# How Things Work: Horizontal Angle Systematic Error Correction

If a repeated number of these observations are taken, it will be possible to determine how much of the discrepancy can be expected due to the applicable random errors and how much is from lack of adjustment of the theodolite portion of the instrument. If, for example, 10 sets of readings are taken, it is possible to then analyze the data by taking the average of the F1 readings and the F2 readings. If the averages turn out to be the same, then the likelihood that there are systematic errors is low. And the variations in circle readings are a representation of the accuracy achievable with the instrument.

If the averages are different however, the discrepancy in the averages will indicate the combination of the systematic errors mentioned in the first paragraph. In that case, it is not possible to isolate the errors from the exercise done so far: more observations need to be made.

The impact on the circle readings caused by either of the systematic errors is to cause a discrepancy for a given target, when the variations for the random errors are eliminated, that is constant between the F1 and F2 readings. However, the horizontal collimation error detected in the horizontal circle readings (that is the error in alignment of the vertical crosshair with respect to the optical axis of the telescope) will be constant in magnitude and sign regardless of the zenith angle of the telescope.

## Horizontal Collimation Error

This is the so-called "double center" error that many surveyors are familiar with. It is most apparent when attempting to prolong a line by inverting the telescope. It is detected by repeating the process, first with the telescope in the F1 position for the initial backsight, and then again with the telescope in the F2 position.

The discrepancy at point C in the figure below, if there are collimation errors will be four times as large as the actual error. Another way to look for this error is to sight a clearly defined target about a 100 m away that is close to the horizon (i.e., the observation is very close to horizontal); record the horizontal circle reading. Then, after releasing the upper motion of the instrument, observe in the opposite face and record the horizontal circle reading. Repeat these many times (10 or 20 times). For example, you may find the F1 average to be 121"42'38". The average F2 may be 301"42'48". The average discrepancy is 10"; but the actual collimation error is 5". Because the average of the F1 and F2 averages is 121"42'43", the correction to a F1 reading is considered to be +5".

## Horizontal Axis Error

This error is also called the "height of standards" error or the "trunnion axis" error. When a point not near the horizon is observed using the same procedure as for the horizontal collimation error, a similar discrepancy will be noted. Assuming that the horizontal collimation error has already been corrected, or after manually applying the above-determined correction, the error for that particular zenith angle can be determined using the same analysis procedures. If the correction turns out to be positive for an angle above the horizontal (i.e., zenith angle less than 90"), the sign will be negative for zenith angles greater than 90". This error occurs when, after the instrument is properly leveled, the horizontal axis on which the telescope rotates is not truly horizontal. This causes the vertical crosshair, when the telescope is elevated or depressed, to trace an inclined plane, rather than the vertical plane it should be tracking.

## Instrument Software

Today, instrument software can be found that corrects for one or both of these errors. Read the instructions from your manufacturer on the procedures for collecting data to determine and correct for these errors using software. It is really important to make sure that if the procedure separately determines the two corrections, that you always perform the horizontal collimation procedure first.

Or you may choose to follow the procedure that is used to adjust theodolites, by adjusting the crosshair to correct for the horizontal collimation error. If you find that the instrument has horizontal axis error, you will need to take it in to a qualified service center to repair this problem.