Posted by
Avi Jacob on
URL: http://confocal-microscopy-list.275.s1.nabble.com/Nyquist-sampling-advice-for-a-short-talk-tp7591495p7591498.html
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Well, the question was specifically about Nyquist, and, I gather, as an
introduction of some sorts, not for advanced physics students.
What I always stress when explaining sampling, is to first differentiate
between the Abbe criterion, explained as the *physics-based theoretical
limit* on resolution, and how we *detect *that resolution. You don't even
need to explain Abbe very well, and the causes and the parts of the
equation, as long as they understand that there exists something called the
"Abbe criterion" that refers to the "best possible
resolution physics allows".
Then, I get into how to detect, or in sciencese, *sample*, what is
allowable by physics.
I have some slides (I think I got them originally from the
wonderful lecture series by Paul Robinson from Purdue) showing the idea of
sampling that Nyquist originated. (e.g. signal, sample, and if not enough
sample, the recreated signal will be lacking thus "undersampled" etc).
Once they understand the concept of sampling in general, it's now easy to
show why pixel size in imaging is sampling and is important to determine
the "Nyquist". (Pixel size for lateral and "slice number" for axial). For
this I use a self-customized (I doubled the disk) version of the Zeiss
"projected size of airy disk on ccd array" graphic showing an airy disk on
four same size FoVs but with different pixel sizes. I show that when
undersampled, even though the center of the disks of the two points of
light are more than say 300nm from each other (so physics is not the
limiting factor), you won't be able to detect it.
I think that explaining the concept in this manner gives a very good
intuitive understanding.
I actually think it's very appropriate to mention point scanning systems,
because only thus can you determine your pixel size. With
camera-based systems, the max sampling is what it is - limited by the
physical size of the chip pixels - you can't oversample even if you wanted
to (though you can undersample by binning, of course.)
Avi
--
Avi Jacob, Ph.D.
The Kanbar Light Microscopy Unit
The Goodman Faculty of Life Sciences
Bar-Ilan University, Ramat-Gan 5290002, Israel
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