fullseye has ops that measure (measure3d / math_metrology / measure1d / contour). But whether the measured values can be said to mean anything is decided outside the ops. This document is not a description of ops; it is teaching material on the conventions needed when reporting dimensions as numbers — terminology, calibration, how to build up uncertainty. The authoritative source for the definitions of terms is the VIM (JCGM 200:2012), and for the evaluation of uncertainty the GUM (JCGM 100:2008).
VIM definitions (with clause numbers; the original is an English–French bilingual text):
| Term | VIM | Definition (gist) |
| --- | --- | --- |
| Accuracy (measurement accuracy) | 2.13 | Closeness of agreement between a measured value and the true value. NOTE 1: this is not a quantity and is not expressed numerically |
| Trueness (measurement trueness) | 2.14 | Closeness of agreement between the average of an infinite number of replicate measured values and a reference value. Inversely related to systematic error, unrelated to random error |
| Precision (measurement precision) | 2.15 | Closeness of agreement between measured values obtained by replicate measurements under specified conditions. Expressed numerically by standard deviation, variance or coefficient of variation |
| Error | 2.16 | Measured value − reference value |
| Systematic error | 2.17 | The component that remains constant or varies predictably in replicate measurements |
| Random error | 2.19 | The component that varies unpredictably in replicate measurements |
| Repeatability condition | 2.20 | Repetition with the same procedure, same operators, same measuring system, same conditions, same location, over a short period |
| Reproducibility condition | 2.24 | Repetition under conditions where location, operators and measuring systems differ |
| Uncertainty | 2.26 | A non-negative parameter characterising the dispersion of the values attributed to a measurand |
| Calibration | 2.39 | An operation in 2 steps (§2) |
| Metrological traceability | 2.41 | The property of being related to a reference through a documented unbroken chain of calibrations |
VIM 2.13 NOTE 2 drives the point home by name — do not use "accuracy" to mean trueness, and do not use "precision" to mean accuracy.
Where this matters in practice:
> A sensor catalogue says "repeatability 0.4 µm". This is precision (2.15), neither accuracy nor trueness. That the same value comes out repeatedly and that the value is correct are > unrelated. If you claim absolute dimensions, you separately need trueness and its basis (calibration).
(The same story is in 3d/guides/depth_sensors.md §2.2–2.3. Some manufacturers state trueness, and some state only precision.)
• Type A — evaluated from the statistical distribution of a series of measurements (characterised by a standard deviation).
• Type B — evaluated from a probability density function based on experience or other information.
Both are put on the same footing (standard uncertainty) before being combined. Expanded uncertainty is the combined standard uncertainty multiplied by a factor greater than 1 (the coverage factor k); k is determined by the probability distribution of the output quantity and the chosen coverage probability. By custom k = 2 (about 95%) is common, but an expanded uncertainty that does not state k has no definite meaning.
VIM 2.39 states explicitly that there are 2 steps:
1. Establish a relation between the quantity values provided by measurement standards (with uncertainties) and the corresponding indications (with uncertainties).
2. Use that information to establish a relation for obtaining a measurement result from an indication.
In other words —
> "Calibrated" = the deviation is known, not that it has been fixed. The measured values change only once you go as far as step 2 (applying the correction).
And a calibration certificate always carries an uncertainty. That uncertainty is added to the uncertainty of your own measurement (VIM 2.41: "each link in the chain contributes to the uncertainty"). In principle you cannot achieve an uncertainty better than that of the standard.
The terms that actually pile up to report 1 dimension:
| Type | Term | Notes |
| --- | --- | --- |
| Type A | Dispersion of repeated imaging of the same part in the same field of view | Measure this first. 10 repetitions are often not enough |
| Type A | Dispersion when the workpiece is re-placed | Measure separately from the above. This is often dominant |
| Type B | Uncertainty on the calibration certificate of the calibration target | Upstream in the chain |
| Type B | Pixel quantisation (resolution / √12 is the standard deviation of a uniform distribution) | A lower bound, not actual capability |
| Type B | Residual of lens distortion | Estimate from the reprojection residuals after calibration |
| Type B | Temperature drift | Measure the difference before and after warm-up. Metals are on the order of 10⁻⁵/K |
| Type B | Illumination variation and edge bias | ★ Specific to image-based measurement and among the largest |
★ In image-based measurement, illumination is among the largest sources of uncertainty, yet the discussion often stops at mechanics and optics. When the illumination changes, the apparent position of an edge moves — with a threshold method by the position of the threshold, and even with sub-pixel methods through asymmetry of the intensity gradient. Measuring the same part with only the illumination changed, and seeing whether the value moves, is the quickest check.
• Even if 1 pixel = 10 µm, that does not mean you can measure to 10 µm. If the edge contrast is high, sub-pixel methods can sometimes reach 1/10, and if it is low, the dispersion can be 1 pixel or more. Pixel size is a guide to resolution, not precision.
• Conversely, do not confuse the number of displayed digits with precision. A display in 0.001 mm does not mean an accuracy of 0.001 mm.
• The diffraction limit (Airy radius) and pixel limit returned by optical_budget are upper limits beyond which things cannot be separated, not achieved values.
A method that splits the dispersion of measurement into repeatability (same person, same machine = the conditions of VIM 2.20) and reproducibility (person and machine change = the conditions of VIM 2.24), decomposing it into variances.
By custom, %GRR relative to the tolerance is judged as < 10% acceptable / 10–30% conditional / > 30% unacceptable (this is AIAG MSA custom; no international standard sets these thresholds).
In image-based measurement there tends to be an assumption that there is no "person", but in reality the human contribution remains:
how the workpiece is placed, adjustment of illumination angle and intensity, setting of thresholds and parameters — these are the "operator" variance. Even on automatic machines it enters at every changeover.
| Target | Strength | Trap |
| --- | --- | --- |
| Checkerboard | Good corner localisation. Effective for estimating distortion | Distortion is not determined unless the corners at the edges are included. Flatness is required |
| Circle grid | Centroids are obtained stably | Under projection, "the centroid of the circle" and "the centre of the circle" diverge (a systematic error under perspective projection). Matters unless telecentric |
| Rings / concentric circles | Strong centre estimation | The same divergence as above remains |
• With a planar target in 1 pose, focal length and distance are degenerate. Vary the pose and take several images.
• The target itself needs a calibration certificate for flatness and scale (the chain in §2). A printed checkerboard is not a calibrated artefact.
| Element | What exists now | What is missing |
| --- | --- | --- |
| Measuring | measure3d / math_metrology / measure1d / contour | Does not return uncertainty (returns values only) |
| Upper limit of resolution | optical_budget (Airy radius, pixel limit) | Usable as one Type B term |
| Calibration targets | None | Generation of checkerboards / circle grids (should be possible with ground truth via optscene) |
| Uncertainty budget | None | An op that builds up Type A / Type B and outputs expanded uncertainty |
| Gage R&R | None | An op for variance decomposition |
If building something next: the sound approach is to generate calibration targets with ground truth in optscene and make it possible to run the closed loop calibration → correction → residual. With synthesis the ground truth is known, so the trueness of the calibration procedure itself can be verified (which cannot be done on real equipment).
| Symptom | Suspect first | How to check |
| --- | --- | --- |
| The value moves every time even for the same part | A precision problem (Type A) | Shoot 30 times without re-placing and compute σ. Then re-place and shoot 30 times. Compare them separately |
| The value is stable but does not agree with other instruments | A trueness problem (systematic error) | Measure a calibrated gauge. If the difference is constant, a correction removes it |
| Values differ between morning and afternoon | Temperature drift | Measure with different warm-up times. Record the equipment and room temperatures |
| The dimension changed after adjusting the illumination | Edge bias | Vary only the illumination, measure how much the value changes, and enter it as Type B in the budget |
| Dimensions disagree only at the edges of the field | Distortion residual / edge points not included during calibration | Plot the reprojection residuals by image position |
| Circle centres shift slightly outward | Centroid shift of circles under perspective projection | Shoot telecentric, or estimate the centre from the circle's contour |
| The display is in 0.1 µm steps but it does not reproduce | Confusing displayed digits with precision | Rewrite with resolution, precision and accuracy stated separately |
| Gage R&R is poor even on an automatic machine | Human contribution from changeover, placement and parameter settings | Repeat with different operators and separate out the reproducibility component |
• JCGM 200:2012 *International vocabulary of metrology (VIM), 3rd edition* — 2.13 accuracy / 2.14 trueness / 2.15 precision / 2.16 error / 2.17 systematic / 2.19 random / 2.20 repeatability condition / 2.24 reproducibility condition / 2.26 uncertainty (NOTEs on Type A and Type B) / expanded uncertainty and coverage factor / 2.39 calibration (2 steps) / 2.41 metrological traceability —
<https://www.bipm.org/documents/20126/2071204/JCGM_200_2012.pdf>
• JCGM 100:2008 *Evaluation of measurement data — Guide to the expression of uncertainty in measurement (GUM)* —
<https://www.bipm.org/documents/20126/2071204/JCGM_100_2008_E.pdf>