Abstract:
Certain embodiments include a computed tomography system including an electron beam source for generating an electron beam, an ion clearing electrode for removing ions from the electron beam using electrical fields, an ion trap for allowing ions to accumulate in a downstream region of the electron beam so that the ions do not drift upstream, a beam tube for housing the ion trap, and a grounded tube conforming an effective electrical radius of the beam tube to the physical radius of the grounded tube to reduce spherical aberrations in the electron beam. Certain embodiments include a method for correcting spherical aberration in an electron beam including producing an electron beam, removing ions from the electron beam using electrical fields, and allowing ions to accumulate in a downstream portion of the electron beam using an ion trap and a grounded tube. The grounded tube adjusts a range of spherical aberration correction of the ion trap.

Description:
BACKGROUND OF INVENTION  
         [0001]    The present invention generally relates to spherical aberration correction in a diagnostic imaging system. In particular, the present invention relates to correcting spherical aberration of an electron beam in an EBT scanner with an extended range of correction.  
           [0002]    Diagnostic imaging systems encompass a variety of imaging modalities, such as x-ray systems, computerized tomography (CT) systems, ultrasound systems, electron beam tomography (EBT) systems, magnetic resonance (MR) systems, and the like. Diagnostic imaging systems generate images of an object, such as a patient, for example, through exposure to an energy source, such as x-rays passing through a patient, for example. The generated images may be used for many purposes. For instance, internal defects in an object may be detected. Additionally, changes in internal structure or alignment may be determined. Fluid flow within an object may also be represented. Furthermore, the image may show the presence or absence of items in an object. The information gained from diagnostic imaging has applications in many fields, including medicine and manufacturing.  
           [0003]    In order to help ensure that diagnostic images may be used reliably, image correction is advantageous in diagnostic imaging systems. The image correction in diagnostic imaging systems is important for several reasons, including image quality and system performance. Poor image quality may prevent reliable analysis of the image. For example, a decrease in image contrast quality may yield an unreliable image that is not usable clinically. Additionally, the advent of real-time imaging systems has increased the importance of generating clear, high quality images. The correction of diagnostic images may help to produce a distinct and usable representation of an object.  
           [0004]    In CT imaging systems, for example, an object, such as a patient, is x-rayed from a plurality of angles to produce a set of x-ray projections, referred to as a sinogram. Reconstruction in CT imaging calculates a reconstructed two-dimensional image from the sinogram data. The resulting image may be a single slice of the interior of the target object. Multiple slices may also be obtained. Inaccuracies or errors in the CT imaging system may result in blurring, streaking, or introduction of ghost images or artifacts in the resulting image. For example, if an electron beam suffers spherical aberrations, distortion in a scanned image may result.  
           [0005]    EBT systems utilize a high energy beam of electrons to strike a target and produce x-rays for irradiating an object to be imaged. The point where the electrons strike the target is called the “beam spot”. The electron beam may be “tuned” and/or corrected to minimize error and more accurately produce a beam spot.  
           [0006]    In order to achieve as high a spatial resolution as possible, it is desirable to produce an electron beam spot that is as small as theoretically possible and compatible with system safety. To produce a small beam spot, electron beam optics should be free of aberrations. Aberrations in a beam optical system may occur when beam focusing forces, due to external components or to ions within the beam itself, are not proportional to the beam radius. Aberrations may cause the electron beam to become non-uniform downstream. Spherical aberrations are created when a focal strength of the electron beam varies with a radius of the electron beam. Spherical aberrations cause forces within the electron beam to become non-uniform (non-linear) and result in haloes surrounding the beam spot. As a result, x-rays produced at the beam spot will also have a halo. A halo surrounding the x-rays will decrease image quality and definition in a resulting image.  
           [0007]    Even though spherical aberration may be corrected, correction may not be perfect. Any beam optical devices that produce some aberration should therefore produce as little spherical aberration as possible. Thus, there is a need for an aberration compensation device to allow use of an electron source with superior beam optics.  
           [0008]    As described in U.S. Pat. Nos. 5,719,914 and 6,208,711, which are incorporated herein by reference in their entirety, an electron beam is produced by an electron source at the upstream end of a vacuum housing chamber. A large negative potential (e.g., −130 kV) on the cathode of the electron gun accelerates the electron beam downstream along the chamber axis. Further downstream, a beam optical system that includes magnetic focusing, quadrupole, and deflection coils focuses and deflects the beam to scan along an x-ray producing target. The final beam spot at the target is smaller than that produced at the anode of the electron source. The beam spot must be suitably sharp and halo-free in order to minimize degradation of quality in an image obtained by the imaging system.  
           [0009]    In the chamber region upstream of the beam optical system, a diverging beam is desired, and the electron beam may advantageously self-expand due to the force created by its own space-charge. By contrast, downstream from the beam optical system, a converging, self-focusing beam is desired to minimize the final beam spot at the x-ray producing target.  
           [0010]    As the electron beam passes through the vacuum chamber, the beam ionizes residual or introduced gas therein, producing positive ions. The positive ions are useful in the downstream chamber region where space charge neutralization and a converging beam are desired. In the upstream region, however, the positive ions would be trapped in the negative electron beam unless removed by an external electrostatic field. Without ion-removal, the space-charge for electron beam self-expansion may be neutralized, and the electron beam may destabilize or even collapse.  
           [0011]    In order to adjust the electron beam optics, current EBT scanners may incorporate some form of an ion clearing electrode (ICE) system (for example, a single potential ion clearing electrode system (SPICE, U.S. Pat. No. 6,208,711), a rotatable ion clearing electrode assembly (RICE), or a periodic ion clearing electrode (PICE)). An ICE system removes positive ions from the electron beam by creating electric fields in the region between the electron source and the beam optical lens system (a magnetic solenoid, for example). Using electric fields to remove positive ions between the electron source and the beam optical lens system advantageously produces an electron beam that is self-repulsive (or self-divergent) in the upstream or first region and that is self-attractive (or self-focusing) in the downstream or second region.  
           [0012]    A typical ICE system is terminated by a Positive Ion Electrode (PIE) or ion trap. The PIE or ion trap preferably segregates the first and second regions of the electron beam. The PIE or ion trap prevents ions that are generated by an electron beam from residual gas downstream from the ICE from drifting upstream. The ions are accumulated downstream of the PIE in order to neutralize the beam&#39;s space charge.  
           [0013]    The PIE is typically a washer-shaped electrode. The PIE is typically coupled to a high positive potential. The magnitude of the PIE potential may be used to determine the relative lengths of the upstream and downstream beam regions. Further, a suitably high PIE potential may prevent ions created downstream from drifting into the upstream region. The PIE may cause a paraboloidal boundary to form between the space-charge-dominated portion of the electron beam in the ICE and the neutralized portion of the electron beam downstream. The paraboloidal boundary produces spherical aberration in self-focusing forces of the electron beam. As mentioned in U.S. Pat. No. 5,719,914, spherical aberration may be controlled by adjusting a voltage applied to the PIE. PIE voltage may be used to cancel or correct spherical aberration produced by other beam line elements, such as an electron source.  
           [0014]    However, correction of spherical aberration by adjusting PIE voltage with reasonable applied potentials has both an upper limit and a lower limit. The upper limit of spherical aberration correction may be extended by increasing the aperture of the PIE. In principle, the lower limit may be extended by increasing the voltage applied to the PIE, but even a small extension of the lower limit may require an order of magnitude higher voltage. An alternative approach of decreasing the lower limit by using a smaller PIE aperture is limited by a need to maintain a safe separation of the electron beam and the electrode. Thus, if an electron source were designed with superior beam optics and less spherical aberration, current PIE designs would be unable to compensate for the spherical aberration. In fact, current PIE designs may worsen spherical aberration in an electron beam with superior optics due to limitations on the upper and lower limits of spherical aberration correction in current PIEs.  
           [0015]    Thus, a need exists for a method and apparatus for extending lower and upper limits of spherical aberration correction to improve image quality with current beam optics and future superior electron beam optics. Additionally, there is a need for a method and system for extending lower and upper spherical aberration limits with reasonable applied voltages to eliminate unreasonable high magnitude potentials necessary with current attempts. There is a further need for a method and system for adjusting spherical aberration correction while maintaining a safe separation between the electron beam and the electrode. Therefore, a need exists for a method and apparatus for correcting spherical aberration of an electron beam in an EBT scanner with an extended range of correction.  
         SUMMARY OF INVENTION  
         [0016]    Certain embodiments include a computed tomography system. The system includes an electron beam generator for generating an electron beam, an ion clearing electrode for removing ions from the electron beam using electrical fields, an ion trap for accumulating ions in a downstream region of the electron beam so that the ions do not drift upstream, a beam tube for housing the ion trap and ion clearing electrode, and a grounded tube conforming an effective radius of the beam tube to the physical radius of the grounded tube to reduce spherical aberrations in the electron beam. In certain embodiments, the grounded tube is a non-magnetic grounded tube. The radius of the grounded tube extends a lower limit of spherical aberration correction of the ion trap. In certain embodiments, the ion trap is a positive ion electrode including an aperture through which the electron beam passes. The size of the aperture is adjusted to provide safe clearance from the electron beam and defines an upper limit of spherical aberration correction of the ion trap. The ion trap uses a voltage to create a neutralization boundary in the electron beam to allow ions to accumulate in the downstream region of the electron beam. The grounded tube decreases the voltage to be applied to the ion trap. The system may also include beam optics to aim and/or focus the electron beam. The system may also include a target producing x-ray radiation in response to impact by the electron beam and a detector for detecting the x-ray radiation produced by the target.  
           [0017]    Certain embodiments include a method for correcting spherical aberration in an electron beam having an upstream region and a downstream region. The method includes producing an electron beam, removing ions from the electron beam using electrical fields in the upstream region of the electron beam, and allowing ions to accumulate in the downstream portion of the electron beam using an ion trap and a grounded tube. The grounded tube adjusts a range of spherical aberration correction of the ion trap. The method also includes adjusting an aperture in the ion trap to adjust the range of spherical aberration correction of the ion trap. Additionally, a voltage may be applied to the ion trap to form a neutralization boundary to trap the ions downstream in the electron beam. The voltage applied to the ion trap to form the neutralization boundary decreases as a radius of the grounded tube decreases. The ion trap may be a positive ion electrode. In certain embodiments, the electrical fields used to remove ions are generated by an ion clearing electrode. 
       
    
    
     BRIEF DESCRIPTION OF DRAWINGS  
       [0018]    [0018]FIG. 1 illustrates an EBT imaging system formed in accordance with an embodiment of the present invention.  
         [0019]    [0019]FIG. 2 illustrates a portion of an electron beam housing formed in accordance with an embodiment of the present invention.  
         [0020]    [0020]FIG. 3 illustrates an electrode assembly formed in accordance with an embodiment of the present invention.  
         [0021]    [0021]FIG. 4 depicts a flow diagram for a method for correcting spherical aberration in an electron beam according to an embodiment of the present invention.  
         [0022]    [0022]FIG. 5 illustrates a graph depicting spherical aberrations versus PIE voltage based on grounded tube radius in accordance with an embodiment of the present invention.  
         [0023]    [0023]FIG. 6 depicts spherical aberration of the electron beam versus grounded tube radius based on PIE voltage in accordance with an embodiment of the present invention.  
         [0024]    [0024]FIG. 7 compares a conventional system using PIE to an improved system using PIE with a grounded tube in accordance with an embodiment of the present invention.  
         [0025]    [0025]FIG. 8 illustrates the positioning of the PIE and the grounded tube in the EBT imaging system according to an embodiment of the present invention. 
     
    
       [0026]    The foregoing summary, as well as the following detailed description of certain embodiments of the present invention, will be better understood when read in conjunction with the appended drawings. For the purpose of illustrating the invention, there is shown in the drawings, certain embodiments. It should be understood, however, that the present invention is not limited to the arrangements and instrumentality shown in the attached drawings.  
       DETAILED DESCRIPTION  
       [0027]    For the purpose of illustration only, the following detailed description references a certain embodiment of an Electron Beam Tomography (EBT) imaging system. It is understood that the present invention may be used with other imaging systems and other electron beam systems.  
         [0028]    [0028]FIG. 1 illustrates an EBT imaging system  100  formed in accordance with an embodiment of the present invention. The EBT system  100  includes a housing  110 , a target  160 , an object positioner  170 , and a detector  180 . As illustrated in greater detail in FIG. 2, the housing  110  includes an electron source  120 , an electrode assembly  140 , and beam optics  150 . As shown in FIG. 3, the electrode assembly  140  includes an ion clearing electrode (ICE)  142 , a Positive Ion Electrode (PIE)  144 , and a grounded tube  146 .  
         [0029]    The electron source  120  provides a source of electrons that may be used to form an electron beam  105  for use in imaging. The electron beam  105  from the electron source  120  is used to produce radiation, such as x-ray radiation, for use in imaging at the target  160 . The electron source  120  may be connected to a voltage generator (not pictured) and is used to generate an electron beam  105 . For example, the electron beam  105  is generated at the cathode of the electron source  120  in response to a −130 kV voltage from the voltage generator.  
         [0030]    The electrode assembly  140  controls positive ions in an upstream region of the electron beam  105  using the ICE  142 , washer-shaped PIE  144 , and grounded tube  146 . For example, the electrode assembly  140  may control positive ions by surrounding and subjecting an electron beam  105  to electric fields transverse to the electron beam  105  velocity that advantageously extract positive ions from the electron beam  105  while minimizing net electron beam  105  deflection.  
         [0031]    The ion clearing electrode (ICE)  142  removes positive ions from the electron beam  105 . The ICE  142  may be a multi-sided rotatable field ion clearing electrode (RICE), multiple multi-sided ion clearing electrodes (ICE), a periodic axial field ion controlling electrode (PICE), or a single potential ion clearing electrode (SPICE), for example. The ICE  140  is terminated by the PIE or ion trap  144 .  
         [0032]    The SPICE, for example, extracts positive ions from the electron beam  105  using an ion clearing electrode assembly that is operable from a single source of operating potential and produces essentially zero net beam deflection and displacement. The SPICE is normally installed inside a magnetic solenoid (focusing) lens, concentric about the Z-axis of the system  100 , and uses two basic arrays of electrode cross-sections that alternate along the Z-axis to generate electric fields to cancel or minimize focusing and aberration-producing fields around the electron beam  105 .  
         [0033]    The PIE  144  or ion trap prevents ions generated by residual gas in the electron beam  105  downstream from the ICE  142  from drifting upstream into the ICE  142 . The ions are accumulated in the downstream portion of the electron beam  105  to neutralize space-charge exhibited by the electron beam  105 . The PIE  144  may be a washer-shaped electrode. A voltage potential applied to the PIE  144  produces a paraboloidal neutralization boundary  148  to form between the space-charge-dominated portion of the electron beam  105  in the ICE  142  and the neutralized portion of the electron beam  105  downstream. Ions accumulate downstream from the paraboloidal neutralization boundary  148 . The accumulated ions neutralize the electron beam  105  and cause the electron beam  105  to be self-focusing.  
         [0034]    The paraboloidal boundary  148  between the space-charged beam and the neutralized beam causes beam  105  self-focusing forces which are proportional to beam  105  radius cubed. Focusing forces that are proportional to the beam  105  radius cubed are a classical condition for spherical aberrations. The magnitude of the spherical aberrations is proportional to the axial extent of the neutralization boundary  148 . The extent the boundary  148  is controlled by the voltage applied to the PIE  144  and by the dimensions of the PIE  144  and the grounded tube  146 . A voltage potential applied to the PIE  144  may be used to cancel or correct spherical aberrations produced by other beam line elements, such as the electron source  120 , by modifying the paraboloidal neutralization boundary  148  (i.e., reducing the extent of the boundary  148 ).  
         [0035]    The grounded tube  146  shifts the range of spherical aberration correction of the PIE  144  to lower values using an applied potential. The grounded tube  146  is a metal tube, such as aluminum, non-magnetic stainless steel, or copper, for example. The grounded tube  146  is grounded in the system  100  by attachment to an ICE support frame  145  or the inside wall of the housing or beam tube  110 , for example. In an embodiment, the grounded tube  146  is an aluminum tube having a length of 80 mm, a radius of 30 mm, and a thickness of 1.6 mm. The dimensions, composition, and positioning of the grounded tube  146  may vary.  
         [0036]    The grounded tube  146  is positioned downstream from the PIE  144  in the beam tube  110 . The grounded tube  146  is sufficiently spaced from the PIE  144  to prevent arcing between the grounded tube  146  and the PIE  144  (for example, spacing of a few millimeters). For example, a spacing of two millimeters or more may prevent arcing between the grounded tube  146  and the PIE  144  at an applied voltage potential of 1000 V. In a certain embodiment, the space between the grounded tube  146  and the PIE  144  is smaller than the grounded tube  146  and the PIE  144  radii (for example, less than 6 mm). In a certain embodiment, the end of the grounded tube  146  facing the downstream region of the electron beam  105  is several electron beam  105  diameters beyond the paraboloidal neutralization boundary  148  formed by the PIE  144 .  
         [0037]    [0037]FIG. 8 illustrates the positioning of the PIE  144  and the grounded tube  146  in the EBT imaging system  100  according to an embodiment of the present invention. The grounded tube  146  and the PIE  144  are centered symmetrically around the axis along which the electron beam  105  travels through the beam tube  110 . The PIE  144  and the grounded tube  146  are mounted in the ICE support frame  145  within the beam tube  110 . In an embodiment, the grounded tube  146  and the PIE  144  are each attached to the support frame  145  by three fasteners that are spaced 120 degrees apart.  
         [0038]    When the grounded tube  146  is positioned downstream from the PIE  144 , the radius of the grounded tube  146  (for example, 30 mm) becomes the effective “electrical” radius of the beam tube or housing  110  surrounding the electron beam  105  downstream from the PIE  144 . That is, when the grounded tube  146  is present downstream from the PIE  144 , the grounded tube  146  becomes the beam tube  110  from an electrostatic perspective. However, from a vacuum or physical perspective, the beam tube  110  has a larger radius than the grounded tube  146  (for example, 76 mm). If the grounded tube  146  is not present, the electrical radius (radius in an electrostatic sense) and the vacuum/physical radius of the beam tube  110  are the same (for example, 76 mm). The beam tube provides vacuum pumping for the ICE  142 /PIE  144  system.  
         [0039]    In certain embodiments, the electrostatic potential at the paraboloidal neutralization boundary  148  produced by the PIE  144  is equal to the voltage potential due to the PIE  144  plus the voltage potential of the electron beam  105 . Downstream from the PIE  144 , the magnitude of the voltage potential of the electron beam  105  decreases as the radius of the grounded tube  146  decreases. If the grounded tube  146  radius were reduced to equal the electron beam  105  radius (i.e., the beam  105  would touch the grounded tube  146 ), the voltage potential of the edge of the electron beam  105  would be zero.  
         [0040]    Spherical aberrations of the electron beam  105  are affected by the voltage potential of the PIE  144 , the radius of the PIE  144 , and the radius of the beam tube  110 . Changes to the voltage potential applied to the PIE  144  may be impractical beyond a certain threshold. Modification of the PIE  144  aperture may also be of limited effectiveness after a certain threshold. The introduction of the grounded tube  146  effectively reduces the radius of the portion of the beam tube  110  downstream from the PIE  144  in electrical terms, while leaving the physical beam tube  110  radius unchanged. That is, the effective electrical radius of the beam tube  110  conforms to the physical radius of the grounded tube  146 . The grounded tube  146  restricts the potential of the electron beam  105  and helps to minimize spherical aberrations downstream from the PIE  144 . As further described below in relation to FIGS. 5, 6, and  7 , for the same spherical aberration (the same neutralization boundary length, for example), the potential due to the PIE  144  and the voltage applied to the PIE  144  decrease as the radius of the grounded tube  146  and the magnitude of the potential due to the beam  105  decrease.  
         [0041]    The electron beam  105  is focused by the beam optics  150 . The beam optics  150  may adjust radius, angle, and/or timing of the electron beam  105 , for example. The beam optics  150  may include a quadrupole coil, a deflection coil, and a magnetic lens. The coils focus and shape the electron beam  105  to impact the target  160  for use in imaging.  
         [0042]    The target  160  produces radiation, such as x-ray radiation, upon contact by the electron beam  105 . The location at which the electron beam  105  strikes the target  160  is referred to as the beam spot. The target  160  is struck by the beam  105  at the beam spot, and x-rays are produced. The x-rays travel away from the target  160 . The target  160  may be a metal target, such as a tungsten target, for example.  
         [0043]    The object positioner  170  positions an object to be imaged at least partially in the path of the radiation emitted from the target  160  at the beam spot. The object on the object positioner  170  is irradiated as the x-rays travel from the target  160 . The object positioner  170  may be movable or immovable and may position the object horizontally and/or vertically.  
         [0044]    The detector  180  detects radiation impinging upon it from the target  160 . X-rays from the target  160  irradiate the object on the object positioner  170  and then strike the detector  180 . X-rays passing through the object are attenuated to varying degrees depending on the density of the matter through which the x-rays pass. X-rays impacting on the detector  180  generate an electrical response corresponding to the intensity of the attenuated radiation. A diagnostic image is formed from the electrical response.  
         [0045]    In operation, the voltage generator and the electron source  120  generate an electron beam  105  from the cathode of the electron source  120 . The electron beam  105  passes from the cathode of the electron source  120  to the electrode assembly  140 . Within the electrode assembly  140 , electrodes in the ICE  142  produce electric fields that remove positive ions from the electron beam  105 . Thus, the electron beam  105  is charged within the ICE  142 .  
         [0046]    Next, the electron beam  105  enters the PIE  144 . The PIE  144  traps or confines ions to the downstream portion of the electron beam  105 . The PIE  144  produces a boundary  148  that blocks the ions. The ions neutralize the electron beam  105  downstream from the ICE  142 .  
         [0047]    Spherical aberrations are introduced by ion clearing and ion trapping and by the electron source  120 , as well as other components. The PIE  144  voltage controls the spherical aberrations due to ion trapping. The PIE  144  may cancel spherical aberrations in the electron beam  105  due to other components. However, if the degree of spherical aberrations to be cancelled becomes excessive, a large voltage must be applied to the PIE  144  to correct the spherical aberrations. The PIE  144  voltage may become too large. However, with the introduction of the grounded tube  146 , the PIE  144  and grounded tube  146  cooperate to adjust the spherical aberration characteristics and provide a wider range for correction of spherical aberrations.  
         [0048]    When used alone, the PIE  144  has an inherent upper limit and lower limit to its spherical aberration correction capabilities. The upper limit of correction is extended by increasing the aperture or opening of the PIE  144 . The lower correction limit is extended by increasing the voltage applied to the PIE  144 . Without the grounded tube  146 , a small extension of the lower limit requires an increase in applied voltage by an order of magnitude. The grounded tube  146  allows extension of the lower limit of spherical aberration correction based on the radius of the grounded tube  146  in relation to the beam tube  110  housing the electrode assembly  140 .  
         [0049]    After the electron beam  105  has passed through the PIE  144  and the grounded tube  146  and the beam optical system  150 , spherical aberration in the electron beam  105  has been minimized. The PIE  144  with the grounded tube  146  reduces the halo surrounding the electron beam  105  at the beam spot caused by spherical aberrations. Thus, the electron beam  105  that strikes the target  160  produces x-rays from the target  160  that possess a reduced halo.  
         [0050]    X-rays generated at the target  160  travel outwards through the object positioner  170  and irradiate an object positioned on the object positioner  170 . The x-rays that are not blocked by the object then impinge upon the detector  180 . Signals are generated based on the strength of the x-rays impacting the detector  180 . The signals are used to produce an image. X-rays with reduced halo help to improve image quality in the resulting image.  
         [0051]    [0051]FIG. 4 depicts a flow diagram for a method  400  for correcting spherical aberrations in the electron beam  105  according to an embodiment of the present invention. First at step  410 , an electron beam  105  is generated. Next, at step  420 , ions are cleared from the upstream electron beam  105  through electrical fields that are produced by the ICE  142 . At step  430 , ions are allowed to accumulate in a downstream portion of the electron beam  105 . Ion accumulation beyond the paraboloidal neutralization boundary  148  occurs automatically. Thus, the portion of the electron beam  105  downstream from the neutralization boundary  148  is largely neutralized and contains a number of ions equal to the number of electrons. For example, a washer-shaped ion trap, such as the PIE  144 , with an opening in the center, may be used to create a paraboloidal boundary  148  blocking the ions from moving upstream.  
         [0052]    However, ion trapping has limits in spherical aberration correction. Therefore, at step  440 , the correction limits of the ion trap, such as the PIE  144 , are shifted. For example, the upper limit of the PIE  144  may be adjusted by adjusting the size of the opening or aperture in the PIE  144 . Additionally, the lower limit of spherical aberration correction of the PIE  144  may be adjusted by placing a grounded tube  146  downstream from the PIE  144 . As discussed further below in relation to FIG. 5, the dimensions of the grounded tube  146  decrease the limits of spherical aberration correction.  
         [0053]    An upper limit of spherical aberration correction is increased by widening an aperture of an ion trap, such as the PIE  144 , through which an electron beam  105  passes. The ion trap allows ions to accumulate in the electron beam  105  at a downstream portion of the electron beam  105 . A lower limit of spherical aberration correction is expanded by positioning a grounded tube  146  beyond the ion trap to shift the range of correction of the ion trap to lower values. The dimensions of the grounded tube  146  affect electrical interaction between the ion trap and the electron beam  105  and lower the range of spherical aberration correction provided by the ion trap.  
         [0054]    Then, at step  450 , the corrected electron beam  105  is aimed and/or focused by the beam optics  150 . At step  460 , the electron beam  105  impacts the target  160  and produces x-rays. Next, at step  470 , the x-rays travel from the target  160  and pass through an object located on the object positioner  170 , irradiating the object. At step  480 , the x-rays impinge upon the detector  180 . The x-rays produce signals at the detector  180  in proportion to the intensity with which the x-rays arrive at the detector  180  after irradiating the object on the object positioner  170 . Finally, at step  490 , the signals are used to produce an image representative of the object through which the x-rays passed.  
         [0055]    [0055]FIG. 5 illustrates a graph depicting spherical aberrations versus PIE  144  voltage based on different grounded tube  146  radii. FIG. 5 shows a shift of voltage for constant spherical aberrations as the grounded tube  146  radius decreases. At a smaller physical grounded tube  146  radius, and thus a smaller effective electrical radius of the beam tube  110 , a lower voltage potential applied to the PIE  144  achieves the same reduction of spherical aberrations in the electron beam  105  as a higher voltage potential applied with a larger effective electrical radius. In FIG. 5, the spherical aberrations at the edge of the electron beam  105  is the same at 0.2 diopter with a PIE  144  voltage of 710 V and a grounded tube  146  radius of 7.62 cm and with a PIE  144  voltage of 330 V and a grounded tube  146  radius of 3.0 cm. Thus, a small grounded tube  146  radius allows a given reduction in spherical aberration at a lower applied voltage potential.  
         [0056]    [0056]FIG. 6 depicts spherical aberration of the electron beam  105  versus grounded tube  146  radius based on PIE  144  voltage. FIG. 6 shows how spherical aberration generally increases as the radius of the grounded tube  146  increases for a given voltage potential applied to the PIE  144 . At a constant voltage, a decrease in the radius of the grounded tube  146 , and thus a decrease in the effective electrical radius of the beam tube  110 , allows for an extended range of reduction in spherical aberrations of the electron beam  105 . FIG. 6 illustrates spherical aberration versus grounded tube  146  radius for a PIE  144  applied potential of 1000V and a minimum applied PIE  144  potential. For example, with a grounded tube  146  radius of 3.0 cm, spherical aberration correction of the electron beam  105  is 0.225 diopter at a minimum PIE  144  voltage and 0.08 diopter at a PIE  144  voltage of 1000V.  
         [0057]    [0057]FIG. 7 compares a conventional system using PIE  144  to an improved system using PIE  144  with a grounded tube  146  in accordance with an embodiment of the present invention. FIG. 7( a ) illustrates a conventional system using PIE  144  with a large radius r w  between the center of the electron beam  105  and the wall of the beam tube. FIG. 7( b ) graphs PIE  144  potential near the z-axis of the PIE  144  and the neutralization boundary  148  formed by voltage applied to the PIE  144 . The voltage potential due to the PIE  144  is shown with respect to distance along the z-axis. The PIE  144  voltage potential and the extent of the neutralization boundary  148  along the z-axis of the electron beam  105  impact spherical aberrations within the electron beam  105 .  
         [0058]    An improved PIE  144  with the grounded tube  146  is shown in FIG. 7( c ). As shown in FIG. 7( c ), the radius r w  is greatly reduced from the center of the electron beam  105  to the wall of the grounded tube  146 , rather than the wall of the beam tube or housing  110 . Additionally, the neutralization boundary  148  is formed by the PIE  144  closer to the PIE  144  than in the prior art and is of reduced extent. By reducing the radius and shortening the extent of the boundary  148  along the z-axis of the electron beam  105 , spherical aberrations may be reduced. The addition of the grounded tube  146  improves the reduction and ease of reduction in spherical aberration of the electron beam  105  and, thus, improves resulting image quality as well.  
         [0059]    While the invention has been described with reference to certain embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from its scope. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed, but that the invention will include all embodiments falling within the scope of the appended claims.