02 Imaging
Rose model SNR
SNR = C √(N A) for a large-area object against a Poisson background.
Listen
Listen · English
Simulation
Rose model SNR — 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.
Open this machineFormula
Variables
Results
SNR
Signal-to-noise ratio
45.8258
SNR/5
Relative to Rose criterion
9.1652
Curve
Explanation
What it means
Albert Rose asked how many quanta you need to see an object of contrast C and area A. With Poisson statistics the signal is C·N·A and the noise is √(N A), so SNR = C √(N A). Empirically a human observer needs SNR ≈ 5 (the Rose criterion) to detect a low-contrast lesion reliably. This is the ancestor of every detective-quantum-efficiency argument. 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.
Radiography room · Open this machineHow to use it
Enter contrast (fraction), fluence N (quanta/mm²) and area A (mm²). A 3 mm nodule, C=0.1, N=3×10⁴ mm⁻² → SNR ≈ 9, visible. Drop N by 4 (dose/4) and SNR halves. Change one input and watch the curve and the simulation follow.
Symbols
- CContrast0.1
- NQuanta fluence30,000 mm⁻²
- AArea7 mm²
Worked example
A typical case from the default values: C = 0.1 (Contrast); N = 30,000 mm⁻² (Quanta fluence); A = 7 mm² (Area). Substituting into the relation gives SNR = 45.8258; SNR/5 = 9.1652. These are teaching numbers — align them with your machine.
Typical values give
- SNR = 45.8258
- SNR/5 = 9.1652
Where it comes from
The displayed formula is the working relation. SNR = C √(N A) for a large-area object against a Poisson background. Usual reference: Rose 1948 / ICRU 54. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: Rose 1948 / ICRU 54
Assumptions & limits
Large-area, known-location, white (Poisson) noise, no display/observer inefficiency. Real observers need a d′ that includes internal noise; DQE < 1. Does not describe structured (anatomical) noise, which dominates chest CT.
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 Do not quote DLP as if it were effective dose without a k-factor. Large-area, known-location, white (Poisson) noise, no display/observer inefficiency. Real observers need a d′ that includes internal noise; DQE < 1. Does not describe structured (anatomical) noise, which dominates chest CT.
Keep this
Technique is physics: kV sets contrast, mAs sets noise, filtration sets the spectrum. Large-area, known-location, white (Poisson) noise, no display/observer inefficiency. Real observers need a d′ that includes internal noise; DQE < 1. Does not describe structured (anatomical) noise, which dominates chest CT.
In this specialty