X射线光栅相衬成像中的信息分离以及计算机断层重建
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摘要
自上世纪九十年代中期以来,多种X射线相位衬度成像(简称相衬成像)方法相继被提出,不同于传统基于吸收的X射线成像,该类成像方法通过探测物体对X射线波阵面的调制获得物体的内部信息。物体在X射线波段的折射率通常用复数表示,其实部减小量反映相移信息,虚部反映吸收信息。在硬X射线波段,软组织的折射率实部减小量是虚部的几百到几千倍,也就是说相衬图像理论上有着更高的灵敏度,因此利用相移信号成像可以获得更高的图像质量。
经过二十年的发展,X射线相衬成像形成了五种主流方法,其中部分方法由于较小的成像视场,较高的机械稳定性和光源相干性要求,难以广泛应用于实际。近年来,基于光栅的X射线微分相衬成像(简称光栅相衬成像)吸引了越来越多的关注,被X射线成像领域研究者认为是极有可能应用于临床医学的成像方法。相比其它的相衬成像方法,光栅相衬成像方法主要有两大显著优势：较低的光源相干性要求以及较大的成像视场。本论文将主要讨论光栅相衬成像中的信息分离以及计算机断层重建(Computed Tomography (CT))。
相衬成像图像包含吸收,折射以及散射信号,三种信号对应物体不同的物理特性。为了获取各个物理量的独立定量信息,涌现了大量的信息分离方法。目前光栅相衬成像方法中主要有三种信息分离方法：傅立叶分析方法,相位步进方法以及正反投影方法。其中,正反投影方法是我们研究组在2010年提出的一种快速低剂量成像方法。本文我们将研究该方法在扇束几何中的推广,相干性影响以及噪声特性,并讨论该方法与传统相位步进方法的定量比较。这些研究将促进并指导光栅相衬成像方法的临床应用。
计算机断层成像利用具有穿透能力的射线,在不破坏物体的情况下实现对物体内部结构的观察,是一种常见的三维成像手段。X射线计算机断层成像(X-CT)已在临床医学,无损检测以及材料科学等领域得到广泛应用。尤其是X-CT在医学诊断中的应用,为疾病的发现和病灶的定位带来了巨大帮助。然而,X-CT对软组织成像时,衬度较低,即便使用造影剂也难以获得较清晰的图像。相比之下,相衬成像方法可以获得高衬度的二维图像,与X-CT结合形成相衬CT (PC-CT)成像方法,获得优质的三维图像。由于投影机制的差异,PC-CT与传统X-CT拥有不同的重建方法,在滤波反投影方法中表现为不同的滤波函数。本论文第四章将详细介绍平行束和等角射线型扇束几何中的吸收CT和相衬CT。
临床中,成像速度和辐射剂量是X射线成像技术最关心的问题。在光栅PC-CT中,利用相位步进方法分离信息时,光栅平移运动与CT旋转运动交替进行,降低了成像速度,增加了样品受辐照时间。而正反投影方法巧妙利用平行束几何中互为正反投影图像的共轭特性(即具有相同的吸收和相反的折射角),一定程度上实现了快速低剂量的相衬CT成像。然而该方法只适用于平行束几何,这是因为正反向投影图在非平行束几何中不再共轭。本文通过考虑更小的射线单元,把正反投影方法成功推广到扇束几何。
本文主要内容包括七部分：
1.概述不同相衬成像方法；
2.详细介绍光栅相衬成像方法
3.讨论光栅相衬成像现有的信息分离方法；
4.回顾吸收和相衬滤波反投影重建方法；
5.正反投影方法在扇束几何中的推广；
6.光源空间相干性对正反投影方法提取结果的影响；
7.正反投影方法的噪声分析以及与传统相位步进方法的定量比较。
本论文的创新性可总结为以下四点：
1.首次把正反投影方法推广到扇束几何；
2.首次分析光源相干性对正反投影方法提取结果的影响；
3.利用误差传递公式,首次讨论正反投影方法的噪声特性；
4.首次完成了正反投影方法和相位步进方法的定量比较。
Many X-ray phase contrast imaging methods have been developed since the1990s. Different from traditional X-ray attenuation-based imaging, they allow obtaining inner structure of an object by detecting the phase modulation derived from its internal structure. The object's refraction index is usually expressed by a complex number, whose decrement of the real part accounts for refraction information while its imaginary part is related to absorption information. Working in the hard X-ray domain, the decrement of the real part of refraction index of soft materials like tissues is two orders of or three orders of magnitudes bigger than the imaginary part. In other words, phase contrast image has a higher sensitivity from theoretical point of view, so we can obtain higher image quality using phase contrast imaging methods.
In the last20years X-ray phase contrast imaging has achieved important progress and at least five main methods have been established. However, some are unsuitable for wide practical applications due to small field of view, high requirement on mechanical stability and coherence of light source. Recently, the grating-based phase contrast imaging (GBPCI), attracting a lot of attentions in the field of X-ray imaging, is considered as a potential phase contrast imaging method for clinical applications. Compared to other phase contrast imaging methods, GBPCI offers two main advantages:low requirement on time and spatial coherence of the light source and a large field of view. In this thesis, we will discuss information extraction and computed tomography (CT) in GBPCI.
Phase contrast image contains absorption, refraction and scattering signals, which relate to the object's different physical characteristics. In order to calculate these physical quantities, many different information separation methods have been proposed. Currently, three are widely used in GBPCI:the Fourier analysis method, the phase stepping (PS) method and the reverse projection (RP) method. The last is a low dose and fast method, proposed by our group in2010. In this manuscript, we will present its generalization, the effect of the coherence, the noise properties, and compare it with the PS method. All these works accelerate and guide foreseen clinic applications of GBPCI.
Using the ray with penetrating power, computed tomography is able to probe the inner3D structure of an object in a non-destructive way, and represents a common three-dimensional (3D) tool. X-ray CT (X-CT) is already widely applied in clinical medicine, non-destructive testing and materials science. In particular, the application in medicine helps to identify and locate a pathological status. However, when the sample is a soft tissue, traditional X-CT provides a poor contrast even using contrast agent. In contrast, phase contrast imaging provides high contrast two-dimensional iamge. Combination with X-CT develops into "PC-CT" method providing a superior3D image. Because of the different projection mechanisms, the reconstruction algorithms are different, e.g. different filters in the filter back-projection (FBP) algorithms are used. In this manuscript, we will present and discuss X-CT and PC-CT algorithm for parallel beam and equiangular fan beam geometry.
In clinical applications, the speed and the released dose of X-ray imaging mthod are the critical issues. In X-ray grating-based PC-CT, the alternation between the translation of the grating of the PS method and the circular scan of CT determines low imaging speed and high radiation dose. On the contrary, taking use of the conjugate characteristic of the identical attenuation and opposite refraction angle between mutual reverse projections, the RP method achieves a faster and lower dose acquisition. However this approach is only compatible with parallel beam geometry, because the conjugate characteristic between mutual reverse projections is not fulfilled in non-parallel beam geomety. In this thesis, we successfully generalize the RP method to fan beam geometry by considering the single ray as the probe.
The main contents are summeried in seven sections:
1. Overview the different phase contrast imaging methods;
2. Introduction to the GBPCI method;
3. Discussion on the information seperation methods in GBPCI.
4. Review of filtered back-projection algorithms in absorption and phase contrast imaging;
5. Generalization of the RP method in fan beam geometry;
6. The influence of the spatial coherence of the light source on the results of the RP method;
7. The noise analysis of the RP method and comparison between the RP and PS methods;
The main achievements presented in this research can be summarized as follows:
1. A first generalization of the RP method to fan beam geometry.
2. A first analysis on the effect of the spatial coherence of the light source on the results of the RP method;
3. A first discuss of the noise property of the RP method using the error propagation formula;
4. A first attempt to compare RP and PS methods in a quantitative way.
经过二十年的发展,X射线相衬成像形成了五种主流方法,其中部分方法由于较小的成像视场,较高的机械稳定性和光源相干性要求,难以广泛应用于实际。近年来,基于光栅的X射线微分相衬成像(简称光栅相衬成像)吸引了越来越多的关注,被X射线成像领域研究者认为是极有可能应用于临床医学的成像方法。相比其它的相衬成像方法,光栅相衬成像方法主要有两大显著优势：较低的光源相干性要求以及较大的成像视场。本论文将主要讨论光栅相衬成像中的信息分离以及计算机断层重建(Computed Tomography (CT))。
相衬成像图像包含吸收,折射以及散射信号,三种信号对应物体不同的物理特性。为了获取各个物理量的独立定量信息,涌现了大量的信息分离方法。目前光栅相衬成像方法中主要有三种信息分离方法：傅立叶分析方法,相位步进方法以及正反投影方法。其中,正反投影方法是我们研究组在2010年提出的一种快速低剂量成像方法。本文我们将研究该方法在扇束几何中的推广,相干性影响以及噪声特性,并讨论该方法与传统相位步进方法的定量比较。这些研究将促进并指导光栅相衬成像方法的临床应用。
计算机断层成像利用具有穿透能力的射线,在不破坏物体的情况下实现对物体内部结构的观察,是一种常见的三维成像手段。X射线计算机断层成像(X-CT)已在临床医学,无损检测以及材料科学等领域得到广泛应用。尤其是X-CT在医学诊断中的应用,为疾病的发现和病灶的定位带来了巨大帮助。然而,X-CT对软组织成像时,衬度较低,即便使用造影剂也难以获得较清晰的图像。相比之下,相衬成像方法可以获得高衬度的二维图像,与X-CT结合形成相衬CT (PC-CT)成像方法,获得优质的三维图像。由于投影机制的差异,PC-CT与传统X-CT拥有不同的重建方法,在滤波反投影方法中表现为不同的滤波函数。本论文第四章将详细介绍平行束和等角射线型扇束几何中的吸收CT和相衬CT。
临床中,成像速度和辐射剂量是X射线成像技术最关心的问题。在光栅PC-CT中,利用相位步进方法分离信息时,光栅平移运动与CT旋转运动交替进行,降低了成像速度,增加了样品受辐照时间。而正反投影方法巧妙利用平行束几何中互为正反投影图像的共轭特性(即具有相同的吸收和相反的折射角),一定程度上实现了快速低剂量的相衬CT成像。然而该方法只适用于平行束几何,这是因为正反向投影图在非平行束几何中不再共轭。本文通过考虑更小的射线单元,把正反投影方法成功推广到扇束几何。
本文主要内容包括七部分：
1.概述不同相衬成像方法；
2.详细介绍光栅相衬成像方法
3.讨论光栅相衬成像现有的信息分离方法；
4.回顾吸收和相衬滤波反投影重建方法；
5.正反投影方法在扇束几何中的推广；
6.光源空间相干性对正反投影方法提取结果的影响；
7.正反投影方法的噪声分析以及与传统相位步进方法的定量比较。
本论文的创新性可总结为以下四点：
1.首次把正反投影方法推广到扇束几何；
2.首次分析光源相干性对正反投影方法提取结果的影响；
3.利用误差传递公式,首次讨论正反投影方法的噪声特性；
4.首次完成了正反投影方法和相位步进方法的定量比较。
Many X-ray phase contrast imaging methods have been developed since the1990s. Different from traditional X-ray attenuation-based imaging, they allow obtaining inner structure of an object by detecting the phase modulation derived from its internal structure. The object's refraction index is usually expressed by a complex number, whose decrement of the real part accounts for refraction information while its imaginary part is related to absorption information. Working in the hard X-ray domain, the decrement of the real part of refraction index of soft materials like tissues is two orders of or three orders of magnitudes bigger than the imaginary part. In other words, phase contrast image has a higher sensitivity from theoretical point of view, so we can obtain higher image quality using phase contrast imaging methods.
In the last20years X-ray phase contrast imaging has achieved important progress and at least five main methods have been established. However, some are unsuitable for wide practical applications due to small field of view, high requirement on mechanical stability and coherence of light source. Recently, the grating-based phase contrast imaging (GBPCI), attracting a lot of attentions in the field of X-ray imaging, is considered as a potential phase contrast imaging method for clinical applications. Compared to other phase contrast imaging methods, GBPCI offers two main advantages:low requirement on time and spatial coherence of the light source and a large field of view. In this thesis, we will discuss information extraction and computed tomography (CT) in GBPCI.
Phase contrast image contains absorption, refraction and scattering signals, which relate to the object's different physical characteristics. In order to calculate these physical quantities, many different information separation methods have been proposed. Currently, three are widely used in GBPCI:the Fourier analysis method, the phase stepping (PS) method and the reverse projection (RP) method. The last is a low dose and fast method, proposed by our group in2010. In this manuscript, we will present its generalization, the effect of the coherence, the noise properties, and compare it with the PS method. All these works accelerate and guide foreseen clinic applications of GBPCI.
Using the ray with penetrating power, computed tomography is able to probe the inner3D structure of an object in a non-destructive way, and represents a common three-dimensional (3D) tool. X-ray CT (X-CT) is already widely applied in clinical medicine, non-destructive testing and materials science. In particular, the application in medicine helps to identify and locate a pathological status. However, when the sample is a soft tissue, traditional X-CT provides a poor contrast even using contrast agent. In contrast, phase contrast imaging provides high contrast two-dimensional iamge. Combination with X-CT develops into "PC-CT" method providing a superior3D image. Because of the different projection mechanisms, the reconstruction algorithms are different, e.g. different filters in the filter back-projection (FBP) algorithms are used. In this manuscript, we will present and discuss X-CT and PC-CT algorithm for parallel beam and equiangular fan beam geometry.
In clinical applications, the speed and the released dose of X-ray imaging mthod are the critical issues. In X-ray grating-based PC-CT, the alternation between the translation of the grating of the PS method and the circular scan of CT determines low imaging speed and high radiation dose. On the contrary, taking use of the conjugate characteristic of the identical attenuation and opposite refraction angle between mutual reverse projections, the RP method achieves a faster and lower dose acquisition. However this approach is only compatible with parallel beam geometry, because the conjugate characteristic between mutual reverse projections is not fulfilled in non-parallel beam geomety. In this thesis, we successfully generalize the RP method to fan beam geometry by considering the single ray as the probe.
The main contents are summeried in seven sections:
1. Overview the different phase contrast imaging methods;
2. Introduction to the GBPCI method;
3. Discussion on the information seperation methods in GBPCI.
4. Review of filtered back-projection algorithms in absorption and phase contrast imaging;
5. Generalization of the RP method in fan beam geometry;
6. The influence of the spatial coherence of the light source on the results of the RP method;
7. The noise analysis of the RP method and comparison between the RP and PS methods;
The main achievements presented in this research can be summarized as follows:
1. A first generalization of the RP method to fan beam geometry.
2. A first analysis on the effect of the spatial coherence of the light source on the results of the RP method;
3. A first discuss of the noise property of the RP method using the error propagation formula;
4. A first attempt to compare RP and PS methods in a quantitative way.
引文
陈博,朱佩平,刘宜晋,等.2008.X射线光栅相衬成像的理论和方法[J].物理学报57：1576-1581.
曾更生.2009.医学图像重建入门[M].北京：高等教育出版社.
朱佩平,吴自玉.2007.X射线相位衬度成像[J].物理36：443-451.
庄天戈.1992.CT原理与算法[M].上海：上海交通大学出版社.
Alberto B, Paola C and Pekka S.2013. X-ray phase-contrast imaging: from pre-clinical applications towards clinics[J]. Phys. Med. Biol.58:R1-R35.
Bech M, Bunk O, Donath T, et al.2010. Quantitative x-ray dark-field computed tomography[J]. Phys. Med. Biol.55:5529-5539.
Bech M, Tapfer A, Velroyen A, et al.2013.1n-vivo dark-field and phase-contrast x-ray imaging[J]. Scientific Reports 3:3209.
Bennett E E, Kopace R, Stein A F, et al.2010. A grating-based single-shot x-ray phase contrast and diffraction method for in vivo imaging[J]. Med. Phys.37:6047-6054.
Berujon S, Ziegler E, Cerbino R, et al.2012. Two-Dimensional X-Ray Beam Phase Sensing[J]. Phys. Rev. Lett.108:158102.
Bevins N, Zambelli J, Li K, et al.2012. Multicontrast x-ray computed tomography imaging using Talbot-Lau interferometry without phase stepping[J]. Med. Phys.39:424-428.
Bonse U and Hart M.1965. An x-ray interferometer[J]. Appl. Phys. Lett.6:155-156.
Chapman D, et al.1997. Diffraction enhanced x-ray imaging[J]. Phys. Med. Biol.42:2015-2025
Chen G H, Zambelli J, Li K.2011. Scaling law for noise variance and spatial resolution in differential phase contrast computed tomography[J]. Med. Phys.38:584-588.
Chen R C, Rigon L and Longo R.2011. Quantitative 3D refractive index decrement reconstruction using single-distance phase-contrast tomography data[J]. J. Phys. D: Appl. Phys.44:495401.
Chen R C, Rigon L and Longo R.2013. Comparison of single distance phase retrieval algorithms by considering different object composition and the effect of statistical and structural noise. Opt. Express 21:7384-7399.
Chou C Y and Anastasio M A.2010. Noise texture and signal detectability in propagation-based x-ray phase-contrast tomography[J]. Med. Phys.37:270-281.
David C, No'hammer B, Solak H H, et al.2002. Differential x-ray phase contrast imaging using a shearing interferometer[J]. Appl. Phys. Lett.81:3287-3289.
Davis T J, Gureyev T E, Gao D, et al.1995. X-Ray Image Contrast from a Simple Phase Object[J]. Phys. Rev. Lett.74:3173-3176.
Diemoz P C, Bravin A, and Coan P.2011. Theoretical comparison of three X-ray phase-contrast imaging techniques: propagation-based imaging, analyzer-based imaging and grating interferometry[J]. Opt. Express 20:2789-2805.
Diemoz P C, Endrizzi M, Zapata C E, et al.2013a. X-Ray Phase-Contrast Imaging with Nanoradian Angular Resolution[J]. Phys. Rev. Lett.110:138105.
Diemoz P C, Hagen C K, Endrizzi M, et al.2013b. Sensitivity of laboratory based implementations of edge illumination X-ray phase-contrast imaging[J]. Appl. Phys. Lett. 103:244104.
Donath T, Pfeiffer F, Bunk O, et al.2008. Phase-Contrast Imaging and Tomography at 60 keV using a Conventional X-ray Tube[J]. Proc. of SPIE 7078:707817.
Du Y, Liu X, Lei Y H, et al.2011. Non-absorption grating approach for X-ray phase contrast imaging[J]. Opt. Express 19:22669-22674.
Endrizzi M, Diemoz P C, Millard T P, et al.2014. Hard X-ray dark-field imaging with incoherent sample illumination[J]. Appl. Phys. Lett.104:024106.
Faris G W and Byer R L.1988. Three-dimensional beam-deflection optical tomography of a supersonic jet[J]. Appl. Opt.27:5202-5212.
Feldkamp L A, Davis L C, and Kress J W.1984. Practical cone-beam algorithm[J]. J. Opt. Soc. Am. A 1:612-619.
Fogarty D P, Reinhart B a, Tzvetkov Tochko, et al.2011. In-laboratory diffraction-enhanced X-ray imaging of an equine hoof[J]. J. Equine Vet. Sci.31:365-369.
Fu J, Velroyen A, Tan R, et al.2012. A reconstruction method for cone-beam differential x-ray phase-contrast computed tomography[J]. Opt. Express 20:21512-21519.
Ge X, Wang Z L, Gao K, et al.2011. Investigation of the partially coherent effects in a 2D Talbot Interferometer[J]. Anal. Bioanal. Chem.401:865-870.
Grass M, Kohler T and Proksa R.2000.3D cone-beam CT reconstruction for circular trajectories[J]. Phys. Med. Biol.45:329-347.
Guigay I.1971. On Fresnel diffraction by one-dimensional periodic objects, with application to structure determination of phase objects[J]. Optica Acta.18:677-682.
Guigay J P.1977. Fourier transform analysis of Fresnel diffraction patterns and in-line holograms[J]. Optik 49:121-125.
Gureyev T E, Nesterets Y I, Stevenson A W, et al.2008 Some simple rules for contrast, signal-to-noise and resolution in in-line x-ray phase-contrast Imaging[J]. Opt. Express 16:3223-3241.
Huang Z F, Kang K J, Zhang L, et al.2006. Direct computed tomographic reconstruction for directional-derivative projections of computed tomography of diffraction enhanced imaging[J]. Appl. Phys. Lett.89:041124.
Huang Z F, Kang K J, Zhang L, et al.2009. Alternative method for differential phase-contrast imaging with weakly coherent hard x rays[J]. Phys. Rev. A 79:013815.
Huang Z F, Chen Z Q, Zhang L, et al.2010. Large phase-stepping approach for high resolution hard X-ray grating-based multiple information imaging[J]. Opt. Express 18:10222-10229.
Itoh H, Nagai K, Sato G, et al.2011. Two-dimensional grating-based X-ray phase-contrast imaging using Fourier transform phase retrieval[J]. Opt. Lett.17:12540-12545.
Jerjen I, Revol V, Brunner V J, et al.2013. Detection of stress whitening in plastics with the help of X-ray dark field imaging[J]. Polym. Test.32:1094-1098.
Kohler T and Noo F.2009. Comment on "region-of-interest tomography for grating-based X-ray differential phase-contrast imaging"[J]. Phys. Rev. Lett.102:039801.
Kohler T, Engel K J and Roessl E.2011. Noise properties of grating-based x-ray phase contrast computed Tomography[J]. Med. Phys.38:S106-S116.
Kondoh T, Date T, Yamaguchi T, et al.2014. Sparse phase-stepping in two-dimensional X-ray phase contrast imaging[J]. Appl. Optics (http://dx.doi/org/10.1364/A0.99.099999")
Kudo H, and Saito T.1994. Derivation and implementation of a cone-beam reconstruction algorithm for nonplanar orbits[J]. IEEE T. Med. Imaging 13:196-211.
Kudo H, Rodet T, Noo F, et al.2004. Exact and approximate algorithms for helical cone-beam CT[J]. Phys. Med. Biol.49:2913-2931.
Langer M, Cloetens P, Guigay J P, et al.2008. Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography[J]. Med. Phys.35:4556-4566.
Lei Y H, Liu X, Guo J C, et al.2011. Development of x-ray scintillator functioning also as an analyser grating used in grating-based x-ray differential phase contrast imaging[J]. Chinese Phys. B 20:042901.
Lewis R A.2004. Medical phase contrast x-ray imaging: current status and future prospects[J]. Phys. Med. Biol.49:3573-3583.
Liu J K, Ning R L, and Cai W X.2013. Phantom study for volume-of-interest breast imaging using differential phase contrast cone beam CT (DPC-CBCT)[J]. Proc. of SPIE 8668:866850.
Liu X, Guo J C, Peng X, et al.2007. Visibility in differential phase-contrast imaging with partial coherence source[J]. Chinese Phys.16:1632-1636.
Liu X, Guo J C, and Niu H B.2010. A new method of detecting interferogram in differential phase-contrast imaging system based on special structured x-ray scintillator screen[J]. Chinese Phys. B 19:070701.
Liu X S, Li E R, Zhu P P, et al.2010. Comparative analysis of phase extraction methods based on phase-stepping and shifting curve in grating interferometry[J]. Chin. Phys. B 19:040701.
Mayo S C, Stevenson A W and Wilkins S W.2012. In-Line Phase-Contrast X-ray Imaging and Tomography for Materials Science[J]. Materials 5:937-965.
Miao H X, Chen L, Bennett E E, et al.2013. Motionless phase stepping in X-ray phase contrast imaging with a compact source[J]. PNAS.110:19268-19272.
Millard T P, Endrizzi M, Ignatyev K, et al.2013. Method for automatization of the alignment of a laboratory based x-ray phase contrast edge illumination system [J]. Rev. Sci. Instrum.84: 083702.
Modregger P, Pinzer B R, Thuring T, et al.2011. Sensitivity of X-ray grating Interferometry[J]. Opt. Express 19:18324-18338.
Momose A, Takeda T, ITAI Y, et al.1996. Phase-contrast X-ray computed tomography for observing biological soft tissues[J], Nat. Med.2:473-475.
Momose A.2003. Phase-sensitive imaging and phase tomography using X-ray interferometers[J]. Opt. Express 11:2303-2314.
Momose A, Kawamoto S, Koyama I, et al.2003. Demonstration of X-Ray Talbot Interferometry[J]. Jpn, J. Appl. Phys.42:L866-L868.
Momose A.2005. Recent Advances in X-ray Phase Imaging[J]. Jpn, J. Appl. Phys.44:6355-6367.
Momose A. and Kawamoto S.2006. X-ray Talbot Interferometry with Capillary Plates[J]. Jpn, J. Appl. Phys.45:314-316.
Momose A, YashiroW, Takeda Y, et al.2006. Phase Tomography by X-ray Talbot Interferometry for Biological Imaging[J]. Jpn, J. Appl. Phys.45:5254-5262.
Momose A, YashiroW, and Takeda Y.2008. Sensitivity of X-ray Phase Imaging Based on Talbot Interferometry[J]. Jpn. J. Appl. Phys.47:8077-8080.
Momose A, Yashiro W, Kuwabara H, et al.2009a. Grating-Based X-ray Phase Imaging Using Multiline X-ray Source[J]. Jpn, J. Appl. Phys.48:076512.
Momose A, Yashiro W, Maikusa H, et al.2009b. High-speed X-ray phase imaging and X-ray phase tomography with Talbot interferometer and white synchrotron radiation[J]. Opt. Express 17:12540-12545.
Morgan K S, Paganin D M, and Siu K K W.2012. X-ray phase imaging with a paper analyzer[J]. Appl. Phys. Lett.100:124102.
Morgan K S, Modregger P, Irvine S C, et al.2013. A sensitive x-ray phase contrast technique for rapid imaging using a single phase grid analyzer[J]. Opt. Lett.38:4605-4608.
Munro P T, Ignatyev K, Speller R D, et al.2012. Phase and absorption retrieval using incoherent X-ray sources[J]. PNAS 109:13922-13927.
Nesterets Y I and Gureyev T E.2014. Noise propagation in x-ray phase-contrast imaging and computed tomography[J]. J. Phys. D: Appl. Phys.47:105402.
Noo F, Defrise M, Clackdoyle R, et al.2002. Image reconstruction from fan-beam projections on less than a short scan[J]. Phys. Med. Biol.47:2525-2546.
Olivo A,Arfelli F, Cantatore G, et al.2001. An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field[J]. Med. Phys. 28:1610-1619.
Olivo A and Speller R.2007. A coded-aperture technique allowing x-ray phase contrast imaging with laboratory sources[J]. Appl. Phys. Lett.91:074106.
Olivo A, Ignatyev K, Munro P R T, et al.2011. Noninterferometric phase-contrast images obtained with incoherent x-ray sources[J]. Appl. Opt.50:1765-1769.
Olivo A, Gkoumas S, Endrizzi M, et al.2013. Low-dose phase contrast mammography with conventional x-ray sources[J]. Med. Phys.40:090701.
Paganin et al.2002. Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object[J]. J. Microsc.206:33-40
Pagot E,, Fiedler S, Cloetens P, et al.2005. Quantitative comparison between two-phase contrast techniques: diffraction enhanced imaging and phase propagation imaging[J]. Phys Med. Biol. 50:709-724.
Pan X Q, Sidky E Y and Vannier M.2009. Why do commercial CT scanners still employ traditional, filtered back-projection for image reconstruction?[J]. Inverse Probl.25:123009.
Parker D L.1982. Optimal short scan convolution reconstruction for fanbeam CT[J]. Med. Phys. 9:254-257.
Pelliccia D D, Rigon L, Arfelli F, et al.2013. A three-image algorithm for hard x-ray grating interferometry[J]. Opt. Express 21:19401-19411.
Pelzer G, Weber T, Anton G, et al.2013. Grating-based x-ray phase-contrast imaging with a multi energy-channel photon-counting pixel detector[J]. Opt. Express 21:25677-25684.
Pfeiffer F, Weitkamp T, Bunk O, et al.2006. Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources[J]. Nat. phys.2:258-261.
Pfeiffer F, Kottler C, Bunk O, et al.2007a. Hard X-Ray Phase Tomography with Low-Brilliance Sources[J]. Phys. Rev. Lett.98:108105.
Pfeiffer F, Bunk O, David C, et al.2007b. High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography[J]. Phys. Med. Biol.52:6923-6930.
Pfeiffer F, Bech M, Bunk O, et al.2008a. Hard-X-ray dark-field imaging using a grating interferometer[J]. Nat. Mater.7:134-137.
Pfeiffer F, David C, Bunk O, et al.2008b. Region-of-interest tomography for grating-based X-ray differential phase-contrast imaging[J]. Phys. Rev. Lett.101:168101.
Raupach R and Flohr T G.2011. Analytical evaluation of the signal and noise propagation in x-ray differential phase-contrast computed tomography[J]. Phys. Med. Biol.56:2219-2244.
Revol V, Kottler C, Kaufinann R.2010. Noise analysis of grating-based x-ray differential phase contrast imaging [J]. Sci. Instrum.81:073709.
Revol V, Kottler C, Kaufinann R, et al.2011. X-ray interferometer with bent gratings:Towards larger fields of view[J]. Nucl. Instrum. Meth. A 648:S302-S305.
Revol V, Kottler C, Kaufmann R, et al.2012. Orientation-selective X-ray dark field imaging of ordered systems[J]. J Appl. Phys.112:114903.
Rigon L, Arfelli F and Menk R H.2007. Generalized diffraction enhanced imaging to retrieve absorption, refraction and scattering effects[J]. J. Phys. D Appl. Phys.40:3077-3089.
Rigon L, Besch H J, Arfelli F, et al.2003. A new DEI algorithm capable of investigating sub-pixel structures[J]. J. Phys. D 36:A107-A112.
Snigirev A, Snigireva I, Kohn V, et al.1995. On the possibility of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation[J]. Rev. Sci. Instrum. 66:5486-5492.
Stutman D and Finkenthal M.2012. Glancing angle Talbot-Lau grating interferometers for phase contrast imaging at high x-ray energy[J]. Appl. Phys. Lett.101:091108.
Sun W Y, Liu Z G, Sun T X, et al.2014. Numerical design of in-line X-ray phase-contrast imaging based on ellipsoidal single-bounce monocapillary[J]. Nucl. Instrum. Meth. A (in press) http://dx.doi.Org/10.1016/j.nima.2014.02.013i
Szafraniec M B, Millard T P, Ignatyev K, et al.2014. Proof-of-concept demonstration of edge-illumination x-ray phase contrast imaging combined with tomosynthesis[J]. Phys. Med. Biol.59:N1-N10.
Takeda M, Ina H, and Kobayashi S.1982. Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry[J]. J. Opt. Soc. Am.72:156-160.
Takeda Y, Yashiro W, Suzuki Y, et al.2007. X-Ray Phase Imaging with Single Phase Grating[J]. Jpn. J. Appl. Phys.46:L89-L91.
Takeda Y, Yashiro W, Hattori T, et al.2008. Differential Phase X-ray Imaging Microscopy with X-ray Talbot Interferometer [J]. Appl. Phys. Express 1:117002.
Talbot H F.1836. Facts relating to optical science[J]. Philos. Mag.9:401-407.
Tapfer A, Bech M, Zanette I, et al.2014. Three-dimensional imaging of whole mouse models: comparing nondestructive X-ray phase-contrast micro-CT with cryotome-based planar epi-illumination imaging[J]. J. Microsc.253:24-30.
Thuering T, Modregger P, Grund T, et al.2011. High resolution, large field of view x-ray differential phase contrast imaging on a compact setup[J]. Appl. Phys. Lett.99:041111.
Uehara M, Yashiro W, and Momose A.2013. Effectiveness of X-ray grating interferometry for non-destructive inspection of packaged devices[J]. J Appl. Phys.114:134901.
Wang D J, Wang Z L, Gao K, et al.2014. A dual detector approach for X-ray differential phase contrast imaging[J]. Radt. Phys. Chem.95:86-90.
Wang J Y, Zhu P P, Yuan Q X, et al.2006. Reconstruction of the refractive index gradient byx-ray diffraction enhanced computed tomography [J]. Phys. Med. Biol.51:3391-3396.
Wang J Y, Zhu P P, Yuan Q X, et al.2007. Experimental and theoretical investigations ofdiflraction enhanced imaging[J]. Nucl. Instrum. Meth. A 580:803-807.
Wang Z L, Zhu P P, Huang W X, et al.2010a. Quantitative coherence analysis with an X-ray Talbot-Lau interferometer[J]. Anal. Bioanal. Chem.397:2091-2094.
Wang Z L, Zhu P P, Huang W X, et al.2010b. Analysis of polychromaticity effects in X-ray Talbot interferometer[J]. Anal. Bioanal. Chem.397:2137-2141.
Wang Z L, Liu X S, Zhu P P.2010c. Analysis of partial coherence in grating-based phase-contrast X-ray imaging[J]. Nucl. Instrum. Meth. A 619:319-322.
Wang Z L, Gao K, Zhu P P, et al.2011. Grating-based X-ray phase contrast imaging using polychromatic laboratory Sources[J]. J. Electron. Spectrosc.184:342-345.
Wang Z L, Gao K, Ge X, et al.2013. X-ray phase radiography and tomography with grating interferometry and the reverse projection technique[J]. J.Phys. D:Appl. Phys.46:494003.
Wang Z L, Gao K, Wang D J, et al.2014. Single-shot x-ray phase imaging with grating interferometry and photon-counting detectors[J]. Opt. Lett.39:877-879.
Wang Z T, Huang Z F, Zhang L, et al.2011. Low dose reconstruction algorithm for differential phase contrast imaging[J]. J. X-Ray Sci. Technol.19:403-415.
Wang Z T, Kang K J, Huang Z F, et al.2009. Quantitative grating-based x-ray dark-field computed tomography[J]. Appl. Phys. Lett.95:094105.
Weber T, Bartl P, Bayer F.2011. Noise in x-ray grating-based phase-contrast imaging [J]. Med. Phys.38:4133-4140
Weitkamp T, Diaz A, David C, et al.2005. X-ray phase imaging with a grating interferometer[J]. Opt. Express 13:6296-6304.
Weitkamp T, David C, Kottler C, et al. Tomography with grating interferometers at low-brilliance Sources:Proceeding of SPIE, San Diego, Aug 15-17,2006 [C].
Wen H H, Bennett E, Kopace R, et al.2010. Single-shot x-ray differential phase contrast and diffraction imaging using two-dimensional transmission gratings[J]. Opt Lett.35:1932-1934.
Wen H, Miao H X, Bennett E E, et al.2013. Flexible retrospective phase stepping in X-Ray scatter correction and phase contrast imaging using structured illumination[J]. Plos One 8:e78276.
Wesarg S, Ebert M, and Bortfeld T.2002. Parker weights revisited[J]. Med. Phys.29:372-378.
Wilkins S W, Gureyev T E, Gao D, et al.1996. Phase-contrast imaging using polychromatic hard X-rays[J]. Nature 384:335-338.
Willner F, Bech M, Herzen J, et al.2013. Quantitative X-ray phase-contrast computed tomography at 82 keV. Opt. Express 21:4155-4166.
Wu X, and Liu H.2005. X-Ray cone-beam phase tomography formulas based on phase-attenuation duality [J]. Opt. Express 16:600-6014.
Wu Z, Gao K, Wang Z L, et al.2013. A new method to retrieve phase information for equiangular fan beam differential phase contrast computed tomography[J]. Med. Phys.40:031911.
Wu Z, Wang Z L, Gao K, et al.2014a. A generalized reverse projection method for fan beam geometry under partially coherent illumination[J]. Radt. Phys. Chem.95:280-283.
Wu Z, Wang Z L, Gao K, et al.2014b. Signal-to-noise analysis of X-ray grating interferometry with the reverse projection extraction method[J]. J. Electron. Spectrosc. p://www.sciencedirect.com/science/article/pii/S0368204814000954)
Xi Y, Kou B Q, Sun H H, et al.2012. X-ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility [J]. J. Synchrotron. Rad.19:821-826.
Yaroshenko A, Bech M, Potdevin G, et al.2014. Non-binary phase gratings for x-ray imaging with a compact Talbot interferometer [J]. Opt. Express 22:547-556.
Yashiro W, Takeda Y, Momose A, et al.2008. Efficiency of capturing a phase image using conebeam x-ray Talbot interferometry[J]. J. Opt. Soc. Am. A 25:2025-2039.
Yashiro W, Takeda Y, Takeuchi A, et al.2009. Hard-X-Ray Phase-Difference Microscopy Using a Fresnel Zone Plate and a Transmission Grating[J]. Phys. Rev. Lett.103:180801.
Yoneyama A, Wu J, Hyodo K, et al.2008. Quantitative comparison of imaging performance of x-ray interferometric imaging and diffraction enhanced imaging[J]. Med. Phys.35:4724-4734.
Zanette I, Weitkamp T, Donath T, et al.2010. Two-Dimensional X-Ray Grating Interferometer [J]. Phys. Rev. Lett.105:248102.
Zanette I, Weitkamp T, Lang S, et al.2011a. Quantitative phase and absorption tomography with an X-ray grating interferometer and synchrotron radiation. Physica Status Solidi (A), 208:2526-2532.
Zanette I, Bech M, Rack A, et al.2012. Trimodal low-dose X-ray tomography[J]. PNAS 109:10199-10204.
Zanette I, Bech M, Pfeiffer F, et al.2011b. Interlaced phase stepping in phase-contrast x-ray tomography[J]. Appl. Phys. Lett.98:094101.
Zanette I, Lang S, Rack A, et al.2013. Holotomography versus X-ray grating interferometry: A comparative study[J]. Appl. Phys. Lett.103:244105.
Zeng K, Chen Z Q, Zhang L, et al.2004. An error-reduction-based algorithm for cone-beam computed tomography [J]. Med. Phys.31:3206-3212.
Zhang K, Hong Y L, Zhu P P, et al.2011. Study of OSEM with different subsets in grating-based X-ray differential phase-contrast imaging[J]. Anal. Bioanal. Chem.401:837-844.
Zhou S A and Brahme A.2008. Development of phase-contrast x-ray imaging techniques and potential medical applications[J]. Phys. Med.24:129-148.
Zhou T, Lundstrom U, Thiiring T, et al.2013. Comparison of two x-ray phase-contrast imaging methods with a microfocus source[J]. Opt. Express 21:30183-30195.
Zhu N, Chapman D, Cooper D, et al.2011. X-ray diffraction enhanced imaging as a novel method to visualize low-density scaffolds in soft tissue engineering[J]. Tissue Eng.17:1071-1080.
Zhu P P, Wang J Y, Yuan Q X, Huang W X, et al.2005. Computed tomography algorithm based on diffraction-enhanced imaging setup[J]. Appl. Phys. Lett.87:26410.
Zhu P P, Yuan Q X, Huang W X, et al.2006. Diffraction enhanced imaging: a simple model[J]. J. Phys. D:Appl. Phys.39:4142-4147.
Zhu P P, Zhang K, Wang Z L, et al.2010. Low-dose, simple, and fast grating-based X-ray phase-contrast imaging[J]. PNAS.107:13576-13581.
曾更生.2009.医学图像重建入门[M].北京：高等教育出版社.
朱佩平,吴自玉.2007.X射线相位衬度成像[J].物理36：443-451.
庄天戈.1992.CT原理与算法[M].上海：上海交通大学出版社.
Alberto B, Paola C and Pekka S.2013. X-ray phase-contrast imaging: from pre-clinical applications towards clinics[J]. Phys. Med. Biol.58:R1-R35.
Bech M, Bunk O, Donath T, et al.2010. Quantitative x-ray dark-field computed tomography[J]. Phys. Med. Biol.55:5529-5539.
Bech M, Tapfer A, Velroyen A, et al.2013.1n-vivo dark-field and phase-contrast x-ray imaging[J]. Scientific Reports 3:3209.
Bennett E E, Kopace R, Stein A F, et al.2010. A grating-based single-shot x-ray phase contrast and diffraction method for in vivo imaging[J]. Med. Phys.37:6047-6054.
Berujon S, Ziegler E, Cerbino R, et al.2012. Two-Dimensional X-Ray Beam Phase Sensing[J]. Phys. Rev. Lett.108:158102.
Bevins N, Zambelli J, Li K, et al.2012. Multicontrast x-ray computed tomography imaging using Talbot-Lau interferometry without phase stepping[J]. Med. Phys.39:424-428.
Bonse U and Hart M.1965. An x-ray interferometer[J]. Appl. Phys. Lett.6:155-156.
Chapman D, et al.1997. Diffraction enhanced x-ray imaging[J]. Phys. Med. Biol.42:2015-2025
Chen G H, Zambelli J, Li K.2011. Scaling law for noise variance and spatial resolution in differential phase contrast computed tomography[J]. Med. Phys.38:584-588.
Chen R C, Rigon L and Longo R.2011. Quantitative 3D refractive index decrement reconstruction using single-distance phase-contrast tomography data[J]. J. Phys. D: Appl. Phys.44:495401.
Chen R C, Rigon L and Longo R.2013. Comparison of single distance phase retrieval algorithms by considering different object composition and the effect of statistical and structural noise. Opt. Express 21:7384-7399.
Chou C Y and Anastasio M A.2010. Noise texture and signal detectability in propagation-based x-ray phase-contrast tomography[J]. Med. Phys.37:270-281.
David C, No'hammer B, Solak H H, et al.2002. Differential x-ray phase contrast imaging using a shearing interferometer[J]. Appl. Phys. Lett.81:3287-3289.
Davis T J, Gureyev T E, Gao D, et al.1995. X-Ray Image Contrast from a Simple Phase Object[J]. Phys. Rev. Lett.74:3173-3176.
Diemoz P C, Bravin A, and Coan P.2011. Theoretical comparison of three X-ray phase-contrast imaging techniques: propagation-based imaging, analyzer-based imaging and grating interferometry[J]. Opt. Express 20:2789-2805.
Diemoz P C, Endrizzi M, Zapata C E, et al.2013a. X-Ray Phase-Contrast Imaging with Nanoradian Angular Resolution[J]. Phys. Rev. Lett.110:138105.
Diemoz P C, Hagen C K, Endrizzi M, et al.2013b. Sensitivity of laboratory based implementations of edge illumination X-ray phase-contrast imaging[J]. Appl. Phys. Lett. 103:244104.
Donath T, Pfeiffer F, Bunk O, et al.2008. Phase-Contrast Imaging and Tomography at 60 keV using a Conventional X-ray Tube[J]. Proc. of SPIE 7078:707817.
Du Y, Liu X, Lei Y H, et al.2011. Non-absorption grating approach for X-ray phase contrast imaging[J]. Opt. Express 19:22669-22674.
Endrizzi M, Diemoz P C, Millard T P, et al.2014. Hard X-ray dark-field imaging with incoherent sample illumination[J]. Appl. Phys. Lett.104:024106.
Faris G W and Byer R L.1988. Three-dimensional beam-deflection optical tomography of a supersonic jet[J]. Appl. Opt.27:5202-5212.
Feldkamp L A, Davis L C, and Kress J W.1984. Practical cone-beam algorithm[J]. J. Opt. Soc. Am. A 1:612-619.
Fogarty D P, Reinhart B a, Tzvetkov Tochko, et al.2011. In-laboratory diffraction-enhanced X-ray imaging of an equine hoof[J]. J. Equine Vet. Sci.31:365-369.
Fu J, Velroyen A, Tan R, et al.2012. A reconstruction method for cone-beam differential x-ray phase-contrast computed tomography[J]. Opt. Express 20:21512-21519.
Ge X, Wang Z L, Gao K, et al.2011. Investigation of the partially coherent effects in a 2D Talbot Interferometer[J]. Anal. Bioanal. Chem.401:865-870.
Grass M, Kohler T and Proksa R.2000.3D cone-beam CT reconstruction for circular trajectories[J]. Phys. Med. Biol.45:329-347.
Guigay I.1971. On Fresnel diffraction by one-dimensional periodic objects, with application to structure determination of phase objects[J]. Optica Acta.18:677-682.
Guigay J P.1977. Fourier transform analysis of Fresnel diffraction patterns and in-line holograms[J]. Optik 49:121-125.
Gureyev T E, Nesterets Y I, Stevenson A W, et al.2008 Some simple rules for contrast, signal-to-noise and resolution in in-line x-ray phase-contrast Imaging[J]. Opt. Express 16:3223-3241.
Huang Z F, Kang K J, Zhang L, et al.2006. Direct computed tomographic reconstruction for directional-derivative projections of computed tomography of diffraction enhanced imaging[J]. Appl. Phys. Lett.89:041124.
Huang Z F, Kang K J, Zhang L, et al.2009. Alternative method for differential phase-contrast imaging with weakly coherent hard x rays[J]. Phys. Rev. A 79:013815.
Huang Z F, Chen Z Q, Zhang L, et al.2010. Large phase-stepping approach for high resolution hard X-ray grating-based multiple information imaging[J]. Opt. Express 18:10222-10229.
Itoh H, Nagai K, Sato G, et al.2011. Two-dimensional grating-based X-ray phase-contrast imaging using Fourier transform phase retrieval[J]. Opt. Lett.17:12540-12545.
Jerjen I, Revol V, Brunner V J, et al.2013. Detection of stress whitening in plastics with the help of X-ray dark field imaging[J]. Polym. Test.32:1094-1098.
Kohler T and Noo F.2009. Comment on "region-of-interest tomography for grating-based X-ray differential phase-contrast imaging"[J]. Phys. Rev. Lett.102:039801.
Kohler T, Engel K J and Roessl E.2011. Noise properties of grating-based x-ray phase contrast computed Tomography[J]. Med. Phys.38:S106-S116.
Kondoh T, Date T, Yamaguchi T, et al.2014. Sparse phase-stepping in two-dimensional X-ray phase contrast imaging[J]. Appl. Optics (http://dx.doi/org/10.1364/A0.99.099999")
Kudo H, and Saito T.1994. Derivation and implementation of a cone-beam reconstruction algorithm for nonplanar orbits[J]. IEEE T. Med. Imaging 13:196-211.
Kudo H, Rodet T, Noo F, et al.2004. Exact and approximate algorithms for helical cone-beam CT[J]. Phys. Med. Biol.49:2913-2931.
Langer M, Cloetens P, Guigay J P, et al.2008. Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography[J]. Med. Phys.35:4556-4566.
Lei Y H, Liu X, Guo J C, et al.2011. Development of x-ray scintillator functioning also as an analyser grating used in grating-based x-ray differential phase contrast imaging[J]. Chinese Phys. B 20:042901.
Lewis R A.2004. Medical phase contrast x-ray imaging: current status and future prospects[J]. Phys. Med. Biol.49:3573-3583.
Liu J K, Ning R L, and Cai W X.2013. Phantom study for volume-of-interest breast imaging using differential phase contrast cone beam CT (DPC-CBCT)[J]. Proc. of SPIE 8668:866850.
Liu X, Guo J C, Peng X, et al.2007. Visibility in differential phase-contrast imaging with partial coherence source[J]. Chinese Phys.16:1632-1636.
Liu X, Guo J C, and Niu H B.2010. A new method of detecting interferogram in differential phase-contrast imaging system based on special structured x-ray scintillator screen[J]. Chinese Phys. B 19:070701.
Liu X S, Li E R, Zhu P P, et al.2010. Comparative analysis of phase extraction methods based on phase-stepping and shifting curve in grating interferometry[J]. Chin. Phys. B 19:040701.
Mayo S C, Stevenson A W and Wilkins S W.2012. In-Line Phase-Contrast X-ray Imaging and Tomography for Materials Science[J]. Materials 5:937-965.
Miao H X, Chen L, Bennett E E, et al.2013. Motionless phase stepping in X-ray phase contrast imaging with a compact source[J]. PNAS.110:19268-19272.
Millard T P, Endrizzi M, Ignatyev K, et al.2013. Method for automatization of the alignment of a laboratory based x-ray phase contrast edge illumination system [J]. Rev. Sci. Instrum.84: 083702.
Modregger P, Pinzer B R, Thuring T, et al.2011. Sensitivity of X-ray grating Interferometry[J]. Opt. Express 19:18324-18338.
Momose A, Takeda T, ITAI Y, et al.1996. Phase-contrast X-ray computed tomography for observing biological soft tissues[J], Nat. Med.2:473-475.
Momose A.2003. Phase-sensitive imaging and phase tomography using X-ray interferometers[J]. Opt. Express 11:2303-2314.
Momose A, Kawamoto S, Koyama I, et al.2003. Demonstration of X-Ray Talbot Interferometry[J]. Jpn, J. Appl. Phys.42:L866-L868.
Momose A.2005. Recent Advances in X-ray Phase Imaging[J]. Jpn, J. Appl. Phys.44:6355-6367.
Momose A. and Kawamoto S.2006. X-ray Talbot Interferometry with Capillary Plates[J]. Jpn, J. Appl. Phys.45:314-316.
Momose A, YashiroW, Takeda Y, et al.2006. Phase Tomography by X-ray Talbot Interferometry for Biological Imaging[J]. Jpn, J. Appl. Phys.45:5254-5262.
Momose A, YashiroW, and Takeda Y.2008. Sensitivity of X-ray Phase Imaging Based on Talbot Interferometry[J]. Jpn. J. Appl. Phys.47:8077-8080.
Momose A, Yashiro W, Kuwabara H, et al.2009a. Grating-Based X-ray Phase Imaging Using Multiline X-ray Source[J]. Jpn, J. Appl. Phys.48:076512.
Momose A, Yashiro W, Maikusa H, et al.2009b. High-speed X-ray phase imaging and X-ray phase tomography with Talbot interferometer and white synchrotron radiation[J]. Opt. Express 17:12540-12545.
Morgan K S, Paganin D M, and Siu K K W.2012. X-ray phase imaging with a paper analyzer[J]. Appl. Phys. Lett.100:124102.
Morgan K S, Modregger P, Irvine S C, et al.2013. A sensitive x-ray phase contrast technique for rapid imaging using a single phase grid analyzer[J]. Opt. Lett.38:4605-4608.
Munro P T, Ignatyev K, Speller R D, et al.2012. Phase and absorption retrieval using incoherent X-ray sources[J]. PNAS 109:13922-13927.
Nesterets Y I and Gureyev T E.2014. Noise propagation in x-ray phase-contrast imaging and computed tomography[J]. J. Phys. D: Appl. Phys.47:105402.
Noo F, Defrise M, Clackdoyle R, et al.2002. Image reconstruction from fan-beam projections on less than a short scan[J]. Phys. Med. Biol.47:2525-2546.
Olivo A,Arfelli F, Cantatore G, et al.2001. An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field[J]. Med. Phys. 28:1610-1619.
Olivo A and Speller R.2007. A coded-aperture technique allowing x-ray phase contrast imaging with laboratory sources[J]. Appl. Phys. Lett.91:074106.
Olivo A, Ignatyev K, Munro P R T, et al.2011. Noninterferometric phase-contrast images obtained with incoherent x-ray sources[J]. Appl. Opt.50:1765-1769.
Olivo A, Gkoumas S, Endrizzi M, et al.2013. Low-dose phase contrast mammography with conventional x-ray sources[J]. Med. Phys.40:090701.
Paganin et al.2002. Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object[J]. J. Microsc.206:33-40
Pagot E,, Fiedler S, Cloetens P, et al.2005. Quantitative comparison between two-phase contrast techniques: diffraction enhanced imaging and phase propagation imaging[J]. Phys Med. Biol. 50:709-724.
Pan X Q, Sidky E Y and Vannier M.2009. Why do commercial CT scanners still employ traditional, filtered back-projection for image reconstruction?[J]. Inverse Probl.25:123009.
Parker D L.1982. Optimal short scan convolution reconstruction for fanbeam CT[J]. Med. Phys. 9:254-257.
Pelliccia D D, Rigon L, Arfelli F, et al.2013. A three-image algorithm for hard x-ray grating interferometry[J]. Opt. Express 21:19401-19411.
Pelzer G, Weber T, Anton G, et al.2013. Grating-based x-ray phase-contrast imaging with a multi energy-channel photon-counting pixel detector[J]. Opt. Express 21:25677-25684.
Pfeiffer F, Weitkamp T, Bunk O, et al.2006. Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources[J]. Nat. phys.2:258-261.
Pfeiffer F, Kottler C, Bunk O, et al.2007a. Hard X-Ray Phase Tomography with Low-Brilliance Sources[J]. Phys. Rev. Lett.98:108105.
Pfeiffer F, Bunk O, David C, et al.2007b. High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography[J]. Phys. Med. Biol.52:6923-6930.
Pfeiffer F, Bech M, Bunk O, et al.2008a. Hard-X-ray dark-field imaging using a grating interferometer[J]. Nat. Mater.7:134-137.
Pfeiffer F, David C, Bunk O, et al.2008b. Region-of-interest tomography for grating-based X-ray differential phase-contrast imaging[J]. Phys. Rev. Lett.101:168101.
Raupach R and Flohr T G.2011. Analytical evaluation of the signal and noise propagation in x-ray differential phase-contrast computed tomography[J]. Phys. Med. Biol.56:2219-2244.
Revol V, Kottler C, Kaufinann R.2010. Noise analysis of grating-based x-ray differential phase contrast imaging [J]. Sci. Instrum.81:073709.
Revol V, Kottler C, Kaufinann R, et al.2011. X-ray interferometer with bent gratings:Towards larger fields of view[J]. Nucl. Instrum. Meth. A 648:S302-S305.
Revol V, Kottler C, Kaufmann R, et al.2012. Orientation-selective X-ray dark field imaging of ordered systems[J]. J Appl. Phys.112:114903.
Rigon L, Arfelli F and Menk R H.2007. Generalized diffraction enhanced imaging to retrieve absorption, refraction and scattering effects[J]. J. Phys. D Appl. Phys.40:3077-3089.
Rigon L, Besch H J, Arfelli F, et al.2003. A new DEI algorithm capable of investigating sub-pixel structures[J]. J. Phys. D 36:A107-A112.
Snigirev A, Snigireva I, Kohn V, et al.1995. On the possibility of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation[J]. Rev. Sci. Instrum. 66:5486-5492.
Stutman D and Finkenthal M.2012. Glancing angle Talbot-Lau grating interferometers for phase contrast imaging at high x-ray energy[J]. Appl. Phys. Lett.101:091108.
Sun W Y, Liu Z G, Sun T X, et al.2014. Numerical design of in-line X-ray phase-contrast imaging based on ellipsoidal single-bounce monocapillary[J]. Nucl. Instrum. Meth. A (in press) http://dx.doi.Org/10.1016/j.nima.2014.02.013i
Szafraniec M B, Millard T P, Ignatyev K, et al.2014. Proof-of-concept demonstration of edge-illumination x-ray phase contrast imaging combined with tomosynthesis[J]. Phys. Med. Biol.59:N1-N10.
Takeda M, Ina H, and Kobayashi S.1982. Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry[J]. J. Opt. Soc. Am.72:156-160.
Takeda Y, Yashiro W, Suzuki Y, et al.2007. X-Ray Phase Imaging with Single Phase Grating[J]. Jpn. J. Appl. Phys.46:L89-L91.
Takeda Y, Yashiro W, Hattori T, et al.2008. Differential Phase X-ray Imaging Microscopy with X-ray Talbot Interferometer [J]. Appl. Phys. Express 1:117002.
Talbot H F.1836. Facts relating to optical science[J]. Philos. Mag.9:401-407.
Tapfer A, Bech M, Zanette I, et al.2014. Three-dimensional imaging of whole mouse models: comparing nondestructive X-ray phase-contrast micro-CT with cryotome-based planar epi-illumination imaging[J]. J. Microsc.253:24-30.
Thuering T, Modregger P, Grund T, et al.2011. High resolution, large field of view x-ray differential phase contrast imaging on a compact setup[J]. Appl. Phys. Lett.99:041111.
Uehara M, Yashiro W, and Momose A.2013. Effectiveness of X-ray grating interferometry for non-destructive inspection of packaged devices[J]. J Appl. Phys.114:134901.
Wang D J, Wang Z L, Gao K, et al.2014. A dual detector approach for X-ray differential phase contrast imaging[J]. Radt. Phys. Chem.95:86-90.
Wang J Y, Zhu P P, Yuan Q X, et al.2006. Reconstruction of the refractive index gradient byx-ray diffraction enhanced computed tomography [J]. Phys. Med. Biol.51:3391-3396.
Wang J Y, Zhu P P, Yuan Q X, et al.2007. Experimental and theoretical investigations ofdiflraction enhanced imaging[J]. Nucl. Instrum. Meth. A 580:803-807.
Wang Z L, Zhu P P, Huang W X, et al.2010a. Quantitative coherence analysis with an X-ray Talbot-Lau interferometer[J]. Anal. Bioanal. Chem.397:2091-2094.
Wang Z L, Zhu P P, Huang W X, et al.2010b. Analysis of polychromaticity effects in X-ray Talbot interferometer[J]. Anal. Bioanal. Chem.397:2137-2141.
Wang Z L, Liu X S, Zhu P P.2010c. Analysis of partial coherence in grating-based phase-contrast X-ray imaging[J]. Nucl. Instrum. Meth. A 619:319-322.
Wang Z L, Gao K, Zhu P P, et al.2011. Grating-based X-ray phase contrast imaging using polychromatic laboratory Sources[J]. J. Electron. Spectrosc.184:342-345.
Wang Z L, Gao K, Ge X, et al.2013. X-ray phase radiography and tomography with grating interferometry and the reverse projection technique[J]. J.Phys. D:Appl. Phys.46:494003.
Wang Z L, Gao K, Wang D J, et al.2014. Single-shot x-ray phase imaging with grating interferometry and photon-counting detectors[J]. Opt. Lett.39:877-879.
Wang Z T, Huang Z F, Zhang L, et al.2011. Low dose reconstruction algorithm for differential phase contrast imaging[J]. J. X-Ray Sci. Technol.19:403-415.
Wang Z T, Kang K J, Huang Z F, et al.2009. Quantitative grating-based x-ray dark-field computed tomography[J]. Appl. Phys. Lett.95:094105.
Weber T, Bartl P, Bayer F.2011. Noise in x-ray grating-based phase-contrast imaging [J]. Med. Phys.38:4133-4140
Weitkamp T, Diaz A, David C, et al.2005. X-ray phase imaging with a grating interferometer[J]. Opt. Express 13:6296-6304.
Weitkamp T, David C, Kottler C, et al. Tomography with grating interferometers at low-brilliance Sources:Proceeding of SPIE, San Diego, Aug 15-17,2006 [C].
Wen H H, Bennett E, Kopace R, et al.2010. Single-shot x-ray differential phase contrast and diffraction imaging using two-dimensional transmission gratings[J]. Opt Lett.35:1932-1934.
Wen H, Miao H X, Bennett E E, et al.2013. Flexible retrospective phase stepping in X-Ray scatter correction and phase contrast imaging using structured illumination[J]. Plos One 8:e78276.
Wesarg S, Ebert M, and Bortfeld T.2002. Parker weights revisited[J]. Med. Phys.29:372-378.
Wilkins S W, Gureyev T E, Gao D, et al.1996. Phase-contrast imaging using polychromatic hard X-rays[J]. Nature 384:335-338.
Willner F, Bech M, Herzen J, et al.2013. Quantitative X-ray phase-contrast computed tomography at 82 keV. Opt. Express 21:4155-4166.
Wu X, and Liu H.2005. X-Ray cone-beam phase tomography formulas based on phase-attenuation duality [J]. Opt. Express 16:600-6014.
Wu Z, Gao K, Wang Z L, et al.2013. A new method to retrieve phase information for equiangular fan beam differential phase contrast computed tomography[J]. Med. Phys.40:031911.
Wu Z, Wang Z L, Gao K, et al.2014a. A generalized reverse projection method for fan beam geometry under partially coherent illumination[J]. Radt. Phys. Chem.95:280-283.
Wu Z, Wang Z L, Gao K, et al.2014b. Signal-to-noise analysis of X-ray grating interferometry with the reverse projection extraction method[J]. J. Electron. Spectrosc. p://www.sciencedirect.com/science/article/pii/S0368204814000954)
Xi Y, Kou B Q, Sun H H, et al.2012. X-ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility [J]. J. Synchrotron. Rad.19:821-826.
Yaroshenko A, Bech M, Potdevin G, et al.2014. Non-binary phase gratings for x-ray imaging with a compact Talbot interferometer [J]. Opt. Express 22:547-556.
Yashiro W, Takeda Y, Momose A, et al.2008. Efficiency of capturing a phase image using conebeam x-ray Talbot interferometry[J]. J. Opt. Soc. Am. A 25:2025-2039.
Yashiro W, Takeda Y, Takeuchi A, et al.2009. Hard-X-Ray Phase-Difference Microscopy Using a Fresnel Zone Plate and a Transmission Grating[J]. Phys. Rev. Lett.103:180801.
Yoneyama A, Wu J, Hyodo K, et al.2008. Quantitative comparison of imaging performance of x-ray interferometric imaging and diffraction enhanced imaging[J]. Med. Phys.35:4724-4734.
Zanette I, Weitkamp T, Donath T, et al.2010. Two-Dimensional X-Ray Grating Interferometer [J]. Phys. Rev. Lett.105:248102.
Zanette I, Weitkamp T, Lang S, et al.2011a. Quantitative phase and absorption tomography with an X-ray grating interferometer and synchrotron radiation. Physica Status Solidi (A), 208:2526-2532.
Zanette I, Bech M, Rack A, et al.2012. Trimodal low-dose X-ray tomography[J]. PNAS 109:10199-10204.
Zanette I, Bech M, Pfeiffer F, et al.2011b. Interlaced phase stepping in phase-contrast x-ray tomography[J]. Appl. Phys. Lett.98:094101.
Zanette I, Lang S, Rack A, et al.2013. Holotomography versus X-ray grating interferometry: A comparative study[J]. Appl. Phys. Lett.103:244105.
Zeng K, Chen Z Q, Zhang L, et al.2004. An error-reduction-based algorithm for cone-beam computed tomography [J]. Med. Phys.31:3206-3212.
Zhang K, Hong Y L, Zhu P P, et al.2011. Study of OSEM with different subsets in grating-based X-ray differential phase-contrast imaging[J]. Anal. Bioanal. Chem.401:837-844.
Zhou S A and Brahme A.2008. Development of phase-contrast x-ray imaging techniques and potential medical applications[J]. Phys. Med.24:129-148.
Zhou T, Lundstrom U, Thiiring T, et al.2013. Comparison of two x-ray phase-contrast imaging methods with a microfocus source[J]. Opt. Express 21:30183-30195.
Zhu N, Chapman D, Cooper D, et al.2011. X-ray diffraction enhanced imaging as a novel method to visualize low-density scaffolds in soft tissue engineering[J]. Tissue Eng.17:1071-1080.
Zhu P P, Wang J Y, Yuan Q X, Huang W X, et al.2005. Computed tomography algorithm based on diffraction-enhanced imaging setup[J]. Appl. Phys. Lett.87:26410.
Zhu P P, Yuan Q X, Huang W X, et al.2006. Diffraction enhanced imaging: a simple model[J]. J. Phys. D:Appl. Phys.39:4142-4147.
Zhu P P, Zhang K, Wang Z L, et al.2010. Low-dose, simple, and fast grating-based X-ray phase-contrast imaging[J]. PNAS.107:13576-13581.
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