It's been a while since I cracked those textbooks, but...

As I remember long-past classes in signal processing, the extra 0.3 is a fairly heuristic buffer to ensure that you have sufficient high frequency information to recover data at the band limit. For an in-focus widefield microscope the modulation transfer function (MTF) decreases in a near-linear fashion, with average intensities (zero frequencies) coming through intact, and frequencies near the cutoff having very low values. 

Frequencies just below the sampling limit are, however, _just_ detectable, and that may be impossible in the presence of noise. Sampling somewhat _above_ the Nyquist limit prevents the sampling limit (where frequencies are barely, theoretically, detectable) from utterly compounding the MTF reduction, and provides some chance of accurately capturing (and potentially restoring, for example through deconvolution) those high frequencies. And in practice 2.3 has been a reasonable factor for this across multiple application domains. 


Kevin Ryan
Media Cybernetics, Inc.


-----Original Message-----
From: Confocal Microscopy List [mailto:[log in to unmask]] On Behalf Of Steffen Dietzel
Sent: Monday, January 19, 2015 6:33 AM
To: [log in to unmask]
Subject: Nyquist and the factor 2.3

*****
To join, leave or search the confocal microscopy listserv, go to:
http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
Post images on http://www.imgur.com and include the link in your posting.
*****

Hi all,

Nyquist again: I gather that the actual Nyquist criterion says that pixel size must be smaller than 1/2 the physical resolution. In the literature, I also find the factor 1/2.3 and I wonder where the 2.3 comes from. Is this just one interpretation of <1/2  or is this the result of some calculation of which I could not find the source?

(I am aware that if the structure of interest is oriented diagonally to the pixel pattern, an additional factor of 1.41 comes into play, see discussion on this list in April 2012 or chapter 4 in the Handbook, so that it could be argued the factor should rather be <1/2.8 or 1/3.2, but my question is about the origin of the 2.3).

Steffen

 

--
------------------------------------------------------------
Steffen Dietzel, PD Dr. rer. nat
Ludwig-Maximilians-Universität München
Walter-Brendel-Zentrum für experimentelle Medizin (WBex) Head of light microscopy

Marchioninistr. 27
D-81377 München
Germany