Nyquist Sampling Criterion

• In order to sample a finite object without aliasing need to have $L$ greater than $L_{object}$, or in terms of $k$-space sampling which is what we need to know when sampling data, have

  
  

  $$\Delta k = \frac{1}{L} = \frac{1}{FOV} < \frac{1}{L_{object}}$$ (11.6)

  
  

• Go back to imaging, to remember what this implies to $\Delta t$ (readout) [assuming constant gradient during ]
  

  $$\Delta k_{R} = \gamma \!\!\!\!\!-G_{R} \Delta t < \frac{1}{L_{object,read\;direction}}$$ (11.7)

  
  

• and $\Delta G_{pe}$ (phase encode) [assuming a real boxcar imaging gradient]
  

  $$\Delta k_{PE} = \gamma \!\!\!\!\!-\Delta G_{PE} \tau_{PE} < ... ...e\;direction}}\;\;\;\;\;\; (\mbox {rectangular gradient lobe})$$ (11.8)

  
  

• (IN-CLASS PROBLEM[s])