Assessment of Subsampling Schemes for Compressive Nano-FTIR Imaging

Abstract

Nano-FTIR imaging is a powerful scanning-based technique at nanometer spatial resolution that combines Fourier transform infrared spectroscopy (FTIR) and scattering-type scanning near-field optical microscopy (s-SNOM). Recording large spatial areas using nano-FTIR is, however, limited because its sequential data acquisition entails long measurement times. Compressed sensing and low-rank matrix reconstruction are mathematical techniques that can reduce the number of these measurements significantly by requiring only a small fraction of randomly chosen measurements. However, choosing this small set of measurements in a random fashion poses practical challenges for scanning procedures and does not save as much time as desired. We therefore consider different sub-sampling schemes of practical relevance that ensure rapid data acquisition, much faster than random sub-sampling, in combination with a lowrank matrix reconstruction procedure. It is demonstrated that the quality of the results for almost all sub-sampling schemes considered, namely original Lissajous, triangle Lissajous, and random reflection sub-sampling, is similarly to that achieved for random sub-sampling. This implies that nano-FTIR imaging can be significantly extended to also cover samples extended over large areas while maintaining its high spatial resolution.

Compressed AFM-IR hyperspectral nanoimaging

“…Translation of data reduction into a similar reduction of data acquisition time is possible by continuously measuring and moving all three axes. Metzner et al [45] provides a first description of suitable data acquisition schemes and their impact on data reconstruction quality, which remain to be experimentally realized. We conclude that the data acquisition times required for full hyperspectral measurements in AFM-IR procedures may be significantly reduced by low-rank matrix reconstruction schemes, promoting scanning based methods for hyperspectral imaging for which so far only parallel schemes qualify.…”

D5.1 - Compressed nano-FTIR Hyperspectral Imaging for Characterizing Defects in Semiconductors

“…The random selection of data may lead to idle times during the measurement when transferring between different datapoints. This issue has been discussed in Ref [8] where specific continuous measurement routes have been suggested which do not significantly affect the reconstruction quality using the low-rank algorithm. This will facilitate hardware implementations in commercially available instruments, such as the one employed in this work.…”

Integration of liquid crystal optical delay and mechanical stage optical delay for measurement of ultrafast autocorrelations and terahertz pulses

“…Interferometry is a fundamental optical technique, typically achieved through mechanical delay lines. Interferometry manifests itself in Fourier transform infrared spectroscopy [1][2][3], terahertz time domain spectroscopy [4][5][6], and autocorrelation measurements of ultrafast lasers [7,8]. For many applications, small temporal step size is crucial.…”