Dennis Hunter mentioned an issue with a calibration baseline below and that brought the whole subject of the design of calibration baselines to mind, with the "GeeOddesist" formerly known as Donald Mulcare giving a link to descriptions of the EDMI calibration procedures required of land surveyors in the State of Victoria, Australia.
Once upon a time, land surveyors depended upon EDMI to measure very long distances that nowadays would be routinely measured by GPS methods. I'd have to get out some project files, but I doubt I've measured that many distances much over about 1000 ft. since I got GPS equipment. In fact, the EDMI/total station is used mostly to measure distances under about 800 ft.
That being the case, if I were to design a calibration baseline for my instrument, I would mainly be interested in characterizing its performance in measuring distances between 5 ft. and 800 ft. I have to wonder whether other surveyors with GPS equipment are mostly using EDMI to measure such relatively short distances. If so, sites for EDMI calibration baselines ought to be much easier to find for a maximum interval of 800 ft. than for 1000m.
>sites for EDMI calibration baselines ought to be much easier to find for a maximum interval of 800 ft. than for 1000m
But a longer distance is desirable.
The errors in EDM measurement are mostly a combination of:
-Prism constant.
-Tribrach leveling error affecting centering.
-Random centering error. Just be careful.
-Cyclic error in the EDM machinery.
-Instrument scale factor.
Test tribrachs first.
Test prism constant by AB+BC+error=AC on an uncalibrated straight line. Cyclic error could confuse this result, but can be avoided by making approximately AB=BC=N*10+2.5 meters (or other cycle length)
To detect cyclic error you need cal points that are not a multiple of the instrument period (typically 10 meters), or an alternative procedure as discussed below.
To detect scale error, you want a calibration line as long as practical in order to make scale factor the dominant error and wash out the others.
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Here's my alternative procedure for detecting cyclic error in an instrument with 10 meter cycle length. I haven't seen it published, but I did it and got apparently good results
Mark points separated by perhaps 100 meters. This needs to be a multiple of the cycle length, within a few cm to keep the cyclic error from canceling out between the two directions.
Mark at least 5 points near the middle of the line 1 meter (+/- a few cm) apart and on line. (10 points makes the result easier to understand but are unnecessary)
Place reflectors at both ends.
Set up the EDM on each of the intermediate points and do AB+BC+error=AC at each point. The plot of error versus position will form a half-cycle of a sinusoid if it is dominated by cyclic error. The amplitude of the sinusoid is twice the maximum cyclic error. I got a sinusoid, but was surprised that it wasn't the half cycle I predicted on the basis of light leakage between emitter and detector.
Cyclic error is probably largest for weak reflected signals, so you might want to tape a cover over a little more than half the prisms except for a small exit hole for the reflected light (light returns from the opposite side of the prism from where it entered).
I had a 831 ft leg of a traverse last week which is pretty rare.
What I use all depends on accessibility and mobilization and my comfort zone.
This was rolling pasture land (not maintained for the last 5 years) and I was fortunate to have 2 stations on rises in the terrain.
The I -guy did not mutter or grumble about any heat refraction issues.
Every job has it's own 'story' as far as GPS.
I have a backpack for the TS but not for the GPS.
I thought it was Mike P. posting below. oh well.
> Here's my alternative procedure for detecting cyclic error in an instrument with 10 meter cycle length. I haven't seen it published, but I did it and got apparently good results
>
> Mark points separated by perhaps 100 meters. This needs to be a multiple of the cycle length, within a few cm to keep the cyclic error from canceling out between the two directions.
>
> Mark at least 5 points near the middle of the line 1 meter (+/- a few cm) apart and on line. (10 points makes the result easier to understand but are unnecessary)
>
> Place reflectors at both ends.
>
> Set up the EDM on each of the intermediate points and do AB+BC+error=AC at each point. The plot of error versus position will form a half-cycle of a sinusoid if it is dominated by cyclic error.
I'm having a hard time seeing how that does anything other than cancel the cyclic errors. For example if the endpoints of the line are 100m apart and you set up a total station with an EDMI having a cyclic error that repeats every 10m, if you measure:
41m and 59m
42m and 58m
...
45m and 55m
then the cyclic errors ought to come close to cancelling if the form of the error function is approximately sinusoidal and has approximate nulls at 10m multiples.
For example, in that case, the cyclic errors in the 41m and 59m ranges should be approximately the same absolute value, but opposite in sign, so would not show up.
For the instrument I tested this with, I did find error at d=4 cycles (only 40 meters not 100) and the largest error was at x=15, 20, 25, and 30 (alternating signs) but maybe that isn't the general case.
I know there is a good test in this idea, but maybe I didn't get all the details yet.
If there IS cyclic error at 50 meters (or 20 in my test), you get the same error looking each way, so the total is off by twice the error. As you move away from that point, one distance getting longer and the other shorter, there will be places the error has opposite sign and cancels in the sum and other places that have double negative error.
You are right that if the error nulls at 50 meters , then it will cancel out of the sum for any other EDM points also.
In that case, it would take another test with total distance approximately 105 meters (for instance) to be sure you have checked for both sine and cosine components. The maximum cyclic error for the instrument would then be sqrt((E100/2)^2 + (E105/2)^2).
Math
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If error= e * sin(x+a) where x is distance from one reflector in cycle lengths, and a is an arbitrary offset in where the cycle starts, then the total error for a spacing of d cycle lengths is
E= e*sin(x+a) + e*sin(d-x+a) = 2e * sin(d/2 +a) * cos(d-2x)
This says that the maximum error is measured at x=d/2 but the spacing d that gives maximum error depends on that arbitrary constant 'a' that may depend on the instrument. Changing d by a half cycle will change it as sin((d+0.5)/2 + a) = cos(d/2+a) so you measure the other component.
So maybe the steps are:
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Set points at 0, 50, 52.5, 55, 57.5, 100, 105 meters in a straight line (add or subtract any multiple of cycle length as desired and adjust midpoints). A tolerance on distances of a few cm is acceptable.
Set reflectors at 0 and 100. Set the EDM at 50, take both distances, and add. Move EDM to 55 meters and repeat. The Sin component of the cyclic error is half the difference in the two totals.
Move one reflector to 105 meters. Set the EDM at 52.5 and find total distance. Move EDM to 57.5 and repeat. The Cos component of cyclic error is half the difference in these totals.
Combine errors as square root of sum of squares.
Bill, don't you think that a much more efficient scheme would be to set marks at increments covering the basic measuring unit of the EDMI (that used to be 10m for nearly all instruments in use) and then simply measure the distances between them with a tape?
That way, the cyclic correction can be evaluated at various ranges since you don't have to know the actual distances to the five or ten marks on the cyclic errors test baseline as long as you know quite accurately the distances between the five or ten marks themselves.
I will say, though, that about 20 years ago, when EDMI calibration was more critical for land surveying work than it is in the GPS era, the very best results I had were obtained on a baseline that had been standardized with an ultra-high-precision EDMI, an MA200 Tellurometer with a standard error of about +/-0.1mm. That baseline made it possible to evaluate all of the components of EDMI errors in one go: cyclic errors, additive constant, non-linear distance dependent correction, and scale errors.
> Kent here is Soz
>
> radu
Richard, in the era of GPS is EDMI calibration still getting as much attention in Australia? I may be dead wrong, but I would bet you that the entire impetus was from Professor J.M. Rueger at the University of NSW (not to be confused with the University Coeds who are NSFW). With GPS available to control scale and validate EDMI results, is there still a constituency for the expense and labor of maintaining the calibration lines?
kENT, I was always skeptical about the process and necessity. I went down the line of QA when it was a fad and sent the troupes out . Come to think about it I never recall seeing the error results. I could not reason how a Mr Leica would sell a dodgy instrument that you would see was in error when comparing a previously surveyed line. Seems to me the academics invented it in early days of EDM when you had cyclic error in tellurometers et al and boffins could not trust the physics. Given the accuracy required the rats prick differences the base line found you were still well with in tolerance for the boundary work.
Actually I was surveying in outback SA last few weeks which was surveyed and physically marked to excess by government surveyors , so much that the survey time is wasted looking for these old marks, but that is another story. Ie had coordinated control permanent marks every 150 or so metres, pegs marking corners and recovery marks offset from corners. Sad as when found offset marks had to make boundary adjustments.
Any rate the area is ideal for GPS so no matter what with adjusted network control nothing fits to the cm! So used a local base fixed from results of locating about 30 coordinated marks. Then localized each job wit small shift onto closet coordinated mark.
Any rate I digress thinking about rats prick differences resulting from base lione survey procedure and how GPS can pump out such a reliable bearing and distance , especially on long lines.
RADU
Your method of just taping out distances over one cycle is better IF your centering and taping are sufficiently accurate, which with care should be no problem.
The advantage of the method I was developing is that centering is not critical to measuring the cyclic error, and no distance measurements are needed other than with the instrument under test.
Tell me about the non-linear distance dependent correction, as that is something I'm not familiar with. Is it a basic physics thing (maybe related to refraction?) or a characteristic of certain measuring instruments?
>
> Tell me about the non-linear distance dependent correction, as that is something I'm not familiar with. Is it a basic physics thing (maybe related to refraction?) or a characteristic of certain measuring instruments?
The non-linear distance-dependent errors result from a variety of causes, but are generally most prominent at ranges below 100m. I have some examples that I'll post when I get a chance. J.M. Rüeger discusses them in detail in his "Electronic Distance Measurement", 3rd Ed., Springer-Verlag, 1990
> Any rate I digress thinking about rats prick differences resulting from base lione survey procedure and how GPS can pump out such a reliable bearing and distance , especially on long lines.
Yes, GPS "takes the worry out of being close", as the old advertising slogan went.
CLOSE TAKES THE WORRY ABOUT BEING MUM........
> CLOSE TAKES THE WORRY ABOUT BEING MUM........
I'm trying to think of whether I've ever seen condoms advertised on TV in the US.
Close was an under arm roll on deodorant here....
RADU
