02 Imaging

CT noise scaling

Pixel noise scales as 1/√(mAs · slice · dose).

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Simulation

CT noise scaling — Change the numbers; the scene follows.

Where it works

Radiography room

Bucky / detector

In the Bucky / detector: grid, AEC, DQE, and the pixel that samples the image.

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Formula

\frac{\sigma_2}{\sigma_1}=\sqrt{\frac{mAs_1\cdot h_1}{mAs_2\cdot h_2}}

Variables

σ₁ · Original noiseHUmAs₁ · Original mAsmAsh₁ · Original slicemmmAs₂ · New mAsmAsh₂ · New slicemm

Results

σ₂
New noise
16.9706HU
σ₂/σ₁
Ratio
1.4142

Curve

Explanation

\frac{\sigma_2}{\sigma_1}=\sqrt{\frac{mAs_1\cdot h_1}{mAs_2\cdot h_2}}

What it means

In quantum-limited CT, pixel noise σ scales as 1/√(dose × slice thickness × pixel area). Halving mAs multiplies noise by √2 ≈ 1.41. Thinner slices look noisier at the same mAs. This is a working relation in Diagnostic imaging.

Where it is used

Clinically it sits on the Radiography room — Bucky / detector. In the Bucky / detector: grid, AEC, DQE, and the pixel that samples the image. Diagnostic equations live on the tube, the detector, and the patient: magnification, air kerma, CTDI, and why bone lights up at 70 kV. They turn a technique chart into physics you can defend.

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How to use it

Use it to predict the noise cost of a low-dose or thin-slice protocol. Iterative reconstruction breaks the simple 1/√N rule — treat the result as an upper bound. Change one input and watch the curve and the simulation follow.

Symbols

σ₁Original noise12 HU
mAs₁Original mAs200 mAs
h₁Original slice5 mm
mAs₂New mAs100 mAs
h₂New slice5 mm

Worked example

A typical case from the default values: σ₁ = 12 HU (Original noise); mAs₁ = 200 mAs (Original mAs); h₁ = 5 mm (Original slice); mAs₂ = 100 mAs (New mAs); h₂ = 5 mm (New slice). Substituting into the relation gives σ₂ = 16.9706 HU; σ₂/σ₁ = 1.4142. These are teaching numbers — align them with your machine.

Typical values give

σ₂ = 16.9706HU
σ₂/σ₁ = 1.4142

Where it comes from

The displayed formula is the working relation. Pixel noise scales as 1/√(mAs · slice · dose). Usual reference: Bushberg / AAPM. Derive it in the specialty lesson, then return here to pin the numbers.

Reference: Bushberg / AAPM

Assumptions & limits

Quantum noise only. Electronic noise, reconstruction kernel, and AEC along z are omitted. Not valid below the quantum-limited regime (very low dose, small detectors).

Pitfalls

kVp is not the same as effective energy. CTDI is not patient dose — SSDE and organ dose come after. Do not quote DLP as if it were effective dose without a k-factor. Quantum noise only. Electronic noise, reconstruction kernel, and AEC along z are omitted. Not valid below the quantum-limited regime (very low dose, small detectors).

Keep this

Technique is physics: kV sets contrast, mAs sets noise, filtration sets the spectrum. Quantum noise only. Electronic noise, reconstruction kernel, and AEC along z are omitted. Not valid below the quantum-limited regime (very low dose, small detectors).

In this specialty

Diagnostic imaging