Compressed sensing FTIR nano-spectroscopy and nano-imaging.

Infrared scattering scanning near-field optical microscopy (IR s-SNOM) provides for spectroscopic imaging with nanometer spatial resolution, yet full spatio-spectral imaging is constrained by long measurement times. Here, we demonstrate the application of compressed sensing algorithms to achieve hyperspectral FTIR-based nano-imaging at an order of magnitude faster imaging speed to achieve the same spectral content compared to conventional approaches. At the example of the spectroscopy of a single vibrational resonance, we discuss the relationship of prior knowledge of sparseness of the employed Fourier base functions and sub-sampling. Compressed sensing nano-FTIR spectroscopy promises both rapid and sensitive chemical nano-imaging which is highly relevant in academic and industrial settings for fundamental and applied nano- and bio-materials research.