• High Power Laser Science and Engineering
  • Vol. 7, Issue 3, 03000e49 (2019)
Zhiyu He1, Guo Jia1、†, Fan Zhang1, Xiuguang Huang1、2, Zhiheng Fang1, Jiaqing Dong1, Hua Shu1, Junjian Ye1, Zhiyong Xie1, Yuchun Tu1, Qili Zhang3, Erfu Guo1, Wenbing Pei1、2, and Sizu Fu1、2
Author Affiliations
  • 1Shanghai Institute of Laser Plasma, CAEP, Shanghai 201800, China
  • 2IFSA Collaborative Innovation Center, Shanghai Jiao Tong University, Shanghai 200240, China
  • 3Institute of Applied Physics and Computational Mathematics, Beijing 100094, China
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    DOI: 10.1017/hpl.2019.27 Cite this Article Set citation alerts
    Zhiyu He, Guo Jia, Fan Zhang, Xiuguang Huang, Zhiheng Fang, Jiaqing Dong, Hua Shu, Junjian Ye, Zhiyong Xie, Yuchun Tu, Qili Zhang, Erfu Guo, Wenbing Pei, Sizu Fu. Calibration and verification of streaked optical pyrometer system used for laser-induced shock experiments[J]. High Power Laser Science and Engineering, 2019, 7(3): 03000e49 Copy Citation Text show less

    Abstract

    Although the streaked optical pyrometer (SOP) system has been widely adopted in shock temperature measurements, its reliability has always been of concern. Here, two calibrated Planckian radiators with different color temperatures were used to calibrate and verify the SOP system by comparing the two calibration standards using both multi-channel and single-channel methods. A high-color-temperature standard lamp and a multi-channel filter were specifically designed for the measurement system. To verify the reliability of the SOP system, the relative deviation between the measured data and the standard value of less than 5% was calibrated out, which demonstrates the reliability of the SOP system. Furthermore, a method to analyze the uncertainty and sensitivity of the SOP system is proposed. A series of laser-induced shock experiments were conducted at the ‘Shenguang-II’ laser facility to verify the reliability of the SOP system for temperature measurements at tens of thousands of kelvin. The measured temperature of the quartz in our experiments agreed fairly well with previous works, which serves as evidence for the reliability of the SOP system.
    $$\begin{eqnarray}L(\unicode[STIX]{x1D706})=\frac{\unicode[STIX]{x1D700}(\unicode[STIX]{x1D706})}{\unicode[STIX]{x1D706}^{5}}\frac{2hc^{2}}{e^{hc/\unicode[STIX]{x1D706}kT}-1},\end{eqnarray}$$(1)

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    $$\begin{eqnarray}T=\frac{hc}{\displaystyle \unicode[STIX]{x1D706}k\ln \left(\frac{2hc^{2}\unicode[STIX]{x1D700}}{L_{m}\unicode[STIX]{x1D706}^{5}}+1\right)},\end{eqnarray}$$(2)

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    $$\begin{eqnarray}\unicode[STIX]{x1D6FF}T=\sqrt{\left(\frac{\unicode[STIX]{x2202}T}{\unicode[STIX]{x2202}L_{m}}\right)^{2}\left(\unicode[STIX]{x1D6FF}L_{m}\right)^{2}+\left(\frac{\unicode[STIX]{x2202}T}{\unicode[STIX]{x2202}\unicode[STIX]{x1D706}}\right)^{2}\left(\unicode[STIX]{x1D6FF}\unicode[STIX]{x1D706}\right)^{2}+\left(\frac{\unicode[STIX]{x2202}T}{\unicode[STIX]{x2202}\unicode[STIX]{x1D700}}\right)^{2}\left(\unicode[STIX]{x1D6FF}\unicode[STIX]{x1D700}\right)^{2}},\end{eqnarray}$$(3)

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    $$\begin{eqnarray}\displaystyle \frac{\unicode[STIX]{x2202}T}{\unicode[STIX]{x2202}L_{m}} & = & \displaystyle \frac{hc}{\displaystyle \unicode[STIX]{x1D706}k\left[\ln \left(\frac{2hc^{2}\unicode[STIX]{x1D700}}{L_{m}\unicode[STIX]{x1D706}^{5}}+1\right)\right]^{2}\left(L_{m}+\frac{\unicode[STIX]{x1D706}^{5}}{2hc^{2}\unicode[STIX]{x1D700}}L_{m}^{2}\right)}\nonumber\\ \displaystyle & = & \displaystyle \frac{T}{\displaystyle \ln \left(\frac{2hc^{2}\unicode[STIX]{x1D700}}{L_{m}\unicode[STIX]{x1D706}^{5}}+1\right)\left(L_{m}+\frac{\unicode[STIX]{x1D706}^{5}}{2hc^{2}\unicode[STIX]{x1D700}}L_{m}^{2}\right)},\end{eqnarray}$$(4)

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    $$\begin{eqnarray}\displaystyle \frac{\unicode[STIX]{x2202}T}{\unicode[STIX]{x2202}\unicode[STIX]{x1D706}} & = & \displaystyle \frac{hc}{k}\left[\frac{5\times 2hc^{2}\unicode[STIX]{x1D700}}{\displaystyle L_{m}\unicode[STIX]{x1D706}^{7}\left[\ln \left(\frac{2hc^{2}\unicode[STIX]{x1D700}}{L_{m}\unicode[STIX]{x1D706}^{5}}+1\right)\right]^{2}\left(\frac{2hc^{2}\unicode[STIX]{x1D700}}{L_{m}\unicode[STIX]{x1D706}^{5}}+1\right)}\right.\nonumber\\ \displaystyle & & \displaystyle -\left.\frac{1}{\displaystyle \unicode[STIX]{x1D706}^{2}\ln \left(\frac{2hc^{2}\unicode[STIX]{x1D700}}{L_{m}\unicode[STIX]{x1D706}^{5}}+1\right)}\right]\nonumber\\ \displaystyle & = & \displaystyle T\left[\frac{5\times 2hc^{2}\unicode[STIX]{x1D700}}{\displaystyle L_{m}\unicode[STIX]{x1D706}^{6}\ln \left(\frac{2hc^{2}\unicode[STIX]{x1D700}}{L_{m}\unicode[STIX]{x1D706}^{5}}+1\right)\left(\frac{2hc^{2}\unicode[STIX]{x1D700}}{L_{m}\unicode[STIX]{x1D706}^{5}}+1\right)}-\frac{1}{\unicode[STIX]{x1D706}}\right],\nonumber\\ \displaystyle & & \displaystyle\end{eqnarray}$$(5)

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    $$\begin{eqnarray}\displaystyle \frac{\unicode[STIX]{x2202}T}{\unicode[STIX]{x2202}\unicode[STIX]{x1D700}} & = & \displaystyle -\frac{hc\times 2hc^{2}}{\displaystyle \unicode[STIX]{x1D706}^{6}kL_{m}\left[\ln \left(\frac{2hc^{2}\unicode[STIX]{x1D700}}{L_{m}\unicode[STIX]{x1D706}^{5}}+1\right)\right]^{2}\left(\frac{2hc^{2}\unicode[STIX]{x1D700}}{L_{m}\unicode[STIX]{x1D706}^{5}}+1\right)}\nonumber\\ \displaystyle & = & \displaystyle -T\frac{2hc^{2}}{\displaystyle L_{m}\unicode[STIX]{x1D706}^{5}\ln \left(\frac{2hc^{2}\unicode[STIX]{x1D700}}{L_{m}\unicode[STIX]{x1D706}^{5}}+1\right)\left(\frac{2hc^{2}\unicode[STIX]{x1D700}}{L_{m}\unicode[STIX]{x1D706}^{5}}+1\right)}.\end{eqnarray}$$(6)

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    $$\begin{eqnarray}\displaystyle \unicode[STIX]{x1D6FF}T & = & \displaystyle T\nonumber\\ \displaystyle & & \displaystyle \times \,\left\{\frac{(\unicode[STIX]{x1D6FF}L_{m})^{2}}{\displaystyle \left[\ln \left(\frac{2hc^{2}\unicode[STIX]{x1D700}}{L_{m}\unicode[STIX]{x1D706}^{5}}+1\right)\right]^{2}\left(L_{m}+\frac{\unicode[STIX]{x1D706}^{5}L_{m}^{2}}{2hc^{2}\unicode[STIX]{x1D700}}\right)^{2}}\right.\nonumber\\ \displaystyle & & \displaystyle +\,\left[\frac{5\times 2hc^{2}\unicode[STIX]{x1D700}}{\displaystyle L_{m}\unicode[STIX]{x1D706}^{6}\ln \left(\frac{2hc^{2}\unicode[STIX]{x1D700}}{L_{m}\unicode[STIX]{x1D706}^{5}}+1\right)\left(\frac{2hc^{2}\unicode[STIX]{x1D700}}{L_{m}\unicode[STIX]{x1D706}^{5}}+1\right)}-\frac{1}{\unicode[STIX]{x1D706}}\right]^{2}(\unicode[STIX]{x1D6FF}\unicode[STIX]{x1D706})^{2}\nonumber\\ \displaystyle & & \displaystyle +\left.\left[\frac{2hc^{2}(\unicode[STIX]{x1D6FF}\unicode[STIX]{x1D700})^{4}}{\displaystyle L_{m}\unicode[STIX]{x1D706}^{5}\ln \left(\frac{2hc^{2}\unicode[STIX]{x1D700}}{L_{m}\unicode[STIX]{x1D706}^{5}}+1\right)\left(\frac{2hc^{2}\unicode[STIX]{x1D700}}{L_{m}\unicode[STIX]{x1D706}^{5}}+1\right)}\right]^{2}\right\}^{1/2}.\nonumber\\ \displaystyle & & \displaystyle\end{eqnarray}$$(7)

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    $$\begin{eqnarray}\displaystyle \frac{\unicode[STIX]{x1D6FF}T}{T} & = & \displaystyle \left\{\frac{(\unicode[STIX]{x1D6FF}L_{m})^{2}}{\displaystyle \left[\ln \left(\frac{2hc^{2}\unicode[STIX]{x1D700}}{L_{m}\unicode[STIX]{x1D706}^{5}}+1\right)\right]^{2}\left(L_{m}+\frac{\unicode[STIX]{x1D706}^{5}L_{m}^{2}}{2hc^{2}\unicode[STIX]{x1D700}}\right)^{2}}\right.\nonumber\\ \displaystyle & & \displaystyle +\,\left[\frac{5\times 2hc^{2}\unicode[STIX]{x1D700}}{\displaystyle L_{m}\unicode[STIX]{x1D706}^{6}\ln \left(\frac{2hc^{2}\unicode[STIX]{x1D700}}{L_{m}\unicode[STIX]{x1D706}^{5}}+1\right)\left(\frac{2hc^{2}\unicode[STIX]{x1D700}}{L_{m}\unicode[STIX]{x1D706}^{5}}+1\right)}-\frac{1}{\unicode[STIX]{x1D706}}\right]^{2}(\unicode[STIX]{x1D6FF}\unicode[STIX]{x1D706})^{2}\nonumber\\ \displaystyle & & \displaystyle +\left.\left[\frac{2hc^{2}(\unicode[STIX]{x1D6FF}\unicode[STIX]{x1D700})^{4}}{\displaystyle L_{m}\unicode[STIX]{x1D706}^{5}\ln \left(\frac{2hc^{2}\unicode[STIX]{x1D700}}{L_{m}\unicode[STIX]{x1D706}^{5}}+1\right)\left(\frac{2hc^{2}\unicode[STIX]{x1D700}}{L_{m}\unicode[STIX]{x1D706}^{5}}+1\right)}\right]^{2}\right\}^{1/2}.\end{eqnarray}$$(8)

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    $$\begin{eqnarray}\displaystyle & & \displaystyle \unicode[STIX]{x1D6FF}L_{m}=\sqrt{\left(\frac{\unicode[STIX]{x2202}L_{m}}{\unicode[STIX]{x2202}C_{m}}\right)^{2}\left(\unicode[STIX]{x1D6FF}C_{m}\right)^{2}+\left(\frac{\unicode[STIX]{x2202}L_{m}}{\unicode[STIX]{x2202}C_{s}}\right)^{2}\left(\unicode[STIX]{x1D6FF}C_{s}\right)^{2}+\left(\frac{\unicode[STIX]{x2202}L_{m}}{\unicode[STIX]{x2202}L_{s}}\right)^{2}\left(\unicode[STIX]{x1D6FF}L_{s}\right)^{2}}\nonumber\\ \displaystyle & & \displaystyle \quad =L_{m}\sqrt{\left(\frac{\unicode[STIX]{x1D6FF}C_{m}}{C_{m}}\right)^{2}+\left(\frac{\unicode[STIX]{x1D6FF}C_{s}}{C_{s}}\right)^{2}+\left(\frac{\unicode[STIX]{x1D6FF}L_{s}}{L_{s}}\right)^{2}},\end{eqnarray}$$(9)

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    $$\begin{eqnarray}\displaystyle & & \displaystyle \unicode[STIX]{x1D6FF}\unicode[STIX]{x1D700}=\unicode[STIX]{x1D6FF}R_{\text{SOP}}=\unicode[STIX]{x1D6FF}R_{\text{VISAR}}\nonumber\\ \displaystyle & & \displaystyle \quad =R_{\text{VISAR}}\sqrt{\left(\frac{\unicode[STIX]{x1D6FF}C_{\text{VISAR}}}{C_{\text{VISAR}}}\right)^{2}+\left(\frac{\unicode[STIX]{x1D6FF}C_{\text{base}}}{C_{\text{base}}}\right)^{2}+\left(\frac{\unicode[STIX]{x1D6FF}R_{\text{base}}}{R_{\text{base}}}\right)^{2}},\nonumber\\ \displaystyle & & \displaystyle\end{eqnarray}$$(10)

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    $$\begin{eqnarray}S_{X}=\frac{\unicode[STIX]{x0394}T/T}{\unicode[STIX]{x0394}X/X},\end{eqnarray}$$(11)

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    Zhiyu He, Guo Jia, Fan Zhang, Xiuguang Huang, Zhiheng Fang, Jiaqing Dong, Hua Shu, Junjian Ye, Zhiyong Xie, Yuchun Tu, Qili Zhang, Erfu Guo, Wenbing Pei, Sizu Fu. Calibration and verification of streaked optical pyrometer system used for laser-induced shock experiments[J]. High Power Laser Science and Engineering, 2019, 7(3): 03000e49
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