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Abstract
The motion law of complex fluids under extreme conditions is an important aspect of high energy density physics research. It has been demonstrated that using multi-channel curved crystals and a framing camera to observe the laser-produced target pellets doped with tracer elements is an appropriate method for investigating this law. This paper presents a feasible design scheme for a multi-channel toroidal imager, with the ray trace model used to verify the rationality of the evaluation method and the aberration of single toroidal crystal imaging. We demonstrate that the field of view (FOV) consistency of the four-channel Ge(400) toroidal crystal imager is less than 50 µm, while the best spatial resolution is ∼4 µm and the FOV of each channel is >2.2 mm.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Multi kiloelectron volt (keV) monochromatic X-ray microscopy has many important applications [1] in the diagnosis of inertial confinement fusion. This includes observing the distribution of certain elements at different stages of the fusion to examine the Rayleigh-Taylor instability growth, the radiating shocks, and other essential aspects [2]. In order to distinguish the characteristic X-rays generated by the energy level transition of tracer elements from the radiation background, the imaging system is required to have a high monochromaticity ($E/\Delta E>200$) and a large field of view (>500 µm). Mainstream X-ray microscopes for ICF diagnosis, like pinhole microscopes, do not have monochromatic imaging capabilities; although Kirkpatrick-Baez microscopes and Wolter microscopes have large light collection efficiency and high spatial resolution, their spectral resolution capabilities depend on the energy bandwidth of the film [3].
Crystals are a natural spectroscopic material and curved crystals able to converge all X-rays of the same wavelength. There are two main types of curved crystal, the first of which is the Von Hamos [4] crystal with a cylindrically curved surface used for spectral diagnosis [5], while the second is the spherical or toroidal curved crystal that is used for two-dimensional monochromatic imaging. Since spherical curved crystals involve the astigmatism problems [6] caused by off-axis X-ray sources, the diffraction angle of the characteristic line is often required to be close to $90^\circ$ to reduce the astigmatism. However, as the diffraction angle increases, how to shield the X-ray directly irradiated by the target will be an issue, with the effective characteristic X-ray difficult to distinguish from the background X-ray noise and a reduction in the resolution of the spherical curved crystal likely.
Meanwhile, toroidal crystals allow for a smaller Bragg angle, which facilitates the integration of multiple channels, and when the meridional radius ($R_m$) and sagittal radius ($R_s$) of the curved crystal satisfies $R_s=R_m\sin ^2\theta$ [7], the astigmatism is eliminated and the resolution is significantly improved.
In 2000, Ingo Uschmann [8,9] designed a 10-channel monochromatic X-ray imager (five channels use Si(311) crystals and five channels use Ge(311) crystals) and obtained a spatial resolution better than 5 µm. However, due to the arrangement of the image points, the Bragg angle of the crystal in each channel needs to be slightly deviated. Since the full width at half maximum (FWHM) of the rocking curve of the crystal is very small, such a division will cause the diffraction angle of each channel to be slightly different, thereby affecting the consistency of the spectrum.
In view of this, the current study involves initially determining the optical design of the four-channel curved crystal imager, using cross-light and reasonable image point arrangement to ensure that each channel is completely rotationally symmetric. To further explore the imaging performance of toroidal crystals, including in terms of system energy bandwidth, field of view (FOV), effective area, and collection solid angle, we regard the imaging of the toroidal crystal as the convolution of the spectrum of the incident X-ray with the rocking curve of the crystal. The aberration expression of the toroidal crystal was derived from the method devised by Noda [10] and Howells [11]. At the same time, the OrAnge SYnchrotron (OASYS) suite software [12] and our own ray tracing program to simulate the resolution resulting from the assembly error and the spectral intensity curve in relation to the FOV. Finally, through the X-ray offline backlight imaging experiment, we demonstrate that the FOV consistency of the four-channel Ge(400) toroidal crystal imager is less than 50 µm, while the best spatial resolution is $\sim$4 µm and the FOV of each channel >2.2 mm.
2. Theory and simulation
2.1 Evaluation of imaging performance
2.1.1 System energy bandwidth
The crystal reflection needs to satisfy the Bragg condition [7], that is, the source energy $E$ and its incident angle $\theta$ need to be matched to produce great intensity:
where n is the diffraction order, h is the Planck constant, and d is the lattice spacing. The above aspect inspired us to regard the diffraction imaging of the crystal as a convolution [7,13] between the source spectrum and the rocking curve. Since the size of the implosion target is relatively small($\sim$1 mm), the X-ray spatial intensity distribution has a negligible effect on the spectral range, assuming that the spectral curve of the source $f_s\left (E \right )$ and the rocking curve of the crystal $g_r\left (E \right )$ are subject to the Gaussian distribution, and the size of the crystal is large enough such that the convolution result remains a Gaussian distribution:The FWHM of $I^\prime (E)$ can be expressed as follows:
Here, $\Delta E_c$ describes the broadening effect of the crystal’s rocking curve on the source, $\Delta E_0$ is the energy bandwidth of the source, and $\Delta \theta _B$ is the angle bandwidth of the crystal rocking curve. The differential expression $E/\Delta E=\Delta \theta /\tan \theta$ of Eq. (1) is used here to solve the energy bandwidth $\Delta E_r$. The spectral resolution of the crystal can be expressed as $E_0/\Delta E_r$.
2.1.2 Spectral acceptance
In fact, crystals will have a certain size, and not all X-ray energy can be reflected by the crystal. Here the spectral acceptance refers to the spectral range that crystals can reflect. It is limited by the size $L$ and object distance $p$ of the crystal, as shown in Fig. 1. For the Johansson-type curved crystal, all X-rays emitted from a point on the Roland circle will have the same incidence angle [14]. It is worth noting that while the Johann-type crystal is an approximation of the Johansson type, there is actually little difference in the incident angle of X-rays in the same direction and they can be handled in the same way. Thus, the length of $S$ represents the angle range of the incident ray, while according to Bragg’s law, it also represents the spectral acceptance. Define scale factor $\gamma$
Fig. 1. Optical path diagram of self-emissions imaging of toroidal curved crystals. $S$ (red) is the crystal $L$ projected on the Rowland circle with the central FOV as the vertex, and $S_1,S_2$ (green) are based on the edge of the FOV as the vertex. $S_c$ (orange) corresponds to $\Delta E_c$.
The radius of curvature R of the crystal surface is the diameter of the Rowland circle. Given the meridian length of crystal $L_m\ll p$, the arc $S$ can be approximately regarded as $s=\gamma L_m$. The spectral acceptance $\Delta E_s$ can be calculated according to the following:
For an ideal crystal, the effect of the crystal’s rocking curve on the spectral acceptance is minimal. If we introduce the design parameters $R$=290 mm, $\gamma$=0.875, $L_m$=10 mm, $E_0$=4.51 keV and $\theta =76.3^\circ$, such that $\Delta E_s$=32.8 eV, $\Delta E_s$ is the upper limit of $\Delta E_c$, when $\Delta E_c<\Delta E_s$, the effective area of the crystal imager does not cover the entire crystal surface, which depends on the deviation of the incident angle and the Bragg angle on different positions of the crystal surface. Uschmann [15] notes the approximate distribution of the deviation $\theta -\theta _B=\sigma (\alpha ,\varphi )$ with the divergence angle $\alpha$ and $\phi$ of the horizontal and vertical directions.
The magnification $M=q/p$ is determined according to the image distance $q$ and the object distance $q$. As shown in Fig. 2, the angle change in the horizontal direction is more rapid, which means that when calculating the effective area and the FOV, only the meridional direction generally needs to be considered, and the sagittal direction is considered to be large enough.
Fig. 2. Since the divergence angle $(\alpha ,\phi )$ is proportional to the aperture $L_m=2p\alpha ,L_s=2p\phi$, it is more intuitive to use the aperture as the abscissa. Given $M$=15 and $\theta _B=76.3^\circ$, the incident angle $\theta$ in the horizontal direction changes with the aperture, but there is no clear change in the vertical direction. The incidence angle range is approximately $\pm 1^\circ$.
According to Eq. (6) and reference [13], the area where the crystal can reflect X-rays, known as the effective area $S_{active}$, is a narrow band. The precise effective area can be derived using a complex theory [16] or ray tracing. However, $S_{active}$ can be simply approximated as
$L_m,L_s$ are the meridional and sagittal direction sizes of the crystal and $\Delta d_s$ is the diameter of the source. Given $L_m$=10 mm,$L_s$=10 mm and $M$=15, OASYS software was used to explore the imaging characteristics of toroidal curved crystals. Table 1 shows the effective area size of the crystal under different energy bandwidth conditions for a point light source, where the relative error between the effective area width calculated by the formula and generated via OASYS simulation was less than $10\%$. Figure 3(a) shows the setting interface of OASYS, while Fig. 3(b) shows the imaging result of a point source (not a circular discrete spot due to factors such as coma and surface profile), and Fig. 3(c) shows the imaging result of a circular light source with a diameter of 200 µm. Figure 3(d) shows the effective area of the crystal when the light source bandwidth was 10 eV. The collection solid angle is also given by the effective area:
Fig. 3. (a) The setting interface of OASYS. The Bragg angle was used to generate the diffraction profile of the crystal. The PlotXY program can draw the image plane at different distances. (b) and (c) are the imaging results of a point source and a circular source, respectively. Lastly, when the image distance is set to 0, the effective area of the crystal is drawn at (d).
Table 1. The relationship between the effective area of the crystal and the energy bandwidth of the source.
2.1.3 Field of view
The FOV of spherical or toroidal crystals can reach several millimeters. For self-emission, the FOV of the imager is limited by the crystal’s size and the energy bandwidth $\Delta E_c$. It can be ascertained from Fig. 2 that the crystal is not sensitive to angle changes in the sagittal direction and that the entire crystal range in this direction can be used, meaning the shape of the effective area on the crystal surface is often a narrow band or full aperture. The relationship between the FOV in the meridian direction and the energy bandwidth of the source is discussed here. Koch [17] provided the FOV of the spherical mirror, while Schollmeier [7] developed a form of convolution method to calculate the FOV of the self-mission and backlight system, while the method appears to be relatively complicated and largely unintuitive. The $FOV_m$ estimation method suitable for self-emission is outlined from a geometric perspective. Assuming that there is a large uniform rectangular light source on the object plane, after being reflected by the crystal, a partial rectangular image is obtained on the image plane. In the ray tracing program, the $FOV_m$ is defined as the distance between half the maximum intensity on the image surface divided by the magnification. The following discussion is divided into two scenarios:
- 1) In Fig. 1(a), when $\Delta E_c\leq \Delta E_s$, as $\Delta E_c$ grows, the $FOV_m$ will not change. This is because $S_1=S_2\geq S_c$ and the projection of the edge ray of the FOV on the Roland circle always intersects the midpoint of the $S_c$. Through simple derivation, the FOV satisfies Eq. (9):
- 2) In Fig. 1(b), when $\Delta E_c>\Delta E_s$, similarly, $S_1\cap S_c=S_2\cap S_c=\frac {1}{2}S\cap S_c$, and the edge ray of the FOV begin to move outwards and the FOV gradually increases:
To verify the model, as Fig. 4 shows, the ray tracing program was used to simulate the reflection of a point source with a uniform narrow spectrum at different field points. The field point where the reflection intensity is half the central field point is taken as the edge of the field point. The simulated data were consistent with the theoretical FOV curve.
Fig. 4. The curve of the FOV with source energy bandwidth $\Delta E_0$, given that size $L_m$=10 mm, object distance $p$=150 mm, and the radius of the crystal $R_m$=290 mm.
2.1.4 Spectral response function
While the rocking curve of an ideal crystal is very narrow, the broadening effect brought about by the energy spectrum of the source and the crystal aperture ensure the imager has a large FOV (Eq. (9)). From an experimental point of view, it is not difficult to find a suitable angle to reflect X-rays by adjusting the posture of the crystal. However, the size of the crystal limits the angular range of the incident light. According to the Bragg formula, we know that even with a full aperture, the response energy of the crystal is only around tens of eV. In Eq. (2), the crystal imaging process was regarded as convolution and the influence of the crystal size and the angle distribution of the incident ray were not considered. For a broad-spectrum self-emission model, we can still hold that most of the surface of the crystal is used. However, if it involves backlight imaging, the X-ray emitted from the source will have a limited divergence angle, which means the crystal may only illuminate a small part. Thus, different FOVs use different areas on the crystal, and the energy response will be complicated. It is thus necessary to use a simple and widely adaptable concept to describe the relationship between the FOV and the energy response under different imaging modes. As such, Eq. (2) can be re-written as follows:
where $I(E)$ is the energy distribution of the incident light, $R(\theta ,E)$ is the crystal rocking curve, with the incident angle and the source energy as independent variables since, according to Bragg’s law, the energy of incident light can be converted into the angle $\theta _B=\arcsin (nhc/2dE)$. Finally, $dist(\theta )$ is the normalized angular distribution of the angle between the light emitted from a certain point in the FOV and the crystal surface, which causes the difference between backlight imaging and self-emission imaging. In other words, the effective area determines the range of $\theta$. If the effective area is approximately regarded as a rectangle [16], or a rectangular diaphragm limit is added to the optical path, according to Eq. (6) we can consider that $dist(\theta )$ is uniformly distributedIf every point on the FOV utilizes the entire aperture of the crystal, the difference between $\theta _1$ and $\theta _2$ will be constant, and the energy spectrum response of the crystal can only be determined by the rocking curve and the incident spectrum. In the case of backlight imaging, the divergence angle of the source or the diaphragm size determine the upper and lower limits of the integral of Eq. (11), which is not the case with self-emission imaging. Finally, the results shown in Fig. 5 could be obtained. In comparing the theoretical $I^\prime _{rect}(E)$ and the spectral distribution obtained via ray tracing, the results were found to be highly consistent.
Fig. 5. Simulated spectrum curve at the center FOV. The FWHM of the peak of the light source at 4.51 keV was set to 50 eV, the size of the crystal = 10 mm, and both sides of the reflection spectrum were cut off.
2.2 Imaging aberration analysis
The resolution of the curved crystal imaging system is not only related to the aperture of the curved crystal and the FOV, but also related to the energy bandwidth of the source and Bragg angle. While Monte Carlo ray tracing can be used to obtain useful parameters such as resolution more accurately, theoretically establishing the relationship between aberration and resolution is beneficial to evaluating the imager. The greatest benefit of the toroidal curved crystal is the elimination of any astigmatism. However, there exist numerous other aberration terms. Noda [10] conducted an in-depth study of the geometric theory of the grating. The optical path function was used to calculate the aberration caused by the surface shape error and the deviation of the object point spatial position. However, the main disadvantage is that the calculation process is too complicated. Subsequently, Howells [11] simplified the discussion initiated by Noda, and Schollmeier [7] applied it to the spherical curved crystal. In the following section, the formulas of partial aberrations are given directly:
The total aberration is expressed as the algebraic sum of $\Delta y'_{ij0}$ and $\Delta z'_{ij0}$. The general expression of the optical path function $F_{ijk}$ could be calculated with reference to the data in the relevant literature [11]. We can ascertain that the defocus line $\Delta y_{200}$ and $\Delta z_{020}$ will increase linearly with the aperture, the spherical aberration $\Delta y_{400}$ will increase with the cube of the aperture, and the aperture defect $\Delta y_{300}$ will be proportional to the square of aperture. All $\Delta y$ values decrease along with the Bragg angle growth.
Put the parameters in Table 2 into the Eq. (13) to get the aberration curve in the Fig. 6. Curves a and b present the amount of defocus generated in the meridian and sagittal directions when the object point deviated along the optical axis, meaning its abscissa represents the object distance. Curves c, d, and e represent the spherical aberration term, the aperture defect term, and the line curve term, respectively, meaning the object point is in an ideal position and the abscissa represents the aperture. From the point of view of the curve growth rate, the aperture defect and line curve are the main aberration terms. However, it should be noted that the aperture of the curved crystal depends on the effective area of the crystal rather than the crystal’s size.
Fig. 6. All curves are divided by the magnification. The abscissa of curves a and b is the object distance, with the aperture set to 10 mm; since $\sin \theta \approx 1$, they are very close. The abscissa of the remainder of the curve is the aperture, while the object point is in the ideal object plane. The best way to reduce the aberration is to control the crystal aperture or select a more suitable crystal plane to increase the Bragg angle.
Table 2. Optical parameters of the toroidal crystal imager.
The ray tracing program was used to obtain the curve of the resolution varying with the deviation of the object point, in order to compare with the aberration curve and guide the experimental assembly. Figure 7 shows the change in resolution when a point light source moves along the potical axis and the non-optical axis, where the encircled energy as the evaluation standard of resolution. Here, the bandwidth of the light source was set to 10 eV. The plotting result indicated that the crystal is an imaging system with a small depth of field. The deviation along the optical axis caused the resolution to deteriorate rapidly, while the sagittal resolution changed at the slowest rate [18]. In fact, as the bandwidth of the light source increases, the resolution will decrease and the effective area of the crystal will increase until the entire crystal surface is used, at which point, the encircled energy curves in the meridional and sagittal directions will be nearly identical.
Fig. 7. All curves are divided by the magnification. The abscissa is the distance of object point from the ideal object point and the vertical axis used $80\%$ of the encircled energy as the evaluation criterion of the image spot size.
3. Experimental prototype
To adapt the requirements of the diagnostic platform and to cooperate with the framing camera, An optical geometric design was devised, as shown in Fig. 8, with the detailed parameters of the system presented in Table 2. The crystal was located on the circumference of the radius $R$, and the X-rays emitted from the target were reflected by the crystal, the beams of the four channels crossed at the diaphragm and then converged on the microstrip of the framing camera. The channels are completely rotationally symmetrical to ensure that the reflection efficiency of the same FOV of each channel is consistent, thereby reducing the errors of the time framing diagnosis of the online test experiment.
Here, $\beta$ is defined as the angle between the normal of the crystal surface and the axis, while $d$ is the distance from the image point to the center of the framing camera. At the intersection of the four reflected beams, a diaphragm could be set to block stray light, while at the position of closing to the target, a thick lead plate was placed to block the X-rays coming directly from the target [19]. The angle $\alpha =\pi -2\theta$. Thus, Eq. (14) could be easily derived:
Schollmeier compared the Bragg angle and diffraction efficiency of various crystals at 1-25keV [20]. For 4.51keV, two crystals are more suitable: Ge(400) and Qtz(203), both of which have large diffraction efficiency, but due to the Bragg angle of Qtz (203) is very close to $90^\circ$($88.43^\circ$) and cannot be coupled to multiple channels, so Ge (400) is selected as the optical element and the detailed parameters of the system are shown in Table 2.
The laboratory backlight imaging experiment layout and experimental prototype diagram are shown in Fig. 9, a titanium-anode X-ray tube was used as the backlight X-ray source with a large focal spot ($\geq$2 mm). Since the $K\alpha$ line of titanium is severely attenuated in an air environment, the entire optical path needs to be covered in a helium pipeline. The indicator point is used to indicate the position of the central FOV, it can be replaced with a four-quadrant golden grid and the target in Fig. 8 under dual optical lenses monitoring [21]. The images were acquired using a hard X-ray charge coupled device (CCD). Prior to the imaging experiment, the position of the image point was determined via a three coordinates measuring machine. Following this, the crystal and the substrate were connected to the electronically controlled six-axis adjustment frame through an adapter.
Since the X-ray tube cannot illuminate multiple channels at the same time, to achieve the same FOV among multiple channels, we used a precision turntable to ensure that the indicator point was always at the center of rotation of the four channels. When each crystal is installed and adjusted, the imaging relationship between the crystal and the object point will not change, even if the channel is turned away. The experiment involved the use of dual optical lenses to monitor the movement of the indicator point during the rotation of the multi-channel curved crystal imager, with the results indicating that positioning error was within 50 µm. In addition, the image point of each channel will eventually be imaged at the same pixel position of the CCD, so the deviation of the image point can be ignored. The indicator point positioning error here is mainly determined by the accuracy and stability of the turntable. To some extent, it can be regarded as the evaluation standard for FOV consistency between multiple channels.
The key points for system adjustment were as follows. First, the crystal position and angle were adjusted to identify the grid image and to move it to the center of the CCD. Second, since the crystal had a large FOV, meaning the posture of the crystal was not unique, a diaphragm was added in front of the crystal to limit the imaging area of the crystal so as to reduce the adjustable angle and position. Third, the diaphragm was removed and the best object-image relationship was identified by adjusting the object distance of the crystal. Finally, after fixing the crystal postures of all channels, three indicating lasers was used to indicate the center of the image plane.
4. Experimental results
The X-ray backlight imaging results of the four-quadrant grid and the knife edge are shown in Fig. 10 and the orange line in Fig. 10 corresponds to the resolution evaluation curve in Fig. 11. The entire grid is uniformly illuminated, and all grid lines are relatively clear. The background noise of the knife edge images has been removed. The knife edge of CH-1 is slightly blurred, while the knife edge of CH-4 is sharper, because the curved crystal imager is sensitive to the depth of field, it may be caused by assembly errors or crystal qualities. The titanium-anode X-ray tube was operated at 20 kV/15 mA with an exposure time of 600 s. The diameter of the four-quadrant grid is 2.2 mm, and the four spatial periods are 62 µm, 83 µm, 126 µm and 165 µm. In order to obtain a complete grid image with large FOV, a large area (72 mm$\times$48 mm) CCD (PSL X-ray VHR-11M-90) with a pixel size of 18 µm and 4008$\times$2672 pixels was used. The images of knife edge were acquired using a small area (12.5 mm$\times$10 mm) CCD (PSL X-ray FDS 5.02 MP) with a pixel size of 4.54 µm and 2750$\times$2200 pixels.
Fig. 10. Four-channel toroidal curved crystal imager grid and knife edge backlight X-ray imaging results, and the scales are divided by the magnification.
In Fig. 11, the spatial resolution was calibrated using the conventional $10\%-90\%$ standard. Here, taking a certain line on the central area of the grid or knife edge (the orange line in Fig. 10), and the distance corresponding to the intensity distribution from $10\%$ to $90\%$ divided by the magnification is regarded as the resolution. There are two factors that may affect the resolution judgment, the first is that the edges of the grid are not strictly sharp edges, while the second is that the long exposure will lead to more noise. The resolution evaluation of the knife edge is better than the grid. Figure 11(a) and Fig. 11(b) both show that the resolution of CH-1 is poor, and the resolution of CH-4 is the best. According to the imaging results of the knife edge, the resolution of the central FOV of the four channels can reach 9.2 µm, 5.5 µm, 7.5 µm, and 4 µm, respectively.
The four-channel curved crystal imager needs to work with the framing camera to achieve the time resolution, which means it is necessary to verify the intensity consistency between the channels. Under dual-lens monitoring, the grid was replaced with a 15 µm pinhole, and an Amptek CdTe detector (SDD) with a detection area of $5\times 5$ mm$^2$ was placed in the center of the image plane. The detector was operated at 10 kV/4 mA, and the counting time was 90 s. While moving the pinhole within the range of $\pm$700 µm in the meridian and sagittal directions, we moved the SDD placed at the end of the image plane to record the photon counts at different field points. After the measurement of all channels was completed, the crystal was replaced with the SDD to record the photon counts of the backlight source in different FOVs.
Figure 12(a) shows the spectral curve of the four channels and the source at the central FOV. Here, it can be seen that the reflected spectral curves of the four channels basically overlapped and filtered out the $\beta$ line from the source. However, due to the low spectral resolution capability ($\sim$120 eV) of the SDD used in the experiment, the spectral acceptance of the curved crystal was around 32 eV ($\sim$10 mm), which is obviously smaller than the spectral resolution of the SDD, meaning the curve in the figure was a result of time accumulation and it was impossible to infer an accurate FWHM from the measured X-ray spectrum. This also caused the measured spectrum curve to be wider than the reflected spectrum curve in Fig. 5.
The measured curve of the reflection efficiency of the curved crystal changing with different FOVs is shown in Fig. 12(b). Here, it can be seen that the reflection efficiency between the channels was very close. The reflection efficiency $R$ was modified to a certain extent in the original photon count, taking into account the influence of the light path attenuation $K$ and the solid angle of the light collection $\Omega$; however, $K$ and $\Omega$ are approximate quantities, meaning the absolute value of reflectance is for reference only.
As shown in the Fig. 12(b), it describes the measured curves of the system reflection efficiency with the FOVs, which represents the overlapping effect of the reflectivity of different energy ranges in the X-ray source spectrum. The ’Y Axis’ represents the sagittal direction, as shown in Fig. 2, the incident angle of X-ray in this direction varies little with the aperture, so the reflection efficiency in this direction changes relatively gently. However, in the meridian direction, since the incident angle of the X-ray changes with the FOV, this leads to a change in the energy response range and a certain tilt in the reflection efficiency curve.
5. Conclusion
This article presented the development of a four-channel toroidal crystal X-ray imager for monochromatic imaging of the $K\alpha$ line emitted by the tracer element titanium doped in the fusion target pellet. The various experiments demonstrated that the resolution of the imager central FOV of the four channels can reach 9.2 µm, 5.5 µm, 7.5 µm, and 4 µm, respectively, and achieve a large FOV of $\sim$2.2 mm at least. The channels exhibited good intensity and energy spectrum consistency, with FOV consistency of less than 50 µm. According to the theoretical calculation, the spectral acceptance of the toroidal curved crystal is $\sim$32 eV, and the FOV exceed 4.5mm. The system provides a powerful observation method for diagnosing the complex fluid motion law of the fusion implosion process and the next step will be to carry out online measurement experiments on the China’s laser fusion facility.
Funding
National Key Research and Development Program of China (2017YFA0403302, 2017YFA0403304); National Natural Science Foundation of China (12005157).
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.
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