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.

在激光等离子体电子加速中，电子束的质量对激光参数和等离子体密度很敏感。对于给定的激光器，较高的等离子体密度可能有利于较高的电荷，而较低的密度对于较长的加速通道更好，以电荷为代价产生更高的峰值能量。因此，电子束参数对等离子体密度的依赖性对于找到应用的操作条件至关重要。靶室抽真空后，在实验过程中可以远程控制等离子体密度和激光束在等离子体通道中的焦点位置。通过从捕获的干涉图中提取相位信息，然后通过数值计算使用阿贝尔反演得出的积分，可以获得等离子体密度。我们建议在典型的计算过程之前处理 FFT 滤波和重构 (FR) 的简单想法，该过程是用于相移的连续小波变换 (CWT) 和用于 Abel 积分的傅立叶-汉克尔变换 (FH)这里反转。FFT滤波可以抑制噪声引起的误差，而重构可以选择条纹之间的不同数据点，以减少系统误差，提高干涉图的可见度。我们确认FR-CWT-FH方法可以提供均匀区域的平均等离子体密度和高精度的纵向通道结构，使原位监测成为可能。重构中的条纹间距和 CWT 中的小波频率可以根据等离子体密度的形状进行不同的选择，例如均匀或上升（或下降），