Computational scattering-type near-field optical microscopy

Near-field scanning optical microscopy circumvents the diffraction limit known from classical optics and provides for diffraction unlimited spatial resolution. Among those techniques infrared (IR) vibrational scattering-type scanning near-field optical microscopy (s-SNOM) has advanced to become a powerful nanoimaging and spectroscopy tool. Ultra-broadband synchrotron radiation from the Metrology Light Source (MLS) provides IR-radiation suited for performing nano-FTIR spectroscopy [1]. However, for many applications nano-imaging of soft matter or quantum materials requires hyperspectral imaging, resulting in a large number of spectral data sets and therefore long acquisition time. Here we will present results from applying novel computational imaging methods to the s-SNOM for enhanced spatio-spectral imaging speed.
1) In the application of compressed sensing (CS), this provides improvement in the spatio-spectral imaging acquisition time by reducing the number of sampling points to 1/9th [2]. The saved measurement time may be used to increase the integration time for each of the measurements, thereby increasing the signal-to-noise ratio.
2) While the above computational imaging method has advantages particularly for broadband radiation (such as synchrotron radiation) conversely for light sources with intermediate bandwidth an approach involving shifting the spectroscopic carrier frequency into the rotating frame also reduces the number of data points required [3]. Borrowing from computational methods and techniques used in nuclear magnetic resonance (NMR) spectroscopy, as well as 2D IR spectroscopy, we demonstrate improvement in acquisition time compared to conventional s-SNOM. This approach complements CS s-SNOM, yet is fully deterministic and still Nyquist limited and particularly advantageous for limited bandwidth and broad vibrational resonances as typically encountered in biological systems.
We show the novel approach developed for spatio-spectral s-SNOM where, by transforming into the rotating frame of the IR carrier frequency in combination with utilizing prior knowledge of the vibrational resonances to be probed, IR excitation spectrum, and other general sample characteristics, we are able to accelerate IR s-SNOM data collection by more than 10-fold for each spatial and spectral dimension. We apply this to chemical nano-imaging of protein sheets which reveals multi-scale spatial heterogeneities in the prismatic region in oyster shells. Rotating frame s-SNOM (R-sSNOM) is particularly powerful for chemical nano-imaging of systems with broad resonances (~50 cm^-1) as is common in biological materials.
We discuss applications of computational s-SNOM and the perspective of further improvements towards full spatio-spetral imaging using broadband radiation sources.

Acknowledgement
Parts of this work were financially supported by the European Union, Horizon 2020 EMPIR programmes, the B-IGSM, the NSF Science and Technology Center on Real-Time Functional Imaging, DMR-1548924 and the Alexander v. Humboldt Stiftung, Bessel Award.

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