Is the sampling rate a function of the structure that you're modeling?
About the Nyquist rate-I can imagine that SNR limits resolution. But how does SNR work into the formula in the manual, that looks like pure optics to me? If you had a structure with details that measured, say, 80 nm, wouldn't you necessarily need a sampling interval of 40 nm in x, y, and/or z?
No, it is a function of the optical properties of your system. <br>
It all revolves around the Shannon theorem, that states that for a bandlimited system (all our microscopes) it is totally sufficient to sample at the Nyquist rate. Now suppose the maximum spatial frequency passing a microscope is one cycle per 100nm (1.3 NA oil, confocal, 488/520nm, sampling at 50nm to sample peaks and valleys of the 100nm periodic wave). If you have a periodic structure of lumps spaced 80nm apart then this structure is not imaged, apart from its average value, nothing of it. Can't restore it, no way. If there is omly one single object and you know it is a sphere then restoration could consist of determining its center of mass. The accuracy of that depends on the SNR, but you could easily reach 10nm. Job done!!! The regular restoration procedure could also do it for you, but obviously to get such an accuracy in determining the peak location of the object you would have to resample the data to a higher sampling interval of 10nm. (You could also play it a bit dirty by not deconvolving with the PSF, but with the known image of the object; out comes a single peak where the center of the object is). A more interesting object is for instance a two-blob object with a spacing at the Nyquist rate. Now the most interesting parts of the object spectrum are cut off by the microscope. The problem now is that the transmitted piece is the same for a whole family of objects. The family which has a spectrum quite like it is even larger. The restoration algorithm must now choose among them, the first selection being to exclude all objects with negative values. The better the SNR, the better the restoration algorithm can exclude objects of which the spectrum is slightly dissimilar to the measured spectrum. For confocals the situation is worse because they already attenuate everything beyond say 60% of the band practically to zero (depending on the pinhole). So in practice there is little hope for resolving objects at the edge of the band.
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Keywords: bandlimited system shannon sampling<br>
Categories: Faq Deconvolution, Faq Microscopy, Huygens Faq, Imported Faqs<br>
Platforms: Irix Windows Mac<br>
Related products: Hu Ess Hu Pro<br>
