X-ray spot size measurement with pinhole
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摘要: 通过针孔成像法得到X光源强度空间分布图像，直接读取图像数据得到X光源的半高宽焦斑（FWHM）尺寸，对图像数据进行傅里叶变换得到调制传递函数，并计算得到X光源的等效焦斑尺寸（50%MTF）。应用针孔成像法测量多脉冲电子直线感应加速器产生的X光源焦斑尺寸，测量结果表明，加速器性能稳定。定义焦斑形状因子参数并用于描述X光源分布，结果表明，该加速器X光源分布在高斯分布和本涅特分布之间变化。Abstract: The high intense pulse electron beam emitted and accelerated by linear induction accelerator (LIA) is focused to heavy metal target to produce X-ray pulses via bremsstrahlung mechanism. The X-ray is applied to high energy flash radiography. The X-ray spot size is a critical parameter for LIA and the main factor which degrades resolution of the flash radiography. This paper describes a pinhole imaging system measuring the X-ray spot size. The full width at half maximum (FWHM) of the X-ray spot size can be obtained from the pinhole image data. The modulation transfer function (MTF) which is derived from the X-ray spot image by Fourier transform is applied to calculate the 50%MTF spot size. In the continuous experiments of multi-pulse electron linear induction accelerator (MPELIA), the X-ray spot size is measured and the results demonstrate reliable performance of MPELIA. The concept of form factor is introduced, and the measured results show that the MPLIA X-ray spot distribution changes between Gaussian and Bennett distribution.
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Key words:
- high energy X-ray spot /
- spot size /
- pinhole /
- MTF /
- form factor
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表 1 不同分布的点扩展函数、线扩展函数和调制传递函数
Table 1. PSF, LSF and MTF of different distribution
distribution PSF（x，y） LSF（x） MTF（k） FWHMP FWHML KV $\left\{ {\begin{array}{*{20}{c}} {{1 / {{\text{π}} {a^2}}};{x^2} + {y^2} \leqslant {a^2}} \\ {{\rm{ 0}};\;\;\;\;{x^2} + {y^2} > {a^2}} \end{array}} \right.$ $\left\{ {\begin{array}{*{20}{c}} {\dfrac{2}{{{\text{π}} {a^2}}}\sqrt {{a^2} - {x^2}} ;x < a} \\ {{\rm{ 0}};\;\;\;\;x \geqslant a} \end{array}} \right.$ $2\dfrac{{\left| {{J_1}(ka)} \right|}}{{ka}}$ $2a$ $\dfrac{{0.705}}{{{f_{0.5}}}}$ $\sqrt 3 a$ GS $\dfrac{1}{ { {\text{π} } {a^2} } }{e^{ - { {({x^2} + {y^2})} / { {a^2} } } } }$ $\dfrac{1}{ {a\sqrt {\rm{ {\text{π} } } } } }{e^{ - { { {x^2} } / { {a^2} } } }}$ $\mathop e\nolimits^{ - {k^2}{a^2}/4} $ $2\sqrt {\ln 2} a$ $\dfrac{{0.441}}{{{f_{0.5}}}}$ $2\sqrt {\ln 2} a$ BNT $\dfrac{1}{ { {\rm{ {\text{π} } } }{ {\rm{a} }^2} } }{\left(1 + \dfrac{ { {x^2} + {y^2} } }{ { {a^2} } }\right)^{ - 2} }$ $\dfrac{1}{ {2a} }{\left(1 + \dfrac{ { {x^2} } }{ { {a^2} } }\right)^{ - {3 / 2} } }$ $ka{K_1}(ka)$ $2\sqrt {\sqrt 2 - 1} a$ $\dfrac{{0.257}}{{{f_{0.5}}}}$ $2\sqrt {{2^{1.5}} - 1} a$ 
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表 2 MPELIA X光焦斑尺寸测量结果
Table 2. X-ray spot size measurement results of MPELIA
No. Ee/ MeV Ie/ kA FWHM size/
mmstd of
FWHM/ mmdirection FWHMxy size/
mmresult image
fi0.5/（mm·lp−1）X-ray spot
fs0.5/（mm·lp−1）50%MTF
size/mm516A 19.0 2.03 1.18 0.08 x 1.33 0.0380 0.0511 3.18 y 1.11 0.0402 0.0575 2.83 516B 19.0 2.06 1.44 0.22 x 1.71 0.0389 0.0527 3.09 y 1.18 0.0418 0.0619 2.63 516C 18.9 2.04 1.24 0.10 x 1.12 0.0371 0.0494 3.29 y 1.29 0.0319 0.0418 2.89 518A 19.0 2.02 1.33 0.07 x 1.34 0.0405 0.0579 2.81 y 1.40 0.0392 0.0566 2.88 518B 19.0 2.04 1.33 0.11 x 1.18 0.0408 0.0620 2.62 y 1.44 0.0366 0.0492 3.30 518C 19.0 2.06 1.50 0.23 x 1.43 0.0369 0.0496 3.28 y 1.66 0.0286 0.0365 4.45 523A 18.9 2.04 1.32 0.06 x 1.38 0.0424 0.0617 2.73 y 1.39 0.0428 0.0630 2.68 523B 18.9 1.98 1.35 0.10 x 1.24 0.0403 0.0607 2.78 y 1.45 0.0374 0.0503 3.35 523C 18.8 2.07 1.45 0.25 x 1.27 0.0404 0.0567 2.97 y 1.58 0.0327 0.0414 4.07 524A 19.0 2.03 1.26 0.08 x 1.27 0.0415 0.0589 2.86 y 1.20 0.0414 0.0594 2.83 524B 18.8 2.04 1.36 0.10 x 1.27 0.0405 0.0603 2.79 y 1.52 0.0402 0.0579 2.91 524C 18.7 2.08 1.40 0.15 x 1.51 0.0393 0.0526 3.20 y 1.22 0.0356 0.0458 3.68 525A 19.0 2.05 1.32 0.06 x 1.47 0.0419 0.0597 2.82 y 1.32 0.0412 0.0594 2.84 525B 19.0 2.08 1.41 0.13 x 1.26 0.0414 0.0614 2.74 y 1.48 0.0410 0.0600 2.81 525C 18.9 2.09 1.49 0.19 x 1.67 0.0399 0.0533 3.16 y 1.26 0.0364 0.0469 3.59
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表 3 MPELIA X光源焦斑形状因子
Table 3. X-ray spot form factor of MPELIA
No. FWHMx/mm FWHMy/mm 50%MTFx/mm 50%MTFy/mm Cx Cy 516A 1.33 1.11 3.18 2.83 2.39 2.55 516B 1.71 1.18 3.09 2.63 1.81 2.23 516C 1.12 1.29 3.29 2.89 2.94 2.24 518A 1.34 1.40 2.81 2.88 2.10 2.06 518B 1.18 1.44 2.62 3.30 2.22 2.29 518C 1.43 1.66 3.28 4.45 2.29 2.68 523A 1.38 1.39 2.73 2.68 1.98 1.93 523B 1.24 1.45 2.78 3.35 2.24 2.31 523C 1.27 1.58 2.97 4.07 2.34 2.58 524A 1.27 1.20 2.86 2.83 2.25 2.36 524B 1.27 1.52 2.79 2.91 2.20 1.91 524C 1.51 1.22 3.20 3.68 2.12 3.02 525A 1.47 1.32 2.82 2.84 1.92 2.15 525B 1.26 1.48 2.74 2.81 2.17 1.90 525C 1.67 1.26 3.16 3.59 1.89 2.85
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