How Things Work: Collimation Corrections with Total Station Software
Professional Surveyor Magazine - August 2003
"Collimation" error, strictly speaking, refers to the misalignment between the line of sight of the telescope, as represented by the crosshairs and the barrel of the telescope. This misalignment can be for horizontal angles as well as vertical angles. When speaking of this misalignment for horizontal angles, the error is best understood by describing it as the "double center error." There are many ways to check for this error, but the method that most people readily grasp is by setting up the instrument, sighting a point a few hundred feet away (A in Figure 1), and then inverting the telescope, without releasing the horizontal motion clamps, and marking a point an equal distance away (B in Figure 1). One of the horizontal motion clamps is then released and the instrument alidade is rotated so that the crosshairs are now again placed on point A. Then the telescope is again inverted and pointed towards B. If the crosshairs do not strike B, but C instead, the gap between them and B represents four times the actual angular error. The typical adjustment is to move the crosshairs one-fourth of the apparent distance back toward B.
To detect this error for vertical angles, one method is to sight a level rod placed perhaps 30 feet away and record the reading. After the telescope is clamped, a level rod is placed about 300 feet away along that line of sight and that reading recorded. The telescope is inverted and the crosshairs are placed on the previous rod reading on the near rod and the telescope clamped. When the far rod is now observed, any discrepancy from the previously observed reading represents twice the angular error.
With modern theodolites and total stations of high enough resolution, both of these errors may be simultaneously detected more simply. This is done by observing a point in face 1 (telescope in normal position), and recording the horizontal and vertical circle readings. The telescope is then inverted (face 2) and the upper motion clamp, if it is a two motion instrument, is released and the readings observed again. If the horizontal circle reading does not differ from the first one by exactly 180º, the difference is twice the horizontal collimation error. If the sum of the vertical circle readings do not sum to exactly 360º, the difference is twice the vertical collimation error. Random error theory tells us that we should make several observations (perhaps five or ten of each of the circle readings and pointings) before drawing any conclusions.
Total station software is often available to automatically record these readings, average them, and determine the differences, thus finding the horizontal and vertical collimation errors. Readings made in one face only can be automatically corrected for these errors. Experience will show that this check must be done frequently to monitor the size and sign of the error over time. The standard way to eliminate this error before such software was available was to take readings in both faces and average them.
The surveyor should be aware that horizontal angle errors due to other reasons may be falsely detected as collimation errors if the technique commonly used to detect collimation errors and then make corrections via software is used. These two errors arise from misleveling of the instrument and misalignment of the horizontal or trunnion axis.
With misleveling of the instrument, except for two positions of the horizontal circle, the effect is to tilt the horizontal axis of the instrument. When the telescope is raised or lowered with this condition, the effect of this error is to move the crosshairs further away from the true vertical (Figure 2).
With misalignment of the trunnion axis (the horizontal axis on which the telescope is mounted), the crosshair similarly moves away from the true vertical line as the telescope is raised or lowered from the horizontal.
While these errors appear to be manifested in the same way, it must be realized that the deviation of the crosshair from the true vertical varies due to misleveling error and depends upon which part of the horizontal circle is being observed. There are two points on the circle where the error will be at a maximum (though opposite in sign) and two points where it will be zero. The trunnion axis error, on the other hand, remains the same (for a particular inclination of the telescope).
Keeping in mind that observations for collimation error can include the effects of errors from these two additional sources, the user must be aware of how the software in the instrument works. If the simplest case is being tested and corrected for, the user must observe additional points after the error has been apparently corrected that lie well above (20º or more) or below the horizon. In addition, it is advisable to carry out these tests at various horizontal circle readings. As to avoid measurements where the error due to misleveling is zero, the circle readings should be varied by 45º or 30º.
If the software in your instrument corrects for these additional sources, you should see no variation in the observed collimation error. Your instrument's manual, your dealer, and manufacturer's representative can provide additional information to investigate these matters.
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