According to a Leica rep. all of the instruments come off of the same assembly line, and then tested to see if they are a 1,3,5. He also stated that a 1 could be labeled as a 5 if they are needing 5's.
Jones, post: 374199, member: 10458 wrote: According to a Leica rep. all of the instruments come off of the same assembly line, and then tested to see if they are a 1,3,5. He also stated that a 1 could be labeled as a 5 if they are needing 5's.
What Conrad demonstrated by testing was that the real story for the Leica total stations is that the software installed in a particular instrument is what determines that precision of the angle readings. The circles and centers are nominally identical, so the software takes what is nominally a 1" total station (or better) and degrades the apparent accuracy of the angle readings by introducing modeled errors to the quantities output. The errors are generated by a relatively simple method, however, and so can be corrected once the parameters that describe the error function are characterized.
Kent McMillan, post: 374200, member: 3 wrote: What Conrad demonstrated by testing was that the real story for the Leica total stations is that the software installed in a particular instrument is what determines that precision of the angle readings. The circles and centers are nominally identical, so the software takes what is nominally a 1" total station (or better) and degrades the apparent accuracy of the angle readings by introducing modeled errors to the quantities output. The errors are generated by a relatively simple method, however, and so can be corrected once the parameters that describe the error function are characterized.
this idea was also supported in a post by surveythemark who stated they are mechanically built to the same spec, and it's the software that determines whether it is a 1", 2", 3" or 5" model.
rfc, post: 374096, member: 8882 wrote: Following the line Kris Morgan initiated, if you superimposed the two error eclipses, one of a 5" gun; the other of a 3" gun, like so:
If you take a greater number of observations with the 5" gun, wouldn't a percentage of them be within the error ellipse of the 3" gun? And if you took enough of them, wouldn't there then be a greater number from the 5" gun within the 3" ellipse than there would be from the 3" gun?
If so, wouldn't this support the "ayes" as opposed to the "nays"?
in my experience with the Leica 1200+ and TS15 series this diagram does not represent the reality of taking directions, if indeed it is what is intended to approximate. The PRECISION of our 5" instrument when taking directions from a stable setup is around 1". You don't get whacky random errors to the same target from a stable setup. That's why the problem is not one of purely of random numbers. It's a problem of procedure to beat the in-built 'errors', like wrapping the angles. And it is why, as I showed in a previous thread, I can wrap 3 arcs with my 5" instrument and instantly get 1" out of it. Which is quicker than expected according to the sqrt(n) rule, as it should be, because these aren't random errors.
Conrad, post: 374204, member: 6642 wrote: That's why the problem is not one of purely of random numbers. It's a problem of procedure to beat the in-built 'errors', like wrapping the angles. And it is why, as I showed in a previous thread, I can wrap 3 arcs with my 5" instrument and instantly get 1" out of it. Which is quicker than expected according to the sqrt(n) rule, as it should be, because these aren't random errors.
Conrad: Please allow me to interrupt this discussion (which has clearly gone "deep end"), for a grasshopperish question:
What, exactly, is "wrapping" angles as it pertains to an electronic directional total station? I know how to do it with a two plate repeating theodolite, but I thought none of that applied? Is it just using the "HSET" button, turning to the back sight, and allowing the instrument to add the angles? No difference there than doing the angle three times, and dividing by three. What am I missing?
We now return to your regularly scheduled program (which I'm really enjoying, by the way).:-)
rfc, post: 374211, member: 8882 wrote: Conrad: Please allow me to interrupt this discussion (which has clearly gone "deep end"), for a grasshopperish question:
What, exactly, is "wrapping" angles as it pertains to an electronic directional total station? I know how to do it with a two plate repeating theodolite, but I thought none of that applied? Is it just using the "HSET" button, turning to the back sight, and allowing the instrument to add the angles? No difference there than doing the angle three times, and dividing by three. What am I missing?
We now return to your regularly scheduled program (which I'm really enjoying, by the way).:-)
no worries rfc, ask away as it's your thread we are indulging ourselves in!
I was referring to changing the instrument position by lifting it and placing it down in the new stud position. nothing new - just the procedure as described in my instrument testing threads. Not technically wrapping the angle the same way as one would with a 2-plate instrument, but it achieves the same end for me. I could add the angles on the instrument with [hold] and [release] button procedure to make it look like a repeating theodolite if I wanted, but i'd rather feed the angles into whatever software i'm using and let it do the averaging.
the stud turning is a method to reduce the systematic influences on the Hz angles of our instruments. Sampling the instrument encoder at these 3 equally spaced points around the circle will have a positive influence on reducing the effect of any regular waveform error of a period that is not a multiple of 3.
Kent McMillan, post: 374194, member: 3 wrote: Yes, I agree. It makes more sense that the dithering of results would be via software, that the basic hardware of circle and circle reading system are quite similar between different models in the same line. I have a Sokkia CX-105 that might be interesting to test for the presence of a bounded periodic error similar to what you found in the Leica line.
The absolute encoders in your CX Series instrument and all Topcon and Sokkia instruments are 100% unique to our products and based on some incredible technology. We produce total stations that are accurate to 0.5 seconds and 0.5 mm (NET05AXII/ MS05AXII) and that same encoder and EDM technology is in your CX-105.
pmoran, post: 374240, member: 8922 wrote: The absolute encoders in your CX Series instrument and all Topcon and Sokkia instruments are 100% unique to our products and based on some incredible technology. We produce total stations that are accurate to 0.5 seconds and 0.5 mm (NET05AXII/ MS05AXII) and that same encoder and EDM technology is in your CX-105.
That would tend to confirm that there is a program within the software that adds errors to the circle readings to produce the lower precision specified for the instrument model. If so, those errors should be systematic and predictable.
Kent McMillan, post: 374255, member: 3 wrote: That would tend to confirm that there is a program within the software that adds errors to the circle readings to produce the lower precision specified for the instrument model. If so, those errors should be systematic and predictable.
Yeah I wouldn't go that far- the sharing of technology between instruments is not the same as they are all built the same. If you'd like to read a white paper on the technology of a .5" instrument- http://monitoring.topcon.co.jp/NET05AX_1AX_TF.pdf
Kent McMillan, post: 374255, member: 3 wrote: That would tend to confirm that there is a program within the software that adds errors to the circle readings to produce the lower precision specified for the instrument model. If so, those errors should be systematic and predictable.
Is the software used in these total stations based on open source code (like Linux?). Curious.
pmoran, post: 374264, member: 8922 wrote: Yeah I wouldn't go that far- the sharing of technology between instruments is not the same as they are all built the same. If you'd like to read a white paper on the technology of a .5" instrument- http://monitoring.topcon.co.jp/NET05AX_1AX_TF.pdf
What the brochure linked above describes is what could be essentially identical to the Leica method of producing instruments of varying precision from the same hardware. Per the brochure:
"1. Angle Measurement
Each NET AX instrument has a twin absolute rotary encoder capable of taking highly accurate angle measurements. The unit consists of:
- a glass dis on which a slit pattern is printed,
- an LED that illuminates the disc,
- and an image line sensor that detects the slit pattern.
The slit widths are arranged in a pattern that encodes the absolute angle; the angle can be measured simply by processing the signal from the sensor.
Original IACS (Independent Angle Calibration System) automatically generates an internal reference angle value that can be compared against the measured value to produce extremely high-precision angular measurements.
Specifically, the unit can deliver precision of 0.5" when measuring an angle of about a 0.5mm center diameter - the diameter of a typical mechanical pencil lead - from a distance of 200 meters."
The automatically-generated "reference angle" is most likely the software correction in the instrument. I had momentarily forgotten that the Leica system involved using a circle with a highly regular periodic graduation error (that repeated every 45å¡, if I recall) and that had the effect of introducing a predictable raw circle reading error at every absolute circle graduation. The errors exhibited a sinusoidal variation that could be modeled quite exactly by a Fourier function, which was evidently what the instrument software did to convert the raw circle reading to an output with a precision corresponding with that specified for the instrument model. That is, by tinkering with the Fourier components, once could reduce the raw circle reading error to zero or to some other other target multiple of the graduation error.
I'd wager that is exactly what the Topcon/Sokkia circle reading system does. It should be easy enough to test.
rfc, post: 374269, member: 8882 wrote: Is the software used in these total stations based on open source code (like Linux?). Curious.
Unlikely. The ability of the manufacturer to maintain the internal software settings either in their factory or service facilities is the essential proprietary ingredient of the product.
Moe Shetty, post: 373975, member: 138 wrote: Mathematically and statistically, yes, accumulating angles will get you better than a theodolite's least count. Accumulating angles was a technique for theodolites with upper and lower motions.
Bear in mind that there will likely be a point of diminishing returns; I doubt you could (reasonably) get one arc second results from a twenty second theodolite within a worthwhile amount of time.
I totally agree, and I think I said all that, but in different words. I especially agree about getting one second results. Very few instruments have optics that good. In fact the "diminishing returns" (looked at and analyzed statistically) is what tells you what you can get from the instrument.
Kris Morgan, post: 374011, member: 29 wrote: Yes to a point again. We didn't have dual compensator instruments until sometime in the late 90's. Not that they weren't available but that we didn't have them. With a single compensator gun, you need to flip the barrel to see the error in the plate as that axis was not compensated for.
With dual compensators, if everything is in adjustment, this is no longer necessary; however, we still flip the barrel because an instrument left to sit can and will go out of level and you won't know it unless you're instrument man is on his game, or you flip the barrel.
So long as the angles are encoded on a physical object, winding or wrapping angles works as described. Typically, this means it will work on any instrument that has a separate upper and lower motion (upper and lower locks and adjustments). For me, at first there was a metal ring (on american transits. Then it was optical theodolites, where the ring with the angles inscribed on it was glass. Later still, there were some instruments which used moire patterns, and then used some sort of bar codes or other encoding to allow the reading of an angle. One the "read" amount of angle was converted to a digital readout, it could also be rounded to the nearest whatever, so as to only produce the rated angle. But, the unread part of the angle was still on the "plate" whatever that was, and could be accumulated until it was readable, which is the whole point of wrapping angles.
BUT
There are instruments where there is no physical object that stays linked to the telescope when you turn back to re backsight. In those cases, wrapping angles gets you no benefit. All the digital total stations I ever used had separate upper and lower motions, and wrapping angles on those works very well to get angles that are at least twice as good as the least count, and you only need to wrap the angles four or five times (direct or direct and reversed depending on how good your controls needed to be). So, getting back to the original question, the answer would be YES you can get an instrument to give you better results than it's least count, at the cost of more time turning angles, with the caveat that the angle wrapping method needed to do that will not work with some single motion instruments. There is never any reason not to try out the procedure on your instrument, and determine statistically whether the improvement is worth the additional time spent at each setup. For me, it is.
Kent McMillan, post: 374270, member: 3 wrote: I had momentarily forgotten that the Leica system involved using a circle with a highly regular periodic graduation error (that repeated every 45å¡, if I recall) and that had the effect of introducing a predictable raw circle reading error at every absolute circle graduation.
Kent, as I mentioned unthread, I now believe (due to more looking since my testing ended) the circle is pure, and that the 'errors' are injected by software alone. Something like:
Hz(display)=Hz(pure)+sin(multiple*Hz(pure))*[amplitude]
Where [amplitude] is the desired spec.
I can imagine a few other ways manufacturers could degrade a perfectly good encoder system to produce a spec. One could be to turn off one sensor out of a diametric sensor pair. This could do it via circle eccentricity alone. You could also sample only a couple of slits of the encoder track which may give you the spec through noisier readings.
If anyone else was thinking of doing similar testing to mine I would add that I think what helped me have confidence in my testing when I was chasing the absolute error in my instruments was that I had established through earlier tests what the precision/repeatability of my observations were. So with an idea of how precise my observations were I could be sure that effects that appeared above that noise level were most likely real. Actually, the solid repeatability of my instruments when I knew that they turned 'bad' angles is what made me suppose that the 'errors' were not random but systematic, and hence, likely findable. If my early tests were like -/+5" of fuzz then I probably wouldn't have looked any further.
Conrad, post: 374350, member: 6642 wrote: Kent, as I mentioned unthread, I now believe (due to more looking since my testing ended) the circle is pure, and that the 'errors' are injected by software alone. Something like:
Hz(display)=Hz(pure)+sin(multiple*Hz(pure))*[amplitude]
Where [amplitude] is the desired spec.If anyone else was thinking of doing similar testing to mine I would add that I think what helped me have confidence in my testing when I was chasing the absolute error in my instruments was that I had established through earlier tests what the precision/repeatability of my observations were..
I was thinking about testing my Sokkia CX-105 to see whether it exhibits a similarly periodic pattern of errors that can be modeled, and am specifically thinking about the *EASIEST* way to to it. My first hypothesis would be that any error function that is used to dither the output from the circle reading would be a simple sin function similar in form to what you found for your Leica.
I suppose that the obvious first thing to determine is the apparent period of any bounded error. After that, I'd think a sparser target array could be used to estimate the error function, maybe twice the number of targets that are minimally necessary.
Kent McMillan, post: 374353, member: 3 wrote: I was thinking about testing my Sokkia CX-105 to see whether it exhibits a similarly periodic pattern of errors that can be modeled, and am specifically thinking about the *EASIEST* way to to it. My first hypothesis would be that any error function that is used to dither the output from the circle reading would be a simple sin function similar in form to what you found for your Leica.
I suppose that the obvious first thing to determine is the apparent period of any bounded error. After that, I'd think a sparser target array could be used to estimate the error function, maybe twice the number of targets that are minimally necessary.
My preference would be for a known angle(s) test. It's trivially easy to establish a known angle to less than a second with a good EDM. You can then sample the circle at regular intervals. Once you have a large enough sample of angles derived from the absolute directions that you record you could use the SOLVER function of excel to find a best fit to minimise the sum of squared residuals, or sum of absolute residuals. A sinusoidal error should yield to this analysis. If one became apparent then you can design a test to sample it precisely the same way you sample an EDM wave over its unit length. If the specification of the instrument comes about simply due to noise in the angle reading system then then it may be a good sqrt(n) type of instrument.
Conrad, post: 374355, member: 6642 wrote: My preference would be for a known angle(s) test. It's trivially easy to establish a known angle to less than a second with a good EDM. You can then sample the circle at regular intervals. Once you have a large enough sample of angles derived from the absolute directions that you record you could use the SOLVER function of excel to find a best fit to minimise the sum of squared residuals, or sum of absolute residuals. A sinusoidal error should yield to this analysis. If one became apparent then you can design a test to sample it precisely the same way you sample an EDM wave over its unit length. If the specification of the instrument comes about simply due to noise in the angle reading system then then it may be a good sqrt(n) type of instrument.
Hmm. Surveying the array geometry by trilateration means distances on the order of about 200m from instrument to target if the EDM has a standard error around 1mm. That would tend to mean 200m long lines of sight at tripod height above the ground, which would be a bit ugly in Central Texas daytime June conditions.
I thought that what was clever about your short-range test setup was that refraction was a negligible factor and I was inclined to use a somewhat similar scheme, possibly with a Lovar level rod oriented horizontally as the target array or just printed targets on an Invar band.
Kent McMillan, post: 374363, member: 3 wrote: Hmm. Surveying the array geometry by trilateration means distances on the order of about 200m from instrument to target if the EDM has a standard error around 1mm. That would tend to mean 200m long lines of sight at tripod height above the ground, which would be a bit ugly in Central Texas daytime June conditions.
I thought that what was clever about your short-range test setup was that refraction was a negligible factor and I was inclined to use a somewhat similar scheme, possibly with a Lovar level rod oriented horizontally as the target array or just printed targets on an Invar band.
I did encounter refraction on a couple of occasions indoors but it was easy to prevent the conditions again. Once over the hot bonnet of my just-driven car and another time sighting over a halogen lamp.
if you ever get around to it I'll be interested to see your write-up.
Kent McMillan, post: 374363, member: 3 wrote: Hmm. Surveying the array geometry by trilateration means distances on the order of about 200m from instrument to target if the EDM has a standard error around 1mm. That would tend to mean 200m long lines of sight at tripod height above the ground, which would be a bit ugly in Central Texas daytime June conditions.
I thought that what was clever about your short-range test setup was that refraction was a negligible factor and I was inclined to use a somewhat similar scheme, possibly with a Lovar level rod oriented horizontally as the target array or just printed targets on an Invar band.
For my tests, I have to use a subtense bar. I have 10 points set at 1' increments of subtended angle. And any accurate baseline distance is a known accurate subtended angle. If I had leveling rod, that would great. Hundreds of perfect targets with hundreds of high accuracy known angles.
