Scattering scanning near-field optical microscopy (s-SNOM) provides spectroscopic imaging from molecular to quantum materials with few nanometer deep subdiffraction limited spatial resolution. However, in its conventional implementation s-SNOM is slow to effectively acquire a series of spatio-spectral images, especially with large fields of view. This problem is further exacerbated for weak resonance contrast or when using light sources with limited spectral irradiance. Indeed, the generally limited signal-to-noise ratio prevents sampling a weak signal at the Nyquist sampling rate. Here, we demonstrate how acquisition time and sampling rate can be significantly reduced by using compressed sampling, matrix completion, and adaptive random sampling, while maintaining or even enhancing the physical or chemical image content. We use fully sampled real data sets of molecular, biological, and quantum materials as ground-truth physical data and show how deep under-sampling with a corresponding reduction of acquisition time by 1 order of magnitude or more retains the core s-SNOM image information. We demonstrate that a sampling rate of up to 6× smaller than the Nyquist criterion can be applied, which would provide a 30-fold reduction in the data required under typical experimental conditions. Our smart s-SNOM approach is generally applicable and provides systematic full spatio-spectral s-SNOM imaging with a large field of view at high spectral resolution and reduced acquisition time.

Infrared (IR) spectroscopy has evolved into a powerful analytical technique to probe molecular and lattice vibrations, low-energy electronic excitations and correlations, and related collective surface plasmon, phonon, or other polaritonic resonances. In combination with scanning probe microscopy, near-field infrared nano-spectroscopy and -imaging techniques have recently emerged as a frontier in imaging science, enabling the study of complex heterogeneous materials with simultaneous nanoscale spatial resolution and chemical and quantum state spectroscopic specificity. Here, we describe synchrotron infrared nano-spectroscopy (SINS), which takes advantage of the low-noise, broadband, high spectral irradiance, and coherence of synchrotron infrared radiation for near-field infrared measurements across the mid- to far-infrared with nanometer spatial resolution. This powerful combination provides a qualitatively new form of broadband spatio-spectral analysis of nanoscale, mesoscale, and surface phenomena that were previously difficult to study with IR techniques, or even any form of micro-spectroscopy in general. We review the development of SINS, describe its technical implementations, and highlight selected examples representative of the rapidly growing range of applications in physics, chemistry, biology, materials science, geology, and atmospheric and space sciences.