Specification of multiple image characteristics viewed through a grating

Abstract

When a person observes an object, illuminated incoherently by a quasi-monochromatic source, through a grating, he will see more than one image. Angular positions of these images are derived in terms of wavelength, period of the grating, separation between the object and the grating, and position of the object relative to the observer. In a special case, when the object is another grating, the condition of coincidence of its multiple images is investigated. The relation derived is, to some extent, similar to that seen in the Lau effect. As a secondary outcome, it is shown that the sum of the squared modulus of the odd Fourier series coefficients for a binary grating function is equal to that of the even coefficients.