Measurement resolution and accuracy
Resolution is the smallest change that produces a perceptible change in an instrument’s measurement. It is easy to treat as a minor spec, and it has a failure mode that is anything but. If you take time measurements from a wall clock showing only hours and minutes, you will never resolve seconds.
Imagine the same set of measurements taken on four different grids, dividing the measurement range very finely or very coarsely. The grid represents the resolution of the measurement, likely limited by the resolution of the instrument making it. There is no interpolation within a cell — the grid’s marks are the units of measurement, and every reading has to land on one.
If the left panel above showed repeated measurements of the position of a fixed antenna, the fine (high-resolution) grid would clearly show our position measurement wandering. Knowing that our antenna is fixed, we can conclude that our measurements have resolution beyond their precision. Even though the data is noisy, this is not a bad place to be.
The coarse (low-resolution) grid panel on the right with only a single data point leaves a critical question. Do we have highly repeatable measurements all landing on the same value due to the high precision of our measurements? Or do we have low-precision measurements that only appear highly repeatable due to the low resolution of our measurements?
Being able to see noise in your measurements is comforting, and it is worth being exact about what it does and does not tell you.
Seeing noise means your resolution is at least as good as your precision. The grid is fine enough to reveal scatter, so nothing is being hidden from you by the reporting alone.
That is all it means. In particular it says nothing about whose noise you are looking at, and the two extremes are both entirely consistent with the same picture:
- The thing you are measuring could be perfectly steady, and every bit of the scatter your own measurement noise — a bolted-down antenna read by a noisy receiver.
- Or the instrument could be essentially noise-free and every bit of the scatter a real variation in the thing you are measuring.
Observed scatter is the variation in what you are measuring plus the noise in how you measure it, added together — and one set of readings cannot separate them. Splitting them needs something from outside the measurement — which is exactly what the fixed-antenna example above supplies. Knowing the antenna cannot move is what licenses attributing the wander to the measurement; without that knowledge the same picture would have been equally good evidence of a moving antenna.
What matters here is the other direction. The moment the noise disappears, even that modest guarantee goes with it. A single repeated value is consistent with genuinely excellent precision and with a grid too coarse to show scatter that is still there, and now you cannot tell which — the instrument has stopped being able to warn you, and it will go on returning that clean, confident number indefinitely.
So visible noise is not a defect to engineer away. It is the instrument declining to flatter itself.
Coarse resolution does not merely limit precision — it counterfeits it. A counter ticking every 10 ns, watching a source that jitters by 1 ns, is perfectly repeatable and tells you nothing at all. Repeatability that comes from an inability to see is indistinguishable, from the outside, from repeatability that comes from a good oscillator.
Which gives the three terms their natural order:
Resolution bounds what you can see. Precision is what you see once resolution stops hiding it. Trueness is what no amount of seeing will reveal.
See also: contrasting accuracy and precision.