X-RAY TUBE ANODE

Abstract

An anode for an X-ray tube is provided. The anode has a shape configured such that, in use: an electron beam impinges upon the anode at a focal spot on the surface of the anode, and the anode is heated by the electron beam from a first state to a predetermined second state and undergoes resulting thermal expansion causing a change in the location of the focal spot on the surface of the anode, wherein the configured shape of the anode is such that the spatial position of the focal spot with respect to the X-ray tube is substantially the same for the first state and the second state. A method of producing an anode for an X-ray tube is also provided.

Claims

1. An anode for an X-ray tube, wherein the anode has a shape configured such that, in use: an electron beam impinges upon the anode at a focal spot on the surface of the anode, and the anode is heated by the electron beam from a first state to a predetermined second state and undergoes resulting thermal expansion causing a change in the location of the focal spot on the surface of the anode, wherein the configured shape of the anode is such that the spatial position of the focal spot with respect to the X-ray tube is substantially the same for the first state and the second state.

2. An anode for an X-ray tube, wherein the anode has a shape configured such that, in use: the electron beam impinges upon the anode at a focal spot in a target region on the anode, and at least a part of the surface of the anode within the target region lies substantially along a straight line coincident with the focal spot and parallel to a direction of thermal expansion of the anode at the focal spot.

3. An anode according to claim 2, wherein, in use, the straight line is coincident with a centroid of an attachment region of the anode at which the anode is attached to the X-ray tube.

4. An anode according to claim 2, wherein the configured shape of the anode is such that, in use, non-uniform heating of the anode proximal to the focal spot causes the said part of the surface of the anode to lie substantially along the said straight line.

5. An anode according to claim 4, wherein the said configured shape is such that, in absence of the said non-uniform heating, a predetermined deviation angle is subtended between the orientation of the said part of the surface of the anode and the said straight line, the predetermined deviation angle being configured to be substantially equal in magnitude to a change in inclination of the surface of the anode proximal to the focal spot caused by the said non-uniform heating.

6. An anode according to claim 1, wherein a distance between the spatial position of the focal spot with respect to the X-ray tube for the first state and the spatial position of the focal spot with respect to the X-ray tube for the second state is less than or equal to 10% of a distance between: a spatial position, for the first state, of a focal spot for a second anode when in use in the X-ray tube, the second anode having a shape configured such that its principal axis of expansion is parallel with a window axis of the X-ray tube; and a spatial position, for the second state, of the focal spot for the second anode with respect to the X-ray tube.

7. An anode according to claim 1, wherein a distance between the spatial position of the focal spot with respect to the X-ray tube for the first state and the spatial position of the focal spot with respect to the X-ray tube for the second state is less than or equal to 6×10.sup.−4 m.

8. An anode according to claim 2, wherein the anode is adapted such that at least a portion of the anode, including the target region, is rotatable with respect to the X-ray tube when the anode is mounted within the X-ray tube, and wherein the configured shape of the anode is rotationally symmetrical such that, in use, during rotation of the said rotatable portion with respect to the X-ray tube, the spatial position of the focal spot with respect to the X-ray tube remains substantially the same for the first state and the second state.

9. An anode according to claim 8, wherein the rotational symmetry of the anode is such that, in use, during rotation of the said rotatable portion with respect to the X-ray tube, at least a part of the surface of the anode within the target region remains lying substantially along the said straight line coincident with the focal spot and parallel to the direction of thermal expansion of the anode at the focal spot.

10. An anode according to claim 2, wherein a maximum distance between the said part of the surface of the anode within which the target region lies and the said straight line is less than 1.25×10.sup.−3 m.

11. An anode according to claim 1, wherein the second state corresponds to a predetermined temperature distribution within the anode that is achieved by way of the anode being heated under a predetermined set of heating conditions.

12. An anode according to claim 11, wherein the predetermined set of heating conditions comprises any one or more of: average anode temperature increase, total applied electron beam energy, average electron beam power, and electron beam impingement duration.

13. An X-ray tube comprising an anode according to claim 1.

14. A method of generating X-rays using an X-ray tube according to claim 13, the method comprising: causing an electron beam to impinge upon the anode at a focal spot on the surface of the anode so as to generate X-rays and to heat the anode from the first state to the second state.

15. A method according to claim 14, further comprising continuing to operate the X-ray tube so as to generate X-rays, under a set of operating conditions whereby the anode is maintained at the second state.

16. A method of producing an anode for an X-ray tube, the method comprising: configuring the shape of the anode, the said configuring comprising the steps of: a) obtaining input anode shape data representative of a shape of an X-ray tube anode; b) identifying, based on the input anode shape data, a first location, on the surface of the anode, of a focal spot at which an electron beam will impinge in use when the anode is at a first state; c) identifying, based on the input anode shape data, a second location, on the surface of the anode, of the focal spot, when the anode, in use, is at a second state having been heated thereto by the electron beam from the first state and having undergone resulting thermal expansion such that the first and second locations on the surface of the anode are different; d) generating, based on the input anode shape data and the identified first and second locations, modified anode shape data representative of a modified shape of an X-ray tube anode, wherein the spatial position, with respect to the X-ray tube, of the first location on the surface of the anode having the modified shape when the anode is at the first state is substantially the same as the spatial position, with respect to the X-ray tube, of the second location on the surface of the anode having the modified shape when the anode is at the second state, and forming an anode according to the modified anode shape data.

17. A method according to claim 16, wherein the generating modified anode shape data comprises: calculating a modification to the shape represented by the input anode shape data to reduce the distance between the location, with respect to the X-ray tube, of the first position on the surface of the anode having the modified shape when the anode is at the first state and the location, with respect to the X-ray tube, of the second position on the surface of the anode having the modified shape when the anode is at the second state; and applying the calculated modification to the input anode shape data so as to obtain the modified anode shape data.

18. A method according to claim 16, wherein the input anode shape data comprises a set of parameters having values, the parameters comprising: a window angle parameter representative of an angle between the anode axis and the window axis; and a target tilt parameter representative of and angle between the anode axis and the anode surface at the target region, and wherein the generating the modified anode shape data comprises adjusting the values of the window angle parameter and the target tilt parameter such that the angle between the window axis and the anode surface at the target region is unchanged.

19. A method according to claim 16, wherein the said configuring further comprises: identifying, based on the input anode shape data, a straight line coincident with the focal spot and parallel to a direction of thermal expansion of the anode at the first position resulting from heating by the electron beam from the initial state; and wherein the said generating is performed such that, for the shape represented by the modified anode shape data, at least a part of a target region in which the electron beam impinges on the surface of the anode in use lies substantially along the straight line when the anode is at the initial state.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Examples of the present invention will now be described, with reference to the accompanying drawings, wherein like reference numerals indicate like features, and in which:

[0068] FIG. 1 is a cross section view of a typical X-ray tube according to the prior art;

[0069] FIG. 2 shows simulated thermal expansion in the horizontal direction within the X-ray tube according to the prior art;

[0070] FIG. 3 shows simulated thermal expansion of the prior art X-ray tube elements in the vertical direction;

[0071] FIG. 4 is a cross section showing a first example anode according to the invention within an X-ray tube;

[0072] FIG. 5 shows a section of a target surface of the first example anode;

[0073] FIG. 6 shows a section of the target surface of a second example anode according to the invention;

[0074] FIG. 7 shows a cross section view of the second example anode within an X-ray tube;

[0075] FIG. 8 shows a third example anode according to the invention within an X-ray tube;

[0076] FIG. 9 is a graph showing displacement of an electron beam spot in use caused by thermal expansion of the third example anode;

[0077] FIG. 10 is a close-up schematic view showing the geometry of a target surface of a typical anode arranged in an “end window” configuration according to the prior art;

[0078] FIG. 11 is a close-up schematic view showing the geometry of a target surface of an anode according to the prior art in a typical “side window” configuration;

[0079] FIG. 12 shows part of an anode similar to the first example illustrating the geometry of the target surface in greater detail;

[0080] FIG. 13 shows part of an anode similar to the second example, depicting the geometry of the target surface in greater detail;

[0081] FIG. 14 and FIG. 15 each shows a graph visualising the apparent transverse movement of the beam focal spot as a function of the principal axis of expansion for various example anodes according to the invention and comparative examples;

[0082] FIG. 16 is a cross section view of a typical rotating-anode X-ray tube according to the prior art;

[0083] FIG. 17 is a cross section view of a fourth example anode according to the invention;

[0084] FIG. 18 is a cross section view of a fifth example anode according to the invention; and

[0085] FIG. 19 is a graph visualising, for various examples according to the invention and comparative examples, of rotating-anode configurations, of the orientation of the principal expansion axis on the apparent transverse movement of the beam spot in use.

DESCRIPTION OF EMBODIMENTS

[0086] FIG. 1 shows a cross-section of a typical existing X-ray tube and anode with a “side window”, stationary target, reflection target arrangement. The electron gun 104 is shown at the left of the figure, with the anode 142, and target surface thereof 123, being shown on the right. The X-ray window 106 is at the upper part of the figure. FIG. 2 shows simulated values, obtained by way of a finite element analysis simulation, for thermal expansion of the components of this conventional X-ray tube and anode arrangement. FIG. 2 shows thermal expansion in the vertical direction as depicted, of FIG. 3 shows the vertical components of the thermal expansion. As can be seen from this visualisation, the expansion in the components of the tube, in particular the anode surface, that results from heat dissipation of the electron beam in the target, relative to the centre of the window cause the apparent position of the focal spot from which resulting X-rays are omitted, to shift during the operation of the tube. Due to the expansion in the horizontal direction, the location at which the X-rays are generated thus shifts to the left in the depicted example. This beam spot movement, that is transverse to the viewing or window axis defined by the position of the window 106 relative to the target surface 123, can cause misalignment with optical elements. Movement of the beam spot in the vertical direction can, to a lesser degree, also cause misalignment or defocussing of the optical elements.

[0087] These deleterious effects are alleviated by the present invention. A first example anode is now described. FIG. 4 shows a first example anode 401 according to the invention. The high-voltage anode is shaped such that the target region 409 of the anode surface is on a plane which is coincident with and parallel to the direction of thermal expansion 411. This principal expansion axis of material at the beam spot 407 can be defined as the straight line joining that spot with the mounting centroid location 413, away from which thermal expansion of anode material is principally directed. This arrangement illustrates a manner of realizing a key concept of anode designs according to this disclosure, in that the thermal expansion of the anode along the plane of the target surface does not affect the position in space of the electron beam 403 impact location, that is, the intersection of the beam and the anode, relative to the X-ray window 406. This configuration results in a vast reduction in movement of the focal spot 407 as the anode is heated in use from a first state, corresponding in this example to an initial start-up low temperature equilibrium condition, to a second state corresponding to a condition of high-temperature equilibrium. Moreover, to a lesser degree, the displacement of the spot from its location at the initial state is also reduced for any non-equilibrium conditions in between the initial and high-temperature equilibrium states.

[0088] However, in the present example, because the heating and resulting thermal expansion is not homogeneous throughout the anode body, with the region around the focal spot being hotter in use than other parts of the anode, an additional component of thermal expansion also occurs in a direction normal to the target face 409. FIG. 5 shows a cross section of a horizontally oriented target in which the vertical dimension is highly exaggerated for illustrative purposes. The peak on the target surface 509 is located under the electron beam 503 and shows how the target material expands toward the electron beam due to extreme heating and thermal expansion of the material directly under the beam spot 507. In addition to this normal expansion component, in use the material moves tangentially to the surface owing to the principal expansion component. This tangential expansion is significantly greater in magnitude than the normal component, despite the less extreme temperatures that cause it, because of the large size of the anode compared to the localized peak region 529. The combination of these two expansion components define a small tip angle α. In order to compensate for the small additional thermal movement of the surface toward the electron beam, in some examples the target surface may be tipped slightly in relation to the principal axis of thermal expansion. The tip angle to be applied when configuring the anode can be calculated as the arctangent of the ratio of the normal and tangential expansion components.

[0089] FIG. 6 is a similarly exaggerated illustration of the surface profile of a second example anode, in which the target surface is tipped in relation to the electron beam. Thus as the heating occurs, the two movements cancel one another, and the position in space of the location on the target surface at which the electron beam 603 impinges when the anode is hot 633 is unchanged from the position in space of the location 631 on the target surface with which the beam intersects when the anode is cold. To maintain the original desired angle of the target in relation to the electron beam and the window of the X-ray tube, the body of the anode is tipped in the opposite direction to the small angle correction applied to the target surface.

[0090] FIG. 7 accordingly shows the second example anode, which is similar to the first example anode, and includes a modification by way of this small tip angle being introduced into the design. Thus in the present example the target face 709 is no longer coplanar with the anode axis 735 but is tilted (anti-clockwise in the illustration). The anode body is tilted clockwise in order to maintain the relative angles between the target face electron beam and the window axis 737.

[0091] In the first and second examples the focal spot 707 where the electron beam hits the target is coincident with the anode axis 723. FIG. 8 shows a third example, illustrative the more general case of arrangements in which the focal spot is not necessarily coaxial with the anode. By contrast with the previous examples, the third example anode includes additional material between the axis of the anode 835 and the spot location. The presence of this extra anode material causes additional thermal displacement of the target surface in a direction normal to the plane of the target. To maintain the advantageous, spot displacement-reducing configuration, this additional movement must be compensated for by introducing a larger tip angle β. Nonetheless, despite this requirement for a greater tip angle, it has been found that the effect of thermal expansion of the target can be successfully compensated for anodes with shapes such as that of the present example. As with the preceding examples, the anode is tipped in the opposite direction to the target tip angle, which maintains the desired angles between the electron beam 803 and the window central axis 837.

[0092] The preceding description of example anodes involves the second, operating state of the anode corresponding to a state of thermal equilibrium reached by the anode when operating at a given power level. However, it has been found by way of simulations that, even under a non-equilibrium condition, the thermal displacement of the surface of some example anodes is significantly reduced in comparison with the uncorrected, uncompensated movement experienced with conventional anodes. Uncompensated movement of the spot location can typically be several tens of microns in magnitude, whereas, even in a transient, non-equilibrium state, the spot movement of the spatial position of the focal spot for anodes according to the present disclosure is less than 10 microns. Thus for a given one of such anodes the second state may correspond to a non-equilibrium state at which the intersection of the target surface and the beam is substantially unmoved in space from its position at the first, comparatively unheated state.

[0093] FIG. 9 shows a graph of the thermal expansion of an anode similar to that of the third example, whereby the spot is not on-axis with the anode. The figure illustrates the normal and tangential components of thermal displacement of the focal spot for the anode, in which the initial intersection of the beam and the target surface is a distance of 5 mm from the anode axis, in use with an X-ray tube operating at 50 W over an operating period of 20 minutes. It can be seen that the greatest degree of expansion occurs during the first 10 minutes of that period, after which the movement largely subsides. Although the tangential movement of the target surface is large and is about 70 microns in the operating duration, this component does not contribute the spot movement, and so is not detrimental. The thermal movement of the spot in a direction normal to the target peaks, at approximately 2.4 microns, in about 10 seconds, and subsequently approaches zero over a duration of approximately 5 minutes. As alluded to above, the different time constants of these two movement components result from the different quantities of materials involved. The tangential motion of the spot involves the expansion of the entire anode, whereas the expansion of the spot normal to the target involves only a small amount of material directly under the spot.

[0094] The geometries of the examples depicted are in part based upon an assumption that, under thermal equilibrium, the X-ray tube component temperatures change in proportion to the applied power. This assumption leads to the configured anode shape including a target surface that is flat or linear along one direction, namely the principal axis of expansion. That is to say, the assumed movement of the surface both tangent and normal to the target is always in direct proportion to the applied power. However, because the removal of heat from the anode might, in practice, occur by way of a non-linear process, such as via convection, small residual errors in the surface location might occur when the power is at intermediate levels. In order to compensate for these small errors, the surface may be curved or shaped in such a way that the path defined across it is no longer linear. Linear shapes can additionally include cone-shaped targets, as used in rotating anodes such as those described later in this disclosure, as they have a linear cross section in one direction.

[0095] It will be understood that, beyond configuring an anode shape that substantially eliminates beam spot displacement between a first and second operating state, the above-described principles may also be applied in order to determine the exact shape of a surface which would compensate for thermal movement over intermediate operating points. However, typically a planar (or conical, in the case of rotating anodes) target surface is typically a more practical geometry, owing to difficulty in manufacturing other, more complex shapes. For example, the surface might be spherical, ellipsoidal or toroidal in shape, but would be so designed as to compensate for the non-linear behaviour of the X-ray tube as a function of power. A wide variety of target shapes are envisaged, which are constructed, positioned and oriented so as to cancel substantially the apparent movement of the beam spot attributable to thermal expansion of the anode and target.

[0096] Thus it is possible to mount anodes having such geometries within an X-ray tube and orienting the anode and target surface in such a way that the thermal expansion tangential to the target does not contribute to spot movement, and thermal expansion normal to the target is compensated for with that addition of a small tip angle. Because this target plane must typically be visible to the X-ray tube window from an angle in the range 5 to 45 degrees above the plane surface, the anodes can accordingly be mounted with their axis at an angle that is neither perpendicular to, nor parallel with, the desired direction of X-ray emission. This leads to the need for a modified X-ray tube device, in which the anode is mounted such that its axis is set at an angle in the range 5 to 45 degrees in relation to the desired angle of emission or X-ray window axis, or observation angle. For ease of construction, conventional X-ray tubes have anodes with axes that are either collinear with the X-ray window axis or observation angle, or the electron beam axis. Such conventional geometries are typically less suitable for use with anodes according to this disclosure. An X-ray tube can be constructed with a large X-ray window with an axis less than 5 degrees from the target plane or offset from the anode axis. However, observations must be made at an angle with respect to this axis. It will be understood that this is not an optimal geometry for practical purposes of mounting or X-ray collection. Therefore, the most optimal and useful geometries require an X-ray tube device that is adapted to accommodate an anode mounted at an angle that departs from the aforementioned arrangements used in conventional X-ray tube designs.

[0097] The manner in which these examples reduce the spot movement effects from which conventional arrangements suffer is illustrated further by FIGS. 10-13. FIG. 10 and FIG. 11 show example anode geometries according to the prior art. FIG. 10 depicts a typical “end window” configuration, while FIG. 11 shows a typical “side window” configuration. In each case the orientation of the anode surface at the target region 1023, 1123 with respect to the direction in which the surface expands, owing to heating in use, away from the location 1013, 1113 at which the anodes are fixed to the X-ray tube is such that the intersection of the surface and the electron beam 1003, 1103 is caused to move relative to the X-ray tube. This causes the transverse spot movement, with respect to the X-ray detector direction, depicted in the figures.

[0098] FIGS. 12 and 13 depict a part of an anode similar to the first example anode and the second example anode respectively. It can be seen that the transverse spot movement with respect to the window access 1237, 1337 is significantly reduced compared with the prior art comparative examples. In FIG. 12, the alignment of the principal expansion axis of material at the beam spot in the target region is aligned with the plane of the target region. Thus the principal component of the expansion experienced by the materials directly under the beam spot does not cause any transverse spot movement. However, in the example of FIG. 12, non-uniform thermal expansion causes a peak or bulge to form proximal to the electron beam 1203 intersection point as a result of surface heating. As a result, a small degree of axial spot movement, compared with the movement experienced in the prior art examples of FIGS. 10 and 11, occurs. Consequently the location of the beam spot when the anode is cold, or at its first state 1231 is slightly different from the spot location when the anode has been heated such that the peak forms 1233.

[0099] The corrective tilt described above in relation to the second example anode can be seen in FIG. 13 to compensate for the localised surface heating that causes the transverse spot movement shown in FIG. 12. The location of the beam spot at the first state 1331 has the same position and space as the location on the surface of the beam spot in the second, heated state 1333, as a result of the normal expansion component being cancelled by the tilt angle. The surface movement attributable to the bulk heating of the anode moves material away from the beam by the same amount as, but in the opposite direction to, the surface bulge that forms because of localised heating under the beam 1303.

[0100] FIGS. 14 and 15 illustrate the effect of the orientation, with respect to the window axis or X-ray detector, of the principal axis of expansion of example anodes upon the observable transverse displacement of the focal spot caused by thermal expansion. The graphs demonstrate the advantageous effect achieved by examples according to this disclosure alongside comparative examples. The various examples are depicted together with their corresponding spot movement and temperature values for that geometrical configuration.

[0101] In the examples shown on the graph in FIG. 14, the anode geometry is such that the focal spot is coincident with the centre line of the anode 1435, principal axis of expansion. It can be seen that the 180-degree case, Example B, which corresponds to examples in this disclosure, produces transverse spot movement of less than 1/30 of the spot movement produced by the comparative example of the “side window” configuration, and 1/10 of the spot movement produced by the comparative example of the “end window” configuration. For the 178.45-degree case, Example A, which also corresponds to an example according to this disclosure, the transverse spot movement is eliminated entirely.

[0102] The graph additionally shows the effect of the expansion axis orientation upon the spot temperature under the example operating conditions shown. For Examples A and B the spot temperature is higher, owing to the presence of less anode material under the spot than in the comparative examples illustrated. However, it is possible to compensate for this effect and the resulting localized thermal expansion as described with reference to the following examples.

[0103] FIG. 15 similarly depicts the relationship between expansion axis orientation-spot movement relationship, for example anodes that are shaped such that the spot is not coincident with the centre line of the anode 1535. As a result of the offset spot location, Example D (the 180-degree case) according to the present disclosure produces transverse movement of only 1/10 of the spot movement produced by the “side window” comparative example and ¼ of the spot movement produced by the “end window” comparative example. However, for Example C (the 174.92-degree case) according to this disclosure, the spot transverse movement is eliminated entirely, as with Example A. However, the high spot temperatures experienced with Examples A and B are not seen with Examples C and D. With the geometries of these examples in FIG. 15, the temperature is reduced by way of the extra anode material present beneath the beam spot permitting heat to be dissipated from that region at a faster rate.

[0104] As alluded to above, the design principles applied in the preceding examples may also be applied to rotating-anode designs wherein the target face of a rotating anode X-ray tube is perpendicular to the axis of rotation and thermal expansion along the axis of rotation can be controlled by appropriate mounting methods. An example of a typical conventional rotating anode is shown in FIG. 16. Such designs include an anode 1642 adapted to spin about an axis of rotation that is parallel with the electron beam 1603. The target region 1609 of the surface under the beam at a given time is part of a truncated conical surface 1648. This surface moves due to thermal expansion in the depicted direction, causing X-ray spot movement as seen in conventional stationary-target X-ray tubes.

[0105] The following examples illustrate how the shapes of rotatable anodes, as with the stationary examples described above, may be configured so as to eliminate substantially the thermal beam spot movement.

[0106] FIG. 17 shows a fourth example anode arranged in a rotating-anode X-ray tube similar to the convention or arrangement shown in FIG. 16, and applying the spot movement-reducing principles described above. In the present example the direction of thermal expansion of anode material on the target surface 1709 under the beam 1703 is radial with respect to the anode rotation axis. This is because the principal expansion experienced as the anode 1701 is heated in use is away from the central rotation axis around which the anode is rotatably mounted using the bearings and rotor schematically depicted, while the rotation mechanism is configured such that thermal expansion parallel to the rotation axis does not occur. This latter affect may be achieved by way of conventional, passive thermal expansion compensation techniques. Accordingly, the present example has a geometry adapted to eliminate radial thermal expansion, and is therefore shaped such that the target surface 1709 lies in a plane orthogonal to the rotation axis. This allows the movement of the beam spot that would be seen in relation to the instrument/observer axis to be substantially eliminated.

[0107] A fifth example anode according to the invention, which is also a rotating anode, is shown in FIG. 18. In this example, passive compensation techniques are not applied to the bearings and rotor part of the arrangement, and accordingly the geometry of the anode 1801 is adapted to compensate for a component of thermal expansion parallel to the rotation axis.

[0108] It can be seen that the target surface 1809 is therefore shaped so as to be aligned with the direction of thermal expansion away from the mounting location within the X-ray tube 1813. This conical section target surface, which is swept by the beam 1803 in use therefore allows the total elimination of thermal expansion beam spot displacement that would otherwise arise from a combination of radial and axial components.

[0109] Anode geometries such as these may be applied and, combined with conventional temperature compensation techniques (if necessary, using materials with differing coefficients of thermal expansion) applied to the anode mount, reduce spot movement relative to existing rotating anode designs.

[0110] FIG. 19 shows, for rotating-anode examples according to the invention and comparative rotating anode examples, the effect of the anode geometry on visible spot movement in the same way as FIGS. 14 and 15. It has been found that, because of the non-uniform construction of the anode, aligning the principal axis of expansion with the target face (180-degree case) does not result in elimination of thermal displacement. Rather, this configuration produces a 40% reduction in spot movement, as illustrated. However, for Example E according to the present disclosure (the 160.64-degree case), the spot transverse movement is eliminated entirely.

[0111] An example method for determining an anode shape according to the preceding examples will now be described. For this example method, a number of initial assumptions are made: (1) There exists an electron beam with a well-defined central axis; (2) The central axis of the electron beam is fixed in space in relation to some virtual or real reference point on the exterior of the X-ray tube such as for example, the centre of an X-ray window or the centroid of all mounting locations; (3) At the instant of initial operation of the X-ray tube, called the initial state and corresponding to the first state in this example, with the X-ray tube at a uniform room temperature, the target surface location is fixed in space or that in the absence of vibration, a rotating target swept surface is fixed in space; (4) At the point of initial operation, the initial state, the electron beam strikes the target surface to form an X-ray spot and that the centroid of this spot is called the initial X-ray spot location; (5) There is significant heat produced by the X-ray spot in operation, and without proper heat management the target under the spot will melt or evaporate before the desired X-ray tube operating lifetime; (6) There is an anode which is affixed to or is a part of the X-ray target which performs two functions: (a) providing the electrical potential and conduct electrical current necessary to accelerate and capturing electrons from the electron beam, and (b) conducting heat away from the X-ray spot location; (7) There is a final operating state, corresponding to the second state in this example, such that either: (a) under steady operation, the target, anode, and X-ray tube approaches a steady state distribution of temperatures, or that (b) there is a well-defined repeatable final distribution of temperatures after an a priori known operating time; (8) The initial X-ray spot is defined as the intersection of the electron beam and the surface of the target. X-rays are also produced within the volume of the target. However, for the purpose of this design process it is only necessary to consider the X-rays produced at the surface of the target; (9) The electron beam need only intersect the surface at any desired angle necessary to achieve the spot size and shape desired. Scenario 1: In order to produce a spot on the surface which spreads out the electron beam energy, the electron beam axis will be chosen to be close to parallel with the surface. Scenario 2: In order to obtain a round spot on the target surface from an almost-round electron beam, the electron beam axis will be almost normal to the surface. That is to say, the angle is chosen to achieve the desired final X-ray spot characteristics, but a wide range of variants is envisaged; (10) The angle between the normal vector of the target surface at the spot centroid and the observation or exposure angle, or X-ray window axis, is also chosen to achieve the desired design goals. Scenario 1: Observation or exposure angles are chosen to be nearly normal to the target surface tend to have a higher X-ray flux. Scenario 2: Observation or exposure angles are closer to tangential to the surface and tend to produce an apparent spot which is foreshortened in one direction. That is, the angle is chosen to achieve the desired final X-ray output characteristics, but a wide range of variants is envisaged.

[0112] As explained earlier in this disclosure, the goal of the design process is to ensure that the initial-state spot centroid location, as defined above, coincides exactly in space with the final state spot centroid location on the target (or rotating anode swept target surface in the case of rotating-anode arrangements).

[0113] The present example design process proceeds in steps and is iterative:

[0114] Step 1. The design electron beam angle and observation angle are chosen as described in assumptions (7) and (8) above.

[0115] Step 2. The target surface orientation under the spot is chosen to satisfy the conditions in Step 1.

[0116] Step 3. A plane tangent to the initial condition target surface at the spot centroid is defined as the “target tangent plane”.

[0117] Step 4. A single centroid of the anode mounting locations is chosen to be in the plane defined in Step 3 such that other conditions within the X-ray tube design are satisfied. For example, there is a general requirement for X-ray tubes, that the anode have a very high positive electrical potential relative to the electron gun and that there needs to be a sufficient thickness and length of insulation between the mounting locations and the electron gun and other parts of the X-ray tube to assure that this potential may be maintained without electrical breakdown. And yet, the end of the anode must be as close as possible to the spot to reduce the spot temperature in operation. The centroid of mounting locations and the centroid of the spot define a line which will be called the “principal axis of expansion”.

[0118] Step 5. Having chosen a centroid and a mounting location for the anode, an anode material much as copper, which has a high thermal conductivity, is chosen to remove as much heat as possible over the length of the anode from the spot to some heat sink or heat exchanger on the opposite end of the anode. For rotating anodes, most of the heat is removed through radiation and so not all heat is removed through conduction. Most typical materials used in X-ray tubes will expand when heated and this causes the surface under the spot to move away from the centroid of the mounting location along the principal axis of expansion. It is in fact this property for conventional X-ray tubes where the target plane does not lie along the principal axis of expansion which causes the unwanted spot movement in existing designs. To an initial level of refinement, the design process according to this example can be ended at this stage. Most of the thermal expansion of the anode will be along this axis which in this invention at this step of the design, the expansion is coincident with the initial plane of the target and spot centroid.

[0119] Step 6. However, heating of the target and the anode are not uniform and while most thermal expansion occurs away from the anode mounting centroid, some expansion occurs normal to the target surface near the spot location and these subsequent steps will relate to compensating for that component of the thermal expansion.

[0120] Step 7. Because a greater cross-sectional area of conductive material along the heat conduction path reduces the temperature drop caused from heat dissipation at the spot, the centroid of the anode mounting locations can be offset from the principal axis of expansion to create more material near the spot location. This, however, results in additional expansion of the material under the spot away from the principal axis of expansion, and this must also be compensated for in the final, fully refined design. The offset is determined as a trade-off between the reduction in the spot temperature and the physical constraints on the exterior and interior dimension of the X-ray tube and the added complexity of the compensation mechanism outlined below.

[0121] Step 7. Either through numerical computer simulation, detailed theoretical calculation, approximation, or actual measurement, the intermediate spot location is then determined at the final operating state considering all thermal expansion of the target and anode as a whole. The spot location will not, in general, be in the initial target tangent plane. As thus calculated, this intermediate spot location will not be at the desired location of final refined embodiment. This is due to non-uniform heating and thermal expansion at and below the surface of the target.

[0122] Step 8. Having now determined the intermediate spot location, the normal distance from the intermediate spot centroid to the initial target tangent plane is determined and is now called distance “Y”. Also, the distance along the original target tangent plane from the intermediate spot location to the original spot location is determined and is now called distance “X”. These two distances are perpendicular to each other.

[0123] Step 9. A direction which is normal to the target tangent plane and points out of the target surface is defined as the “target normal”. The direction from the spot centroid toward the anode mounting centroid is defined as the “principal direction”. A direction is defined by the right-hand rule which is perpendicular to target normal and the principal direction and is in the plane of the target, and is in the direction defined by the target normal cross product with principal direction. A straight line in this direction which coincides with the spot centroid is defined as the “tilt axis”.

[0124] Step 10. If the original target tangent plane was tilted by this “tilt angle” on the tilt axis by a positive amount equal to the arctangent of the ratio of Y over X, then as the target surface moves in a direction due to thermal expansion along the principal direction of expansion by an amount Y, the surface will have moved away from the original spot location an amount X. However, due to thermal expansion of the surface, the true surface of the target expands by exactly this amount X and so caries the spot back to its original location. So, the spot will not have moved at all in relation to the original initial location.

[0125] Step 11. However, if the target tangent plane is tilted as in Step 10 above, the original conditions from Step 2 will be violated. So, to keep the conditions from Step 2, the principal axis of expansion must be tilted in the opposite sense to compensating tilt angle. That is, the original target tangent plane is rotated by the tilt angle and the principal axis of expansion is rotated by a negative tilt angle. In this way, the original conditions for Step 2 are maintained and the target expands in such as way so that the original spot location and the final spot location coincide.

[0126] Step 12: Since in practice, a slight change to the relative location of the anode with respect to other parts of the X-ray tube may need non-trivial changes to the other components of the X-ray tube, the above Steps 7 through 11 are repeated until no further adjustments in the design are required. This concludes example design process, and anode having the specified shape may be formed and mounted within the X-ray tube in accordance with the determined geometry.