【作者】 路宏年； 邵军明； 杨民； 梁丽红；

【Author】 LU Hong-nian SHAO Jun-ming YANG Min LIANG Li-hong (Beijing University of Aeronautics and Astronautics,Beijing,100083)

【机构】 北京航空航天大学；

【摘要】 射线CT数学基础是Radon变换,均是以射线对物体投影的物理方法实现其正变换,其逆变换是基于这种投影的序列对物体介质射线衰减系数加以层析。所以扫描投影是CT 成像的物理基础。本文研究目的即在于探讨扫描投影系统的一种物理模型。该模型是基于射线透照系统与透照投影场强转换的级联而构建的。更多还原

【Abstract】 As we all know,the mathematic foundation of X-ray CT is Radon transform.All theforward transform is based on X-ray projection of object independence on the type of data scan andthe backward transform is the reconstruction of X-ray attenuation coefficients of the object with theprojection series.So the CT is based on the projection physically.The aim of the paper is to studyand build a physical model which presents the projecting progress.The model introduced in thepaper is based on the analysis of x-ray projection system and the power transfer of the projection.For the modulation of the signal of zero frequency by（1,2）the X-ray projection system,acontrast model is given by the paper based on the concept of imaging proportion to project X-raypower with narrow spectrum.The contrast ΔD of object is given by（1,2,3）:where D isbackground intensity of feature projection;ΔI/I is intensity contrast of penetrating feature rays;（?）、（?） are equivalent attenuation coefficients of feature and its background,respectively;ΔT_e isequivalent thickness of ray penetrating feature medium;n is scattering ratio;ΔD_min isminimum distinguishable contrast of projection image;C is noise modulating contrast factor（c≈2-5）;σ is projection standard deviation;ΔP is detector sampling interval;W is thewidth of tested feature perpendicular to ray direction;M is magnifying ratio of feature projection.Equation（1）indicates feature projection contrast ΔD is positively proportional to ΔI/I,and itsintensity transform sensitivity is determinate by（5,6）D.Furthermore,the contrast is affected by（4）ΔD_min.To PSF or MTF of imaging system modulating feature projection,the paper gives a modelbased on secant function（4,5,6）,where FW is Half-width at half-maximum of PSF（x,y）.If FW_gof imaging geometry system and FW_d of detector are known,we have（7）,where a is focuseffective size and M is magnifying ratio of feature projection.FW can also be got from theLSF（Line Spread Function）according to the model described in formula（8）.When the pixel sizeis known,the Nyquist frequency of the projection is:（8）According to formula（5）and formula,thelimited frequency of the testing system f_max is deduced as following:（9）.The testing sensitivitymodel of the simple two dimensional characters is also gave as following:(10.where ΔTe is as sameas described in formula（2）.The physical model has been verified by experiments.It is very instructive to deciding thetechnique index,designing the CT system,optimizing the scanning parameters and designing thereconstruction software.The physical model has been verified by experiments.It is very instructiveto deciding the technique index,designing CT system,optimizing the scanning parameters anddesigning reconstruction software.更多还原