Quantitative characterization of iridescent colours in biological studies: a novel method using optical theory
Résumé
Iridescent colours are colours that change with viewing or illumination geometry. While they are widespread in many living organisms, most evolutionary studies on iridescence do not take into account their full complexity. Few studies try to precisely characterize what makes iridescent colours special: their angular dependency. Yet, it is likely that this angular dependency has biological functions and is therefore submitted to evolutionary pressures. For this reason, evolutionary biologists need a repeatable method to measure iridescent colours as well as variables to precisely quantify the angular dependency. In this study, we use a theoretical approach to propose five variables that allow one to fully describe iridescent colours at every angle combination. Based on the results, we propose a new measurement protocol and statistical method to reliably characterize iridescence while minimizing the required number of time-consuming measurements. We use hummingbird iridescent feathers and butterfly iridescent wings as test cases to demonstrate the strengths of this new method. We show that our method is precise enough to be potentially used at intraspecific level while being also time-efficient enough to encompass large taxonomic scales.
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| Origine | Fichiers produits par l'(les) auteur(s) |
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| Format | Figure, Image |
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| Commentaire | Graphical representation of the variables we used for hue H (wavelength at peak reflectance Rmax; called H1 in Montgomerie 2006), brightness B (average of reflectance over the wavelength range of interest; B2 in Montgomerie 2006) and saturation S (full width at half maximum; no equivalent in Montgomerie 2006) |
| Format | Figure, Image |
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| Commentaire | Schematic representation of a tilted multilayer (angle between the multilayer and the sample surface or tilt t = 40°) and incoming and reflected light rays relative to the multilayer structure (with angles θi and θr respectively) and relative to the sample surface (with angle Φ incand Φ col respectively). There is a relationship involving the tilt t between angles relative to the multilayer structure (θi and θr ) and angles relative to the sample surface (Φinc and Φcol ): θi = Φinc − t and θr = Φcol + t. The positive direction for each angle is figured by an arrowhead. The multilayer is composed of an alternance of two layers characterised by the optical indices n1 and n2 and their thicknesses e1 and e2 . A schematic representation at a different scale, focusing on the goniometer is available in ESM. |
| Format | Figure, Image |
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| Commentaire | Colour variables ((a): brightness; (b): hue; (c) and (d): hue & brightness) of an iridescent multilayer (with tilt t ̸ = 0) in the angle space relative to the sample surface (Φinc , Φcol ). The colour lines in (d) indicate alternative bases: the angle space relative to the multilayer structure (θi , θr ) in blue and (Φinc + Φcol = 0, Φinc − Φcol = t) in orange and illustrates the terms ‘constant illumination’, ‘constant collection’, ‘constant angle bisector’ and ‘constant span’ used in table 3 and throughout this article. |
| Format | Figure, Image |
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| Commentaire | Spectra (top row) and corresponding values of brightness (middle row) and hue (bottom row) at different angle configurations for the breast patch of the hummingbird Heliomaster furcifer along the Φinc − Φcol = cst (left column; data points with round shape) and Φinc + Φcol = cst (right column; data point with square shape) lines. Colours correspond to the conversion of the spectra in human vision using the CIE10 visual system. As expected, brightness is constant when Φinc − Φcol = cst and has a Gaussian shape when Φinc + Φcol = cst. Conversely, hue has a cosine shape wen Φinc − Φcol = cst and is constant when Φinc + Φcol = cst. The red lines correspond to the fit of the functions after parameters estimation, with the values of the parameters. The R script to produce this figure is available in ESM. |
| Format | Figure, Image |
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| Commentaire | Correlation between Bmax and directionality 1/γB . The dots are the data points. The lines show the result of the linear model. |