Biomedical Engineering Reference
In-Depth Information
Figure 11.4
Calculated spatial Fourier spectrum of the spiral structures
shown in Fig. 11.1. The reciprocal space structure of a (a)
α
1
spiral, (b)
α
2
spiral, (c)
α
3
spiral, (d)
α
4
spiral, (e) GA spiral, (f)
β
1
spiral (g)
β
2
spiral,
(h)
β
3
spiral, and (i)
β
4
spiral are plotted. Reproduced from Ref. [37] with
permission of the Optical Society, Copyright 2012.
the discrete Fourier transform (DFT) of the spiral arrays shown in
Fig. 11.3.
We can appreciate that all the spectra in Fig. 11.4 lack Bragg
peaks and display diffuse circular rings (Fig. 11.4a-i). The many
spatialfrequencycomponentsinVogel'sspiralsgiverisetoadiffuse
background, as for amorphous and random systems. Interestingly,
despitethelackofrotationalsymmetryofVogelspirals,theirFourier
spectra are highly isotropic (approaching circular symmetry), as a
consequenceof a high degree of statistical isotropy [34, 52].
Aspreviouslyreported[34,52,57],theGAspiralfeaturesawell-
defined and broad scattering ring in the center of the reciprocal
space (Fig. 11.4e), which corresponds to the dominant spatial fre-
quencyofthestructure[52].PerturbingtheGAspiralbyvaryingthe
