From: behzatsahin@gmail.com   
      
   Dr Phil, Sir, please watch your language, there are children around! software   
   guy? I am a 15 yr rf-photonics engineer, and been building prototype mm sub-mm   
   imaging systems for the last 7 yrs. My team and I have built a W band material   
   (plaster, foam,    
   composite laminate etc.)inspection purpose reflection and transmission   
   michelson interferometric imaging system last year, w/ 1.5 mm su   
   er-resolution. That is half lambda btw, in mm land we love our huge waves.   
   Regards and respects and happy holidays,    
   Asaf.   
   On Thursday, December 14, 2017 at 5:58:03 PM UTC+3, Phil Hobbs wrote:   
   > On 12/13/2017 02:36 PM, Behzat Sahin wrote:   
   > > On Wednesday, December 13, 2017 at 2:36:45 AM UTC+3, RichD 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.   
   > >>    
   > >> Don't these look much analogous? Especially as λ = 1/f   
   > >>    
   > >> Ruminating  a bit more... 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?   
   > >>    
   > >> I can't be the first to ever conjecture this -   
   > >>    
   > >> -- Rich   
   > >    
   > > Both Rayleigh Limit and Nyquist Rate are so 20th century.. They are   
   > > basically hard limits for differentiation between two close entities   
   > > (in time or space). It has been shown that you can operate below   
   > > these limits; that is for good enough snr optical systems yo can   
   > > achieve resolutions below rayleigh limit, and for sparse or   
   > > compressible (lossy usually) data you can use undersampling or   
   > > compressive sampling. It is in the EOTB, if you can understand what   
   > > you see or hear that is enough. Regards, Asaf    
   > > http://www.laserfocusworld.com/articles/print/volume-52/issu   
   -12/world-news/imaging-theory-breaking-rayleigh-s-limit-imaging-   
   esolution-not-defined-by-the-criterion.html   
   > >   
   > >    
   > statweb.stanford.edu/~markad/publications/ddek-chapter1-2011.pdf   
   > >    
   >    
   > Spoken like a true software guy. ;)   
   >    
   > Cheers   
   >    
   > Phil Hobbs   
   >    
   > --    
   > Dr Philip C D Hobbs   
   > Principal Consultant   
   > ElectroOptical Innovations LLC / Hobbs ElectroOptics   
   > Optics, Electro-optics, Photonics, Analog Electronics   
   > Briarcliff Manor NY 10510   
   >    
   > http://electrooptical.net   
   > http://hobbs-eo.com   
      
   --- SoupGate-Win32 v1.05   
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