The colorful wing patterns of butterflies have inspired researchers to study these insects for many years. Some butterfly wings have multilayer thin-film structures in their scales, which produce a colorful iridescence from reflected sunlight. The multilayer structures have evolved to take advantage of the optical interference with sunlight. In the visible spectrum one can see that on a macroscale level (naked eye), the spectral reflectivity is a function of ( 1) the angle of incidence of sunlight (θi
), and (2) the angle of view of an observer (ϕ) (see Fig. 1
). The incident sunlight is reflected and scattered over a wide range of angles, and different colors are observed at different viewing angles. In addition, some iridescent butterfly wings such as Morpho menelaus
show shifts in color as the rotation of the wing in the plane of the surface is changed. On closer inspection on the microscale level, thin-film structures are revealed to be responsible for the iridescence and color shifts.
Each butterfly wing is covered with millions of scales, each approximately 100 µm long, as depicted in Fig. 2
. A butterfly scale generally resembles a gathered sack consisting of lower and upper laminae.1
The lower lamina is a flat plate from which trabaculae rise to join the upper lamina. The upper lamina is a complex structure consisting of ridges, microribs, and cross ribs, a combination of which forms a fine grid.2
The scale structures are made of organic material containing a material called chitin. From this general shape of the scale, specializations occur that can produce thin-film interference.
Many different structural specializations occur in butterflies. This study focuses on Papilio blumei
, a tropical butterfly species from Indonesia. It has a full wingspan of approximately 10 cm and a band of green iridescent scales (approximately 1 cm wide) across each wing. Its scale microstructure differs from a general scale by having as many as 10 layers of laminae between upper and lower laminae, each separated by air gaps. The thin-film layers are curved to form a series of frames, separated by ridges and cross ribs. A cross section of a P. blumei
scale showing multiple layers of thin films is shown in Fig. 3
. The longitudinal cross section is similar to the transverse cross section shown.
When thin films have thicknesses that are of the order of a wavelength, as is the case with the air and lamina layers in P. blumei
scales, thin-film interference plays a significant role in determining the spectral reflectivity of the structure.3
For planar thin films, we can calculate the spectral reflectivity by following the path of a single ray of radiation as it passes through a multilayer structure (see Fig. 4
). As this single ray of radiation hits the first interface, a portion of it is reflected while the remainder is transmitted into the layer, where it may be partially absorbed. With each subsequent interface, part of the ray is reflected and part is transmitted. The net reflectivity is the sum of all portions of the single ray that are reflected back into the original medium, taking into account the phase differences of the reflected light. The spectral reflectivity of a thin-film structure depends on the film thickness, film material, the wavelength of the incident light, and the angle of incidence.
Fig. 1. Schematic of butterfly for macroscale investigation.
Fig. 2. General architecture of a butterfly scale.
Fig. 3. Papilio blumei specialization of cross sections.
Fig. 4. Thin-film interference of a single wavelength of radiation.
Fig. 5. Effect of curvature of thin films on normally incident light.
For nonplanar thin films, a combination of thin-film interference and scattering due to surface roughness create an effect that is termed here as nonplanar specular reflection. Figure 5
illustrates this phenomenon for normally incident light. In Fig. 5
, the incoming rays are all parallel to the global normal N
. However, because of the curvature of the films, they have nonzero angles of incidence θ relative to the local normals n
. The incoming rays obey the law of reflection locally; therefore the outgoing rays are no longer parallel to N
or to each other. The reflected light from each location is seen at a view angle of ϕ, which is equal to 2θ. The change of the local angle of incidence effectively changes the thickness of thin-film layers by changing the length of the optical path, thereby affecting the spectral reflectivity. This change in spectral reflectivity is observed as a different color for different angles of view. This observed phenomenon is enhanced when the surface roughness is not random but has a repeating pattern with pattern dimensions that are much larger than the wavelengths of incident light.
For P. blumei scales, the ridges and the cross ribs create a repeating pattern in the thin-film structure, resulting in an ideal setting for nonplanar specular reflection. Note that there are two requirements for nonplanar specular reflection to occur: (1) the pattern dimension must be much larger than the wavelength of incident light, and (2) a thin-film structure must be present. In the case in which the pattern dimension is of the same order of magnitude as the incident wavelength, the resulting effect would include diffraction. If surface roughness occurs without thin-film structures, the result will simply be random scattering. Interestingly, the diffuse appearance of nonplanar specular reflection may be easily confused with scattering; however, it is important to distinguish this from scattering, which is a random process with no predictable color shifts with changes in angles.
When the pattern separation is of the order of the wavelength of incident light, diffraction becomes significant in producing iridescent color. The spectrum of solar emission for which butterflies are adapted carries most of its energy between 0.5- and 2.0-µm wavelengths. Note that the ridges on the P. blumei are unlikely to cause significant diffraction, because of the large separation distance between adjacent ridges (approximately 5 µm); however, diffraction does occur in other species.4 The color change in P. blumei can be better explained by nonplanar specular reflection, in which the repeating patterns of ridges and cross ribs in the thin-film layers change the angle of incidence of light locally and produce changes in color with a changing view angle.
Fig. 6. Schematic of a P. blumei numerical model.
Butterfly scale microstructures are believed to be multifunctional; the uses include camouflage, display, signaling, and thermoregulation.5 Understanding the optical and the radiative properties of the wings will lead to a better understanding of the biological behavior of butterflies. In addition, the thin-film structures of butterfly wing scales have a highly selective spectral reflectivity, and a full understanding of the structures’ interaction with light may lead to the development of better interference filters in humanmade thin-film industry. In this paper we present an investigation into the spectral reflectivity of butterfly wings on a macroscale and a microscale level by using both numerical and experimental tools.
2. Numerical Modeling
The spectral reflectivity of P. blumei wing scales was determined numerically by use of models of wing scale microstructures. The numerical calculations were based on the film structure, the index of refraction (n) of the film material, the extinction coefficient (k) of film material, the angle of incidence, and scale patterns. The spectral reflectivities at normal incidence as well as at oblique angles of incidence were determined numerically.
The film stacks of P. blumei
consist of alternating laminae and air layers, with each layer parallel to the scale surface. The air layers are supported by a series of spacers. The laminae and the spacers are both made of cuticles containing chitin, with a reported real index of refraction of 1.58 in the visible range.3 This value, however, will be challenged for the infrared range in the sections below. A schematic of the numerical model is shown in Fig. 6
The index of refraction of the air layer was found with an average index method, which determines the effective index of the layer by use of the weighted average of air and chitin indices:
where F is the fill factor d/D.6 The fill factor and the thickness of the layers were estimated from a scanning electron microscope picture of a P. palinurus scale.4 The P. palinurus butterfly belongs to the same family as the P. blumei, and they exhibit a similar scale structure. Furthermore, it was assumed that each chitin layer had the same thickness, as did the air layers. The thicknesses of laminae and the air layers were estimated to be 0.095 and 0.085 |xm, respectively. The fill factor for the air layer was approximately 0.5.
Fig. 7. Schematic of the macroscale illumination apparatus.
The actual Papilio scales consist of approximately 20 layers. The numerical program developed can determine the spectral reflectivity for any number of thin films, assuming that the light remains fully coherent through its entire optical path. However, a typical light source, such as sunlight, is coherent over only a few wavelengths; the average coherence length in the wavelength range of interest is approximately equal to 2 µm. The optical path within the first seven layers is approximately equal to 2 µm, making the light fully coherent within these layers. With a greater number of layers, partial coherence is encountered; however, thin-film interference in partially coherent regime is not well understood, and therefore only the first seven layers were used in this analysis.
The reduction of the number of layers can be further justified by consideration of the absorption of light as it penetrates through the thin-film layers. In the numerical analysis, the extinction coefficient of chitin was assumed to be zero, that is, the material is nonabsorbing. However, this may not be true, and if the light is absorbed by the chitin as it propagates through the layers, it may be attenuated sufficiently within the first seven layers so that the remaining layers can be considered insignificant. Calculations based on 20 layers showed large fluctuations in spectral reflectivity with changing wavelength, which are not observed experimentally.
The spectral reflectivities calculated from the above model were then scaled down by the percentage of scale area that is iridescent. We can find this by image processing a scale picture and measuring the fraction of the total image area that is reflective. For P. blumei, the factor used is 36%.3
3. Experimental Setup
The macroscale study was done with an illumination apparatus designed to observe the effects of varying the angle of incidence of white light onto a thin-film structure (see Fig. 7
). A 30-W tungsten halogen lamp is mounted on an articulating arm that allows the angle of incidence of the light to be adjusted. The samples, consisting of a butterfly wing or a portion of a wing taped flat against a microscope slide, are placed on a rotary mount assembly that allows for full rotation of the sample in the plane of the base. Images at various angles of view are recorded by a camera.
Fig. 8. Schematic of the MRS.
With this apparatus, the butterfly wings were analyzed from normal incidence to a 90° angle of incidence. At different angles of incidence, the samples were observed at various angles of view and recorded by a camera. It is important to note that the colors seen with the tungsten halogen lamp may not be the same as those seen under sunlight. This is due to the difference in the spectral distribution of sunlight and the lamp. The solar spectrum has its peak emission at approximately 500 nm, as opposed to the peak emission of the lamp at approximately 800 nm. Thus the solar spectrum has a stronger blue component than the lamp, and the observed image will appear more yellow or red with the experimental apparatus than if it were seen under natural sunlight.
The microscale analysis was done with the microscale-reflectance spectrometer (MRS) shown in Fig. 8
. The MRS was developed to measure the spectral radiative properties of different samples ranging from thin-film microelectronic wafers to insect scales.7
This apparatus consists of a light source, monochromator, microscope, and detectors. The monochromatic light is used to illuminate the sample on the microscope. The sample again consists of a wing or portion of a wing taped onto a microscope slide. The reflected light is recorded at the microscope eyepiece by a silicon or germanium photodiode, as well as a CCD camera. The monochromator and the photodiode are controlled by a computer with RS-232 interfaces and LabVIEW programming codes. The photodiode’s output currents are proportional to the amount of light it receives from the sample.
Fig. 9. Color observed under different angles of view for P. blumei.
The reflectivity of a sample is determined by the relation of the intensity of reflected light to the readings from a sample with known reflectivity, such as silicon. The reflectivity is calculated by the equation
where ρ is the reflectivity and I is the reading returned from the photodiode. This setup can be used to determine the spectral reflectivity of a sample for wavelength range of 500–1450 nm. The silicon and the germanium photodiodes were used for wavelength ranges of 500–1000 nm and 1000–1450 nm, respectively. Because of the sensitivity limits of the photodiodes, readings near 500, 1000, and 1450 nm have a high degree of uncertainty. Video images were captured on the computer by the CCD camera and can be examined to determine the different structures that affect the reflectivity.
4. Results and Discussion
The macroscale results for the P. blumei
show interesting effects of changing the angle of incidence of light and the angle of view of an observer. Figure 9
(a) shows the observed color seen at a set angle of incidence of 45° and angles of view varying from -90° to 90°. The Papilio
appears green when viewed from the angle of incidence (45° angle of view). At a 0° angle of view, a bluish-green light is observed. Blue light appears at an angle of view of -20° and purple appears at -45°. At a -90° angle of view, white light is seen on the Papilio
. Figure 9
(b) shows the appearance of the Papilio
under normal incidence. Green light is observed at an angle of view of 0°, and for this case blue light is not seen until an angle of view of ±70° is reached. Note that purple is not seen reflected under normal incidence.
Images from the microscale reflectance spectrometer help explain where on the scale the light is reflecting. As a result of the structure of the Papilio
, seen in Fig. 3
, the curvature of thin-film layers creates ridges and cross ribs that form frames. Figure 10
is a digitally enhanced image of a P. blumei
scale illuminated by light at 550 nm (green) at normal incidence and normal viewing. It shows that the light gets reflected only in these frames, ridges, and cross ribs. The curvature of the frames explains why a rainbow of colors can be seen when the scales are viewed on a macroscopic level from different angles. Because of nonplanar specular reflection off the curved portions of each scale, different colors are observed from different angles. As the angle of incidence and angle of view are changed, a change from yellow to purple can be seen reflected from the wing.
Fig. 10. Digitally enhanced image of the P. blumei iridescent scale under normal incidence with 550-nm light, observed at normal view.
Changing the orientation of the P. blumei wing by rotating it about its normal does not affect the color observed. This is due to the symmetry of the wing scale microstructures. There is no significant difference between the cross sections of wing scales of P. blumei seen parallel and perpendicular to the ridge direction. Some butterfly species have highly anisotropic microstructures; in such cases, a large color shift can be observed with changes in orientation.
The microscale results show the normal spectral reflectivity of the P. blumei
under normal incidence and normal viewing obtained experimentally and numerically (see Fig. 11
). The solid curve represents the values found numerically based on the model, and the filled circles indicate data obtained from MRS measurements. The two show good agreement from 500 to 800 nm. The peak reflectivity occurs at approximately 525 nm, which is green, as indicated by the green iridescence of P. blumei
Beyond 800 nm, however, the experimental result deviates from the numerical result. The discrepancy can be attributed to several possible causes. First, indices of refraction of organic materials are not constant over a range of wavelength. For example, the index of refraction of human skin ranges between approximately 2.5 to 5.5 in visible and infrared spectra.8
For this reason, the spectral reflectivity at normal incidence and viewing was calculated for indices of refraction of 1.8 and 2.0 as well, and the results are shown in Fig. 12
along with the experimental results. As the real part of the index of refraction increases, the spectral reflectivity curve shifts toward higher wavelengths and the amplitude of each peak increases. At wavelengths higher than 800 nm, the experimental results show better agreement with higher-index reflectivities. This is a good indication that the index of refraction of chitin is indeed not a constant, but in fact may increase from 1.58 in the visible spectrum to over 2.0 in the infrared.
Fig. 11. Spectral reflectivity of P. blumei at normal incidence and normal view.
Fig. 12. Spectral reflectivity of P. blumei for various indices of refraction at normal incidence and normal view.
Recall that the numerical model calculated the spectral reflectivity for seven layers of thin films in a fully coherent situation, as opposed to the experimental result, which comprises data obtained from a 20-layer, partially coherent interference. The partial-coherence regime is highly nonlinear and is not well understood, and the discrepancy in the infrared region may be due to effects still unknown because of thin-film interference by partially coherent light.
The difference between experimental and numerical results may be due to other factors as well. It may be due to a phenomenon not studied in this model, such as diffraction in the air layers that is due to the spacers. The effects of melanin, which are dark pigments present in the film stack close to the lower lamina, were neglected in this model, and must also be considered. The percentage of scale area that is iridescent may be changing with increasing wavelengths. More light may be reflected specularly rather than scattered as the wavelength approaches the separation distance between repeating patterns on scales. Finally, the optics in the microscope used in this setup does not focus in the infrared wavelength and may be affecting the results as well.
As the angles of incidence and view are increased simultaneously, the color of P. blumei
wing scales changes from green to blue. The numerical result indicating this is shown in Fig. 13
. The reflectivities in Fig. 13
are calculated with n
=1.58 because of good agreement with the experimental in the visible range. The results indicate a shift in location of the peak reflectivity from green to blue at an angle of incidence of approximately 45°. However, the actual wing scales do not appear blue until the angle of incidence is increased to greater than 60°. This discrepancy can be attributed to the spectral contents of light used for observation, which has lower power in the blue. The numerical results also indicate an increase in reflectivity in the red (600–700 nm). It is important to note that a combined reflection in blue and red may result in a green color, depending on the ratio of the two components.
Fig. 13. Spectral reflectivity of P. blumei at various angles of incidence.
The numerical results for changing angles of incidence are also important in further explaining the nonplanar specular reflection effect. As shown in Fig. 5
, the reflected light from each location is seen at a view angle of ϕ, equal to 2θ. This means that the spectral reflectivity seen at a view angle of ϕ should equal the numerical results of an angle of incidence ϕ/2. The colors seen at various view angles match the numerical spectral reflectivities found at their respective angles of incidence, shown in Fig. 13
. This evidence shows that the geometry of the scales, namely the curvature of thin-film layers, is causing the changes in color of P. blumei
wings at various view angles.
Although the biological significance of the changes in color is not yet understood, there are some speculations. The shift in color as the angle of view increases to near 90° may act as a camouflage for the butterfly to avoid being preyed on from a disadvantageous position. The change in color at high angles of incidence may help the butterfly to be camouflaged during early morning hours, when its body has not yet warmed enough for flight.
Despite the bright iridescence, the spectral reflectivity of the P. blumei scale is such that a large portion of solar energy is still absorbed to be used in thermoregulation. The scale structures have evolved to both produce bright colors for visual impact and absorb much solar radiation for heat.
The multilayer thin-film structures that make up a butterfly wing produce a bright iridescence from reflected sunlight. This iridescence is due to thin-film interference, scattering, and diffraction caused by multilayer structures. A combination of these effects produces a phenomenon, nonplanar specular reflection, which can be seen with the naked eye.
In nonplanar specular reflection, the color changes are the result of light interacting with a large, repeating pattern in the thin-film structure resulting in regular, predictable changes in reflected color. The separation distance of the repeating pattern must be much larger than the wavelength of incident light. These conditions are satisfied by the P. blumei scales, which consist of curved thin-film structures with ridges and cross ribs repeating at approximately 5-µm intervals. This phenomenon must be distinguished from random scattering, in which nonspecular reflection is due to random surface roughness and the resulting colors are unpredictable, and from diffraction, in which the surface pattern separations are of the same order as the wavelength. Diffraction also results in predictable shifts in color; however, the mechanism by which the colors are produced is different from that of nonplanar specular reflection.
Because of the multifunctionality of butterfly wing scales, understanding the optical properties of butterfly wing scales not only affects the visual appearance but also the thermoregulation of these insects. The biological behavior of butterflies will be better understood by a further study of the optical and the radiative properties of their wing scale microstructures.
This research was sponsored by the U.S. National Science Foundation under grants CTS-9157278 and DBI-9605833.