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It is well known that the wing scales of butterflies and moths have elaborated microstructures that cause various optical effects. structural colors occur when the microstructures have a size comparable with the wavelength of light. On the other hand, the wing scales of some species are structurally modified at a size much larger size than the light wavelength. Here we show for the Madagascan sunset moth that not only the microstructures but also the large-size modifications can play an important role in scale coloration. The wing of the sunset moth shows a striking iridescence that is caused by the air-cuticle multilayer structure inside the wing scales. Further, the scale itself is highly curved from its root to distal end. Owing to this strong curvature, a deep groove structure is formed between adjacent two rows of the regularly arranged scales. We find that this groove structure together with multilayer optical interference produces an unusual optical effect through an inter-scale reflection mechanism; the wing color changes depending on light polarization. A model is proposed that quantitatively describes this color change.
©2007 Optical Society of America
1. Introduction
It is well known that the wing scale of butterflies and moths exhibits various optical effects owing to the interaction between the microstructures inside the scale and light [1, 2, 3, 4]. A wing scale generally consists of several structural elements called ridge, crossrib, microrib, trabeculae [5, 6]. When at least one of those elements is modified into a periodical structure comparable with the wavelength of light, it can cause optical interference to result in beautiful iridescence. A lot of such modifications have been already known. For example, a discrete multilayer structure is found inside the ridges of the famous Morpho butterflies’ scales [7, 8, 9], and a photonic-crystal-like structure exists in the lower part of the scale of butterflies [10, 11].
Another distinctive example of structural color is the Madagascan sunset moth whose wings exhibit striking iridescence as shown in Fig. 1. In the early 20th century,Mason performed thorough optical investigations of this moth and reached the conclusion that the optical properties of the wing were consistent with those of a stack of 5-10 thin layers, which were expected to lie in the basal part of the scale [12]. As it was expected by Mason, the existence of the air-cuticle multilayer structure was actually confirmed later by electron microscopy [13]. Since then, this structural feature has attracted much attention as the origin of the striking iridescence.
On the other hand, Mason reported another characteristic of the scale; it is highly curved along its longer side. Namely, the scale has the shape of a longitudinally curved rectangular plate having a length of about 250 μm, a width of 100 μm and a thickness of several μm. Unlike the multilayer characteristic of the structure, the optical function of this strong curvature has not been paid much attention to as if it has been forgotten since Mason’s first observation.
Here we report that the strong curvature of the scale plays a very important role in the coloration mechanism of the Madagascan sunset moth; it produces an unusual polarization effect of the wing through the inter-scale dual reflection. Therefore, the structural color of this moth does not solely come from the multilayer optical interference, but from the cooperation between the two structural modifications in completely different sizes.
2. Materials and methods
The sample of the Madagascan sunset moth, Chrysiridia rhipheus Drury 1773, was purchased from Mushi-sha, Japan. (Several scientific names refer to this species such as Urania ripheus.)
The microscopic structure of the wing scale was observed by a transmission electron microscope (TEM), Hitachi H-7650. The surface structure of the scale was observed by a scanning electron microscope (SEM), Hitachi S-800, after the sample was sputtered with platinum.
The arrangement on the wing scales was observed by an optical microscope, Olympus BX- 50, equipped with a Xe lamp under epi-illumination. To investigate the polarization dependence, the reflected light was analyzed by a plane polarizing filter while the illumination was kept unpolarized. For this purpose, we employed a polarization-insensitive cube beam splitter (Edmund Optics) inside the microscope that reflected the illuminating light from the lamp downward.
The polarization dependence of the reflectance spectrum was investigated using an optical system shown in Fig. 2. The light reflected into a direction by 8 ° deviated from the incident beam was collected by a lens with an aperture of about ±1 ° and focused on one end of an optical fiber, while the other end was connected to a spectrometer, Ocean Optics USB2000. The polarization dependence of the spectrometer was nullified by a quartz-made depolarizer. The sample was placed such that the longer side of the scale was in the plane of reflection and it was illuminated with a spot size of several mm2. The reflectance was obtained by dividing the spectrum by that of the white standard of a BaSO4 plate. We define s- and p-polarization in the conventional way; the electric vector of the s-polarized light is perpendicular to the plane of reflection, while that of p-polarized light is parallel to the plane.
3. Structural investigation
The wing of the Madagascan sunset moth is variously colored as shown in Fig. 1. We have investigated several areas with different colors. However, here we restrict our description within the red purplish area of the ventral hind wing, since the color difference is largely due to the variation in the thickness of the multilayer structure, and the optical characteristics can be analogically discussed. The complete description of the color variation will be published elsewhere.
First we have investigated the micro- and macroscopic structure of the scale. Figure 3(a) shows a cross-section of the hind wing, where the scales on the wing membrane are longitudinally sectioned. The upper surface corresponds to the ventral side and the lower does to the hairy part of the dorsal side. It is immediately noticed that the scales are highly curved as reported previously [12]. In the proximal part the scales are almost flat. However, they are gradually curved up, reach the top, and steeply bent down to the distal end. Owing to this strong curvature, the two adjacent rows of scales form a valley-like deep groove between them, whose angle is found to be 80-100°. It is also noticed that a scale overlaps the proximal part of the next scale. In general, a lepidopteran wing is covered with two kinds of scales, called ground and cover scales [5, 14]. The curved scale of this moth belongs to the cover scale, and there exist almost flat, black ground scales below the layer of the curved cover scales.
Fig. 2. Experimental setup for the measurement of the polarization dependence of the reflectance spectrum. Unpolarized white light from a Xe lamp is focused on the sample after the spot size is controlled by an aperture to be several mm2. The light reflected into 8° from the incident light beam is collected by a lens and focused on one end of an optical fiber, which guides the light into a spectrometer. The reflected light passes through a polarizer and also a quartz-made depolarizer that nullifies the polarization dependence of the spectrometer.
The upper surface of the scale has been observed by using a scanning electron microscope. Figure 3(b) shows that longitudinal ridges are present on the surface. However, the width of ridges is rather thin, 0.4 μm, and they are sparsely located to each other with a large separation of 3.5 μm. Further, the cross-ribs, which connect the adjacent longitudinal ridges, are not present unlike generally in lepidopteran scales [5, 6]. These observations indicate that the reflection of the scale is mostly due to the basal layer of the scale.
Figure 3(c) shows transmission electron microscopic images of a longitudinal cross-section of a scale. It is clear that the basal layer consists of air- cuticle alternate layers all over the scale. However, the number of the cuticle layers is not uniform; there exists only one cuticle layer in the proximal part, while the layer number rapidly increases to a maximum of 6 before reaching the top of the curved scale. Detailed inspection of various parts of one scale reveals that one cuticle layer has an almost uniform but slightly distributed thickness of 170 ± 20 nm, while the air-spacing between the cuticles layer is more distributed from 100 to 150 nm, with average 130 nm. The cuticle layers are stratified with the randomly-located connecting blocks of cuticle that maintain the air spacing. In Fig. 3(c), the air spacing seems to slightly increase around the distal part. However, this increase is not reproducibly observed in other scales.
4. Optical investigation
Figures 4(a) and (b) show the scale arrangement observed with a polarization microscope. It looks very peculiar at a glance; a stripe pattern is observed that consists of two differently colored bands, a narrow red-purplish band and a broader yellow one. These bands run laterally from one scale to another and are observed to be metallically glittering, implying that the reflection is rather specular. Careful inspection reveals that the red-purplish band is located at the top part of the curved scale, while the yellow band exists around the valley formed between adjacent two scales. Further, the intensity of the yellow band strongly depends on the analyzing direction, while the red-purplish band does not.
Fig. 3. Structure of the wing scales and their arrangement. (a) Microscopic image of a longitudinal cross-section of the hind wing. The upper surface corresponds to the ventral side of the red-purplish area and the lower to the dorsal side of the black hairy part. Scale bar: 300 μm. (b) Scanning electron microscopic image of the upper surface of the scale. Scale bar: 12 μm. (c) Transmission electron microscopic (TEM) images of the longitudinal cross-section of the scale. The center shows an assembled TEM image showing the whole curvature of the scale. The centeral black part is a part of the metal grid upon which the cross-sectioned sample was placed. Note that the longitudinal cross-sections of two scales are seen because they laterally overlapped. The surrounding eight TEM images under higher magnification show an alternate air-cuticle multilayer structure. Scale bar: 2 μm.
Fig. 4. Polarization dependence of the red purplish part of the ventral hind wing and a schematic illustration of the reflection mechanism. (a) and (b): Polarization-dependent images of the scale arrangement taken with the same exposure time. White arrows show the analyzing direction of the reflected light, while the illuminating light is unpolarized. The right upper black area corresponds to the wing area of the black patch. Scale bar: 200 μ of the scales (purplish red arrow) and the other path is the dual reflection between adjacent scales (yellow arrows). (d) and (e): Wing-color change depending on the analyzer direction, indicated by white arrows, under unpolarized light illumination. Scale bar: 3 mm
These peculiar phenomena can be understood by the two paths of reflection as depicted in Fig. 4 (c): one is the direct reflection from the top flat part of the scale and the other is the dual reflection between adjacent scales. The color difference of the two bands is qualitatively explained by the incidence angle of light to the multilayer structure, since the interference condition is satisfied at shorter wavelength under oblique incidence, which is the case of the dual reflection path. Further, the observed polarization dependence is consistent with the general feature of the oblique reflection; s-polarized light is more strongly reflected than p-polarized light. These features will be quantitatively discussed later.
Since the two bands are located too closely to be separately observed by the naked eyes, the mixture of the two different colors is perceived as the wing color as the whole. Further, it is expected that the wing color changes depending on the polarization owing to the large intensity change in one of the two bands. Figures 4(d) and (e) show that the color change is actually observed from orange to purplish red depending on the analyzing direction.
Fig. 5. Experimentally determined reflectance of the wing and a schematic illustration of multilayer optical interference. (a) Reflectance of the wing for two analyzing directions of the reflected light under the illumination of unpolarized light. The black and grey lines show the results for s- and p-polarization, respectively, and the broken line is the difference of the two. The accompanying letters, s, p and s-p, indicate the polarization. The experimental setup for this measurement is shown in Fig. 2. (b) A schematic illustration of multilayer optical interference. The parameters nc (na), dc (da), and θc (θa) are a refractive index, a thickness, and a refraction angle in the cuticle layer (the air spacing), respectively.
We have measured the reflection spectrum to quantitatively characterize this color change. It is found that the reflectance obtained from the experiments have two broad components; one is a small peak around 420 nm commonly observed for the two polarizations (Fig. 5(a)). The other is a broad reflection band in a longer wavelength region. Inspection of the spectral line shape of the shorter wavelength side reveals that the reflectance of the s-polarized light starts increasing around 530 nm, while that of p-polarized light does around 550 nm. As a consequence, the difference of the two spectra appears as a broad peak in the wavelength region 550-800 nm. This difference is thought to be attributed to the intensity change of the yellow band of the dual reflection.
5. Analysis
5.1. Optical interference condition of the multilayer structure
Here we consider the optical interference condition of the multilayer structure, shown in Fig. 5(b), to explain the wavelength of the reflected light. the results of the electron microscopic observations, the following structural parameters are used for this analysis; the thickness of the cuticle layer dc=170 nm, whose refractive index (nc) is assume to be 1.55, and the air spacing da=130 nm with refractive index na=1.0. The wavelengths (λ) of the constructively interfering light under normal incidence are calculated to be 787 and 394 nm for m=1 and 2, respectively, where m is an integer defined in the interference condition 2 (ncdc+nada)=mλ. Since the reflection of the direct reflection path occurs under normal incidence, it is roughly understood that the long-wavelength reflectance and the smaller peak near 400 nm are caused by the first and second order optical interference, respectively. For the dual reflection path, assuming an incidence angle of 45° gives the maximum reflectance at λ=653 nm for m=1 according to the relation, 2(ncdc cosθc+nada cosθa)=mλ , where θc=27° and θa=45° are the angles of refraction inside the cuticle and air layer, respectively. This wavelength corresponds to the peak of the difference spectrum fairly well (Fig. 5(a)), and this correspondence strongly supports the idea that the color change originates from the polarization-dependent reflectance under oblique incidence.
5.2. A model of the uniform and regular multilayer structure
As discussed above, the interference condition can successfully explain the wavelengths of the peak of the reflectance. However, it is also meaningful to discuss the spectral line shape, because the perceived color is not solely determined by the peak wavelength but by the whole spectrum of reflection. Further, we will come to know the quantitative aspects of the reflection mechanism by decomposing the spectral line shape into two for the two reflection paths. Here we consider a simple optical model for this purpose. We assume two terms in the reflectance Ri(λ) of the wing for i-polarized light,
The first and second terms correspond to the direct and dual reflection path, respectively, and R 0(λ) and R i 45(λ) are the reflectance of the multilayer structure under 0° and 45° incidence for i-polarized light, respectively. The factor A is the ratio of the illumination areas of the two contributions. To determine the factor A, we consider an optical model for the arrangement of the curved scales as shown in Fig. 6, which consists of laterally arranged arcs of 90°. This model is not exactly similar to the cross section shown in Fig. 3(a). However, it is one of the simplest structures that cause both the direct and dual reflection of the light, which are the essential parts of the coloration mechanism. We can trace the ray of reflection on the basis of geometrical optics and estimate the effective areas that reflect light into the angular range of the observation as follows. Here we assume that the incident light comes from the direction that is normal to the plane of the arranged arcs, which is depicted as the dashed-dotted line in the left arc in Fig. 6, which specify the direction of the reflected light and the illuminated part on the arc, respectively. Further, it is assumed for simplicity that the light reflected in the angular range -1° <qref <1° is detected by the spectrometer, although the light was experimentally collected at the direction slightly shifted from that of the incident light beam. It is easily understood that the light that falls on the range -0.5° <qarc < 0.5° of the arc is directly reflected into the observation range. On the other hand, a numerical ray-tracing calculation reveals that the light illuminating the edge of the arc with the angular range of 0.25° (44.75° <θarc < 45°) approximately contributes to the observation through the dual reflection path. Thus, A is calculated to be A≈0.25/0.5cos45° ≈0.35, where cos45° is the inclination factor of the plane to the incident flux.
Fig. 6. Optical model for the surface structure of the curved scales. It consists of laterally arranged arcs of 90°. The angles θref and θarc are defined as the angles from the direction normal to the plane of the arranged arcs, which is depicted by the dashed-dotted line in the left arc.
Fig. 7. Reflectance of the multilayer system and of the wing of the moth. (a) Reflectance determined by the transfer matrix method for the multilayer system which is assumed to consist of 6 cuticle layers and 5 air gaps with thicknesses of 170 and 130 nm, respectively. A refractive index 1.55 is used for the cuticle layer. Black and broken lines show the calculated reflectance for s- and p- polarizations under 45 ° incidence, respectively, and the grey line is the reflectance under normal incidence. (b) The polarization dependence in the reflectance of the wing. The spectra are calculated according to Eq. (1) with A=0.35 by using the reflectance shown in (a). Black and grey lines are the results for R s(λ) and R p(λ), respectively and the broken line shows the difference of the two.
We have theoretically determined the reflectance R 0(λ) and R i45(λ) by using the transfer matrix method for 6 cuticle layers as shown in Fig. 7(a). The same structural parameters are used as in the above discussion. We can see that there is a distinctive difference in magnitude between the two polarizations for 45° incidence; the reflectance of s-polarized light is almost saturated to be unity from 570 to 800 nm, while that of p-polarized light is only a broad peak centered at 665 nm. According to Eq. (1), this difference should cause the polarization dependence of the wing reflectance as shown in Fig. 7(b). Compared with the experimental results (Fig. 5(a)), the calculation roughly reproduces the tendency of the polarization dependence. However, poor agreement is noticed when we compare the spectral line shape. This disagreement obviously results from the characteristic line shapes of the reflectance shown in Fig. 7(a). In the transfer matrix method, uniform and perfectly smooth layers are assumed. This perfect regularity causes optical interference of the reflected lights with a constant phase relationship even after the infinite times of reflection among the multilayer structure. This causes the saturation of the reflectance and multiple side bands besides the main band. On the other hand, the biological reflector usually involves structural irregularities such as an uneven surface, existence of scattering particles, and a variable layer thickness [4, 15, 16]. In fact, the TEM images show that there are a lot of connecting blocks between the cuticle layers that may scatter the light. Further, the layer thickness is not perfectly uniform but distributed. Thus, it is necessary to take these irregular aspects into account to reproduce the experimental results.
5.3. A modified model for partially irregular multilayer structure
A general optical theory for partially irregular multilayer system has not been developed. However, it is thought that the irregularities, for example, small particles or bumps on the multilayer, scatters light into a broad angular range of direction, which is different from that considered in multilayer optical interference. Actually, it has been reported that the reflection from a single scale of the sunset moth is not perfectly specular but broadened to some extent [17]. This can be accounted for by considering the imaginary part of the refractive index as the effect of this scattering. That does not mean the inclusion of optical absorption but the empirical introduction of the extinction of the light wave in the treatment of optical interference. Further, it is possible to treat the distribution of the layer thickness as a statistical average. Figure 8(a) shows an example of a reflectance spectrum obtained with these considerations; the refractive index of the cuticle is assumed to be 1.55+0.1i and the statistical average is imposed for the distribution of the layer thickness with a distribution function exp(-x 2/a 2), where x is the percentage deviation from the mean thickness and a=10 % is assumed. In this calculation, assuming that the thicknesses of the all layers deviated by the same percentage from the original thickness, the reflectance can be determined by the transfer matrix method as a function of x, and averaged with the above distribution function. Figure 8(b) shows the polarization dependence of the wing reflectance expected from this model. Although not completely perfect, a much better agreement with the experimental results is seen. The introduction of the imaginary part of the refractive index dulls the square-like spectral shape and the distribution of the thickness smoothes the dip between the main and side bands. One remaining disagreement is caused by the smaller factor of A, since it makes the contribution of the dual reflection smaller. The microscopic images of Figs. 4(a) and (b) show that the yellow band looks rather broad indicating its larger contribution, while the model shown in Fig. 6 expects that the dual reflection is effective only in the vicinity of the edge of the arcs. Thus, better agreement can be obtained if we consider a more complicated model which has a similar surface structure to the actual shape of the cross section.
Fig. 8. Reflectance of the multilayer system with irregularities and of the wing of the moth. (a) Reflectance calculated by a theoretical model containing the irregular aspects of the multilayer structure. The complex refractive index and the distribution of the layer thickness are assumed. See the text for detail. Black and broken lines are the reflectance of 45° incident light for s- and p- polarizations. The grey line is the result for normal incidence. (b) Polarization dependence of the reflectance of the wing. The spectra are calculated according to Eq. (1) with A=0.35 by using the reflectance shown in (a). Black and grey lines are the results for R s(λ) and R p(λ), respectively, and the broken line shows the difference of the two.
We do not infer that the present treatment is exclusive for the irregularities-involved multilayer system. Nevertheless, it is obvious that the usual uniform multilayer model is too simple to explain the optical properties of the actual wing of the sunset moth. The irregularities of the structure largely affect the angular dependence of reflection; it becomes more diffuse rather than specular. The diffuse nature of the reflection may have some biological significance as is suggested in other species of butterflies [7, 18] and a crab [15].
6. Discussion
It has been already reported that the wing scale of an Indonesian Papilio butterfly exhibits the dual reflection of light and produces the color mixing effect of two different colors [19].
However, a polarization-dependent wing color is not observed in this butterfly, since the spherical nature of the surface structure is the origin of the dual reflection. On the other hand, the cylindrical characteristic of the grooves formed by the scale row causes the stronger polarization effect in the sunset moth. Namely, even under illumination of unpolarized light such as sunlight, the wing color can be observed differently depending on the polarization. Recently, several studies have shown that some species of butterflies utilize the information carried by polarized light [20, 21, 22]. Although the biological significance is unknown at the present stage, the polarization-dependent wing color may work as a visual signal among these species, if they have the polarization and color vision, which is usual for insects. Physiological and behavioral studies are strongly encouraged to demonstrate whether or not the sunset moth indeed employs this signaling system.
In investigating the mechanism of structural colors of animals, it is obviously important to clarify microstructures having a comparable size with the wavelength of light. However, our results clearly demonstrate that optical effects can be produced in a more comprehensive way that includes much larger structural modifications.
Acknowledgments
The authors thank Dr. C. Koshio (Naruto University of Education) and Dr. U. Jinbo (The University of Tokyo) for their help in taxonomy. This work is supported by a Grant-in-Aid for Scientific Research (No. 18740261) from the Ministry of Education, Culture, Sports, Science and Technology.
References and links
1. M. Srinivasarao, “Nano-optics in the biological world: beetles, butterflies, birds, and moths,” Chem. Rev. 99, 1935–1961 (1999). [CrossRef]
2. A. R. Parker, “515 million years of structural color,” J. Opt. A: Pure Appl. Opt. 2, R15–R28 (2000). [CrossRef]
3. P. Vukusic and J. R. Sambles, “Photonic structures in biology,” Nature 424, 852–855 (2003). [CrossRef] [PubMed]
4. S. Kinoshita and S. Yoshioka, “Structural colors in Nature: the role of regularity and irregularity in the structure,” ChemPhysChem 6, 1442–1459 (2005). [CrossRef] [PubMed]
5. H. Ghiradella, “Light and color on the wing: structural coors in butterflies and moths,” Appl. Opt. 30, 3492–3500 (1991). [CrossRef] [PubMed]
6. H. Ghiradella, “Hairs, bristles, and scales,” in Microscopic anatomy of invertebrates, 11A: Insecta, M. Locke ed. (Wiley-Liss, New York, 1998), pp. 257–287.
7. P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, “Quantified interference and diffraction in single Morpho butterfly scales,” Proc. R. Soc. Lond. B 266, 1403–1411 (1999). [CrossRef]
8. S. Kinoshita, S. Yoshioka, and Kawagoe, “Mechanisms of structural color in theMorpho butterfly: cooperation of regularity and irregularity in an iridescent scale,” Proc. R. Soc. Lond. B 269, 1417–1421 (2002). [CrossRef]
9. S. Berthier, E. Charron, and J. Boulenguez, “Morphological structure and optical properties of the wings of Morphidae,” Insect Science 13, 145–157 (2006). [CrossRef]
10. R. B. Morris, “Iridescence from diffraction structures in the wing scales of Callophrys rubi, the Green Hairstreak,” J. Ent. (A) 49, 149–154 (1975).
11. L. P. Birò, Zs. Bálint, K. Kertész, Z. Vértesy, G. I. Márk, Z. E. Horváth, J. Balázs, D. Méhn, 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). [CrossRef]
12. C. W. Mason, “Structural colors in insects. II,” J. Phys. Chem. 31, 321–354 (1927). [CrossRef]
13. W. Lippert and K. Gentil, “Über lamellare Feinstrukturen bei den SchillerSchuppen der Schmetterlinge vom Urania- und Morpho- Typ,” Z. Morph. Ökol. Tiere 48, 115–122 (1959). [CrossRef]
14. H. F. Nijhout, The development and evolution of butterfly wing patterns (Smithonian Institution Press, Washington, 1991).
15. A. R. Parker, D. R. Mckenzie, and S. T. Ahyong, “A unique form of light reflector and the evolution of signalling in Ovalipes (Crustacea: Decapoda: Portunidae),” Proc. R. Soc. Lond. B 265, 861–867 (1998). [CrossRef]
16. S. Yoshioka and S. Kinoshita, “Effect of macroscopic structure in iridescent color of the peacock feather,” Forma 17, 169–181 (2002).
17. S. Yoshioka and S. Kinoshita, “Single-scale spectroscopy of structurally colored butterflies: measurements of quantified reflectance and transmittance,” J. Opt. Soc. Am. A , 23, 134–41 (2006). [CrossRef]
18. S. Yoshioka and S. Kinoshita, “Wavelength-selective and anisotropic light-diffusing scale on the wing of the Morpho butterfly,” Proc. R. Soc. Lond. B 271, 581–587 (2004). [CrossRef]
19. P. Vukusic, J. R. Sambles, and C. R. Lawrence, “Color mixing in scales of a butterfly,” Nature 404, 457 (2000). [CrossRef] [PubMed]
20. A. Sweeney, C. Jiggins, and S. Johnsen, “Polarized light as a butterfly mating signal,” Nature 423, 31 (2003). [CrossRef] [PubMed]
21. A. Kelber, C. Thunell, and K. Ariwaka, “Polarization-dependent color vision in Papilio butterflies,” J. Exp. Biol. 204, 2469–2480 (2001). [PubMed]
22. R. HegedÜs and G. Horváth, “Polarizational colors could help polarization-dependent color vision systems to discriminate between shiny and matt surfaces, but cannot unambiguously code surface orientation,” Vision Research 44, 2337–2348 (2004). [CrossRef] [PubMed]
