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I wonder if the diffraction pattern after Laserlight going thru a grating pattern (say 10 slots) has anything to do with the Fourier transform of the grating pattern.

I am not a physicist, but have some knowledge of Fourier math.

I think the spacial frequencies of the grating pattern plus the wavelength of the laser determin the diffraction pattern, and mathematically it has something to do with the FT of the grating pattern, but I am not sure!?

can anybody elaborate on this a little bit?

here is an example of the kind of diffraction pattern i mean

http://demonstrations.wolfram.com/DiffractionGratingIntensities/