Hackaday

Diffraction gratings naturally perform Fourier transforms due to fundamental wave physics. When light passes through a sample, it creates spherical waves according to Huygens principle. These waves superpose at observation points, and the mathematical summation of all contributing waves simplifies to a Fourier transform integral. This explains why diffraction patterns represent frequency decompositions of specimen features, and why JPEG compression patterns of microscope images resemble actual laser diffraction patterns from the same samples.

Why Diffraction Gratings Create Fourier Transforms