02 Imaging
Nyquist frequency
f_N = 1 / (2 Δx). Spatial frequencies above f_N alias.
Listen
Listen · English
Simulation
Nyquist frequency — 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
f_N
Nyquist frequency
3.3333lp/mm
f_N
Nyquist frequency
3.3333mm⁻¹
Explanation
What it means
A pixel of width Δx can faithfully represent at most one line-pair every two pixels. That limiting frequency is Nyquist. Sampling a bar pattern finer than f_N produces Moiré / aliasing — the classic grid-line artefact on CR, or wrap of high-frequency contrast in MRI. Detector MTF is usually already small at f_N, which is why we get away with it. 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 pixel size in mm. A 150 μm DR panel has f_N = 3.33 lp/mm. Mammography 50 μm → 10 lp/mm. CT 0.5 mm → 1 lp/mm. Change one input and watch the curve and the simulation follow.
Symbols
- ΔxPixel size0.15 mm
Worked example
A typical case from the default values: Δx = 0.15 mm (Pixel size). Substituting into the relation gives f_N = 3.3333 lp/mm; f_N = 3.3333 mm⁻¹. These are teaching numbers — align them with your machine.
Typical values give
- f_N = 3.3333lp/mm
- f_N = 3.3333mm⁻¹
Where it comes from
The displayed formula is the working relation. f_N = 1 / (2 Δx). Spatial frequencies above f_N alias. Usual reference: Bushberg / Shannon. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: Bushberg / Shannon
Assumptions & limits
1-D sampling of a square pixel. Rectangular pixels have a different Nyquist on x and y. Focal-spot MTF and geometric unsharpness usually band-limit the signal before f_N.
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 Do not quote DLP as if it were effective dose without a k-factor. 1-D sampling of a square pixel. Rectangular pixels have a different Nyquist on x and y. Focal-spot MTF and geometric unsharpness usually band-limit the signal before f_N.
Keep this
Technique is physics: kV sets contrast, mAs sets noise, filtration sets the spectrum. 1-D sampling of a square pixel. Rectangular pixels have a different Nyquist on x and y. Focal-spot MTF and geometric unsharpness usually band-limit the signal before f_N.
In this specialty