IMG-00 · laboratory
Larmor, SNR, CT dose, Beer projection, Nyquist and modulation transfer.
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33 governing sheets
ω = γ B0, f = γ B0 / 2π. Precession of a spin in B0.
MRISNR ∝ Δx Δy Δz √(NEX Ny Ts). Voxel and averaging set the noise floor.
Image qualityfs > 2 fmax. The sampling rate that avoids aliasing.
SamplingCTDIvol = (1/pitch)(⅓ CTDIc + ⅔ CTDIp). Weighted, pitch-corrected CT dose index.
CT doseDLP = CTDIvol × L. The scan-length integral used for DRL audits.
CT dosep = −ln(I/I0) = μ L. The line integral a CT inverts.
CTMTF(f) = exp(−2 π² σ² f²). Gaussian-PSF contrast transfer.
Image qualityΔx = FOV / N. The reconstructed pixel.
GeometryMz = M0 (1 − e^{−t/T1}) after saturation. Longitudinal recovery.
MRIMxy = M0 e^{−t/T2}. Transverse decay of a spin echo.
MRIS = M0 sinα (1−E1)/(1−cosα E1) e^{−TE/T2*}, E1=e^{−TR/T1}.
MRIS = M0 (1 − e^{−TR/T1}) e^{−TE/T2}. The classical SE contrast.
MRIΔf = δ (γ/2π) B0. Water–fat is 3.5 ppm.
MRIΔz = BW_rf / (γ Gss). RF bandwidth over the slice-select gradient.
MRIΔk = 1/FOV = γ G τ / 2π. The sample spacing that sets FOV.
MRIBW_pix = BW_read / Nx. Hertz per pixel along readout.
MRIz = c t / 2 with c ≈ 1540 m/s in soft tissue. Round-trip ranging.
UltrasoundΔf / f0 = 2 v cosθ / c. Blood-flow ultrasound.
UltrasoundR = 2 ε² A e^{−μd}. True coincidences through a pair of detectors.
PETR = √(R_int² + R_coll²). Intrinsic plus collimator in quadrature.
SPECTMGD = DgN × K. Conversion from entrance air kerma.
MammographyDAP = K × A. Inverse-square invariant kerma–area product.
Fluoroscopyp = I / (N T). Table feed per rotation over total collimation.
CTHU = 1000 (μ − μw)/μw. Water is 0, air is −1000.
CTg = clip((HU − WL)/WW + ½). Display grey from window level and width.
Displayf50 = √(ln2 / (2 π² σ²)). Spatial frequency where Gaussian MTF = 0.5.
Image qualityDQE = MTF² / (q NPS). How well the detector uses incoming quanta.
Image qualitySNR = C √n ≥ k. Detection needs about k ≈ 5.
Image qualityCNR = |Sa − Sb| / σ. Two-region detectability.
Image qualityΔf = (γ/2π) Gx x. Position becomes a frequency under the readout gradient.
MRIA_dB = 2 α f z. Soft-tissue α ≈ 0.5 dB cm⁻¹ MHz⁻¹.
UltrasoundK ∝ kVp² mAs / d². Air kerma from a diagnostic tube.
RadiographyBlood-flow US.
Imaging