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Materials Science and Engineering B 169 (2010) 16–22

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Materials Science and Engineering B

journa l homepage: www.e lsev ier .com/ locate /mseb

Modeling the vivid white color of the beetle Calothyrza margaritifera

J. Lafait a,∗, C. Andrauda, S. Berthiera, J. Boulengueza,1, P. Calletb,S. Dumazetb, M. Rassart c, J.-P. Vigneronc

a Institut des Nanosciences de Paris, CNRS–Université Pierre et Marie Curie, INSP - 140, rue de Lourmel, 75015 Paris, Franceb Lab. Mathématiques Appliquées aux Systèmes, Ecole Centrale Paris, Francec Facultés Universitaires Notre-Dame de la Paix, Namur, Belgium

a r t i c l e i n f o

Article history:Received 19 July 2009Received in revised form18 November 2009Accepted 6 December 2009

Keywords:Optical propertiesBiophotonicsColorLight scatteringBiological matter

a b s t r a c t

The elytra of the longhorn Calothyrza margaritifera exhibit bright white zones which appear, under SEM,to be composed of structures looking like long white hairs: flat cone-shaped rods of 100–200 �m inlength and a base of 10–20 �m. Each hair is composed of an envelope of chitin or chitin and associ-ated proteins, filled with small agglomerated spheres of the same material, of mean diameter 550 nm.The optical properties of this multiscale structure have been characterized: hemispherical reflectancespectra, bidirectional reflectance spectra, spatial scattering maps. A multiscale optical model, taking intoaccount this complex structure has been developed for predicting the optical properties. Starting fromthe SEM image, the representative basic scattering structure is extracted, from the scale of the nanometerto the millimeter. By using the Mie theory and solving the Radiative Transfer Equation, the local opticalproperties of this structure are calculated. Thanks to a 3D modeler the basic structural element is thenduplicated with small deviations in its shape, position and orientation for reproducing the overall SEMimage. A photon-mapping is then implemented on this 3D structure with a spectral evaluation of illu-mination maps based on Monte–Carlo ray shooting. The first predictions of this multiscale model arein qualitative and almost quantitative agreement with the white color measured on the elytron of thisinsect and of its spatial dispersion. The brightness of the visual effect is explained by considerations aboutthe human vision.

© 2009 Elsevier B.V. All rights reserved.

1. Introduction

The longhorn beetle Calothyrza margaritifera (Cerambycidae)(see Fig. 1) is an insect popular among collectors, probably becauseit displays a very strange contrasted black and white pattern on itselytra and part of its pronotum (thorax), that gives the insect itspeculiar appearance.

Bright white insects are not rare. All of them use light scatteringby specific structures to produce the broad flat spectrum required.Butterfly wings often display such white structural color, as in thevast family of Pieridae [1]. Diffusive white also appears on tropicalweevils such as Eupholus albofasciatus [2], where grey and whitezones alternate on the cuticle. White and metallic lead to a shiningsilver appearance, which is frequently encountered, as in Chrysinaoptima. Moreover, a complex circularly polarizing chirped multi-layer has been identified on the cuticle of this scarab beetle forwhich, to our knowledge, no consolidated explanation has been

∗ Corresponding author. Tel.: +33 1 4427 4353; fax: +33 1 4427 3982.E-mail address: jacques.lafait@insp.jussieu.fr (J. Lafait).

1 Now at: Hautes Etudes d’Ingénieur, Lille, France.

proposed yet, while similar effects observed on all species of Plusio-tis have been already explained by Caveney as soon as the beginningof the seventies [3].

Brilliant white coloration of some insects, only due to structuraleffects, has recently been investigated. The genus Cyphochilus hasbeen reported [4] to display a whiteness that equals or even sur-passes especially made structures, even though the thickness ofthe hairs is as thin as about 5 �m. The longhorn beetle studiedin our paper announces similar performances, but, as we will see,the physical structure responsible for this whiteness is quite dif-ferent. Calothyrza margaritifera presents a texture which resemblesa white fur. It leads to a mat or diffusive appearance, neverthelessvery bright.

The specimens used in the present study have been obtainedfrom a commercial provider, who identified it to the species level.The origin of these insects can be traced back to Thailand, wherethese longhorns are frequent. Little is known about the biology ofthis insect, so that the functions of these white patches are stilldifficult to assess.

In the next section, we will describe the multiscale structureof the cuticle as observed by different microscopies and deter-mine the relevant quantitative parameters of this structure. We

0921-5107/$ – see front matter © 2009 Elsevier B.V. All rights reserved.doi:10.1016/j.mseb.2009.12.026

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Fig. 1. Adult Calothyrza margaritifera. The dorsal side bears white patches which arethe main object of the present study.

will then present (Section 3) spectral and spatial optical measure-ments, characterizing the color and the associated visual effect. Wewill finally describe (Section 4) the multiscale optical model thatwe have elaborated, which gives a good account of both the whitecolor of the insect and the spatial dispersion of the scattered light,characteristic of the visual effect.

2. Multiscale structure

2.1. Macroscopic and mesoscopic morphology

The regions of interest are the white patches on the elytron onthe back of the insect. The elytron is itself a modified anterior wingdue to the sclerotization of the cuticle. The white is basically dif-fusive, although, under appropriate illumination and orientation,it may give a some fugitive impression of a silver shine. Exam-ination under the reflection optical microscope reveals that thewhite patches are actually a white cuticle covered with a densearray of white hair-like structures that we will name for simplic-ity “hairs”. These hairs are opaque enough to completely hide thecuticle, which can only be seen at places where the hairs have beenaccidentally removed (see Fig. 2). The scanning electron microscope(SEM) confirms the presence of this structure (see Fig. 3). A moredetailed view of the hairs is presented in Fig. 4. The hairs are long(150 �m) and sharp. At their widest they show a thickness of about10–20 �m. But, as can be seen at a higher SEM magnification (seeFig. 5), the cross-section of the hairs is not circular. Moreover, they

Fig. 2. Optical microscope image of a white patch of the elytron of Calothyrza mar-garitifera. White modified scales looking like hairs (150 �m long) cover the whitecuticle, visible in the center where hairs have been teared out.

Fig. 3. Scanning electron microscope (SEM) image of the elytron of Calothyrza mar-garitifera at the separation between white (on the right) and black (on the left)patches. The white modified scales totally cover the cuticle. The colors are invertedas compared to the optical microscope image (the white cuticle looks black becauseit absorbs the electrons).

Fig. 4. SEM image of the surface of the hair-like scales covering the white patcheson the Calothyrza margaritifera elytron. Mean sizes of the hair-like scales: 150 �m(length) × 10–20 �m (largest width).

are slightly flattened with longitudinal ridges only on their dorsalvisible face. The hairs are rigid and obliquely attached to the cuticle,so that they have a visible and a hidden face. The substrate in whichthey are inserted looks like a thin foil of chitin or close materials

Fig. 5. SEM image at higher magnification of the hair-like scales covering the whitepatches on the Calothyrza margaritifera elytron. The cross-section of the hair-likescales is not circular and the surface of the scales bears longitudinal groves on thevisible side.

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Fig. 6. SEM image of the cross-section of the substrate in which the hair-like scalesare planted. A thin chitin foil covers a porous thick layer of chitin agglomerates.

(sclerotized chitin) covering a porous thick layer of agglomeratedballs (see Fig. 6).

2.2. Nanoscopic morphology

In order to identify the intimate structure of each hair-scale, apiece of elytron was cut in liquid nitrogen. As observed in Fig. 7,some of the hairs were cut, at different part of their length, show-ing an interesting internal structure. The hair external surface isactually a hard cortex, presumably made of chitin or chitin withassociated proteins, 520 nm thick, which encloses an empty spacepartially filled with agglutinated spherical chitin particles. No clear

Fig. 7. SEM image of the cross-section of an ensemble of hairs (shown in Figs. 4 and 5)confirming that they are flattened with longitudinal ridges only on their dorsal visi-ble face (a). At higher magnification, the hairs look like bags containing agglomeratedspheres of roughly 550 nm in diameter.

ordering of the spheres is perceivable on any picture. The diameteris remarkably constant, approximately 550 nm for each sphere. Thedistribution of the sphere centers is highly disorganized, except fora tendency to agglutinate into short chains. We have not preciselydetermined the exact composition of the cuticle and the hairs. Nev-ertheless, it is evidently basically chitin, possibly with associatedproteins. Under the point of view of modeling the optical prop-erties, these possible differences in composition will not stronglyaffect the index of refraction of the material. In the following, againfor simplicity, we will therefore use the term “chitin”. It is finallyworth noticing that the bright white colour has been observed andmeasured on a died insect. As usual, the colour due to a struc-tural effect looks very robust and insensitive to the death of theinsect.

3. Optical properties

3.1. Experimental measurements and setup

Three kinds of optical measurements have been performed tocharacterize the optical behavior and the visual aspect of the whitepatches on the back of Calothyrza margaritifera (the angle definitionis represented in Fig. 8): (i) The hemispherical reflectance spectrum,with an illumination under normal incidence (�inc = 0◦), has beenmeasured using an Avaspec 20048/2 fibre-optic spectrophotome-ter equipped with an integrating sphere. A standard diffusive whiteceramic reflector has been used for normalization. This kind of mea-surement reflects very closely the visual aspect perceived by anobserver looking perpendicularly to the cuticle of the insect, whenit is illuminated by natural light (diffuse white light). (ii) A mappingof the scattered flux for different angles of illumination has beenrealized in white light using a scatterometer EZ Contrast (ELDIM).This apparatus images and records in a few seconds the light fluxesscattered in all directions by a sample, in the Fourier plane of alens working with a very large aperture (up to 88◦, limited in ourcase to 60◦). (iii) The BRDF (Bidirectional Reflectance DistributionFunction) spectra have been measured using a goniospectropho-tometer built in the INSP group [5]. The directions of illuminationand detection have been chosen in accordance with the relevantdirections identified on the maps realized with the scatterometer.A standard diffusive reference has again been used for normal-ization. As will be seen further, the results of measurements (ii)and (iii) can be directly compared to the calculations of the modelwhich simulates the same conditions of illumination and detec-tion.

For all these measurements, the positioning of the sample wasa delicate task, due to the bend of the sample and the difficultyto define its orientation. It was nevertheless essential for ensur-ing the reproducibility of the results. The measurements have beenperformed on the right inferior part of the elytra, on a circular areaof about 3 mm in diameter.

Fig. 8. Conventions for the representation of the directions of the illumination (inci-dent: inc) and detected (scattered: sca) flux.

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3.2. Hemispherical reflectance spectrum (Fig. 9)

Under normal incidence illumination, the hemisphericalreflectance of a white zone of the elytron exhibits a quasi flat behav-ior with a slight lack in the lowest part of the visible spectrum, in theviolet-blue, which is overall characteristic of a white aspect. Nev-ertheless, the total reflectance, as normalized by a white reference,is not larger than 60%. The vivid white aspect can therefore onlybe explained by a non-uniform spatial dispersion of the scatteredreflected flux or contrast effects (see further).

3.3. Spatial mapping of the scattered flux (Fig. 10)

This hypothesis is checked by realizing the mapping of the scat-tered flux, also normalized by a white lambertian reference. Theresults are gathered in Fig. 10 where six maps corresponding tosix different angles of illumination �inc (10–60◦) are presented. Thefalse colors (from blue to red) or grey levels (from white to black)represent the intensity of the scattered white light flux. A stronganisotropy of the scattering is observed. A large accumulation ofenergy is noticed on kinds of stripes, perpendicular to the plan

Fig. 9. Experimental hemispherical reflectance spectrum of a white patch on theCalothyrza margaritifera elytron, illuminated under normal incidence, showing aquasi flat response in the visible, with a slight lack in the violet-blue.

Fig. 10. Experimental spatial mapping of the flux scattered by a white patch on the Calothyrza margaritifera elytron, illuminated under variable incidence �inc (10◦ , 20◦ , 30◦ ,40◦ , 50◦ , 60◦ from top to down and left to right). Polar representation: � angles are represented as the radii of the circles (from −10◦ to −60◦ on the left and +10◦ to +60◦ onthe right), while � angles are positioned from 0◦ to 360◦ on each circle.

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Fig. 10. (Continued ).

of incidence, centered on a direction little further the direction ofspecular reflexion. The absolute value of the angles is questionabledue to the bend of the cuticle of the insect. The smaller the angleof incidence, the wider the stripe. A non-neglectible backscatteredflux can also be noticed for low angles of incidence. This kind ofspatial dispersion of the scattered light can be qualitatively under-stood as an incoherent scattering by cylindrical structures muchlarger than the wavelength, located in the plan of incidence. If thehairs were more regularly distributed like the groves of a diffrac-tion grating with sizes comparable to the wavelength, the scatteredlight had been distributed roughly on the same areas but under theform of dots corresponding to the diffraction orders. It has beenalready observed on Morpho butterfly wings [6].

In our case, this anisotropy of the scattered light may partiallyexplain that in some peculiar, but broad, solid angles, the cuticlemay look, for a human observer, whiter than white (i.e. than a whitelambertian reference).

3.4. BRDF spectra (Fig. 11)

BRDF spectra, measured on the goniospectrophotometer andnormalized by the BRDF of a white lambertian standard measured

Fig. 11. Experimental BRDF spectra of the flux scattered by a white patch on theCalothyrza margaritifera elytron, illuminated under an incidence (�inc = 30◦ , �inc = 0◦).The direction of detection is variable (�sca from −10◦ to −60◦ , �sca = 0◦). The overallresponse is flat with a slight lack in the violet-blue. A maximum is observed around�sca ≈ −20◦ .

in the same conditions, are presented in Fig. 11. The illumination isunder the incidence (�inc = 30◦, �inc = 0◦). The direction of detec-tion is variable (�sca from −10◦ to −60◦, �sca = 0◦). As expectedknowing the BRDF mapping presented above (see Section 3.3),the scattered flux exhibits a maximum, here around 20–30◦, at anangle little smaller than expected, but we recall the difficulty toaccurately determine the angles on the elytron. These measure-ments are in overall agreement with the BRDF mapping (Fig. 10).As already observed on the hemispherical measurements, the spec-tral response is almost flat in the visible, with again a slight lack inthe violet-blue. Nevertheless, the relative intensities, as comparedto the white reference, are not so high, less than 60% in average, inagreement with the hemispherical values.

This ensemble of results questioned the vivid white perceptionof a human observer. We have already pointed out the anisotropicspatial dispersion of the light reflected by the elytron, in a solidangle with stripe shape, which can enhance, by contrast, the feelingof white. Moreover, knowing the sensitivity of the human percep-tion to the simultaneous contrast of irradiance, we think that thecontrast between the white and the black zones of the elytron mayreinforce this feeling (see Fig. 1). The vital question for the insect isnevertheless the vision of the predators (birds more than humans).One can imagine that even if their spectral sensitivity is differ-ent (more extended in the ultra-violet), they are also sensitive tothe black/white contrast and can therefore also perceive this whitewhiter than white.

4. Multiscale optical modeling

It is well known, following the Mie scattering principles, thatnon-absorbing particles or agglomerated particles of size compa-rable or larger than the wavelength may produce a white colorin the visible spectrum. It is, for instance, the phenomenon whichoccurs in white clouds. The visual aspect of the structure that wehave observed on the white patches of the Calothyrza margaritiferaelytron is therefore not surprising. The exact role played by themultiscale structure of the fur inserted in the cuticle needed nev-ertheless to be understood and modeled.

4.1. The multiscale model

With this aim, starting from the SEM images we have extractedthe characteristic sizes of the almost similar and representa-

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tive basic scattering structures from the length scale of thenanometer to the millimeter. These parameters have been usedas input in three different optical models applied at three differentscales.

(i) At nanoscopic scale, the scale of the grains present in the chitinbags of the hairs, we have calculated the scattering propertiesof one spherical chitin grain by using the full electromagneticMie model [7]. Our assumptions at this step are relativelycrude: spherical grains, no size distribution (we have takenan average radius of the clusters of 500 nm), no dispersion ofthe chitin optical index taken equal to 1.56, no absorption dueto a possible presence of melanin.

(ii) At mesoscopic scale, the scale of one hair, we have evaluatedthe local reflectance properties of the hair by assimilating, alsocrudely, its structure to a multilayer composed of three par-allel flat layers: (1) an homogeneous chitin layer (thicknessnon-relevant because of the incoherent treatment of light flux)mimicking the first wall of the hair; (2) an heterogeneous layercomposed of a random dispersion of the chitin grains modeledin (i), with a volume fraction estimated to 0.40 and an overallthickness of the layer depending on the thickness of the hairat the position under consideration (between 5 and 15 �m);(3) an homogeneous chitin layer analogous to (1). The opticaldiffuse reflectance of layer (2) has been calculated by solvingthe Radiative Transfer Equation within the 4Flux method [8].This method assumes that the flux scattered by the systemis isotropically distributed in space, in addition to a specu-lar flux. This assumption seemed justified by the roughness ofthe interfaces, which has not been directly taken into accountin the calculation, but which will homogenize the scattering.The properties of this intermediate layer have been then intro-duced in a matrix calculation of the optical isotropic reflectanceof the multilayer [8]. At this step, coherent effects involving thephase of the electromagnetic field have been lost, while theywere present in step (i). On the other hand, multiple scatteringof these fields (in intensity) has been taken into account.

(iii) At macroscopic scale, the scale of the fur, the shape of one hairhas been modeled and, thanks to a 3D modeler, this basic struc-tural element has been then duplicated with small deviationsin its shape, position and orientation for reproducing the over-all SEM image (400 hairs are thus taken into account in thecalculation). A photon-mapping has been then implementedon this 3D structure with a spectral evaluation of illuminationmaps based on Monte–Carlo ray shooting [9,10]. The opticaltrajectory and intensity of any incident ray on the 3D structuredepend on the local orientation of each basic element and itsbidirectional reflectance calculated at the second step (ii). Dueto the difficulty to calculate the exact path of the light througha hair, we assumed a lambertian scattering at each point ofthe hair surface. The model computes, for each spectral band(wavelength), the light reflected in a specific direction of obser-vation (B), which comes from a parallel light source (A) (seeFig. 12).

4.2. Predictions of the model

We will directly present the results of the multiscale modelwhich are the only ones which can be compared with experimentalmeasurements. It is nevertheless worth noticing that as soon as thesecond step (mesoscopic scale) of modeling, the spectral behaviorof the reflectance is already white.

Fig. 13 presents the predictions of the multiscale model for theBRDF spectra of the modeled multiscale structure of the Calothyrzamargaritifera elytron, illuminated under the incidence (�inc = 30◦,�inc = 0◦). The simulated direction of detection is variable (�sca from

Fig. 12. At the scale of the fur (ensemble of hairs), the model computes, for eachspectral band, the light reflected in a specific direction of observation (B), whichcomes from a parallel light source (A).

−60◦ to +60◦, �sca = 0◦). The calculation exactly corresponds to theconditions of the experiment on the goniospectrophotometer, theresults of which have been presented in Fig. 11. An almost flatbehavior, as a function of the wavelength, is observed in these pre-dictions like in the experiment. Nevertheless, the BRDF is slightlyincreasing with the wavelength, whereas a decrease is observedessentially and more clearly in the violet-blue in the experiment.The mean value of the BRDF is in the same range as the experi-ment, around 60%, whereas the maximum also observed around20◦ is larger, 90%. The periodic ripple appearing in the spectra isdue to coherent effect occurring in the scattering by scatterers withmono disperse size, in the framework of the electromagnetic Miecalculation. If a size distribution had been taken into account, thisripple should disappear. The profile of the calculated BRDF hasbeen drawn for the wavelength 550 nm (see Fig. 14). The corre-sponding experimental points of the BRDF measurements on thegoniospectrophotometer have also been put on this graph for com-parison. Their variations follow the calculations and the absolutevalues of the BRDF are in fairly good agreement considering thecomplexity of both the modeling and the measurements. They arealso in fair agreement with the experimental maps realized withthe scatterometer, again with a small shift in the angles due to theexperimental difficulty mentioned repeatedly in this paper. Consid-ering the relatively crude assumptions made in the modeling of thestructure, especially at nano- and meso-scale, we can conclude thatthe mutiscale model tested here for the first time is able to glob-ally predict the optical properties of such a multiscale structure andespecially the white color observed and measured. The decrease ofthe BRDF in the violet-blue region could have been reproduced byintroducing some absorption in the index of refraction of the cuti-cle in this spectral range. However, as we had no evidence of the

Fig. 13. Calculated BRDF spectra of the flux scattered by a model of the multiscalestructure of the Calothyrza margaritifera elytron, illuminated under an incidence(�inc = 30◦ , �inc = 0◦). The direction of detection is variable (�sca from −60◦ to +60◦ ,�sca = 0◦). The overall response is flat with a slight lack in the violet-blue. A maxi-mum is observed around �sca ≈ −10◦ . The ripples are due to coherent effects in theelectromagnetic Mie calculation applied to scatterers with monodisperse size.

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Fig. 14. Calculated (red cross) BRDF profile (at � = 575 nm) of the flux scattered bya model of the multiscale structure of the Calothyrza margaritifera elytron, illumi-nated under an incidence (�inc = −30◦ , �inc = 0◦). The direction of detection is variable(�sca from −60◦ to +60◦ , �sca = 0◦). The blue dots refer to the corresponding measure-ments using the goniospectrophotometer (Section 3.4 and Fig. 12). Measurementsand calculations are normalized to a white lambertian reference.

presence of melanin in the structure, we preferred not to use thishelp. Eventually, the predictions, if they confirm the white behav-ior of this structure, also confirm the measurements showing thatthe values of the BRDF as normalized by the reflectance of a whitereference, do not exceed 60% in average.

5. Conclusion

We have shown that the white color of some zones of theelytra of the longhorn Calothyrza margaritifera mentioned for thefirst time, to our knowledge, in the physics literature, is due toa multiscale structure scaling from the nanometer to the mil-limeter. The main effect at the origin of the white color is theMie scattering occurring inside hair-like structures covering theelytron, due to the presence in these hairs of randomly distributed,agglomerated spherical nanoparticles of chitin. The multiple scat-tering inside each hair is reinforced by the optical incoherent

interactions between hairs covering the cuticle. These effects havebeen observed and measured by using complementary opticaltechniques allowing the measurement of hemispherical and bidi-rectional reflectance together with the mapping of the scatteredflux. The multiscale model developed for describing these prop-erties confirmed the validity of our interpretation. Nevertheless,both the measurements and the model confirm that, even if non-isotropically scattered, the brightness of the white color is neverlarger than a white lambertian reference. We conclude, that thefeeling of vivid white perceived by a human observer can only beexplained by the well known sensitivity of the human perceptionto the simultaneous contrast of irradiance between the white andblack zones of the elytra of Calothyrza margaritifera. Concerning theoptical multiscale model, we can conclude that it is a new tool welladapted to account for the optical properties of multiscale scatter-ing structures. It is presently under improvement in order to be ableto calculate the interaction between not only the light flux reflectedby a structure, but also the transmitted ones.

Acknowledgements

The study was partly supported by the EU through FP6 BIO-PHOT (NEST/Pathfinder) 012915 project. The authors wish to thankFlorent MAHIEU and Raphaël ALFREDO, in Master training courseat INSP, for their help in the experimental characterization of theinsect.

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