Multi-dimensional coherent spectroscopy typically relies on a technique called spectral interferometry to retrieve the signal phase. Because the phase of the of the signal encodes the indirect frequency axis (i.e. those not resolved directly, but rather by sampling of a time delay), a reference pulse must be used to retrieve the phase change in the signal field as the coherence time is sampled. The interference of the reference field and the signal field is sensitive to the relative phase between them.

Recently, we exploited another type of interference to extract the signal phase called spatial interferometry. When the phase fronts of two pulses of light are tilted with respect to one another, spatial fringes appear depending on the magnitude of the ** k** vectors and the angle between them. In this way, spatial interferometry is directly analogous to spectral interferometry with the time delay between the two fields replaced by the angle between their

**vectors. Just as with spectral interferometry, one can retrieve the relative phase between the two electric fields. The advantage of spatial interferometry are two fold: 1) interferometric stability is substantially increases since the angle between the phase fronts is kept very small (10s of microns versus hundreds of nanometers), and 2) the requisite resolution of the spectrometer is greatly reduced since one only needs to resolve the emission spectrum and not high frequency spectral fringes. Both of these technical advancements result in a higher signal-to-noise measurement by relaxing the phase stability requirements and by increasing throughput of the spectrometer. When combining spectral and spatial interferometry (SSI), once can optimize each coordinate (spatial interferometry along vertical coordinate and spectral interferometry along horizontal coordinate) to achieve an optimal mixture of isolating the signal from unwanted DC contributions and achieving high throughput detection.**

*k***On a more fundamental level, SSI is a complete generalization of four-wave mixing (4WM) which exploits both the spectral and spatial properties of light.**We recently combined SSI with GRAPES in order to demonstrate the versatility of the method to measure single-shot 2D spectra of systems with dramatically different line widths. Specifically, we measured the 2D spectra of pressure-broadened Rb vapor which has a line width of only a few cm-1, and the light-harvesting pigment protein complex LH2 which has electronic transitions with line widths exceeding 100 cm-1.

A. P. Spencer, B. Spokoyny, and E. Harel, Enhanced-Resolution Single-Shot 2DFT Spectroscopy by Spatial Spectral Interferometry, **J Phys Chem Lett,** 6, 945-950 (2015). PDF