Theodolite
A theodolite is a precision optical instrument for measuring angles between designated visible points in the horizontal and vertical planes. The traditional use has been for land surveying, but it is also used extensively for building and infrastructure construction, and some specialized applications such as meteorology and rocket launching.
It consists of a moveable telescope mounted so it can rotate around horizontal and vertical axes and provide angular readouts. These indicate the orientation of the telescope, and are used to relate the first point sighted through the telescope to subsequent sightings of other points from the same theodolite position. Depending on the instrument, these angles can be measured with accuracies down to microradians or seconds of arc. From these readings a plan can be drawn, or objects can be positioned in accordance with an existing plan. The modern theodolite has evolved into what is known as a total station where angles and distances are measured electronically, and are read directly to computer memory.
A transit theodolite has a telescope short enough to rotate about the instrument's horizontal trunnion axis, turning the scope through the vertical plane and its zenith; vertical rotation in non-transit instruments is restricted to a limited arc.
The optical level is sometimes mistaken for a theodolite, but it does not measure vertical angles, and is used only for leveling on a horizontal plane.
Principles of operation
Preparation for making sightings
Temporary adjustments are a set of operations necessary in order to make a theodolite ready for taking observations at a station. These include its setting up, centering, leveling up and elimination of parallax, and are achieved in four steps:- Setting up: fixing the theodolite onto a tripod along with approximate leveling and centering over the station mark.
- Centering: bringing the vertical axis of theodolite immediately over station mark using a centering plate also known as a tribrach.
- Leveling: leveling of the base of the instrument to make the vertical axis vertical usually with an in-built bubble-level.
- Focusing: removing parallax error by proper focusing of objective and eye-piece. The eye-piece only requires adjustment once at a station. The objective will be re-focused for each subsequent sighting from this station because of the different distances to the target.
Sightings
The earliest angular readouts were from open vernier scales directly visible to the eye. Gradually these scales were enclosed for physical protection. scales were also used. Finally, angle readings became an indirect optical readout, with convoluted light paths to bring them to a convenient place on the instrument for viewing. The modern digital theodolites have electronic displays.
Micrometers are also used in telescopes and microscopes to measure the apparent diameter of celestial bodies or microscopic objects or the angular distances between two such objects. The micrometer used with a telescope was invented about 1638 by William Gascoigne, an English astronomer.
Errors in measurement
; Index error: The angles in the vertical axis should read 90° when the sight axis is horizontal, or 270° when the instrument is transited. Half of the difference between the two positions is called the index error. This can only be checked on transit instruments.; Horizontal axis error: 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 half the amount the bubble has run off using the adjusting screw, then re-level, test and refine the adjustment.
; Collimation error: The optical axis of the telescope 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
Historical background
Prior to the theodolite, instruments such as the groma, geometric square and the dioptra, and various other graduated circles and semicircles were used to obtain either vertical or horizontal angle measurements. Over time their functions were combined into a single instrument that could measure both angles simultaneously.The first occurrence of the word theodolite is found in the surveying textbook A geometric practice named Pantometria by Leonard Digges. The origin of the word is unknown. The first part of the Neo-Latin theo-delitus might stem from the Greek wikt:θεάομαι 'to behold or look attentively upon' The second part is often attributed to an unscholarly variation of the Greek word: wikt:δῆλος 'evident' or 'clear'. Other Neo-Latin or Greek derivations have been suggested as well as an English origin from alidade.
The early forerunners of the theodolite were sometimes azimuth instruments for measuring horizontal angles, while others had an altazimuth mount for measuring horizontal and vertical angles. Gregorius Reisch illustrated an altazimuth instrument in the appendix of his 1512 book Margarita Philosophica. Martin Waldseemüller, a topographer and cartographer made the device in that year calling it the polimetrum. In Digges's book of 1571, the term theodolite was applied to an instrument for measuring horizontal angles only, but he also described an instrument that measured both altitude and azimuth which he called a instrument. Possibly the first instrument approximating to a true theodolite was the built by Josua Habemel in 1576, complete with compass and tripod. The 1728 Cyclopaedia compares graphometer to half-theodolite. 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 to combine the essential features of the modern theodolite was built in 1725 by Jonathan Sisson. This instrument had an altazimuth mount with a sighting telescope. The base plate had spirit levels, compass and adjusting screws. The circles were read with a vernier scale.
Development of the theodolite
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. Ramsden's instruments were used for the Principal Triangulation of Great Britain. At this time the highest precision instruments were made in England by such makers as Edward Troughton. Later the first practical German theodolites were made by Breithaupt together with Utzschneider, Reichenbach and Fraunhofer.As technology progressed the vertical partial circle was replaced with a full circle, creating the transit theodolite. Developed from 18th-century astronomical transit instruments used to measure accurate star positions, these had finely graduated vertical and horizontal circles. The transition into a transit was pioneered by early 19th century by instrument makers and became the standard theodolite design. Development of the theodolite was spurred on by specific needs, such as the British Ordnance Survey, which produced a 1820s requirement for theodolites capable of providing sufficient accuracy for large scale triangulation and mapping. The Survey of India at this time produced a requirement for more rugged and stable instruments, such as the lower center of gravity Everest pattern theodolite.
Railway engineers working in the 1830s in Britain commonly referred to a theodolite as a "Transit". The 1840s was the start of a period of rapid railway building in many parts of the world which resulted in a high demand for theodolites wherever railways were being constructed. It was also popular with American railroad engineers pushing west, and it replaced the railroad compass, sextant and octant. 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 1920s a step change in theodolite design occurred with the introduction of the Wild T2 made by the Swiss Wild Heerbrugg company. Heinrich Wild designed a theodolite with divided glass circles with readings from both sides presented at a single eyepiece close to the telescope so the observer did not have to move to read them. The Wild instruments were not only smaller, easier to use and more accurate than contemporary rivals but also sealed from rain and dust. Canadian surveyors reported that while the Wild T2 with 3.75 inch circles was not able to provide the accuracy for primary triangulation it was the equal in accuracy to a 12 inch traditional design. The Wild T2, T3, and A1 instruments were made for many years.
In 1926 a conference was held at Tavistock in Devon, UK where Wild theodolites were compared with British ones. The Wild product outclassed the British theodolites so manufacturers such as Cooke, Troughton & Simms and Hilger & Watts set about improving the accuracy of their products to match their competition. Cooke, Troughton and Simms developed the and later the Vickers V. 22.
Wild went on to develop the DK1, DKM1, DM2, DKM2, and DKM3 for Kern Aarau company. With continuing refinements, instruments steadily evolved into the modern theodolite used by surveyors today. By 1977 Wild, Kern and Hewlett-Packard were all offering "Total stations" which combined angular measurements, electronic distance measurement and microchip functions in a single unit.