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

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.