Interferometry analysis with fringe normalization and matrix Abel inversion for plasma diagnostics

In plasma diagnostics using interferometry, the phase shift caused by the plasma in the fringes is extracted to determine the plasma density. The common method to extract the phase shift from the fringes is the fast-Fourier-Transform (FFT), but this technique encounters challenges when dealing with insufficient fringe numbers, spatially varying fringe frequencies, or extremely sharp phase changes. These challenges result in errors and hinder the acquisition of precise phase measurements. To tackle this issue, we introduced the fringe normalization (FN) method. The simulations demonstrated that the FN method extracts accurate phase information, surpassing the capabilities of the FFT method. As a result, this advancement enables more precise plasma diagnostics by mitigating errors that arise during the phase data processing. Furthermore, we improved the code for the inverse matrix Abel inversion to convert phase information into density. The simulation employing this code showed that the developed code provides more accurate values in the analysis of plasmas with a sharp density profile, assisting in electron beam manipulation in laser-plasma acceleration.