title: Pulsed field gradient
text: # Pulsed field gradient
  
  A pulsed field gradient is a short, timed pulse with spatial-dependent field intensity. Any gradient is identified by four characteristics: axis, strength, shape and duration.
  
  Pulsed field gradient (PFG) techniques are key to magnetic resonance imaging, spatially selective spectroscopy and studies of diffusion via diffusion ordered nuclear magnetic resonance spectroscopy (DOSY). PFG techniques are widely used as an alternative to phase cycling in modern NMR spectroscopy.
  
  ## Common field gradients in NMR
  
  The effect of a uniform magnetic field gradient in the z-direction on spin I, is considered to be a rotation around z-axis by an angle = $γ_IGz;$ where Gz is the gradient magnitude (along the z-direction) and $γ_I$ is the gyromagnetic ratio of spin I. It introduces a phase factor to the magnetizations:
  
  Φ (z,τ) = $(γ_I)(Gz)(τ)$
  
  The time duration τ is in the order of milliseconds.
  
  