Fig. 1. Comparison of incoherent and coherent scattering mechanisms of biological structural colour production. (A) Incoherent scattering is differential scattering of wavelengths by individual light-scattering objects. In Rayleigh (also known as Tyndall) scattering, smaller wavelengths are preferentially scattered. The phase relationships among light waves scattered from different objects are ignored and assumed to be random. (B) Coherent scattering is differential interference or reinforcement of wavelengths scattered by multiple light-scattering objects (x, y). Coherent scattering of specific wavelengths is determined by the phase relationships among the scattered waves. Scattered wavelengths that are out of phase will cancel each other out, but scattered wavelengths that are in phase will be constructively reinforced and coherently scattered. Phase relationships of wavelengths scattered by two different objects (x, y) are given by the differences in the path lengths of light scattered by the first object (x: 1–1') and a second object (y: 2–2') as measured from planes perpendicular to the incident (a) and reflected (b) waves in the mean refractive index of the media.