How do you make a 5" total station - and can you make it 1"?

Most of the modern TS have a setting to display to 00°00'01".

An instrument that is well cared for and well adjusted can pull that off, as you say, under ideal conditions.

That is the trick. IDEAL CONDITIONS does not mean consistently.

What it will do is to assure that you can use a TS to the best possible result with proper technique.

I have a sheet from TxDOT we were required to fill out by turning multiple sets for a project back in the 1980s to establish control on US59 from middle of Cass County to the north Harrison County line.

It was complicated proceedure involving over a dozen readings of forward and reverse and flop the scope that would produce the same results by using a 5sec gun or using a 1sec gun.

B-)

I am surprised at the regular pattern you are finding. Comments from instrument manufacturers would be interesting - and appreciated.

But making a 5 second gun a 1 second gun by multiple observations is nothing new. Multiple observations on different parts of the circle was SOP in the days of running control by NGS or even the higher quality private firms.

And taking it even further, the old procedure of "winding" angles with a transit was an attempt to get better angles than you read directly.

But the final observation would be that even a one second gun won't necessarily get you one second precision with a single reading. Thoroughly understanding your instrument, its limitations, and proper techniques of use is critical for any professional.

:good:

> And taking it even further, the old procedure of "winding" angles with a transit was an attempt to get better angles than you read directly.

Does this term refer to "doubling" angles with a two plate instrument? I.e. Measure, Lock the Upper plate, rotate lower plate; lock, measure, etc.?

> 0* 00' 00.4" = st.dev
>
> For the angle size tested, with the stud-turning procedure, reading both faces with this 5" instrument, it appears you can determine the true angle to within 1" under ideal conditions.
>
> Thoughts?

I think you've cracked the oyster. It only makes sense that Leica would use the identical circle thoughout its series of instruments by adding a noise pattern to the graduations that can be corrected through the instrument software.

While rotating the intrument in tribrach is an immediately practical solution, it would even be cuter to to figure out how to store the harmonic coefficients in the instrument's internal memory so that the onboard software that would correct all angles.

> I am surprised at the regular pattern you are finding. Comments from instrument manufacturers would be interesting - and appreciated.
>
> But making a 5 second gun a 1 second gun by multiple observations is nothing new.

What is extraordinary about Conrad's results, though, is that the circle graduation "errors" are regular and cancel, not by multiple observations, but by multiple observations with the circle rotated 120 degrees between sets. This is what swapping instrument lugs in the tribrach accomplishes. Simply turning the angle a zillion times without rotating the circle never cancels the periodic circle graducation errors.

Yes, but winding the angles could be 5, 10, 15 or more times. Kind of a crazy technique but sometimes you gotta do what you gotta do.

For their high accuracy instruments like the old TC2002, which was rated at 0.5" if memory serves me correctly, Leica had a machine that analyzed the circles and modeled any eccentricities; this data was then programmed into the instrument. This was an expensive and time consuming process that - at least back then - was not used on regular total stations. I toured the factory in 1998, so my memories are a little fuzzy, but I believe all of the 1100 series instruments were manufactured pretty much identically; it was the subsequent testing that determined which ones went out as 2", 3", or 5" guns; demand may also have played a part. I would imagine that this is still the case.

This may have been settled before, but it seems that the implication is a deliberate action taken to lower the quality of angular measure. Is this the case or is it a lack of a paid option to increase the quality of angular measure?

The former makes less sense to me (not saying I have a problem with it), because you would think the better business model would be to make them all 1" total stations and charge a little more than the 5" instrument (probably the best seller) and sell a lot more instruments because of more readily accessible quality in measure.

I can imagine a scenario where fabrication techniques would cause a similar regularity to the variances in readings. For instance, an orbital polisher operating on a jig in a pre-determined pattern.

there are several instances where the "complete" product is what is always manufactured and you have to pay to unlock options. GPS, software, ...

> This may have been settled before, but it seems that the implication is a deliberate action taken to lower the quality of angular measure. Is this the case or is it a lack of a paid option to increase the quality of angular measure?

> The former makes less sense to me (not saying I have a problem with it), because you would think the better business model would be to make them all 1" total stations and charge a little more than the 5" instrument (probably the best seller) and sell a lot more instruments because of more readily accessible quality in measure.

The same thing was done at one time with the EDMs in total stations by some manufacturers, i.e. taking the raw distance output by the EDM and applying various software corrections to it to remove various systematic errors.

The clever thing about selectively degrading the regularity of the circle graduations as Conrad reports is that you could, in theory, produce total stations with any standard error between the outside uncertainty of +/-5" s.e. and the inner limit, which may be below +/-1" s.e., just by changing the coefficients input into the instrument software to correct the main sine-wave pattern of error.

The report on his instrument that a Leica maintenance shop produced confirms that the instrument firmware has at least three different correction values, two sine-wave correction coefficients (which I'd suppose are one for each angle encoder), and one correction table that is probably a set of values for a lookup table of smaller, semi-random corrections.

Before I concluded that the pattern was intentional, I'd have to do a lot of trigonometry to see what the combined effects were of various imperfections in instrument assembly.
-eccentricity of the circle mounting
-radial positions of each of two sensors
-center of rotation of circle relative to the line between sensors

Even if each effect individually mostly cancels out, is there an interaction among the imperfections that produces higher harmonics such as Conrad illustrates?

Is there something about light scattering and the binary pattern that accounts for it? (This was alluded to in a prior thread.)

Does another instrument of the same model produce essentially the same pattern?

It is remarkable that two parameters (phase and amplitude of a sinusoid) can model this so well. Indeed, it would seem that the manufacturer can put the effort (expense) into calibration to obtain the better models.

> While rotating the intrument in tribrach is an immediately practical solution, it would even be cuter to to figure out how to store the harmonic coefficients in the instrument's internal memory so that the onboard software that would correct all angles.

It's highly unlikely that you could access that software (although I'm not sure I've ever seen ANY discussion, here or elsewhere, on what OS the instrument uses, whether the code is compiled, and if so, which compiler was used, etc.).

Far simpler than doing that, would be to build a correction algorithm, and apply it (in Starnet, Excel, or wherever), according to the absolute direction of each individual measurement.

I'm assuming Conrad has confirmed that the wave form IS absolute (and not random) with respect to a particular lug on the instrument.

Doing this would be doing what noise canceling headphones do.

> It's highly unlikely that you could access that software (although I'm not sure I've ever seen ANY discussion, here or elsewhere, on what OS the instrument uses, whether the code is compiled, and if so, which compiler was used, etc.).

Normally, I'd think that would be done via the total station keyboard. The user wouldn't be changing the software in the instrument, only storing the harmonic coefficients in registers that are already allocated.

> Is there something about light scattering and the binary pattern that accounts for it? (This was alluded to in a prior thread.)
>
> Does another instrument of the same model produce essentially the same pattern?
>
> It is remarkable that two parameters (phase and amplitude of a sinusoid) can model this so well. Indeed, it would seem that the manufacturer can put the effort (expense) into calibration to obtain the better models.

That's the beauty of having the circle errors built into the thing as manufactured. Only the very highest accuracy instruments would need to be calibrated on the super-duper Leica table in order to derive the very small random corrections to be pulled out of a correction table in the instrument's memory. The harmonic coefficients would already be known.

It may well be that the next step up from 5" in that series of Leica instruments is made by entering only the harmonic corrections for one angle encoder.

> Thoughts?

The other thought I have is to ask how closely the errors of angles measured with the sinusoidal distribution resemble a Gaussian distribution, i.e. whether the angle errors have a significantly different distribution that has some implications for rejection limits, etc.

> The other thought I have is to ask how closely the errors of angles measured with the sinusoidal distribution resemble a Gaussian distribution, i.e. whether the angle errors have a significantly different distribution that has some implications for rejection limits, etc.

The answer is that the two distributions are quite similar in form over the 3-sigma interval.

http://www.johndcook.com/blog/2010/04/29/simple-approximation-to-normal-distribution/

> An instrument that is well cared for and well adjusted can pull that off, as you say, under ideal conditions.

Hello A Harris,

I'm not sure I agree with, or understand exactly what you are saying. But this instrument didn't pull off anything when used normally. It produced a spread of about 14" when trying to read the one, exact, unchanging angle. It was only when I noted the pattern in my earlier testing that I as able to virtually eliminate the error by a pretty simple, stud-turning procedure.

> That is the trick. IDEAL CONDITIONS does not mean consistently.

Under anything but ideal conditions a 0.5" instrument will be something worse than a 0.5" instrument. Given the decadent image scintillation we experience here in the warmer months you would never get near 0.5" accuracy with the best total station with regular field procedures.

> What it will do is to assure that you can use a TS to the best possible result with proper technique.

My testing reveals that no 'normal' procedures will eliminate the errors in this instrument. You could sit there all day and take as may direct and reverse readings between stations and you will always have a 'dud' angle. I personally have never seen any published recommendation to change instrument stud positions when reading angles before, so it was, as far as I'm aware, a procedure I had to test to eliminate this particular pattern error in this instrument only.

Just taking multiple readings with this instrument will ensure you get the same answer every time. But by turning the studs and combining just 3 sets took this instrument from a published 5" to a 1" for these angles. Without turning the studs you could observe as many sets as you like but you're not going past the accuracy Leica appear to have built in to this instrument.

> I am surprised at the regular pattern you are finding. Comments from instrument manufacturers would be interesting - and appreciated.

Hello Dave,

Why surprise? How else to make a 5" instrument? The circle sorting story oft reported does not make any real sense to me. You can bet the leading (debatable?) manufacturer of the total stations can make 1" circles all day long without breaking a sweat. The procedures and machines involved in spitting out varying 1" - 10" circles at random would be intolerable to a precision manufacturer.

> But making a 5 second gun a 1 second gun by multiple observations is nothing new. Multiple observations on different parts of the circle was SOP in the days of running control by NGS or even the higher quality private firms.

What are the recommended procedures involved for total stations with fixed circles (non-repeating total stations)? I'm eager to integrate them into my own procedures. I'm also curious as to whether they'd work on my instrument with this pattern of errors.

> But the final observation would be that even a one second gun won't necessarily get you one second precision with a single reading. Thoroughly understanding your instrument, its limitations, and proper techniques of use is critical for any professional.

Agreed.

> > It's highly unlikely that you could access that software (although I'm not sure I've ever seen ANY discussion, here or elsewhere, on what OS the instrument uses, whether the code is compiled, and if so, which compiler was used, etc.).
>
> Normally, I'd think that would be done via the total station keyboard. The user wouldn't be changing the software in the instrument, only storing the harmonic coefficients in registers that are already allocated.

Hello Kent,

Sadly no such user-entered parameters exist. It's service only stuff.