Exploring modern alternatives to the Whittaker-Shannon-Nyquist sampling theorem in THz Spectroscopy

We present simulations for a THz cross-correlation spectroscopy (THz-CCS) optical system. The aim is using compressed sensing (CS) to reconstruct the THz signal from a random under sampling of the signal and potentially replacing a delay stage unit of the THz-CCS system to increase robustness and cost-effectiveness of the optical system. We present results from using the CS to attempt to reduce the number of samples required to interpolate the THz signal in question. We compared Shannon-Whittaker interpolation to CS reconstruction in a multitude of basis. We conclude that within the current implementation of CS Shannon-Whittaker interpolation beats CS for our simulated THz signal. We have however only just begun to explore the multitude of potential CS implementations for THz spectroscopy systems and see a host of additional explorations to be conducted in the near future.