Abstract
Nano-Fourier-transform infrared spectroscopy (nano-FTIR) combines infrared spectroscopy with scanning probe microscopy (SPM) techniques and enables spectroscopic imaging of molecular and electronic properties of matter at nanometer spatial resolution. The spectroscopic imaging can be used to derive chemical mappings, i.e. the spatial distribution of concentrations of the species contained in a given sample. However, due to the sequential scanning principle underlying SPM, recording the complete spectrum over a large spatial area leads to long measurement times. Furthermore, the acquired spectrum often contains additional signals from species and lineshape effects that are not explicitly accounted for. A compressive chemical mapping approach is proposed for undersampled nano-FTIR data that utilizes sparsity of these additional signals in the spectral domain. The approach combines a projection technique with standard compressed sensing, followed by a spatially regularized regression. Using real nano-FTIR measurements superimposed by simulated interferograms representing the chemical mapping of the contained species, it is demonstrated that the proposed procedure performs well even in cases in which the simulated interferograms and the sparse additional signals exhibit a strong spectral overlap.
Highlights
Photons in the mid-infrared (IR) energyrange between 400 and 4000 cm−1, corresponding to wavelengths between 2.5 and 25 μm, can induce a large number of light/matter interactions
Using real nano-FTIR measurements superimposed by simulated interferograms representing the chemical mapping of the contained species, it is demonstrated that the proposed procedure performs well even in cases in which the simulated interferograms and the sparse additional signals exhibit a strong spectral overlap
In order to assess the effectiveness of the proposed compressive chemical mapping approach, the 3D nano-FTIR data set communicated in [15] was augmented by simulated regression components representing hypothetical contained species
Summary
Photons in the mid-infrared (IR) energyrange between 400 and 4000 cm−1, corresponding to wavelengths between 2.5 and 25 μm, can induce a large number of light/matter interactions. These interactions can be exploited to gain specific information on the chemical composition and spatial distribution of the species contained in the sample [1]. The achievable spatial resolution of these optical techniques is limited by diffraction to about one half of the wavelength [10] This restricts IR spectral imaging to a lateral resolution of several microns, which is often insufficient for accessing electrical, chemical, and thermal material properties of functional nanomaterials. Due to the limited spatial resolution it is not possible to derive an understanding of the interactions between molecular species and biological matter
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