# Precision

See also:

## Contents

## Precision in the context of manipulation with actuators

(**TODO:** elaborate)

## Precision in the context of measurements with sensors

**Precision:**

- The narrowness (linguistic use) or wideness (math use) of the random distribution in the (nowadays digital and discrete) measurement readout.

Usually expressed in standard deviation, FWHM or similar. - Not(!) the possibly present random distribution in the "real" value.

(Note the problem pf drawing the line betwene noise in the "real" value and noise in the measurement system!) - inverse of random measurement deviation
- The unit of precision (when used in the linguistic sense) is the inverse of the measurement quantity

("more precise" <=> higher value of inverse standard deviation) - Precision (of single measurements**) can never exceed (be finer than) resolution.

Precision sits on top of resolution!

**Resolution:**

- The size of the steps of the measurement readout (no further sub-steps).
- In case precision is far lower than resolution a one step difference is pretty meaningless.
- The unit of resolution is: readable steps per unit of measurement quantity
- Resolution is always higher than Precision (of single measurements**)

When precision closes in on resolution discretization error joins the party complicating things.

**Accuracy:** (trueness)

- how near the expectation value comes to a reference value ("true" value) - (a qualitative term?)
- inverse of the systematic measurement deviation

If accuracy is low highly precise measurements are consistently wrong.

An error that can be potentially compensated.

### Lowering bandwidth to increase resolution and precision

By taking many measurements and averaging them out precision can be improved**. Measuring this way takes more time so the maximum frequency of measurements (bandwidth) gets lower. This is why noise in measurement readouts falls/(rises) with falling/(rising) bandwidth.

In case of manual averaging over many sub measurements at some point
precision hits the resolution limit. Quite a bit before that happens one should start to store the averaged values with a higher resolution. While the new precision must still be higher than the new resolution (fundamental fact), the new higher precision (harbored in the new higher resolution) **can** exceed the old resolution.

**The continuum:**

Even a single measurement takes finite time. So it can be seen as an average
over many much shorter sub measurements with much lower precision each.
Higher bandwidth <=> more noise.

This is related to the Heisenberg uncertainty principle.

Note that in mechanical nanosystems at room temperature quantum "noise" can be significantly overpowered by thermal noise.

## External links

### Wikipedia

- en: Accuracy_and_precision =>
**validity**~ seldom: Exactness

(accuracy ~ seldom: correctness ~ ISO: trueness)

de: Richtigkeit & Präzision => Genauigkeit ~ selten:**Exaktheit**~ selten: Validität

(Richtigkeit ~ selten: Akkuratheit)

- Random and systematic errors:

Observational_error; Errors_and_residuals;

de: Zufällige Abweichung & Systematische_Abweichung => Messabweichung

- noise; standard deviation; bandwith

- Discretization_error
- Nyquist–Shannon sampling theorem Aliasing Anti-aliasing Spatial_anti-aliasing Moiré_pattern