03 Nuclear
Collimator geometric resolution
R_g ≈ d (L_eff + b) / L_eff for a parallel-hole collimator.
Listen
Listen · English
Simulation
Collimator geometric resolution — Change the numbers; the scene follows.
Where it works
Gamma camera
Collimator
At the collimator face — geometric resolution grows with source-to-collimator distance.
Open this machineFormula
Variables
Results
L_eff
Effective length
34.2mm
R_g
Geometric resolution
5.886mm
Curve
Explanation
What it means
Parallel-hole collimator resolution worsens linearly with distance: R_g = d (L_eff + b) / L_eff. Longer, narrower holes improve resolution and kill sensitivity. L_eff = L − 2/μ accounts for septal penetration. This is a working relation in Nuclear medicine.
Where it is used
Clinically it sits on the Gamma camera — Collimator. At the collimator face — geometric resolution grows with source-to-collimator distance. Nuclear-medicine relations sit in the hot lab, on the camera, and in the voxel: decay, SUV, TOF, and counting statistics. They decide whether an uptake is real or a clock error.
Gamma camera · Open this machineHow to use it
LEHR: d ≈ 1.1–1.5 mm, L ≈ 24–35 mm. Plot R_g vs distance — at 20 cm a general-purpose collimator may be 12–15 mm FWHM before adding R_i. Change one input and watch the curve and the simulation follow.
Symbols
- dHole diameter1.5 mm
- LHole length35 mm
- μLead attenuation2.5 mm⁻¹
- bSource-to-collimator distance100 mm
Worked example
A typical case from the default values: d = 1.5 mm (Hole diameter); L = 35 mm (Hole length); μ = 2.5 mm⁻¹ (Lead attenuation); b = 100 mm (Source-to-collimator distance). Substituting into the relation gives L_eff = 34.2 mm; R_g = 5.886 mm. These are teaching numbers — align them with your machine.
Typical values give
- L_eff = 34.2mm
- R_g = 5.886mm
Where it comes from
The displayed formula is the working relation. R_g ≈ d (L_eff + b) / L_eff for a parallel-hole collimator. Usual reference: Cherry. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: Cherry
Assumptions & limits
Parallel-hole, photopeak μ. Pinhole, fan-beam and convergent collimators have different formulae. Sensitivity is not computed here.
Pitfalls
Activity is not counts. SUV needs the true injected activity, the residual, and the correct decay time — a clock off by 10 min on ¹⁸F is a several-percent error. Do not compare SUVs across reconstructions. Parallel-hole, photopeak μ. Pinhole, fan-beam and convergent collimators have different formulae. Sensitivity is not computed here.
Keep this
Write the assay time next to every activity. Decay does the rest. Parallel-hole, photopeak μ. Pinhole, fan-beam and convergent collimators have different formulae. Sensitivity is not computed here.
In this specialty