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Highly dynamic solar eruptive activities occurring over the corona and transition region, triggered off by magnetic field reconnection, are the driving source of disastrous space weather, and the space imaging and spectroscopic measurements of solar eruptive activities are a key data source for accurate space weather forecasting. The He II 30.4 nm resonance line comes from the Lyman α transition of singly ionized helium, which has an anomalous intensity, an order of magnitude higher than the intensities of other transition region lines. In this paper, we propose and design a two-dimensional spectroscopic tomographic imaging instrument operating at He II 30.4 nm wavelength to make up for the shortcomings of conventional solar extreme ultraviolet imager and imaging spectrometer, and adopt a slitless three-order (–1, 0, +1) simultaneous diffraction imaging configuration with a single snapshot to achieve two-dimensional spectroscopy instantaneous imaging with a large field of view. Owing to the confusion of spatial and spectral information of the three orders of images, the three-dimensional data cube I (x, y, λ) of the observed target is reconstructed using a spectral data inversion algorithm with a limited tomographic projection angle.
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Keywords:
- solar extreme ultraviolet /
- tomographic imaging /
- imaging spectrometer /
- spectral data inversion
[1] 王水, 魏奉思 2007 地球物理学进展 22 1025
Google Scholar
Wang S, Wei F S 2007 Prog. Geophys. 22 1025
Google Scholar
[2] 汪景琇, 季海生 2013 中国科学: 地球科学 43 883
Google Scholar
Wang J X, Ji H S 2013 Sci. China Earth Sci. 43 883
Google Scholar
[3] Hurford G J, Schmahl E J, Schwartz R A, Conway A J, Aschwanden M J, Csillaghy A, Dennis B R, Johns-Krull C, Krucker S1, Lin R P, Mctiernan J, Metcalf T R, Sato J, Smith D M 2002 Solar Phys. 210 61
Google Scholar
[4] Milligan R O, Gallagher P T, Mathioudakis M, Bloomfield D S, Keenan F P, Schwartz R A 2006 Astrophys. J. 638 L117
Google Scholar
[5] Underwood J H, Neupert W M 1974 Solar Phys. 35 241
Google Scholar
[6] Tousey R, Bartoe J D F, Brueckner G E, Purcell J D 1977 Appl. Opt. 16 4
Google Scholar
[7] Neupert W M, Epstein G L, Thomas R J, Thompson W T 1992 Solar Physics 137 87
Google Scholar
[8] Brosius W, Davila J M, Thomas A. 1998 Astrophys. J. Suppl. Ser. 119 255
Google Scholar
[9] Brosius J W, Thomas R J, Davila J M 2000 Astrophys. J. 543 1016
Google Scholar
[10] Curdt W, Brekke P, Feldman U, Wilhelm K, Dwivedi B N, Schuhle U, Lemaire P 2001 Astron. Astrophys. 375 591
Google Scholar
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Google Scholar
[12] Kosugi T, Matsuzaki K, Sakao T, et al. 2007 Solar Phys. 243 3
Google Scholar
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[14] Pesnell W D, Thompson B J, Chamberlin P C 2012 Solar Phys. 275 3
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
Gan W Q, Huang Y, Yan Y H 2012 Sci. Sin. Phys. Mech. Astron. 42 1274
Google Scholar
[19] 甘为群, 颜毅, 华黄宇 2019 中国科学: 物理学 力学 天文学 49 059602
Google Scholar
Gan W Q, Yan Y H, Huang Y 2019 Sci. Sin. Phys. Mech. Astron. 49 059602
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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图 1 成像光谱仪的三维数据立方体I (x, y, λ)
Figure 1. Three-dimensional data cube I (x, y, λ) for imaging spectrometers.
图 2 太阳极紫外层析成像光谱仪的基础光学架构
Figure 2. Fundamental optical configuration for solar EUV tomography imaging spectrometer.
图 3 TVLS光栅示意图
Figure 3. Schematic of toroidal varied line space grating.
图 4 太阳极紫外层析成像光谱仪光路原理图
Figure 4. Optical layout of solar EUV tomographic imaging spectrometer.
图 5 –1级次像面上的均方根点列图
Figure 5. RMS spot diagram in –1 order imaging surface
图 6 0级次像面上的均方根点列图
Figure 6. RMS spot diagram in 0 order imaging surface.
图 7 +1级次像面上的均方根点列图
Figure 7. RMS spot diagram in +1 order imaging surface.
图 8 反演目标G(x, y0, λ)的有限角度层析投影
Figure 8. Limited angle tomography projection for inversion object G(x, y0, λ).
图 9 太阳极紫外光谱图 (a)仪器带宽内的谱线强度分布; (b) He II 30.4 nm谱线高斯轮廓分布
Figure 9. Solar extreme ultraviolet spectrogram: (a) Spectral lines intensity distribution in instrument bandwidth; (b) Gaussian distribution of He II 30.4 nm spectral line profile.
图 10 初始图像和重建图像对比 (a) 初始图像; (b) 重建图像
Figure 10. Comparison of the initial image and the reconstructed image: (a) Initial image; (b) reconstructed image.
图 11 谱线的中心位置
Figure 11. Central position of line.
图 12 谱线偏移误差
Figure 12. Error of line shift.
表 1 层析成像光谱仪的技术指标和系统参数表
Table 1. Specifications and system parameters for tomographic imaging spectrometer.
参数 取值 Specifications Spectral range/nm 29.4 — 31.4 FOV/arcmin2 10 arcmin × 10 arcmin Spectral resolution/nm 0.003 Spatial resolution/arcsec 0.42 Line-of-sight velocity/(km·s–1) > 29.61 System focal length/mm 6500 Pixel size/μm 13 Optical volume/mm3 1050 mm×
330 mm×60 mmTelescope design RT/mm 1888.190 Conic –1 Δ/mm 80 Spectral imaging system design 1/d0/mm–1 3200 rA/mm 150 β 6.87× i/(°) 5.56 R/mm 263.514 ρ/mm 259.940 b2 0.0938 Ruling area/mm2 20 mm × 20 mm 
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表 2 层析成像光谱仪的数据重建算法SMART
Table 2. Data reconstruction algorithm SMART for tomography imaging spectrometer.
Smooth multiplicative algebraic reconstruction technique 1. Initial guess: $G(x, \lambda ) = {I_0}(x){I_\infty }(\lambda )/N$ 2. Projection: $[{I'_{ - 1}}, {I'_0}, {I'_{ + 1}}, {I'_\infty }] = P[G]$ 3. Correction: $\begin{aligned} G = G{\left[ {\frac{ { {I_{ - 1} }(x - \lambda )} }{ { { {I'}_{ - 1} }(x - \lambda )} } } \right]^\gamma }{\left[ {\frac{ { {I_0}(x)} }{ { { {I'}_0}(x)} } } \right]^\gamma }\\ \times{\left[ {\frac{ { {I_{ + 1} }(x + \lambda )} }{ { { {I'}_{ + 1} }(x + \lambda )} } } \right]^\gamma }{\left[ {\frac{ { {I_\infty }(\lambda )} }{ { { {I'}_\infty }(\lambda )} } } \right]^\gamma }\end{aligned}$ 4. Smoothing: $G = G \otimes \displaystyle\frac{1}{ {1 + 2 t + 2 s} }\left[ {\begin{array}{*{20}{c} } 0& t & 0 \\ s& 1 & s \\ 0& t & 0 \end{array} } \right]$ 5. Reprojection: $[{I'_{ - 1}}, {I'_0}, {I'_{ + 1}}, {I'_\infty }] = P[G]$ 6. Evaluate goodness of fit: $\chi _m^2 = 1 + \displaystyle\sum\limits_{x, y} \dfrac{(I'_m - I_m)^2}{N}$ 7. Adjust smoothing parameters: $t = \dfrac{t}{\chi _{ - 1}^2\chi _{ + 1}^2},~~ s = \dfrac{s}{\chi _0^2}$ 8. Loop to step 3
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表 3 反演效果评价指标
Table 3. Evaluation indicators for the reconstruction
Quantized indicators τ k δRMS Parametric inversion 0.862 0.668 0.294
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[1] 王水, 魏奉思 2007 地球物理学进展 22 1025
Google Scholar
Wang S, Wei F S 2007 Prog. Geophys. 22 1025
Google Scholar
[2] 汪景琇, 季海生 2013 中国科学: 地球科学 43 883
Google Scholar
Wang J X, Ji H S 2013 Sci. China Earth Sci. 43 883
Google Scholar
[3] Hurford G J, Schmahl E J, Schwartz R A, Conway A J, Aschwanden M J, Csillaghy A, Dennis B R, Johns-Krull C, Krucker S1, Lin R P, Mctiernan J, Metcalf T R, Sato J, Smith D M 2002 Solar Phys. 210 61
Google Scholar
[4] Milligan R O, Gallagher P T, Mathioudakis M, Bloomfield D S, Keenan F P, Schwartz R A 2006 Astrophys. J. 638 L117
Google Scholar
[5] Underwood J H, Neupert W M 1974 Solar Phys. 35 241
Google Scholar
[6] Tousey R, Bartoe J D F, Brueckner G E, Purcell J D 1977 Appl. Opt. 16 4
Google Scholar
[7] Neupert W M, Epstein G L, Thomas R J, Thompson W T 1992 Solar Physics 137 87
Google Scholar
[8] Brosius W, Davila J M, Thomas A. 1998 Astrophys. J. Suppl. Ser. 119 255
Google Scholar
[9] Brosius J W, Thomas R J, Davila J M 2000 Astrophys. J. 543 1016
Google Scholar
[10] Curdt W, Brekke P, Feldman U, Wilhelm K, Dwivedi B N, Schuhle U, Lemaire P 2001 Astron. Astrophys. 375 591
Google Scholar
[11] Thompson W T, Brekke P 2000 Solar Phys. 195 45
Google Scholar
[12] Kosugi T, Matsuzaki K, Sakao T, et al. 2007 Solar Phys. 243 3
Google Scholar
[13] Culhane J L, Harra L K, Doschek G A, Mariska J T, Watanabe T, Hara H 2005 Adv. Space Res. 36 1494
Google Scholar
[14] Pesnell W D, Thompson B J, Chamberlin P C 2012 Solar Phys. 275 3
Google Scholar
[15] Lemen J R, Title A M, Akin D J, et al. 2012 Solar Phys. 275 17
Google Scholar
[16] Müller D, Cyr O C S, Zouganelis I, et al. 2020 Astron. Astrophys. 642 A1
Google Scholar
[17] Anderson M, Appourchaux T, Auchère F, et al. 2020 Astron. Astrophys. 642 A14
Google Scholar
[18] 甘为群, 黄宇, 颜毅华 2012 中国科学: 物理学 力学 天文学 42 1274
Google Scholar
Gan W Q, Huang Y, Yan Y H 2012 Sci. Sin. Phys. Mech. Astron. 42 1274
Google Scholar
[19] 甘为群, 颜毅, 华黄宇 2019 中国科学: 物理学 力学 天文学 49 059602
Google Scholar
Gan W Q, Yan Y H, Huang Y 2019 Sci. Sin. Phys. Mech. Astron. 49 059602
Google Scholar
[20] Tu C Y, Schwenn R, Donovan E, Marsch E, Wang J S, Xia L D, Zhang Y M 2008 Adv. Space Res. 41 190
Google Scholar
[21] Wang J S, Zhang J 2007 Adv. Space Res. 40 1770
Google Scholar
[22] Zanna G D, Mason H E 2018 Living Rev. Sol. Phys. 15 5
Google Scholar
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