Ideal Observer CT Resolution Calculator

Interactive calculator for the theoretical minimum detectable feature size and spatial-frequency limit of a CT scanner, derived from the projection-domain ideal observer (Rose criterion, SKE/BKE). The result is a reconstruction-independent upper bound on detectability.

Authors: Falk L. Wiegmann & Nancy L. Ford, University of British Columbia, 2026.

For AI agents

llms.txt — short, LLM-friendly summary
llms-full.txt — full derivation in plain text
formulas.json — typed JSON: inputs, outputs, formulas, worked example

Closed-form formula (at isocentre)

Inputs:

N0 — photons per pixel in the unattenuated beam
mu_bg — background linear attenuation coefficient (mm⁻¹)
L — path length through background (mm)
N_theta — number of projection angles
delta_a_obj — object-plane pixel pitch at isocentre (mm)
delta_mu — linear attenuation contrast of the feature (mm⁻¹); for HU contrast: delta_mu = (delta_HU / 1000) * mu_water
d_prime_threshold — Rose detectability threshold (classical: 3; Hsieh et al. 2022: 5)

Compute:

N_bg                = N0 * exp(-mu_bg * L)
d_min               = (3 * d_prime_threshold^2 * delta_a_obj
                       / (2 * N_theta * N_bg * delta_mu^2)) ^ (1/3)        # mm
resolution_lp_per_mm = 1 / (2 * d_min)                                     # lp/mm

Off-axis (fan-beam) extension

For a feature at voxel P=(x,y) inside a uniform phantom of radius R, with a point source at distance D (SOD), the source at projection angle theta sits at S(theta) = (D·cos theta, D·sin theta). Two corrections enter:

chord(theta, P) = 2 * sqrt( (S . d_hat)^2 - (D^2 - R^2) )    # d_hat = (P-S)/|P-S|
delta_a_obj(P, theta) = delta_a_obj * |P - S(theta)| / D     # local pixel pitch

d_min(P) = ( 3 * d_prime_threshold^2 * delta_a_obj
             / ( 2 * delta_mu^2 * D
                 * sum_theta [ N0 * exp(-mu_bg * chord(theta, P)) / |P - S(theta)| ] ) )^(1/3)

Sum is over all N_theta projection angles in the scan arc. Reduces to the at-isocentre formula as D → ∞ or at P = (0,0). For partial arcs the map is no longer radially symmetric — the source-facing side sees shorter chords and higher magnification.

Worked example

GE eXplore CT 120 at 80 kVp, 500 HU object contrast:

N0 = 4203, mu_bg = 0.0219, L = 80, N_theta = 220,
delta_a_obj = 0.0249, delta_mu = 0.01095, d_prime_threshold = 3

N_bg               = 729 photons/pixel
d_min              = 0.260 mm
resolution         = 1.93 lp/mm

License & citation

MIT licensed. Cite via the repository's CITATION.cff or BibTeX in the README.