A theodolite is a precision instrument for measuring angles in the horizontal and vertical
planes.
Theodolites are used mainly for surveying applications, and have been adapted for specialized
purposes in fields like meteorology and rocket launch technology.
A modern theodolite consists of a movable telescope mounted within two perpendicular
axes—the horizontal or trunnion axis, and the vertical axis.
When the telescope is pointed at a target object, the angle of each of these axes can
be measured with great precision, typically to seconds of arc.
Theodolites may be either transit or non-transit.
Transit theodolites are those in which the telescope can be inverted in the vertical
plane, whereas the rotation in the same plane is restricted to a semi-circle for non-transit
theodolites.
Some types of transit theodolites do not allow the measurement of vertical angles.
The builder's level is sometimes mistaken for a transit theodolite, but it measures
neither horizontal nor vertical angles.
It uses a spirit level to set a telescope level to define a line of sight along a level
plane.
Concept of operation
A theodolite is mounted on its tripod head by means of a forced centering plate or tribrach
containing four thumbscrews, or in modern theodolites, three for rapid levelling.
Before use, a theodolite must be precisely placed vertical above the point to be measured
using a plumb bob, optical plummet or laser plummet.
The instrument is then set level using levelling footscrews and circular and more precise tubular
spirit bubbles.
Both axes of a theodolite are equipped with graduated circles that can be read through
magnifying lenses.
The vertical circle which 'transits' about the horizontal axis should read 90° when
the sight axis is horizontal, or 270° when the instrument is in its second position,
that is, "turned over" or "plunged".
Half of the difference between the two positions is called the "index error".
Errors in measurement The horizontal and vertical axes of a theodolite
must be perpendicular, if not then a "horizontal axis error" exists.
This can be tested by aligning the tubular spirit bubble parallel to a line between two
footscrews and setting the bubble central.
A horizontal axis error is present if the bubble runs off central when the tubular spirit
bubble is reversed.
To adjust, the operator removes 1/2 the amount the bubble has run off using the adjusting
screw, then re-level, test and refine the adjustment.
The optical axis of the telescope, called the "sight axis", defined by the optical center
of the objective lens and the center of the crosshairs in its focal plane, must also be
perpendicular to the horizontal axis.
If not, then a "collimation error" exists.
Index error, horizontal axis error and collimation error are regularly determined by calibration
and are removed by mechanical adjustment.
Their existence is taken into account in the choice of measurement procedure in order to
eliminate their effect on the measurement results of the theodolite.
History
The term diopter was sometimes used in old texts as a synonym for theodolite.
This derives from an older astronomical instrument called a dioptra.
Prior to the theodolite, instruments such as the geometric square and various graduated
circles and semicircles were used to obtain either vertical or horizontal angle measurements.
It was only a matter of time before someone put two measuring devices into a single instrument
that could measure both angles simultaneously.
Gregorius Reisch showed such an instrument in the appendix of his book Margarita Philosophica,
which he published in Strasburg in 1512.
It was described in the appendix by Martin Waldseemüller, a Rhineland topographer and
cartographer, who made the device in the same year.
Waldseemüller called his instrument the polimetrum.
The first occurrence of the word "theodolite" is found in the surveying textbook A geometric
practice named Pantometria by Leonard Digges, which was published posthumously by his son,
Thomas Digges.
The etymology of the word is unknown.
The first part of the New Latin theo-delitus might stem from the Greek θεᾶσθαι,
"to behold or look attentively upon" or θεῖν "to run", but the second part is more puzzling
and is often attributed to an unscholarly variation of one of the following Greek words:
δῆλος, meaning "evident" or "clear", or δολιχός "long", or δοῦλος
"slave", or an unattested Neolatin compound combining ὁδός "way" and λιτός "plain".
It has been also suggested that -delitus is a variation of the Latin supine deletus, in
the sense of "crossed out".
There is some confusion about the instrument to which the name was originally applied.
Some identify the early theodolite as an azimuth instrument only, while others specify it as
an altazimuth instrument.
In Digges's book, the name "theodolite" described an instrument for measuring horizontal angles
only.
He also described an instrument that measured both altitude and azimuth, which he called
a topographicall instrument [sic].
Thus the name originally applied only to the azimuth instrument and only later became associated
with the altazimuth instrument.
The 1728 Cyclopaedia compares "graphometer" to "half-theodolite".
Even as late as the 19th century, the instrument for measuring horizontal angles only was called
a simple theodolite and the altazimuth instrument, the plain theodolite.
The first instrument more like a true theodolite was likely the one built by Joshua Habermel
in Germany in 1576, complete with compass and tripod.
The earliest altazimuth instruments consisted of a base graduated with a full circle at
the limb and a vertical angle measuring device, most often a semicircle.
An alidade on the base was used to sight an object for horizontal angle measurement, and
a second alidade was mounted on the vertical semicircle.
Later instruments had a single alidade on the vertical semicircle and the entire semicircle
was mounted so as to be used to indicate horizontal angles directly.
Eventually, the simple, open-sight alidade was replaced with a sighting telescope.
This was first done by Jonathan Sisson in 1725.
The theodolite became a modern, accurate instrument in 1787 with the introduction of Jesse Ramsden's
famous great theodolite, which he created using a very accurate dividing engine of his
own design.
The demand could not be met by foreign theodolites owing to their inadequate precision, hence
all instruments meeting high precision requirements were made in England.
Despite the many German instrument builders at the turn of the century, there were no
usable German theodolites available.
A transition was brought about by Breithaupt and the symbiosis of Utzschneider, Reichenbach
and Fraunhofer.
As technology progressed, in the 1840s, the vertical partial circle was replaced with
a full circle, and both vertical and horizontal circles were finely graduated.
This was the transit theodolite.
Theodolites were later adapted to a wider variety of mountings and uses.
In the 1870s, an interesting waterborne version of the theodolite was invented by Edward Samuel
Ritchie.
It was used by the U.S. Navy to take the first precision surveys of American harbors on the
Atlantic and Gulf coasts.
In the early part of the 20th century, Heinrich Wild produced theodolites that became popular
with surveyors.
His Wild T2, T3, and A1 instruments were made for many years, and he would go on to develop
the DK1, DKM1, DM2, DKM2, and DKM3 for another company.
With continuing refinements instruments steadily evolved into the modern theodolite used by
surveyors today.
Operation in surveying
Triangulation, as invented by Gemma Frisius around 1533, consists of making such direction
plots of the surrounding landscape from two separate standpoints.
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 measuring one distance both in the real terrain and
in the graphical representation.
Modern triangulation as, e.g., practised 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
dividing engine for 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 benchmark 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 "flip" 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
West.
Previously the user rotated the telescope on its horizontal circle to 180 and had to
carefully check the angle when turning 180 degree turns.
Use with weather balloons There is a long history of theodolite use
in measuring winds aloft, by using specially-manufactured theodolites to track the horizontal and vertical
angles of special weather balloons called ceiling balloons, or pilot balloons or pibal.
Early attempts at this were made in the opening years of the nineteenth century, but the instruments
and procedures weren't fully developed until a hundred years later.
This method was extensively used in World War II and thereafter, and was gradually replaced
by radio and GPS measuring systems from the 1980s onward.
The pibal theodolite uses a prism to bend the optical path by 90 degrees so the operator's
eye position does not change as the elevation is changed through a complete 180 degrees.
The theodolite is typically mounted on a rugged steel stand, set up so it is level and pointed
north, with the altitude and azimuth scales reading zero degrees.
A balloon is released in front of the theodolite, and its position is precisely tracked, usually
once a minute.
The balloons are carefully constructed and filled, so their rate of ascent can be known
fairly accurately in advance.
Mathematical calculations on time, rate of ascent, azimuth and angular altitude can produce
good estimates of wind speed and direction at various altitudes.
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, 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, costing up to $10,000 apiece, are equipped with integrated
electro-optical distance measuring devices, generally infrared based, 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.
This technique is called a resection solution or free station position surveying and is
widely used in mapping surveying.
The instruments, "intelligent" theodolites called self-registering tacheometers 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 as data collectors for this purpose.
Gyrotheodolites
A gyrotheodolite is used when the north-south reference bearing of the meridian is required
in the absence of astronomical star sights.
This occurs mainly in the underground mining industry and in tunnel engineering.
For example, where a conduit must pass under a river, a vertical shaft on each side of
the river might be connected by a horizontal tunnel.
A gyrotheodolite can be operated at the surface and then again at the foot of the shafts to
identify the directions needed to tunnel between the base of the two shafts.
Unlike an artificial horizon or inertial navigation system, a gyrotheodolite cannot be relocated
while it is operating.
It must be restarted again at each site.
The gyrotheodolite comprises a normal theodolite with an attachment that contains a gyroscope
mounted so as to sense rotation of the Earth and from that the alignment of the meridian.
The meridian is the plane that contains both the axis of the Earth’s rotation and the
observer.
The intersection of the meridian plane with the horizontal contains the true north-south
geographic reference bearing required.
The gyrotheodolite is usually referred to as being able to determine or find true north.
A gyrotheodolite will function at the equator and in both the northern and southern hemispheres.
The meridian is undefined at the geographic poles.
A gyrotheodolite cannot be used at the poles where the Earth’s axis is precisely perpendicular
to the horizontal axis of the spinner, indeed it is not normally used within about 15 degrees
of the pole because the east-west component of the Earth’s rotation is insufficient
to obtain reliable results.
When available, astronomical star sights are able to give the meridian bearing to better
than one hundred times the accuracy of the gyrotheodolite.
Where this extra precision is not required, the gyrotheodolite is able to produce a result
quickly without the need for night observations.
See also Clinometer
Dumpy level Leica Geosystems
LIDAR Macrometer
Plane table Rankine's method
Surveying Tacheometry
Total station Tribrach
Tripod Survey camp
Temporary adjustments of theodolite References