-
平响应XRD在实验靶室的排布如图2所示,通过研究FXRD阴极对X射线的响应特性,考虑整体强度和阴极的饱和,设计了整套系统。辐射源发射辐射流经过腔室内传播,到达靶室壁,进入飞行管道,依次通过中性衰减片、限孔光阑、平响应滤片、XRD阴极,产生的电子经过偏压收集,信号传输至示波器,衰减后得到波形。最后示波器得到的电压信号U可以表示为:
$$\begin{split} U = &\int {I(E)} \left( {{A_s}\frac{S}{{{r^2}}}\cos \theta } \right){R_N}(E){R_f}(E){R_{{\rm{XRD}}}}\left( R \right)\dfrac{Z}{A}{\rm{d}}E=\\ & \int {I(E)} R(E){\rm{d}}E \end{split}$$ (1) 式中:
$I(E)$ 为单位立体角单位面积能谱分布;${A_s}$ 为黑腔诊断孔面积;$S$ 为探测器前限孔光阑面积;$r$ 为限孔到辐射源距离;$\theta $ 为探测器视线相对黑腔诊断孔法向角度;${R_N}(E)$ 为中性衰减片的透过率函数;${R_f}(E)$ 为平响应滤片透过率函数;${R_{{\rm{XRD}}}}(E)$ 为XRD阴极响应函数;$Z$ 为示波器同轴阻抗;$A$ 为衰减器衰减倍率;$R(E)$ 为综合计算的整套系统响应函数。FXRD的设计目的在于将最后的$R(E)$ 调整为整个能带的平响应函数,这样之后由示波器数据反演,辐射流能谱分布就变得简单了。配平$R(E)$ 关键在于配平${R_f}(E) \cdot {R_{{\rm{XRD}}}}(E)$ ,目前典型的配平曲线如图3所示。数据处理的方法是将辐射源谱
$I(E)$ 看做黑体谱加一定本底谱的加权函数,计算FXRD对能谱$I(E)$ 进行测量时的平均值$\overline R $ 。由FXRD响应平均值和示波器测量的电压时间分辨曲线,还原计算能谱积分,得到辐射流能谱积分时间变化曲线。由此计算过程可以看出,FXRD的响应曲线的平整性和完整性对结果的计算有很重要的作用。 -
整形脉冲实验中采用功分器将一路信号一分为二,两个信号分别使用不同的衰减器连接到示波器上。调节合适的示波器量程得到两个信号,一个通道的信号得到完整的波形,包括低台阶以及高台阶辐射流信号,但是低台阶信号的信噪比较差;另一个通道测量波形的低台阶信号表征很好,同时信噪比较高,但是高台阶信号超量程,呈现过载状态。通过计算方法对两个通道获得的波形进行时间对齐,并且将两者电压幅度进行处理,还原得到辐射流强度信息,再将两个信号进行拼接。信号幅值较低部分采用信噪比更好的测量通道数据,而高台阶部分完整信号还是采用完整波形的通道,这样低台阶和高台阶都保持比较好的信噪比。典型的实验发次中的数据形式如图4所示,示波器两个通道采用不同衰减和量程,蓝色曲线是完整波形,黄色曲线是信噪比更好的低台阶信号测量。将两者还原辐射流之后的计算结果放到同一个时间坐标系下,如图5所示。
图 4 两台阶整形脉冲产生辐射流示波器测量结果:通道1和3为完整信号;通道2和4为调整量程后的低通信号
Figure 4. Oscilloscope measurement results of radiation flux under two-step shaped pulses : channels 1 and 3 are complete signals; channels 2 and 4 are low-pass signals after adjusting the range
由于一个通道超过很多量程,根据示波器使用说明,超量程后回归信号的时刻是不可预知的,对于某些型号的示波器甚至会产生波形失真;同时两个通道之间由于衰减器以及示波器内部结构等原因,存在一定的时间差异,所以需要对两路信号进行数据处理。首先将两个信号分别还原成辐射流结果,然后将低通辐射流的量程内部分,包括超量程前和超量程后两个部分,分别调整时间后与完整辐射流比较,直到轮廓重叠后,替换另一个通道测量的完整辐射流的相应部分,得到信噪比较好的完整辐射流时间变化曲线。
对齐数据的算法如下。首先将两路信号
$A = \left[ {{a_1},{a_2}, \cdots } \right]$ 和$B = \left[ {{b_1},{b_2}, \cdots } \right]$ 分别插值到同一时间轴,将A取不同延时(对应数据点偏移N)后进行计算:$$C\left( N \right) = \sqrt {\sum {{{\left( {{A_N} + B} \right)}^2}} } - \sqrt {\sum {{{\left( {{A_N} - B} \right)}^2}} } $$ (2) $C$ 代表取不同延时后A和B之间的偏差评估函数,若A和B完全对齐,在噪声较小的情况下,公式(2)理论上接近最大值:$$\begin{aligned} {C_{{\rm{max}}}} = \sqrt {\displaystyle \mathop \sum \limits_{\begin{array}{*{20}{c}} {i \in signal}\\ {i + N \in signal} \end{array}} {{\left( {{a_{i + N}} + {b_i}} \right)}^2} + \mathop \sum \limits_{\begin{array}{*{20}{c}} {i \in noise}\\ {i + N \in noise} \end{array}} {{\left( {{a_{i + N}} + {b_i}} \right)}^2}} -\\ \sqrt {\displaystyle\mathop \sum \limits_{\begin{array}{*{20}{c}} {i \in signal}\\ {i + N \in signal} \end{array}} {{\left( {{a_{i + N}} - {b_i}} \right)}^2} + \mathop \sum \limits_{\begin{array}{*{20}{c}} {i \in noise}\\ {i + N \in noise} \end{array}} {{\left( {{a_{i + N}} - {b_i}} \right)}^2}} \approx \\ \sqrt {\displaystyle \mathop \sum \limits_{\begin{array}{*{20}{c}} {i \in signal}\\ {i + N \in signal} \end{array}} {{\left( {{a_{i + N}} + {b_i}} \right)}^2}} - \sqrt {\displaystyle \mathop \sum \limits_{\begin{array}{*{20}{c}} {i \in signal}\\ {i + N \in signal} \end{array}} {{\left( {{a_{i + N}} - {b_i}} \right)}^2}} \end{aligned}$$ (3) 与之相对,若A和B在时间轴上完全分离,则:
$$\begin{aligned} {{C_{{\rm{min}}}} = }{\sqrt {\begin{array}{*{20}{l}} {\displaystyle \mathop \sum \limits_{\begin{array}{*{20}{c}} {i \in signal}\\ {i + N \in noise} \end{array}} {{\left( {{a_{i + N}} + {b_i}} \right)}^2} + \displaystyle \mathop \sum \limits_{\begin{array}{*{20}{c}} {i \in noise}\\ {i + N \in signal} \end{array}} {{\left( {{a_{i + N}} + {b_i}} \right)}^2}}\\ { + \displaystyle \mathop \sum \limits_{\begin{array}{*{20}{c}} {i \in noise}\\ {i + N \in noise} \end{array}} {{\left( {{a_{i + N}} + {b_i}} \right)}^2}} \end{array}} }- \\ { \sqrt {\begin{array}{*{20}{l}} {\displaystyle\mathop \sum \limits_{\begin{array}{*{20}{c}} {i \in signal}\\ {i + N \in noise} \end{array}} {{\left( {{a_{i + N}} - {b_i}} \right)}^2} + \mathop \sum \limits_{\begin{array}{*{20}{c}} {i \in noise}\\ {i + N \in signal} \end{array}} {{\left( {{a_{i + N}} - {b_i}} \right)}^2}}\\ { + \displaystyle \mathop \sum \limits_{\begin{array}{*{20}{c}} {i \in noise}\\ {i + N \in noise} \end{array}} {{\left( {{a_{i + N}} - {b_i}} \right)}^2}} \end{array}} }{ \approx 0}\\ \end{aligned}$$ (4) 此时
$C$ 趋于0,其他情况则介于$0 - {C_{{\rm{max}}}}$ 之间。此算法遍历时间数据,由于数据量较大,效率比较低,为减少计算量,引入判断计算值${C_m}$ :$${C_m} = \sum {A \cdot B} $$ (5) 实际上即使A和B时间上完全对应,由于噪声等影响,两者仍存在差异,且A或B通常不完整。所以取最大值附近足够范围,并插值到更细分的时间轴上,再判断(A-B)的方差,将最小值处作为对齐位置。
现理论证明此对齐方法。首先写出
${C_m}$ 的函数形式:$${C_m}\left( \tau \right) = \displaystyle \mathop \int \limits_{ - \infty }^{ + \infty } f\left( t \right) \cdot f\left( {t - \tau } \right){\rm{d}}t$$ (6) 对其做傅里叶变换:
$${\cal C}\left( \xi \right) = \sqrt {2\pi } \cdot {\cal F}\left( \xi \right) \cdot {\cal F}\left( { - \xi } \right) = \sqrt {2\pi } {\left| {{\cal F}\left( \xi \right)} \right|^2}$$ (7) 其中,
$\mathcal{F}\left( \xi \right) = \dfrac{1}{{\sqrt {2\pi } }}\displaystyle \mathop \int \limits_{ - \infty }^{ + \infty } f\left( \tau \right){e^{i\xi \tau }}{\rm{d}}\tau$ ,做傅里叶逆变换:$$\begin{split} {C_m}\left( \tau \right) =& \dfrac{1}{{\sqrt {2\pi } }}\displaystyle \mathop \int \limits_{ - \infty }^{ + \infty } \sqrt {2\pi } {\left| {{\cal F}\left( \xi \right)} \right|^2}{e^{ - i\xi \tau }}{\rm{d}}\xi =\\ & \displaystyle \mathop \int \limits_{ - \infty }^{ + \infty } {\left| {{\cal F}\left( \xi \right)} \right|^2}\cos \left( {\xi \tau } \right){\rm{d}}\xi -\\ & i\displaystyle \mathop \int \limits_{ - \infty }^{ + \infty } {\left| {{\cal F}\left( \xi \right)} \right|^2}\sin \left( {\xi \tau } \right){\rm{d}}\xi \end{split}$$ (8) 公式(8)第二项中被积函数为奇函数,所以第二项值为零。第一项中,
$$\begin{split} {\left| {F\left( \xi \right)} \right|^2} =& \dfrac{1}{{2\pi }}\left[ {{{\left( {\displaystyle \int\limits_{ - \infty }^{ + \infty } f \left( \tau \right)\cos \left( {\xi \tau } \right){\rm{d}}\tau } \right)}^2} + } \right.\\ &\left. {{{\left( {\displaystyle \int\limits_{ - \infty }^{ + \infty } f \left( \tau \right)\sin \left( {\xi \tau } \right){\rm{d}}\tau } \right)}^2}} \right] \geqslant 0 \end{split}$$ (9) 所以从下式可知,当
$\tau = 0$ 时,${C_m}\left( \tau \right)$ 为最大值:$$\begin{split} {C_m}\left( \tau \right) =& \displaystyle \mathop \int \limits_{ - \infty }^{ + \infty } {\left| {{\cal F}\left( \xi \right)} \right|^2}\cos \left( {\xi \tau } \right){\rm{d}}\xi \leqslant \displaystyle \mathop \int \limits_{ - \infty }^{ + \infty } {\left| {{\cal F}\left( \xi \right)} \right|^2}{\rm{d}}\xi =\\ & {C_m}\left( 0 \right) \end{split}$$ (10) 由公式(10)引入判据一:
$\forall \tau ,{C_1}\left( \tau \right) \leqslant {C_1}\left( {{\tau _m}} \right)$ ,其中,$$\begin{aligned} {C_1}\left( \tau \right) =& \displaystyle \mathop \int \limits_{{L_1}}^{{L_2}} f\left( t \right) \cdot f\left( {t - \tau } \right){\rm{d}}t= \\ & {C_m}\left( \tau \right) - \displaystyle \mathop \int \limits_{ - \infty }^{{L_1}} f\left( t \right) \cdot f\left( {t - \tau } \right){\rm{d}}t - \displaystyle \mathop \int \limits_{{L_2}}^{ + \infty } f\left( t \right) \cdot f\left( {t - \tau } \right){\rm{d}}t \end{aligned}$$ (11) 可见,在信噪比较差,或区间
$\left[ {{L_1},{L_2}} \right]$ 内信号不完整的条件下,当$\tau = 0$ 时,${C_1}\left( \tau \right)$ 不一定是最大值。将公式(11)进行变形,得到:$$ \begin{split} {C_1}\left( \tau \right) =& \frac{1}{4}\left( {\int\limits_{{L_1}}^{{L_2}} {{{\left( {f\left( t \right) + f\left( {t - \tau } \right)} \right)}^2}} {\text{d}}t - } \right. \hfill \\ & \left. {\int\limits_{{L_1}}^{{L_2}} {{{\left( {f\left( t \right) - f\left( {t - \tau } \right)} \right)}^2}} {\text{d}}t} \right) \hfill \\ \end{split} $$ (12) 令
$$\begin{split} a\left( \tau \right) = \sqrt {\displaystyle \mathop \int \limits_{{L_1}}^{{L_2}} {{\left( {f\left( t \right) + f\left( {t - \tau } \right)} \right)}^2}{\rm{d}}t}\\ b\left( \tau \right) = \sqrt {\displaystyle \mathop \int \limits_{{L_1}}^{{L_2}} {{\left( {f\left( t \right) - f\left( {t - \tau } \right)} \right)}^2}{\rm{d}}t} \end{split}$$ (13) 有
$$\begin{split} {C_2}\left( \tau \right) =& a\left( \tau \right) - b\left( \tau \right)= \\ & \sqrt {\displaystyle \mathop \int \limits_{{L_1}}^{{L_2}} {{\left( {f\left( t \right) + f\left( {t - \tau } \right)} \right)}^2}{\rm{d}}t} -\\ & \sqrt {\displaystyle \mathop \int \limits_{{L_1}}^{{L_2}} {{\left( {f\left( t \right) - f\left( {t - \tau } \right)} \right)}^2}{\rm{d}}t} \end{split}$$ (14) 将
${C_1}\left( \tau \right)$ 和${C_2}\left( \tau \right)$ 对τ求导,并整理得:$${C'_2}\left( \tau \right) = \left( {\dfrac{{4{{C'}_1}\left( \tau \right)/b'\left( \tau \right) + 2b\left( \tau \right)}}{{2a\left( \tau \right)}} - 1} \right)b'\left( \tau \right)$$ (15) 将
${C_1}\left( \tau \right)$ 最大值处${\tau _{m1}}$ 代入公式(15),并利用${C'_1}\left( {{\tau _{m1}}} \right) = 0$ ,得到$${C'_2}\left( {{\tau _{m1}}} \right) = \left( {\dfrac{{b\left( {{\tau _{m1}}} \right)}}{{a\left( {{\tau _{m1}}} \right)}} - 1} \right)b'\left( {{\tau _{m1}}} \right)$$ (16) 如果仅考虑
${\tau _{m1}}$ 在0附近的情况,假定$b\left( \tau \right)$ 在区间$\left[ {0,{\tau _{m1}} + \delta } \right]$ 或$\left[ {{\tau _{m1}} - \delta ,0} \right]$ 为单调函数是合理的,且有$b\left( 0 \right) = 0$ 为最小值,所以,$b'\left( {{\tau _{m1}}} \right)$ 总是与${\tau _{m1}}$ 同号。又由于$\dfrac{{b\left( {{\tau _{m1}}} \right)}}{{a\left( {{\tau _{m1}}} \right)}} - 1 \leqslant 0$ ,所以${C'_2}\left( {{\tau _{m1}}} \right)$ 总是与${\tau _{m1}}$ 反号。因此,${C_2}\left( \tau \right)$ 最大值处${\tau _{m2}}$ 在一定限制下比${\tau _{m1}}$ 更接近于0:$$\left| {{\tau _{m1}}} \right| \geqslant \left| {{\tau _{m2}}} \right| \geqslant 0$$ (17) 在
${\tau _m}$ (${\tau _{m1}}$ 或${\tau _{m2}}$ )的邻域内引入判据二:$\forall \tau \in \left( {{\tau _m} - } \right. \left. {\delta ,{\tau _m} + \delta } \right),$ ${C_3}\left( \tau \right) \geqslant {C_3}\left( 0 \right) $ ,其中$${C_3}\left( \tau \right) = \displaystyle \mathop \int \limits_{{L_1}}^{{L_2}} {\left( {f\left( t \right) - f\left( {t - \tau } \right)} \right)^2}{\rm{d}}t$$ (18) 若信号
$f\left( t \right)$ 不是常数,且位于可观测区间$\left[ {{L_1},{L_2}} \right]$ 内,则容易证明,当$\tau = 0$ 时,${C_3}\left( 0 \right) = 0$ 是唯一最小值。需要说明的是,对信号的开高次方处理也会使信噪比变差,因此如公式(14)中仅取开二次方。 -
一般实验过程中实验结果不确定度可以给出,但是在整形脉冲辐射流测量过程中,还会引入另一个不确定性因素。在常规实验过程中,利用了FXRD在100 eV~4 keV的平响应特性,这就要求辐射能谱的分布应位于此区间。但在整形脉冲测量中,对应低通信号的辐射流角强度很低,在大部分这类实验中,往往意味着辐射温度也很低。当辐射温度较低时,其很大一部分能谱分布于100 eV以下,而FXRD响应的有效标定范围仅为80 eV~5 keV,这就导致使用标定的FXRD响应函数进行辐射流还原计算会出现偏差。
首先进行理论计算。令I为总光强,
$f\left( E \right)$ 是其归一化的能谱分布,即:$$\displaystyle \mathop \int \limits_0^\infty f\left( E \right){\rm{d}}E = 1$$ (19) 则FXRD的实际测量信号为:
$${\rm{Y}} =\displaystyle \mathop \int \limits_0^\infty R\left( E \right) \cdot {{I}}f\left( E \right){\rm{d}}E$$ (20) 这里
$R\left( E \right)$ 是FXRD灵敏度曲线,假设$\bar R$ 为迭代后使用的灵敏度均值,则可得计算光强${{I'}} = \dfrac{Y}{{\bar R}}$ ,所以计算相对偏差为:$${{{U}}_I} = \dfrac{{{{I'}} - {{I}}}}{{{I}}} = \frac{{\displaystyle \mathop \int \nolimits_0^\infty R\left( E \right)f\left( E \right){\rm{d}}E}}{{\bar R}} - 1$$ (21) 若迭代后的
$\bar R$ 使${U_I} = 0$ ,则有理论灵敏度均值:$${\bar R_{0,\infty }} = \displaystyle \mathop \int \limits_0^\infty R\left( E \right)f\left( E \right){\rm{d}}E$$ (22) 如果令
$f'\left( E \right)$ 为根据$I'$ 得到的归一化谱分布,区间$[{{{E}}_1},{{{E}}_2}]$ 足够大,则有实际使用值:$$\bar R = \dfrac{{\displaystyle \mathop \int \nolimits_{{{{E}}_1}}^{{{{E}}_2}} R\left( E \right)f'\left( E \right){\rm{d}}E}}{{\displaystyle \mathop \int \nolimits_{{{{E}}_1}}^{{{{E}}_2}} f'\left( E \right){\rm{d}}E}}$$ (23) 另一方面,令
$R\left( E \right) = \bar R + \Delta R\left( E \right)$ ,则有:$$\begin{split} {{{U}}_I} = &\dfrac{{\displaystyle \mathop \int \nolimits_0^\infty \left( {\bar R + \Delta R\left( E \right)} \right)f\left( E \right){\rm{d}}E}}{{\bar R}} - 1 =\\ & \dfrac{{\displaystyle \mathop \int \nolimits_0^\infty \Delta R\left( E \right)f\left( E \right){\rm{d}}E}}{{\bar R}} \approx \\ & \dfrac{{\displaystyle \mathop \int \nolimits_0^{{{{E}}_2}} \Delta R\left( E \right)f'\left( E \right){\rm{d}}E}}{{\bar R}} + \\ & \dfrac{{\displaystyle \mathop \int \nolimits_0^{{{{E}}_2}} \Delta R\left( E \right)\left( {f\left( E \right) - f'\left( E \right)} \right){\rm{d}}E}}{{\bar R}} \end{split}$$ (24) 公式(24)假定了当
$E > {{{E}}_2}$ 时,$f'\left( E \right) \to 0$ ,$f\left( E \right) \to 0$ 。公式(24)中第一项,设为${\varepsilon _R}$ ,可以使用辐射流处理程序进行计算得到,主要是因为$\bar R \ne {\bar R_{0,\infty }}$ 带来的偏差;第二项,设为${\varepsilon _f}$ ,主要是实际能谱与假定能谱的不同带来的偏差,这就是第2节关于数据处理过程中响应函数不平整带来的还原误差。这里假设${\varepsilon _f}$ 可以忽略,只估算${\varepsilon _R}$ 。令$R\left( E \right) = S + \Delta S\left( E \right)$ ,其中$S = \bar R + \delta $ ,为平响应区间均值,则$\Delta R\left( E \right) = \Delta S\left( E \right) + \delta $ ,所以有:$$\begin{split} {{{U}}_I} \approx {\varepsilon _R} = &\dfrac{{\displaystyle \mathop \int \nolimits_0^{{{{E}}_2}} \left( {\Delta S\left( E \right) + \delta } \right)f'\left( E \right){\rm{d}}E}}{{\bar R}} =\\ & \dfrac{{\displaystyle \mathop \int \nolimits_0^{{{{E}}_2}} \Delta S\left( E \right)f'\left( E \right){\rm{d}}E}}{{\bar R}} + \dfrac{\delta }{{\bar R}} \end{split}$$ (25) 根据实际的FXRD灵敏度情况,设定在区间
$[0,{{{E}}_0})$ 内,$R\left( E \right) = 0$ ,在区间$[{{{E}}_0},{{{E}}_{{S}}}]$ 内,$R\left( E \right)$ 从0单调增加到S,在区间$\left( {{{{E}}_{{S}}}, + \infty } \right)$ 内,$\Delta S\left( E \right)$ 相对S为小量,则有:$$\begin{split} {{{U}}_I} \approx &\dfrac{{\displaystyle \mathop \int \nolimits_0^{{{{E}}_0}} \left( { - S} \right)f'\left( E \right){\rm{d}}E}}{{\bar R}} + \dfrac{{\displaystyle \mathop \int \nolimits_{{{{E}}_0}}^{{{{E}}_{{S}}}} \Delta S\left( E \right)f'\left( E \right){\rm{d}}E}}{{\bar R}}+ \\ & \dfrac{{\displaystyle \mathop \int \nolimits_{{{{E}}_{{S}}}}^{{{{E}}_2}} o\left( S \right)f'\left( E \right){\rm{d}}E}}{{S - \delta }} + \dfrac{\delta }{{\bar R}} \end{split}$$ (26) 当
$\delta $ 相对S为小量时,忽略公式(26)第三项,如果同时假定${{{E}}_{{S}}} \to {{{E}}_0}$ ,则可忽略第二项,则得到估算值:$${{{U}}_I} \approx \dfrac{\delta }{{\bar R}} - \dfrac{S}{{\bar R}}\displaystyle \int_0^{{{{E}}_0}} {f'\left( E \right){\rm{d}}E} = \dfrac{S}{{\bar R}}\displaystyle \int_{{{{E}}_0}}^{{{{E}}_2}} {f'\left( E \right){\rm{d}}E} - 1$$ (27) 以实验中具体的一个FXRD为例,如图6所示,黑色实线为实际的响应曲线,80 eV以下是理论拟合值,红色实线是由此计算的平响应区间均值。
由此可以计算得到
$\bar R$ 和${U_I}$ 。当使用不同的积分范围时(即不同的$[{{{E}}_1},{{{E}}_2}]$ ),会带来不同的偏差,具体的计算结果如图7所示。可以看到当使用[1 eV,5000 eV]积分范围时,带来的偏差已经很小,但是如果只考虑平响应区间范围[100 eV,4000 eV],在辐射流温度${T_r} = 50\;{\rm{eV}}$ 处,辐射流强度积分的计算会比实际值小14%,在${T_r} = 30\;{\rm{eV}}$ 处更是会偏小37%。如果计算辐射温度的偏差,如图8所示,即使是高温辐射源峰值,辐射温度计算也会偏差0.1~0.2 eV,在50 eV处偏低达到1.88 eV,单独这一项带来的辐射流温度相对不确定度就达到3.7%。因此,计算程序应该把计算$\bar R$ 的范围从平响应区间扩展到更大,在不能标定的区域,实行理论模拟补全的方式,这样带来的误差会减少很多。 -
由公式(1)可知辐射流
$\int {I\left( E \right)} $ 的不确定度来源于电压U、中性衰减片透过率${R_N}(E)$ 、FXRD系统响应函数、限孔大小S、安装距离r、示波器阻抗Z、衰减器衰减倍率A、辐射源面积${A_s}$ 和相对辐射源法向角度θ。FXRD系统响应函数由滤片透过率${R_f}(E)$ 和阴极响应函数${R_{{\rm{XRD}}}}(E)$ 决定,计算中分别考虑两者不确定度。其中每个参数的不确定度由多个影响因素决定,比如实验测量带来的不确定度、标定带来的不确定度、算法带来的不确定度、机构精度带来的不确定度等。具体的类目如表1[12]所示。表 1 辐射流强度不确定度来源汇总表
Table 1. Summary table of sources of radiation flux intensity uncertainty
Category Components Source of uncertainty Uncertainty of component Comprehensive uncertainty Measurement Oscilloscope Voltage measurement noise 2% 3.17% (changes with Tr) Verification accuracy 1% Cable Transmission loss 1%+1% Attenuator Attenuation bias 0.3% Verification accuracy 1% Calibration Neutral filter Calibration accuracy 2% 8.9% (changes with Tr) Face uniformity 2% flat-response filter Calibration accuracy 2% Face uniformity 1% XRD Calibration accuracy 1.5% Face uniformity 8% Algorithm Reduction algorithm Response flatness 1% (peak) 1% (changes with Tr) without reduction algorithm Response flatness of F/M-XRD <15% <15% (eliminated) Mechanical Solid angle Aperture punching accuracy 0.5% 1.1% (stable) Distance from aperture to target Angle Effect of installation angle on field of view 1% 实际使用加权算法还原谱与响应函数的相互作用,消去未使用还原的不确定度,但是标定数据会因为加权还原算法带来额外的不确定度,这一部分引入的不确定度必须有真实辐射源的能谱与加权用能谱的差来进行计算,涉及非线性迭代还原方法,所以主要依靠蒙特卡罗方法进行计算,表1中已经考虑此因素。同时整形脉冲中低温辐射温度下也会带来算法不确定度,其随温度变化函数已于前文中进行计算。而示波器、电缆、衰减器、衰减片、滤片、XRD阴极等不确定度都会随辐射温度的变化而变化,由于机构带来的不确定是不随辐射温度变化的。各个影响因素的相对不确定度随辐射温度变化的曲线如图9所示,注意
$\displaystyle \int {I(E){\rm{d}}E} \sim {T^4}$ ,所以表格数据和图像数据是经过转化得到的。从图9可以看出,在辐射温度较低区间,整体的不确定度会发生陡升,主要影响因素就是低温辐射温度下FXRD的响应存在的不确定性带来的算法不确定度。
Signal processing method for shaped pulse and radiation flux deviation in low temperature
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摘要: 平响应X射线二极管目前已经广泛应用在国内外大型激光装置,用于角分布X射线辐射流的测量。在实际实验中,平响应X射线二极管会对整形脉冲驱动辐射源产生台阶变化的辐射流图像进行测量。为了保证信噪比良好,单一信号会接入示波器多通道,然后对不同通道信号进行数据处理,并且拼接得到最后信噪比很好的图像。该研究主要对这种数据处理方式进行了介绍,并给出了理论计算,同时对低温辐射流还原计算中的一种偏差做了理论近似和数值模拟,得到了偏差的相对不确定度。耦合所有因素的不确定度,得到了平响应X射线二极管的整体不确定度随辐射温度的变化曲线,实现了精密化诊断,完成了实验对于诊断的需求。Abstract: Flat response X-ray diodes have been widely used in large-scale laser devices at home and abroad for the measurement of angularly distributed X-ray radiation flux. In practical experiments, flat-response X-ray diodes measure radiation flux images that have a step change in a shaped pulse-driven radiation source. In order to ensure a good signal-to-noise ratio, a single signal will be connected to multiple channels of the oscilloscope, and then the signals of different channels will be processed, and the final image with good signal-to-noise ratio will be stitched. The research in this paper mainly introduced this data processing method and gave theoretical calculations. At the same time, a theoretical approximation and numerical simulation of a deviation in the calculation of the low temperature radiation flow reduction were made, and the relative uncertainty of the deviation was obtained. Coupled with the uncertainty of all factors, the curve of the overall uncertainty of the flat-response X-ray diode as a function of the radiation temperature was obtained, which realized precise diagnosis and completed the experimental needs for diagnosis.
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表 1 辐射流强度不确定度来源汇总表
Table 1. Summary table of sources of radiation flux intensity uncertainty
Category Components Source of uncertainty Uncertainty of component Comprehensive uncertainty Measurement Oscilloscope Voltage measurement noise 2% 3.17% (changes with Tr) Verification accuracy 1% Cable Transmission loss 1%+1% Attenuator Attenuation bias 0.3% Verification accuracy 1% Calibration Neutral filter Calibration accuracy 2% 8.9% (changes with Tr) Face uniformity 2% flat-response filter Calibration accuracy 2% Face uniformity 1% XRD Calibration accuracy 1.5% Face uniformity 8% Algorithm Reduction algorithm Response flatness 1% (peak) 1% (changes with Tr) without reduction algorithm Response flatness of F/M-XRD <15% <15% (eliminated) Mechanical Solid angle Aperture punching accuracy 0.5% 1.1% (stable) Distance from aperture to target Angle Effect of installation angle on field of view 1% -
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