**5. Advances in plasma diagnostics with interferometry**

There are numerous examples of plasma diagnostics with optical and x-ray interferometry. This section highlights a few to illustrate the specific advances in plasma science. Much of the interferometry science with plasma seeks to reconstruct the signal phase and refractive index of the plasma as a means to measure the electron

density. However, the various types of plasmas and interferometers have shown additional benefits of the interferometric diagnostic.

For example, Feister et al. [47] developed a temporally multi-scale interferometer to investigate the target pre-ablation by ultra intense pulses (>10<sup>18</sup> <sup>W</sup> cm2). The setup acquired three-phase interference images using a laterally sheared Michelson setup. The combination of phase reconstruction from the interferogram and the ultrafast shadowgraphy confirmed how self-emission that corrupted the electron density measurement was caused by pre-ablation of the sample. The femtosecond time scale confirmed that the leading edge of the intense pulse caused the pre-ablation and led to images showing nanosecond formation of pre-plasma, femtosecond interaction of the ultra-intense main pulse, and picosecond hydrodynamic expansion. The physical insights gained by the different time-sequenced views were applied to modeling and simulation and subsequent hardware design. In the x-ray approach of Nilsen and Johnson [48], a 14.7-nm Pd laser x-ray interferometry confirmed how bound electrons caused anomalous fringe behavior in Al plasma that resulted in a refractive index less than one.

Since then, other works [9, 20] investigated physical behavior of expanding plasma volumes when created from two electrically exploded wires. In [9], aluminum (Al) and polymide-coated tungsten (W) plasma from a 1-kA current was observed with dualwavelength (532 and 1064 nm) interferometry. They found that the atomization of Al expanded with a constant velocity of several km/s before stagnating in the middle region of the two wires. They concluded the Al plasma comprised mostly atoms as observed by the density calculations and comparison to the linear wire density. They also discussed how the W wires were more difficult to transition to vapor due to the higher melting point and concluded that a dual-pulse generator would be needed in future experiments. A similar study of mixing flow of two expanding plasma was reported in [20] where they also used two electrically exploded wires to study the hot plasma coronas as they collided. The modeling and simulation study showed that a thin layer between the expanding coronas can be sustained in high Mach number flows resulting from hydrodynamic mixing. It also showed how the dense core material enhances a thin shell instability but has yet to be mapped to observation.

In the recent work of [23], the spontaneous magnetic fields that arise during laser ablation were studied using simultaneous measurement of the polarization plane rotation and plasma electron density. A 1016 <sup>W</sup> <sup>m</sup><sup>2</sup> iodine laser irradiated planar and thick Cu targets to generate a plasma in air. However, unlike other types of plasma studies, the phase *ϕ* and amplitude *b* are necessary to measure the polarization state. Thus, the paper presents a detailed summary of FTM and intermediate steps to recover the amplitude. The introduction of [23] includes a historical perspective of the polaro-interferometry methods for SMF measurement. Ultimately, the work reported a new multi-frame complex interferometry system that can measure the distributions of the magnetic field and electron density from the same interferogram.
