englishman Leonard Digges was found an ancient writing and first used in this context.

Method of construction

Some - especially the elderly - devices share the horizontal circle into 360 degrees, and enter instead of the zenith angle, the slope in percent. In the artillery aiming circle is called a theodolite and is divided into degrees instead of in line.

Forerunner of the theodolite were the Dioptra ( Antiquity), the Azimutalquadrant ( 1500) and the alidade. Exact universal instruments were built from 1850 onwards for triangulation and astronomy. When Repetitionstheodolit could be increased by the addition of angles, the measurement accuracy. Tachymeter allowed the distance measurement for curves in the visual field - which today is done with laser and electronics.

The Theodolitunterbau or limbus contains the horizontal circle ( 1) and the vertical axis ( vertical axis ) (S). He wears the alidade (Arabic ), the superstructure consisting of two supports (2), the horizontal tilt axis (K ), the telescope ( 3), the circle reading ( 4) and the vertical circle (5). The telescope has a reticle ( reticle in the eyepiece ) through which the target axis is defined (Z ), and an inner lens to focus ( focus).

The base sits on the base plate, which is mounted on a tripod and leveled with three leveling screws and level. The centering on the measurement point is made by moving the instrument to the horizontal tripod plate, then the heart of the tripod screw from the bottom is her tightened.

Depending on measurement accuracy and application distinguishes between

Theodolite (robust and light, about ± 10 ")
Tachymeter (including distance measurement, since about 1990 mostly digital readout and automatic tilt compensation of the vertical axis )
Precision or Sekundentheodolit (± 1 " for engineering geodesy )
And the universal instrument (± 0.1 ", eg DKM3 and Wild T4 ) for astro- geodesy.
Built similar to the theodolite are also some passages instruments and special equipment for military and satellite geodesy (eg, the Moonwatch Apogee or the previous Kinetheodolite ).

Possible instrument error

The four essential instrument error ( adjustment or manufacturing inaccuracy, deviations from the theoretical ideal state) theodolites are

Target axis error: the optical axis of the telescope is not perpendicular to the tilting axis of the telescope.
Tilt Axis: The tilting axis of the telescope is not perpendicular to the vertical axis of the theodolite.
Index error: The zero mark of the vertical circle is not the zenith at horizontiertem theodolite. If there is no index error, the zenith direction corresponds to a leg of the zenith angle. The other limb points towards the observation target.
Cyclotomic Error: The scale division on the graduated circles differs generally unsystematic from the ideal uniform pitch.

Instrument error ( precision mechanics ) can be described by

Measurements in two faces, and averaging eliminate
Repeated measurement with different pitch positions minimize
Eliminate subsequent reduction calculation or reduce the impact and / or
High optical-mechanical precision ( at least 1 micron ) minimize the impact.

Other minor influences such as thermal effects or residual mechanical stresses in Theodolitaufbau remain ia less than 1 " and are thus negligible.

Not entirely eliminated, however, is the Stehachsfehler. It occurs when the vertical axis is not parallel to the direction of gravity. Then the leveling is wrong. One reason for this may be a misalignment of the land used for leveling instruments. The Stehachsfehler is an operating or Aufstellfehler. A residual tilt of the vertical axis to the perpendicular direction can be measured internally by a two-axis tilt sensor in modern total stations and automatically attached to the measuring elements.

The vertical axis is perpendicular to the vial axis. The target axis is perpendicular to the tilt axis. The tilt axis is perpendicular to the vertical axis. All three axes intersect ideally at one point.

Approach the direction Measuring with theodolite or total station

The instrument is to level up just before the measurements and additionally mostly centered over a ground point ( surveying or measuring point ) to set up. The leveling is done using the spirit level attached to the alidade and causes the vertical axis of the instrument with the plumb line coincides. The centering is carried out simultaneously with the leveling by a special procedure schematized. Aids in centering is either a plumb bob, which in the knurled screw ( screw heart ) of the tripod is mounted, or a built- in tripod or theodolite optical plummet.

With the help of the rotatable measuring telescope ( telescope with crosshairs - today: reticle ) then successively all target points are targeted. By reading at a fixed angular scale ( circle ), the directions are determined at any destination point. Technically speaking, various auxiliary equipment, such as incremental or absolute encoder is used to accelerate the reading and to eliminate personal reading errors.

In electronic theodolites and total stations, the pitch circles are scanned electronically. The analog angle values are converted by analog - to-digital conversion in digits, displayed and stored. The benefits of an automatic circle reading are that observation times are shorter and occur errors in detecting less. Therefore, this method is less tiring for the observer, especially as the data directly stored and can be digitally processed later.

For automatic detection of the pitch circle is coded and scanned with different techniques (optical - electronic, electrical, magnetic). The electro- magnetic sensing is known as the inductosyn. An electrical scanning is technically outdated. Are in widespread use today, however, optical-electronic scanning. It is important to distinguish between the transmitted light and the incident light technology. When the transmitted light method is coded by means of darkness, arise translucent and opaque regions. The coding is illuminated from one side and on the other side of the photo diode is mounted as a receiver. Incident light in the transmitter and receiver on the same side are arranged. Since the pitch circle having different reflective properties, different degrees of light beams can be recorded. The encoder disks are usually provided with a Gray code.

The angle between two target points with respect to the instrument point is calculated by adding the difference of the two measured directions.

A distinction is made between readings on the horizontal and on the vertical circle. The reference direction in the horizontal direction is the direction of measurement at an arbitrary target point. Therefore, these directions oriented not by Electromagnetic, geographic or grid - north-north directions are comparable. By surveying typically target points with known coordinates official (so-called trigonometric points or attachment points (APs) ) are targeted. This can then be calculated based on grid north the north. So will the direction angle from horizontal directions.

The reference direction of the readings on the vertical circle is the zenith, which runs parallel to the direction of gravity with the correct leveling. Since the vertical reference direction in this way a firm and each point is the same, readings must not be oriented on the vertical circle. Already oriented and the readings correspond to angles, the vertical angles. With horizontally aligned telescope measuring the zenith angle is exactly 100 gon (90 °). This is also spoken by Nivellierblick.

Observation and accuracy. Goals are to eliminate errors measured in a sentence (sometimes in half- sentences A sentence consists of two series of measurements ( 2/2 sets ), where for the second series of the telescope by beaten ( about the tilt axis to the other side of the device is rotated ), the superstructure is rotated 180 ° and the objectives to be targeted again. Thereby, the readings of the target directions take place at diametrically opposite points on the horizontal circle and at corresponding locations on the vertical circle. influences of the target, tilting-axis and vertical index error have in both faces the same magnitude but opposite sign. When averaging the horizontal direction and the zenith angle from both faces, one obtains observations that are free from the influence of axis error.

The measured quantities that can be observed with a theodolite, a distinction is made

Horizontal angle: A horizontal angle is the difference between the direction of observation to two destinations,
Zenith angle: vertical angle or outdated also: zenith distance,
Angle differences: distance measurement using the two Reichenbach spacer threads or Reduktionstachymetern
Measurement with movable reticle: only in special theodolites, see impersonal micrometer.

Known manufacturers

F.W. Breithaupt & Sohn
Geo -Fennel (formerly Fennel )
Trimble Navigation: Carl Zeiss ( historical ), went up in Trimble Navigation
GDM ( historical ), went up in Trimble Navigation

Kern & Co (until 1992, then went up in Leica Geosystems )
Wild Heerbrugg ( historical ), merged in 1990 Leica Geosystems