Detection and Signal Processing for Near‐Field Nanoscale Fourier Transform Infrared Spectroscopy

Researchers from a broad spectrum of scientific and engineering disciplines are increasingly using scattering‐type near‐field infrared spectroscopic techniques to characterize materials non‐destructively with nanoscale spatial resolution. However, a sub‐optimal understanding of a technique's implementation can complicate data interpretation and act as a barrier to entering the field. Here the key detection and processing steps involved in producing scattering‐type near‐field nanoscale Fourier transform infrared spectra (nano‐FTIR) are outlined. The self‐contained mathematical and experimental work derives and explains: i) how normalized complex‐valued nano‐FTIR spectra are generated, ii) why the real and imaginary components of spectra qualitatively relate to dispersion and absorption respectively, iii) a new and generally valid equation for spectra which can be used as a springboard for additional modeling of the scattering processes, and iv) an algebraic expression that can be used to extract an approximation to the sample's local extinction coefficient from nano‐FTIR. The algebraic model for weak oscillators is validated with nano‐FTIR and attenuated total reflectance Fourier transform infrared (ATR‐FTIR) spectra on samples of polystyrene and Kapton and further provides a pedagogical pathway to cementing some of the technique's key qualitative attributes.