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(2011) have reported the MIR and FIR reflectance spectra (at 30 degrees incidence angle) of selected clay minerals and zeolites at various stages of dehydration and/or dehydroxylation, as a reference database for planetary research.Ĭonsistent with the previously discussed prospective, a backscatter is mainly modeled in two ways: specular reflection and Bragg scattering. Nevertheless, some near-normal reflectance studies have been reported on pressed pellets to study the Si O stretching envelope of montmorillonite subjected to ion-exchange and heating treatments ( Karakassides et al., 1997, 1999). Hofmeister and Bowey, 2006 Kamitsos, 2015).Ĭlay minerals are not expected to fulfil the requirement for a strongly absorbing, bulk semiinfinite system that is needed to perform quantitative specular reflectance analysis.
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The Kramers-Kronig transformation or the analysis of dispersion in terms of a sum of damped harmonic oscillators can then be employed to calculate both the complex refractive index ( n*) and the dielectric permittivity ( ɛ*) of the sample (e.g. Hofmeister et al., 2003 Kitamura et al., 2007).
#The angle of incidence equals the angle of reflection full
The resulting spectra can be merged to provide the full response of the material over very broad wavenumber ranges that can, in some cases, extend from the FIR to the visible or UV (e.g. The main advantage of specular reflectance studies is that the same sample and sampling accessory can be employed to different spectral ranges. Hofmeister et al., 2003 or Kamitsos, 2015). The detailed account of the optical dispersion formalism can be found in many reference books and articles (e.g. At fixed Γ, high-frequency distortions decrease upon decreasing oscillator strength (not shown). Also note that among the loss curves shown, only ɛ 2 is symmetric around ν o, whereas both k and α = 4 πνk are skewed on the high-wavenumber side. Note that, for a given oscillator strength, sharp bands ( Γ/ ν ο ≤ 0.05 for ɛ s− ɛ ∞ = 0.5) exhibit negative values of ɛ 1 on the high-wavenumber side of the peak maximum and pronounced asymmetries of n. Based on the value of α( ν ο), a transmission measurement of a sample with Γ = 25 cm − 1 and thickness of d ≈ 0.7 μm, or with Γ = 250 cm − 1 and d ≈ 2.3 μm would yield a value of maximum measured absorbance A = − log I/ I o = 1. Simulated normal incidence angle reflectance ( R), extinction coefficient ( α = 4 πνk), real and imaginary parts of the complex dielectric permittivity ( ɛ* = ɛ 1 + iɛ 2) and refractive index ( n* = ( ɛ*) 1/2 = n + ik) as a function of wavenumber ν, of a Lorentz oscillator with ν ο = 1000 cm − 1 (marked with a vertical dashed line), variable damping coefficient (width) Γ = 25, 50, 75, 125 and 250 cm − 1 increasing from top to bottom, ɛ ∞ = 2.5, oscillator strength ( ɛ s− ɛ ∞ = 0.5). In the simplest case of near-normal incidence ( θ o < 15 degrees, commonly 11 degrees), the functions of θ cancel out and the polarisation of the electric field becomes irrelevant if the sample is isotropic perpendicularly to the plane of incidence. The Fresnel equations define reflectance as a function of the complex refractive index of the sample ( n*), which is a function of the relative (dielectric) permittivity ( ɛ* = ɛ 1 + iɛ 2 = n* 2), the trigonometric functions of the angle θ and the polarisation of the light ( p- or s-, in and perpendicular to the plane of incidence, respectively). The reason for this difference is that R depends strongly on both the real ( n) and imaginary ( k) parts of the complex reflective index ( n* = n + ik) of the sample, as described by the Fresnel equations, whereas transmittance, T, is solely a function of the imaginary part.
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Regardless of the angle of incidence, spectra produced by specular reflectance are very different than those collected from transmission measurements ( Fig. The specular reflectance spectrum, R, is recorded as the ratio I R/ I o, where I R is the reflected signal from the sample and I o is the reference spectrum collected from a front-coated Al or Au mirror, placed instead of the sample. The reflected ( I R) beam lies in the plane of incidence and at an angle that is identical to the incidence angle. Specular reflection applies ideally to absorbing bulk samples with infinite thickness and one optically flat surface ( semiinfinite).
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