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This study investigates the reduction in the resolution of the striations from the center to the edge through analysis of the imaging principle and the static experimental test of a streak tube. To improve the edge spatial resolution of the streak, we apply the compressed sensing to the X-ray streak camera imaging system and construct the compressed sensing (CS) reconstruction model for the streak camera and we implement the CS objective function by the orthogonal matching method. The reconstruction performance of the Gauss measurement matrix, Bernoulli measurement matrix, and M series family measurement matrix are compared, and the reconstruction parameters are optimized. A comparison between the original imaging results and the reconstruction results shows that the contrast ratio of the CS reconstruction is 12.2% higher than that of the original, and the limit resolution is 5 lp/mm higher than that of the original image. Furthermore, the improvement effect far from the central area is better than that at the central area. The CS reconstruction on the M series family measurement matrix can improve the image contrast ratio on the edge of the image, and, thus, static and dynamic spatial resolutions of the image are improved.

In the inertial confinement fusion (ICF) research, the characteristics of the main diagnostic object are the following: the spatial scale is small (approximately 100 ^{3}). The X-ray streak camera, as a scientific instrument with high spatial and temporal resolution, is the main diagnostic tool in the ICF research. The core part of the streak tube is composed of a photocathode, accelerating grid, electrostatic focusing system, deflection system, and fluorescent screen. The basic principle is to map the time information of the X-ray radiation into the spatial information of visible light on the screen. Time resolution, spatial resolution, and dynamic range are three main performance indicators of a streak camera. Academician Niu Hanben [

The position of the electron beam emitted from different heights of the streak tube is not on the same plane, but on a parabola. An ordinary streak camera uses a flat screen or a spherical fluorescent screen; however, the actual surface of the electron beam is not a complete sphere. As a result, the image and the screen are not completely fitted; therefore, defocus will occur when the nontangent position of the electron beam is projected on the screen. In actual testing, when adjusting the focus voltage to achieve the best resolution at the center of the cathode, the other off-axis electron beams are not on the optimal image plane. This behavior is similar to that of the optical mirror field curve and, thus, the central axis is the focus area, high static spatial resolution can be obtained, the off-axis area is a defocus area, and the spatial resolution is reduced.

Compressed sensing (CS) can recover from undersampled sparse data to achieve optimal real target images. When the imaging system reduces the intensity of the light source and reduces the exposure time of a charge-coupled device (CCD), the image is reconstructed by CS, and a target image similar to the original condition can be obtained. The Shenzhen advanced technology research institute of CAS applied CS to solve the defocus problem caused by the midfield curvature of acousto-optic imaging [

The X-ray streak camera mainly consists of the following core parts: micro-channel plate enhancement module, high-voltage and low-voltage power supply modules, scanning circuit control module, image acquisition module (CCD), and image recording system (computer). The imaging principle is that the diagnostic information, such as time, time interval, intensity distribution, and other diagnostic information of the X-ray incident pulse are linearly transmitted to the electronic pulse by the photoelectric effect of the photocathode. Next, the electron beam is accelerated and focused by an electro-optical imaging system consisting of electrostatic focusing or magnetic focusing. After the deflection of the scanning circuit, the time information of the electron beam is projected onto the space dimension, the electro-optical conversion is conducted through the screen, and the location and intensity information are recorded through the CCD to the computer [

Schematic diagram of the experiment and the soft realization flow chart. (a) Schematic diagram of the streak camera experiment. (b) CS-OMP realization flow chart.

By combining a streak camera with 2D detectors such as a CCD, it can provide all types of ultrafast time information, spatial information, and intensity (or spectral) information; correspondingly, the main parameters are the time resolution, spatial resolution, and dynamic range [

For a practical electronic optical system, because of aberration, the image formed by a point passing through the system is not an ideal point. Its intensity extends outward from the center and spreads into a bright spot, which is darkened all around. The distribution of space can be represented by a point spread function (PSF) [

The CS method can use undersampling to recover sparse and compressed signals. Compressed observation is denoted as y = Φx, where y is the observed vector (M×1), and x is the original signal(N×1) (M≪N). x is generally not sparse; however, it is sparse in a transformation domain Ψ, such as the cosine transform, Fourier transform, and wavelet transform, which have a transformation in the form of x = Ψ^{−1}x. At this point, CS becomes a part of the X-ray scanning imaging system. The reconstruction of sparse transformation Ψ can be obtained by solving the optimization problem under the condition of bundle [

The fluorescent screen (Φ52 mm) is coupled to a reduced cone (1.3:1) of light; thus, the PI2048 CCD of size 27.6 × 27.6 mm^{2} cannot cover the entire cone of light on the side of full cover the fluorescent. The streak contrast value obtained from the test image is given in the first column. From 1.2 mm near the off-center axis, the fluorescent screen was sampled at intervals of 3.5 mm and values of 4.7 mm, 8.2 mm, and 11.7 mm, with contrast of 21.6%, 30.2%, 45.1%, and 48.4%, respectively; the spatial resolution is the limit resolution when the contrast transfer function CTF is 0.05. The central resolution of the image tube can be calculated using formula (

The objective function of CS is solved using the orthogonal matching method [

Assuming that ^{0} = 1,

Let n be positive integers; thus, the trace function from GF

The measurement matrix of M sequence family is a bipolar matrix composed of +1 and −1. The size is fixed to

According to the length of information N =

Select the original domain elements _{1}. Another primitive domain element on GF (_{2} can be obtained.

In the two matrices obtained above, the line extension is in the form of

To generate a sampled K sparse signal x, the support position is selected randomly, and the Gauss distribution with the support value obeys the standard; its length is

Comparison of the effect of measurement matrix reconstruction. (a) Reconstruction probability under different degrees of sparsity. (b) Output signal-to-noise ratio under different degrees of sparsity.

In the observable cathode range, the background noise of the image should be deducted in practical application. The formula for calculating the contrast in actual calculation is as follows [

Comparison of the static spatial resolution of the streak camera in the experiment.

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22 | 1.2 | 21.6% | 23.7% | 24.2% | 25.2% |

18 | 4.7 | 30.2% | 35.2% | 38.1% | 40.5% |

12 | 8.2 | 45.1% | 50.1% | 54.2% | 60.4% |

10 | 11.7 | 48.4% | 55.8% | 65.8% | 68.1% |

SSR: streak spatial resolution; DCA: distance from the centre of the axis; OR: original image; GM: Gaussian measurement; BM: Bernoulli measurement; MSMM: M sequence family measurement matrix.

Comparison of the limit spatial resolution of the streak camera in the experiment.

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22 | 1.2 | 31 | 32 | 32 | 32 |

18 | 4.7 | 28 | 30 | 32 | 33 |

12 | 8.2 | 23 | 25 | 27 | 29 |

10 | 11.7 | 20 | 23 | 26 | 28 |

SSR: streak spatial resolution; DCA: distance from the center of the axis: LSR: limit spatial resolution.

Comparison of the effect of measurement matrix reconstruction. (a) The original image; (b) reconstruction on the Gaussian matrix; (c) reconstruction on the Bernoulli matrix; (d) reconstruction on the MSMM.

Comparison of the central line strength graphs in the streak camera static image. (a) Central line strength of original image; (b) central line strength of reconstruction on Gaussian matrix; (c) central line strength of reconstruction Bernoulli matrix; (d) central line strength of reconstruction on the MSMM.

Comparison of time resolved channel in the streak camera dynamic image. (a) Streak camera dynamic image. (b) The line strength graph of single time resolved channel after reconstructed and original image.

The position of an electron beam emitting at different heights on the streak cathode is not on the same plane, but is on a parabola. Through analysis of the static spatial resolution test data of the streak image tube, the off-center axis area is the defocus area, and the CS algorithm is applied to improve the imaging quality of the defocus region of the streak tube camera. To achieve the best image restoration effect of a streak tube camera, a reconstruction model based on CS was constructed. The optimization of the reconfiguration parameters can be achieved by examining different combinations of equilibrium parameters. The experimental results showed the following: the static image contrast increased by 12.2%, and the limit resolution of the static test image increased by 5 lp/mm on average. At a distance of 1.2 mm from the center to the center of the axis, the contrast increase is 3.6%, limit resolution is increased by 1 lp/mm, contrast is raised by 19.7% at the center distance of the off-axis, and the limit resolution is improved by 8 lp/mm. This result showed that the contrast improvement of the edge is more obvious and the M sequence family measurement matrix compression sensing method has a certain compensation effect on the edge defocus caused by the field curve, thereby providing a new approach for improving the spatial resolution of the streak tube camera.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare no conflicts of interest.

This research was funded by National Natural Science Foundation, Grant no. 11805137, the Shenzhen City Science Research Fund, Grants no. JCYJ20170818141616714 and no. JCYJ20170818102618203, and the Construct Program of the Key Discipline in Hunan University of Science and Engineering, Grant no. CS201801.