Scattering in Infrared Microspectroscopy

Abstract

Mid-infrared absorbance spectra obtained from spatially inhomogeneous and finite samples often contain scattering effects that undermine the Beer-Lambert law assumption. Such spectra contain generally non-linear contributions from the scattering material’s complex refractive index, which may result in derivative-like bands with shifted peak positions. It is first shown using Mie theory for spherical scatterers, that these band distortions may be interpreted and accurately modeled by Fano theory when the imaginary part of its complex dielectric function is small and Lorentzian in nature—as is the case for many biological media. By fitting Fano line shapes to isolated absorbance bands, recovery of the peak position and pure absorption strength can be obtained with high accuracy. Additionally, for small and optically soft spherical scatterers, recovery of one or the other of constant refractive index or radius (given approximate knowledge of the other), is possible. Next, these methods from Fano modeling are generalized to multiple, overlapping absorbance bands (as they naturally occur in practice). To account for stronger absorbance strengths encountered in materials such as polystyrene, a second-order model is proposed, with an iterative fitting algorithm provided. The algorithm can model, up to a scaling factor, the imaginary refractive index of a weakly-scattering sphere when it is composed of Lorentzian oscillators. The methods are demonstrated on a polystyrene (PS) sphere embedded in a potassium-bromide (KBr) pellet. Given knowledge of the sphere’s size (known from the manufacturer, and its brightfield measurement), recovery of the constant refractive index difference between PS and KBr, along with a region of the imaginary refractive index and its scaling factor are demonstrated. Finally, a technique for measuring the phase and amplitude of spatially- and spectrally-resolved samples in the mid-infrared is presented. The design builds on the Mach Zehnder interferometer, with the addition of a high-precision variable-path scanner. The principles of traditional Fourier-Transform Spectroscopy are adapted for use in a Mach Zehnder interferometer, where a sample is placed inside one of the paths as opposed to outside of the interferometer. In this modified setup, an interferogram is measured by varying the path length, as it is in classic Fourier Transform Spectroscopy; however, the resulting spectrum after Fourier transformation of the interferogram is complex, with its phase and amplitude related to that of the scattered field. The additional phase information may help improve scatter correction and three-dimensional hyperspectroscopy, as well as providing quantitative phase imaging techniques.