Department of Radiology, University of Alabama at Birmingham, Birmingham, AL 35233, USA.
J Xray Sci Technol. 2003 Jan 1;11(1):33-42.
The in-line phase-contrast imaging has great potential for clinical imaging applications. This work presents a general theoretical formalism for the in-line phase-contrast imaging. The theoretical formalism developed in this work is derived by taking a new strategy to calculate the Fourier transform of image intensity directly. Different from the transport of intensity equation (TIE) formalism for phase-contrast imaging in literature [6], this general formalism covers both the near field regime and the holography regime of phase-contrast imaging. The image intensity formulas have been derived in both the image space and frequency space. Especially our results show that the Fresnel diffraction image intensity is a sum of convolutions of the cosine- and sine-Fresnel filters with the object attenuation A20(x) and attenuated phase A20(x)φ(x), respectively. The Pogany-Gao-Wilkins (PGW) formalism is recovered as a special case of our general formalism. In addition, in the low-resolution approximation, the general formula is reduced a spherical wave-generalization of the TIE-based formula for phase-contrast imaging. This spherical wave-generalization will be useful for phase-contrast imaging with a micro-focus x-ray tube. The transition of the formalism from 1-D to 2-D cases has been provided as well.
在线相位对比成像是具有很大潜力的临床成像应用。本工作提出了一种通用的在线相位对比成像理论公式。本工作中开发的理论公式是通过采取一种新的策略来直接计算图像强度的傅里叶变换而推导出来的。与文献[6]中用于相位对比成像的强度传输方程（TIE）公式不同，这个通用公式涵盖了相位对比成像的近场和全息术两个领域。已经在像空间和频率空间中推导出了强度公式。特别是，我们的结果表明，菲涅耳衍射强度是余弦和正弦菲涅耳滤波器与物体衰减 A20(x)和衰减相位 A20(x)φ(x)的卷积和。Pogany-Gao-Wilkins（PGW）公式是我们的一般公式的一个特例。此外，在低分辨率近似下，一般公式被简化为基于 TIE 的相位对比成像公式的球面波推广。这个球面波推广将对使用微焦点 X 射线管的相位对比成像有用。还提供了从 1-D 到 2-D 情况的公式转换。
