Three-dimensional images of the interior of objects are currently generated, using conventional X-ray systems, for a variety of purposes, including security inspection, medical diagnostics, process imaging and non-destructive testing.  Several different system configurations currently exist for generating the image scanning data which is used to create the three-dimensional images. 
In one exemplary system, X-ray source is rotated about the object under inspection.  A collimated fan-beam of X-rays from the source passes through the object under inspection to a one-dimensional array of X-ray detectors located on the opposite side of the object from the source.  Transmission X-ray data is collected at each of a number of angles to form a two-dimensional sinogram.  This information is passed through an image reconstruction algorithm to create a two-dimensional cross-sectional image of the object under inspection. 
In another exemplary system, an X-ray source emits X-rays into a cone of radiation which passes through the object to a two-dimensional array of X-ray detectors which are directly opposed to the source.  The source and detector array are rotated about the object under inspection and the resulting X-ray projection data is reconstructed into a three-dimensional image. 
In another exemplary system, the object being inspected is translated along a substantially linear trajectory, while the source and detector assembly rotate in a plane perpendicular to the axis of object motion, to form an improved three-dimensional image.  In this case, the source describes a helical motion about the object, the locus of source point being situated on the surface of a cylinder about the object.  The rate at which the object moves through the plane of the source and detectors is related to the rate at which the source and detector assembly rotate about the object, this ratio being described as the pitch of the helix. 
Applicant has developed a new generation of X-ray systems that implement X-ray sources with more than one electron gun and one or more high voltage anodes within a single vacuum envelope.  In this system, an X-ray source allows non-sequential motion of an X-ray beam about an object under inspection through the use of multiple grid controlled electron guns which can be excited in any chosen sequence, the electron beam from each source being directed to irradiate anode sections which are distributed around the object under inspection.  This allows non-helical source trajectories to be described at high speeds consistent with the requirements for dynamic and high-throughput object imaging.  Additionally, the rapid switching of electron guns under electrostatic control enables the fast movement of the effective focal spot of the X-ray tube and the rapid generation of sets of tomographic X-ray scan data without the use of moving parts. 
By configuring the firing sequence of the electron guns appropriately, an optimal set of X-ray projection data can be collected at rates far higher than in conventional systems.  Examples of such systems are disclosed in the applications which are listed above and incorporated herein by reference. 
While Applicant has previously described an approach to sequentially firing the electron guns, there is a need to develop an improved method of optimally firing the sequence of electron guns to avoid the creation of image artifacts. 
In particular, Applicant has recognized that the conventional helical motion of the X-ray source results in a sub-optimal sampling of the projection space within the object with the consequent formation of image artifact due to this limited sampling.  Applicant has further recognized that, through the use of multi-emitter X-ray source technology, an optimal source firing sequence can be determined which does not represent a helical scanning geometry and which would result in the generation of improved three-dimensional images.