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To make it short, my interpretation of the Fourier transform in optics is that is transforms positions (and phase) of the rays at some given plane, to their angles. One given angle corresponds to one given oscillation of the phase, i.e. one point on the Fourier space.

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X-ray diffraction is certainly possible for metals! Most X-ray diffraction experiments are carried out with hard X-rays (photon energies of about 4keV or higher); among the most frequently used photon energies in laboratories are 8.04keV (Cu K$\alpha$ fluorescense) and 18keV (Mo K$\alpha$), for example. There are mainly two reasons for choosing hard X-rays: ...

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To give an unmathematical catchy answer, let's look at Fraunhofer diffraction in double slit experiment. Interference at the observation plane depends on slit parameter $d$. What is the frequency of slits? E.g. $1\,\text{mm}\frac{1}{d}$: number of slits per length. Concluding frequiency in the setup. The following argumentation links this frequency to the ...

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