Accelerating Ultrafast Spectroscopy with Compressive Sensing

Ultrafast spectroscopy is an important tool for studying photoinduced dynamical processes in atoms, molecules, and nanostructures. Typically, the time to perform these experiments ranges from several minutes to hours depending on the choice of spectroscopic method. It is desirable to reduce this time overhead not only to shorten time and laboratory resources, but also to make it possible to examine fragile specimens that quickly degrade during long experiments. In this article, we motivate using compressive sensing to significantly shorten data acquisition time by reducing the total number of measurements in ultrafast spectroscopy. We apply this technique to experimental data from ultrafast transient absorption spectroscopy and ultrafast terahertz spectroscopy and show that good estimates can be obtained with as low as 15% of the total measurements, implying a sixfold reduction in the data acquisition time.

Figure 1

Comparison between conventional and CS-accelerated experiments. (a) shows a conventional experiment which requires $N$ measurements for the fully resolved result. (b) shows the CS-accelerated scheme with $M\ll N$ measurements to yield an estimate of the fully resolved result.

Figure 2

Ultrafast transient absorption spectroscopy. Panel (a) shows a schematic of the experimental setup. The terms saph xtal, OPA and BS denote sapphire crystal, optical parametric amplifier, and beam splitter, respectively. Panel (b) shows the observed change in absorbance across different wavelengths. In panel (c) we demonstrate that the full experimental data is very sparse in the DCT domain. This allows CS to reconstruct signals with a fraction of the measurements of a conventional experiment. In (d) we plot the normalized root-mean-square error for DCT, Haar, and Hadamard as a function of the sampling percentage. Panels (e)–(g) show the CS reconstruction with 15%, 20%, and 25% samples, respectively.

Figure 3

Ultrafast terahertz spectroscopy. Panel (a) shows the schematic of the experimental setup. The terms OPA and BS denote optical parametric amplifier and beam splitter, respectively. (b) Change in transmitted terahertz probe intensity as a function of pump pulse application time $\mathrm{\Delta }{t}_1$ and electro-optical sampling probe delay time $\mathrm{\Delta }{t}_2$. The inset here and those in panels (e)–(g) show a typical profile in $\mathrm{\Delta }{t}_2$ for a fixed $\mathrm{\Delta }{t}_1=30$ ps. In (c) we show the sparsity of the signal in the DCT domain. Almost all the information is contained in about 7% of the frequency coefficients. This allows CS to reconstruct the full signal with a fraction of the measurements of a conventional experiment. In (d) we show a comparison between normalized RMSE for DCT, Haar, and Hadamard as a function of the sampling percentage. In (e)–(g) we show the CS reconstruction with 15%, 20%, and 25% samples, respectively.