Scanning Electron Microscopy of Butterfly Wings.

The periodic microstructures present in the butterfly wings were analyzed using scanning electron microscopy (SEM) imaging with a Philips XL-30 microscope of the right dorsal hindwing of each specimen. The images shown in Fig. 1 depict the mesh-like microstructures present on the wing scales of the butterfly specimens. These microscale meshes contain periodic ridges linked together by cross-links in the transverse direction.

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Fig. 1.

Optical images and SEM images for the right dorsal hindwings from (A) A. demophoon, (B) C. echo, (C) H. sara, and (D) L. arthemis. The images depict the presence of periodic microstructures on the wing scales of the butterflies. The periodic microstructures are present as mesh-like features with prominent ridges and cross-links that traverse the ridges (depicted as Inset schematics). (E−H) The microstructures are modeled as a unit cell based on dimensions from the SEM images.

Periodic microstructures have been hypothesized to correspond to structural coloration of butterfly wing scales (17⇓⇓–20, 23, 28, 49). Hence, we compared the SEM images from various locations on the butterfly wing specimens (SI Appendix, Fig. S1). From optical imaging, A. demophoon and L. arthemis wings have distinct structurally colored regions, while H. sara appears mostly blue except for the edge of the wing. C. echo displays uniform visible coloration. Under SEM imaging, however, the varying regions of the wing all display periodic mesh-like microstructures across the varying colored regions (SI Appendix, Fig. S1).

The dimensions for the ridge periodicity (a), cross-link periodicity (b), ridge thickness (c), and cross-link thickness (d) were measured from the SEM images and are reported with their respective SD values from measurements at 100 locations across multiple scales for each specimen (Fig. 1). The dimensional parameters vary across the different species, with a ranging between 1 and 2 µm, b ranging between 0.5 and 1 µm, c between 0.25 and 0.5 µm, and d at 0.2 µm. The parameter e was taken from measurements of angled SEM images of the specimens (SI Appendix, Fig. S2), with e = 1.2 ± 0.1 µm, and is comparable to the existing literature (50⇓–52). The biological nature of the specimens presents an inherent natural variation in the structural parameters ranging between 0.01 and 0.2 µm, and could lead to broadband optical and thermal control (53⇓–55) (SI Appendix, Fig. S3).

Optical Properties of Butterfly Wings.

Spectroscopy on the butterflies was carried out on the right dorsal hindwing of individual specimens of A. demophoon (n = 5), C. echo (n = 4), H. sara (n = 4), and L. arthemis (n = 9) (56). The measurements provide the emissivity [and, consequently, the absorptivity, assumed equal to the emissivity by Kirchhoff’s Law (42)] as unity minus the sum of the reflectivity and transmissivity (42, 57) (Fig. 2).

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Fig. 2.

Spectral emissivity (absorptivity) values for the butterfly wing specimens (right dorsal hindwing). (A) UV/Vis spectroscopy for A. demophoon (yellow), H. sara (red), C. echo (gray), and L. arthemis (blue) measures the spectral emissivity in the wavelength range of 0.3 to 2.5 µm. The results depict moderately high emissivity (absorptivity) values throughout the UV/Vis spectrum, with the average values being around 0.82 for H. sara, 0.69 for C. echo, 0.67 for L. arthemis, and 0.55 for A. demophoon. (B) FTIR spectroscopy performed in the wavelength range of 2.5 to 20 µm to evaluate the mid-IR emissivity (absorptivity) profiles for the butterfly wing specimens. The results depict mid-IR (7.5 to 14 µm) emissivity (absorptivity) values ranging from around 0.54 for H. sara (red), 0.42 for A. demophoon (yellow), 0.3 for L. arthemis (blue), and 0.18 for C. echo (gray), in decreasing order. The spectra are depicted with an overlay of the atmospheric transmission spectrum (7.5 to 14 µm) which aids in reemission of heat to outer space and, consequently, heat loss (58).

The UV/Vis spectroscopy yields absorptivity/emissivity dips (and, hence, reflectivity peaks; SI Appendix, Fig. S4) for A. demophoon (with a reflectivity peak of 0.26 centered at 0.4 µm), H. sara (reflectivity peak of 0.11 around 0.37 to 0.41 µm), and L. arthemis (reflectivity peak of 0.32 between 0.38 and 0.42 µm), with a near-uniform reflectivity of 0.33 for C. echo. The solar absorptivity allows for absorption of incident solar irradiation to aid in heating of the butterflies by absorption of incident solar irradiation (30). We observed moderately high solar absorptivity values for all 4 species (>0.5) within the Vis spectrum (0.3 to 0.7 µm), slowly tapering down to 0.2 to 0.6 as the near-IR wavelength regions are approached (Fig. 2A). The average solar absorptivity of the specimens contains an uncertainty of ±0.03 for A. demophoon and C. echo, ±0.05 for H. sara, and ±0.04 for L. arthemis.

The mid-IR emissivity values were then recorded by Fourier-transform IR (FTIR) measurements (SI Appendix, Fig. S5). While the mid-IR emissivity in the wavelengths of 8 to 14 μm remained at 0.2 to 0.3 for C. echo and L. arthemis, A. demophoon and H. sara showed a mid-IR average emissivity of 0.4 to 0.6 (Fig. 2B). The average mid-IR emissivity of the specimens contains an uncertainty of ±0.03 for A. demophoon, ±0.02 for C. echo, and ±0.05 for H. sara and L. arthemis. There are prominent emissivity peaks in the wavelengths of 3 and 6 µm due to the presence of chitin (43) (SI Appendix, Fig. S7), seen across all butterfly specimens. The mid-IR wavelengths of 7.5 to 14 µm are critical for thermoregulation by means of mid-IR heat loss (58⇓⇓–61). Changes in thermal performance of butterfly wings by varying mid-IR emissivity as observed here might aid in thermoregulation of the butterflies.

Validation of Mid-IR Emissivity by IR Thermography.

Next, we sought to validate the FTIR measurements of mid-IR emissivity by using IR thermography to measure the average mid-IR emissivity of the butterfly wing specimens between the wavelengths of 7.5 and 14 µm (SI Appendix, Fig. S6). The spectral average mid-IR emissivity values from IR thermography range from a low of 0.24 ± 0.04 for C. echo to a high of 0.52 ± 0.05 for H. sara, with intermediate values of 0.33 ± 0.04 for L. arthemis, and 0.42 ± 0.05 for A. demophoon. The IR thermography results were then compared with the average emissivity (in the 7.5- to 14-µm-wavelength range) taken from FTIR spectroscopy and showed similar values (Fig. 3).

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Fig. 3.

Comparison of average mid-IR emissivity for various right dorsal hindwing specimens between the wavelengths of 7.5 and 14 µm using IR thermography and FTIR measurements for (A) L. arthemis, (B) C. echo, (C) H. sara, and (D) A. demophoon. The IR mapping presented here depicts variations in emissivity values across the wing specimens, with lower emissivity regions moving toward the blue colors on the map, and higher emissivity regions moving toward the red. While C. echo depicts an average mid-IR emissivity of 0.24, the values remain at 0.33 for L. arthemis and at 0.42 for A. demophoon, and reach a value of 0.54 for the H. sara. The uncertainty of the measured emissivity values includes the uncertainty in the measurement temperature and the inherent uncertainty of the instrument itself. The results for the 4 species depict close similarity in values for the different methods and validate the measurement observations.

The IR imaging in Fig. 3 depicts nearly uniform mid-IR emissivity across the right dorsal hindwing specimens, measured as a function of the perceived temperature on the IR map. On the A. demophoon wing, we noticed regions of lower emissivity closer to the proximal region, with a nearly uniform higher emissivity present toward the edge of the wing. For the C. echo wing, we observed a near-uniform low emissivity across the specimen, with a near-uniform high emissivity on the H. sara wing barring high emissivity black regions closer to the wing hinge. The L. arthemis wing depicts minimal variation in emissivity across the wing moving from the hinge to the edge. The IR imaging thus depicts no clear mid-IR distinction across the visibly distinct colored regions of the specimens (SI Appendix, Fig. S5), and indicates the possibility that different microstructures are responsible for thermoregulation and coloration. The measurement of mid-IR emissivity by IR imaging at a temperature of 69 to 70 °C yields comparable results to the FTIR spectroscopy done at 20 to 22 °C, depicting negligible variation of optical properties with changes in specimen temperature.

Optical Computations.

Using the microstructures obtained from the SEM imaging of the butterfly wing specimens (Fig. 1), we evaluated the spectral absorptivity/emissivity for the specimens by rigorous coupled-wave analysis (RCWA) (61⇓–63), with custom-modified open-source code (61⇓–63). The geometric dimensions for computation were gathered from the SEM images as shown in Fig. 1, and the refractive index and extinction coefficient of chitin were taken from the literature (43, 64, 65). The natural variations and disorder in the structural parameters (SI Appendix, Fig. S3) do not permit perfect periodicity, and hence we used the measured average of each of the geometric dimensions of the microstructures in order to impose periodicity.

The RCWA results for each of these specimens depict mid-IR emissivity values ranging between 0.2 and 0.6, show similar optical behavior across the computation and spectroscopic measurements, and demonstrate the suitability of using a unit cell approximation to model the butterfly wing microstructures (Fig. 4). The results were also compared with finite-difference time-domain (FDTD) methods (66) (SI Appendix, Fig. S7B) for validation.

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Fig. 4.

Experimental and computational emissivity data between 7.5 and 14 µm wavelengths (within the atmospheric transmission spectrum) for the sample butterfly species (with schematics for the specimens) for (A) A. demophoon, (B) H. sara, (C) C. echo, and (D) L. arthemis. (E) The emissivity values are computed using RCWA based on structural dimensions (A–D) from SEM imaging. The emissivity values are plotted with respect to the wavelength and corresponding blackbody temperature [calculated using the Wien’s displacement law (75)]. Both the measured and computed emmisivity values indicate distinct differences among the four butterfly species.

Thermal Properties of Butterfly Wings.

We comparatively evaluated the steady state temperatures attained by the wings under a control environment to analyze the effects of structural thermoregulation. The measurements were performed between 9 AM and 3 PM on July 31, 2018, with the air temperature ranging from 20 to 27 °C, wind speeds between 0.26 and 0.44 m⋅s⁻¹, and a near-constant humidity of 46 to 48%.

Our wing temperature measurements using an FLIR A655sc IR camera (Fig. 5C) showed a wing temperature of 36 to 38 °C for A. demophoon, with C. echo attaining 42 to 45 °C at 12 noon (56). The temperature of the specimens was also predicted using an energy balance analysis (59, 61, 67), with the specimens exposed to solar irradiation (P_sun″) and heat radiated from the atmosphere (P_atm″) = ∫cosθ dΩ∫₀^∞I_BB(T,λ)ε(λ,Ω)ε_atm(λ,Ω)dλ (I_BB: blackbody radiation; ε: emissivity of the specimen and the atmosphere (atm); θ: zenith angle [taken to be 30° on average]; Ω: solid angle interacting with the specimen surface). The specimens emit radiation to outer space at 3 K (via the atmospheric transmission window) with P_rad″ = ∫cosθ dΩ∫₀^∞I_BB(T,λ)ε(λ,Ω)dλ, and exchange heat with the environment via conduction and convection (P_cond+conv″ = h_eff(T–T_air); h_eff: effective heat transfer coefficient; T_air: ambient air temperature). This gives a net radiative power (P_net″), given by Eq. 1 (59, 61, 67), ofPrad″(T) – Patm″(Tair) – Psun″ + Pcond+conv″ = Pnet″.[1]The net heat flux into the specimens at an ambient air temperature of 27 °C at 12 noon (P_sun″ + P_atm″) was computed to be 575 W⋅m⁻² for A. demophoon, 642 W⋅m⁻² for C. echo, 786 W⋅m⁻² for H. sara, and 613 W⋅m⁻² for L. arthemis. The net heat flux out of the specimens at an ambient air temperature of 27 °C at 12 noon (P_rad″) was computed to be 320 W⋅m⁻² for A. demophoon, 276 W⋅m⁻² for C. echo, 538 W⋅m⁻² for H. sara, and 270 W⋅m⁻² for L. arthemis. The sum of the net heat flux into and out of the specimens gives the net heat flux required to maintain the specimen at its steady-state temperature from the ambient temperature. The steady-state temperature of the specimen is attained when the sum of all heat fluxes for the specimen is zero. The steady-state temperatures of the specimens were then compared with the measured values (Fig. 5C). C. echo and L. arthemis, in general, heat up throughout the day consistently higher than A. demophoon and H. sara under similar ambient conditions in a controlled environment. The relatively lower wing temperature values for the warmer climate butterflies A. demophoon and H. sara thus depict the effects of mid-IR heat losses by periodic microstructures in the butterfly wings.

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Fig. 5.

Thermal analysis of butterfly wings. (A) Schematic of temperature measurement setup under a control environment with the energy balance considered for the thermal analysis, including incoming heat from the sun and atmosphere, outgoing radiation to outer space, and conductive and convective losses. (B) Optical image of temperature measurement on the A. demophoon right dorsal hindwing specimen. The specimen is held with clamps placed on a specimen holder mounted on thermal isolation legs. (C) Measured temperature comparison of the 4 specimens of butterflies under similar ambient climate conditions in a control environment (Irvine, CA) on July 31, 2018. While A. demophoon (yellow) and H. sara (red) attained wing temperatures of 37 °C at noon, C. echo (gray) and L. arthemis (blue) heated up further to 41 to 42 °C, highlighting the role of mid-IR heat losses in warmer climate butterflies. The measurements are validated by computational temperature predictions. (D and E) Theoretical predictions of the butterfly wing temperatures in their respective habitat conditions for the 2 species, (D) A. demophoon and (E) C. echo, depicting a surface temperature of 47 to 51 °C [within the habitable range of 20 to 50 °C (30, 34, 35)] with an effective heat transfer coefficient of 10 W⋅m⁻²⋅K⁻¹ (a gentle breeze) at 12 noon. The habitat air temperatures were taken as an average in July for the past decade (2007–2017) and the dashed lines representing the incident solar irradiation (47).

We also predicted the steady-state temperatures attained by the wings in their respective habitats, with the temperature and solar irradiation data taken for July over the past decade (2007−2017) (47, 48, 68, 69) in Santa María Huatulco, Oaxaca, Mexico, for A. demophoon (70), and Deckers, CO, for C. echo (47, 48). The temperature data were also compared with other weather stations within their habitats, such as Azulillo, Oaxaca, Mexico, and Estes Park, CO (48, 71) (SI Appendix, Figs. S8 and S9). While inherent variation in data exists across multiple sources, the sources we used are considered reliable and should account for locational variation. The data are thus expected to accurately depict the thermal environment of the butterflies, barring other sources of variation in their thermal microhabitat as discussed below. The specimens were assumed to be exposed to incident solar irradiation (P_sun″) taken to be varying at 580 to 1,000 W⋅m⁻² for each location correspondingly. While the butterflies’ habitats may offer forest cover or other obstacles to solar irradiation, the butterflies generally bask under direct sunlight (31, 72, 73), and, as such, the forest cover can be assumed to have minimal effect on the incident solar radiation. The specimens interact with the surroundings by means of convective and conductive losses (P_cond+conv″), with h_eff taken to be 5 W⋅m⁻²⋅K⁻¹ (for calm air), 10 W⋅m⁻²⋅K⁻¹ (for a gentle breeze), or 20 W⋅m⁻²⋅K⁻¹ (for a strong breeze). Increasing convection from the wings to the surrounding air for both butterflies would result in surface temperatures that gradually approach the air temperature. We computed the net radiative power (P_net″) using Eq. 1 (61).

The calculations (Fig. 5 D and E) show a steady-state wing temperature of 47 to 51 °C attained by both specimens with respect to their corresponding habitats at 12 noon with peak solar irradiance. The temperatures remained within 20 to 50 °C and likely aid in survival by thermoregulation (30, 34, 36). The analysis predicts the upper limit for daytime wing temperature, as it assumes clear skies, and overpredicts nighttime radiative losses by assuming the entire dorsal wing is exposed to the cold sky. The actual butterflies at nighttime are likely perched under leaves, within rock crevices, in clusters, or with the dorsal side of the wings hidden (37, 74).

The present study analyzes the steady-state wing temperatures of the butterflies at rest. During flight, the energy balance is expected to differ from the rest condition, due to changes in the thermal processes associated with the butterflies. While the major changes involve variations in convection, there is also the possibility of metabolic heat generation (72), and other related thermal processes. Flight is expected to increase the convection coefficient (h) for the butterflies, due to increase in associated wind velocity over the wings, leading to possible lowering of wing temperatures (Fig. 5 D and E). For example, an increase in the h from 10 W⋅m⁻²⋅K⁻¹ to 20 W⋅m⁻²⋅K⁻¹ leads to a decrease in the wing temperature for A. demophoon and C. echo from 50 to 51 °C to 40 to 44 °C. Meanwhile, the flight activity itself could lead to increased metabolism and, correspondingly, a possible increase in the butterflies’ temperatures. The temperature prediction for butterfly wings during flight requires further investigations and transient heat transfer analysis with information about convection and metabolic properties (73).