Posted by
Michael Schmid on
Aug 15, 2008; 12:51pm
URL: http://imagej.273.s1.nabble.com/2D-FFT-of-HCP-lattice-Inconsistency-with-line-plot-tp3695379p3695380.html
Hi Mason,
a 2D FFT of a non-rectangular lattice gives the distance between
parallel *lines*, which is different from the lattice constant
measured along a lattice direction.
In physics, this is known as reciprocal lattice.
Also note that the reciprocal lattice vectors are perpendicular to
the lines of the original lattice, and their length corresponds to
the distance measured in that direction.
So you get the side length of the triangles multiplied by sqrt(3)/2.
Michael
____________________________________________________________________
not that reciprocal lattic;
On Thu, 14 Aug 2008 15:46:05 -0500 Mason Guffey <
[hidden email]>
wrote:
>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 | (773) 834-1877
>The University of Chicago |
http://schererlab.uchicago.edu>