微聚焦X射线成像的相位效应分析

根据Fresnel-Kirchhoff衍射理论,结合临床实际,考虑振幅近似和相位缓变条件,由傅里叶变换和卷积定理,导出了微聚焦X射线相衬成像(X-ray Phase-contrast Imaging,X-PCI)在像平面上焦斑尺寸范围内的能量密度分布函数.结果显示,像密度函数是吸收效应滤波函数FA(x)和相位效应滤波函数FP(x)分别与吸收项A2(x)和相位项A2(x)φ(x)作卷积运算后的和.利用mathematica软件分析讨论了该函数的分布规律,并给出了理论解释.结果表明,吸收效应对像密度的影响在焦斑范围内保持不变;相位效应对像密度的影响在焦斑范围内逐渐加强;在焦斑一定范围内,相位效应的影响远大于吸收效应.

Analysis of the Absorption and the Phase-effect on Micro-focus X-PCI

Based on Fresnel-Kirchhoff diffraction theory, taking the clinical conditions of the amplitude approximation and the moderate variation condition for phases into account,the image intensity formulas of micro-focus X-PCI in the range of focal aperture on the image plane are derived by Fourier transform and the convolution theorems. The results indicate that the image intensity formula actually is a sum of convolutions of the absorption-effect filter formula F_A (χ) and the phase-effect filter formula F_P(χ) with the object attenuation A~2 (χ)and attenuated phase A~2 (χ) φ(χ), respectively. After the analysis of the regularities of the formulas by mathematica ,the theoretical explanations of the regularities we given and the conclusions obtained are that; first,the effect of the absorption-effect on the image intensity remains constant in the range of focal aperture; second, the effect of the phase-effect on the image intensity gradually strengthens in the range of focal aperture; third, the effect of the phase-effect on the image intensity is much more than the one of the absorption-effect in a given rang of focal aperture.