Infographics / CT Physics

Spatial resolution: pixel/voxel size, FOV, matrix, focal spot & sampling

A line-pair (bar) test pattern with bars getting finer left to right; low frequencies resolve as sharp black bars, but past a limiting frequency the bars blur and merge into uniform grey. Spatial frequency is labelled in line pairs per mm. A lower panel shows that a pixel grid must place at least two samples per line pair, giving the Nyquist limit fN equals one over two times the pixel size. A second lower panel shows a finite focal spot casting a penumbra past an object edge onto the detector, with magnification equals source-to-image distance over source-to-object distance, and edge blur Ug approximately equals focal-spot size times object-to-image distance over source-to-object distance.

Spatial resolution: line-pair test pattern and the limits set by pixel size, Nyquist sampling, focal-spot size and magnification A line-pair (bar) test pattern with bars getting finer left to right; low frequencies resolve as sharp black bars, but past a limiting frequency the bars blur and merge into uniform grey. Spatial frequency is labelled in line pairs per mm. A lower panel shows that a pixel grid must place at least two samples per line pair, giving the Nyquist limit fN equals one over two times the pixel size. A second lower panel shows a finite focal spot casting a penumbra past an object edge onto the detector, with magnification equals source-to-image distance over source-to-object distance, and edge blur Ug approximately equals focal-spot size times object-to-image distance over source-to-object distance. A bar test pattern resolves finer detail up to a limiting frequency increasing spatial frequency (finer bars) 0.5 1 2 3 4 5 lp/mm limiting resolution (highest resolvable) beyond cut-off: bars merge / unresolved Pixel size and the Nyquist limit 1 line pair = 2 pixels p = pixel size at least 2 samples needed per line pair Nyquist limit: fₙ = 1 / (2p) larger p → lower fₙ (fewer lp/mm) pixel size = FOV / matrix Focal spot and magnification focal spot (width F) object edge detector Ug = edge blur (penumbra) SOD OID M = SID / SOD Ug ≈ F × OID / SOD Limited by pixel / detector size and Nyquist sampling, plus focal-spot size and magnification (geometric unsharpness).

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