On Fri, Feb 07, 2014 at 11:12:25AM +0100, Mathias Müller wrote: > I recently wanted to extract lattice constants from FFT images. I am > using reference values obtained from a commercial software. Employing > the transformation rule from real space to reciprocal space (and vice > versa) I do not succeed in calculating the correct values. However, > when multiplying the fft coordinates with 2*pi it fits pretty well.
This is one of the many Fourier transform pitfalls. Gwyddion uses agnular frequencies for FFT (except the 2D FFT module, for historical reasons). > This leads to one of my questions. Did you implement the crystallographic > notation (a_real * a_rec = 1) or the > solid state notation (a_real * a_rec = 2*pi) for reciprocal space? (just to > ensure the correct transformation) It is more like that we use spatial frequency which is 2π times the quantity you want. > The second question concerns the result's quality. Using the same data from > the commercial software results in two pretty equal > lattice constants of the unit cell. Calculating by hand from the very same > FFT coordinates (peaks) results in two similar but > different values. Using neighbor pixels slightly varies the result, but never > matches. > > For example a hexagonal structure: > > lattice constant commercial/nm Gwyydion-manually/nm > > |a| 1.25 1.29 > |b| 1.24 1.22 > > The question is why does it differ? Do I have to correct the coordinates if > the angle between two vectors of neighbor peaks > is != 60 degree (i.e. hexagonal structure)? Should I calculate the center of > mass of each FFT peak ? Maybe the latter improves > the precision. However, am I overcritical about a difference of 3 % ? I'm not sure about this but you should definitely take the mass centre. Generally, the maximum does not lie in a pixel centre. Also, did you try the new affine correction module? It works in the real space using ACF but if you have something like a regular lattice it should provide quite good lattice vectors (including directions). Regards, Yeti ------------------------------------------------------------------------------ Managing the Performance of Cloud-Based Applications Take advantage of what the Cloud has to offer - Avoid Common Pitfalls. Read the Whitepaper. http://pubads.g.doubleclick.net/gampad/clk?id=121051231&iu=/4140/ostg.clktrk _______________________________________________ Gwyddion-users mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/gwyddion-users
