Recovery of Absorption Spectra from Fourier Transform Infrared (FT-IR) Microspectroscopic Measurements of Intact Spheres

Abstract

An infrared spectrum recorded from a microscopic sample depends on spectral properties of the constituent material as well as on morphology. Many samples or domains within heterogeneous materials can be idealized as spheres, in which both scattering and absorption from the three-dimensional shape affect the recorded spectrum. Spectra recorded from such objects may be altered to such an extent that they bear little resemblance to spectra recorded from the bulk material; there are no methods, however, to reconcile the two from first principles. Here we provide the mathematical description of the optical physics underlying light-spherical sample interaction within an instrument. We use the developed analytical expressions to predict recorded data from spheres using Fourier transform infrared (FT-IR) spectroscopic imaging. Recorded spectra are shown to depend strongly on the size of the sphere as well as the optical arrangement of the instrument. Next, we present theory and experiments demonstrating the recovery of the complex refractive index of the material using data recorded from a sphere. The effects of the sample morphology on the measured spectra can be removed, and using the imaginary part of the index, the shape-independent IR absorption spectrum of the material is recovered.

BIM-Sim: Interactive Simulation of Broadband Imaging Using Mie Theory

“…We are able to achieve interactive performance by minimizing the computational load and limiting the simulation domain to regions visualized by the user. In addition, fast evaluation is useful in situations where iterative evaluation of the forward model is required to solve an inverse problem [9,11].…”

“…In particular, a pre-computed representation of a field at the demonstrated magnitude and dimension would require an impractical amount of storage space and would be difficult to query efficiently. In addition, a fast forward model of particle scattering provides a framework for solving inverse problems, such as spectral un-mixing [9] and localization of probes within an imaged field. Measured and predicted absorbance spectra for PMMA (top) and polystyrene (bottom) microspheres.…”

“…We have recently demonstrated a method for computing the refractive indices of spheres composed of polymers measured using mid-infrared point spectroscopy [9]. However, these nonlinear solutions require iterative computation of the forward model.…”

“…Since Mie theory is computationally expensive, this solution becomes impractical for multidimensional spectroscopic images. In particular, a fast forward model is necessary for iterative calculations of inverse solutions [9], characterization of imaging systems with multiple interacting optical components [10], and iterative fitting of large numbers of particles [11].…”

“…A change in sphere position parallel to the direction of propagation of the plane wave will result in a phase delay. Applying this phase shift results in the final scattering equation: (9) where c = p s − p f is the vector from the focal point p f to the center of the sphere p s .…”