Spatial Encoding, Gradients, and Image Formation
Core concepts
Spatial localization uses three orthogonal gradients. Slice selection applies a gradient during a shaped RF pulse; slice thickness = bandwidth / (γ·G_slice). Frequency encoding applies a readout gradient during acquisition, mapping position to precession frequency. Phase encoding applies a brief gradient before readout, imparting position-dependent phase that is resolved by repeating at different amplitudes.
k-space
The raw data live in k-space; the Fourier transform converts k-space to image. Central k-space lines carry contrast and low spatial frequencies; peripheral lines carry edges and fine detail. Phase-encoding steps determine matrix size in that direction; readout sampling determines the frequency-encode matrix.
Traps
- Confusing gradient amplitude (determines slice thickness) with slew rate (determines how fast gradients switch).
- Forgetting that phase encoding is repeated, so scan time = TR × N_phase × NEX.
- Mixing up field of view and resolution: FOV = 1/(Δk); resolution = 1/(k_max).
Worked example
Slice thickness = Δf / (γ/2π · G). With RF bandwidth 2 kHz and G = 10 mT/m: thickness = 2000 Hz / (42.58 MHz/T × 0.010 T) ≈ 4.7 mm. Doubling gradient halves slice thickness.