From: r_delaney2001@yahoo.com   
      
   On December 13, Phil Hobbs wrote:   
   >> Consider the Nyquist criterion for sampling a continuous    
   >> waveform - 2x bandwidth - then the Rayleigh resolution    
   >> principle - peaks must separate by at least 1 wavelength.     
   >> Nyquist sampling can be    
   >> viewed as a mandate to sample each period, at least    
   >> twice.  And, Rayleigh mandates that the image be    
   >> 'sampled' twice, in the sense of a peak and trough.   
   >> It strikes me they may be equivalent, in some deeper    
   >> sense.  Has anyone ever tried to derive such a result,    
   >> mathematically?   
   >   
   > The Rayleigh criterion also uses both real and Fourier space, but it's a   
   > heuristic based on visual or photographic detection, and not anything   
   > very fundamental.  The idea is that if you have two point sources    
   > close together, you can tell that there are two   
   > and not just one if they're separated by at least the diameter of the   
   > Airy disc (the central peak of the point spread function).  The two are   
   > then said to be _resolved_.   
      
   The confusing bit is, the Rayleigh criterion is usually    
   presented as a hard limit, something mathematically precise,    
   not as a heuristic.   
      
      
   > Usually when we use a   
   > telescope or a microscope, we just want to look and see what's there,   
   > without having some a priori model in mind.  In that case, resolution   
   > does degrade roughly in line with Rayleigh, though there's no aliasing   
   > or spectral leakage as there is with poorly-designed sampling systems.   
      
   In other words, diffraction limited, as the spacing decreases?   
      
       
   > There is an analogue of aliasing in optics, namely grating orders.   
      
   That would be, if the grating spacing is larger than λ?   
      
      
   --   
   Rich   
      
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