Variable multilayer reflection together with long-pass filtering pigment determines the wing coloration of papilionid butterflies of the nireus group

T he dorsal wing surfaces of papilionid butterflies of the nireus group are marked by bands of brilliant blue-green-colored cover scales. The thin, cuticular lower lamina of the scales acts as a blue reflector. The thick upper lamina forms a dense two-dimensional cuticular lattice of air cavities with a pigment acting as a long-pass optical filter. Reflectance spectra of small scale areas oscillate, but for large scale areas and the intact wing they are smooth. Theoretical modeling shows that the oscillations vanish for a scale ensemble with varying layer thicknesses and cavity dimensions. The scales combine in a subtle way structural and pigmentary coloration for an optical effect.


ChapTer 6
Variable multilayer reflection together with long-pass filtering pigment determines the wing coloration of papilionid butterflies of the nireus group aBstract T he dorsal wing surfaces of papilionid butterflies of the nireus group are marked by bands of brilliant blue-green-colored cover scales.The thin, cuticular lower lamina of the scales acts as a blue reflector.The thick upper lamina forms a dense two-dimensional cuticular lattice of air cavities with a pigment acting as a long-pass optical filter.Reflectance spectra of small scale areas oscillate, but for large scale areas and the intact wing they are smooth.Theoretical modeling shows that the oscillations vanish for a scale ensemble with varying layer thicknesses and cavity dimensions.The scales combine in a subtle way structural and pigmentary coloration for an optical effect.

introduction
The beautiful patterns displayed by butterflies are determined by the scattering properties of the scales that imbricate the wings [1].Scattering arises when incident light interacts with the structural elements of the scales.Generally, these are composed of a more or less unstructured lower lamina and a highly structured upper lamina.The upper lamina is marked by longitudinal ridges that are connected by crossribs.Pillar-like cuticular structures, trabeculae, often connect both laminae [2].The scales have a pigmentary coloration when they contain pigments that absorb in a specific wavelength range.This is the dominant coloration method of most butterfly species, especially in many nymphalids and pierids [1,[3][4][5].However, a structural coloration arises when the scale structures have periodicities in the nanometer range [6][7][8][9][10].The best studied example of structural coloration is that of Morpho butterflies, which have scale ridges folded into multilayers, causing a striking, metallic-blue color [11][12][13].Many lycaenids (Polyommatinae and Theclinae) exhibit metallic blue and green structural colours due to multilayers in the wing scale interior [11,14,15], while other lycaenids (e.g.Callophrys rubi) and also papilionids (e.g.Parides sesostris) create diffuse green colorations with gyroid scale structures [7,[16][17][18][19][20].
The forewings and hindwings of the four papilionid species investigated in this paper, Papilio bromius, P. epiphorbas, P. nireus, and P. oribazus, belonging to the nireus group, are dorsally marked by brilliant blue-green bands surrounded by black margins (note: the nomenclature of the species is not unambiguous; here we follow WorldFieldGuide.com).The striking coloration has been studied by several investigators, who put forward a variety of interpretations.Firstly, Mason [21] compared the coloration and scale structure of Papilio nireus and P. zalmoxis and remarked that their scales are essentially similar.He stated that there is a 'mesh structure on the upper surface of the scales, which gives them a matte lustre.The seat of the iridescence is beneath this layer, and is very brilliant from the underside of the scale.' (ref.[21], p. 335, 336).Huxley, in his detailed study of the blue scales of P. zalmoxis, found that the upper lamina of the colored cover scales contained a most elaborate formation of crossribs creating a network of channels.He also noted that the cover scales of P. zalmoxis exhibited a distinct fluorescence and that the cover scales of 'P.bromius appear identical in structure, as judged from scanning electron micrographs (SEMs) of the upper surface, and also contain a blue-fluorescing pigment.The blues of the species-group to which bromius belongs all look rather similar and are very likely generated in the same way'.Ghiradella [22] similarly reported that 'in the cover scales of Papilio epiphorbas, P. nireus, P. oribazus, and P. zalmoxis, the network is refined into a series of regular channels'.Huxley [23], who called the channels alveoli, hypothesized that they caused the bluish scale color by Tyndall scattering.This view was critically challenged by Prum and co-workers [24], who argued that the closely packed cavities cannot be considered as independent scatterers, and they therefore concluded that the scales derive their color from coherent scattering in the regular array of cavities in the upper lamina.Vukusic and Hooper [25] on the other hand proposed that not only is the fluorescence emission of the wing scales influenced by the cylindrical air cavities in the scales' upper lamina, but that it is also directionally controlled by the presence of a three-layer distributed Bragg reflector (DBR) that forms the scales' bottom lamina and which is tuned in its reflectance with the fluorescence emission band.
We have revisited the complex coloring system of the nireus group of butterflies by applying a variety of optical methods, among others (micro)spectrophotometry and imaging scatterometry, to unravel the spectral and spatial reflection properties of the papilionid scales.In addition, we have performed scanning electron microscopy to determine the scale parameters, and we have applied computational modeling of the scale structures to interpret the measured reflectance spectra quantitatively.
material and methods 1

Animals
The optical properties of the wings of four closely related papilionid species were investigated: Papilio bromius, P. epiphorbas, P. nireus, P. oribazus.Specimens were obtained from World Wide Butterflies (Dorset, UK).

Photography
Specimens were photographed using a Canon EOS 30D camera equipped with an F70 macro objective.

Anatomy
The structure of the wing scales was investigated, after sputtering with palladium, by SEM using a Philips XL30-ESEM and a FEI Novalab 600 Dual beam SEM.The upper lamina of the cover scales of the investigated papilionids was found to consist of cylindrical cavities.The filling fraction of the material creating the holes was estimated by thresholding the greyscale SEM images into a blackand-white mask that discriminated the scale material from the cylindrical voids and then calculating the fraction of white pixels.In addition to the SEM, transmission electron microscopy (TEM) sections were observed with a JEOL 110S TEM instrument [12].
1 Materials and Methods are presented in more detail in Chapters 2 and 3. results

Reflectance spectra of the colored wing areas are due to the cover scales
The upperside of the wings of the four investigated papilionid butterfly species are marked by similar blue-green colored bands (figure 1).The bands slightly differ in color hue and pattern, locally throughout each wing and also among the species.
To characterize the colored bands we have measured reflectance spectra from small wing areas with an integrating sphere [27].The reflectance spectra of the four species appear to be very similar, showing a main, somewhat asymmetric band with a maximum at about 500 nm, with a minor side band near 300 nm (figure 2).There is also a steady rise of the reflectance above 800 nm.The main reflectance band of P. oribazus is marginally blueshifted compared to that of the other species (figure 1d).
Microscopic observation immediately showed that the primary colored elements of the wings are the cover scales.The underlying ground scales are dark brown or black (figure 3), like all scales in the darkly colored wing margins.
Not surprisingly, reflectance spectra measured from individual, isolated cover scales with a microspectrophotometer (figure 4) closely resembled the spectra measured from the intact wing (figure 2).The reflectance amplitude slightly varied across the scale surface.When the measurement area spanned almost the whole scale's width, the spectra were smooth (figure 4a).However, when the measurement area was made small (of the order of a few micrometer in diameter), the spectra exhibited an oscillatory fine structure (figure 4b).

Pigmentation of the scales
Observing the scales with an epi-illumination microscope and applying ultraviolet (or blue) illumination revealed that the colored scales exhibit a distinct blue-green fluorescence.The scales hence must contain a short-wavelength absorbing pigment, which will affect the reflectance spectrum.To determine the absorbance spectrum of the pigment, we measured the transmittance of isolated scales while effectively eliminating the light loss due to scattering by immersing the scales in a fluid with refractive index 1.56, matching the refractive index of the scale material [12,30].The cover scales of the four papilionids all showed very similar absorbance spectra restricted to the (ultra)violet wavelength range and with a maximal absorbance of ~0.5-0.7 at the peak wavelength of ~390 nm (figure 4c).The absorbance peak coincides with the minimum in the reflectance spectra.

Spatial distribution of the scale reflections
To investigate the spatial reflection characteristics of the cover scales, we isolated single scales and then glued the individual scales at the tip of a glass pipette.We positioned the scale at the first focal point of the imaging scatterometer and illuminated a small area of either the scale underside or upperside with a narrow-aperture, focused light beam (circles in figure 5a,c), and monitored the spatial distribution of the far-field scattered light (figure 5b,d).As can be seen from the spotty appearance of the near-field reflection pattern, the scale underside was clearly not perfectly flat (figure 5a).The near-field photographs are, like the applied illumination, limited by the 5° aperture of the central hole in the ellipsoidal mirror of the scatterometer.The far-field reflection pattern appeared nevertheless to be   highly directional, with a spread of no more than a few degrees.The deviations from flatness are therefore minor.Rotation of the scale in steps of 15° resulted in a shift of the reflection pattern in steps of 30°, which demonstrated that the scale underside reflected specularly.With increasing angle of incidence, the pattern's color became more bluish.Such an iridescence phenomenon is a well-known property of reflecting multilayers [8,9].
Illumination of the upperside of the scale also yielded a slightly spotted pattern in the nearfield, although more diffuse than that of the underside (figure 5c).The pattern's center closely resembles the reflection spots obtained from the scale's underside.Rotation of the scale in steps of 15° again resulted in displacements of the reflection pattern in steps of 30° (figure 5d).The iridescence, that is the color change of the reflection pattern with increasing angle of incidence, was less prominent than that of the underside, however (figure 5b).Furthermore, the reflection pattern of the upperside, although quite directional, was slightly more diffuse than that of the underside.

Cover scale anatomy and refractive indices
Knowledge of the scales' nanostructure is a requirement for a quantitative interpretation of the measured spectra as well as of their spatial reflection characteristics.For this reason we studied the anatomy of single scales using scanning electron microscopy (SEM) and transmission electron microscopy (TEM).Figure 6a presents a SEM-image from a cover scale of P. nireus cut with a razor blade, showing a thick upper lamina and a thin lower lamina, with trabeculae in between.Longitudinal ridges extend above the upper lamina, which appears to contain a matrix of cuticle with cylindrical air cavities arranged in a disordered lattice (figures.6a,b and 7a).The hole-lattice layer has a thickness of approximately 1 μm and is separated by an about 1.5 μm thick space containing the sparsely distributed thin pillars (the trabeculae) above the lower lamina (figure 6a,b).The lower lamina is relatively thin (ca.200 nm) and comprised of three distinctive layers visible in TEM (figure 6b).The thicknesses of these three layers are approximately 75 nm, 50 nm and 75 nm [25].The outer layers of the lower lamina showed a much higher contrast, indicating the presence of pigment in the cuticle [31].The diagram of figure 6c shows an idealized and simplified version of the scale structure.
For close to normal light incidence, the upper lamina can be treated to a first approximation as a uniform layer.Together with the three layers of the lower lamina and the air space in between the upper and lower lamina, the scale thus becomes effectively a 5-layer system with layer thicknesses approximately 1000, 1500, 75, 50 and 75 nm, respectively.For quantitative modeling of the multilayer's reflectance the refractive indices of the layers have to be known.The refractive index of the air space between the laminae, with thickness 1500 nm, is close to 1.0, because of the minor volume occupied by the trabeculae and other filaments.The refractive index of the other, dark stained layers is complex in the wavelength range < 450 nm, i.e., where the pigment absorption is substantial and leads to fluorescence emission.The contribution of the fluorescence to the overall appearance is, however, negligible [32].The real part of the refractive index of the scale medium, chitin, can be assumed to be 1.56 [12,30].However, this value is only appropriate for the cuticle layers of the lower lamina.Because of the cylindrical air-filled cavities traversing the upper lamina, the effective refractive index of the upper lamina will be reduced in proportion to the filling  fraction of the cuticle.The fraction of the upper lamina taken up by the cuticle was estimated by analyzing top-view SEM images (figure 7a).The images were first segmented into regions containing individual cavities with subsequent thresholding of each region to discriminate between the air cavities and the cuticle.However, thresholding of the whole image with a fixed grey level value lead to poor results due to variation of the image background intensity and presence of the scale ridges.For this reason a multi-step image processing procedure was applied.The processing started with pre-filtering to remove high frequency noise, followed by segmentation with the watershed transform and autothresholding of each segmented region.To limit bias coming from image processing artifacts only regions with the Euler number equal to zero were retained in the analyses, i.e., we considered only the regions containing just one hole.The filling fraction was obtained by calculating the fraction of white pixels in the retained regions of the thresholded image (figure 7b).The values calculated for the four papilionid species appeared to be very similar.The mean, area-equivalent diameter of the segmented regions was ~320 nm and the filling fraction of the cuticle ~0.64.
Figure 7a shows that the cavities in the upper lamina form a rather irregular pattern.To determine the order of the cylindrical air-hole structure, we applied a Fast Fourier Transform (FFT) to figure 7a.This yielded a uniform ring-like pattern together with a patterned, about horizontal line (figure 7c).The ring indicates a close-range order, which is angularly isotropic.The radius of the ring is 0.022 nm-1, which translates to an ensemble periodicity of the cavities of 285 nm.The horizontal line pattern in figure 7c arises due to the vertical scale ridges of figure 7a.
With the cuticle filling fraction value 0.64 and the (real part of the) refractive index 1.56, the (real part of the) effective refractive index of the upper lamina becomes 1.56×0.64+ 1×0.36 = 1.36.If the fluorescent pigment is uniformly distributed in the pigmented (dark stained) cuticular media of the upper and lower lamina, the effective thickness of the scale's absorbing media in the transmittance measurements was d = (1000×0.64)+ 75 + 75 = 790 nm.The peak absorbance was about A = 0.60 at wavelength λ = 390 nm, or the absorbance coefficient there is κ = ln(10) A/d = 0.0035 nm-1.The imaginary part of the refractive index at 390 nm then is Im(n) = κλ/(4π) = 0.11.Consequently, the complex refractive index of the two 75 nm thick layers of the lower lamina is 1.56-0.11iat 390 nm, and the peak effective refractive index of the 1000 nm thick upper lamina is 1.36-0.07i.These values were used in the following calculations of the reflectance spectrum of the 5-layer system of the scale, using classical multilayer theory.

Modeling the scale reflectance spectra
As an example, figure 8a shows the reflectance spectra of the lower lamina and the upper lamina considered separately.Because the pigment absorbs only in the short-wavelength range, we first neglected the pigment absorbance, i.e., we assumed the refractive indices to have the same real value at all wavelengths, thus reducing the 5-layer system into a 3-layer system.The lower lamina then has a very broad-band reflectance spectrum peaking in the blue wavelength range, at ~400 nm (figure 8a).The reflectance spectrum of the upper lamina is highly oscillatory with a periodicity decreasing with increasing wavelength (figure 8a). Figure 8a also shows reflectance spectra of the combined system of lower and upper lamina separated by an air layer of 1450 or 1550 nm.The spectra show the features of both subsystems; a main broad band, modulated with high periodicity (figure 8a).The upper lamina strongly modulates the reflectance spectrum of the lower lamina but otherwise seems to contribute relatively little to the overall magnitude of the reflectance, because the average of the two reflectance spectra obtained with air gap thicknesses 1450 and 1550 nm approximates the spectrum calculated for the isolated lower lamina.The spectra deviate somewhat at the longer wavelengths, where the reflectance of the lower lamina is minor.
The experimental reflectance spectra measured from large scale areas were smooth, but those measured from smaller areas featured modulations (figure 4a,b).The wavelengths of the local maxima and minima slightly varied among the different locations (not shown), indicating that the thicknesses of the scale layers vary across the scale.Due to this thickness variation, the modulations in the reflectance spectra of larger areas vanish.The upper lamina with its violet-absorbing pigment (figure 4c) can then be treated as a simple long- pass filter in front of the reflective lower lamina.Taking a value 0.07 at 390 nm for the imaginary refractive index of the upper lamina, the reflectance spectrum of the lower lamina (figure 8a,b, blue curves) is strongly long-wavelength shifted to a spectrum peaking at ~470 nm (figure 8b, red curve), very similar to the reflectance spectra measured from intact scales (figure 4a,b).

Effects of locally scaled variations
We have further investigated the extent to which the modulations in the reflectance spectra will be smoothed due to variations in the scale parameters.We therefore have calculated the averaged reflectance spectrum for an unpigmented 3-layer system, while varying the thicknesses of the individual layers stochastically.The amount of introduced randomness was controlled by specifying the standard deviation of the layers' thicknesses as a percentage of their mean value.A gamma distribution was used for generating random samples to ensure non-negative values.Reflectance spectra were obtained as an average from a few thousand random structures generated per each wavelength of the spectrum.Thus obtained spectra were then smoothed for presentation, but just enough to remove the noise inherent in stochastic simulation and without affecting them otherwise.
Figure 9a shows the average reflectance spectrum resulting from a varying air gap thickness between the upper and lower lamina, and the minimum-maximum envelope of attainable reflectance values is shown as the shaded region.It is apparent that the modulations cannot be fully removed through variation of this parameter alone.Figure 9b shows the average reflectance spectrum calculated for a varying filling fraction of the upper lamina.The distribution of the filling fraction could be obtained quite accurately from the image analysis of SEM micrographs and was approximated by a beta distribution for the purpose of practical computations in order to restrict the sampled values of the filling fraction to the range between 0 and 1.There is only a very minor influence of this parameter and the averaged spectrum is in fact nearly the same as the one obtained for the mean value of the filling fraction (figure 9b). Figure 9b also shows an envelope of minimum and maximum reflectance values attainable by varying the filling fraction.It is again clear that changing this parameter alone is not sufficient to remove the modulations from the spectrum.Figure 9c shows the average reflectance spectrum of the spectra calculated by varying only the thickness of the upper lamina, which leads to the same conclusion.Finally, the combined effect of varying together the thicknesses of all layers comprising the scale structure is shown in figure 9d for several different levels of the added noise.With increasing level of randomization, the reflectance spectrum becomes progressively smoother up to about 5-10% variation from the mean values of these parameters.Beyond this point the spectrum starts to flatten and becomes increasingly featureless (whitish) for highly randomized structures.Thus, this 5-10% randomization is optimal with respect of removing the effect of modulation but without affecting the overall color.
With a suitable choice of thickness parameters for the upper and lower scale lamina and the level of their randomization it is in fact possible to approximate the experimentally measured spectra fairly closely, not only in shape but also in magnitude.An example is shown in figure 10 for the total reflectance of the colored patches on wings of P. oribazus from figure 2. The modeled spectrum was calculated for the 1000/1500/220 nm 3-layer system, with 10% randomization of the upper lamina thickness and its distance from the lower lamina and including the effect of absorption in the top layer.Absorption in the lower lamina is essentially negligible and is thus neglected from the analysis.For these parameters the modeled spectrum is in fairly good agreement with the measured spectrum, except for the infrared region, where an increasing discrepancy is observed at longer wavelengths.This discrepancy presumably originates from the increased contribution to the total reflectance signal coming from the black ground scales lying beneath the colored cover scales (cf.reflectance of black and colored patches from P. nireus in figure 2).

discussion
The wings of papilionid butterfly species of the nireus group are colored due to special structured cover scales.The scales consist of a lower and an upper lamina, which together reflect mainly the blue-green component of incident light in an approximately mirror-like fashion.Comparing the directional reflection of the scale's underside and upperside shows that the upper lamina, which consists of a mesh of air cavities, causes a slight angular spreading of the reflected light (figure 5).The isolated lower lamina has a broad-band reflectance spectrum, covering the ultraviolet to green wavelength range (figure 8).In the intact scale, the upper lamina in principle causes severe modulations of the reflectance spectrum, but these oscillations are effectively smoothed out due to inhomogeneities in the thickness of the laminae, in the filling fraction of the upper lamina, and in the distance between upper and lower lamina (figure 9).The scale's broad-band reflectance spectrum is curtailed to the blue-green due to the presence of a selectively (ultra)violet-absorbing pigment (figure 4c).
Our findings confirm the early observations of Mason [21], who noticed that the scale's iridescence emerged from below a mesh structure.This structure, the upper lamina, was later recognized to be a very elaborate formation of the crossribs, the scale elements that connect adjacent ridges [2,22,23].Compared to the lower lamina, the upper lamina is relatively thick (~200 and 1000 nm, respectively), arguably because of the necessity of storing sufficient pigment so that an effective high pass filter can be realized [32], but otherwise this thick layer does not significantly alter the reflectance from the lower lamina, since introduced modulations are effectively averaged out.A peak absorbance of ~0.6 was measured in scales immersed in a refractive index matching fluid, but of course effectively twice this value holds for the light that is ultimately reflected from the lower lamina.The important outcome of this study is that the variation in the thicknesses of the multilayers causes a strongly smoothed reflectance spectrum.Generally in biological photonic systems small variations in the anatomical properties will occur already at the micrometer scale.Optical spectra are virtually always measured from areas with size well above the micrometer scale and therefore this will result in substantially smoothed spectra [33][34][35].
The blue-green fluorescence emission that is generated by the strongly absorbing pigment present in the investigated papilionids is certainly reflected by the DBR of the bottom lamina, but the contribution to the appearance offered by this fluorescence has been measured to be negligible (see ref. [32]).
The structural organization of the cover scales of the papilionids Parides sesostris and Teinopalpus imperialis is similar to that of the cover scales of the nireus group papilionids [7,[36][37][38].In all cases, a thick elaborate upper lamina is situated above a reflecting photonic oribazus measured with an integrating sphere and the spectrum calculated for a 3-layer 1000/1500/220 nm system with 10% variation in both the thickness of the (absorbing) upper lamina and its distance from the lower lamina.
structure.In P. sesostris and T. imperialis, however, a so-called honeycomb structure is immediately on top of a layer composed of gyroid domains, which act as 3D photonic crystals [17,18,20].Not unlike the nireus group of butterflies, the cover scales of P. sesostris have a distinct green color, but upon removal of the upper lamina a blue color remains [19,38].These scales therefore contain a blue-absorbing pigment in the upper lamina which also functions in this case as a long-pass filter for the underlying structurally colored region [19].
The studied papilionid species have revealed a novel technique to fine-tune the butterfly wing coloration to a narrowband blue-green, in addition to other methods that have been already discovered, for instance, with sculpted multilayers of P. palinurus and P. blumei scales [31,39], perforated multilayers in lycaenids [15], gyroid 3D-photonic crystals of the lycaenid Callophrys rubi and the papilionids Papilio sesostris [17,18,20], and bile pigments of Graphium species and other papilionids and nymphalids [40,41].Interestingly, in the latter case certain species (e.g.Graphium sarpedon) use a long-pass filter (lutein) to change the pigmentary coloration due to the bile pigment sarpedobilin from blue into green [42], not dissimilar to the case of the four nireus papilionids and P. sesostris that use a long-pass filter to change the wing color; however, here the coloration has a structural basis.Butterflies can clearly employ a rich variety of optical tools to tune their colors.

Figure 2 .
Figure 2. Reflectance spectra of the colored bands in the wings of the four butterfly species of figure 1 (colored curves), together with a reflectance spectrum of the black marginal area of P. nireus (gray curve), measured at near normal illumination (~8°) with an integrating sphere.

Figure 3 .
Figure 3. Epi-illumination light microscopic image of a colored wing area of P. oribazus.The cover scales have a distinct blue color.The ground scales have a dark brown color (arrows; scale bar: 100 μm).

Figure 4 .
Figure 4. Reflectance and absorbance spectra of single, isolated wing scales of the four investigated papilionids measured with a microspectrophotometer (MSP).(a) Reflectance spectra measured at the upperside of single scales from an area 30x30 µm 2 .(b) Reflectance spectra measured from an area 4x4 µm 2 .(c) Absorbance spectra calculated from transmittance spectra measured from single scales immersed in refractive index matching fluid.

Figure 6 .
Figure 6.Anatomy of the cover scales of the papilionids of figure 1.(a) A SEM image of a cut cover scale of P. bromius shows an upper lamina with thickness of approx. 1 μm, with ridges.The upper lamina has cylindrical cavities and rests on small pillars controlling the distance to the cuticle-air-cuticle triple layer (white arrows; scale bar: 2 μm).(b) TEM image of P. nireus showing the internal scale structure of the upper lamina of the scale and the lower lamina, which consists of three layers; the two outer layers are pigmented (black arrow; scale bar: 1 μm).(c) Diagram of the cover scale of the four investigated papilionid species.

Figure 7 .
Figure 7. Arrangement of the cavities in the upper lamina of the cover scales.(a) Top-view of the scale structure in P. oribazus (SEM image).(b) Result of the image analysis routine after segmentation of (a); only the image portion spanned by the white areas and the holes they contain was used for further data analysis.(c) Fast Fourier Transform (FFT) of (a).The ring-like structure indicates the order of the air holes (scale bars, in (a) and (b): 2 μm; in (c): 0.02 nm -1 ).

Figure 8 .
Figure 8. Reflectance spectra calculated for various multilayers for normal light incidence.(a) Reflectance spectra of the lower lamina, with thickness 200 nm and refractive index 1.56 (blue curve), of the isolated upper lamina, with thickness 1000 nm and effective refractive index 1.36 (red curve), and of the 3-layer system, consisting of the lower and upper lamina with either a 1450 or a 1550 nm air gap in between.The magenta curve is the average of the latter two, highly oscillating spectra.(b) The reflectance spectrum of the lower lamina of (a) together with the spectrum obtained by filtering this spectrum by the pigmented upper lamina which has the absorbance spectrum of figure 4c (compare also with figure 4a).

Figure 9 .
Figure 9. Reflectance spectra when the thicknesses of the three layers the cover scales vary stochastically.Averaged reflectance spectra (blue curves) resulting from a 10% variation in the distance between the lower and upper lamina (a), the filling fraction of the upper lamina (b), and the thickness of the upper lamina (c).(d)Averaged reflectance spectra resulting from simultaneous variation of all thicknesses in the 3-layer system with different amounts of added noise.An increase in noise leads to a progressive smoothing of the spectra.

Figure 10 .
Figure 10.Reflectance spectrum of P.oribazus measured with an integrating sphere and the spectrum calculated for a 3-layer 1000/1500/220 nm system with 10% variation in both the thickness of the (absorbing) upper lamina and its distance from the lower lamina.