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Hello Gents,
Previous threads on EDM testing inspired me to do some testing of my own on our Leica R400 TCRP1205+.
The EDM is specced to 1mm+1.5ppm by the manufacturer, and experience with these instruments has led me to believe they are at least that precise. Before I started testing I frankly thought I would be hard pressed to see any pattern at all; just noise.
My recent testing of the angular accuracy of this instrument has led me to understand well how to detect cyclic errors once you know the frequency you are testing for. By brute force (way overdetermined least squares) I determined the frequency of the angular error and was then able to test it precisely. Luckily EDM cyclic errors are better known so I was able to immediately test for the known cyclic wavelength: 1.5m in the case of this instrument.
The procedure was fiendishly simple and precise. I got a piece of wood (thermally stable) the same length as the cyclic wavelength (1.5m) and made a series of small marks with the tip of the mini prism I would be using along its length (no centring errors). The marks were spaced so that the sum of residuals should be zero along it's length. 5 Distances were taken to each of the 9 marks to a steadied mini prism. The board was advanced 1/3 of the cyclic wavelength, distances recorded to the 9 targets again, and the board was advanced another 1/3 wavelength. The instrument was roughly the same level as the board, looking lengthwise down the board, and the board was moved away from the instrument.
The procedure should produce a precise result because it is perfectly suited to detecting a cyclic error. This is for 2 reasons. Firstly, the spacing of the marks on the board means the average of the 9 distances along the board in the first 1/3 wavelength position will be directly comparable to the average of the distances at the other 2, 1/3 wavelength positions. The distances can be reduced to a common zero position. Now secondly, the residual differences in individual distances to each of the average prism positions (1-9) should be now only due to the remaining cyclic error. This residual from the average of the 3 positions to each target sums to zero as does any 3 equally spaced radial vectors around a circle.
The other advantage of this method is it dispenses with the need for clumsy comparison with another (potentially inaccurate) length standard. Calibrated tapes, slides, tension, magnification, etc. all are potential sources of error. I should note this EDM compares with a certified baseline to around the 0.1mm and 1ppm level at 1-sigma.
I initially only did 1 wavelength and the results looked like a wave, but to be sure it wasn't lucky noise I did it a second time over the next wavelength. Graphically it looks like this:
The standard deviation of each group of 5 distances to each target did not exceed 0.2mm; the EDM is immensely precise. The software Leica makes available to export observations allows for the 5 decimal places that I wanted for the distances. The procedure was not as controlled as I could have made it, though the results suggest I will be wasting my time chasing improvements. I processed the data as 2 groups of 3 and 1 group of 6. I presented the results from the 2 groups of 3 as I don't think I controlled the alignment of the board well enough, and the instrument was moved between the 2 sets.
The wave I visually fit to the data has an amplitude of 0.2mm. The standard deviation of the raw residuals is 0.14mm and the deviation after fitting is a ridiculous 0.07mm! This was just a visual fit. The deviations without fitting are so small anyway I couldn't be bothered with a best-fit as we are waaaaaay below the accuracy requirements of anything I do even with the uncorrected EDM results. This is in contrast with the angular post processing which I am now doing and making real-world differences.
It looks like the EDM in Leica's 1200+ series of instruments contains measurable cyclic effects which can be modelled. The EDM system in the 1200+ series instruments appears to be a fantastically precise (and accurate) system which, even uncorrected, would hold it's own in some industrial applications.
Comments welcomed.
Posted : April 11, 2015 6:27 am
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Beautiful work again Conrad.
Posted : April 11, 2015 7:11 am
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Thanks for the kind words Shawn.
Posted : April 11, 2015 7:16 am
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> The procedure was fiendishly simple and precise. I got a piece of wood (thermally stable) the same length as the cyclic wavelength (1.5m) and made a series of small marks with the tip of the mini prism I would be using along its length (no centring errors). The marks were spaced so that the sum of residuals should be zero along it's length. 5 Distances were taken to each of the 9 marks to a steadied mini prism. The board was advanced 1/3 of the cyclic wavelength, distances recorded to the 9 targets again, and the board was advanced another 1/3 wavelength. The instrument was roughly the same level as the board, looking lengthwise down the board, and the board was moved away from the instrument.
> Comments welcomed.
I'd say that is a very clever approach, although if it were used on an EDM that makes software corrections for the cyclic error, I think it's worth noting that the software corrections would need to be turned off before testing.
One handicap to testing the cyclic errors of EDMs seems to be that not all of the manufacturers are very forthcoming about the modulation frequencies they use. I wonder if you have any thoughts about determining those or, even more specifically, the basic measuring length of the EDM or wavelength of the cyclic error.
Posted : April 11, 2015 8:47 am
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> The procedure was fiendishly simple and precise. I got a piece of wood (thermally stable) the same length as the cyclic wavelength (1.5m) and made a series of small marks with the tip of the mini prism I would be using along its length (no centring errors). The marks were spaced so that the sum of residuals should be zero along it's length. 5 Distances were taken to each of the 9 marks to a steadied mini prism. The board was advanced 1/3 of the cyclic wavelength, distances recorded to the 9 targets again, and the board was advanced another 1/3 wavelength. The instrument was roughly the same level as the board, looking lengthwise down the board, and the board was moved away from the instrument.
> Comments welcomed.
Totally impressive work and results.
How far away from the total station was the board, either at it's closest or most distant set? Did you do it indoors?
Posted : April 11, 2015 3:00 pm
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Hello Kent,
>...if it were used on an EDM that makes software corrections for the cyclic error, I think it's worth noting that the software corrections would need to be turned off before testing.
Yes of course. No such option is available to the user on the 1200+ instruments though, and the spectre of software correction threatened a nonsense result. The possibility of a software correction still exists and this test would then be revealing the remaining, un-modelled amount.
> One handicap to testing the cyclic errors of EDMs seems to be that not all of the manufacturers are very forthcoming about the modulation frequencies they use. I wonder if you have any thoughts about determining those or, even more specifically, the basic measuring length of the EDM or wavelength of the cyclic error.
No, I haven't thought about it. But the Leica 1200+ user manual offers the following specs for the prism measuring mode:
Max power: 0.33 mW
Pulse duration: 800 ps
Pulse repetition frequency: 100 MHz - 150 MHz
Wavelength: 650 nm - 690 nm
Is the info you seek contained within these numbers?
Posted : April 11, 2015 5:46 pm
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Hello rfc,
> How far away from the total station was the board, either at it's closest or most distant set? Did you do it indoors?
The shortest distance measured was 2m and the farthest 5m. All done inside the 'Conrad indoor precision calibration laboratory (garage)'!
Posted : April 11, 2015 5:50 pm
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> No, I haven't thought about it. But the Leica 1200+ user manual offers the following specs for the prism measuring mode:
>
> Max power: 0.33 mW
> Pulse duration: 800 ps
> Pulse repetition frequency: 100 MHz - 150 MHz
> Wavelength: 650 nm - 690 nm
>
> Is the info you seek contained within these numbers?
Hmmm. I've taken a quick look at the 3rd Ed. of Rueger. A pulse with a duration of 800 picoseconds would be roughly 0.24m long in vacuo and a modulation frequency of an infrared carrier in the range quoted 150 MHz would give wavelength of the modulated signal on the order of about 1m. I suspect that if I worked out the group phase velocity of the carrier of your EDM, it would get closer to 1.5m
Posted : April 11, 2015 6:36 pm