Laser tracker network uncertainty calculator

Place the tracker stations, enter your instrument specification, and see how well every target in your measurement volume is likely to be measured. It runs a Monte Carlo simulation in your browser, so nothing you enter is uploaded.

Your set-up

Measurement volume
Tracker stations
Number of stations
S1
S2
S3
S4

Station coordinates in metres (X, Y, Z). The volume sits between 0 and its length, width and height.

Instrument

The presets are illustrative class values, not any manufacturer's datasheet. For a better estimate, enter your instrument's MPE or the results of its interim test.

Environment and targets

Air figures are the uncertainty in your weather-sensor readings (1σ).

Part, datum and tolerance

Running…

A rough answer is free. A defensible one comes with evidence.

The calculator uses class-level figures and a simplified geometry, which is right for comparing layouts and spotting weak points. A number that goes into a quality record or a customer submission needs more behind it.

What this calculator gives you

  • A fast, indicative 3D uncertainty for every target in your volume
  • A ranking of the error sources, so you know what to fix first
  • A side-by-side feel for one, two, three or four stations
  • A quick check against the tolerance you need to verify

What a defensible report adds

  • Your instrument's real performance, taken from its calibration certificate or interim test, not a class figure
  • Line-of-sight checks against your actual part and fixture geometry
  • An uncertainty budget built from your shop-floor conditions, with the assumptions written down
  • A full non-linear network analysis, with the number of trials checked for convergence
  • A written budget in the GUM framework, with guidance on decision rules and guard bands
Send me your scenario

Ask for a defensible report

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How the calculator works

Each station measures every target within range as a range and two angles. Those measurements are combined in a network adjustment: station S1 defines the coordinate frame, and every other station is free to move and rotate (six degrees of freedom), so it has to be located by the targets it shares with the rest of the network. The calculator then repeats the whole measurement 2,000 times with random errors drawn from the figures you entered, and records how far each adjusted target lands from its true position. This is the same idea as the Monte Carlo method in JCGM 101 (Supplement 1 to the GUM).

Error sources included

  • Range and angular error, growing with distance as set by your specification. A specification quoted as a maximum permissible error is read as a 2σ bound unless you say otherwise.
  • Target centring, an error in where the sphere's centre sits, which does not average out with repeat readings.
  • Air compensation, a scale error common to each station, from the uncertainty in your temperature, pressure and humidity readings. The sensitivities used are about 0.93 ppm per °C, 0.27 ppm per hPa and 0.01 ppm per %RH.
  • Part thermal expansion, an optional scale error on the part about its centre, from the material's expansion coefficient and your part temperature uncertainty.

What it leaves out

  • Line of sight. Targets are assumed visible if they are within range, so no part or fixture blocks a beam.
  • Systematic errors inside the tracker, such as axis misalignments and encoder eccentricity, which the interim test is designed to find.
  • Air temperature gradients and turbulence, vibration, floor movement and drift between set-ups.
  • Target mount stability and operator effects.
  • Non-linear effects. The adjustment is linearised around the true geometry, which is accurate at the sizes involved. I checked it against an independent non-linear solver using range, azimuth and elevation measurements, and the results agreed to within about 2%.

Because of these limits, treat the output as indicative. It is good for comparing layouts and for seeing what matters, not for signing off a measurement. To check your own instrument, read the 2021 interim test explained.

References

  1. JCGM 100:2008. Evaluation of measurement data: Guide to the expression of uncertainty in measurement (GUM).
  2. JCGM 101:2008. Evaluation of measurement data: Supplement 1 to the GUM, propagation of distributions using a Monte Carlo method.
  3. ISO 10360-10:2021 and ASME B89.4.19-2021. Performance evaluation of laser trackers.
  4. ISO 14253-1. Decision rules for verifying conformity or non-conformity with specifications.