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当柱面反射晶体弯制完成后,从表面看是均匀光滑且无裂纹缺角等明显缺陷的。但在将柱面反射弯晶真正用于物理实验前,还有两方面的参数需要检定。其一是柱面反射晶体的曲率半径是否如预期的要求。在光源、探测器以及柱面弯晶的转轴位置都固定的情况下,当柱面反射弯晶样品绕着转轴旋转时,如果晶体弯制得好,晶面就是均匀规则的,那么在记录面上特征谱线的衍射位置将是固定的,如果弯晶的曲率半径在弯制过程中有变化,特征谱线出射到记录面的位置也会发生相应改变。通过特征谱线的位移变化,就可以评估柱面反射晶体曲率半径与预设的标准值的偏差情况。其二是实际参与X射线衍射的晶面是否在弯制过程中受损。在实际使用中,有些晶体虽然可见光看来很正常,但在与X射线作用时谱线明显扭曲变形。如果谱线的形状出现局部的扭曲、变形,甚至分裂,那么就可以判断对应位置的晶体区域在弯制过程中受到损伤,则该弯晶样品不能用于大型激光装置实验,以避免对实验数据产生误判或误读。
柱面弯晶的检测原理如图1所示,实验时以X射线管作为光源,弯晶的转轴和记录面位置保持不变,柱面弯晶绕着转轴可以任意旋转。建立如图2的坐标系,其中X射线源位置为原点
$ O $ ,晶体的曲率圆心位置为S(xc, yc),晶体的曲率半径为$ R $ ,对应特征谱线波长的Bragg角为$ \theta $ ,特征谱线在晶体表面的衍射点位置为D(xd, yd),记录面到x轴的距离为$ L $ 。可以看到,当半径$ R $ 的值变化时,对应同样Bragg角$ \theta $ 的衍射点$D'$ 的位置处于S、O、D 3点决定的圆弧上。由此可以计算出$D'$ 的坐标,再根据对称关系算出衍射线的偏移量。理论上,D点的位置可以随意放置,但为了便于实验排布和计算,实际实验中选择了让$ \overline{SD} $ 平行于探测器表面的方向。取
$ {y}_{c}=H $ ,则:$$ {x}_{c}=R+H \cdot \rm tan\left(\theta \right) $$ (1) $$ {x}_{d}=H \cdot \rm tan\left(\theta \right) $$ (2) $$ {y}_{d}=H $$ (3) 此时,衍射线在记录面上的坐标为
${(x}_{0},L)$ ,则:$$ {x}_{0}=2H \cdot {\rm tan}\left(\theta \right)-L $$ (4) 要计算某一条已知波长的特征谱线,会对应同样的Bragg角
$ \theta $ ,那么由S、O、D 3点决定的圆的圆心坐标为${{S}}'\left({x}_{c}', {y}_{c}'\right)$ $$ {x}'_{c}=[R/2+H \cdot \rm tan(\theta \left)\right] $$ (5) $$ {y}'_{c}=\frac{H}{2} \cdot [1-{\rm tan}^{2}\left(\theta \right)]-\frac{R}{2} \cdot {\rm tan}\left(\theta \right) $$ (6) 如果
$ R $ 的值发生变化,即$R'=R-\Delta R$ ,那么角度$ \theta $ 对应的衍射点的位置为D'(x'd, y'd),从而在记录面上衍射线的位置也会改变。在图3中可以看到,衍射线的位置改变量与曲率半径和记录面到晶体的距离有密切联系。晶体曲率半径差别越大,相同Bragg角下的衍射位置与标准衍射位置偏差也越大,再经过晶体衍射后到达记录面的位置改变量也就越大,这个偏差是非线性的。记录面距离晶体越远,到达记录面的位置变化就越明显。在综合考虑了信号强度、空间限制等因素后,采用L为500 mm的排布方式来对柱面弯晶进行实验考核。
High accuracy inspection of cylindrical curved crystal with X-ray source
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摘要: 以实验室中的X射线管作为光源,配合CMOS 探测器涂层闪烁体纤维面板实时在线记录设备,建立了柱面弯晶检测平台。通过高精度的同轴转台设计,将整个柱面弯晶曲面转换为多个线段区间来分别进行检测,并对光路排布以及谱线的位置移动进行了解析计算。选用铁靶材X射线管(
$K_\alpha$ 特征谱线波长为0.193 6 nm)作为实验光源,曲率半径120 mm的石英柱面弯晶作为样品,实验获得了清晰的铁特征谱线(Fe-Kα和Fe-Kβ)。通过分析柱面弯晶上9个采样位置的图像,发现Fe-Kα谱线位置移动了96 μm,对应的半径偏差为40 μm,$\Delta {R}/{R}$ 为0.033%。经过检测的石英柱面弯晶已经在大型激光装置上应用,并获得高质量的光谱图像,证明了该实验方法对柱面弯晶品质检测的有效性。Abstract: A novel method of cylindrical curved crystal inspection is presented utilized the X-ray tube as the light source and the CMOS detector coated scintillator fibre faceplate as the on-line recorder. According to the design of the high accuracy coaxial turntable, the whole cylindrical curved crystal surface is converted into several line segments to be detected separately, and the arrangement of optical paths and the position shift of spectral lines are calculated analytically. The iron target X-ray tube (the wavelength of Kβ feature spectral line is 0.193 6 nm) is selected as the experimental light source. The iron material X-ray tube is chosen as the X-ray source. The sample is quartz cylindrical curved crystal with the 120 mm radius of curvature. The feature spectral lines of Fe-Kα and Fe-Kβ are observed clearly. The Fe-Kα spectral line is shifted 96 μm through analyzing image of 9 sample locations on the cylindrical curved crystal. The deviation of the radius is 40 μm and ΔR/R is 0.033%. It shows that the sample was curved in high accuracy. The tested cylindrical curved crystal has been applied on the experiments carried on the large laser facility and the high performance spectral data is acquired. It demonstrates that the method of curved crystal inspection is available and useful.-
Key words:
- X-ray diffraction /
- cylindrical curved crystal /
- high accuracy /
- characteristic spectra /
- CMOS detector
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