同轴和微分相衬成像理论与数值分析研究
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摘要
X射线相衬成像是近年来X射线成像发展的一个焦点,这种成像方法弥补了传统X射线成像不能对弱吸收物体成像的不足,在医学、生物学及材料学等领域有着极大的应用潜力。目前已有多种相衬成像方法相继被提出,相衬成像方法大致可分为以下几类:类Zernike方法、干涉相衬、衍射增强、同轴相衬和基于Talbot干涉仪的微分相衬。类Zernike方法对光源的单色性要去较高,同时光学聚焦的器件制作也是一个挑战。但是这类方法的空间分辨率可以达到很高,适合应用于显微成像。干涉的方法对光源相干性、设备的机械稳定性及光学器件的精度要求很高。衍射增强目前只同步辐射源上开展过,适用性差。同其他方法相比,同轴相衬及微分相衬对光源要求低,更具有应用的潜力。
同轴相衬类似于Gabor全息成像原理,在X射线传播的过程中遇到相位物体时,其波前相位发生变化,进一步传播时,这种变化会以强度的形式表现出来,即光强中包含相位信息。这种方法不需要其他的光学器件,系统结构简单,结构紧促,容易实施。对光源的时间相干性要求低,较宽光谱也可以成像。同时放大率的存在降低了对探测器分辨率的要求。对弱吸收物体,低空间频率物体成像强度同其相位分布的二阶微分成正比,某些频率处的强度正比于相位分布。其它情况下对应关系不明确。影响成像的因素有:光源到物体的距离R,物体到成像距离z,成像的波长,光源的焦斑。z影响系统的传递函数,不同的物体空间频率有一个最佳的成像距离。R同z的比值会影响图像的放大率和源的空间相干性,较大的放大率时,光源有较低的空间相干性,要根据成像的要求及探测器的性能来确定R和z值的选择。较短的波长有利于图像的锐度,但会降低衬度。小焦斑的源有利于成像。
基于Talbot干涉仪微分相衬利用周期性的物体自成像形成干涉条纹,相位物体引起条纹的变形,从畸变的条纹中计算出相位的分布。条纹的强度的相位分布同物体相位的一阶微成正比,所以称为微分相衬。对光栅来说,要求有高衍射效率和能形成对比度好的干涉条纹。衍射效率受光栅材料、凹槽厚度、占空比和所使用波长的影响。条纹对比度受光源谱分布、成像距离、光源空间相干性这些因素的影响,对参数的研究给出了它们的参考值。探测器前加上分析光栅降低了对探测器的要求。相位的计算有Fourier变换算法和Phase-Step算法,文中给出了这两种方法具体的计算过程及各自优缺点。
Since the middle of 1990s, X-ray phase-contrast imaging has been attracting increasing attention because of its advantage that an extremely high sensitivity achieved for weak-absorbing material, which generates a poor contrast by conventional method based on absorbing. Phase-contrast imaging should find broad application in medicine, biological and material science et al. Several methods of phase-contrast imaging, including Zernike-type, interferometric phase-contrast, diffraction enhanced imaging (DIE), in-line phase-contrast and differential phase-contrast based on Talbot interferometer, have been developed. The requirement of monochromatic x-ray in Zernike-type is strict and fabricate of optical instrument focusing X-ray is a challenge. However the resolving power of Zernike-type can be down to submicron. The requirements of coherence, mechanical stability of instrument and precision of optical device in interferometric methods are strict. So far method of DIE only can be performed with synchrotron source, so the application is restricted. Compared with other methods, in-line phase-contrast and differential phase-contrast are easily performed in conventional laboratory and very widely used because of their moderate requirement on coherence.
In-line phase-contrast imaging is a holography method which generates intensity distribution including phase information. Variations in thickness and X-ray refractive index of a sample lead to a change in the shape of an X-ray wavefront on passing through the sample. No optical instruments used in this imaging system lead to sample and compact setup, easy performance. Because of chromatic coherence of lesser important, broadband microfocus sources can give useful phase-contrast images. Taking advantage of the magnification, the requirement of detector resolution is not strict. For the weak-absorbing material, contrast is proportional to the second derivative of phase distribution when the spatial frequency is small enough. Various factors, including the distance between source and specimen R, the distance between specimen and imaging plane z, wavelength used and lateral coherence of source, can influence the contrast of image. There is a suitable z for some spatial frequency according to the variations of transfer function with z. Magnification and spatial coherence of imaging system are determined by the ratio z/R. While increasing the magnification, the spatial coherence could be decreased. So the distances R and z should be determined by the requirement of image and resolution power of detector. The image sharpness will high when shorter wavelength of X-ray is used, but contrast of image decrease. Microfocus source will benefit image.
Phase object in front of interferometer cause the distorted interference fringes, which base on Talbot effect. And the phase information, which is proportional to the first derivative of phase distribution, can be obtained from the fringes. With respect to phase grating, the high efficiency of diffraction and visibility are essentially to grating imaging. The efficiency of phase grating is limited by groove depth, material, duty ratio and wavelength. Various parameters insisting of spectrum of source, imaging distance and spatial coherence can influence visibility of fringes. Their referential values were presented in this paper. The absorbing grating in front of detector decreases the requirement of resolution for detector. Methods of Fourier transform and phase-step, which be used for calculating phase information, were introduced and simulation were presented, too.
同轴相衬类似于Gabor全息成像原理,在X射线传播的过程中遇到相位物体时,其波前相位发生变化,进一步传播时,这种变化会以强度的形式表现出来,即光强中包含相位信息。这种方法不需要其他的光学器件,系统结构简单,结构紧促,容易实施。对光源的时间相干性要求低,较宽光谱也可以成像。同时放大率的存在降低了对探测器分辨率的要求。对弱吸收物体,低空间频率物体成像强度同其相位分布的二阶微分成正比,某些频率处的强度正比于相位分布。其它情况下对应关系不明确。影响成像的因素有:光源到物体的距离R,物体到成像距离z,成像的波长,光源的焦斑。z影响系统的传递函数,不同的物体空间频率有一个最佳的成像距离。R同z的比值会影响图像的放大率和源的空间相干性,较大的放大率时,光源有较低的空间相干性,要根据成像的要求及探测器的性能来确定R和z值的选择。较短的波长有利于图像的锐度,但会降低衬度。小焦斑的源有利于成像。
基于Talbot干涉仪微分相衬利用周期性的物体自成像形成干涉条纹,相位物体引起条纹的变形,从畸变的条纹中计算出相位的分布。条纹的强度的相位分布同物体相位的一阶微成正比,所以称为微分相衬。对光栅来说,要求有高衍射效率和能形成对比度好的干涉条纹。衍射效率受光栅材料、凹槽厚度、占空比和所使用波长的影响。条纹对比度受光源谱分布、成像距离、光源空间相干性这些因素的影响,对参数的研究给出了它们的参考值。探测器前加上分析光栅降低了对探测器的要求。相位的计算有Fourier变换算法和Phase-Step算法,文中给出了这两种方法具体的计算过程及各自优缺点。
Since the middle of 1990s, X-ray phase-contrast imaging has been attracting increasing attention because of its advantage that an extremely high sensitivity achieved for weak-absorbing material, which generates a poor contrast by conventional method based on absorbing. Phase-contrast imaging should find broad application in medicine, biological and material science et al. Several methods of phase-contrast imaging, including Zernike-type, interferometric phase-contrast, diffraction enhanced imaging (DIE), in-line phase-contrast and differential phase-contrast based on Talbot interferometer, have been developed. The requirement of monochromatic x-ray in Zernike-type is strict and fabricate of optical instrument focusing X-ray is a challenge. However the resolving power of Zernike-type can be down to submicron. The requirements of coherence, mechanical stability of instrument and precision of optical device in interferometric methods are strict. So far method of DIE only can be performed with synchrotron source, so the application is restricted. Compared with other methods, in-line phase-contrast and differential phase-contrast are easily performed in conventional laboratory and very widely used because of their moderate requirement on coherence.
In-line phase-contrast imaging is a holography method which generates intensity distribution including phase information. Variations in thickness and X-ray refractive index of a sample lead to a change in the shape of an X-ray wavefront on passing through the sample. No optical instruments used in this imaging system lead to sample and compact setup, easy performance. Because of chromatic coherence of lesser important, broadband microfocus sources can give useful phase-contrast images. Taking advantage of the magnification, the requirement of detector resolution is not strict. For the weak-absorbing material, contrast is proportional to the second derivative of phase distribution when the spatial frequency is small enough. Various factors, including the distance between source and specimen R, the distance between specimen and imaging plane z, wavelength used and lateral coherence of source, can influence the contrast of image. There is a suitable z for some spatial frequency according to the variations of transfer function with z. Magnification and spatial coherence of imaging system are determined by the ratio z/R. While increasing the magnification, the spatial coherence could be decreased. So the distances R and z should be determined by the requirement of image and resolution power of detector. The image sharpness will high when shorter wavelength of X-ray is used, but contrast of image decrease. Microfocus source will benefit image.
Phase object in front of interferometer cause the distorted interference fringes, which base on Talbot effect. And the phase information, which is proportional to the first derivative of phase distribution, can be obtained from the fringes. With respect to phase grating, the high efficiency of diffraction and visibility are essentially to grating imaging. The efficiency of phase grating is limited by groove depth, material, duty ratio and wavelength. Various parameters insisting of spectrum of source, imaging distance and spatial coherence can influence visibility of fringes. Their referential values were presented in this paper. The absorbing grating in front of detector decreases the requirement of resolution for detector. Methods of Fourier transform and phase-step, which be used for calculating phase information, were introduced and simulation were presented, too.
引文
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