The diffraction grating under nonuniform illumination

A grating illuminated by a beam with a spatial distribution of intensity produces a diffraction pattern that appears to consist of copies of the incident beam. The copies are centered at the classical diffraction angles given by nλ=d sin φ. In this article, this is indeed shown to be the case if the incident beam has a very narrow spread in wavelength and direction. If the incident beam has a very narrow spread in direction, but not in wavelength, only the zeroth-order diffracted beam is a copy of the incident beam. The higher-order diffracted beams are spread out in wavelength. A black-and-white lantern slide projected through a grating shows the picture in black and white in zeroth-order and as colored images in higher orders.