NMD-30

Poisson counting noise

σ = √N, SNR = √N. Counting statistics of a nuclear measurement.

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CountingPoisson

Governing equation

\sigma=\sqrt N,\quad \mathrm{SNR}=\sqrt N

$N \in \left[10, 1\times 10^{7}\right]$

where

N: Counts (—)
\sigma: Std. deviation (—)
SNR: Counting SNR (—)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\sigma=\sqrt N,\quad \mathrm{SNR}=\sqrt N

$N \in \left[10, 1\times 10^{7}\right]$

$N = 10$ $\sigma = 3.162$

Along the curve

②

Domain of the variable — blue

N_{\min} = 10,\quad N_{\max} = 1\times 10^{7}

$N \in \left[10, 1\times 10^{7}\right]$

$N = 10$ $N = 10$

Along the curve

③

Response curve — green

\sigma=\sqrt N,\quad \mathrm{SNR}=\sqrt N

$N \in \left[10, 1\times 10^{7}\right]$

$N = 10$ $\sigma = 3.162$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\sigma}{\mathrm{d}N}

$N \in \left[10, 1\times 10^{7}\right]$

$N = 62903$ $\sigma^{\prime} = 0.003$

Along the curve

Lecture brief

Historical brief

MIRD schema, in-vivo decay, uptake fractions and PET coincidence turned unsealed sources into organ dose. The sheets compute activity, residence and well-counter geometry. This sheet (NMD-30 — Poisson counting noise) is the form associated with Poisson. Working symbols: $N$ $\rightarrow$ $\sigma$ , $SNR$ . Relative error 1/√N. A million counts give 0.1 %. Background adds in quadrature.

Purpose

Purpose: compute

\sigma

SNR

from

N

in Nuclear medicine via

\sigma=\sqrt N,\quad \mathrm{SNR}=\sqrt N

σ = √N, SNR = √N. Counting statistics of a nuclear measurement. Use it when a real nuclear medicine question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

N = 10000.000\,\mathrm{—}

, the governing relation

\sigma=\sqrt N,\quad \mathrm{SNR}=\sqrt N

yields

\sigma = 100.0\,\mathrm{—}

SNR = 100.00\,\mathrm{—}

. A count total and its error bar. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Counts N10000 —

Outputs

Std. deviation \sigma100.0 —
Counting SNR SNR100.00 —

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Narration of this film

A count total and its error bar.

Relative error 1/√N. A million counts give 0.1 %. Background adds in quadrature.

Reading speed

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