2D FFT of HCP lattice -- Inconsistency with line plot?

Posted by Mason Guffey on Aug 14, 2008; 8:46pm
URL: http://imagej.273.s1.nabble.com/2D-FFT-of-HCP-lattice-Inconsistency-with-line-plot-tp3695379.html

Hi all,

I've been having a problem with ImageJ related to 2-d fourier transform
of ordered images. Essentially, if I take an FFT of any hexagonally
close-packed lattice (e.g.
http://content.answers.com/main/content/wp/en-commons/thumb/c/c0/180px-Tile_3,6.svg.png 
) and compare that with a line plot of the objects I get inconsistent
results.

Specifically, take a line plot down any lattice direction of that image.
Divide the length of the line plot by the number of triangles it passes
through (i.e. the total number of lattice spacings). Compare that with
what you get from the FFT. The line plot yields a lattice constant of
about 14.5 pixels per cycle while the fourier transform peaks are all
right around 12 pixels / cycle.

Does anyone know what's going on here? This same phenomena has repeated
for just about any image of hexagonal close-packed circles that I load
into it.... The line plot method reveals X for a lattice constant, while
the FFT peak is at Y. There's a factor of about 1.2 between them.

However, if you do the same thing with an array of straight lines, the
FFT and the line profile match eachother perfectly. (As is shown on the
imageJ website for the FFT demo).

Thanks in advance

--
Mason Guffey | Gordon Center for Integrative Science ESB09B
Scherer Group | [hidden email]
Department of Chemistry | [phone]
The University of Chicago | http://schererlab.uchicago.edu