Modified calculation method using FFT filtering and reconstructing of an interferogram for monitoring a laser-plasma density

In a laser-plasma electron acceleration, the quality of electron beams is sensitive to the parameters of a laser and a plasma density. With a given laser, higher plasma density may be good for higher charge, while lower density is better for longer acceleration channel, generating higher peak energy at the expense of charge. The dependence of electron beam parameters on the plasma density is, therefore, crucial to find the operating condition for applications. After the target chamber is evacuated, the plasma density and the focal position of the laser beam in the plasma channel can be remotely controlled during the experiments. The plasma density can be obtained by extracting the phase information from captured interferogram, followed by numerically computing the integral derived using Abel inversion. We suggested the simple idea of FFT Filtering and Reconstructing (FR), to be processed prior to a typical computing process, which is the continuous wavelet transform (CWT) for phase shift and the Fourier–Hankel transform (FH) for the integral of Abel inversion here. The FFT filtering can suppress the errors due to the noise, while the reconstructing can select the different data points between the fringes to reduce the systematic error and improve the visibility in interferograms. We confirm the FR-CWT-FH method can provide the average plasma density in uniform region and the longitudinal channel structure with high accuracy, letting the in-situ monitoring possible. The fringe spacing in reconstruction and the wavelet frequency in CWT can be selected differently depending on the shape of plasma density, such as uniform or rising (or falling), and its length of each region to obtain the detailed structure of plasmas.