Generalized Curvilinear Diffraction Gratings: I. Image diffraction patterns

Abstract

This paper is the first in a series on the diffraction and imaging properties of generalized curvilinear diffraction gratings. The ‘image diffraction pattern’ (IDP) of a generalized grating is defined as the optical image that is observed by the naked eye focused on the grating when it is illuminated by an arbitrarily extended diffuse source. In this paper, a general theory of the IDP is derived in both the scalar wave and geometric optics approximations. As an application of the theory, it is shown how the IDP of a generalized grating may be simulated by an optical data processing system in which the Fresnel transform of a low line density representation of the grating is filtered by an aperture of the same shape and orientation as the source. The theory is shown to lead to a simple explanation of the moiré effect first observed by Hamann and to a new technique for performing optical map transformations. As a practical test on the theory, the IDP of a circular diffraction grating is calculated and shown to be in good agreement with experiment.