QUANTITATIVE-ANALYSIS OF MULTICHROMATIC MOIRE EFFECTS IN THE SUPERPOSITION OF COLORED PERIODIC LAYERS

In the present article we give a full quantitative analysis of the mul tichromatic moire effects in the superposition of coloured periodic la yers, which is based both on the Fourier theory and on the theory of c olorimetry and colour vision. This is done by introducing both into th e image domain and into the Fourier frequency domain a new dimension l ambda, representing the visible light wavelengths. In the image domain we represent each layer by the chromatic reflectance (or transmittanc e) function r(x, y; lambda), which is a generalization of the reflecta nce (or transmittance) function r(x, y) in the monochromatic case. Con sequently, in the Fourier spectral domain each impulse amplitude becom es a function of lambda. All the results previously obtained by our Fo urier-based approach in the monochromatic case remain valid in the mul tichromatic case, too, for every wavelength lambda separately. This en ables us to find, for every point (x, y) of any given moire, the full colour spectrum {r(x, y; lambda)/380 less than or equal to lambda less than or equal to 750} which expresses the visible colour at the point (x, y) of the moire in question. We illustrate the discussion by seve ral multichromatic superpositions, some of which showing very spectacu lar, colourful moire effects.