Quantitative analysis of multichromatic moiré effects in the superposition of coloured periodic layers

Abstract

In the present article we give a full quantitative analysis of the multichromatic moiré effects in the superposition of coloured periodic layers, which is based both on the Fourier theory and on the theory of colorimetry and colour vision. This is done by introducing both into the image domain and into the Fourier frequency domain a new dimension λ, representing the visible light wavelengths. In the image domain we represent each layer by the chromatic reflectance (or transmittance) function r(x, y; λ), which is a generalization of the reflectance (or transmittance) function r(x,y) in the monochromatic case. Consequently, in the Fourier spectral domain each impulse amplitude becomes a function of λ. All the results previously obtained by our Fourier-based approach in the monochromatic case remain valid in the multichromatic case, too, for every wavelength λ separately. This enables us to find, for every point (x,y) of any given moiré, the full colour spectrum {r(x,y; λ) | 380 ≤ λ ≤ 750} which expresses the visible colour at the point (x,y) of the moiré in question. We illustrate the discussion by several multichromatic superpositions, some of which showing very spectacular, colourful moiré effects.