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Abstract
The measurement of hotspot electron temperature is a paramount technique of implosion physics research in inertial confinement fusion. This study proposes a novel quasi-coaxis dual-energy flat spectral response high-resolution X-ray imaging instrument comprising a dual-channel total-reflection Kirkpatrick-Baez microscope and two flat non-periodic multilayer mirrors, which can image at 6.4 ± 0.5 and 9.67 ± 0.5 keV simultaneously. Various theoretical simulations were performed to verify the performance and feasibility of the imaging instrument, which was assembled and characterized in a laboratory. Experimental results show that the imaging instrument could achieve a high spatial resolution of 5 µm in a ± 150 µm field of view (FOV), the root mean square(RMS) deviation values of the measured reflection efficiency are 1.71% and 1.82% for the 6.4 keV and 9.67 keV imaging channels, respectively, in the ± 150 µm FOV.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In the study of laser inertial confinement fusion (ICF), the ultimate target of implosion compression is to achieve high density and high electron temperature for hotspot [1]. High-resolution X-ray imaging and spectroscopy are crucial diagnostic techniques in laser ICF. High-resolution X-ray imaging results and spectral information can reflect the hotspot electron temperature and density distributions, characterizing the hotspot plasma’s symmetry and implosion hydrodynamics [2].
The Ross filter diagnostic [3–5] and Multimonochromatic X-Ray Imager (MMI) [2,6] are mainly employed to measure hotspot electron temperature. The former adopts differential filtering to describe the broadband spectral information of the imploded core. It entails selecting energy by combining filters of different thicknesses and materials. However, it requires additional theoretical calculations [7]. Meanwhile, the latter employs pinhole array and Bragg mirror to realize narrowband X-ray imaging and energy selection. The spatial resolution and collection efficiency of MMI are too low. MMI obtains electron temperature and density by diagnosing the characteristic lines of doped elements in a target, but the radiation cooling effect produced by the doped elements in a hotspot cannot be ignored.
Multi-channel Kirkpatrick-Baez(KB) microscope is a powerful technique for plasma X-ray imaging diagnosis in laser ICF [8]. It has better spatial resolution and a higher collection efficiency than pinhole imager. Conventional metal single-layer KB microscopes show flat spectral response without energy selectivity [9]. Periodic multilayer KB microscopes have energy selectivity, but the energy response efficiency decreases rapidly when the object deviates from the central field of view(FOV). Meanwhile, non-periodic multilayer KB microscope can achieve a flat spectral response and select energy points [10]. However, it is difficult to achieve a small angle of view(AOV) difference and image point spacing simultaneously for non-periodic multilayer KB microscope. For multi-channel KB microscope, the different two imaging channels observe a hotspot from two directions. The AOV difference between the different imaging channels is often the sum of the grazing incidence angles of the two imaging channels [11]. The FOV difference of various imaging channels due to AOV difference cannot be ignored; it will cause the spatial distribution and spectral information of X-rays emitted from the different positions in a hotspot diagnosed by different imaging channels. A large AOV difference will cause inaccurate measurement of hotspot electron temperature.
This study proposes a quasi-coaxis dual-energy flat spectral response X-ray imaging instrument for measuring electron temperature. To meet the requirements of quasi-coaxis and flat spectral response, a total-reflection KB microscope and flat non-periodic multilayer mirrors were combined in the proposed imaging instrument. This study focuses on the design issues and details the theoretical and mechanical designs. Theoretical calculations and energy response simulations were performed to test the feasibility of the imaging instrument. The proposed imaging instrument has been calibrated via offline X-ray backlit imaging experiments; the characterization results show a 5 $\mathrm{\mu}$m resolution achievable in the $\pm$ 150 $\mathrm{\mu}$m FOV of interest. The root mean square(RMS) deviation values of the measured reflection efficiency are 1.71% and 1.82% for the 6.4 keV and 9.67 keV imaging channels, respectively, in the $\pm$ 150 $\mathrm{\mu}$m FOV.
2. System design
2.1 Measurement principle of hotspot electron temperature
X-ray self-radiation from ICF implosion mainly includes Bremsstrahlung radiation from free-free transitions. The Bremsstrahlung intensity of the hotspot per unit mass at an arbitrary position ($x$, $y$) can be expressed as follows [12]:
Considering that in the actual measurement, the energy response of the diagnostic instrument always has a bandwidth $\Delta E$, so Eq. (1) can be rewritten as [12]:
Therefore, for the energy $E_{1}\pm \Delta E_{1}$ and $E_{2}\pm \Delta E_{2}$, the hotspot electron temperature can be calculated according to Eq. (3):
The X-rays with energy point $E$ emitted from the position ($x$, $y$) of the implosion target through a diagnostic instrument, the intensity of the image obtained on the detector needs to consider the spectrum response of the instrument, which can be expressed as:
where $R_{\left (\theta _{x},\theta _{y},E \right )}$ is the reflection efficiency of the instrument for energy point $E$. Therefore, the X-ray emission intensity $I_{(x,y,E)}$ from the imploding target can be calculated according to the image intensity $I^{'}_{(x,y,E)}$ on the detector. In addition, the spectral reflection efficiency $R_{\left (\theta _{x},\theta _{y},E \right )}$ should be calibrated.The image intensity $I^{'}_{(x,y,E)}$ on the detector should be an integral intensity for different energy points within the energy bandwidth $\Delta E$ of the diagnostic instrument. To invert the X-ray emission intensity $I_{(x,y,E)}$ from the imploding target, the system’s reflection efficiency $R_{\left (\theta _{x},\theta _{y},E \right )}$ for different energy points should be relatively flat in its energy bandwidth.
In this study, a dual-channel X-ray diagnostic imaging instrument was proposed to measure the hot spot electron temperature distribution. The two imaging channels must diagnose the intensity of two different energy points $E_{1}$ and $E_{2}$, respectively, at the same hotspot position $(x,y)$. However, the FOV differences between the two imaging channels when the imaging instrument observes the hotspot are inevitable [11]. This can induce the X-ray emission intensity $I_{(x,y,E_{i})}$ ($i=1,2$) emitted from the different hotspot positions observed by the two channels. In order to reduce the FOV differences between the two channels, the AOV between them should be made sufficiently small, meaning the dual-channel imaging instrument is quasi-coaxis.
2.2 Optical design
KB microscope is commonly used for X-ray imaging and spectral diagnosis. The optical configuration of the KB microscope was first proposed by Kirkpatrick and Baez in 1948 [13]. The focus equation of the KB microscope for each reflecting surface in the tangential plane can be expressed as [9]:
where $u$ is the distance from the object to the mirror center, $v$ is the distance from the mirror center to the image plane, $f$ is the focal distance, $R$ is the radius of the curvature of the mirror, and $\theta$ is the grazing angle of the mirror. So the magnification is $M=\frac {v}{u}$.The effective solid angle $\Omega$ of the KB microscope can be expressed as follows [14]:
where $d$ is the length of the mirror along the optical axis.The proposed imaging instrument should achieve a flat spectral response, spectral energy selection and quasi-coaxis. The KB microscope with single-layer metal X-ray film can achieve a flat spectral response and quasi-coaxis; however, it cannot achieve energy selection for X-rays emitted from the imploded target. The periodic multilayer KB microscope can achieve energy selection but not the flat spectral response. The non-periodic multilayer KB microscope can achieve energy selection and flat spectral response; however, to achieve quasi-coaxis to reduce the FOV differences between the two channels, the distances of two image positions on the detector will be very large(e.g., the optical parameters of a non-periodic multilayer KB microscope are as follows: $u$=200 mm, $M$= 12, $\theta$=0.8$^\circ$, and the distance of the two image positions on the detector = 90 mm). Considering the size limitation of a vacuum charged-couple device(CCD) used at the China’s 100 kJ laser facility, a non-periodic multilayer KB microscope cannot be employed to measure hot spot electron temperature.
Two flat non-periodic multilayer mirrors are introduced behind the KB microscope to select energy. The beam path schematic of the proposed imaging instrument is shown in Fig. 1. We choose 6.4 keV(Fe K$\alpha _{1}$ characteristic line) and 9.67 keV(W L$\beta _{1}$ characteristic line) as the imaging instrument’s working energy points because the self-radiation low energy X-rays are much self-absorbed [11,15]. We use three spherical mirrors to form a dual-channel KB microscope, namely M1, M2, and M3. To achieve quasi-coaxis when the proposed imaging instrument observes hotspot, the working surfaces of the three KB mirrors are coated with single-layer metal X-ray films. So, the KB microscope covers a wide energy range in the image. Two flat non-periodic multilayer mirrors reflect the X-ray wavelengths that satisfy Bragg’s law to restrict the spectral bandwidth. In addition, the two flat non-periodic multilayer mirrors with supersmooth working surfaces redirect X-rays and do not affect imaging quality theoretically. The KB microscope focuses object points on the source and projects them onto the two flat non-periodic multilayer mirrors, P1 and P2. The distance from the object to the first mirror center is $u$; the two flat non-periodic multilayer mirrors are placed at the distance of $S1$ and $S2$, respectively, from the KB microscope. The distance between the KB microscope and the image plane is $v$.
The three spherical mirrors are arranged into a rigid array; the two imaging channels share M1. The two imaging channels are formed in the corners of the "crossed" mirrors. The working surfaces of the three spherical mirrors rested against two polished fused silica that served as reference cores. The optical parameters of the KB microscope are shown in Table 1. The AOV difference between the two imaging channels is 0.69$^\circ$, which meets the requirement of quasi-coaxis.
Table 1. Optical parameters of the dual-channel KB microscope.
For the optical parameters design of the two flat non-periodic multilayer mirrors, we should consider the FOV, the distances of two non-periodic multilayer mirrors from the KB microscope, beam divergence angle, and aperture after being focused by the KB microscope. The typical size of a hotspot is $\sim$ 100 $\mathrm{\mu}$m for China’s 100 kJ laser facility. Considering the engineering uncertainty, we select the imaging FOV as $\pm$ 150 $\mathrm{\mu}$m. To make the X-rays in the $\pm$ 150 $\mathrm{\mu}$m FOV emitted from the object be received within the non-periodic multilayer mirrors’ angular bandwidth after being focused by the KB microscope, the non-periodic multilayer mirrors’ angular bandwidth should be larger than the beam’s divergence angle focused by the KB microscope. The divergence angle $\Delta \theta$ can be obtained from Eq. (7), as shown in Fig. 2.
For the KB microscope, each mirror in the two directions functions as an aperture stop; the mirrors can be called aperture mirrors. Then, the non-periodic multilayer mirrors are placed behind the KB microscope; their lengths along the optical axis should be sufficiently long to avoid losing the X-rays focused by the KB microscope. The non-periodic multilayer mirrors can be called field mirrors. The length of the non-periodic multilayer mirrors is determined by the aperture of the X-rays focused by the KB microscope and the incident angle; it can be calculated according to the following, as shown in Fig. 2(b):
where $W$ is the aperture at position $S$ from the back of the KB microscope, $L$ is the non-periodic multilayer mirror length along the optical axis. The right side of Eq. (8) consists of two terms: the first one is the beam aperture related to the $\pm q$ FOV and magnification($\frac {s+d/2}{u}$); the second one is the aperture of the point in the FOV determined by the mirror length $d$ and grazing angle $\theta$.We now consider the field conditions at China’s 100 kJ laser facility to measure hotspot electron temperature. The two flat non-periodic multilayer mirrors’ central grazing angles were selected as 0.8$^\circ$ and placed at 100 mm and 300 mm, respectively, away from the KB microscope. Detailed optical design parameters of the two non-periodic multilayer mirrors are listed in Table 2. Therefore, the relevant parameters are substituted into Eq. (8) and Eq. (9), and the lengths of two flat non-periodic multilayer mirrors along the optical axis can be calculated as $\sim$ 16.6 mm and $\sim$ 38 mm, respectively. Considering the adjustment errors, the lengths of the two flat non-periodic multilayer mirrors along the optical axis are 30 mm and 50 mm, respectively. According to the optical design parameters, the offsets $\Delta z$ and $\Delta y$ of the images relative to the optical axis on the tangential and sagittal planes can be calculated easily from Eq. (10). The offsets between the two images and the optical axis in the tangential plane are both 12.5 mm. In contrast, the offsets between the two images and the optical axis in the sagittal plane are 76.8 mm and 45.1 mm, respectively. So, the distance between the two images on the detector is 31.7 mm.
Table 2. Optical parameters of two non-periodic multilayer mirrors.
2.3 Multilayer design
The working surfaces of three KB mirrors are coated with Pt single-layer X-ray films(thickness = 30 nm), the grazing angles of the three KB mirrors are less than the critical angle based on the expected photon energy. So, the KB microscope covers a wide energy range and has a high tolerance of object aiming. Single-layer film reflectivity as a function of the grazing angle is shown in Fig. 3(a), calculated by IMD [16]. Single-layer reflectivity as a function of the X-ray energy is shown in Fig. 3(b).
Fig. 3. Reflectivity versus grazing angle and energy curves. (a) 30 nm thick Pt single-layer reflectivity versus grazing angle; (b) 30 nm thick Pt single-layer reflectivity versus energy; (c) non-periodic multilayer reflectivity versus grazing angle; (d) non-periodic multilayer reflectivity versus energy.
When the grazing angle is 0.3255$^\circ$ and 0.3403$^\circ$, the reflectivity is about 0.87 at 6.4 keV, 0.87, and 0.86 at 9.67 keV. The proposed KB microscope covers a wide energy range. In order to record two images at 6.4 keV and 9.67 keV simultaneously, two flat mirrors(P1 and P2) are coated with non-periodic multilayers working at 6.4 $\pm$ 0.5 keV and 9.67 $\pm$ 0.5 keV, respectively. The non-periodic multilayer reflectivity curves are shown in Fig. 3(c)-(d). When the grazing angle is 0.8$^\circ$, the peak reflectivity is about 0.50 and 0.37 at 6.4 keV and 9.67keV, respectively. As shown in Table 2, the divergence angles of X-rays emitted from the object after being focused by the KB microscope at P1 and P2 are 0.08$^\circ$. The flat-top angular bandwidth of non-periodic multilayers is larger considering the adjustment errors. The flat-top angular bandwidths of 6.4 keV and 9.67 keV non-periodic multilayers are about 0.15$^\circ$ and 0.1$^\circ$; the corresponding full width at half maximum(FWHM) values are about 0.23$^\circ$ and 0.14$^\circ$, with FOVs of about 851 $\mathrm{\mu}$m and 518 $\mathrm{\mu}$m, respectively. In addition, the flat-top energy bandwidths of 6.4 keV and 9.67 keV non-periodic multilayers are about 1.16 keV and 1.2 keV; the corresponding FWHM values are about 1.8 keV and 1.7 keV, respectively.
2.4 Simulation
In this study, physical diagnosis requires that the proposed imaging instrument’s RMS deviation of reflectivity efficiency is less than 5%, which means the proposed imaging instrument is a flat spectral response. The RMS deviation of reflectivity efficiency indicates the RMS value of the reflection efficiency difference between the each data point and the central FOV data point of the central energy(6.4 keV and 9.67 keV). We performed ray tracing to present the energy response maps in the $\pm$ 150 $\mathrm{\mu}$m FOV at 6.4 $\pm$ 0.5 keV and 9.67 $\pm$ 0.5 keV. The proposed imaging instrument’s two-dimensional(2D) energy response was simulated at ten energy points; the results are shown in Fig. 4(a)-(j). As can be seen from Fig. 4(a) to (j), the RMS deviation values of reflectivity efficiency are 1.1% and 1% within 6.4 $\pm$ 0.5 keV and 9.67 $\pm$ 0.5 keV, respectively, in the $\pm$ 50 $\mathrm{\mu}$m FOV. Therefore, the proposed imaging instrument can achieve a flat spectral response for 100 $\mathrm{\mu}$m hotspot. Considering the target aiming error in the actual measurement, the FOV satisfying flat spectral response should be larger than hotspot size. From Fig. 4(a) to (j), the RMS deviation values of reflectivity efficiency are 1.4% and 2.1% within 6.4 $\pm$ 0.5 keV and 9.67 $\pm$ 0.5 keV, respectively, in the $\pm$ 80 $\mathrm{\mu}$m FOV. So the FOV satisfying flat spectral response is $\pm$ 80 $\mathrm{\mu}$m. Therefore, the target aiming error should be less than 60 $\mathrm{\mu}$m.
Fig. 4. Energy response simulation of the imaging instrument at ten energy points.(a)-(e) are five intensity simulation results versus $\pm$ 150 $\mathrm{\mu}$m FOV at the five energy points(5.9 keV, 6.2 keV, 6.4 keV, 6.7 keV, and 6.9 keV) that we chose at 6.4 $\pm$ 0.5 keV; (f)-(j) are five intensity simulation results versus $\pm$ 150 $\mathrm{\mu}$m FOV at the five energy points(9.17 keV, 9.47 keV, 9.67 keV, 9.87 keV, and 10.17 keV) we chose at 9.67 $\pm$ 0.5 keV.
The reflection efficiencies of the central and edge $\pm$ 80 $\mathrm{\mu}$m FOVs in the energy response map of each energy were extracted from Fig. 4(a) to (j), and we used error bar graph Fig. 5 to illustrate the peak-valley values of reflection efficiency considering the energy points and FOVs. The five red error bars represent the maximum and minimum reflectivity efficiencies of five energy points(5.9 keV, 6.2 keV, 6.4 keV, 6.7 keV, and 6.9 keV) within the $\pm$ 80 $\mathrm{\mu}$m FOV. The five blue error bars represent the maximum and minimum reflection efficiencies of five energy points(9.17 keV, 9.47 keV, 9.67 keV, 9.87 keV, and 10.17 keV) within the $\pm$ 80 $\mathrm{\mu}$m FOV. The green circles and pink rectangles present the reflection efficiencies of the central FOV; the upper and lower limits of the error bar represent the maximum and minimum reflection efficiencies, respectively, within the $\pm$ 80 $\mathrm{\mu}$m FOV. It can be seen from Fig. 5 the peak-valley values of reflection efficiency are 9% and 14% within 6.4 $\pm$ 0.5 keV and 9.67 $\pm$ 0.5 keV, respectively, within the $\pm$ 80 $\mathrm{\mu}$m.
Fig. 5. Reflectivity of ten energy points within the energy range of 6.4 $\pm$ 0.5 keV and 9.67 $\pm$ 0.5 keV in the central and edge of $\pm$ 80 $\mathrm{\mu}$m FOV.
3. Instrument mechanical design
3.1 Overview of the proposed imaging instrument layout
The target chamber of China’s 100 kJ laser facility is a spherical cavity with a 6.4 m diameter. It needs to maintain a high vacuum environment, so all diagnostic instruments must be transported and operated by the Diagnostic Instrument Manipulator(DIM) [17]. An X-ray general diagnostic equipment was proposed for China’s 100 kJ laser facility X-ray microscope; in this study, it is applied to load the dual-energy flat spectral response X-ray imaging instrument, shown in Fig. 6(a)-(d). It will be fielded at China’s 100 kJ laser facility for measuring hotspot electron temperature. The boundary dimension of this instrument is 1145 $\times$ 202 $\times$ 150 mm; multiple components make up the imaging instrument. Starting from the left-hand side, the figure shows the target pointer for indicating the common object position of the two imaging channels, debris protection shield, dual-channel KB microscope, flat non-periodic multilayer mirror P1, target visible aiming system, flat non-periodic multilayer mirror P2, image pointer, and 2D regulating mechanism used to adjust the instrument.
Fig. 6. Dual-energy flat spectral response X-ray instrument for use in a DIM in China’s 100 kJ laser facility: (a) oblique view and (b) top view of solid model; (c) exploded view of all imaging components; (d) photograph; (e) image obtained using an image measuring instrument at $\times$ 22.2.
The images will be recorded with the vacuum CCD. Therefore, the imaging instrument is adjusted by the 2D electric regulating mechanism to avoid the images from not falling in the vacuum CCD’s working area. The 2D regulating mechanism includes angle adjustment in both pitch and yaw directions. The pitch and yaw angle adjustments are realized using a corresponding vacuum linear motor and spherical gimbal joint, respectively.
The resolution of the KB microscope is mainly limited by the spherical aberration on-axis, coma, and curvature of the field off-axis. The aiming accuracy of the object plane needs to be $\sim$ $\pm$ 20 $\mathrm{\mu}$m, and the aiming accuracy along the optical axis needs to realize $\sim$ $\pm$ 100 $\mathrm{\mu}$m [18]. A tantalum sheet with a 25 $\mathrm{\mu}$m wide cross reticle by laser ablation is used as the object point indicator instead of the previous analog needle, as shown in Fig. 6(e). Figure 6(e) is obtained using an image measuring instrument at $\times$ 22.2 magnification. The object point accuracy can reach $\pm$ 12.5 $\mathrm{\mu}$m. This method has a relatively higher mechanical robustness and is unaffected by the illumination angle than the previous method [17].
3.2 Assembly and adjustment of optical components
Before fielding the instrument on the China’s laser facility, the imaging instrument must be assembled and adjusted through an offline X-ray backlit imaging experiment. As mentioned above, the two polished fused silica are used as the reference cores for the two channels of the KB microscope. They were precisely machined within a tolerance range validated by ray tracing. For this system, the dual-channel KB microscope was first adjusted by the X-ray backlit imaging results of a metal grid to determine the common object position with the best resolution. Then, the two flat non-periodic multilayer mirrors were adjusted, respectively. The adjustment of the proposed KB microscope first used a Fe X-ray tube and finally used a W X-ray tube to perform verification imaging on one of the image channels.
The critical points for adjusting the two flat non-periodic multilayer mirrors are described below. Each flat non-periodic multilayer mirror needs three-dimensional precision adjustment mechanisms, including a precision manual rotation stage and a 2D manual translation stage along X and Z axes to adjust, respectively. The dimension of the entire instrument is strictly limited, so only the precision manual rotation stage was loaded on the instrument, as shown in Fig. 6(a)-(b). The two flat non-periodic multilayer mirrors were adjusted using an external adjustment frame along the X and Z axes. An iron-anode(Fe K$\alpha _{1}$ characteristic line) and a tungsten-anode X-ray tube(W L$\beta _{1}$ characteristic line) were used as the backlit imaging X-ray sources for adjusting flat non-periodic multilayer mirrors P1 and P2, respectively. If the grazing angle of the X-ray focused by the dual-channel microscope, projected on the two flat non-periodic multilayer mirrors, deviates from 0.8$^\circ$, the selected energy bandwidth and the FOV will change. The FOV deviation $\Delta FOV$ due to the angle deviation $\Delta \alpha$ can be calculated by Eq. (11). Degradations of imaging performance influenced by different errors were evaluated by ray tracing. The machining and adjustment error allowance of the system are illustrated in Table 3. The errors in the first six rows of Table 3 mainly affect the resolution of the proposed imaging instrument. The errors of the flat non-periodic multilayer mirrors in the last three rows mainly affect the energy spectrum response of the proposed imaging instrument.
Table 3. Machining and adjustment error allowance of the imaging instrument.
3.3 Debris protection
The generation of hypervelocity debris and high-temperature plasma from high-energy laser experiments can irreversibly damage essential diagnostic optical components [19]. High-temperature plasma coated on the working surfaces of the optical elements will reduce the reflectivity, and the debris will destroy the surface shape and roughness.
In order to protect the essential optical components, a debris protection shield system has been developed for China’s 100 kJ laser facility. The design principle of the debris protection shield system is that the protective materials have reliable protection performance and high X-ray transmittance. The protective materials comprise three layers. The first layer, polyimide(PI), has excellent high-temperature resistance. The second layer, polycarbonate(PC), has good mechanical properties. The third layer, metal filters, can select X-ray photon energy and protect optical elements. For the third layer of protective material, different metal filters, such as Be, Fe, Al, Ni, can be used to select different X-ray photon energy for different imaging channels. All mechanical metal parts are made of 6061 Aluminum Alloy and have holes where X-rays can penetrate.
The debris protective shield system has been tested on the China’s 100 kJ laser facility many times; the results showed that the system has high reliability. According to the experimental results, we propose that the combination of materials with different thicknesses should be selected for different laser energies, it can be seen in Table 4. It is expected to use the protection combination in the third row of Table 4 for this study.
Table 4. Combination of different thickness materials for different laser energy.
4. Experimental results
4.1 X-ray backlit imaging results
The X-ray backlit imaging results of #600 gold mesh with pitch width of 42 $\mathrm{\mu}$m and bar width of 6 $\mathrm{\mu}$m are shown in Fig. 7. The iron-anode and tungsten-anode X-ray tubes were operated at 40 kV and 20 mA with an exposure time of 1800 s. The images were recorded using a CCD(Photonic Science X-ray FDS 5.02 MP) with a pixel size of 4.54 $\mathrm{\mu}$m and 2750 $\times$ 2200 pixels.
Fig. 7. Results of X-ray backlit imaging: (a) result of gold mesh with a Fe X-ray source for the 6.4 keV imaging channel; (d) result of gold mesh with a W X-ray source for the 9.67 keV imaging channel; (b) and (e) intensity profiles along the green lines in (a) and (d), respectively; (c) and (f) measured and simulated spatial resolution for the 6.4 keV and 9.67 keV imaging channels, respectively. All the scales are divided by the magnification.
The imaging results for 6.4 keV and 9.67 keV channels are shown in Fig. 7(a) and (d), respectively. Accordingly, the FOVs of 6.4 keV and 9.67 keV imaging channels are 763 $\mathrm{\mu}$m and 459 $\mathrm{\mu}$m. The intensity profiles of the two imaging channels are shown in Fig. 7(b) and (e), corresponding to the green lines in Fig. 7(a) and (d), respectively. The measured spatial resolution was calibrated according to an intensity profile’s 10% - 90% evaluation criterion. The measured and simulated spatial resolution data points of the 6.4 keV and 9.67 keV imaging channels are shown in Fig. 7(c) and (f), respectively. The spatial resolution of the central FOV of the 6.4 keV and 9.67 keV imaging channels can reach 3.1 $\mathrm{\mu}$m and 3.5 $\mathrm{\mu}$m, respectively. The resolution of the 6.4 keV and 9.67 keV imaging channels can reach 4.7 $\mathrm{\mu}$m and 5 $\mathrm{\mu}$m, respectively, within the $\pm$ 150 $\mathrm{\mu}$m FOV. It can be seen from Fig. 7(a) and (d) the FOVs of the two imaging channels are different because of the angular bandwidth of the corresponding non-periodic multilayer films.
4.2 Spectral calibration results
Another essential part is the energy spectrum calibration of the imaging instrument to verify whether the proposed instrument meets the requirement of flat spectral response. The energy spectrum response calibration was performed after the imaging calibration was completed. The detector was operated at 30 kV and 20 mA, with a counting time of 60 s and 90 s for the 6.4 keV and 9.67 keV imaging channels, respectively. The mesh grid was replaced with a 15 $\mathrm{\mu}$m pinhole made of tantalum under dual-visible lens monitoring. Then, the CCD was replaced with a Si-PIN detector(Amptek, XR-100CR), and the detection area was 6 $\times$ 6 ${\rm mm}^{2}$. The schematic diagram of spectrum calibration is shown in Fig. 8. First, the detector was used to count the output spectrum of the 6.4 keV imaging channel. Then, the imaging instrument was removed from the optical path, and a 1.0 $\times$ 1.0 mm$^2$ rectangular hole was placed in front of the detector to block stray light for measuring the incident spectrum count. All operations were the same for the 9.67 keV imaging channel, except for the backlit X-ray source. Energy spectrum response data were measured several times for both imaging channels. Considering the solid angle, the reflection efficiency $R$ can be calculated by Eq. (12).
where $R$ is the reflection efficiency; $C_{input}$ and $C_{output}$ are the incident and output counts, respectively, measured by the detector; $\Omega _{input}$ can be calculated using $\frac {1.0^{2}}{u+v}$, whereas $\Omega _{\rm KB}$ can be calculated using Eq. (6).Fig. 9(a) and (d) show the spectral curves of incident and output spectra for 6.4 keV and 9.67 keV imaging channels, respectively, at the central FOV. From these two figures, the two image channels filter out the low- and high-energy X-ray of Bremsstrahlung for the incident spectrum emitted from the source. However, because the energy bandwidth of the non-periodic multilayers is broader than that of periodic multilayers, there are still peaks of Fe K$\beta _{1}$ and W L$\alpha _{1}$ characteristic lines for 6.4 keV and 9.67 keV imaging channels, respectively.
Fig. 9. (a) and (d) are the measurement incident and output spectra of the central FOV for 6.4 keV and 9.67keV imaging channels, respectively; (b) and (c) are the measurement reflection efficiencies of 6.4 keV imaging channel; (e) and (f) are the measurement reflection efficiencies of 9.67 keV image channel.
The calibrated and theoretical curves of the reflection efficiency for the 6.4 keV imaging channel at the different positions changing with different FOVs are shown in Fig. 9(b) and (c). In contrast, those for the 9.67 keV imaging channel are shown Fig. 9(e) and (f), respectively. The red curves in (b), (c), (e), and (f) show the theoretical reflection efficiency changing with different FOVs along the X or Y-axis; the blue curves show the measurement reflection efficiency of different FOVs along the X or Y-axis. Twenty-one sampling points with a 20 $\mathrm{\mu}$m interval for each calibrated curve were selected within the $\pm$ 200 $\mathrm{\mu}$m FOV along the X or Y-axis. The error bars represent the standard deviation of multiple measurements. As shown in Fig. 9(b) and (c), the RMS deviation value of the measured reflection efficiency is 1.71% for the 6.4 keV imaging channel in the $\pm$ 150 $\mathrm{\mu}$m FOV. Meanwhile, as shown in Fig. 9(e) and (f), the RMS deviation value of the measured reflection efficiency is 1.82% for the 9.67 keV imaging channel in the $\pm$ 150 $\mathrm{\mu}$m FOV. The significant RMS deviation values of the measured reflection efficiency may be due to the spatial nonuniformity of the backlit X-ray source. The decrease in the measured reflection efficiency compared with the theoretical curve is due to the degradation of the X-ray films in the air.
5. Conclusion
In this study, we propose a novel quasi-coaxis dual-energy flat spectral response X-ray imaging instrument for measuring electron temperature of the China’s 100 KJ laser facility. The imaging instrument comprises a dual-channel total-reflection KB microscope and two flat non-periodic multilayer mirrors. In addition, we propose a set of X-ray general diagnostic equipment and a debris protection shield for vital optical components. The proposed imaging instrument was assembled and characterized via offline X-ray backlit imaging experiments. Experimental results show that the proposed imaging instrument can reach 4.7 $\mathrm{\mu}$m and 5 $\mathrm{\mu}$m, and the RMS deviation values of the measured reflection efficiency are 1.71% and 1.82% for the 6.4 keV and 9.67 keV imaging channels in the $\pm$ 150 $\mathrm{\mu}$m FOV, respectively. According to the theoretical simulation, the RMS deviation values of reflection efficiency are 1.4% and 2.1% within 6.4 $\pm$ 0.5 keV and 9.67 $\pm$ 0.5 keV, respectively, in the $\pm$ 80 $\mathrm{\mu}$m FOV. Next, the instrument will measure the hotspot electron temperature on the China’s 100 kJ laser facility.
Funding
Ministry of Science and Technology of the People's Republic of China (2017YFA0403300); National Natural Science Foundation of China (12005157); National Natural Science Foundation of China (11905281); Foundation of President of China Academy of Engineering Physics (YZJJLX2019011).
Acknowledgments
The authors acknowledge the researchers and technicians of China Academy of Engineering Physics (CAEP) for their support and suggestions on the experimental scheme design.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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