Diffraction pattern and Fourier Transform

[transform]

hello
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 spatial 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/

 

[cmos]

https://www.amazon.com/dp/0974707724/?tag=pfamazon01-20

 

[transform]

the book seems to cover all the aspects of FT and holography which I am interested in and want to know!
I just continued to look in the web for more information on diffraction pattern and FT. In one paper I found the notion that the actual (Fraunhofer) diffraction pattern gives back the intensity wave of the FT function, not directly the FT.
So can one say that the diffraction pattern gives a kind of picture what the FT of the grating pattern looks like?

 

[Andy Resnick]

The far-field diffraction pattern of an aperture is the (complex) Fourier transform of the aperture. Placing a lens after the aperture slightly alters this, but *if* the aperture is located at the entrance pupil of the lens, *then* the field at the back focal plane is the complex Fourier transform of the aperture. Moving planes around adds phase factors, essentially. Laue patterns, x-ray crystallography, Bragg scattering etc. all use this phenomonon.

Note it's the *field* that is transformed, not the intensity, and it is indeed a complex transform. Detectors (in the visible region) are sensitive to the intensity only; that has an effect but not a conceptual change. For coherent detection (phase-sensitive detectors), the transfer function is the field at the entrance pupil; for incoherent detection (intensity detection), the transfer function is the autocorrelation of the entrance pupil. For aberration-free imaging, the cutoff frequency in incoherent detection is twice that of coherent detection.