A Soft X-ray Spectral Recovery Method Of Laser Inertial Confinement Fusion Based On Compressive Sensing

The recovery spectrum of soft X-ray,as an important diagnostic test in inertial confinement fusion experiment,can be analyzed to obtain the experimental parameters in the implosion process,for example the radiation temperature.However,the detection channels of soft X-ray spectrometer used to measure the soft X-ray spectrum is large in size,the installation and their orientation leads them to interfere with each other,the possible install position of detection channels is limited.The existing recovery methods may need more redundant measurement data to achieve good recovery performance for a spectrum,which means the recovery spectrum can be under-fitting with a few measurement data.To solve the problem of spectrum unfolding with limited detection channels data,this paper proposed a new recovery method to unfold a spectrum based on compressive sensing?CS?,and achieve the followings:According to the structure of soft X-ray spectrometer,the process of soft X-ray spectrum recovery is analyzed and deduced,and the principle of soft X-ray spectrum recovery is further revealed.The Dante soft X-ray spectrometer based on filtering method converts the spectrum information into time domain information by the integral effect of the detection channel response and measured energy spectrum,and the converted voltage signal is recorded by an oscilloscope.The recovery spectrum can be obtained from the inverse solution of the measured value of the known detection channel and the voltage signal.The compressive sensing theory can reconstruct the original signal with a few measurements by converting the signal into low-dimensional space through a small number of non-adaptive sampling.Therefore,the spectrum recovery is formulated as a problem of accurate signal recovery from a few measurements?i.e.,compressive sensing?,which applies the measurement matrix to convert the spectrum signal into a voltage signal,and enables the signal be reconstructed with a small amount of measured data.The characteristics of soft X-ray spectrum is smooth and multi-peak,which is consistent with Legendre polynomial image.Legendre orthogonal basis can provide a dictionary with large scale and rich performance for sparse representation of soft X-ray spectrum signal.The proper basis atoms are selected adaptively over the Legendre orthogonal basis dictionary with a large size and Lasso regression in the sense of the7)₁ norm,which enables the spectrum to be recovered with high accuracy from the small amount of measured data of the limited detection channels.In order to prove the performance of the recovery method based on compressive sensing,we conducted self-inspection of the numerical test for recovering two spectra.Taking the root mean square error and the mean absolute error as the evaluation criteria,the proposed method and several typical methods can be compared in spectrum recovery accuracy under different number of detection channels.The experimental results show that for the soft X-ray spectrum with photon energy range of 50-6000eV,comparable accuracy can be achieved from only 8spectrometer detection channels as was previously achieved from 14 detection channels by using the proposed method.42.86%of the installation space of the detection channel can be saved for the soft X-ray spectrometer.The soft X-ray spectrum recovery method presented in this paper solves the spectrum recovery under-fitting problem with limited detection channels.It can not only save the cost of construction and operation,but also provide favorable conditions for the installation of other equipment and produce direct economic benefits in the ICF experiment.