GIAA Mailbag: On Electronic Compensator Adjustment and Maximum Electronic Angle Accuracy Error
Q: What, if anything, can I adjust on the electronic compensator on my total station?
A: Mechanically, there is nothing that the user can (or should) adjust on a total station's electronic compensator. Just as the plate vial does, the electronic tilt sensor measures the tilt of the vertical axis in the direction of the line of sight through the telescope. It may also sense tilt in the direction at right angles to the telescope. If it only has the former sensing capability, it is sometimes referred to as a "single-axis" compensator. The latter is called a "dual-axis" compensator. Depending on the manufacturer, it is likely that your product's manual includes instructions on adjusting the compensator, just as its mechanical counterparts, electronic compensators can go out of adjustment. Because the workings of the compensator are buried within the instrument's body, and the adjustments are generally made using the application software on the instrument, it is particularly easy to overlook this critical component to making accurate measurements.
If the tilt of the instrument can be displayed digitally, checking to see if it is working is as simple as checking the plate or tubular vial on your transit or theodolite. Set up the instrument with the tripod feet firmly in the ground and level it up. When you think you have it level, align the telescope so that the vertical plane through it passes through one of the leveling screws. Set the instrument's display to indicate tilt (if it is dual axis, it will display in both directions). If they are both not zero, turn the leveling screws to bring them to zero. If it is too hard to bring them to zero, particularly if the readout is to one arc-second or less, bring them as close as possible to zero (see Figure 1). Now rotate the alidade 180Âº without inverting the telescope. If the compensator is in adjustment, the display should indicate that the tilt is zero or very nearly so. If the values are significantly different from zero, then one-half of the difference is the error in your compensator's adjustment (see Figure 2). If this is a dual-axis compensator, you may discover that the compensator is in adjustment in one direction (axis) but not in the other. To make the adjustment, you will need to follow your manufacturer's procedure; this is best learned from reading your manual.
Q: Electronic angle accuracy on my instrument is given by my manufacturer as Â±3". I was told that it is the maximum error possible. Is this true?
A: If the manufacturer has expressed accuracy using a standard referred to as DIN 18723, the angle accuracy actually represents the standard deviation; however, it does not directly tell you angle accuracy. The specification actually gives the uncertainty in the average of a Face I (telescope direct) and Face II (telescope reverse) pointing to a single target. The specification is written this way because it is more common worldwide to measure angles using the concept of directions. Thus, an angle is determined by observing two directions.
For your particular case, you need to apply basic principles of error propagation to evaluate what your expected angle accuracy may be. When each direction of a single angle is measured in Face I and II, this is equivalent to measuring an angle by repetition, where the first angle is measured in Face I and the second in Face II. In that case, for your instrument, the expected standard deviation of the angle would be approximately Â±4.2". This is calculated by multiplying the standard deviation of each direction (Â±3") by the square root of two (the number of directions). If you only measured the angle in one face, you would multiply the standard deviation of the angle by the square root of two again, to get Â±6". If, on the other hand, you measure each angle by taking two sets of observations in Face I and two sets in Face II, you would divide the angle uncertainty by the square root of the number of times you have made the basic measurement. So the result would be Â±3".
Keep in mind that these values are standard deviation, which means that there is an approximately 68 percent probability that the value you get is correct. To have a higher confidence, you would find the correct multipliers. For example, if you get Â±4.2" for the standard deviation, it would be Â±8.4" for 95 percent confidence, and Â±12.6" for 99.9 percent confidence. These are all, of course, true only if you have ensured several things: all systematic errors in the angle measurement have been eliminated; and all other angle measurement procedures are correct, such as having a clear target, a stable target, clear lines of sight with no atmospheric instability, correctly plumbed targets and instruments, etc.
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