fig1 shows a side view illustrating the geometry of a multi - slice cone beam according to the prior art . a cylindrical volumetric region of interest ( vroi ) 10 having a patient axis 12 is scanned by an x - ray source 13 , while rotating about a rotation ( ct ) axis 18 , which is shown as being coincident with axis 12 for the prior art system shown . a patient 14 moves in a direction 12 . marked on vroi 10 are a series of slices 20 ( only a few of which are indicated ), for which images are desired . in the prior art system , when transaxial slices ( as shown ) are to be imaged , the patient axis and the ct axis are coincident . for the purposes of description of the present invention , the presentation of fig2 , which is equivalent to that of fig1 , is useful . while in fig1 , the patient is considered to have the motion along its axis and the x - ray source is considered to have a pure rotational motion , in fig2 , source 13 is shown as describing a helical motion 15 and the patient is considered to be stationary . the axis of the helix is the same as the axis of rotation of the x - ray source . the two descriptions are , of course completely equivalent . fig3 , which corresponds to fig2 shows a side view of the same vroi 10 and the same desired transaxial ( with respect to patient axis 12 ) slices 20 . however , unlike the situation in prior art fig1 , patient axis 12 and ct rotation axis 18 are offset by an angle . alpha .. this angle is preferably chosen to minimize the amount of radiation to the patient by minimizing the number of rotations of the x - ray tube about the patient . although the angular offset is shown as being about 12 °, the actual offset in various embodiments of the invention , is usually much smaller . it should also be noted that in fig3 , the patient is shown as being tilted . however , in practice it is generally more convenient to tilt the plane of the gantry , generally tilting both the circle of rotation of the x - ray source and the detectors 17 by a same angle . alpha .. since many modem ct imagers have the facility for such tilting , the practice of the present invention generally does not require the use of special equipment . a controller 100 , controls the x - ray source , and received data signals from the detectors 17 , as in conventional systems . it also determines an angle of tilt , as described below and controls the tilt of the gantry ( or the table ) to provide the tilt angle . alpha .. in general the term controller is used to include the apparatus and software necessary for computing and displaying tomographic images based on the determined attenuation values . while the path of the x - ray source is shown as a helix , this is true only with respect to a moving reference , as described below . while the following explanation is not strictly speaking , required for an understanding of the invention , it is included to further orient the reader . for the purpose of formulating the orientation of the vroi with respect to the helical path , it is convenient to chose a cartesian system of coordinates ( soc ) that has a z - axis with the same direction as the rotation axis of the tilted gantry . the origin of the soc is fixed to the center of the cylinder , i . e ., the origin of the soc moves with the patient . this is the same movement that was used to generate the helix shown in fig2 . in the embodiment of fig1 and 2 , the movement is perpendicular to the rotation plane of the rotation of the x - ray source , such that in the soc , the movement of the x - ray source is a true helix with a fixed axis . in the embodiment of fig3 , the origin of the soc does not move in the direction normal to the rotation plane , so the analysis is somewhat more complex . in the soc of fig3 , the outside surface of the vroi is defined parametrically with respect to ( p and h , as : where r is the radius of the cylinder of the vroi , α is the gantry tilt angle , φ is a parameter that varies between 0 and 2π and h is a parameter that varies between − h / 2 and + h / 2 , where h is the height of the cylinder . in the coordinate system indicated above , the helical path of the x - ray source is given by : x s = z s * tan ( α )+ r * cos ( θ o + 2π * z s /( m * cos ( α )) and ( 4 ) y s = r * sin ( θ o + 2π * z s /( m * cos ( α ))). ( 5 ) where r is the radius of the x - ray source rotation around the gantry iso - center , m is the helical pitch and θ o is a phase of the helical path . the term z s * tan ( α ) in equation ( 4 ) reflects the fact that for a tilted gantry ( with the origin of coordinated fixed in the center of the vroi ), the path of the x - ray source is a helical path with respect to a point that moves . while the direction of the z - axis is the same as the direction of the helix axis , the position of the axis in the x - y plane moves with respect to the center of the helix . for simplicity , we assume that the tilt is in the x - z plane . it should be understood that the above equations 4 and 5 highlight that there are two degrees of freedom in the tilt , namely the tilt angle α and the phase of the helix θ o . the dose can be reduced by properly choosing the angle , with further optimization being based on a choice of the helix phase . it is noted that the angle of the helix with respect to vroi 10 is such that the helix path is parallel to one and preferably to both of end faces 22 of vroi 10 ( parallel to one end , in the embodiment shown ), as the x - ray tube passes the end faces . this congruency and the reasons why it is desirable are explained with the aid of fig4 . fig4 , shows an end view of vroi 10 , together with a circle 24 , representing the rotation path of the x - ray source . also shown are a plurality of beams 26 , 28 , 30 and 32 , corresponding to a some of the group of beam paths of ct “ view ” for reconstruction of an image of an end slice of the vroi . this group of beam paths is provided by rebinning of the fan / cone beam data to parallel views , by any of the many methods known in the art . in accordance with an embodiment of the invention , one of the parallel views necessary for reconstructing the slice is derived during a single partial rotation of angle β , as indicated on the drawing . optionally , each of the elements in the group making up a particular view , are provided from the same fan of the cone beam . by simple geometry , it can be seen that β = 2 * arc sin ( r / r ). in fig4 , 34 and 36 represent two pixels at the extreme of the reconstruction circle of the particular view ( i . e ., the vroi ) and 38 and 40 correspond to the positions of the x - ray source when these beams are acquired . it is clear that in order for the same fan beam to be used for all the elements of the group , the x - ray source should move ( δz ), during a rotation β , by a distance given as : where m is the movement of the bed during one gantry rotation ( i . e ., the pitch of the helix ). movement by this amount will provide for the same fan to remain aligned with the slice during the rotation through the angle β . in order to achieve this condition , patient axis 12 and helix axis 18 should be tilted by an angle : which is approximately equal to the helix angle , for values of r / r of less than about 0 . 5 and somewhat larger than the helix angle for larger values of r / r . in all practical cases , the above analysis yields a value of a within 15 % or 25 % of the helix angle . while the calculated value gives optimum results , values between 0 . 7 and 1 . 5 times the helix angle also give a substantial reduction in the radiation dose . more preferably , a is between the helix angle and 1 . 25 times the helix angle . optimally , it is substantially equal to the angle defined by the above equations ( i . e ., within 0 . 25 , 0 . 5 or 1 degrees ) for example , for r = 285 mm , and m = 100 ( for a multi - slice scanner ), a is between approximately 3 . 3 ° and 3 . 7 °, for a range of r between 125 and 250 . this angle is , of course dependent on r , r and m and will vary depending on the value of these variables . it is believed that in practical situations a will be between 0 . 5 ° and 5 °. for most structures it will be between 1 ° and 4 °. for some structures it will be between 2 ° and 3 °. in accordance with the above analysis , the total rotation required to produce all of the views for the slice is just 180 °+ β . the above analysis describes the optimization of the acquisition of the data for reconstructing one of the end slices . the above analysis describes an optimization procedure for a slice at one end of vroi 10 . optimally , the amount of radiation is reduced by a maximum amount if the same conditions apply at the other end of the vroi . this occurs when the length of the vroi is an integer multiple of the pitch . under these circumstances , the helical path can be reduced by 2 * arc sin ( r / r ). for example , if r = 0 . 667r , the decrease is over 83 °. where the length of the vroi is equal to a small multiple of the pitch , the reduction in radiation can be quite substantial . this gives over 10 % decrease in radiation dose , when a large helix pitch is used . when a smaller helix pitch is used , so that several rotations of the x - ray source are required , or where r / r is smaller , the improvement will be smaller . in order to acquire all of the attenuation values for the central view from the central fan , the x - ray should be on just as the fan first intersects the end surface . however , since this is the central view , the earlier views are acquired earlier . this means that the x - ray is preferably turned on 90 ° of rotation of the x - ray source before this first intersection . when the length of the vroi is equal to an integer number of pitches , this will result optimization at both ends of the vroi . utilizing the cartesian system described above , the phase angle of the helix at which the scan commences is optimally is : for other lengths , a compromise starting angle can be chosen or only one end is optimized . alternatively , the pitch is adjusted to optimize the radiation , consistent with image quality requirements . further alternatively , under some circumstances the angle is made somewhat different than the calculated a . generally , some combination of these variations can be used . the exact values that give the lowest dosage will depend , to some extent on the particular geometry of the system and the length of the vroi , such that a general formulation may not be possible . however , utilizing the general basis as described herein , the angle α for any optimization are expected to be 25 % of the value calculated above . the above embodiment describes the application of the present invention to system in which parallel views are generated by rebinning the data into parallel views and reconstructing the image from the parallel views . as such it is directly applicable to wide range of cone beam reconstruction algorithms , such as the above - mentioned paper by kachelrieβ , et al , and m . “ a 3d cone beam reconstruction for circular trajectories ,” by m . grass , et al ., phys . med . biol ., vol . 45 , p329 ( 2000 ). however , the present invention is also applicable to other reconstruction methods , for example three dimensional reconstruction methods such as those described in “ exact radon rebinning algorithm for the long object in helical cone beam ct ”, by schaller , et al , ieee trans . med . imag . vol . 19 , p . 361 ( 2000 ) and “ quasi - exact filtered backprojection algorithm for long - object problem in helical cone - beam tomography ,” by kudo , et al ., ieee trans . med . imag . vol . 19 , p . 902 ( 2000 ). the disclosures of all of these papers are incorporated herein by reference . furthermore , in the above analysis the effect of the use of views having a path that is not parallel to the plane is not dealt with . however , such problems are dealt with in substantially all cone beam reconstruction algorithms . furthermore , the present invention has been described using non - limiting detailed descriptions of exemplary embodiments thereof that are provided by way of example and that are not intended to limit the scope of the invention . variations of embodiments of the invention , including combinations of features from the various embodiments will occur to persons of the art . for example , both third and fourth generation ct scanners can be used as can multiple focal spot systems ( for higher resolution ) and systems in which a ring x - ray source in which a beam impinging a ring target ( the x - ray source ) travels around the patient is used rather than a rotation x - ray tube . furthermore , while the invention has been described for the imaging of a patient , it is well known that ct imaging can also be used to image the interior of other objects such as castings and machined parts . the scope of the invention is thus limited only by the scope of the claims . furthermore , to avoid any question regarding the scope of the claims , where the terms “ comprise ,” “ comprising ,” “ include ,” “ including ” or the like are used in the claims , they mean “ including but not necessarily limited to ”.
computerized tomography apparatus for reconstructing attenuation values within a volume comprising : an x - ray source situated operative to rotate about said volume , in a rotation plane , while irradiating at least a portion of the volume ; a plurality of rows of x - ray detectors illuminated by said rotating x - ray source situated on an opposite side of the volume ; a patient support operative to move a patient through a space between the source and detectors at an angle to the normal to the rotation plane , while the x - ray source illuminates the detectors ; and a controller operative to compute the angle based on at least one of a radius r of said rotation , a radius r of said volume and a helix pitch , m , defined as a distance the patient support moves during a single rotation of the x - ray source .