Radicane: Poisson Counting Statistics
Measurement, Noise & the Lab arc, page 132 of 193. Back to The Pixelated Physics Universe
Who they are
Radicane has one line, and says it often: “Half the error. four times the nights.”
Radicane is a character of the Measurement, Noise & the Lab arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
Poisson counting: σN = √N, so relative error is 1/√N. Halving the error takes four times the counts.
$$ \begin{gathered} \sigma_N = \sqrt{N} \\ \frac{\sigma_N}{N} = \frac{1}{\sqrt{N}} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $N$ | number of counts | — |
| $\sigma_N$ | standard deviation of the count | — |
Sources
- S.-D. Poisson, Recherches sur la probabilité des jugements (1837)
- JCGM 100:2008
Crossovers
Radicane meets Twissa & Hanbra (Hanbury Brown–Twiss Effect). Twissa and Hanbra find that thermal photons bunch. Radicane's √N rule holds only for independent Poisson arrivals; bunched light is noisier than Poisson, and that excess is what the HBT effect measures.
Radicane meets Quadrell (Error Propagation). Radicane's counting error is √N. Quadrell combines it with every other independent uncertainty by adding the squares.
Radicane meets Sensora (Berg–Purcell Limit). Sensora counts molecules arriving by diffusion. Radicane's √N statistics set the Berg–Purcell limit on how well a cell can know the concentration.
Wear the lore
Concept keywords: Poisson Counting Statistics, Radicane, Measurement, Noise & the Lab, physics lore, Pixelated Physics