Interpreting 2-D FFTs of images

[Hyo X]

I have electron microscope images of structures of varying periodicity, ranging from highly crystalline to highly amorphous. It is relatively straightforward to take FFTs of these images, but what i want to do is extract a quantitative value to characterize crystallinity and compare it between samples.

The easier question is, what kind of information can I extract from 2D FFTs about the structures?

The more difficult question is: how can I quantitatively compare FFTs between different images?

I have some ideas, but would appreciate suggestions. These are two example FFTs.

Image1

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Image 2

 

[Claude Bile]

The more highly ordered the structure, the better defined the Fourier peaks, so you can conclude for example that the lower image is from a more amorphous structure (though there is a slight amount of order due to the "ghost" rings on the y-axis).

The FT will also tell you what sort of symmetry is present - e.g. sixfold symmetry typically indicates a hexagonal-packed structure. The number of visible harmonics indicates the "fidelity" of the symmetry.

When comparing FFTs, be sure to normalise the integrated power.

What are your ideas? Presumably you have access to the actual (non Fourier-Transformed) images.

Claude.