with reference to fig1 a ct scanner includes a stationary gantry 10 within which a rotating gantry 12 is mounted for rotation about a subject - receiving bore 14 . the rotating gantry carries an arc of radiation detectors 16 and an x - ray tube 18 which is disposed across the subject receiving bore 14 180 ° opposite a center of the detector arc . an appropriate motor or drive 20 rotates the rotating gantry at a speed of preferably 60 - 120 rpm . an angular position resolver 22 determines the instantaneous angular position of the rotating gantry . a subject support or couch 24 supports a subject in the subject - receiving bore 14 . for volume imaging , the subject support also indexes the subject axially through the bore . a reference detector 16 r detects the instantaneous intensity of radiation from the x - ray tube that has not been attenuated by the subject . each detector in the detector arc 16 outputs a signal that is indicative of the currently received radiation intensity , i . e ., the intensity of radiation after it has been attenuated along a path through the subject . as the rotating gantry 12 rotates , the detectors 16 are repeatedly sampled , preferably about 1100 - 1200 times per revolution . the position of the focal spot on the anode of the x - ray tube is preferably electronically toggled and sampling again in each toggled position to double the number of samplings per revolution . in this manner , a set of fan beam data is sampled at about 0 . 16 ° angular increments . with continuing reference to fig1 and further reference to fig2 each time the detectors are sampled , a set of fan beam data or data line of digital values 30 is generated . when the x - ray tube rotates to the next sampling position , another data line 32 of digital values is sampled , and so forth . at the gantry , data compression circuitry 32 subtractively combines each sampled intensity value with the reference intensity value and converts to the log to form an attenuation value . each attenuation data line is coupled with an identification of the x - ray source position from the angular resolver 22 , and an indication of the detector , hence angular position within the fan , for each attenuation value . a preliminary correction processor 36 makes preliminary corrections on the attenuation values as are known in the art . the corrected data lines 32 are stored in an attenuation data memory 38 as lines 32 of data values 30 are indexed by the source position as illustrated in fig2 . with reference to fig3 the x - ray tube 18 includes an anode 40 on which an electron beam is focused at a focal spot 42 . scattered electrons strike other portions of the anode and other metal structures in the tube creating a background of off - focal radiation 44 . the range of the off - focal radiation visible to the detectors is limited by a collimator 46 . radiation from the focal spot creates a focal ray 48 while the off - focal radiation 44 creates a penumbra of surrounding off - focal rays 50 . as illustrated in fig4 a , the vast majority of the radiation originates from the focal spot 42 with a significant level of off - focal radiation 44 around the focal spot . in fig4 a , the off - focal radiation intensity is modeled as a constant . in fig4 b , the off - focal radiation is modeled with a higher intensity adjacent the focal spot and a diminishing intensity outward . the exact radiation model is determined by the x - ray tube selected . with reference to fig5 off - focal radiation has its most notable effect at edges of objects in the ct image . an exemplary object 60 in the subject has its edge along the focal ray 48 . as the focal ray and the off - focal rays pass the edge of the object , they project onto the detector array 16 with a typical intensity profile , such as shown in fig6 . an ideal edge profile 62 is an abrupt transition from one intensity to another . the off - focal radiation causes a pedestal level on each side of the ideal step . on the low intensity side of the step , there is a slight increase in intensity 64 and on the high intensity side , there is slight decrease in intensity 66 . the effect of this edge intensity profile at the detector is to cause a halo in a reconstructed image 68 as shown in fig7 . for an object that is denser than its surroundings , the pedestal on the low energy side 64 of the transition causes an inner halo 70 and the pedestal on the high energy side 66 causes an outer halo 72 . with reference to fig8 the focal ray 48 has an initial intensity i 0 . radiation along rays initiating at positions k l - k n has corresponding intensities i l - i n as depicted by the radiation profile of fig4 b . these nine rays are attenuated with attenuation values a 0 - a 8 as they pass through a subject 52 , resulting in intensities i 0 - i 8 emerging from the subject . these intensities are summed by an exemplary detector 16 x . of course , the ct scanner attributes all of the intensity to the focal ray 48 and assumes that the sum is i 0 . the present off - focal radiation correction estimates and subtracts the off - focal intensities i 1 - i 8 from the sum to provide i 0 more accurately . with reference to fig9 a and 9b , it will be seen that each off - focal ray for one sampling of a detector substantially follows the same line as the focal ray sampled by a different detector in a different source position . in the example of fig9 a and 9b , the focal ray extending between the x - ray source 18 in an angularly displaced position k 7 by angle θ and a different detector 16 y ( which has rotated into the position originally occupied by detector 16 x ) follows the same path as off - focal ray 507 of fig8 . thus , by looking to a different data point in a different data line and using the appropriate weighting , the contribution of off - focal intensity i 7 can be determined . the intensity i reaching the detector 16 x is reduced in accordance with the off - focal radiation coefficient k 7 of the fig4 b model and the intensity i 7 obtained by detector 16 y at the rotational offset θ . with reference again to fig1 an off - focal radiation correction means 80 determines the corresponding ray and intensity correction for each of the off - focal rays 50 1 - 50 8 contribution to each of the data values of each intensity line . with reference to fig1 , a control circuit 82 determines a line 84 through an exemplary data value 86 in the memory 38 to be corrected . the intensities corresponding to i 1 - i 8 are defined equi - spaced along the line 84 . the controller 82 determines the closest data value from neighboring data lines for each of rays 50 1 - 50 8 . the control circuit 82 also selects an appropriate deconvolution function 88 that corresponds to the position of exemplary detector 86 within the array 16 from a deconvolution function memory 90 . with scatter grids 92 , the amount of off - focal radiation reaching each detector changes as does the relative off - focal radiation intensity contribution along each of the off - focal radiation paths . once the control circuit 82 selects the corresponding data values from the other data lines in memory 38 , an anti - log circuit 94 converts the logarithmic attenuation values a 0 - a 8 to intensity values i 0 - i 8 in non - logarithmic notation . a processor 96 multiplies each intensity value i 0 - i 8 by a corresponding weighting of the selected deconvolution function 88 and combines the values . because the weighting for the correction intensity values i 1 - i 8 are all negative , these contributions are all subtracted from the focal ray intensity i 0 . although the deconvolution function is exemplified as digitized into nine values , it is to be appreciated that a larger or smaller number of values can be selected . after the data value 86 has been corrected , the line 84 is shifted to a next data value 100 in the data line and the process is repeated . as each data value is corrected , it is returned to logarithmic notation by a log circuit 102 and stored in a corrected data memory 104 . the off - focal radiation corrected data in memory 104 can be further corrected or processed , as is conventional in the art . when a plurality of detector arcs 16 collect a plurality of slices concurrently , the correction process is optionally repeated in the longitudinal direction . as the data is corrected , a reconstruction processor 106 reconstructs the data lines into an image representation , which is stored in an image memory 108 . convolution and backprojection or other known reconstruction techniques are completed . a video processor 110 selects portions of the image data from the image memory 108 , such as a slice , projection , or the like , and converts it into appropriate format for display on a human - readable display 112 , such as a video monitor , liquid crystal display , active matrix display , a printer , or the like . optionally , the data from the image memory is also sent to an archive for storage . the deconvolution functions stored in memory 90 can be determined by empirical measurements or calculated mathematically . preferably , the functions are calculated mathematically using the off - focal model : d ( s )= x ( s ){ circle around ( x )}( δ ( s )+ e ( s )) ( 1 ) where d ( s ) represents the measured signal , e ( s ) is the error or off - focal radiation , δ ( s ) is the on - focal radiation , and x ( s ) is the target signal . it should be noted that if e ( s ) goes to zero , then d ( s )= x ( s ) and the measured signal contains no error . solving for x ( s ): x ( s )≅ 2 d ( s )− d ( s ){ circle around ( x )}( δ ( s )+ e ( s )) ( 2 ) x ( s )≅ d ( s )+ ofa · d ( s )− d ( s ){ circle around ( x )} e ( s ) ( 3 ) x ( s )≅ d ( s )+ d ( s ){ circle around ( x )} w ( s ) ( 4 ) with reference to fig1 , when a given detector 16 x lies at an angle p from the central ray and the off - focal radiation source is an at angle a from the current source position , the first challenge is to identify the detector of the array when the source fan is at the angle a that gives the best off - focal radiation path to the detector that is rotated to the position of detector 16 x . a detector that lies at an angle β from the central ray has coordinates relative to isocenter given by : where d is a constant source - to - detector distance . similarly , the x , y position of the second focal spot is given by : where s is the distance source - to - isocenter ( of the bore ) distance . finding the size of the triangle abc of fig1 gives : c ={ square root over (( fsx − px ) 2 +( fsy − py ) 2 )} where the formula for c is the distance formula using point ( fsx , fsy ) and ( px , py ). the law of cosines gives the angle γ as follows : γ = a   cos  ( a 2 - b 2 - c 2 - 2   bc ) ( 8 ) because the angle γ can be either positive or negative , the acosine function only gives positive values for small angles , the sign of γ is determined by : the angle γ of the detector is converted into a detector number by : m = γ δ   β + axis_fs ( 10 ) where δβ is the angular spacing between detectors and axis_fs is the position of the central ray on the detectors . from these formulas , for each detector in the array , the detectors are computed that are used to estimate the off - focal line integrals that exist over a given range of source angle α . it turns out , that this estimate path is very close to linear over a small angular range and the slope of the line changes only slightly from the left side of the detector array to the right side . to compute a detector index from equation 10 for each detector over a range of source angles a , the means slope vector s m gives the off - focal estimates for each detector , as shown in fig1 . preferably , s m is implemented as a precalculated lookup table to speed calculation . of course , the computation could be made directly from equation 10 , without the expedient of precalculated slope vectors . two physical considerations determine the range of ( x over which off - focal radiation exists . these considerations include the width an d location of the tube aperture where the x - rays exit the tube and the size and positioning of the anti - scatter grids 92 mounted on the detectors . with reference to fig1 , the position of the detector at angle β is again defined as ( px , py ). fsx 1 and fsx 2 are the maximum and minimum points where the detector sees the off - focal radiation . beyond these points , the off - focal radiation is blocked by the tube aperture . these two points are defined relative to an origin of px and py at the focal spot by : fsx 1 = a w 2 - a d · ( px - a w 2 ) ( py - a d ) ( 11 ) fsx 2 = a w 2 + a d · ( px + a w 2 ) ( py - a d ) ( 12 ) using similar triangles 120 , 122 , the source angle that corresponds to each of these points is defined by :  α 1 = tan - 1  ( fsx 1 s ) α 2 = tan - 1  ( fsx 2 s ) ( 13 ) these angles represent the maximum and minimum angles where the detector sees the off - focal radiation . because the correction operates in source - fan increments and the fan is sampled only at regular angular increments δα , these angles can be converted into source - fan increments by : these numbers identify the source fans that include the range of data for the removal of all off - focal radiation . referring to fig1 , the geometry of the scatter grids also determines the off - focal radiation that is visible to each detector . the scatter grids begin to cast a shadow on the detector blocking part of the detector from receiving off - focal radiation . as the off - focal angle increases , the shadow grows until the detector crystal is completely blocked by the anti - scatter grid . in order to find the shape of the off - focal radiation , the percentage of the crystal that is blocked by the anti - scatter grid at each angle a is determined . the position of the off - focal radiation spot is again defined as a fsx = s - sin a from which is defined : the two sides of the similar triangles are defined by : p = f - u - d 2   and a = ( d + t · cos  ( β ) - h ) ( 16 ) the length of the shadow from the edge of the anti - scatter grid is : shadow = p a · h ( 17 ) where h is the height of the edges of the anti - scatter grid . the percentage of the crystal covered by shadow is : where ds is the dead space between the crystal and the scatter grid given by ds = d − cw . the percentage of x - rays reaching the crystal is equal to 1 - pct_shadow . this x - ray percentage is defined as the shape of the off - focal radiation . combining the effects of the tube aperture and the anti - scatter grids generates maps of the off - focal radiation from the point of view of each detector as shown in fig1 a - 15e . the amplitude of the off - focal radiation is controlled by the scatter grid effects and the cut - off points at the edges are controlled by the tube aperture . because the cut - off for the radiation is an integer of source - fan increments ( equation 14 ), some of the kernels will vary in width from others . to simplify the correction , the total percentage of off - focal radiation that any detector sees is assumed to be a constant of_amp , which is a very close approximation . the off - focal kernel is normalized for each detector so that it sums to 1 . to make the final deconvolution kernel , all of the off - focal radiation weightings are set negative and the center of the convolution function , which represents the on - focal component , is set equal to + 1 . a sample deconvolution kernel takes on the form shown in fig1 and more accurately to scale in fig1 . the off - focal radiation correction is made in the intensity domain , as opposed to the attenuation domain , where many other corrections are done . this is because the detectors measure an intensity related to the initial intensity of the x - rays and the attenuation along the beam path i = i 0 · e − ƒμ ( l ) dl · as in the off - focal radiation case , the initial intensity of the x - ray beam can vary . the expression for the intensity that each detector measures is i = i 0 e − ƒμ ( l ) dl + i l e − ƒμ ( l 1 ) dl 1 + i 2 e − ƒμ ( l 2 ) dl 2 . + . . . the logarithmic operation does not distribute over the off - focal expressions . therefore , off - focal radiation is preferably removed in the intensity ( unlogged ) domain . for each sample in the set of source fans , nearby detectors from nearby source fans are used to form an estimate of the off - focal radiation that was contributed to the sample and to perform a deconvolution . two matrices are computed : one giving the detector indices to use for estimates for each detector and the other giving the shape of the off - focal kernel to use in the deconvolution . the weighting ( off - focal shape ) matrix w km , where k is the source - fan angle and m is the sample index , and the matrix n km containing the detector indices are used for off - focal correction according to : q  ( l , m ) = p  ( l , m ) + ofa · ∑ k  w k , m · p  ( l + k , m + k · s m ) ( 19 ) where kε {− ofw ( 1 ) ofw } is the index for the source angle increment of the off - focal radiation . this basic algorithm is used to identify nearby neighbors from nearby source fans to form an estimate of the off - focal radiation seen in each current sample . the summation process is performed according to equation 19 . in the preferred embodiment and as illustrated in fig1 , the correction is performed in four steps : ( 1 ) for each new sample that is being corrected , work along one direction ; ( 2 ) multiple the value of each of - estimate sample by the weight given in the kernel shape matrix ; ( 4 ) repeat steps ( 1 )-( 3 ) until all of - estimate samples have been included . the invention has been described with reference to the preferred embodiment . obviously , modifications and alterations will occur to others upon reading and understanding the preceding detailed description . it is intended that the invention be construed as including all such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof .
a third generation ct scanner includes a rotating x - ray source and a detector array . each sampling of the detector array generates a source fan data line of data values that are converted to attenuation values in a logarithmic domain and subject to preliminary corrections . attenuation values from a plurality of adjoining source fans are converted back to a non - logarithmic domain as intensity values . a corresponding deconvolution function from a deconvolution function look - up table corresponding to the detector whose intensity value is being corrected is deconvolved with a line of the intensity values which spans a plurality of adjoining source fan data lines to remove the intensity attributable to off - focal radiation . the intensity data is converted back into attenuation values in the logarithmic domain and reconstructed into an image representation for display on a monitor .