碳的近边吸收精细结构在280~320 eV的能量范围内，对应波长范围为3.8~4.4 nm，为了研究碳的谱线，要求谱仪在3~5 nm波段工作。碳的内层电子从1s轨道跃迁到外层的未占分子轨道引起的吸收峰的典型能量宽度为0.5 eV，为了能准确反映碳的1s NEXAFS谱的特征，谱仪在4.4 nm处的分辨率须在600以上。本文据此要求展开设计。
The corresponding wavelength range of the near edge absorption fine structure of carbon is 3.8-4.4 nm within the energy range of 280-320 eV. In order to study the spectrum of carbon, the spectrometer is required to work at 3-5 nm. The typical energy width of the absorption peak caused by the transition of the inner electrons of carbon from 1s orbital to the outer unoccupied molecular orbital is 0.5 eV. In order to accurately reflect the features of the NEXAFS spectrum of carbon(1s), the resolution of the spectrometer shall be over 600 at 4.4 nm. In this paper, the spectrometer has been designed based on above requirements.
The near edge X-ray absorption spectrometer has been designed using the spectrography in this paper. The “white lights” generated by the light source pass through the sample and then are split. Later on, the intensity of lights with all wavelengths before and after passing through the sample is measured with a 1D or 2D detector so as to obtain the absorption spectrum. With the spectrometer, the intensity of lights with all wavelengths can be obtained simultaneously without scanning, and a transient spectrum analysis can also be made.
设计的掠入射式近边X射线吸收谱仪结构示意图如图 1所示，系统由气体激光等离子体光源、样品、狭缝、光栅和CCD组成。光源以氪气作为靶材，经过滤光产生波长2~6 nm的连续谱软X射线，掠入射到样品表面，反射光经光栅分光，再由CCD测定各波长射线的强度，结合光源的谱线即可得到包含了吸收信息的反射谱。
图 1 掠入射式X射线吸收谱仪示意图
Figure 1. Sketch of the designed X-ray absorption spectrometer under grazing incidence conditions
The sketch of the structure of the designed near edge X-ray absorption spectrometer under grazing incidence conditions is shown in Fig. 1. The system consists of gas laser plasma source, sample, slit, grating and CCD(camera). Krypton is used as the target light source. 2-6 nm continuous spectral soft X-rays are generated through filtering and they are of grazing incidence to the sample surface. The reflected lights are split by the grating, and then the intensity of rays with various wavelengths is measured using the CCD(camera). The reflectance spectrum containing absorption information can be obtained according to the spectral line of the light source.
Fresnel formula gives the relationship between reflectivity and refractive index. Due to existence of absorption, the refractive index of substances to X-ray is not a real number but a complex number related to absorption, i.e. n=1-δ-iβ, where 1-δ denotes dispersion and β denotes absorption. The linear absorption coefficient can be directly obtained from β, i.e. μ=4πβ/λ. Therefore, reflectivity also contains absorption information. Substitute complex refractive index into Fresnel formula to obtain p-polarized X-ray reflectivity and s-polarized X-ray reflectivity under grazing incidence conditions respectively. Fig. 2 is the curve of variation of reflectivity with incidence angle at different absorption intensity in case of δ=0.001. According to the comparison of reflectivity of different polarized lights, in spite of absorption intensity, the reflectivity of two polarized lights is approximately equal, so the total reflectivity can be expressed approximately in the reflectivity of s-polarized light.
Where φ is grazing incidence angle. It can be seen that reflectivity R(E) is the function of δ(E) and β(E), where E is photon energy. NEXAFS spectrum can be extracted from the measured reflectivity spectral line using formula (1) in combination with δ(E) obtained from the database CXRO.
从图 2可以看出，反射率总是随掠入射角的增大而减小，当掠入射角增大到临界角φc，低吸收的反射率迅速下降，这个角即为全反射临界角。为了使反射率谱线能清晰反映吸收的变化，谱仪的掠入射角需小于样品的全反射临界角，考虑到有机物在碳的吸收边4.4 nm附近的全反射临界角约为3°，因此本文设计的谱仪取2°掠入射。
As shown in Fig. 2, reflectivity always decreases as grazing incidence angle increases. When grazing incidence angle increases to the critical angle φc, the reflectivity at low absorption intensity decreases rapidly. This angle is a critical angle of total reflection. In order that the reflectivity spectral line can clearly reflect absorption variation, the grazing incidence angle of the spectrometer would be less than the sample′s critical angle of total reflection. In view of the fact that the critical angle of total reflection of organic substances is about 3° near the carbon's absorption edge of 4.4 nm, the grazing incidence angle of the spectrometer designed in this paper is taken as 2°.
The light splitting element plays a decisive role in the performance of the spectrometer. The resolution capability of an ordinary plane grating is poor and cannot meet the high resolution requirements of X-ray wavelengths. In case of adding focusing mirrors, the system′s efficiency of light energy utilization will be reduced. The conventional concave evenly-spaced grating has functions such as light splitting and focusing, but to minimize aberration, Rowland circle structure must be adopted, and a plane detector cannot be used in acquisition. Therefore, the aberration-corrected holographic varied line-space concave spherical grating is used in this paper, which can achieve both light splitting and focusing and also has flat field characteristics, for convenience of using the area array type CCD to receive information. The schematic diagram of the aberration corrected flat-field grating is shown in Fig. 3, where x axis is the central normal direction of the grating, y axis is the central tangent direction of the grating, α is incidence angle, β is diffraction angle, r is incidence arm length, and r′ is emergence arm length.
Based on Fermat principle, the obtained grating′s dispersion equation and focusing equation in dispersion direction are respectively as follows:
Where d0 is the scale line width of grating center, also called nominal line width; R is the radius of curvature of grating substrate; b2 is the linear density parameter of grating. By selecting appropriate values, the focusing surface of the grating can be approximately a plane.
本文选取Shimadzu的30-001型光栅，该光栅公称线密度n0 2 400线/mm，工作波长范围1~6 nm，入射臂长237 mm，入射角88.65°。图 4给出了该光栅不同入射角对应的聚焦曲线，坐标系定义与图 3中一致，光栅参数来自于文献。可以看出，入射角88.65°时，光栅中心到探测面距离D0为235 mm。不同入射角的聚焦曲线不同，但是都可以拟合成直线，因此可以根据需要改变光栅的使用结构参数。
图 4 不同入射角对应的聚焦曲线，红线表示聚焦曲线，黑色虚线表示其拟合直线，绿线表示不同波长
Figure 4. Focusing curves and fitting straight lines at different incidence angles. The red lines represent the focus curves, the black dashed lines are straight fitting lines and the green lines are different wavelengths
Shimadzu 30-001 grating is selected. The parameters of the grating are the following: nominal linear density n0 is 2 400 lines/mm; wavelength range is 1-6 nm; incidence arm length is 237 nm, and incidence angle is 88.65°. Fig. 4 shows the focusing curves at different incidence angles, where the coordinate system definition is in line with that in Fig. 3, and grating parameters come from the reference . As shown in Fig. 4, when the incidence angle is 88.65°, the distance D0 from the grating center to the detection surface is 235 mm. Focusing curves at different incidence angles are different, but all of them can be fitted into straight lines, so the structure parameters of the grating can be changed as needed.
图 5 光栅的不同使用结构
Figure 5. Structures of the grating (a)the conventional scheme, (b)the optimized scheme
The conventional grating assembly scheme is that the CCD plane is vertical to the tangent plane of the grating center, as shown in Fig. 5. Such scheme is very difficult in an actual application. On one hand, there are too high requirements for the incidence angle precision, and it can be guaranteed with the aid of a high precision adjusting mechanism and measuring device. On the other hand, CCD is closely linked with the grating. When the grating attitude is adjusted, CCD must be adjusted accordingly, thereby increasing the adjustment difficulty.
为了可以分开独立调整光栅和CCD，我们以CCD平面与入射光线方向垂直作为目标对装配结构进行优化，如图 5(b)所示，这样得到的方案下，CCD的倾角不再依赖光栅，从而可以先安装调整好CCD再调节光栅，在真空中只需要转动光栅，使特定波长的谱线的像最窄，就可以获得较高的安装精度。入射角α取88.6°进行设计，利用公式(2)和公式(3)，以聚焦曲线的拟合直线与入射光线方向垂直为目标，获得了对应的最佳入射臂长r和光栅中心到CCD探测面的距离D，结果见表 1。这样在安装时就只有光栅需要在真空中调整，同时也降低了入射角的调整难度。
表 1 优化的装配方案参数
Table 1. Parameters of the optimized installation scheme
Parameters α/(°) r/mm D/mm θ/(°) Value 88.6 270 234.0 91.4
In order that the grating and CCD can be adjusted separately, the assembly structure has been optimized by aiming at making the CCD plane be vertical to the incident ray direction, as shown in Fig. 5(b). In such scheme obtained, the dip angle of the CCD doesn't rely on the grating any longer, so that the CCD can be firstly installed and adjusted well and then the grating is adjusted. High installation precision can be obtained by only turning the grating in vacuum to make the image of the spectral line of the specific wavelength be the narrowest. The incidence angle α is taken as 88.6° in the design. Using formulas (2) and (3) and aiming at making the fitting straight line of the focusing curve vertical to the incident ray direction, the corresponding optimum incidence arm length r and distance D from the grating center to the CCD detection surface have been obtained. The result is shown in Tab. 1. Thus, only the grating needs to be adjusted in vacuum during installation, which also reduces the difficulty in incidence angle adjustment.
Resolution is an important index of an optical spectrum instrument. The resolution of the spectrometer designed in this paper is affected mainly by multiple factors such as entrance slit width S1, grating′s diffraction limit and aberration, CCD pixel size S2, etc. Slit width and grating performance decide the FWHM of monochromatic wavelength spectral line, and pixel size limits the limiting resolution of the spectrometer.
According to the grating equation coupled with the geometrical relationship, the linear dispersion of the grating on the detection surface can be obtained as follows:
If the FWHM of the spectral image at a wavelength is known, the line width of this wavelength can be obtained as follows:
利用光线追迹可以获取特定波长的谱线在探测面上的光谱像，从而综合分析入射狭缝宽度和光栅性能的影响。狭缝宽度设为100 μm，入射臂长为270 mm，入射角为88.6°，光谱探测面放置在D=234 mm处，令光线在入射范围内随机生成，可以模拟获得探测面上的点列图。通过统计宽度方向上各个像素内的光线数量，得到光强统计分布图，对光强分布进行高斯拟合，求出半高宽，即可利用公式(5)计算线宽。图 6为4.4 nm波长的谱线光线追迹获得的点列图、统计直方图以及高斯拟合曲线，半高宽FWHM即像的宽度为13.8 μm，对应线宽为0.003 5 nm。图中横坐标表示谱线的像到入射光线的距离，对应于图 5(b)中的长度l。
图 6 4.4 nm波长的光线追迹结果
Figure 6. The result of ray tracing at 4.4 nm (a)Spot diagram, (b)Histogram, (c)Gauss fitting curve
The spectral image of the spectral line at a specific wavelength on the detection surface can be obtained using the ray tracing method, thus comprehensively analyzing the influence of entrance slit and grating performance. The spot diagram on the detection surface can be obtained on the assumption that the slit width is 100 μm, the incidence arm length is 270 nm, the incidence angle is 88.6°, the spectral detection surface is placed at D=234 mm and rays are generated randomly within the incidence range. The statistical distribution chart of light intensity is obtained from the statistical analysis of rays of each pixel in the width direction. The FWHM is calculated through Gaussian fitting of the light intensity distribution, and then the line width can be calculated using formula (5). Fig. 6 shows the spot diagram, histogram and Gauss fitting curve obtained using ray tracing at 4.4 nm. The FWHM i.e. image width is 13.8 μm, and the corresponding line width is 0.003 5 nm. In the figure, the abscissa denotes the distance from the spectral line image to the incident ray, which is corresponding with the length l in Fig. 5(b).
受探测器像元尺寸的限制，光谱仪的分辨率往往不能直接由谱线线宽决定。根据奈奎斯特抽样定理，为了能真实反映信号特征，采样频率应大于信号频率的两倍，由公式(4)可以得到单个像元对应的谱线线宽ΔλS2，则谱仪极限分辨率为Remax=λ/2ΔλS2。像元宽度为13 μm，4.4 nm的半高宽小于像元尺寸的两倍，因此设计的谱仪可以实现极限分辨率，4.4 nm处分辨率为666，对应线宽0.006 6 nm。使用像元数1 024的CCD，谱仪工作范围超过3 nm，满足设计要求。
Limited by the pixel size of the detector, the resolution of the spectrometer cannot be determined directly by the spectral line width in general. According to Nyquist sampling theorem, the sampling frequency would be larger than twice of the signal frequency in order to truly reflect signal features. According to formula (4), the spectral line width corresponding with a single pixel can be obtained, and then the limiting resolution of the spectrometer is Remax=λ/2ΔλS2. The pixel width is 13 μm, and the FWHM of 4.4 nm is less than twice of the pixel size, so the designed spectrometer can achieve the limiting resolution, its resolution is 666 at 4.4 nm, and the corresponding line width is 0.006 6 nm. The CCD with 1 024 pixels is used and the wavelength range of the spectrometer is over 3 nm, which meets the requirements of the design.
表 2 掠入射式近边X射线吸收谱仪设计参数
Table 2. Design parameters of the Near-edge X-ray absorption spectrometer under grazing incidence conditions
Parameters Value Wavelength range/nm 2~5 Resolution email@example.com nm φ/(°) 2 Width of entrance slit S1/μm 100 n0/mm-1 2 400 Incidence angle α/(°) 88.6 Incidence distance r/mm 270 θ/(°) 91.4 D/mm 234.0 Pixel size(W×H:μm2) 13.5×13.5 Active pixels 1 024×1 024
According to the above analysis, the parameters of the near-edge X-ray absorption spectrometer under grazing incidence conditions designed in this paper are shown in Tab. 2.
图 8展示了搭建完成的小型掠入射式近边X射线吸收谱仪。光谱仪工作在10-4 Pa真空环境下。沿着光路方向(在图中标注光源、各个腔体)，3个真空腔体分别为光源室、样品室和光栅室，激光聚焦到喷出的气体团上形成等离子体，产生X射线辐射输出，经Ti膜后照射到样品表面，Ti膜用于过滤带外光。为了结构紧凑，入射狭缝安置在样品室中，CCD通过波纹管与光栅室相连，以便通过调整机构微调CCD位置。
Fig. 8 shows the well-erected compact near edge X-ray absorption spectrometer under grazing incidence conditions. The spectrometer works in 10-4 Pa vacuum environment. Along the light path direction(light source and each chamber marked in the figure), the three vacuum chambers are light source chamber, sample chamber and grating chamber respectively. Laser is focused onto the ejected gas clumps to form plasma and generate X-ray radiation output. After passing through the Ti membrane, rays shine on the sample surface. The Ti membrane is used to filter out-of-band lights. In order to achieve a compact structure, the entrance slit is placed in the sample chamber, and the CCD is connected with the grating chamber via the corrugated pipe, for convenience of micro-adjusting the CCD position through the adjusting mechanism.
氮气作为激光等离子体光源靶材对光谱仪分辨率进行测试，图 9为实验测得的光谱图。可以看出，氮气在2~5 nm波段的谱线均清晰可见，波长2.478 nm和2.49 nm两条谱线也能明显区分。对这两个光谱峰进行高斯拟合得到曲线C1和C2，曲线C1的半高宽FWHM为1.9，不足两个像元，表明搭建的光谱仪可实现极限分辨，满足设计指标。
The resolution of the spectrometer has been tested using nitrogen as the laser plasma source target. Fig. 9 shows the spectrogram obtained from the test. It can be seen that the spectral lines of nitrogen at 2-5 nm are clearly visible and the two spectral lines at 2.478 nm and 2.49 nm can also be identified obviously. The curves C1 and C2 are obtained from Gauss fitting of the two spectral peaks. The HWHM of curve C1 is 1.9 that is less than two pixels, indicating that the erected spectrometer can achieve the limiting resolution and the design index.
Wavelength calibration is performed using the parameter fitting method. The model is shown in formula (6).
表 3 波长标定结果
Table 3. Results of wavelength calibration
Pixel positions 1 631 777 782 821 841 1 024 Actural wavelength/nm 2.878 7 2.489 8 2.478 1 2.377 4 2.327 7 Calibration wavelength/nm 5.025 2.878 1 2.490 2 2.477 5 2.378 2 2.328 1 2.008 3 Error/nm -0.000 6 0.000 4 -0.000 5 0.000 8 0.000 4
Refer to Fig. 5(b) for the definition of each parameter in the above formula. N is the position of CCD pixel, the upper edge is the position at N=0, and n0 denotes the nominal linear density of the grating. Tab. 3 shows the actual wavelength and calibration wavelength at pixel positions. The results show that the wavelength calibration error is less than 0.001 nm and the actual wavelength range of the spectrometer is 2-5 nm.
表 4 光学系统参数设计值与实际值比较
Table 4. Comparison of the design value with the actual value of optical system parameters
Parameters α/(°) θ/(°) D0/mm x0/mm Design value 88.6 91.4 234 23.74 Actual value 88.634 8 91.389 9 234.011 3 23.682 6
The actual value of each parameter of the system can be calculated through wavelength calibration with the parameter fitting method. The actual value is compared with the theoretical design value. The result is shown in Tab. 4. As shown in the table, the actual value of each parameter is basically consistent with the design value, and all deviations meet the tolerance distribution requirements.
Design of the X-ray absorption spectrometer
Spectrometer structure design
Assembly scheme optimization
Resolution test and wavelength calibration