Jacob
I included a demo using Moire fringes in a crystallography course some
years ago. The diagram I used looks just like the second Moire pattern
(the annotated one) at this site: http://spie.org/x8449.xml . This is a
static Moire pattern; in my demo the two gratings could be translated &
rotated in the plane relative to each other.
Call the horizontal grating the "incident beam" and the inclined grating
the "diffracted beam" and redefine theta in the diagram as 2 theta (i.e.
theta is now the Bragg angle, half the deviation of the diffracted beam).
Also call the spacing between successive lines in the gratings (labelled
"d" in the diagram) "lambda", and call the spacing between successive Moire
fringes (labelled "d_m") "d". The diagram shows the first order Moire
fringe but imagine instead that the spacing d is for the n'th order
fringe. Then the equation relating the variables is:
n lambda = 2 d sin(theta)
It doesn't "prove" Bragg's law of course, that wasn't my intention: rather
it merely demonstrates the geometrical analogy between the Moire pattern
and diffraction.
The Braggs did actually study Moire patterns and this analogy may well have
come to their attention.
Is this what you meant?
Cheers
-- Ian
On 2 June 2014 16:05, Keller, Jacob <[email protected]> wrote:
> Dear Crystallographers,
>
> I have a feeling that Moire finges are the real-space equivalent of the
> Laue zones in reciprocal-space, and this seems like a very basic idea that
> must have been explored--anyone know of a source connecting the
> mathematico-physical dots? Or do the dots not connect?
>
> JPK
>
> *******************************************
> Jacob Pearson Keller, PhD
> Looger Lab/HHMI Janelia Farms Research Campus
> 19700 Helix Dr, Ashburn, VA 20147
> email: [email protected]
> *******************************************
>
