referring now to fig1 imaging energy is applied by source 10 to object 12 and detected by detector 14 . the source 10 typically comprises a cone beam x - ray source and the detector 14 typically comprises an area detector such as a two dimensional array detector having an array of individual detector elements ( separate elements not shown ). the object 12 typically comprises a patient ( human or animal or tissue mass ). alternately , object 12 is an industrial part or other object being imaged using ct . cone beam energy that has passed through the object 12 is detected in detector 14 and converted to corresponding electrical signals and sent to a data acquisition unit 16 that registers the electrical signals . unit 16 in turn sends cone beam data to a processor 18 , which commonly comprises a computer programmed to perform various process steps . various process steps performed within processor 18 are shown in simplified form in fig1 . those steps will be discussed after a discussion of mathematics used in the present invention . at this stage , the processor reconstructs two sets of image data corresponding to two geometrically distinct scan paths such as a circular first scan path followed by an orthogonal linear second scan path or a circular first scan path followed by a circular second scan path tilted relative to the first circular scan path . the processor fourier transforms the two sets , makes adjustments to the two fourier transform sets , combines the two adjusted fourier transform sets , inverse fourier transforms the last two sets , and provides image data , which data is displayed in display 20 and stored in memory 22 . the scanning trajectory will be defined by relative movements of the source 10 , object 12 , and detector 14 respectively controlled by robotic positioners 24 , 26 , and 28 . each of the robotic positioners 24 , 26 , and 28 causes relative scanning movement among the source 10 , object 12 , and detector 14 . the positioners 24 , 26 , and 28 are in turn controlled by processor 18 to realize a scan trajectories discussed below . fig2 will be used to explain basic concepts used by the present invention . the invention provides exact 3d reconstruction , meaning it provides image reconstruction accurate other than measurement errors and discretization errors . measurement errors may arise from , for example , from imprecision of the relative positioning of source and detector . discretization errors can arise , for example , from basing measurements on the assumption that the source is at a plurality of discrete positions as it moves about its trajectory . the geometry of a single circular orbit and a circle - and - line scanning trajectory are shown in fig2 and 3 respectively , where d is the radius of the circular orbit , r is the radius of the spherical functional support of the object and l is the half length of the linear orbit or path . it has been shown that as long as l ≧ 2dr ( d 2 - r 2 ) - 1 / 2 , the scanner satisfies the sufficient condition to provide exact reconstruction . in fact , any plane intersecting the object intersects the circle - and - line orbit 1 , 2 , or 3 times . a cross - section of fig2 is shown in fig4 where a shadow zone is defined . the shadow zone for which the circular orbit does not provide complete data for reconstruction is the shaded area in fig4 . this zone in the cross - section of fig4 is the area within object circle 30 that is also outside of both circles 32 and 34 of diameter d . the shadow zone is completely within a pair of cones 36 extending in opposite direction from the center of the object . the cone spans 2θ where θ = sin - 1 ( r / d ). this cone region will be referred to as the shadow cone , or , more generally , the augmented shadow zone . based on the cross - sectional structure of fig4 it is clear that when two identical circular orbits sharing the same center and with their planes of rotation forming an angle of at least 2 θ degrees , the shadow zone of each orbit would be fully complemented by its counterpart . thus , a scan trajectory having a first circular orbit scan path 38 and a second circular orbit scan path 40 as shown in fig8 with the indicated angle between them have non - overlapping shadow zones such that the two circular orbit complement each other . it is less clear how a linear orbit as defined in fig3 can complement the shadow zone of the circular orbit , but a technique providing such complementing is provided as discussed below . a technique for reconstruction of image data from a line orbit can be done differently from the computationally demanding hu line algorithm technique . from fig3 it is clear that the x - ray source must have a cone angle of 2α to fully encompass the object ( when the former is positioned in the middle of the linear orbit ). a practical way of implementing the line - and - circle orbit would be to move and rotate the object by the following four steps : ( 1 ) hold the source and detector panel still , ( 2 ) translate the object from below the beam until it is lined up with source and the center of the detector panel , ( 3 ) make a 360 degrees of the object to fulfill the circular orbit , and ( 4 ) continue to move the object out of the cone beam . fig5 shows that each detector element collects a set of parallel beams from the object &# 39 ; s linear movement . the detector elements of the same column put together a sequence of parallel beams tilting from - α to α ; these column detectors intercept the same vertical slice of the object . based on the central slice theorem , each reconstructed slice in its own 2d fourier space could only recover a segment of the object &# 39 ; s total frequency components . the two segments ( or sectors ) in frequency domain each subtends an angle of 2α degrees . the detector panel 14 consists of m rows by m columns of closely butted detectors and k snapshots ( or projection views ) have been taken when the object is engaged in the linear motion . following the conventional backprojection procedures ( or , using direct fourier method for a fast algorithm ), m slices of the object are independently reconstructed . due to the cone beam structure , these m slices form a horn - shaped volume . a simple interpolation scheme converts the horn - shaped volume into a regular 3d grid array . the partially recovered object from the linear orbit or path can now be combined with the core image obtained from the circular orbit using the known feldkamp &# 39 ; s algorithm . turning now to the processing blocks within processor 18 of fig1 f c ( r ) and f l ( r ) are the original images reconstructed from the circular and linear orbits via feldkamp &# 39 ; s algorithm and the backprojection procedure described above , respectively . the following steps describe how these two pieces of images from blocks 42 and 44 respectively can be combined : 1 . define a shadow cone in the radon space with its angle subtending 2θ . 2 . the shadow cone in radon space is directly mapped into the 3d fourier space , which appears to be the similar cone of angle 2θ and with a finite support . denote the shadow cone in 3d fourier space as f c . 3 . transform f c ( r ) and f l ( r ) into 3d fourier space at blocks 46 and 48 respectively and denote the transformations as f c and f l respectively . 4 . obtain f sc ( fourier data for the shadow cone ) from f l by deleting the non - shadow cone data within f l at block 50 , while block 46 supplies f ns ( fourier data outside the shadow cone ) by removing shadow cone data from f c at block 52 . 5 . the total or overall fourier data is f t = f sc + f ns combined at block 54 and transformed at block 56 back to the image domain f t at block 58 . the finite grid resolution in both the image and fourier spaces results in the shadow cone in f ns not necessarily being empty ( before patching ). to make a smooth transition between f ns and f sc an appropriate weighting function , w , is used to blend them . that is , f t =( l - w ) f sc + wf ns . accordingly , f t is now a complete image with the redundancy error well taken care . this is done in the process of replacing the shadow zone with the shadow cone in radon space . this is due to the fact that , out of the entire torus - shaped region where the valid radon data reside , only the radon data bordering the surface of the shadow zone have its planes of integral intercepting the circular orbit at one point , while the rest of the radon data within the torus all have two intercepting points . however , this is no longer true after the shadow zone is replaced by the slightly larger shadow cone . that is , all the remaining radon data have its planes of integral intercepting the circular orbit at two different points . while the invention has been described with reference to a preferred embodiment , it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the invention . in addition , many modification may be made to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof . therefore , it is intended that the invention not be limited to the particular embodiment disclosed as the best mode contemplated for carrying out this invention , but that the invention will include all embodiments falling within the scope of the appended claims .
a source applies imaging energy that passes through an object being imaged and is then detected by a detector connected to a processor . a scanning trajectory includes first and second scan paths . the first scan path has a shadow zone where a complete image cannot be obtained from corresponding first scan path data . the second scan path provides data from the shadow zone . partial images from the first scan path and the second scan path are fourier transformed after which some data is removed prior to adding the fourier data together . an inverse fourier transform is then used to provide an overall image .