Reflectance and transmittance of light scattering scales stacked on the wings of pierid butterflies

The colors of butterfly wings are determined by the structural as well as pigmentary properties of the wing scales. Reflectance spectra of the wings of a number of pierid butterfly species, specifically the small white, Pieris rapae, show that the long-wavelength reflectance of the scales in situ, on the wing, is distinctly higher than that of single, isolated scales. An optical model explains that this is due to multiple scattering on overlapping scales by treating the layers of scales on both sides of the wing as a stack of incoherently scattering plates. The model sheds new light on the adaptive significance and evolution of butterfly wing patterns. © 2006 Optical Society of America OCIS codes: (290.0290) Scattering; (290.5880) Scattering, rough surfaces References and links 1. H. F. Nijhout, The Development and Evolution of Butterfly Wing Patterns (Washington, Smithsonian Institution Press, 1991). 2. J. L. Brink and M. E. Lee, “Confined blue iridescence by a diffracting microstructure: an optical investigation of the Cynandra opis butterfly,” Appl. Opt. 38, 5282-5289 (1999). 3. P. Vukusic and J. R. Sambles, “Photonic structures in biology,” Nature 424, 852-855 (2003). 4. S. Kinoshita and S. Yoshioka, “Structural colors in nature: the role of regularity and irregularity in the structure,” Chem. Phys. 6, 1-19 (2005). 5. H. Ghiradella, D. Aneshansley, T. Eisner, R. Silberglied and H. E. Hinton, “Ultraviolet reflection of a male butterfly: Interference color caused by thin-layer elaboration of wing scales,” Science 178, 1214-1217 (1972). 6. R. Silberglied and O. R. Taylor, “Ultraviolet differences between the sulphur butterflies, Colias eurytheme and C. philodice, and a possible isolating mechanism,” Nature 241, 406-408 (1973). 7. R. L. Rutowski, “The use of visual cues in sexual discrimination by males of the small sulphur butterfly Eurema lisa (Lepidoptera, Pieridae),” J. Comp. Physiol. A 115, 61-74(1977). 8. L. P. Biro, Z. Balint, K. Kertesz, Z. Vertesy, G. I. Mark, Z. E. Horvath, J. Balazs, D. Mehn, I. Kiricsi, V. Lousse and J. P. Vigneron, “Role of photonic-crystal-type structures in the thermal regulation of a Lycaenid butterfly sister species pair,” Phys. Rev. E 67, 021907 (2003). 9. N. Yagi, “Note of electron microscope research on pterin pigment in the scales of pierid butterflies,” Annot. Zool. Jap. 27, 113-114 (1954). 10. H. Ghiradella, “Hairs, bristles, and scales,” in: Microscopic Anatomy of Invertebrates, Vol. 11 A: Insecta . M. Locke, ed., (New York, Wiley-Liss, 1998), pp. 257-287. 11. D. G. Stavenga, S. Stowe, K. Siebke, J. Zeil and K. Arikawa, “Butterfly wing colours: scale beads make white pierid wings brighter,” Proc. R. Soc. Lond. B 271, 1577-1584 (2004). 12. R. L. Rutowski, J. M. Macedonia, N. Morehouse and L. Taylor-Taft, “Pterin pigments amplify iridescent ultraviolet signal in males of the orange sulphur butterfly, Colias eurytheme,” Proc. R. Soc. Lond. B 272, 2329-2335 (2005). 13. Y. Obara, “Studies on the mating behavior of the white cabbage butterfly, Pieris rapae crucivora Boisduval. III. Near-ultraviolet reflection as the signal of intraspecific communication,” Z. Vergl. Physiol. 69, 99-116 (1970). 14. Y. Obara and M. E. N. Majerus, “Initial mate recognition in the British cabbage butterfly, Pieris rapae rapae,” Zool. Sci. 17, 725-730 (2000). 15. G. G. Stokes, “On the intensity of the light reflected from and transmitted through a pile of plates,” Proc. Roy. Soc. 11, 545-556 (1862). 16. T. Smith, “On the light transmitted and reflected by a pile of plates,” Trans. Opt. Soc. 27, 317-323 (1926). #69197 $15.00 USD Received 22 March 2006; revised 8 May 2006; accepted 14 May 2006 (C) 2006 OSA 29 May 2006 / Vol. 14, No. 11 / OPTICS EXPRESS 4880 17. P. Baumeister, R. Hahn and D. Harrison, “The radiant transmittance of tandem arrays of filters,” Optica Acta 19, 853-864 (1972). 18. S. Yoshioka and S. Kinoshita, “Single-scale spectroscopy of structurally colored butterflies: measurements of quantified reflectance and transmittance,” J. Opt. Soc. Am. A 23, 134-141 (2006). 19. S. Yoshioka and S. Kinoshita, “Structural or pigmentary? Origin of the distinctive white stripe on the blue wing of a Morpho butterfly,” Proc. R. Soc. Lond. B 273, 129-134 (2006).


Introduction
Butterflies are generally strikingly coloured, due to light reflected by the wing scales, which are arranged on the wing surface like shingles on a roof.The reflected light commonly results from scattering on the scale structures, the prominent longitudinal ridges and the connecting crossribs.A distinct colour is observed when the scales contain a pigment that absorbs part of the scattered light in a restricted spectral band.Butterflies thus combine physical and chemical colouration methods.The scattered light usually is random and spectrally indistinct, but interference can create striking, intense iridescent colours, as occurs in the multilayers in the scales of the blue Morpho and other nymphalid butterflies (Nijhout 1991;Brink & Lee 1999;Vukusic & Sambles 2003;Kinoshita & Yoshioka 2005).Similar multilayers in the wing scales of male sulphurs cause a strong UV reflectance (Ghiradella et al. 1972;Silberglied & Taylor 1973; Butterfly wing scales -pigmentation and structural properties Rutowski 1977).Photonic crystals in the scales of lycaenids (blues and hairstreaks) result in a blue or green colour (Biro et al. 2003).
Many pierids apply a specific method of structural colouration in order to achieve brightly-coloured wings.The scales are studded with beads (Yagi 1954;Ghiradella 1998) that act as strong scatterers, which enhance the reflectance (Stavenga et al. 2004;Rutowski et al. 2005).The wing scales of the yellow sulphurs (Coliadinae) contain pigments that absorb in the ultraviolet as well as blue wavelength ranges.The distinct yellow wing colour thus is due to the combined effect of strong scattering in the long wavelength range and strong absorption at the shorter wavelengths.The scales of male whites (Pierinae) contain an ultraviolet-absorbing pigment, causing a low UV-reflectance, which is well recognized by butterflies, but not by humans (Obara 1970;Obara & Majerus 2000).
The scales on each side of the wing are usually arranged in two layers, a layer of ground scales and an overlapping layer of cover scales.In order to clarify the optical consequences of the scale layering and their biological significance, we have studied the optics of the butterfly wing scale assembly by measuring reflectance and transmittance spectra of intact wings, of partially denuded wings, and of single, isolated scales of pierid butterflies, and we have analyzed the results with a simple model that treats the scales on the wing as a stack of layers, assuming random scattering.We conclude that pierid butterflies realize their bright wing colourations with stacks of strongly scattering scales, which contain short wavelength absorbing pigments.

Animals
All investigated butterflies belong to the family Pieridae.The Small White, Pieris rapae, was obtained from a culture maintained by Dr J.J. van Loon, Entomology department of the Agricultural University in Wageningen, the Netherlands.The Autumn Leaf Vagrant, Eronia leda, was studied in the butterfly collection of the latter department and in the Royal Museum of Central Africa, Brussels (curator Dr U. Dall'Asta).The Common Jezabel, Delias nigrina, was obtained from Dr M. Braby, Australian National University, Canberra.

Anatomy
The wing anatomy was investigated with standard scanning-electronmicroscopical methods.

Spectrophotometry
Reflectance spectra of intact wings were measured with a reflection probe connected to a fibre optic spectrometer (SD2000, Avantes, Eerbeek, the Netherlands).Reflectance and transmittance spectra of intact as well as denuded wings were measured with an integrating sphere (AvaSphere-50-Refl), connected to the fibre optic spectrometer.Spectra of single scales were measured with a home-built microspectrophotometer consisting of a Leitz Ortholux microscope and the fibre optic spectrometer.A white reflectance standard (Spectralon, Labsphere, North Sutton, NH, USA) served as a reference.

Modelling
The optical model that describes light propagation in a stack of layers assumes non-coherent scattering.Each layer is characterized by reflectances r and s, and transmittances t and u, depending on the direction of the incident light (Fig. 1).The reflected and transmitted light fluxes in a two-layer stack with incident light flux I 1 from one side and I 6 from the opposite side are then described by the following set of equations (Fig. 1a): ; .The transmittance, T = I 5 /I 1 , and reflectance, R = I 2 /I 1 , of the two layer stack then are: (2) A stack consists in general of n layers.Equation (1) (where n = 2) can be generalized as: Butterfly wing scales -pigmentation and structural properties where layer i is characterized by matrix A i (Fig. 1b).By introducing 3) is equivalent to:  (5) It is easy to see that Eq. ( 5) is identical to Eq. ( 2) for n = 2.

Reflectance spectra of intact wings of two pierids
The male Autumn Leaf Vagrant, Eronia leda, provides a characteristic example of the colouration of pierid butterflies (Fig. 2).The dorsal forewings are marked by a prominent orange tip, which highly reflects ultraviolet light (Fig. 2, location

Reflectance and transmittance of light scattering scales stacked on the wings of pierid butterflies
Fig. 2. Reflectance spectra of the dorsal forewing of the male Autumn Leaf Vagrant, Eronia leda (inset: upper -UV, lower -RGB), measured with a fibre optic spectrometer.Spectrum 1 is from the orange tip, which exhibits a pronounced UV band, due to interference reflectors in the scale ridges.The orange colour results from scattered light, filtered by a pigment absorbing in the UV, blue and green wavelength range.Spectrum 2 is from the dorsal forewing area outside the orange tip.The yellow colour results from scattered light filtered by a pigment absorbing in the UV and blue wavelength range.
and spectrum 1).The remaining parts of the dorsal forewings and hindwings have yellow colour (Fig. 2, location and spectrum 2).The orange as well as yellow colours are due to pigments that selectively absorb short-wavelength light scattered at the scale structures, the ridges, crossribs as well as the beads that adorn the scales (Ghiradella 1998;Stavenga et al. 2004;Rutowski et al. 2005).The high reflectance of the tips in the UV results from iridescence in the ridge lamellae (Ghiradella et al. 1972;Silberglied & Taylor 1973;Rutowski 1977).The ventral wings of the male Eronia leda are overall yellow, except for a minute UVreflecting spot in the ventral forewing.E. leda has a distinct sexual dichromatism, as the female has pale yellow dorsal and ventral wings and only ventrally a few scattered UV-reflecting spots.
The dorsal wings of the male Common Jezabel, Delias nigrina, have a simple colour pattern (Fig. 3).The tips of the forewings are black, characteristic of a melanin pigment, and they lack iridescence.The remaining parts of the dorsal forewings and hindwings are white, due to strongly scattering scales.The reflectance is low in the ultraviolet, due to a pigment that absorbs exclusively in the UV (Fig. 3, spectra and locations 1-3).The ventral forewings and hindwings are marked by yellow and red bands (spectra and locations 4 and 5) in a mainly brown-black background (spectrum and location 6).Interestingly, the red bands can be seen at the dorsal side as a slight red sheen, which is reflected in the increase in reflectance in the wavelength range above 560 nm (spectra and locations 1 and 3), corresponding to the wavelength range where the reflectance of the red bands increases (spectrum and location 5).2).The low reflectance below 400 nm demonstrates that the white scales contain a UV absorbing pigment.The red sheen in 1 and 3 is due to bands of red scales at the ventral hindwing (5), which contain pterin pigments absorbing throughout the visible wavelength region, except the red.The yellow bands in the ventral forewing (4) contain UV and blue absorbing pterins.Spectrum 4 has a small foot between 400 and 470 nm due to the contribution of white scales that occur in white spots at the dorsal side.The ventral wings are mainly covered by brown-black scales, due to strongly absorbing melanin pigment (6).
This observation demonstrates that the ventral scales contribute to the dorsal wing reflectance.The opposite also holds, namely the white spots in the tip of the dorsal scales contribute to the ventral wing reflectance, as can be seen from the slight foot at wavelengths above 400 nm in spectrum 4 of Fig. 3.The scales in the white spots at the dorsal side add to the reflectance of the scales in the yellow bands.

Reflectance and transmittance spectra of intact and denuded wings of the Small White, Pieris rapae
We have attempted to assess the relative contributions of the scales to the reflectance on both wing sides by considering the butterfly wing as a stack of plates (Fig. 4), using the formalism described in the Methods.The reflectance was

Thesis -Version8
Reflectance and transmittance of light scattering scales stacked on the wings of pierid butterflies measured with an integrating sphere from both sides of intact wings (DWV, VWD; Fig. 5a), from wings with scales removed on one side (DW, WD, WV, VW; Fig. 5a, b) or from fully denuded wings (Wd, Wv; Fig. 5b).The reflectance of the wings with scales is low in the UV and high at wavelengths above 450 nm.The peak reflectance, around 500 nm, is about 0.6 for the intact wing, but the reflectance of the scaleless wing is about 0.1, virtually independent of wavelength (Fig. 5b).The overall spectral dependence of the transmittance, T(λ), resembles that of the reflectance, R(λ); the transmittance is low in the UV and high in the visible wavelength range (Fig. 5c, d).
Accordingly the absorptance, A(λ) = 1 -R(λ) -T(λ), is high in the ultraviolet and negligible at the visible wavelengths (Fig. 5e, f).The scaleless wing absorbs only slightly in the ultraviolet (Fig. 5f).The absorptance spectra of denuded wing and wings with scales differ in shape, indicating that the pigments in wing substrate and scales differ.
The wing covered by scales can be considered as a stack of layers, each with a specific reflectance and transmittance, depending on the direction of the incident light.The intact wing thus is a three layer stack, consisting of a layer of (partly overlapping) scales at the dorsal side, D, the wing substrate, W, and the layer of scales at the ventral side of the wing, V (Fig. 5).The reflectances r and s and the transmittances t and u (Fig. 1) can be calculated for each of the three layers with the formalism of the Methods.The wing reflectances r W and s W (Fig. 5b) as well as the transmittances t W and u W (Fig. 5d) were measured directly, and further spectral data were obtained for various two layer combinations, DW, WD, VW, or VW, where only one layer of scales was present.c, d) spectra measured from wings of the Small White butterfly, Pieris rapae, in various conditions, together with the resulting absorptance spectra (e, f).The measurements were performed with an integrating sphere.The wing was intact for the conditions DWV and VWD, where D indicates the dorsal side of the wing, W is the wing substrate, and V is the ventral side.The order of the letters indicates the direction of the incident light.For DW and WD, the wing scales were removed at the ventral side, and for VW and WV, the wing scales were removed at the dorsal side.For Wv and Wd, both dorsal and ventral scales were removed, and the incident light came from the ventral (v) and dorsal side (d), respectively.The scales contain a strongly UV absorbing pigment, resulting in a very low transmittance, or, a very high absorptance, in the ultraviolet.The wing scales strongly scatter in the visible wavelength range.The wing reflectance is virtually constant throughout the whole spectral range, with amplitude about 0.11 (b), and the wing substrate contains a small amount of pigment that absorbs in the UV (f).The results for the dorsal scales are given in Fig. 6a and those for the ventral scales in Fig. 6b.The absorptance for the D-scales with illumination from the dorsal (d) side was calculated from a Dd = 1 -r D -t D , and the absorptance with illumination from the ventral (v) side from a Dv = 1 -s D -u D (Fig. 6a).Similar expressions hold for the V-scales (Fig. 6b).

Reflectance and transmittance of light scattering scales stacked on the wings of pierid butterflies
Knowing the spectral data for all three layers (D, W, and V) allows calculation of the reflectance and transmittance spectra of the intact wing, for example the three layer stack DWV.This produced the calculated reflectance R c = R DWV and transmittance T c = T DWV (Fig. 6c).The calculated spectra have a similar shape as the measured spectra, R m and T m (Fig. 5a, c), but the calculated reflectance is too small, and the calculated transmittance is too high (Fig. 6c).The corresponding absorptances, A m and A c , calculated from A m,c = 1 -R m,c -T m,c , closely agree.

Reflectance and transmittance spectra of single scales
Butterfly scales are more or less flat structures (Fig. 4), but they are quite asymmetrical.The face toward the side of the wing (adwing) is rather smooth, but the opposite side (abwing) is highly structured (inset Fig. 7b).We have measured the reflectance of single scales, glued to the tip of a thin glass rod, with a microspectrophotometer (Fig. 7a, b).We investigated both faces of ground and cover scales from both the dorsal and ventral side of the scale.The reflectances of both scale faces slightly differ, and the reflectance spectrum also depends Butterfly wing scales -pigmentation and structural properties somewhat on the type of scale.The peak reflectance is roughly 0.3 in both cases, at about 500 nm, but the reflectance in the UV is lower for the scale surface not facing the wing (Fig. 7a).
The reflectance clearly depends on the scattering on the scale structures as well as on the ultraviolet-absorbing pigment.To assess the amount of absorption in a single scale, we measured the transmittance of various scales embedded in xylene, an immersion fluid with a refractive index approximating that of insect cuticle (Stavenga et al. 2004) (Fig. 7c).Fig. 7c also contains a transmittance spectrum calculated from the absorptance spectra of Figs. 5 and 6.The calculation was performed as follows.It was assumed that the absorption process in the layers can be approximated with Lambert-Beer's law.The absorbance then is The absorptance spectra of Figs.5e and 5f thus yielded absorbance spectra, which after normalization appeared to be very similar.The mean of the normalized absorbance spectra was therefore used to calculate a transmittance spectrum (Fig. 7c, bold curve, LB) with an amplitude in the ultraviolet of 0.15, about equal to the transmittance in the UV of the immersed scales.The calculated transmittance spectrum deviates from the measured transmittance spectra.Presumably xylene does not fully annihilate the difference in refractive index of the scale structures with that of the surrounding medium, which can be understood, because probably the refractive index of pierid scales is not constant.The transmittance then remains affected by scattering.Another reason for the deviation may be the limited applicability of the model, which assumes perfectly diffuse light (see Chapter 6).

Reflectance spectra of a stack of scales
We have used the model for a stack of reflecting and absorbing plates (Section 3.2) to calculate the reflectance of a multilayer of butterfly wing scales on the wing.The measurements of Fig. 7 demonstrate that the reflectance slightly depends on the type of scale (cover or ground).The reflectance also depends on which side of the scales faces the incident beam.We nevertheless assumed a stack of identical scales, with abwing (r) and adwing (s) reflectances equal to the mean of the measured spectra (bold curves of Figs.7a and 7b, respectively).The scale transmittances t and u (Fig. 1) were calculated from t = 1 -r -a and u = 1 -s -a, where the absorptance is a = 1 -t LB , with t LB the transmittance given by the bold curve in Fig. 7c.
The resulting reflectance spectra of various stacks of scales on the wing are given by Fig. 8.The reflectances of both sides of the denuded wing were assumed to be equal to the average (W) of the two wing reflectance spectra given in Fig. 5b.Spectrum SW of Fig. 8 presents the reflectance spectrum of a wing with one layer Thesis -Version8 Butterfly wing scales -pigmentation and structural properties Fig. 8. Reflectance spectra calculated for a set of identical scales stacked on the wing.The reflectance of the scaleless wing (W) is the average of the spectra Wd and Wv of Fig. 5b.SW is the reflectance calculated for a single layer of scales at the wing, with the reflectance r taken to be the mean abwing reflectance of Fig. 5b and s is the mean adwing reflectance of Fig. 5b.The illumination is from the side of the scale, S. SWS is the reflectance when a single scale exists on both sides of the wing.SSWS has two layers of scales on the side of the wing from which the illumination comes, and one layer of scales on the other side of the wing; and so on.

Discussion
Butterfly scales are extremely thin, in the order of hundreds of nanometers.Not surprisingly, multilayer interference plays therefore a dominant role in many cases of butterfly colouration.This is specifically the case in the cover scales on the dorsal wings of male sulphur butterflies (Ghiradella et al. 1972;Silberglied & Taylor 1973;Rutowski 1977;Rutowski et al. 2005), and in the tips of male pierid butterflies of the Colotis group (Fig. 2).
Stokes (Stokes 1862) gave the first theoretical treatment of light reflected and transmitted by a pile of plates where interference effects are negligible, which was followed by a few more elaborate studies on stacks of thick layers (Smith 1926;Baumeister et al. 1972).We have presented here a simple recursion procedure for calculating the incoherent light flux in a stack of plates.For the modelling we have assumed that the layers are sufficiently rough so that interference effects are averaged out.The reflectance and transmittance spectra are then determined by light scattering on the scale structures as well as by the absorbing pigments.Using spectra measured on wings of the Small White butterfly (Fig. 5a-d) we have Reflectance and transmittance of light scattering scales stacked on the wings of pierid butterflies derived the reflectance and transmittance of the scale layers on each side of the wing (Fig. 6a, b).The calculated spectra for the reflectance and transmittance of an intact wing did not completely match the measured spectra, however (Fig. 6c).This implies that the assumption of random scattering is not fully valid.In addition, coherence may be not fully negligible.The general features are nevertheless very clear.The wing reflectance of the Small White is not exclusively determined by the scales on one side, but also the scales on the other side of the wing contribute.
The maximal wing reflectance of the Small White is about 0.6 (Fig. 5a).This corresponds to the reflectance value obtained for a stack of two scale layers on each side of the wing (Fig. 8, SSWSS).Light and scanning electron microscopical observations indeed show that in average about two scales overlap at the wings of the Small White (Fig. 4).The wing reflectance of the Large White, Pieris brassicae, can go up to 0.8, in agreement with our observation that stacks of effectively three to four scales overlap in this species.Similarly, the dorsal wings of the Common Jezabel (Fig. 3) have a high reflectance as well as several layers of overlapping scales.In the latter case, the white reflectance is mainly due to scales on the dorsal side of the wings, because most scales at the ventral side contain a dense brown-black pigment.The scales in the striking red bands at the ventral wing noticeably contribute to the dorsal reflectance in the longwavelength region (Fig. 3, spectra 1 and 3).
Enhancement of reflectance by multilayers of scales has been recently reported for Morpho butterflies by Yoshioka and Kinoshita (2006b).They have used a three layer wing model similar to that used above, but the procedure presented here is easier and more generally applicable.
The wing reflectance is only a few percent in the ultraviolet for all cases presented here.This is due to pigments absorbing in the short-wavelength range, even in the white wings.Stacking several scales at the wing enhances the reflectance at the long-wavelengths; meanwhile the short-wavelength reflectance stays low.The pierid butterflies achieve a strong, saturated colour by combining a distinct short-wavelength absorption with strong long-wavelength scattering, which is realized by a multitude of nanometer-sized beads (Stavenga et al. 2004).The strong colouration plays an important role in mutual, intersexual recognition (Obara 1970).This will be especially the case where the male adds a strong direction-depending iridescence in the ultraviolet (Ghiradella 1998;Rutowski et al. 2005) to a yellow or orange pigment colour (Fig. 2).
In conclusion, we have demonstrated that the reflectance of butterfly wings results from the coordinated effect of reflectances of single scale that are arranged in stacks on the wings.This insight will be of considerable significance for biologists working to understand the adaptive significance and evolution of butterfly wing patterns.

.
light I 1 , I 2n+2 = 0 or ρ n+1 = 0, which allows calculation of the values of ρ i and τ i by recursion.Starting from i = n, it follows that τ n = t n , ρ n = r n ,

Fig. 1 .
Fig. 1.Diagrams of the light flux in a pile of plates.a Two rough layers, 1 and 2, each with reflectances r and s and transmittances t and u, separate three media, 1 -3.b Layer i of a stack of n layers separates media i and i+1.

Fig. 3 .
Fig. 3.Reflectance spectra of various parts of the wings of the male Common Jezabel, Delias nigrina (inset: upper -dorsal, and lower -ventral), measured with a fibre optic spectrometer.The reflectance of white areas is high and constant in the visible region (2).The low reflectance below 400 nm demonstrates that the white scales contain a UV absorbing pigment.The red sheen in 1 and 3 is due to bands of red scales at the ventral hindwing (5), which contain pterin pigments absorbing throughout the visible wavelength region, except the red.The yellow bands in the ventral forewing (4) contain UV and blue absorbing pterins.Spectrum 4 has a small foot between 400 and 470 nm due to the contribution of white scales that occur in white spots at the dorsal side.The ventral wings are mainly covered by brown-black scales, due to strongly absorbing melanin pigment (6).

Fig. 4 .
Fig. 4. Scanning electron microscopy of wings of the Small White Pieris rapae.a Rows of cover (c) and ground (g) scales are stacked on the wing substrate.b Side view of a cut wing, showing cover and ground scales on both dorsal and ventral sides of the wing.Bar: 50 µm.

Fig. 5 .
Fig. 5. Reflectance (a, b) and transmittance (c, d) spectra measured from wings of the Small White butterfly, Pieris rapae, in various conditions, together with the resulting absorptance spectra (e, f).The measurements were performed with an integrating sphere.The wing was intact for the conditions DWV and VWD, where D indicates the dorsal side of the wing, W is the wing substrate, and V is the ventral side.The order of the letters indicates the direction of the incident light.For DW and WD, the wing scales were removed at the ventral side, and for VW and WV, the wing scales were removed at the dorsal side.For Wv and Wd, both dorsal and ventral scales were removed, and the incident light came from the ventral (v) and dorsal side (d), respectively.The scales contain a strongly UV absorbing pigment, resulting in a very low transmittance, or, a very high absorptance, in the ultraviolet.The wing scales strongly scatter in the visible wavelength range.The wing reflectance is virtually constant throughout the whole spectral range, with amplitude about 0.11 (b), and the wing substrate contains a small amount of pigment that absorbs in the UV (f).

Fig. 6 .
Fig. 6.Calculations of the reflectance, transmittance and absorptance of the dorsal (a) and ventral (b) scale layers, using the data of Fig. 5 and the formalism described in the Methods.c The reflectance and transmittance spectra measured from the intact wing (Fig. 5a and 5c, DWV), R m and T m , are compared with the calculated spectra, R c and T c .The calculated reflectance (transmittance) is somewhat smaller (larger) than the measured reflectance (transmittance).The absorptances are calculated with A m,c = 1 -R m,c -T m,c .