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Supplementary Material for
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High refractive index of melanin in shiny occipital feathers of a bird of paradise
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Authors: Doekele G. Stavenga, Hein L. Leertouwer, Daniel C. Osorio, and Bodo D. Wilts
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Jamin-Lebedeff interference microscopy
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For interference microscopy, single barbules were cut from a feather with a razorblade on a
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glass microscope slide. The barbules were then immersed in a fluid with refractive index
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between 1.60 and 1.64 (series A of Cargille Labs, Cedar Grove, NJ, US) and covered by a
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cover-slip. Each fluid is supplied with the Abbe number, together with the refractive index at
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589 nm, which allows calculation of the wavelength dependence of the refractive index by
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deriving the parameters A and B of the Cauchy equation n(λ) = A + B/λ2 (λ is the wavelength).
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The microscope slides with barbules were viewed with the Zeiss Universal Microscope set up
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for Jamin-Lebedeff polarizing interference microscopy.1,2 The microscope objective was a
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Zeiss Pol-Int I 10x/0.22. Illumination was by a halogen lamp, with specific wavelengths
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selected by inserting narrowband interference filters below the condenser. At each
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wavelength the analyzer was rotated in 20º steps. The image density of the photograph, taken
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at each step (Coolsnap ES monochrome camera; Photometrics, Tucson, AZ), was evaluated
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with ImageJ (http://rsbweb.nih.gov/ij/),3 and the resulting data was further analyzed in Matlab.
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The Jamin-Lebedeff interferometer uses two perpendicularly polarized beams. One beam
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passes a transparent reference medium, with (real) refractive index nr, and the other beam
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passes the object, with complex refractive index no. The beams are then combined and pass a
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quarter-wave plate and a rotatable analyzer. When the object, with thickness d, is
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homogeneous, the intensity of the resulting light beam varies sinusoidally with the angle of
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the analyzer, α (Fig. S1), according to the function I  a cos 2 [   )]  b , where the
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amplitude a = T½ (Fig. S2a), with T the transmittance of the object, b = (1-a)2/4, and Δα is the
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phase angle Δα = 180( nr- noR)d/λ (Fig. S2b), where noR = Re(no) is the real part of the
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object’s refractive index. By using a set of reference fluids, noR can be derived.1,2
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Measurement of barbule refractive index
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Figure S1 shows a barbule embedded in a fluid with nr = 1.62, with 650 nm illumination and
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analyzer angles: -60º, 0º, and 60º. We recorded the image intensities for each analyzer
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orientation at five locations: one in the reference area (r, Fig. S1b), two in central areas of the
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barbule cell (c, Fig. S1b), and two in peripheral barbule areas (b, Fig. S1b; indicated as
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barbule). At all five locations, image intensities varied sinusoidally with the analyzer angle
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(Fig. S1d; the data and the sinusoidal fits were normalized to the peak intensity value of the
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reference area).
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Figure S2 shows reduced amplitudes of the sinusoidal intensity functions in both the
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center and barbule areas, which is due to light absorption by melanin. The sinusoids’
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amplitudes decreased with decreasing wavelength (Fig. S2a). Furthermore, the sinusoidal fits
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to the analyzer-dependent intensities of the barbule and center areas yielded a phase shift with
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respect to the reference. The wavelength-dependent phase shift was well approximated with a
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linear function of the reference refractive index, nr (Fig. S2b). The value Δα = 0º is reached
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when nr = noR, i.e. where the linear fits of Fig. S2b transect the zero line.2 This yielded the
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data given by the symbols in Fig. 3c.
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The amplitudes of the sinusoids for the barbule and the center area (Fig. S2a) are well
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approximated by the square root of the transmittance spectra (Fig. 3b), in agreement with the
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theoretical prediction a = T½.2 The correspondence is satisfactory in the wavelength range
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where melanin absorption is minor, but it breaks down at wavelengths below 500 nm, where
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melanin absorption rapidly increases. The inevitable presence of scattered light, although
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minor, becomes a noticeable component of the measured signal at the shorter wavelengths,
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and hence causes increasing experimental errors.
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References
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1. Leertouwer HL, Wilts BD, Stavenga DG. Refractive index and dispersion of butterfly scale
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chitin and bird feather keratin measured by interference microscopy. Opt Express 2011; 19:
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24061-24066.
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2. Stavenga DG, Leertouwer HL, Wilts BD. Quantifying the refractive index dispersion of a
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pigmented biological tissue using Jamin-Lebedeff interference microscopy. Light Sci Appl
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2013; 2: e100.
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3. Schneider CA, Rasband WS, Eliceiri KW. NIH Image to ImageJ: 25 years of image
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analysis. Nat Methods 2012; 9: 671–675.
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Figure S1. Jamin-Lebedeff interference microscopy of an occipital feather barbule embedded
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in an immersion fluid with refractive index nr = 1.62 (at 589 nm). The illumination
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wavelength was 650 nm. a-c Images obtained for angular positions of the analyzer -60º (a),
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0º (b), and 60º (c). The circles in b indicate locations of the reference space (r), the center (c)
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and the barbule (b). d Normalized intensities of the images in the reference (ref), center and
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barbule areas, fitted with sinusoidal functions.
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Figure S2. Amplitudes of the sinusoidal intensity functions and phase shifts, obtained with
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the Jamin-Lebedeff method, and the resulting barbule dispersion spectra. a Amplitude values
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for a barbule area as a function of wavelength together with the square-root-transmittance
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following from MSP measurements (reference nr = 1.62). b Angular phase shifts obtained for
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a series of light wavelengths for barbule areas in three immersion fluids with refractive
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indices 1.60, 1.62 and 1.64 (at 589 nm, indicated by arrows). The measurement data are
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approximated with a linear function for each wavelength.
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Figure S3. Oscillations in the reflectance spectra of a thin film with varying thickness. The
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medium was assumed to be homogeneous with real part of the refractive index obtained from
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the Cauchy parameters A = 1.590 and B = 1.48 ·104 nm2, derived from Figure 3c. The
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imaginary part of the refractive index was taken to be 0.56·exp(-λ/270), derived from fits to
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the absorbance spectra. Reflectance spectra with oscillations resembling the experimental
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reflectance spectra were then obtained by assuming that the thickness of the barbule varied in
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a Gaussian way, with mean 2.92 μm and standard deviation 0.10 μm. 11 grey curves are
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shown, for thicknesses 2.72 to 3.12 μm, together with the Gaussian weighted average (red
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curve).
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Figure S4. Angle-dependent reflectance spectra. a Averaged reflectance spectra for TE-
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polarized light, with an angle of incidence 0º-60º, calculated for 36 lanes of the transmission
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electron micrograph of Figure 2f, using refractive index values derived from Figure 3c. b
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Experimental reflectance spectra for TE-polarized light. c As a for TM-polarized light. d As
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b for TM-polarized light.
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Figure S5. Calculated and experimentally measured peak wavelengths of the reflectance
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spectra for the occipital feather barbules of the bird of paradise Lawes’ Parotia, for TE- and
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TM-polarized light, derived from Figure S4.
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