Phase Imaging and Phase Aliasing

• See errors that can be introduced in phase, still sometimes desirable to look at phase images. Need to know what to expect

• Easy to figure out phase in the image
  

  $$\phi(x,y) \equiv {\rm Arg\,}\hat{\rho}(x,y) = \tan^{-1}{\lef... ...{\rm Im}\,\hat{\rho}(x,y)} {{\rm Re}\,\hat{\rho}(x,y)}\right)}$$ (10.3)

  
  

• However, this equation is only unique from $-\pi \rightarrow \pi$ For larger phases, just repeats.

• If the phase error, $k_{0}$, is large, phase will just keep cycling
  

  
  
  
  
  

  (a) (b)
  
  
  (c) (d)