**1. Introduction**

This chapter presents an engineering perspective on recent analysis methods used to measure plasma properties from interferograms [1, 2]. The electron and atomic densities [3, 4], volume distribution, expansion velocity, and atomic polarizability [5] affect the amount of fringe line shift. To recover these properties, the basic two-step approach is to recover the relative phase difference represented by the shifted fringe lines, and to invert the relationship between the phase difference and the desired properties.

However, as described in Section 2 and unlike profilometry applications [6] where the interference pattern is stable over a lengthy observation period, the plasma medium changes rapidly and continually. For example, laser ablation methods produce an abruptly expanding plasma lobe. Whereas the electrically exploded wire produces an expanding cylindrical volume that lasts for a few hundred nanoseconds. In each case, the plasma presents an inhomogeneous, lossy and dispersive medium to the probing laser. These medium properties cause radiometric variation in the fringe pattern such as low contrast and poorly defined fringe lines.

Before addressing the fringe line analysis, Section 3 reviews the mathematical model of the phase function for light wave propagation through the plasma volume. The electromagnetic phase accrual through the inhomogeneous medium, and the plasma's refractive index are represented with line integrals of the electron and atom densities. Thus, there are two integral operations to invert during a density

measurement. The reader is referred to classic references like [1, 2, 7] for additional factors to consider when the experiment includes controlling magnetic and electric fields. Recent works with electrically exploded wires [8, 9] and dual wavelength interferometry are discussed as a means to recover both density profiles.

Then, Section 4 presents a summary of different fringe analysis methods with emphasis on the Fourier Transform Method (FTM) developed by Takeda, Ina and Kobayashi [10] and continuously improved since [11, 12]. FTM is likely the most wellknown method for extracting 2D phase information from the interferogram in surface profilometry and 3D shape measurement. As eloquently described by [13] these applications also give insight into the time–space analog and the time-frequency duality represented by different interferometry experiments.

Section 4 also discusses improvements to FTM which are generally based on iterative filtering [14] or pre-filtering [15]. The latter is presented with examples from exploded wire experiments. Section 5 briefly highlights different works on plasma interferometry and recent advances in the field of plasma science from interferometry. The chapter concludes with some thoughts on how the 2D phase analysis provides a rich understanding of the plasma.
