> Also according to a Leica paper on prisms, at short ranges some of the EDM signal can be reflected off the front of the prism rather than making it to the back of the prism. For this reason the front of Leica's most accurate (and expensive) prism is cut at an angle to avoid direct reflection from the front of the glass. To be safe I would not measure from a position perfectly perpendicular to the prism surface.
I'd forgotten about the effect of front face reflections. rfc could either tilt the prism in the holder or mask off the prism, leaving only a small aperature of perhaps 1/2 in. dia. or less centered on the axis from the instrument to the cube corner of the prism.
> I would like the measured distances down the track, backwards and forwards from each end. To increase your precision you could do this by reading on the m side of the tape and the ft-in side, backwards and forwards and reporting both.
Will do.
> To be safe I would not measure from a position perfectly perpendicular to the prism surface.
This is simple. I can observe the EDM visible light in the prism from the TS. All I need to do is offset the TS from the axis of the beam until I no longer see the reflected light. We know that a 5 degree off angle prism face results in little error. More important, we're talking all relative observations here, so it doesn't matter as long as they're all the same.
Also, just to note: if SOME of my observations were off the face of the glass, and some not, we'd see 35mm or more of error. We don't, so it's somewhat not an issue. It is interesting to know this though, from the perspective of someone running a robot, at the prism, with uncertainties related to the angle of the prism to the robot. Never thought about that before.
> Also, just to note: if SOME of my observations were off the face of the glass, and some not, we'd see 35mm or more of error. We don't, so it's somewhat not an issue. It is interesting to know this though, from the perspective of someone running a robot, at the prism, with uncertainties related to the angle of the prism to the robot. Never thought about that before.
No I don't think you would. It's only a portion of the reflections that will be off the front of the glass, but the most part will be properly reflected. It would have the effect of degrading the accuracy and perhaps biasing it, but it won't be a massive gross error. Leica suggest up to 3mm error which is more than enough to turn your experiment to garbage.
To answer your question about how to calculate the errors from a series of EDM ranges on a rail with regular intervals spanning the basic measuring length, M, of an EDM, here's an example using the mean EDM ranges you posted in this thread for an instrument with a basic 5m measuring length:
[pre]
A B C D E
0 19.7343 0.0000 19.7334 +0.9mm
1 20.2342 0.5000 20.2334 +0.8
2 20.7344 1.0000 20.7334 +1.0
3 21.2336 1.5000 21.2334 +0.2
4 21.7333 2.0000 21.7334 -0.1
5 22.2330 2.5000 22.2334 -0.4
6 22.7333 3.0000 22.7334 -0.1
7 23.2330 3.5000 23.2334 -0.4
8 23.7319 4.0000 23.7334 -1.5
9 24.2329 4.5000 24.2334 -0.5
-----------------------------------
21.9834 2.2500 21.9834 0.0 Means of Columns
[/pre]
Column A is just the number of the station on the rail.
Column B contains the mean horizontal EDM ranges measured to the prism at each station on the rail.
Column C are the taped distances of the stations on rail from station 0. Note that in this example, since we don't yet have the full taping data to work these distance out from, I've just plugged in the target values that you were shooting for. The only reason I did this was to illustrate the calculation. When the actual taped distances are known, this calculation gets reworked using real data in this column.
Column D consists of the numbers in Column C added to: (Mean of Column B)-(Mean of Column C). Note that the mean of Column D is identical with the mean of Column B.
Column E consists of Column B - Column D. These are the apparent cyclical errors of the mean EDM ranges.
The next step is to work out the numerical function that represents this pattern of cyclical errors.
Of some interest might be a paper which tests the EDM ranges of a Leica TDA5000 or similar with a range of Leica corner cubes reflectors for industrial use. The results were to some prisms at short range the usually impressive EDM goes to hell because of the combination of small prism size and an EDM beam which is not emitted coaxially. The beam emerges from one side of the objective and does nasty things at short ranges. The fix is, I think, an aperture arrangement fitted over the objective lens at short ranges.
http://www.aps.anl.gov/News/Conferences/1997/iwaa/papers/gottwald.pdf . Aperture not discussed in paper.
Note also that the distances in Column C could as easily have been the distances taped from some arbitrary zero like the end of the rail as long as the values of taped distances increase along the rail moving away from the instrument. There's nothing magic about Station 0 having a tape reading of zero since what we're really interested in are the relative distances between stations on the rail.
> Of some interest might be a paper which tests the EDM ranges of a Leica TDA5000 or similar with a range of Leica corner cubes reflectors for industrial use. The results were to some prisms at short range the usually impressive EDM goes to hell because of the combination of small prism size and an EDM beam which is not emitted coaxially.
The particularly interesting feature was how the cyclic error dropped off in amplitude so abruptly between 0m and about 14m. My guess would be that comparing the cyclic error patterns at 20m and 100m would give a pretty good idea of how stable it is at even longer ranges (but that's a guess only), if possibly not at shorter ranges.
[pre]
A B C D E
0 19.7343 0.0000 19.7334 +0.9mm
1 20.2342 0.5000 20.2334 +0.8
2 20.7344 1.0000 20.7334 +1.0
3 21.2336 1.5000 21.2334 +0.2
4 21.7333 2.0000 21.7334 -0.1
5 22.2330 2.5000 22.2334 -0.4
6 22.7333 3.0000 22.7334 -0.1
7 23.2330 3.5000 23.2334 -0.4
8 23.7319 4.0000 23.7334 -1.5
9 24.2329 4.5000 24.2334 -0.5
-----------------------------------
21.9834 2.2500 21.9834 0.0 Means of Columns
[/pre]
So, so continue this calculation for the purposes of illustration, Column E above contains the apparent errors of the 10 EDM ranges of Column B.
The next step is to derive the analytic function that fits a sine curve to the pattern of errors in the expectation that since the pattern of errors will repeat every 5m (the basic measuring length of the EDM tested), the errors are somewhat predictable and can even be corrected.
[pre]
A B E F G H I
Error Corr. Rad. FcosG FsinG
0 19.7343 +0.9mm -0.9 24.80 +0.86 -0.30
1 20.2342 +0.8 -0.8 25.43 +0.78 +0.23
2 20.7344 +1.0 -1.0 26.06 +0.61 +0.81
3 21.2336 +0.2 -0.2 26.68 +0.00 +0.21
4 21.7333 -0.1 +0.1 27.31 +0.05 -0.07
5 22.2330 -0.4 +0.4 27.94 +0.37 -0.13
6 22.7333 -0.1 +0.1 28.57 +0.09 +0.03
7 23.2330 -0.4 +0.1 29.20 +0.24 +0.31
8 23.7319 -1.5 +1.5 29.82 +0.03 +1.49
9 24.2329 -0.5 +0.5 30.45 -0.28 +0.40
--------------
+0.274 +0.298 Sum
+0.55 +0.60 Sum x 2
Note that the values of Column E and Column F represent the apparent errors of the
measured ranges (Column E) and the corresponding corrections to the measured ranges
that would be necessary (Column F), both in millimeters.
The values in Column G represent the fraction of the cycle of the error pattern that
repeats every 5m, expressed as radians. One whole cycle of the error pattern is 2?
rad. = 360°.
The values in Column G are simply those of Column B x 2? / 5. The slope ranges are
divided by 5m to get the number of cycles and those are converted to radian measure
since ! cycle = 2? radians.
The values in Column H are those of Column F x cos Column G. Those in Column I are
Column F x sin Column G.
The quantities +0.55 and +0.60 that are twice the sums of the values in Columns H and
I, respectively are the coefficients that are then used to form the function that
describes the sinusoidal pattern of corrections that best fits the apparent errors
determined by the test
CyCorr = (0.55 x cos D) + (0.60 x sin D)
where CyCorr = correction in millimeters to measured range for cyclic error
D = MeasDist x 2?/M
MeasDist = Measured Slope Distance in meters
M = Basic measuring length in meters
[/pre]
So, in this example, what do the residuals look like when the modeled cyclic correction is applied to the measured ranges?
[pre]
Sta Corr(actual) Corr(model) Residual
0 0.00091 0.00032 0.00059
1 0.00081 0.00070 0.00011
2 0.00101 0.00081 0.00020
3 0.00021 0.00061 -0.00040
4 -0.00009 0.00018 -0.00027
5 -0.00039 -0.00032 -0.00007
6 -0.00009 -0.00070 0.00061
7 -0.00039 -0.00081 0.00042
8 -0.00149 -0.00061 -0.00088
9 -0.00049 -0.00018 -0.00031
Mean 0.0000 0.00000 0.00000
Std Err 0.00077 0.00048
[/pre]
The apparent cyclic errors were quite small to begin with. They had an apparent standard error of only 0.77mm before correction and after correction that dropped to an apparent standard error of 0.48mm. Probably the most useful result of the calculation is determining the distances at which the cyclic errors approach zero.
Da measurements along the rail.
Temperature was the same. Measured from both ends using both sides of the tape (to the nearest 32nd of an inch on the inch side. If the mark fell halfway between to mm lines, I called it 1/2 mm.
[pre]
Far End Near End
mm in mm in
425 16-3/4 6000 236-1/4
925 36-13/32 5500.5 216-9/16
1425 56-1/8 5000 196-7/8
1925 75-13/32 4500 177-3/16
2424 95-7/16 4010 157-1/2
2924 115-1/8 3501 137-13/16
3424 134-13/16 3001 118-1/8
2924 154-1/2 2501 98-7/16
4424 174-3/16 2010 78-3/4
4925 193-7/8 1501.5 59-3/32
5425 213-9/16 1000 39-3/8
5924 233-1/4 501 19-11/32
[/pre]
Wish I could get that "pre" thing to work with the formatting out of Excel. Oh well.
Which series of measurements increases in the direction going away from the instrument and which increases toward it? I want to be sure that I'm understanding "Far End" and "Near End" correctly.
> Which series of measurements increases in the direction going away from the instrument and which increases toward it? I want to be sure that I'm understanding "Far End" and "Near End" correctly.
Far end is measured from the end of the rail furthest from the instrument.
Near end is measured from the end of the rail closest from the instrument.
[pre]
Far End Near End
mm in mm in
425 16-3/4 6000 236-1/4
925 36-13/32 5500.5 216-9/16
1425 56-1/8 5000 196-7/8
1925 75-13/32 4500 177-3/16
2424 95-7/16 4010 157-1/2
2924 115-1/8 3501 137-13/16
3424 134-13/16 3001 118-1/8
2924 154-1/2 2501 98-7/16
4424 174-3/16 2010 78-3/4
4925 193-7/8 1501.5 59-3/32
5425 213-9/16 1000 39-3/8
5924 233-1/4 501 19-11/32
[/pre]
Which is actually the measurement?
> [pre]
> 2424 95-7/16 4010 157-1/2
> Which is actually the measurement?
I think that should be 4001, not 4010
Okay, before I spend much time generating a more complete answer, I wish that you would get out the magnififying glass and measure the rail again, estimating to the nearest 0.1 mm. There's no reason to spend time measuring in inches if it is only to the nearest 1/32 inch. Check your work by adding the measurements to the same graduation from both ends. If the sums of all aren't nominally the same (+/-1mm), identify the error.
For clarity, number the rail stations 0 - 9, with 0 the station nearest the instrument.
The preliminary answer is that your EDM has a cyclic error that is corrected by the following function as a first-order harmonic (sine curve with period 5m)
CyCorr = (0.87 x cos D) + (0.32 x sin D)
where CyCorr = correction in millimeters to measured range for cyclic error
D = MeasDist x 2?/M
MeasDist = Measured Slope Distance in meters
M = Basic measuring length in meters
> I wish that you would get out the magnififying glass and measure the rail again, estimating to the nearest 0.1 mm. There's no reason to spend time measuring in inches if it is only to the nearest 1/32 inch. Check your work by adding the measurements to the same graduation from both ends. If the sums of all aren't nominally the same (+/-1mm), identify the error.
I think Conrad made that suggestion. I'll get out the magnifying glass, but I'm going to have to get a different tape as well. There's NO way to get to .1mm with this tape. The lines themselves are almost .2mm wide (around .177mm).
Wouldn't it be easier to run the test again (albeit with a different, more positive method of positioning the prism), but do it first from one end, the reverse the beam and do it again, zeroing out any errors due to the beam marks being slightly out of position?
> > I wish that you would get out the magnififying glass and measure the rail again, estimating to the nearest 0.1 mm. There's no reason to spend time measuring in inches if it is only to the nearest 1/32 inch. Check your work by adding the measurements to the same graduation from both ends. If the sums of all aren't nominally the same (+/-1mm), identify the error.
>
> I think Conrad made that suggestion. I'll get out the magnifying glass, but I'm going to have to get a different tape as well. There's NO way to get to .1mm with this tape. The lines themselves are almost .2mm wide (around .177mm).
The key word was "estimate". You ought to be able to easily estimate the distance from the center of the graduation to the scribe +/-0.15mm. You just look at the two graduations and determine whether the scribe is
[pre]
- exactly on one or the other 0.0mm
- exactly between them 0.5mm
- at edge of graduation 0.1mm 0.9mm
- 1/2 graduation from edge 0.2mm 0.8mm
- graduation from edge 0.3mm 0.7mm
- more than graduation from
edge, not centered 0.4mm 0.6mm
[/pre]
If you have a rigid rule graduated to fractions of a mm, you can verify what the different fractional intervals look like on the tape under magification or you can just look at the tape at close range with your total station, stepping it at 1/10 the angle between millimeter graduations.
> Wouldn't it be easier to run the test again (albeit with a different, more positive method of positioning the prism), but do it first from one end, the reverse the beam and do it again, zeroing out any errors due to the beam marks being slightly out of position?
No, that wouldn't get you there since you don't know the magnitude of the cyclic errors until you determine the true distances between the stations on the rail.
One other important thing that Conrad may have mentioned that I'll underscore is that it would be best to tape to the point on the scribe that falls below the axis of the prism. In top view, that is the intersection of the scribe and a line parallel with the rail drawn though the center of the prism. It would, I take it, be approximately along the midline of the rail.
Plan B!
> If you have a rigid rule graduated to fractions of a mm, you can verify what the different fractional intervals look like on the tape under magification or you can just look at the tape at close range with your total station, stepping it at 1/10 the angle between millimeter graduations.
New Plan. Rather than trying any number of machinations to measure, why not use something that's already measured. My first thought was a perforated stainless steel belt that's used on printers...they're often metric pitch and very, very precisely punched. As long as a length was stretched so that 500 holes measured exactly 5000 mm, I'd know with a great deal of certainty that each of the 10 holes would be in the right place.
I don't have any of that laying around, but I happen to have a bunch of this:
The pitch is exactly 5 mm. Every 100 teeth are .5 m apart. I can lay two pieces of this out, side by side, confirm the total distance (5 m), and have a an instantly calibrated track.
What's more, I can mount two pieces on the underside of my prism bracket and have a built in absolute detent, to locate the prism.
ps: ignore the rust please.
Good thing I'm not taking this up for a living; I'd be broke before I started.:-O
Plan B!
>
>
> The pitch is exactly 5 mm. Every 100 teeth are .5 m apart. I can lay two pieces of this out, side by side, confirm the total distance (5 m), and have a an instantly calibrated track.
Well, you can try it and we'll see what the results look like, but you'd still have the calibration problem for the track, I'd think.
Personally, I'd rather have a rail with mechanical stops on it (such as holes) that a part (such as a pin) on the prism fixture fit into to fix the prism station mechanically, something that could be measured with a tape as well as the tape can be read, which should be about 0.1mm over 5m.
Plan B!
One other preliminary result from analysis of the data posted so far is that it looks as if the cyclic error on your instrument may be very nearly 0.0mm at distances of
24.0m +/- A x 2.5m
Where A is an integer.
In other words, the EDM is returning a range with a cyclic error of 0.0mm at 24.0m and would be expected to do the same every 2.5m step away from 24.0m, i.e. at 26.5m, 29.0m, and so on.
