Got a lot of ideas and/or information according what FT of AFM/MFM images shows. For instance: the directionality of magnetic field, elongation of domains, etc. According to another scientist it is not so obviously. So, is there any paper where exactly/clearly explanation/interpretation of what FT picture presents?
A real image (TEM, SEM, AFM etc) is like a graph with each pixel at location x,y having a value (for e.g. 0 - 255; for an 8-bit image). So the pixel intensity information is provided along X and Y coordinates. When we do fast Fourier transform (FFT), we are 'using a specific algorithm to transform' the X-Y representation to a polar representation (pixel information is provided based on radial distance and angle w.r.t. image center). Here any periodicity in the real image is represented at a certain radial distance (and angle) from the center.
In a simple example, if your real image is simply horizontal black and white lines with a constant thickness, then your FFT image will be a pair of spots equidistant from the image center and aligned vertically. For more complex images each periodicity will be represented as a pair of spots (periodicity can be determined by radial distance), and spots could smudge into several spots with same radial distance (circles, arcs, etc). So FFT is just an image processing algorithm (ideally suited for binary systems-computer programs), and applications are diverse - such as noise reduction in digital images, identification of crystallographic planes in high resolution electron micrographs, etc.
So your interpretation of FFT analyses depends of a priori knowledge of the real image. If it was AFM image of ferromagnetic particles with and without external magnetic field, then FFT of no magnetic field image will probably be featureless (no periodicity), while image of particles under external magnetic field will have clear periodicity (along the magnetic field lines). The angle of the spots can be indicative of the direction of field lines.
Any kind of 'elongation' of domains will result in change in the periodicity (the features in FFT image will have different radial distance from image center).
Any paper with high resolution electron microscopy and analyses for crystallography will have detailed FFT analyses.
Have a look at this Matlab tutorial:
http://www4.ncsu.edu/eos/users/w/white/www/white/ma325/MVlec7.pdf
The mathematical apparatus of FT is well-known. If I have understood right, the question is about the concrete AFM-data analysis applications of FT with practical examples.
I do not use this transformation in routine AFM-data analysis, but it is interesting to see some unobvious examples.
If your real image has periodic features for e.g. rows of lines or dots, irrespective of their physical origin, the FFT images will have features (spots, arcs or even circles) with certain radii and angle from the center. Just download a free software (e.g. ImageJ http://imagej.nih.gov/ij/download.html) and then just start doing FFT of certain parts and look at the FFT patterns. Another very useful tool that you can use with such softwares is the 'inverse FFT' to get back the real image.
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