Q: I usually use a 360oprism with my robotic total station. I was told by a surveyor to use a non-360 oprism for precise applications. I did this on a critical building layout, but when I measured the diagonals, I discovered errors. ...

AB - MA - MB = K

K = the combined prism and instrument constant (unless the instrument constant has been set to zero).

Q:I usually use a 360oprism with my robotic total station. I was told by a surveyor to use a non-360 oprism for precise applications. I did this on a critical building layout, but when I measured the diagonals, I discovered errors. It appears to be a prism constant problem, but I’ve entered the offset printed on the prism. What am I doing wrong or not seeing?

A:With so many total stations now equipped with reflectorless EDM (electronic distance measurement), the use of 360oprisms with robotic instruments, and the widespread use of GPS, some surveyors forget the importance of correcting for prism offsets. This issue arises with prisms because glass is thicker than air and thus has a higher index of refraction than air. The higher index slows down the infrared or visible light signal that is used for the distance measurement. Thus, all measurements made to a prism are longer than the actual distance traveled by the light beam.

This situation implies that all prism constants or offsets should be negative to reduce the measured value by the offset. However, the mounting system of the prism must be considered, too. Prisms can be mounted in a variety of ways with respect to the plumb line that passes through the point on the ground, and that is why prism constants can be negative, positive or even zero.

The surveyor must also be aware of a couple of complicating factors. One is that some manufacturers treat the prisms they manufacture as “zero offset” prisms simply because the total station firmware is hard-coded with the correct offset. Users who combine such instruments with third-party prisms (or vice versa) must verify that they are using the right offset; the number printed on the prism housing may not be the correct offset to use.

Another issue is that some data collectors or field controllers may automatically set the prism constant on the total station to zero and apply the correction to the measured value only after it has been downloaded from the total station to the hand-held unit. Reviewing the user manuals and doing some simple measurement checks (see the next question) are the best antidotes to these problems.

Thankfully, in your case, you followed the correct (and, for surveyors, mandatory) procedure by trying to verify your building layout by independent means. As a result, you were able to detect the problem.

Q:If I want to be sure that my prism constant is correct, what can I do other than measuring a known distance, calling the dealer or inputting a value that may be printed or stamped on the prism housing?

A:When a prism hasn’t been used in a while, it is difficult to remember the prism constant. (That is only one of the scenarios that may cause this question to arise.) The best procedure to use is one described in all complete surveying textbooks--the three-point prism constant determination.

To perform this procedure, lay out three points on a line. The line should be 60 to 100 meters long, and the point in the middle can be estimated. You can do the initial location with pacing and then adjust for convenience. However, when you finally set it, make sure that you use your total station to place it accurately on the line. Let’s call the end points A and B and the middle point M.

Next, set up at M, and using the same prism, measure to A and B. It is helpful if you’ve selected a site where the measurements are close to horizontal so that your analysis is not complicated by large differences between the slope and distance measurements.

Now move to either A or B, and measure to the other end of the line. Taking the horizontal distances, subtract MA and MB from AB. If the result isn’t zero, the difference is either the adjustment you need to make to the prism constant set on your instrument or the prism constant itself depending on what value you’ve set for the instrument’s prism constant.

When you measure, take the average of six to 12 readings where you point the telescope away from the target, and then recenter between each reading. Even though this process is called the “three-point prism constant determination,” you are actually determining the combination of the prism and instrument constant. The instrument’s constant is set at the factory and on most brands of instruments is not user-configurable. As time passes and an instrument undergoes heavy use, it is possible for the instrument constant to change, and this variation will be reflected in the calculations you perform. It is not uncommon for your equipment service center to adjust the instrument constant; thus, it is advisable to perform the prism constant determination every time you get an instrument back from service.

Once you believe you have determined--and set--the correct prism constant in your instrument, always repeat the procedure to check that you have applied it correctly. (For many people, a common error is to apply the correction with the incorrect algebraic sign.)

By the way, checking your EDM and prism against a single premeasured line is not advisable for determining the prism constant since the results are prone to a variety of error sources.

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