Supplemental Material-Scratch iridescene : Wave-optical rendering of diffractive surface structure

Our model builds on tools from Fourier optics [1], specifically the angular spectrum and the concept of diffracted radiance [2], which we review here for completeness. Being part of a scalar theory of light transport, these two tools assume that the electromagnetic field can be described by the (scalar) amplitude of the oscillations that make up the electromagnetic field, as opposed to the commonly used vectorial electric and magnetic fields. This approximation is accurate in the far-field and for diffracting apertures that are larger than the wavelength of the radiation. Without loss of generality, we restrict ourselves to monochromatic radiation at a wavelength of λ. The following discussion assumes that all spatial coordinates are expressed in units of λ, since this leads to simpler mathematical expressions. Let U(x, y, z) denote the scalar amplitude at position (x, y, z) , and let U0(x, y) := U(x, y, 0) denote a planar slice at position z = 0 (here called the aperture plane). A well-studied problem in this domain entails computing U(x, y, z) for z > 0 given the amplitude distribution in the aperture plane U0(x, y). In the context of Fourier optics, solutions can be found by taking the Fourier transform of all quantities in the xy-plane, i.e.