Phase-contrast Imaging Simulation Based on a Micro-CT System

Phase-contrast Imaging Simulation Based on a Micro-CT SystemGUI Jian-bao,ZOU Jing,RONG Jun-yan,HU Zhan-li,ZHANG Qi-yang,ZHENG Hai-rong,XIA DanPaul uterbur Research Center for Biomedical Imaging,Institute of Biomedical and Health Engineering, Shenzhen Institutes of Advanced Technology,Chinese Academy of Sciences,Shenzhen518055,ChinaAbstract.Propagation-based phase-contrast imaging was simulated based onparaxial Fresnel-Kirchoff diffraction integral and spherical wave illumination.Under adeveloped micro-CT system parameters,the effects of focal-spot size and imaginggeometry on phase-contrast imaging have been investigated using a2-mm-thicknesspolystyrene edge phantom.An equivalent mono-energy was used to substitute thepolychromatic spectrum of the micro-focus X-ray source.To consider effects offocal-spot size and detector resolution,the obtained phase-contrast image with an idealpoint source was convolved with source intensity distribution and point spread functionof detector.Simulations show reasonable influences of the two parameters which are ingood agreement with experimental results.Key words：micro-CT;phase-contrast imaging;X-ray;micro-focus source;simulationINTRODUCTIONSince1996,Wilkins[1]firstly implemented phase-contrast imaging(PCI)using polychromatic micro-focus X-ray sources,this technique of propagation-based X-ray phasecontrast imaging(PB-PCI) becomes a hot spot of researches.As we all known,many parameters(focal-spot size,imaging geometry, etc.)can influence the performance.We can recognize the influences of different parameters by experiments,but often,experiments need much time and cost;fortunately,simulations supply a helpful tool as the computer technique progresses.Simulation has become a convenient and important tool to develop and optimize a new imaging system.We can also have a better understanding on the physical mechanism of PCI technique by simulation.Presently,for PB-PCI technique,there are mainly three theory models.A classical and reliable way to model phase-contrast image formation mechanism was provided by Fresnel-Kirchoff diffraction integrals[2-3],which allows a precise prediction of the pattern that would be generated by a monochromaticCLC number:R318.6Document code:A Article ID:1004-0552(2016)02-0087-06Grant sponser:National Natural Science Foundation of China;grant number:61002041,61102161;grant sponser:National973Basic Research Program of China;grant number:2010CB732600;grant sponser:2010-Guangdong Province Innovational Research Team Program and Programs of Shenzhen;grant number:JC201005270313A,JC201005280493A,JC201005280581A,ZYA201006300034ACorresponding author:GUI Jian-bao.E-mail:jb.gui@Received15June2016;revised12September2016point source and recorded with a detector with infinite spatial resolution.Another alternative,simplified approach is provided by the ray tracing technique,in which each X-ray is followed along its path through the sample,and the deviation from its original propagation direction is calculated via the gradient of the projected phase shift introduced by the sample[4].A third approach was developed by Wu and Liu[5],in which the Wigner distribution formalism is used to take the partial coherence into account.In the following,we will focus the effects of two important system parameters(focal-spot size and imaging geometry)on PB-PCI by simulation,which was based on paraxial Fresnel-Kirchoff diffraction integral and monochrome spherical wave illumination.In order to evaluate the simulation validity,the same experiments have been performed using our developed micro-CT.MATERIALS AND METHODSTheoriesIn case of monochromatic radiation of energy E,the complex refractive index n at the position r is as Equation(1):n(E,r)=1-δ(E,r)+iβ(E,r)(1) whereδis the refractive index decrement andβis the absorption index,which is related to the linear absorption coefficientμas Equation(2):μ(E,r)=2kβ(E,r)(2) where k is wave number.Values ofδandμused in this study are obtained from online NIST data.The transmission function t(x,y)represents the phase shift and the attenuation effect due to the sample,t(x,y)is usually written as Equation(3),(4),and(5)[2,6-7]:t(x,y)=e i准(x,y)-μ(x,y)/2=A(x,y)e i准(x,y)(3)准(x,y)=-2πλ乙δ(x,y,z)dz(4)μ(x,y)=4πλ乙β(x,y,z)dz(5) in order to be able to model an object via Equation(3),(4)and(5),the object is supposed to be"thin"for X-rays so that the projection approximation holds true.If d is the object thickness,the object can be deemed thin[8]as long as the size of the finest feature to image is larger than(λd)0.5.PGW modeled the diffracted X-ray wave field for a monochromatic spherical wave illumination with an ideal point source according to the paraxial Fresnel diffraction theory as Equation(6)[6]:f s(x;R1,R2)=iλR2exp(-ikR2)乙exp(-ik X22R2),t(X)exp(-ik(x-X)22R2)d X(6)where R1and R2are source to object-plane distance and object-plane to image-plane distance,x and X are two-dimension vectors in the image-plane and object-plane,respectively,f indicates wave function with spherical wave illumination.In Fourier space as Equation(7):F s(uM ;R1,R2)=exp(-ikR2M)Ｆ{exp(-ik X22R2)t(X)}·exp(iπλR2u2/M)(7)where M=(R1+R2)/R1is the magnification factor,u is spatial frequency vector at the object plane,F isFourier transform.The intensity at image-plane can be written as Equation(8):I(x,y)=f s(x,y)2(8) with the effects of the X-ray focal-spot size and the detector resolution taken into account as presented by Wu and Liu[9],the intensity in Fourier space can be written as Equation(9):I軇(u M ;R1,R2)=I軇point(uM;R1,R2),·OTF G.U.(uM)·OTF det(uM)(9)if the X-ray focal spot was supposed to be a circular disk of diameter f,the modulus of OTF G.U.is given by Equation(10):OTF G.U.(uM )=2J1[πf(M-1)u/M]πf(M-1)u/M(10)where f is the diameter of the focus spot and J1(x)is a Bessel function of the first kind.The modulus of OTF det is as Equation(11):OTF det.(u)=sin c(p ax u xM )sin c(p ay u yM)(11)where sin c(x)is the sinc function and p ax,y is the active pixel size determined from the pixel pitch and the fill factor of the detector.In order to focus on the edge-enhanced phenomenon,a polystyrene sheet with2mm thickness was used as imaging phantom in this simulation and monochromatic radiation of energy E was used. ExperimentsTo evaluate the simulation validity,experimental results were compared and the simulation parameters were set according to the parameters.This imaging system mainly consists of an open X-ray tube(FXE160.51,YXLON)and a cool X-ray CCD imaging detector(Quad-R04320,Princeton Instruments).The focal-spotsize of the X-ray tube can be adjusted from2μm to15μm.The CCD imaging detector employed in our micro-CT system consists of a2084×20842D imaging array with a pixel size of24×24μm2.The source-to-detector distance(SDD) is fixed at720mm.A thin plastic sheet with2mm thickness was used in this study.RESULTS AND DISCUSSIONEffect of focal-spot sizeWe obtained simulated phantom images by setting different values of focal-spot size.Two images are shown in Fig.1(a)and(b)with the focal-spot sizes of3pLm and10μm.One bright vertical line and one dark vertical line can be found in the obtained images,which show a strong phase-contrast edge-enhancement effect.Fig.1(c)shows the profiles of phantom images simulated with four different focal-spot sizes.It can be observed that peaks of edge enhancement become lower when the focal-spot becomes larger,which indicates that the edge-enhancement becomes weaker as the focal-spot size increases.The reason is that X-ray coming from a smaller focal-spot has a better spatial coherence.As shown in Fig.2,we can see a same change trend and a similar peak height as the simulated result shows,meaning that the simulation is reasonable and is in good agreement with experimental results.(a)3μm (b)10μm(c)profiles Fig.1The phantom images simulated with the focal-spot sizes of 3μm(a)and 10μm (b).Display window is [0.81.05].(c)Profiles of the middle horizontal lines in the phantomimages simulated with four different focalspot sizes.Photon energy was 20keV,pixelsize of detector was 24μm and SOD was 50mm.Fig.2Profilesofthe middlehorizontal lines in phantom images obtained by a micro-CTsystem with an open microfocus tubeNote:Tube voltage was 50kVp,pixel size of detector was 24μm and SOD was 50mm.Effect of imaging geometryThe profiles of phantom images simulated with different source-to-object distances (SODs)are shown in Fig.3.We can see that edge enhancement becomes stronger firstly,and then drops as SOD increases.The reason is that the PB-PCI technique depends on X-ray refraction,a sufficient propagation distance(a)3μm(b)10μmR2is favorable to the forming of refraction contrast.However,because of the limited source size(not an ideal point source),the increasing of propagation distance(a larger geometrical magnification)can degrade the phase-contrast effect through penumbral blurring.As shown in Fig.4,we can also see the same change trend.A SOD value near100mm makes the edge enhancement maximum for both simulated result and experimental result,which shows much more about the good agreement between our simulation and experiment.Fig.3Profiles of the middle horizontal lines in the phantom images simulated with seven different SODs Note:Photon energy was20keV,focal-spot size was3μm and pixe1size of detector was24μm.Fig.4Representative pixel intensity values across the images of the plastic edge phantom obtained by the micro-CT system at different SODsNote:Tube voltage was70kVp and focal-spot size was3μm.Propagation-based X-ray phase-contrast imaging was simulated under the developed micro-CT parameters.The preliminary simulations show reasonable influences of two important parameters, focal-spot size and imaging geometry.Results show that our simulations are in good agreement with experimental results,which means that the simulation can be used to optimize our system to obtain a good phasecontrast image.REFERENCES[1]Wilkins SW,Gureyev TE,Gao D,et al.Phase-contrast imaging using polychromatic hard X-rays[J].Nature,1996,384(6607):335-338.[2]Peterzol A,Berthier J,Duvauchelle P,et al.X-ray phase contrast image simulation[J].Section B of NuclearInstruments and Methods in Physics Research,2007,254(2):307-318.[3]Olivo 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