Fourier Blues: Structural Coloration of Biological Tissues
The non-pigmentary colors of the tissues of living organisms are produced by the physical interaction of light with nanostructures in the tissues. Contrary to what has been previously assumed for many decades, it has been established now that many of the
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Abstract The non-pigmentary colors of the tissues of living organisms are produced by the physical interaction of light with nanostructures in the tissues. Contrary to what has been previously assumed for many decades, it has been established now that many of the beautiful blue and green colors observed in the tissues of mammals, birds, and butterflies are the result of coherent scattering or constructive interference. Using Fourier analysis one can show that many structurally colored tissues are quasi-ordered on the appropriate nanoscale to produce the observed colors by constructive interference. Understanding the mechanisms of coloration in animals is very important because of the role that bright colors play in communication, courtship display, and mate selection in many species of the animal kingdom. In this note we give an exposition of some of the extensive work done recently on nanomaterials with noncrystalline, local scale order. The focus of this article is, in particular, on a truly fascinating manifestation of Fourier analysis and synthesis in nature, which provides a way to explain coloration phenomena that are of interest in behavioral and evolutionary biology. Keywords Fourier Transform • FFT • Quasi-order • Nano-scale • Nano-structure(s)(d) • Crystallography • Coloration • Scattering • Iridescent • Interference • Electron micrograph(s) • X-ray(s) • Bragg’s law • Rayleigh scattering • Benedek
R.O. Prum Department of Ecology and Evolutionary Biology, Yale University, New Haven, CT 06520-8105, USA e-mail: [email protected] R.H. Torres () Department of Mathematics, University of Kansas, Lawrence, KS 66045-7594, USA e-mail: [email protected] T.D. Andrews et al. (eds.), Excursions in Harmonic Analysis, Volume 2, Applied and Numerical Harmonic Analysis, DOI 10.1007/978-0-8176-8379-5 20, © Springer Science+Business Media New York 2013
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R.O. Prum and R.H. Torres
1 Introduction The study of the forms of coloration in different materials is a rich, intricate, and multidisciplinary activity. The classic book by Nassau [15] presents a detailed account of at least fifteen different forms of coloration found in our physical world. From a scientific point of view, the explanation of the origin of the colors observed belongs mainly to the m´etiers of physics and chemistry, but the implications of the presence of coloration in different materials extend to many other disciplines. In particular, coloration as mean of communication plays a crucial role in many areas of biology and the study of species capable of analyzing the complicated color signals. Among such species are certainly humans, and color and coloration play a central role in many situations extending from the scientific, through the practical, to the aesthetic aspects of our lives. Colors allow us to discover and understand physico/chemical phenomena taking place both at microscopic scales invisible to our eyes and at intergalactic distance in our universe; they code, guide, warn, and help us in many aspects of our everyday lives, and
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