In the past few decades, infrared (IR) spectroscopy has developed into one of the most powerful techniques for extracting detailed chemical information\nin various types of materials even including intact biological materials. It is possible to obtain the wavelength-dependent pure absorption, i.e., the\nimaginary part of the index of refraction of a specific material by performing IR measurements in chemically homogeneous slabs. When the sample\ncontains spherically shaped objects such as cells, absorption spectra are distorted by non-chemical variances such as Mie-scattering effects. Thus, the\nextraction of detailed chemical information can be complicated. Mie theory, formulated in 1908 by Gustav Mie, provides complete mathematical formulation to evaluate various scattering efficiencies such as pure absorption, scattering, and extinction efficiencies of spherical homogeneous or stratified spheres exposed to linearly polarized radiation. The extinction efficiency is a physical quantity that describes the loss of electromagnetic radiation in the forward direction. For a sphere homogeneously filled with a material of constant index of refraction, the extinction efficiency is a function of radius, wavenumber, and the complex index of refraction. The relationship between the real and the imaginary part of the refractive index is mathematically described by the Kramers-Kronig (KK) transformation. Alternatively, these two quantities may be related via the complex permittivity through the classical Lorentzian oscillator model. Motivated by the\nLorentzian model, the imaginary part of the index of refraction is represented as a sum over Lorentzian peaks, and the real part of the index of refraction\nis then computed analytically via the KK transformation, which results in a sum over functions of a similar form. The representation of the imaginary\npart of the refractive index by a sum over anti-symmetrized Lorentzians is the core idea of the “Lorentz Method” of refractive-index reconstruction.\nAccording to the Lorentz Method, it is possible to formulate Qext in terms of parameters related to the Lorentzian representation of the complex refractive index. Following this idea, various inverse-scattering techniques were developed that can reconstruct the wavelength-dependent real and imaginary refractive index profiles of a single homogeneous sphere and a bi-layered sphere using only the measured or simulated Qext as input. Applying the Lorentz Method it is shown in this thesis that it is possible to extract both the real and imaginary wavenumber-dependent refractive index of several different types of homogeneous polymer spheres with near-perfect accuracy by using exclusively simulated or measured Qext data as input. The Lorentz Method automatically satisfies the KK relations. In practice, therefore, the Lorentz Method is more accurate than other methods described in the literature that use numerical KK transformations, since for an accurate KK transformation the refractive index would have to be known over an infinite range of wavenumbers, which is experimentally impossible. Thus the Lorentz Method is a qualitatively new method, distinct from other methods described in the literature, such as methods based on extended multiplicative signal correction (EMSC) or the methods advanced by the Bhargava group.
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