From: pcdhSpamMeSenseless@electrooptical.net   
      
   On 11/10/2013 12:12 AM, Salmon Egg wrote:   
   > In article <292ab5ee-061b-4ea3-aa77-193901cc792d@googlegroups.com>,   
   >   laloum.eric@gmail.com wrote:   
   >   
   >> Dear All,   
   >>   
   >> Is it possible that an image is correctly sampled according to Nyquist (2 to   
   >> 3 pixel per resolution element) but nevertheless show some pixelization   
   >> effect when sufficiently zoomed ?   
   >> I guess both issues (Digital sampling and pixellisation) are highly   
   >> related...and it's quite easy to conceive that correct Nyquist sampling is a   
   >> necessary condition for avoiding pixelization, but is it also a sufficient   
   >> condition ?   
   >>   
   >>   I would say no but can't explain why ;-(   
   >>   
   >> Thanks,   
   >>   
   >>   Eric   
   >   
   > As most such things do, it depends on details. The sampling theorem and   
   > reconstruction from samples depends upon the signal being band limited.   
   > The bandpass shape is often referred to as a brick wall. Such a filter   
   > is not realizable.   
      
   It's pretty realizable in optics, where evanescent fields die away   
   exponentially with distance.   
      
   >   
   > While you do not give details, it is possible that higher frequencies   
   > left in the incompletely filtered image may introduce artifacts in the   
   > reconstruction. The reconstruction works because the reconstruction   
   > waveform is also not realizable. It goes from -ƒ to +ƒ for x and y   
   > coordinates. This means that there always will be some error.   
   >   
   > I believe Hamming,when at Bell Labs, did a lot of work on this   
   > particular  problem.   
   >   
      
   At NA=1, you can in principle reconstruct the propagating part of the   
   fields exactly.   
      
   Cheers   
      
   Phil Hobbs   
      
      
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