the relevant components of a spiral scan computer tomography apparatus , for explaining the principles of the present invention , are schematically shown in fig1 . the spiral scan computer tomography apparatus has a measurement unit consisting of an x - ray radiator 1 and a radiation detector 2 , the measurement unit being rotatable around an examination subject 5 . the x - ray radiator 1 is supplied by a high - voltage generator 3 , and generates a planar x - ray beam 4 passing through the examination subject 5 . the plane of the x - ray beam 4 extends perpendicularly to the plane of the drawing . the x - ray beam 4 , attenuated by the examination subject 5 , is incident on the radiation detector 2 , which consists of a row of detector elements . each detector element generates an output signal , the output signals being collectively supplied to a computer 6 . the computer 6 calculates a quantity of planar images of the scanned volume of the examination subject 5 from these output signals , respectively for different z - positions . these images are reproduced on a viewing monitor 7 . for three - dimensional scanning of the examination subject 5 , the measurement unit consisting of the x - ray radiator 1 and the radiation detector 2 is rotated around the examination subject 5 , while the examination subject 5 is simultaneously shifted in the z - direction on a patient support 8 . the examination subject 5 is thus spirally scanned by the x - ray beam 4 . in order to analyze the difference between the aforementioned known image calculation and image calculation corresponding to the invention , a central cylinder 9 , shown in fig2 shall be considered . the end face of the central cylinder 9 is assumed to be planar , and defines the reference plane at z = 0 . it is assumed for the relative motion between the measured slice 10 and the cylinder 9 that the feed during a 360 ° revolution of the measurement unit exactly corresponds to the thickness of the measured slice 10 . first , the intensities registered at the radiation detector 2 are identified taking the partial volume effect into consideration . when the cylinder 9 fully enters into the slice , the intensity is measured . the variable z 1 designates the middle of the measured slice 10 , which moves in the + z - direction during the spiral scan . the slice 10 has a thickness d . the value r k , l is the path length of the beam of the k th channel of the l th projection within the cylinder 9 , and μ is the x - ray absorption coefficient of the cylinder 9 . when the cylinder 9 only partially projects into the measured slice 10 , the intensity is composed of the fraction ( d / 2 - z 1 )/ d of attenuated radiation and the fraction ( d / 2 + z 1 )/ d of unattenuated radiation . this results in results in an expression for the intensity of : ## equ1 ## when the cylinder 9 no longer projects into the measured slice 10 at all , the radiation detector 2 receives the full signal : the relationship between intensities and attenuation values is established by ## equ2 ## wherein f is a multiplication factor . the best result that a spiral algorithm can deliver is to provide data which are as close as possible to data which would be obtained in a planar scan in the reference plane . in the present instance , such data would be the attenuation values as a result of the partial volume effect , which also arises in the planar scan , the attenuation value of a cylinder 9 half - projecting into the measured slice 10 , however , is not established simply by but instead is established by equation ( 5 ). as a result , the level in the image of the cylinder 9 is not constant , but varies . this occurs because the contribution to the total level made by the empty ( air - filled ) half of the measured slice 10 leads to a computational lowering of the attenuation in the inner region of the cylinder 9 , as can be seen by comparing equations ( 5 ) and ( 6 ) for an extremely large μr . a detailed example of the interpolation technique of the invention shall be set forth below using a specified interpolation rule . the inventive techniques , however , can be employed with other interpolation rules , as are known to those skilled in the art . for the interpolation employed in this example , data from the region of two successively measured slices are employed . if z 1 is the middle of the first slice , z 1 + d is the middle of the second slice . using this convention , the interpolation rule employed is as follows : ## equ3 ## using this interpolation rule , p can be either intensity or attenuation . the index k can be omitted if a fixed ( single ) channel is considered , for example , that of the central ray . the index l is omitted , because it is unambiguously identifiable by the z - position . the application of the interpolation weighting in accordance with the principles of the present invention is derived using equations ( 1 through 3 ) as follows : ## equ4 ## the function curve for equation ( 8 ) has a shape as indicated by curves b in fig3 . the application of the interpolation weighting to attenuation values yields : ## equ5 ## the function curves for equation ( 9 ) are shown as curves a in fig3 . in fig3 the projection number is entered increasing toward the right and the attenuation value is entered increasing toward the top . as noted above , the curves a are based on an interpolation with attenuation values and the curves b are based on an interpolation with intensities . the curves c are derived from the ideal value . the curves are shown for different values of k . the curves shown for k = 385 show the attenuation values for the beam through the center of the cylinder 9 ( high attenuation ). the curves illustrated for k = 239 show the attenuation values for a beam which barely tangentially intersects the cylinder 9 ( low attenuation ). particularly for higher values of μr , the interpolation with attenuation values clearly leads to level shifts and to inhomogeneities . in comparison thereto , interpolation using intensities comes relatively close to the constant value according to equation ( 5 ) which would be measured in a planar scan in the reference plane , and which is indicated in fig3 by a horizontal straight line . a noticeable improve can be seen in fig3 using the interpolation technique employing intensities in accordance with the principles of the present invention . interpolation using intensities thus supplies demonstrably better results than interpolation using attenuation values . this is also true given employment of the inventive technique using other interpolation rules . the extent of the deviation of the interpolation using intensities from the ideal value according to equation ( 5 ) is dependent on the extent to which data are employed from those regions wherein the cylinder lies either entirely within , or entirely outside , the measured slice . although modifications and changes may be suggested by those skilled in the art , it is the intention of the inventor to embody within the patent warranted hereon all changes and modifications as reasonably and properly come within the scope of his contribution to the art .
a computer tomography apparatus undertakes a three - dimensional scanning of the examination subject with relative motion between the rotating measurement unit and the patient , the relative motion ensuing in the longitudinal direction of the patient support during the acquisition and processing of the detector data , so that a spiral scan is accomplished . for image reconstruction , data corresponding to the scanning of parallel slices are generated from the detector data by spiral interpolation , the interpolation being done with the detector data in the form of the relative intensities registered at the detector .