CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] The Present Patent Application is a continuation-in-part of U.S. Patent Application No. 15/166,274, filed May 27, 2016 and entitled DIVERGING X-RAY SOURCES USING LINEAR ACCUMULATION, which is a continuation-in-part of U.S. Patent Application No. 14/999,147, filed April 1, 2016 and entitled X-RAY SOURCES USING LINEAR ACCUMULATION, which claims the benefit of U.S. Provisional Patent Application No. 62/141,847, filed April 1, 2015 and entitled ADDITIONAL X-RAY SOURCE DESIGNS USING MICROSTRUCTURED TARGETS, and U.S. Provisional Patent Application No. 62/155,449, filed April 30, 2015, and entitled X-RAY TARGET FABRICATION, both of which are incorporated herein by reference in their entirety; and which in turn is also a continuation-in- part of U.S. Patent Application No. 14/490,672, filed Sept. 19, 2014 and entitled X-RAY SOURCES USING LINEAR ACCUMULATION, which claims the benefit of U.S. Provisional Patent Application Nos. 61/880,151, filed on Sep. 19, 2013, 61/894,073, filed on Oct. 22, 2013, 61/931,519, filed on Jan. 24, 2014, and 62/008,856, filed on Jun. 6, 2014, all of which are incorporated herein by reference in their entirety.

BACKGROUND

Field of the Invention

[0002] The embodiments of the invention disclosed herein relate to high-brightness sources of x-rays. Such high brightness sources may be useful for a variety of applications in which x- rays are employed, including manufacturing inspection, metrology, crystallography, spectroscopy, structure and composition analysis and medical imaging and diagnostic systems.

Description of the Prior Art

[0003] X-ray sources have been used for over a century. One common x-ray source design is the electron bombardment reflection x-ray source, in which an electron emitter generates a beam of electrons that are accelerated onto an x-ray target by a voltage differential. The collision of the electrons into the target induces several effects, including the generation of x- rays, including bremsstrahlung continuum and characteristic x-rays of the target material.

[0004] For many techniques such as micro x-ray fluorescence, micro x-ray diffraction, crystallography, etc., there is a general a need for a microfocus x-ray source and optic combination that delivers a high brightness beam of x-rays within a small spot size onto a sample, and preferably of x-ray energies that optimal for the specific application. Common approaches to improving brightness of the source include: use of electron optics to guide and shape the path of the electrons, forming a more concentrated, focused beam at the target, use of target materials with higher atomic number to increase bremsstrahlung production (its efficiency scales with atomic number), and use of thermal strategies that allow higher electron power loading onto the target before melting. Thermal approaches include depositing the x- ray generating material on top of a substrate of high thermal conductivity such as diamond or beryllium, mounting the target onto a heat sink or heat pipe, and/or adding water coolant channels within the target. [0005] In addition, low take-off angles are utilized to maximize apparent brightness. Although x-rays may be radiated isotropically, only the x-ray radiation within a small solid angle produced in the direction of a window in the source will be useful. X-ray brightness (also called "brilliance" by some), defined as the number of x-ray photons per second per solid angle in mrad ² per area of the x-ray source in mm ² , can be increased by adjusting the geometric factors to maximize the collected x-rays. Generally, the surface of an x-ray target in a source is mounted at lower take-off angles (the angle between the target surface and the center of the emitted x-ray cone), so that the apparent spot size is reduced and apparent brightness is increased.

[0006] In principle, it may appear that a take-off angle of 0° would have the largest possible brightness. In practice, radiation at 0° occurs parallel to the surface of a solid metal target for conventional sources, and since the x-rays must propagate along a long length of the target material before emerging, most of the produced x-rays will be attenuated (reabsorbed) by the target material, reducing brightness. Thus, a source with take-off angle of around 6° to 15° (depending on the source configuration, target material, and electron energy) is conventionally used.

[0007] Despite these developments, there are still limits on the ultimate x-ray brightness that may be achieved with micro-focus x-ray sources.

SUMMARY

[0008] The present technology, roughly described, includes an x-ray illumination beam system that includes an electron emitter and a target having one or more target microstructures, collectively referred to as an x-ray source. The one or more microstructures may be the same or different material, and may be embedded or placed atop a substrate formed of a heat-conducting material. The x-ray source may emit x-rays towards an optic system.

[0009] The optic system may include one or more optics that are matched to one or more target microstructures. The matching may can be achieved by selecting optics with the geometric shape, size, and surface coating that collects as many x-rays as possible from the source and at an angle that satisfies the critical reflection angle of the x-ray energies of interest from the target. In some instances, the matching is based on maximizing the numerical aperture (NA) of the optics for x-ray energies of interest. The optic system may be configured to focus or collimate the beam, and may include a monochromator.

[0010] The x-ray illumination system allows for an x-ray source, comprised of an electron emitter and a target having one or more microstructures, to generate x-rays having different energies. The x-ray illumination system can be used in a variety of applications, including but not limited to spectroscopy, fluorescence analysis, microscopy, tomography, diffraction and other applications.

[0011] In some instances, an x-ray illumination beam system can provide multiple characteristic x-ray energies from a plurality of x-ray generating materials selected for its x- ray generating properties. The x-ray illumination system can include a vacuum chamber, first window, and an electron optical system. The vacuum chamber includes an electron emitter. The first window is transparent to x-rays and attached to a wall of the vacuum chamber. The electron optical system focusses an electron beam from the electron emitter. In the x-ray illumination beam system, a target can include a plurality of microstructures coupled to a substrate, wherein each microstructure includes a material selected for its x-ray generating properties, and in which a lateral dimension of said material is less than 250 microns;

[0012] The x-ray illumination beam system can include a means to position the x-ray target relative to the electron beam and a plurality of total external reflection mirror optics. The optics are matched to the x-ray spectra produced by at least one of the plurality of microstructures and positioned to collect x-rays generated by the at least one of the plurality of microstructures when bombarded by the focused electron beam.

BRIEF DESCRIPTION OF THE DRAWINGS

[0013] FIGURE 1 illustrates a schematic cross-section diagram of a standard prior art reflection x-ray source.

[0014] FIGURE 2 illustrates a cross-section diagram the interaction of electrons with a surface of a material in a prior art x-ray source.

[0015] FIGURE 3 illustrates the typical x-ray radiation spectrum for a tungsten target.

[0016] FIGURE 4A illustrates x-ray radiation from a prior art target for a target at a tilt angle of 60 degrees.

[0017] FIGURE 4B illustrates x-ray radiation from a prior art target for a target at a tilt angle of 45 degrees.

[0018] FIGURE 4C illustrates x-ray radiation from a prior art target for a target at a tilt angle of 30 degrees.

[0019] FIGURE 5A illustrates a schematic cross-section view of a prior art rotating anode x- ray source.

[0020] FIGURE 5B illustrates a top view of the anode for the rotating anode system of FIGURE 5A.

[0021] FIGURE 6 illustrates a schematic cross-section view of an embodiment of an x-ray system according to the invention.

[0022] FIGURE 7 illustrates a perspective view of a target comprising a grid of embedded rectangular target microstructures on a larger substrate that may be used in some embodiments of the invention. [0023] FIGURE 8 illustrates a cross-section view of electrons entering a target comprising target microstructures on a larger substrate that may be used in some embodiments of the invention.

[0024] FIGURE 9 illustrates a cross-section view of some of the x-rays radiated by the target of FIGURE 8.

[0025] FIGURE 10 illustrates a perspective view of a target comprising multiple rectangular microstructures arranged in a linear array on a substrate with a recessed region that may be used in some embodiments of the invention.

[0026] FIGURE 11 A illustrates a perspective view of a target comprising a grid of embedded rectangular target microstructures that may be used in some embodiments of the invention.

[0027] FIGURE 11B illustrates a top view of the target of FIGURE 11 A.

[0028] FIGURE 11C illustrates a side/cross-section view of the target of FIGURES 11 A and 11B.

[0029] FIGURE 12 illustrates a cross-section view of a portion of the target of FIGURES 11A - llC, showing thermal transfer to a thermally conducting substrate under electron beam exposure.

[0030] FIGURE 13 illustrates a cross-section view of a target as shown in of FIGURE 12 having an additional overcoat and a cooling channel.

[0031] FIGURE 14 illustrates a collection of x-ray emitters arranged in a linear array to produce linear accumulation as may be used in some embodiments of the invention.

[0032] FIGURE 15 illustrates a plot of the 1/e attenuation length for several materials for x- rays

[0033] FIGURE 16 illustrates a schematic cross-section view of an embodiment of an x-ray system according to the invention comprising multiple electron emitters. [0034] FIGURE 17 A illustrates a schematic cross-section view of an embodiment of the invention comprising a ring pattern of x-ray generating structures on a rotating anode.

[0035] FIGURE 17B illustrates a schematic perspective view of the rotating anode of the embodiment of FIGURE 17 A.

[0036] FIGURE 17C illustrates a cross-section view of the rotating anode of the embodiment of FIGURE 17 A.

[0037] FIGURE 18 illustrates a schematic perspective view of a portion of an embodiment of the invention comprising a line pattern of x-ray generating structures on a rotating anode.

[0038] FIGURE 19A illustrates a cross-section view of the x-ray generating portion of a source according to an embodiment of the invention.

[0039] FIGURE 19B illustrates a perspective view of the x-ray generating portion of the source illustrated in FIGURE 19A.

[0040] FIGURE 19C illustrates detailed cross-section view of the x-ray generating portion of the source illustrated in FIGURE 19A.

[0041] FIGURE 20A illustrates a top-down view of the x-ray generating portion of a target used in the embodiment illustrated in FIGURES 19A - 19C.

[0042] FIGURE 20B illustrates an end view of the x-ray generating portion of a target used in the embodiment illustrated in FIGURES 19A - 19C.

[0043] FIGURE 20C illustrates a cross-section side view of the x-ray generating portion of a target used in the embodiment illustrated in FIGURES 19A - 19C.

[0044] FIGURE 21A illustrates a top-down view of the x-ray generating portion of a target having non-uniform x-ray generating structures. [0045] FIGURE 21B illustrates an end view of the x-ray generating portion of the target of FIGURE 21A.

[0046] FIGURE 21C illustrates a cross-section side view of the x-ray generating portion of the target of FIGURE 21A.

[0047] FIGURE 22A illustrates a top-down view of the x-ray generating portion of the target used in the embodiment illustrated in FIGURES 19A - 19C under electron bombardment.

[0048] FIGURE 22B illustrates an end view of the x-ray generating portion of a target used in the embodiment illustrated in FIGURES 19A - 19C under electron bombardment.

[0049] FIGURE 22C illustrates a cross-section side view of the x-ray generating portion of a target used in the embodiment illustrated in FIGURES 19A - 19C under electron bombardment.

[0050] FIGURE 23 illustrates a cross-section side view of the x-ray generating portion of a target comprising a powder of x-ray generating material.

[0051] FIGURE 24A illustrates a top-down view of the x-ray generating portion of a target comprising structures of x-ray generating material arranged along the length dimension.

[0052] FIGURE 24B illustrates an end view of the x-ray generating portion of the target of FIGURE 24A.

[0053] FIGURE 24C illustrates a cross-section side view of the x-ray generating portion of the target of FIGURE 24A.

[0054] FIGURE 25 illustrates a cross-section view of the x-ray generating portion of a source according to the invention paired with an external x-ray optical element.

[0055] FIGURE 26 illustrates a cross-section view of a rotating anode according to the invention generating x-rays at a 0 ^s take-off angle. [0056] FIGURE 27 illustrates a cross-section view of a rotating anode according to the invention having a beveled surface and a non-zero take-off angle.

[0057] FIGURE 28 is a block diagram of an x-ray beam delivery system.

[0058] FIGURE 29 is a block diagram of a bombarding electron beam and emitted x-rays associated with a target.

[0059] FIGURE 30 is a view of an x-ray beam footprint on a target.

[0060] FIGURE 31 is a top view of a target having multiple microstructures.

[0061] FIGURE 32 is a cross-sectional side-view of a target having multiple embedded wire microstructures.

[0062] FIGURE 33 is a cross-sectional side view of a target having multiple surface mounted wire microstructures.

[0063] FIGURE 34A is a block diagram of an optic that provides a collimated x-ray beam.

[0064] FIGURE 34B is a block diagram of an optic similar to the one described by FIGURE 34A that provides focused x-rays.

[0065] FIGURES 35A-C illustrate example cross-sections of axially symmetric optics with different reflecting interior shapes.

[0066] FIGURES 36A-B illustrate an optic with an interior surface coating.

[0067] FIGURE 37A illustrates an x-ray beam delivery system utilizing a first pair of matched targets and optics.

[0068] FIGURE 37B illustrates the x-ray beam delivery system utilizing a second pair of matched target microstructures and optics. [0069] FIGURE 38 illustrates an x-ray source and optics within a system using X-ray fluorescence (XRF) to analyze a sample.

[0070] FIGURE 39 illustrates a method for providing a matched target and optic from a plurality of pairs of matched targets and optics.

DETAILED DESCRIPTION

1. Exemplary Embodiment

[0071] FIGURE 6 illustrates an embodiment of a reflective x-ray system 80-A according to the invention. As in the prior art reflective x-ray system 80 described above, the source comprises a vacuum environment (typically 10 ^-6 torr or better) commonly maintained by a sealed vacuum chamber 20 or active pumping, and manufactured with sealed electrical leads 21 and 22. The source 80-A will typically comprise mounts 30, and the housing 50 may additionally comprise shielding material, such as lead, to prevent x-rays from being radiated by the source 80-A in unwanted directions.

[0072] Inside the chamber 20, an emitter 11 connected through the lead 21 to the negative terminal of a high voltage source 10 serves as a cathode and generates a beam of electrons 111. Any number of prior art techniques for electron beam generation may be used for the embodiments of the invention disclosed herein. Additional known techniques used for electron beam generation include heating for thermionic emission, Schottky emission (a combination of heating and field emission), or emitters comprising nanostructures such as carbon nanotubes). [For more on electron emission options for electron beam generation, see Shigehiko Yamamoto, "Fundamental physics of vacuum electron sources", Reports on Progress in Physics vol. 69, pp. 181-232 (2006)].

[0073] As before, a target 1100 comprising a target substrate 1000 and regions 700 of x-ray generating material is electrically connected to the opposite high voltage lead 22 and target support 32, thus serving as an anode. The electrons 111 accelerate towards the target 1100 and collide with it at high energy. The collision of the electrons 111 into the target 1100 induces several effects, including the generation of x-rays, some of which exit the vacuum tube 20 and are transmitted through at least one window 40 and/or an aperture 840 in a screen 84.

[0074] In some embodiments of the invention, there may also be an electron beam control mechanism 70 such as an electrostatic lens system or other system of electron optics that is controlled and coordinated with the electron dose and voltage provided by the emitter 11 by a controller 10-1 through a lead 27. The electron beam 111 may therefore be scanned, focused, de-focused, or otherwise directed onto the target 1100.

[0075] As illustrated in FIGURE 6, the alignment of the microstructures 700 may be arranged such that the bombardment of several of the microstructures 700 by the electron beam or beams 111 will excite radiation in a direction orthogonal to the surface normal of the target such that the intensity in the direction of view will add or accumulate in that direction. The direction may also be selected by means of an aperture 840 in a screen 84 for the system to form the directional beam 888 that exits the system through a window 40. In some embodiments, the aperture 840 may be positioned outside the vacuum chamber, or, more commonly, the window 40 itself may serve as the aperture 840. In some embodiments, the aperture may be inside the vacuum chamber.

[0076] Targets such as those to be used in x-ray sources according to the invention disclosed herein have been described in detail in the co-pending US Patent Application entitled STRUCTURED TARGETS FOR X-RAY GENERATION (US Patent Application 14/465,816, filed Aug. 21, 2014), which is hereby incorporated by reference in its entirety, along with the provisional Applications to which this co-pending Application claims benefit. Any of the target designs and configurations disclosed in the above referenced co-pending Application may be considered for use as a component in any or all of the x-ray sources disclosed herein.

[0077] FIGURE 7 illustrates a target 1100 as may be used in some embodiments of the invention. In this figure, a substrate 1000 has a region 1001 that contains an array of microstructures 700 comprising x-ray generating material (typically a metallic material) arranged in a regular array of right rectangular prisms. Electrons 111 bombard the target and generate x-rays in the microstructures 700. The material in the substrate 1000 is selected such that it has relatively low energy deposition rate for electrons in comparison to the x-ray generating microstructure material (typically by selecting a low Z material for the substrate). The material of the substrate 1000 may also be chosen to have a high thermal conductivity, typically larger than 100 W/(m °C). The microstructures are typically embedded within the substrate, i.e. if the microstructures are shaped as rectangular prisms, it is preferred that at least five of the six sides are in close thermal contact with the substrate 1000, so that heat generated in the microstructures 700 is effectively conducted away into the substrate 1000. However, targets used in other embodiments may have fewer direct contact surfaces. In general, when the term "embedded" is used in this disclosure, at least half of the surface area of the microstructure will be in close thermal contact with the substrate.

[0078] A target 1100 according to the invention may be inserted as the target in a reflecting x-ray source geometry (e.g. FIGURE 1), or adapted for use as the target used in the rotating anode x-ray source of FIGURES 5A and 5B.

[0079] It should be noted that the word "microstructure" in this Application will only be used for structures comprising materials selected for their x-ray generating properties. It should also be noted that, although the word "microstructure" is used, x-ray generating structures with dimensions smaller than the micrometer scale, or even as small as nano-scale dimensions (i.e. greater than 10 nm) may also be described by the word "microstructures" as used herein.

[0080] The microstructures may be placed in any number of relative positions throughout the substrate 1000. In some embodiments, as illustrated in FIGURE 7, the target 1100 comprises a recessed shelf 1002. This allows the region 1001 comprising an array of microstructures 700 to be positioned flush with, or close to, a recessed edge 1003 of the substrate, and produce x-rays at or near zero angle without being reabsorbed by the substrate 1000, while providing a more symmetric heat sink for the heat generated when exposed to electrons 111. Some other embodiments may preferably have the microstructures placed near the edge of the substrate to minimize self-absorption.

[0081] FIGURE 8 illustrates the relative interaction between a beam of electrons 111 and a target comprising a substrate 1000 and microstructures 700 of x-ray generating material. Three electron interaction volumes are illustrated, with two representing electrons bombarding the two shown microstructures 700, and one representing electrons interacting with the substrate.

[0082] As discussed in Eqn. 1 above, the depth of penetration can be estimated by Potts' Law. Using this formula, Table II illustrates some of the estimated penetration depths for some common x-ray target materials.

[0083] For the illustration in FIGURE 8, if 60 keV electrons are used, and diamond (Z=6) is selected as the material for the substrate 1000 and copper (Z=29) is selected as the x-ray generating material for the microstructures 700, the dimension marked as R to the left side of FIGURE 8 corresponds to a reference dimension of 10 microns, and the geometric depth DM of the x-ray generating material, which, when set to be 2/3 (66%) of the electron penetration depth for copper, becomes DM ~ 3.5 mm.

Table II: Estimates of penetration depth for 60 keV electrons into some materials.

[0084] The majority of characteristic Cu K x-rays are generated within depth DM. The electron interactions below that depth are less efficient at generating characteristic Cu K-line x-rays but will contribute to heat generation. It is therefore preferable in some embodiments to set a maximum thickness for the microstructures in the target in order to optimize local thermal gradients. Some embodiments of the invention limit the depth of the microstructured x-ray generating material in the target to between one third and two thirds of the electron penetration depth of the x-ray generating material at the incident electron energy, while others may similarly limit based on the electron penetration depth with respect to the substrate material. For similar reasons, selecting the depth DM to be less than the electron penetration depth is also generally preferred for efficient generation of bremsstrahlung radiation.

[0085] Note: Other choices for the dimensions of the x-ray generating material may also be used. In targets as used in some embodiments of the invention, the depth of the x-ray generating material may be selected to be 50% of the electron penetration depth of either the x-ray generating material or the substrate material. In other embodiments, the depth DM for the microstructures may be selected related to the "continuous slowing down approximation" (CSDA) range for electrons in the material. Other depths may be specified depending on the x-ray spectrum desired and the properties of the selected x-ray generating material.

[0086] Note: In other targets as may be used in some embodiments of the invention, a particular ratio between the depth and the lateral dimensions (such as width WM and length LM) of the x-ray generating material may also be specified. For example, if the depth is selected to be a particular dimension DM, then the lateral dimensions WM and/or LM may be selected to be no more than 5XDM, giving a maximum ratio of 5. In other targets as may be used in some embodiments of the invention, the lateral dimensions WM and/or LM may be selected to be no more than 2XDM. It should also be noted that the depth DM and lateral dimensions WM and LM (for width and length of the x-ray generating microstructure) may be defined relative to the axis of incident electrons, with respect to the x-ray emission path, and/or with respect to the orientation of the surface normal of the x-ray generating material. For electrons incident at an angle, care must be taken to make sure the appropriate projections for electron penetration depth at an angle are used.

[0087] FIGURE 9 illustrates the relative x-ray generation from the various regions shown in FIGURE 8. X-rays 888 comprising characteristic x-rays are generated from the region 248 where electron collisions overlap the microstructures 700 of x-ray generating material, while the regions 1280 and 1080 where the electrons interact with the substrate generate characteristic x-rays of the substrate element(s). Additionally, continuum bremsstrahlung radiation x-rays radiated from the region 248 of the microstructures 700 of the x-ray generating material may be stronger than the x-rays 1088 and 1288 produced in the regions 1280 and 1080.

[0088] It should be noted that, although the illustration of FIGURE 9 shows x-rays radiated only to the right, this is in anticipation of a window or collector being placed to the right.

[0089] It should also be noted that materials are relatively transparent to their own characteristic x-rays, so that FIGURE 9 illustrates an arrangement that allows the linear accumulation of characteristic x-rays along the microstructures, and therefore can be used to produce a relatively strong characteristic x-ray beam. However, lower energy x-rays may be attenuated by the target materials, which will effectively act as an x-ray filter. Other selections of materials and geometric parameters may be chosen (e.g. a non-linear scheme) if continuum x-rays are desired, (e.g. for near edge or extended fine structure spectroscopy).

[0090] Up to this point, targets that are arranged in planar configurations have been presented. These are generally easier to implement, since equipment and process recipes for deposition, etching and other planar processing steps are well known from processing devices for microelectromechanical systems (MEMS) applications using planar diamond, and from processing silicon wafers for the semiconductor industry.

[0091] However, in some embodiments, a target with a surface with additional properties in three dimensions (3-D) may be desired. As discussed previously, when the electron beam is larger than the electron penetration depth, the apparent x-ray source size and area is at minimum (and brightness maximized) when viewed at a zero degree (0 ^s ) take-off angle.

[0092] The distance through which an x-ray beam will be reduced in intensity by 1/e is called the x-ray attenuation length, designated by μι,, and therefore, a configuration in which the generated x-rays pass through as little additional material as possible, with the distance selected to be related to the x-ray attenuation length, may be desired.

[0093] An illustration of a portion of a target as may be used in some embodiments of the invention is presented in FIGURE 10. In this target, an x-ray generating region 710 with seven microstructures 711, 712, 713, 714, 715, 716, 717 is configured near a recessed edge 1003 of the target substrate 1000 by a shelf 1002, similar to the situation illustrated in FIGURE 7. As shown, the x-ray generating microstructures 711, 712, 713, 714, 715, 716, 717 are arranged in a linear array of x-ray generating right rectangular prisms embedded in the substrate 1000, and produce x-rays 1888 when bombarded with electrons 111.

[0094] The surface normal in the region of the microstructures 711 - 717 is designated by n, and the orthogonal length and width dimensions are defined to be in the plane perpendicular to the normal of said predetermined surface, while the depth dimension into the target is defined as parallel to the surface normal. The thickness DM of the microstructures 711 - 717 in the depth direction is selected to be between one third and two thirds of the electron penetration depth of the x-ray generating material at the incident electron energy for optimal thermal performance. The width WM of the microstructures 711 - 717 is selected to obtain a desired source size in the corresponding direction. As illustrated, WM ~ DM. AS discussed previously, WM could also be substantially smaller or larger, depending on the shape and size of the source spot desired.

[0095] As illustrated, the length of each of the microstructures 711 - 717 is LM ~WM /lO, and the length of the separation between each pair of microstructures is a distance Leap ~ 2 LM, making the total length of the region 710 comprising x-ray generating material Lm = 7 X LM + 6 x Leap ~ 19 x LM ~ 1.9 x DM. In other embodiments, larger or smaller dimensions may also be used, depending on the amount of x-rays absorbed by the substrate and the relative thermal gradients that may be achieved between the specific materials of the x-ray generating microstructures 711 - 717 and the substrate 1000.

[0096] Likewise, the distance between the edge of the shelf and the edge of the x-ray generating material p as illustrated is p ~ LM, but may be selected to be any value, from flush with the edge 1003 (p=0) to as much as 1 mm, depending on the x-ray reabsorption properties of the substrate material, the relative thermal properties, and the amount of heat expected to be generated when bombarded with electrons. [0097] For a configuration such as shown in FIGURE 10, the total length Lm of the x-ray generating region 710 will commonly be about twice the linear attenuation length for x- rays in the x-ray generating material, but can be selected to be half to more than 4 times that distance.

[0098] The microstructures may be embedded in the substrate (as shown), but in some embodiments may they may also be partially embedded, or in other embodiments placed on top of the substrate.

[0099] The thermal benefits of a structured target such as that illustrated in FIGURE 10 are presented in the U.S. Provisional Application 62/155,449, to which a parent Application of this Application claims the benefit of priority, and which has been incorporated by reference in this Application in its entirety.

[00100] In the cited Provisional Patent Application, calculations therein for two targets are presented using the finite element modeling product Solidworks Simulation Professional.

[00101] The first target modeled has a uniform coating of copper 300 microns thick as the x- ray material, as is common in commercial x-ray targets. Simulation of bombardment of the copper layer with electrons over an ellipse 10 microns wide and 66 microns long predicts an increase in the temperature of the copper to over 700 ^a C.

[00102] The second target, according to an embodiment of the invention, has 22 discrete structures of copper as the x-ray generating material, arranged in a one-dimensional array similar to that illustrated in FIGURE 10. The microstructures of copper are embedded in diamond, and have an axis of orientation perpendicular to the surface normal of the target.

[00103] The length of each x-ray generating structure along the axis of the array LM is 1 micron, and elements are placed with a separation Leap of 2 microns. The width of the elements in the direction perpendicular to the array axis WM is 10 microns, and depth perpendicular from the surface into the target DM is also 10 microns. [00104] In the simulation, both targets are modeled as being bombarded with an electron beam that raises the temperature to the operating temperature of -700 ^a C. The uniform copper target reaches this temperature with an electron exposure of 16 Watts. However, in the case of the second, structured target, the copper reaches the operating temperature of -700 ^a C with an exposure of 65 Watts - a level 4 times higher. Normalizing for the reduced copper volume still gives more than twice the power deposited into the copper regions. Moreover, electron energy deposition rates between the materials is much more substantial in the higher density Cu than in diamond, and is therefore predicted to generate at least twice the number of x- rays. This demonstrates the utility of embedding microstructures of x-ray generating material into a thermally conducting substrate, in spite of a reduction in the total amount of x-ray generating material.

[00105] FIGURES. HA - HC illustrate a region 1001 of a target as may be used in some embodiments of the invention that comprises an array of microstructures 700 in the form of right rectangular prisms comprising x-ray generating material arranged in a two-dimensional regular array. FIGURE HA presents a perspective view of the sixteen microstructures 700 for this target, while FIGURE ΠΒ illustrates a top down view of the same region, and FIGURE HC presents a side/cross-section view of the same region.

[00106] For a structure comprising the microstructures embedded in the substrate with a side/cross-section view as shown in FIGURE HC with depth DM and lateral dimensions in the plane of the substrate of WM and LM, the ratio of the total surface area in contact with the substrate for the embedded microstructures vs. deposited microstructures is

^{EMBE DDE D} = 1 + 2D _M [Eqn. 2]

^A Deuos ited ^ M )

[00107] With a small value for DM relative to WM and LM, the ratio is essentially 1. For larger thicknesses, the ratio becomes larger, and for a cube (DM=WM=LM) in which 5 equal sides are in thermal contact, the ratio is 5. If an overcoat or cap layer of a material with similar properties as the substrate in terms of mass density and thermal conductivity is used, the ratio may be increased to 6.

[00108] The heat transfer is illustrated with representative arrows in FIGURE 12, in which the heat generated in microstructures 700 embedded in a substrate 1000 is conducted out of the microstructures 700 through the bottom and sides (arrows for transfer through the sides out of the plane of the drawing are not shown). The amount of heat transferred per unit time conducted through a material of area A and thickness d increases with the temperature gradient, the thermal conductivity in W/(m ^a C), and the surface area through which heat is transferred. Embedding the microstructures in a substrate of high thermal conductivity increases all these factors.

[00109] FIGURE 13 illustrates an alternative embodiment in which an overcoat has been added to the surface of the target. This overcoat 725 may be an electrically conducting layer, providing a return path to ground for the electrons bombarding the target. For such embodiments, the thin layer of conducting material that is preferably of relatively low atomic number, such as Titanium (Ti) is used. Other conducting materials, such as silver (Ag), copper (Cu), gold (Au), tungsten (W), aluminum (Al), beryllium (Be), carbon (C), graphene, or chromium (Cr) may be used to allow electrical conduction from the discrete microstructures 700 to an electrical path 722 that connects to a positive terminal relative to the high voltage supply. Such overcoats are typically thin films, with thickness on the order of 5 to 50 nm.

[00110] In other embodiments, this overcoat 725 may comprise a material selected for its thermal conductivity. In some embodiments, this overcoat 725 may be a layer of diamond, deposited by chemical vapor deposition (CVD). This allows heat to be conducted away from all sides of the microstructure. It may also provide a protective layer, preventing x-ray generating material from subliming away from the target during extended or prolonged use. Such protective overcoats typically have thicknesses on the order of 0.2 to 5 microns. Such a protective overcoat may also be deposited using an additional dopant to provide electrical conductivity as well. In some embodiments, two distinct layers, one to provide electrical conductivity, the other to provide thermal conductivity and/or encapsulation, may be used. In some embodiments, overcoats may comprise beryllium, diamond, polycrystalline diamond, CVD diamond, diamond-like carbon, graphite, silicon, boron nitride, silicon carbide and sapphire.

[00111] In other embodiments the substrate may additionally comprise a cooling channel 1200, as also illustrated in FIGURE 13. Such cooling channels may be a prior art cooling channel using flowing water or some other cooling fluid to conduct heat away from the substrate, or may be fabricated according to a design adapted to best remove heat from the regions near the embedded microstructures 700.

[00112] Other configurations that may be used in embodiments of the invention, such as a checkerboard array of microstructures, a non-planar "staircase" substrate and various nonuniform shapes of x-ray generating elements, have been described in the above cited parent Applications of the present Application, U.S. Patent Applications Ser. Nos. 14/490,672 and 14/999,147. Additional target configurations presented in U.S. Patent Application Ser. No. 14/465,816 are microstructures comprising multiple x-ray generating materials, microstructures comprising alloys of x-ray generating materials, microstructures deposited with an anti-diffusion layer or an adhesion layer, microstructures with a thermally conducting overcoat, microstructures with a thermally conducting and electrically conducting overcoat, microstructured buried within a substrate and the like.

[00113] Other target configurations that may be used in embodiments of the invention, as has been described in the above cited US Patent Application Ser. No. 14/465,816, are arrays of microstructures that may comprise any number of conventional x-ray target materials patterned as features of micron scale dimensions on or embedded in a thermally conducting substrate, such as diamond or sapphire. In some embodiments, the microstructures may alternatively comprise unconventional x-ray target materials, such as tin (Sn), sulfur (S), titanium (Ti), antimony (Sb), etc. that have thus far been limited in their use due to poor thermal properties. [00114] Other target configurations that may be used in embodiments of the invention, as has been described in the above cited US Patent Application Ser. No. 14/465,816, are arrays of microstructures that take any number of geometric shapes, such as cubes, rectangular blocks, regular prisms, right rectangular prisms, trapezoidal prisms, spheres, ovoids, barrel shaped objects, cylinders, triangular prisms, pyramids, tetrahedra, or other particularly designed shapes, including those with surface textures or structures that enhance surface area, to best generate x-rays of high brightness and that also efficiently disperse heat.

[00115] Other target configurations that may be used in embodiments of the invention, as has been described in the above cited US Patent Application Ser. No. 14/465,816, are arrays of microstructures comprising various materials as the x-ray generating materials, including aluminum, titanium, vanadium, chromium, manganese, iron, cobalt, nickel, copper, gallium, zinc, yttrium, zirconium, molybdenum, niobium, ruthenium, rhenium, rhodium, palladium, silver, tin, iridium, tantalum, tungsten, indium, cesium, barium, germanium, gold, platinum, lead and combinations and alloys thereof.

[00116] The embodiments described so far include a variety of x-ray target configurations that comprise a plurality of microstructures comprising x-ray generating material that can be used as targets in x-ray sources to generate x-rays with increased brightness.

2. Generic Considerations for a Linear Accumulation X-Ray Source.

[00117] FIGURE 14 illustrates a collection of x-ray sub-sources arranged in a linear array. The long axis of the linear array runs from left to right in the figure, while the short axis would run in and out of the plane of the figure. Several x-ray generating elements 801, 802, 803, 804 ... etc. comprising one or more x-ray generating materials are bombarded by beams of electrons 1111, 1112, 1113, 1114, ... etc. at high voltage (anywhere from 1 to 250 keV), and form sub-sources that produce x-rays 818, 828, 838, 848, ... etc. Although the x-rays tend to be radiated isotropically, this analysis is for a view along the axis down the center of the linear array of sub-sources, where a screen 84 with an aperture 840 has been positioned. [00118] It should be noted that, as drawn in FIGURE 14, the aperture allows the accumulated zero-angle x-rays to emerge from the source, but in practice, an aperture which allows several degrees of x-rays radiated at ±3° or even at ±6° to the surface normal may be designed for use in some applications. It is generally preferred that the window be at normal or near normal incidence to the long axis of a linear array, but in some embodiments, a window tilted to an angle as large as 85° may be useful.

[00119] Assuming the ith sub-source 80/ produces x-rays 8/8 along the axis to the right in FIGURE 14, the radiation for the right-most sub-source as illustrated simply propagates to the right through free space. However, the x-rays from the other sub-sources are attenuated through absorption, scattering, or other loss mechanisms encountered while passing through whatever material lies between sub-sources, and also by divergence from the propagation axis and by losses encountered by passage through the neighboring sub-source(s) as well.

[00120] Using the definitions:

Ii as the x-ray radiation intensity 8/8 from the ith sub-source 80/;

Τι,ο as the x-ray transmission factor for propagation to the right of the

1 ^st sub-source 801;

Ίι,ι-ι as the x-ray transmission factor for propagation from the ith sub-source 80/ to the /-1-th sub-source 80(7-1); and

Ti as the x-ray transmission factor for propagation through the ith sub-source 80/ (with To≡ 1),

[00121] the total intensity of x-rays on-axis to the right of the array of N sub-sources can be expressed as:

+ h x T¾2 x Ti x Tzi x Ti x Τι,ο [Eqn. 3]

+ h x T4,3 x Ts x T¾2 x Ti x Tzi x Ti x Τι,ο

+ . . . + IN X TN,N-I X TN-I X TN-I,N-2 X . . . X TZ X ΤΖ,Ι X TI X Τι,ο making

N i-l i-\ i= j = 0 k=0

[00122] For a source design in which all sub-sources produce approximately the same intensity of x-rays

L ~ Io [Eqn. 5]

the total intensity becomes

[00123] Furthermore, if the sub-sources are arranged in a regular array with essentially the same value for transmission between elements:

Τα,α-i = Tzi , a > 1, [Eqn. 7]

[00124] and if the sizes and shapes of the x-ray generating elements are similar enough such that the transmission through any given element will also be the same:

then the total intensity beco

[00125] Note that T< and T -i represent a reduction in transmission due to losses, and therefore always have values between 0 and 1. If N is large, the sum on the right can be approximated by the geometric series

∑x ⁿ for I x l < 1 [Eqn. 10]

o

making the approximate intensity 1

Lot ~ Io Τι,ο - r [Eqn. 11]

[00126] Note that this can also be used to estimate how many generating elements can be arranged in a row before losses and attenuation would make the addition of another x-ray generating element unproductive. For example, if the width of a generating element is TOL, the 1/e attenuation length for x-rays, transmission through the element gives Ti = 1/e = 0.3679. Assuming a transmission between elements of T -i = Tzi = 0.98, this makes

Lot « Jo Τι,ο r = Io Τι,ο (1.564) [Eqn. 12]

(1 - (0.3679X0.98))

[00127] This means that a large number of elements with a width equal to the 1/e length could only improve the intensity by a factor of 1.564. For 2 elements (a total x-ray generation length of 2 x TOL), Eqn. 9 indicates that Lot ~ Io Τι,ο (1.361), 87% of the estimated maximum from Eqn. 12, while for 3 elements (a total x-ray generation length of 3 x TOL), Lot ~ Io Τι,ο (1.490), 95% of the estimated maximum, and for 4 elements (a total x-ray generation length of 4 x TOL), Lot ~ Io Τι,ο (1.537), which is 98% of the estimated maximum degree of linear accumulation from Eqn. 12. This suggests a general rule that linear accumulation near the maximum may be achieved from a total length of x-ray generating material of only 4 x TOL.

[00128] FIGURE 15 illustrates the 1/e attenuation length for x-rays having energies ranging from 1 keV to 1000 keV for three x-ray generating materials: molybdenum (Mo), copper (Cu), tungsten (W); and from 10 keV to 1000 keV for three substrate materials: graphite (C), beryllium (Be) and water (H2O). [The data presented here were originally published by B.L. Henke, E.M. Gullikson, and J.C. Davis, in "X-ray interactions: phot oab sorption, scattering, transmission, and reflection at E=50-30000 eV, Z=l-92", Atomic Data and Nuclear Data Tables vol. 54 (no.2), pp. 181-342 (July 1993), and may be also accessed at: henke.lbl.gov/optical_constants/atten2.html. Other x-ray absorption tables are available at physics.nist.gov/PhysRefData/XrayMassCoef/ chap2.html.]

[00129] The 1/e attenuation length for a material is related to the transmission factors above for a length L by Ti = e- ^a ' ^L = e- ^{L/ L} [Eqn. 13]

Therefore, a larger means a larger Ti .

[00130] As an example of using the values in FIGURE 15, for 60 keV x-rays in tungsten, ~ 200 <§>m, making the transmission of a 20 m wide x-ray generating element

Ti = e ^~L/ML = e- ²⁰ > ²⁰⁰ = 0.905 [Eqn. 14]

[00131] For 60 keV x-rays in a beryllium substrate, ~ 50,000 mm, which makes the transmission of a 100 mm wide beryllium gap between embedded tungsten x-ray generating elements to be:

T -i = = e ^~L/fiL = r ^100/50 < ⁰⁰⁰ = 0.998 [Eqn. 15]

[00132] Therefore, for a periodic array of tungsten elements 20 μτη wide embedded in a Beryllium substrate and spaced 100 m apart, the best-case estimate for the on-axis intensity is:

1

Lot «7o Τι,ο - - = h Τι,ο (10.312) [Eqn. 16]

(1 - (0.905 X0.998) )

which would represent an increase in x-ray intensity by an order of magnitude when compared to a single tungsten x-ray generating element.

3. X-Ray Source Controls.

[00133] There are several variables through which a generic linear accumulation source may be "tuned" or adjusted to improve the x-ray output. Embodiments of the invention may allow the control and adjustment of some, all, or none of these variables.

3.1. E-beam Variations.

[00134] In some embodiments, the beam or beams of electrons 111 or 1111, 1112, 1113, etc. bombarding the x-ray generating elements 801, 802, 803... etc. may be shaped and directed using one or more electron control mechanisms 70 such as electron optics, electrostatic lenses or magnetic focusing elements. Typically, electrostatic lenses are placed within the vacuum environment of the x-ray source, while the magnetic focusing elements can be placed outside the vacuum.

[00135] In many embodiments, the area of electron exposure can be adjusted so that the electron beam or beams primarily bombard the x-ray generating elements and do not bombard the regions in between the elements. A source having multiple electron beams that are used to bombard distinct x-ray generating elements independently may also be configured to allow a different accelerating voltage to be used with the different electron beam sources. Such a source 80-B is illustrated in FIGURE 16. In this illustration, the previous high voltage source 10 is again connected through a lead 21-A to an electron emitter 11-A that emits electrons 111-A towards a target 1100-B. However, two additional "boosters" for voltage 10- B and 10-C are also provided, and these higher voltage potentials are connected through leads 21-B and 21-C to additional electron emitters 11-B and 11-C that respectively emit electrons 111-B and 111-C of different energies. Although the target 1100-B will usually be uniformly set to the ground potential, the individual electron beam sources used to target the different x-ray generating elements may be set to different potentials, and electrons of varying energy may therefore be used to bombard the different x-ray generating elements 801, 802, 803, ... etc.

[00136] This may offer advantages for x-ray radiation management, in that electrons of different energies may generate different x-ray radiation spectra, depending on the materials used in the individual x-ray generating elements. The heat load generated may also be managed through the use of different electron energies.

3.2. Material Variations.

[00137] Although it is simpler to treat the x-ray generating elements as identical units, and to have the intervening regions also be considered identical, there may be advantages in some embodiments to having variations in these parameters. [00138] In some embodiments, the different x-ray generating elements may comprise different x-ray generating materials, so that the on-axis view presents a diverse spectrum of characteristic x-rays from the different materials. Materials that are relatively transparent to x-rays may be used in the position closest to the output window 840 (e.g. the element 801 furthest to the right in FIGURE 14), while those that are more strongly absorbing may be used for elements on the other side of the array, so that they attenuate the other x-ray sub-sources less.

[00139] In some embodiments, the distance between the x-ray generating elements may be varied. For example, a larger space between elements may be used for elements that are expected to generate more heat under electron bombardment, while smaller gaps may be used if less heat is expected.

3.3. Rotating Anode Embodiments.

[00140] The target described above might also be used in an embodiment comprising a rotating anode, distributing the heat as the anode rotates. A system 580-C comprising these features is illustrated in FIGs. 17A - 17C. In this embodiment, many of the elements are the same as in a conventional rotating anode system, as was illustrated in FIGURE 5A, but in the embodiment as illustrated, the rotating mechanism has been rotated 90 ^s relative to the electron beam emitter 11-R and the electron beam 511-R.

[00141] The target in the embodiment as illustrated is a rotating cylinder 5100 mounted on a shaft 530. In one end of the cylinder 5100, a set 5710 of rings of x-ray generating material 5711 - 5717 have been embedded into a layer of substrate material 5000, with a gap between each ring. The "length" (parallel to the shaft axis in this illustration, and perpendicular to the local normal n in the region under bombardment) of each ring may be comparable to the length discussed for the set of microstructures illustrated in FIGURE 10 (i.e. micron-scale), and the spacing may be comparable to Leap, (also micron-scale). The depth (i.e. parallel to the local normal ri) into the substrate 5000 may also be comparable to the depth discussed in the previous embodiments (i.e. micron scale, and related to either the penetration depth or the CSDA depth for either the x-ray generating material or the substrate.) The "width", however, is the circumference, as the rings 5710 circle the entire cylinder 5100.

[00142] This substrate material 5000 may in turn be attached or mounted on a core support 5050 attached to the rotating shaft 530. The core support may comprise any number of materials, but a core of an inexpensive material with high thermal conductivity, such as copper, may be preferred. A solid core/substrate combination that comprises a single material may also be used in some embodiments. The substrate 5000 may be deposited using a CVD process, or pre-fabricated and attached to the core support 5050.

[00143] When bombarded with an electron beam 511-R, the portions of the set of rings 5710 of x-ray generating materials that are exposed will generate heat and x-rays 5588. X-rays radiated at a zero-angle (perpendicular to a local surface normal for the target in the region under electron bombardment) or near zero-angle may experience linear accumulation, and appear exceptionally bright. Embedding the set of rings 5710 of x-ray generating material into the substrate 5000 facilitates the transfer of heat away from the x-ray generating structures, allowing higher electron flux to be used to generate more x-rays without causing damage to the structures, as has been demonstrated for the non-rotating case.

[00144] It should be noted that the illustrations of FIGs. 17A - 17C are provided only to illustrate the functioning of an embodiment of the invention, and that the relative sizes, dimensions, and proportions of the rotating shaft 530, core support 5050, substrate 5000, and rings of x-ray generating material 5711 - 5717 should not be inferred from these drawings. The use of only seven rings in the illustration is also not meant to be limiting, as embodiments with any number of x-ray generating structures may be used.

[00145] In practical embodiments, the substrate thickness may range from a few microns to 200 microns, while the core may typically have a diameter of 2 cm to 20 cm. A cylinder in which the core and substrate are the same material may also be used in some embodiments. Various overcoats for electrical conduction and/or protection, as discussed for planar targets and illustrated in FIGURE 13, may also be applied to embodiments having a rotating anode.

[00146] Although only parallel rings with zero take-off angle have been illustrated in FIGs. 17A - 17C, additional geometries for near-zero take-off angles, such as those using a beveled surface, may have advantages. Likewise, other configurations for the x-ray generating materials may be used. FIGURE 18 illustrates a target cylinder 5101 for a rotating anode comprising a set of parallel lines 5720 that have an orientation perpendicular to that used for the rings of FIGURE 17B. Other target designs, such as checkerboards, grids, etc. as have been illustrated U.S. Provisional Patent Application Ser. No. 62/141,847 (to which the Parent Application of the Present Application claims the benefit of priority) as well various designs and structures illustrated in other planar embodiments of the present Application and the previously mentioned co-pending Applications may be used. Furthermore, additional elements found in other embodiments described in the present Application, such as focused electron beams and the like, different x-ray generating material selections and the like, the use of a powered x-ray generating material, etc., as well as those described the co-pending patent Applications to which it claims priority, may also be applied to rotating anode embodiments.

3.4. Materials Selection for the Substrate.

[00147] For the substrate of a target with microstructures of x-ray generating material, as shown above it is preferred that the transmission of x-rays Tfor the substrate be near 1. For a substrate material of length L and linear absorption coefficient TT _S/

T = e -a _s L

[Eqn. 17]

where μι, Ϊ5 the length at which the x-ray intensity has dropped by a factor of 1/e.

[00148] Generally, L oc X ³ /Z ⁴ [Eqn. 18] where X is the x-ray energy in keV and Z is the atomic number. Therefore, to make μι, large (i.e. make the material more transparent), higher x-ray energy is called for, and a lower atomic number is highly preferred. For this reason, both beryllium (Z=4) and carbon (Z=6) in its various forms (e.g. diamond, graphite, etc.) may be desirable as substrates, both because they are highly transparent to x-rays, but also because they have high thermal conductivity (see Table I).

4. Design Guidelines for Structured Targets.

[00149] The embodiments of the invention disclosed in this Application can be especially suitable for making a high brightness x-ray source for use at one or more predetermined low take-off angles. In some embodiments, the arrangement of discrete structures of x-ray generating material can be arranged to increase the x-ray radiation into a predetermined cone of angles around a predetermined take-off angle. Such a predetermined cone can be matched to the acceptance angles of a defined x-ray optical system to increase or maximize the useful x-ray intensity that may be delivered to a sample in applications such as XRD, XRF, SAXS, TXRF, especially, with microbeams, such as microXRD, microXRF, microSAXS, microXRD, etc. Examples of such an x-ray optical system is one having a monocapillary x-ray optical element with a defined inner reflective surface, such as a paraboloidal collimator or a dual paraboloidal or ellipsoidal focusing surface.

[00150] In other embodiments, the arrangement of discrete structures of x-ray generating material can be arranged to increase the x-ray radiation into a predetermined fan of angles around a predetermined take-off angle. Such a distribution of x-rays may be matched to other x-ray optical elements designed to produce x-ray beams with a line profile or collimated to form a parallel beam instead of a focused spot.

[00151] The design of the layout of the x-ray generating elements in the target can be optimized to increase the x-rays radiated in specific directions using two factors. One is the management of the thermal load, so that heat is efficiently transported away from the x-ray generating elements. With effective thermal transfer, the x-ray generating elements can be bombarded with an electron beam of even greater power density to produce more x-rays. The second is the distribution of the x-ray generating materials such that the self-absorption of x- rays propagating through the remaining volume of x-ray generating material is reduced and linear accumulation of x-rays is optimized.

4.1. An Example: Microstructured Target for a Conical X-ray Beam

[00152] FIGs. 19A - 19C illustrate an example of a target 1100-T comprising a set 710 of embedded microstructures of x-ray generating material 711, 712... 717 embedded within a substrate 1000, similar to the target of FIGURE 10. As illustrated, the microstructures 711 - 717 are embedded near a shelf 1002 at the edge 1003 of the surface of the substrate 1000. When bombarded by electrons 111 within a vacuum chamber, the x-ray generating material produces x-rays 2088.

[00153] For the target 1100-T as illustrated, there is a local surface in the area of the x-ray generating elements that has a surface normal n. This defines an axis for the dimension of depth D into the target for determining the depth of the x-ray generating materials. This axis is also used to measure the electron penetration depth or the electron continuous slowing down approximation depth (CSDA depth).

[00154] For the target as illustrated, there is furthermore a predetermined take-off direction (designated by ray 88-T) for the downstream formation of an x-ray beam. This take-off direction is oriented at an angle θτ relative to the local surface, and the projection of this ray onto the local surface (designated by ray 88-S) in the plane that contains both the take-off angle and the surface normal is a determinant of the dimension of length L for the target. The final dimension of width W is defined as the third spatial dimension orthogonal to both the depth and the length directions.

[00155] As illustrated, the set of discrete structures of x-ray generating material is in the form of a linear array of x-ray generating microstructures, each of length LM, width WM, and depth DM, the same as was that illustrated in FIGURE 10. As illustrated, WM = DM , but in the general case, the width and depth need not be identical. In the target as illustrated in FIGURE 19C, the microstructures are aligned along an axis parallel to the length L dimension, and are separated from each other by a gap Leap, so that the total length of the x-ray generating volume comprising 7 microstructures of x-ray generating material is Lm = 7 LM + 6 Leap. [00156] It should be noted that these dimensions of depth, length and width in a given target may or may not correspond to those that might be intuited merely from the layout of the discrete structures of x-ray generating material. As has already been illustrated, discrete structures of x-ray generating material may be laid out in 1-dimensional and 2-dimensional arrays, grids, checkerboards, staggered and buried structures, etc. and the alignment and relative orientation of these physical arrays and patterns with the predetermined take off angle and the surface normal may or may not be parallel. As defined in these embodiments, the coordinates of depth, length and width are defined only by the surface normal and the predetermined take-off angle.

[00157] As illustrated in FIGURE 19A - 19C, a predetermined set of cone angles is defined, centered around the take-off angle θτ. A ray propagating along the innermost portion of the cone makes an angle θι with respect to the take off angle, while a ray propagating along the outermost portion of the cone makes an angle θι with respect to the take off angle. These cone angles are generally quite small (less than 50 mrad), and the take-off angle is generally between 0 ^s to 6 ^s (0 to 105 mrad).

[00158] The actual design of the x-ray target may be more easily described using the concept of an "x-ray generating volume", as discussed further below. This is the volume of the target from which the substantial majority of the x-rays of a desired energy will be radiated. In the embodiments of the invention, there are four primary factors that may affect the design rules for the structure of x-ray generating material within the x-ray generating volume that may be applied in embodiments of the invention to improve the x-ray brightness radiated into this predetermined cone. These four factors are: the volume fraction of x-ray generating material;

the relative thermal properties of the x-ray generating material and substrate;

the distance of propagation of the X-rays through x-ray generating material; and the depth of x-ray generation. 4.1.1. X-ray Generating Volume.

[00159] The "x-ray generating volume" of a target comprising discrete structures of x-ray generating material is the volume of the target that, when bombarded with electrons, generates x-rays of a desired energy. The energy is typically specified as the characteristic x-ray radiation generated by specific transitions in the selected x-ray generating material, although for certain applications, spectral bandwidths of continuum x-rays from the x-ray generating material may also be designated.

[00160] Two "volumes" must be considered to define the "x-ray generating volume": a "geometric volume" encompassing the x-ray generating material, and the "electron excitation volume" encompassing the region in which electrons deliver enough energy to generate x- rays.

4.1.1A. Geometric Volume

[00161] The "geometric volume" for the x-ray generating material is defined as the minimum contiguous volume that completely encompasses a given set of discrete structures of x-ray generating material and the gaps between them.

[00162] For the x-ray generating structures of FIGs. 19A - 19C, also reproduced FIGs. 20A - 20C, the "geometric volume" 7710 is a rectangle surrounding the microstructures of x-ray generating material.

[00163] For other configurations, such as those shown in FIGURE 21 A - 21C, the "geometric volume" may be more complex. In this example, a set 2710 of non-uniform structures of x-ray generating material 2711, 2712... 2717 are embedded within a substrate 1000, in which structures are tapered smaller as they approach the edge 1003 of the substrate. The "geometric volume" 7711 for this case is not a rectangle, but a tapered polyhedron having square ends of different sizes. 4.1. IB. Electron Excitation Volume.

[00164] The "electron excitation volume" is the volume of the target in which electrons deliver enough energy to generate x-rays of a predetermined desired energy.

[00165] FIGURE 22A - 22C illustrate this situation. In FIGs. 22A - 22C, electron beam 111 bombards a portion of the same target comprising a set 710 of x-ray generating materials embedded in a substrate 1000 - the same target layout as was shown in FIGs. 19A - 19C, and 20A - 20C. However, the extent of the electron beam does not encompass the entire set of structures, but has a beam width of We less than Wvr, and a beam length Le which is less than L and is also not exactly aligned with the edge of the target structures. The overall area of exposure at the surface is therefore the area of the electron beam at the intersection with the surface (the electron beam "footprint"), defined at some threshold value, such as the full- width- at half-maximum (FWHM) value or the 1/e value relative to the peak intensity. In general, the defined boundary for the footprint will be defined at the contour where the electron intensity is at 50% of the maximum electron intensity.

[00166] The electron beam bombarding the target may have various sizes and shapes, depending on the electron optics selected to direct and shape the electron beam. For example, the electron beam may be approximately circular, elliptical, or rectangular. Various accelerating voltages may be used as well, although generally the accelerating voltage will be selected to be at least twice that needed to produce x-rays of a given energy (e.g. to produce x-rays with an energy of ~8 keV, the accelerating voltage is preferred to be at least 16 keV).

[00167] If the entire region of x-ray generating structures is bombarded with an equivalent footprint of electrons of high energy, the x-ray generating volume may be identical to the "geometric volume" as described above. However, in some cases, the depth of the microstructured x-ray generating material DM may be significantly deeper than the electron penetration depth into the substrate, which may be estimated using Potts' Law (as discussed above), or deeper than the continuous slowing down approximation (CSDA) range (CSDA values normalized for element density may be computed using the NIST website physics.nist.gov/ PhysRefData/Star/Text/ESTAR.html). In such cases, the deeper regions of x- ray generating material may be relatively unproductive in generating x-rays, and the x-ray generating volume is preferably defined by the area overlap of the electron footprint upon the sample with the minimal geometric area containing the microstructures and the electron penetration depth of the electrons into the substrate. For 60 keV electrons bombarding copper (density ~ 8.96 g/cm ³ ) the electron penetration depth by Potts' Law is estimated to be -5.2 microns, while the CSDA depth is ~ 10.6 microns. For a diamond substrate (density -3.5 g/cm ³ ), the Potts' Law penetration depth is -15.3 microns, while the CSDA depth for the diamond substrate is - 18.9 microns.

[00168] In some embodiments, the depth of the x-ray generating structures DM measured from the target surface may be limited to be less than the penetration depth of the electrons into the x-ray target substrate material. In most cases (due to the typically lower mass density of the x-ray substrate relative to the x-ray generating material), the entire depth of x-ray generating material will be generating x-rays. In some embodiments, the depth of the x-ray generating structures DM measured from the target surface may be some multiple (e.g. lx - 5x) of the penetration depth of the electrons into the x-ray target substrate material. In this case, the depth DP of the electron excitation volume 7770-E in which x-rays are generated will be less than DM , as illustrated in FIGs. 22A - 22C, and the depth DP will be defined as a predetermined number related to either the electron penetration depth or the CSDA depth. (Note: the depth dimension is defined as parallel to the surface normal, and if the electron beam is incident on the target surface at an angle ® other than 0 ^s (normal incidence), the depth DP of the electron excitation volume must be modified from the normal incidence penetration depth by a factor of cos ΦΦΦΦ

[00169] In other embodiments, the depth of the x-ray generating structures DM measured from the target surface may be limited to be less than the penetration depth of the electrons into the x-ray generating material. This may include IX the penetration depth, or in some cases, preferably a fraction of the penetration depth such as 1/2 or 1/3 of the penetration depth.

[00170] For some embodiments, the depth DP of the electron excitation volume will be defined as being equal to half the penetration depth of the target X-ray generating material, since this is the depth over which the electrons will generate more characteristic x-rays. (See the discussion of FIGURE 2 above for more on the topic of characteristic x-ray generation.

4.1.1C. Synthesis of the X-ray Generating Volume.

For any general embodiment, the x-ray generating volume will be defined as the volume overlap of the "geometric volume" for the x-ray generating material within the target and the "electron excitation volume" for electrons of a predetermined energy and known penetration depth and CSDA depth for materials of the target.

4.1.2. Design Rules for Volume Fraction.

[00171] The volume fraction of the x-ray generating volume is defined as the ratio of the volume of the x-ray generating material within the x-ray generating volume to the overall x-ray generating volume. A typical prior art x-ray target with a uniform target of x-ray generating material will have a volume fraction of 100%. Targets such those illustrated in FIGURE 10, with LM = 1 micron and Leap = 2 microns, have a volume fraction of -37 %.

[00172] A general rule for the x-ray sources according to the invention disclosed here is that the volume fraction of the x-ray generating volume be between 10 and 70%, with the non-x- ray generating portion being filled with material of a high thermal conductivity. The regions of non-x-ray generating material serve to conduct the heat away from the x-ray generating structures, enabling bombardment with an electron beam of higher power, thereby producing more x-rays. [00173] The ideal volume fraction for a target typically depends on the relative thermal properties of the x-ray generating material and the substrate material in the x-ray generating volume. If the target is fabricated by embedding discrete structures of x-ray generating material with moderate thermal properties into a substrate of high thermal conductivity, good thermal transfer is generally achieved. If the thermal transfer between the x-ray generating material and the substrate is poor (for example, in circumstances of when the x-ray generating material has poor thermal properties), a smaller volume fraction may be desired. In general, for the embedded target structures described herein, a volume fraction of 30% - 50% is preferred.

[00174] It should be noted that in some embodiments, the discrete x-ray structures are not manufactured through etching or ordered patterning processes but instead formed using less ordered discrete structures, such as powders of target materials. FIGURE 23 illustrates a target fabricated by such a process. In a substrate 1000, a groove 7001 or set of grooves may be formed using standard substrate patterning techniques. The groove 7001 is then filled with particles of a powder of x-ray generating material 7077. The particles 7077 may be of a predetermined average size and shape, so that a measured volume of the material may be used to produce a desired volume fraction within the groove.

[00175] Once the particles of x-ray generating material have been placed in the groove, the gaps between particles 7006 can be filled with a coating of material deposited by chemical vapor deposition (CVD) processes. This provides the thermal dissipation for the heat produced in the x-ray generating target structures. When bombarded by electrons 111, the x- ray generating material will produce x-rays 8088. As long as the space between particles is small, and the depth of the groove is less than half the penetration depth of the electrons into the substrate, the x-ray generating volume 7070 will be the overlap of the groove (defining the geometric volume) and the projection of the footprint of the electron beam at the surface.

[00176] In some embodiments, the powders may be pressed into an intact ductile substrate material. In some embodiments, additional overcoats as described for more regular structures and illustrated in FIGURE 13 may be used for targets fabricated using powders as well.

[00177] For a target formed using a powder of x-ray generating material, the substrate is preferably a material with high thermal conductivity, such as diamond or beryllium, and the filling material is a matching material (e.g. diamond) deposited by CVD.

4.2.3. Design Rules for Thermal Properties.

[00178] The x-ray source target substrate material is preferred to have superior thermal properties, particularly its thermal conductivity, in respect to the x-ray generating material. Moreover, it is preferred that substrate materials of the target limit the self-absorption of x- rays produced in the target along the low take-off angle. In many embodiments, this leads to the selection of a substrate material having low atomic number, such as diamond, beryllium, sapphire, or some other carbon-based material.

[00179] For some materials, such as diamond, the thermal conductivity is severely reduced in very thin samples of the material. There may therefore be a minimum thickness required for the space between structures of x-ray generating material.

[00180] In general, for diamond having embedded structures of x-ray generating material, suitable results have been achieved when the thickness of the diamond between structures of x-ray generating material is 0.5 micrometer or more.

[00181] Likewise, if the discrete structures of x-ray generating material are too thick, heat cannot transfer efficiently from the center to the outside, and there is therefore a practical limit on how thick a given structure of x-ray generating material should be.

[00182] In general, when being embedded into diamond, suitable results have been achieved when the thickness of the x-ray generating structures is 10 micrometers or less. 4.1.4. Design Rules based on Propagation Length.

[00183] As described previously, there will be a total length for x-ray generation after which additional x-rays generated cease to contribute additional x-rays to the output, due to reabsorption. There is therefore an upper bound on the length ® LM of the x-ray generating material within the x-ray generating volume.

[00184] For a given x-ray energy, which in general may correspond to a characteristic line of the selected x-ray generating material, μι, is be defined to be the 1/e attenuation length for x- rays of that energy in the same material. Values for this number have been illustrated in FIG, 15, and numerical values are shown in Table III below for a few commonly used x-ray generating materials. The x-ray energies are taken from the NIST website physics.nist.gov/PhysRefData/XrayTrans/Html/search.html and the attenuation lengths are calculated using the same sources as were used for the data in FIGURE 15.

Table III: 1/e Attenuation lengths for various x-ray transitions

[00185] As a general rule, the propagation path through x-ray generating material for any given x-ray path should be less than 4 x μι,. For target structures such as the powder structure in FIGURE 23, to insure that no path through the x-ray generating volume is significantly longer than the upper bound for x-ray production, a design rule that the entire length of the groove Lm be less than 4 x μι, may be followed. In other embodiments, a design rule that Lm be less than (4 x μι,) divided by the volume fraction may be followed. [00186] For more defined discrete target structures, such as that illustrated in FIGURE 19C, a design rule limiting the length of the sum of segments in which a predetermined ray overlaps the x-ray generating material may be set.

[00187] In FIGURE 19C, the designated ray is the ray 88-T corresponding to the take-off angle at TTT, shown relative to a ray 88-M running through the midpoint of the x-ray generating volume. The path of this ray 88-T through the x-ray generating volume 7710-E has several segments of overlap 711-S, 712- S, 717-S corresponding to the overlap with the slabs 711, 712, ..., 717 of x-ray generating material. A general design rule can be stated that, for any ray parallel to the take-off angle ray, the sum of the segments of overlap with the x-ray generating material within the x-ray generating volume must be smaller than 4 x μι. In some embodiments, this sum of the segments of overlap with the x-ray generating material within the x-ray generating volume must be smaller than 2 x μι.

[00188] Although FIGURE 19C uses the ray of the take-off angle as a design rule, other embodiments may instead have a restriction on the sum of segments of overlap for a ray within the cone of propagation, i.e. between angles Qi and Θ2.

[00189] Such a target design is illustrated in FIGs. 24A - 24C. In this embodiment, a number of microstructures 2110 in the form of microslabs of x-ray generating material 2111, 2112, ..., 2116, ... etc. are embedded in a substrate 2000, near the edge 2003 of a shelf 2002 in a substrate 2000, but the orientation of the microstructures has the narrowest dimension aligned with the "width" direction and the longest dimension along the length dimension. The geometric volume 2770 in this example is a rectangle of volume L x W x DM.

[00190] If the take-off angle is in the plane of the microstructures, the path for x-rays at or near the take-off angle may be longer than the reabsorption upper bound. However, for x-rays emerging from the sides of the microstructures, low attenuation through the surrounding substrate and other x-ray microstructures may be achieved. The spacing between the microstructures may be adjusted so that x-rays emerging at the maximum cone angle Θ 2 in the plane orthogonal to the plane of the take-off angle (i.e. in the plane of FIGURE 24A) intersect a certain number of additional microstructures, achieving linear accumulation, but do not exceed the reabsorption upper bound. The appropriate metric for the limitation on length segments will therefore be for rays at angles corresponding to certain cone angles out of the plane of the microstructures, and not the take-off angle.

[00191] Note that these cone angles need not be in any particular plane, and therefore a design rule limiting the length of overlap must apply to certain rays within the cone, preferably those out of the plane of orientation for the microstructures. In some embodiments, a design rule limiting the length of the sum of segments will apply to any cone angle within a predetermined subset of cone angles. In some embodiments, a design rule limiting the length of the sum of segments will apply to a majority of cone angles.

[00192] A general design rule can be stated that, for any ray within a predetermined subset of cone of angles greater than or equal to Θ i and less than or equal to Θ 2 relative to the take-off angle ray, the sum of the segments of overlap with the x-ray generating material within the x-ray generating volume must be smaller than 4 x μι. Note that for prior embodiments, this design rule may also be used rather than using the ray along the take-off angle to define the amount of x-ray generating material within a giving x-ray generating volume.

[00193] Design rules may also be placed on having a minimum length for sums of segments of overlap, to ensure that at least some accumulation of x-rays may occur. For some embodiments, the sum of the segments of overlap with the x-ray generating material within the x-ray generating volume must be greater than 0.3 x μι. For other embodiments, the sum of the segments of overlap with the x-ray generating material within the x-ray generating volume must be greater than 1.0 x μι. For other embodiments, the sum of the segments of overlap with the x-ray generating material within the x-ray generating volume must be less than 1 x and in other embodiments this may be 2.0 x μι.

4.1.5. Design Rules for Depth. [00194] As discussed above, the depth DM of the structures of x-ray generating material may be determined by any number of factors, such as the ease of reliably manufacturing embedded structures of certain dimensions, the thermal load and thermal expansion of the embedded structures, a minimum thickness to minimize source degradation due to delamination or evaporation, etc.

[00195] However, creating structures with a depth DM significantly deeper than the electron penetration depth into the substrate will generally result in deep regions that are unproductive in generating x-rays. For 60 keV electrons bombarding copper (density ~ 8.96 g/cm ³ ) the electron penetration depth by Potts' Law is estimated to be -5.2 microns, while the CSDA depth is ~ 10.6 microns. For a diamond substrate (density -3.5 g/cm ³ ), the Potts' Law penetration depth is -15.3 microns, while the CSDA depth for the diamond substrate is -18.9 microns.

[00196] As a general design rule, the depth of the x-ray structures Djvtmeasured from the target surface should be limited to be less than 5 times the penetration depth of the electrons into the x-ray target substrate material. This ensures that the depth of the structures of x-ray generating material, which typically have poorer thermal properties than the substrate, is minimized, as typically only the portion closer to the surface is efficient at generating characteristic x-rays. Although some x-rays are generated at lower depths, there is also associated heat generation. In some embodiments, the depth of the x-ray generating material is preferred to be a fraction (e.g. 1/2) of the electron penetration depth in the x-ray generating material, providing the overlap of electron excitation and x-ray generating material primarily in the zone in which most of the characteristic x-rays are generated (see previous discussion of FIGs. 2, 8 & 9). In some embodiments, the depth of the x-ray generating material is preferred to be a fraction (e.g. 1/2) of the electron penetration depth in the substrate material. In some embodiments, the depth of the x-ray generating material is preferred to be half of the CSDA depth in the substrate material. 4.2. Relation of the X-ray Generating Volume to Take-off Angle.

[00197] Conventional reflection-type x-ray target geometries are often arranged, such that the x-ray beam emitted is centered along a take-off angle of ~ 6° measured from the x-ray target surface tangent. This angle is typically selected in an effort to both minimize apparent x-ray source size (smaller at lower take-off angles) and minimize self- attenuation by the x-ray target (larger at lower take-off angles).

[00198] The disclosed embodiments of the invention are preferably operated at take-off angles less than or equal to 3°, and for some embodiments at 0° take-off angle, substantially lower than for conventional x-ray sources. This is enabled by the structured nature of the x-ray source and the incorporation of an x-ray substrate, as discussed above, comprised of a material or structure that reduces or minimizes self-absorption of the x-ray energies of interest generated by the x-ray target.

[00199] Such a structured target is especially useful as a distributed, high-brightness source for use in systems that make use of an x-ray beam having the form of an annular cone. FIGURE 25 illustrates the matching of the annular cone as defined in the previous embodiments with an aperture or window 2790 and/or beam stop 2794 in the system.

[00200] This annular output can be selected to match the acceptance angle of an x-ray optical element, such as a capillary optic with a reflecting inner surface used for directing (e.g. focusing or collimating) the generated x-ray beam for downstream applications. The predetermined cone of x-rays generated by the x-ray source can be defined to correspond to the angles and dimensions of such downstream optical elements. Likewise, a central beamstop to block the x-rays propagating at the take-off angle τττ (which typically will not be collected by the downstream optical elements such as monocapillaries) can also be used, with the propagation angles blocked by the beam stop being those that correspond to the inner diameter of the predetermined annular x-ray cone. In some embodiments, annular cones may be defined by the acceptance angles of downstream optics, i.e. by the numerical aperture of such optics, or other parameters that may occur in such systems. Matching the volume to, for example, the depth-of-focus range for a collecting optic or to the critical angle of the reflecting surface of a collecting optic may maximize the number of useful x-rays, while limiting the total power that must be expended to generate them.

[00201] The angular range for the annular cone of x-rays is generally specified by having the inner cone angle ττι being greater than 2 mrad relative to the take-off angle, and having the outer cone angle -yi be less than or equal to 50 mrad relative to the take-off angle.

4.3. Rotating Anodes.

[00202] The previous discussion on take-off angles and cones of annular x-rays may also be applied to rotating anodes.

[00203] FIGURE 26 presents a cross-section view of a rotating anode in the form of a cylinder 5102 as may be inserted into a system as was illustrated in FIGURE 17 A. As in the embodiment of FIGs. 17A - 17C, the cylinder 5102 is mounted on a rotating shaft 530, and has a core 5050 of a thermally conducting material such as copper.

[00204] On the outer surface of the cylinder, a layer of substrate material 5000 such as diamond or CVD diamond has been formed, and embedded in this substrate are a number of rings 5711, 5712, ..., 5717 comprising x-ray generating material. As before, the "length" (parallel to the shaft axis in this illustration, and perpendicular to the local normal n in the region under bombardment) of each ring may be comparable to the length discussed for the set of microstructures illustrated in FIGURE 10 (i.e. micron-scale), and the spacing may be comparable to Leap, (also micron-scale). The depth (i.e. parallel to the local normal n) into the substrate 5000 may also be comparable to the depth discussed in the previous embodiments (i.e. micron scale, and related to either the penetration depth or the CSDA depth for either the x-ray generating material or the substrate.) The "width", however, is the circumference, as the rings 5710 circle the entire cylinder 5100. [00205] When a portion of the x-ray generating structures are bombarded by electrons 511-R, an x-ray generating volume 5070 is formed, generating x-rays 5088. Although x-rays may be radiated in many directions, for this system, as with the systems illustrated in FIGs. 19A - 19C, a predetermined take-off angle τττ may be designated, along with a cone of angles ranging from -yi to ττ2 defined relative to the take-off angle. These angles are generally selected to correspond to x-rays that the will be collected downstream to form a beam for use in x-ray optical systems. For the example illustrated in FIGURE 26, the take-off angle is at 0 ^s , making use of the x-rays that linearly accumulate through the set 5710 of rings comprising x- ray generating material. To reduce the attenuation of x-rays in the substrate 5000, the cylinder 5102 may additionally have a notch 5002 near the x-ray generating rings 5710, comparable to the shelf illustrated in the previous planar target configurations.

[00206] FIGURE 27 presents a cross-section view of another embodiment of a rotating anode in the form of a cylinder 5105 as may be inserted into a system as was illustrated in FIGURE 17A. As in the embodiment in FIGURE 26, the cylinder 5105 is mounted on a rotating shaft 530, with a conducting core 5050 and an outer coating of a substrate material 5005, in which a set 5720 of rings comprising x-ray generating material 5721, 5722, ..., 5726 are embedded.

[00207] However, in the embodiment as illustrated, the cylinder is beveled at an angle in the region of the x-ray generating volume, and the take-off angle is at a non-zero angle θτ, similar to the configuration for the planar geometry of FIGURE 19C. The bevel angle is selected so that linear accumulation through the set 5720 of rings may still occur.

[00208] Also illustrated in this embodiment, the cylinder 5105 may also be fabricated with an interface layer 5003, which may be provide a coupling between the beveled substrate 5005 and the core 5055.

[00209] Other rotating anode designs, such as patterns of lines, checkerboards, grids, etc. as have been illustrated U.S. Provisional Patent Application Ser. No. 62/141,847 (to which the Parent Application of the Present Application claims the benefit of priority) as well various designs and structures illustrated in other planar embodiments of the present Application and the previously mentioned co-pending Applications may be used in these configurations as well. These rotating anode embodiments may additionally be fabricated using conducting and/or protective overcoats, as was previously discussed for use with planar targets.

X-Ray Beam Delivery System Comprising Matched Target and Optic

[00210] The present technology, roughly described, provides an x-ray beam delivery system comprised of at least one x-ray source comprising a plurality of x-ray target materials matched with a plurality of x-ray optics. Each matched target material and optic pair provides different spectra, allowing for analysis at different levels of sensitivity. The x-ray system can provide collimated or focused beams and a system with a very high throughput due to the matching of each target material and optic.

[00211] The matching is achieved by selecting optics designed with the geometric shape, size, and surface coating for collecting as many x-rays having energies of interest as possible from the source and at an angle that satisfies the critical reflection angle of the x-ray energies of interest. In some embodiments, the matching is based on maximizing the numerical aperture (NA) of the optics for x-ray energies of interest. The NA is related to the flux an optic can collect from a source. The square of the NA is proportional to the square of the critical angle of reflection of the reflecting surface material for a specific x-ray energy, which is proportional to the inverse of the x-ray energy squared. This can be represented as follows:

[00213] In most embodiments, the optic is matched to one of the characteristic x-ray energies of the selected target material. For example, if the optic is matched for a higher x-ray energy, the critical angle is smaller and the reflecting surface of the optic will be shaped with a shallower slope. Some embodiments in which the NA is maximized for a high x-ray energy comprise a long x-ray optic with shallow slopes.

[00214] In some instances, the x-ray optics have an interior reflecting surface with at least a portion that comprises a quadric profile. The optics are positioned such that a focus of the quadric profile is coincident with the x-ray source spot. In some embodiments, where the quadric shape is ellipsoidal, the spot is at one of the two foci, and in other embodiments, such as paraboloidal or hyperboloidal shapes, the spot is at the single focus. Furthermore, the optics are matched to a characteristic x-ray energy of the x-ray generating microstructure material. This matching is defined such that the incident angle of x-rays with the characteristic energy of interest upon a portion of the reflecting surface are approximately equal to the critical angle of the characteristic x-ray energy of interest. In some instances, the reflecting surface profile of an optic is shaped such that x-rays with the characteristic energy of interest incident upon a portion of the reflecting surface have incidence angles that are between 30 to 100% of the critical angle. In some embodiments, the characteristic x-ray energy is a K-line of the x-ray generating microstructured material. In some other embodiments, this characteristic x-ray energy may be an L or M-line energy.

[00215] FIGURE 28 is a block diagram of an x-ray beam delivery system. The system of FIGURE 28 includes an electron emitter 110 and target 120, which collectively comprise an x- ray source 121. System 100 of FIGURE 28 also includes optics 130, and a beam stop 132. Electron emitter 110 generates an electron-beam 115 directed at target 120. The electron emitter can have an asymmetric shape, with a first dimension and a second dimension, wherein the ratio of the first dimension to the second dimension is between 3-4. The electron beam may be directed at target 120 at an angle less than 90°. More information regarding a source electron-beam striking a target and the generated x-rays are discussed with respect to FIGURE 29. More information regarding the footprint of an electron beam on a target is discussed with respect to FIGURE 30.

[00216] The energies and spectral properties of x-rays generated by striking an electron-beam on a target depend on the material of the target. In some instances, a target may be comprised of multiple thin strips of target material, for example in the form of a microstructure in which there is one long dimension (e.g., a length) and two dimensions <500 urn (e.g., width and depth), deposited on a substrate of high thermal conductivity such as diamond or copper. X- rays generated by an electron beam striking a target material may be collected at a low takeoff angle, such as between 0 degrees to +/- 6 degrees to maximize brightness. The x-rays can be collimated or focused by optics designed to be matched to the target material. X-rays that are not reflected by optics 130 are blocked by beam stop 132. More information for wire targets is discussed with respect to FIGURES 31-33.

[00217] The present x-ray beam delivery system can have a source with one or more targets, with each target comprising one or more target materials, such that there are a plurality of target materials and a plurality of optics. Optics are matched to one or more target materials, as each material has unique spectra and characteristic emission lines, and therefore critical angles θο The critical angle can depend on the interior surface coating of an optic. In particular, different interior surface coatings, such as a platinum coating, can be used to increase the critical angle.

[00218] The optics are matched to one or more target materials and can include total external reflection mirror optics. Each of the plurality of optics in an x-ray illumination beam system can be matched to the x-ray spectra produced by at least one of a plurality of microstructures. Each optic can also be positioned to collect x-rays generated by at least one of the plurality of microstructures when bombarded by a focused electron beam. Examples of optics that may be used to match different targets are discussed with respect to FIGURES 35-36. X-rays with matching targets and optics selected by a user are illustrated with respect to FIGURES 37-38.

[00219] The system of FIGURE 28 may include additional elements and components typically used within an x-ray system, but not illustrated in FIGURE 28 for purposes of simplicity. For example, the x-ray source 121 of FIGURE 28 may also include a helium path or vacuum enclosure, electron optics, and other elements typically found in x-ray sources. The electron emitter may generate a rastering electron beam. The system of FIGURE 28 may also include mechanisms for securing and moving the target 120 and optics 130 into precise locations that satisfy a minimum and maximum tolerance for positioning such elements.

[00220] In some instances, the target 120 is a rotating anode target. In some instances, the target is comprised of a substrate and discrete microstructures having at least two dimensions being <500 μιτι in contact with the substrate. In some instances, the microstructures are embedded within a substrate and in some instances, the microstructures are atop a substrate. In some embodiments, the microstructures are not directly in contact with the substrate and there is at least one layer of material between the microstructures and substrate. Such layers may serve as diffusion barriers to prevent the diffusion of the microstructure material into the substrate material or vice versa, and/or may serve as thermal boundaries to improve the thermal conductivity of heat between the microstructure and the substrate.

[00221] FIGURE 29 is a block diagram of a bombarding electron beam and emitted x-rays associated with a target. FIGURE 29 includes electron beam 115 generated by electron emitter 110 and received by target 120. As shown, the beam angle of incidence with respect to target 120 may be θι. θι may be in the range of between 45° and 90°. When electron-beam 115 strikes the target, x-rays are emitted. The take-off angle Θ2 (the angle between the target surface and the center of the emitted x-ray cone 127) of x-rays with a central ray 125 may be between 0- 20°. In some instances, an emitted x-ray beam can have a take-off angle of less than 6°. Movement of the target(s) to select different target materials to be placed in the electron beam path is relative. In some instances, the target(s) is(are) moved to position a selected target, and in some embodiments, the electron-beam and/or the electron source may move. In some other embodiments, both the target and the source may move.

[00222] FIGURE 30 is a view of an x-ray beam footprint on a target. FIGURE 30 provides more detail for a surface of target 120, corresponding to area 600 of FIGURE 29. A microstructured wire 320 may exist on substrate 310. Substrate 310 may be in contact with multiple microstructures, although only one is shown in FIGURE 30. Electron beam 115 used to strike microstructure 320 has a width that can correspond to the profile of a microstructure wire 320. In some implementations, the width of the electron beam can be about the same, narrower, or wider than the target wire microstructure that receives the beam. In some instances, the footprint of the electron beam is elliptical, as shown by footprint 610. The beam may be elliptical by design, or may be circular with a raster motion to create an elliptical footprint on microstructure 320. The width of the microstructure can be used to limit the spot size of the x-ray source. The dimensions of the footprint of the electron-beam are given as "a" and "b", as shown in FIGURE 30B. The width "a" may be less than or equal to 30 μιτι (microns). In some instances, the ratio of b to a may be about 2 - 20, and a:b may have an aspect ratio of between 1 : 70 and 1 : 10. As such, a compromise can be achieved by using enough power but maintaining a small focus point at the same time. In many embodiments, the takeoff angle is such that the x-rays 127 emitted by the x-ray source appear from a round x-ray spot that has a diameter that is approximately equal to the smaller dimension a.

[00223] FIGURE 31 is a top view of a target having multiple microstructures. Target 200 includes wire microstructures 320 and substrate 310. Spacing between the microstructures 320 may be lower bound to avoid creation of x-rays from an adjacent target when an electron- beam strikes a single target microstructure. Microstructures 320 may be any of a plurality of metals or alloys, such as titanium, aluminum, tungsten, platinum, and gold, and each microstructure can be the same or different materials from other microstructures. Substrate 310 may be any highly thermal conductive material, such as for example diamond or copper. The width of a channel between microstructures Wc can be 15 μιτι (microns) or more. The width of a wire microstructure Ws can be less than or equal to 250 or 300 μιτι (microns). The substrate can extend longer than one or more microstructures, as shown in FIGURE 31, or may have the same length and be flush with one or more microstructures.

[00224] FIGURE 32 is a cross-sectional side-view of a target having multiple embedded wire microstructures 420. As shown in FIGURE 32, wire microstructures 420 are embedded within the substrate. The substrate 410 can be any material of high thermal conductivity and low mass density, such as diamond. The target, comprised of the substrate and microstructure(s), can be moved relative to the electron beam such that any of the microstructures 420 can be placed in the electron beam path. Each wire 420 can comprise a different material to generate x-rays with different spectra. The embedded wires can have a cross section that is rectangular (as illustrated in FIGURE 32), curved, circular, square, or any other shape.

[00225] FIGURE 33 is a side view of a target having multiple surface mounted wire microstructures. Similar to the microstructures in FIGURE 32, the microstructures in FIGURE 33 can each receive an electron-beam and are comprised of a different or the same material. Each wire may be matched with a different optic. In some instances, multiple wires of the same material can be implemented in the present system, to provide a longer use or lifetime of the system.

[00226] In some embodiments but not shown in FIGURE 32 and 33, there may be one or more layer(s) 422 between the microstructures and substrate. These may contain a material that prevents diffusion (e.g. Ta) or a material that improves the thermal conductance between the microstructures and substrate (e.g. Cr between Cu and diamond).

[00227] FIGURE 34A is a block diagram of an optic that provides a collimated x-ray beam. The optics 130 are matched to a microstructure on target 120 such that the angle of incidence of the x-rays 125 on the optics 130 is less than or equal to the critical angle for x-ray energy(ies) of interest. A central stop 132 is used to block x-rays that are not reflected by optics 130.

[00228] The critical angle of x-rays depends on the x-ray energy and reflecting surface material. Optics with different coatings, shapes, and focal lengths and/or source-optic entrance distances may be used. In some embodiments, the optic is axially symmetric, with an inner reflecting quadratic surface, such as: ellipsoidal, paraboloidal, hyperboloidal, etc. In some embodiments, the optic has an outer diameter of <10 mm.

[00229] FIGURE 34B is a block diagram of an optic similar to the one described by FIGURE 34A that provides focused x-rays. In some embodiments, the focal spot produced by the optic is <10 μιτι FWHM. A central stop 132 is used to block x-rays that are not reflected by optics 130. In some instances, the working distance of at least one of a plurality of optics used in the present system can be defined as the distance between the end of the optics to the optic focal spot is between 5 to 50 millimeters. The distance between the source spot and the optic focal spot can be between 30 mm to 1 meter. One focus of a quadric shape optic can be coincident with an x-ray source spot, while another focus of an optic can be coincident with a sample location.. [00230] FIGURES 35A-C illustrate example cross-sections of axially symmetric optics with different reflecting interior shapes. The optics of FIGURES 35A-35C are ellipsoidal shaped optics having a different radius of curvature such that FIGURE 35A has the largest radius and FIGURE 35C has the shortest radius. The optics of FIGURE 35B have curvature that is in between those of 35A and 35C. In some cases, only a portion of the ellipsoidal reflecting surface is used because if the location of the reflection is close to a focus point, the angle of incidence may become greater than the critical angle and no reflection occurs. In some instances, each one or more of the plurality of total external reflection mirror optics have an interior reflecting surface that has a quadric profile and is axially symmetric.

[00231] FIGURES 36A-B illustrate an optic with an interior surface coating. In some embodiments, the coating can be of materials that have a high atomic number, such as platinum or iridium, to increase the critical angle of total external reflection. In some instances, the coating may be a single layer coating (FIGURE 36 A). In some instances, multilayer coating comprised of many layers (e.g. several hundred) of two or more alternating materials (FIGURE 36B). Layers may be of uniform thickness or may vary in thickness between layers or within a single layer, such as in the cases of depth-graded multilayers or laterally-graded multilayers. The multilayer coating will narrow the bandwidth of the reflected x-ray beam and can serve as a monochromator. The materials used in the multilayer coating may be of any known to those versed the art. In some instances, the optics may include a demagnifying optic to provide better focused x-rays.

[00232] FIGURE 37A illustrates an x-ray beam delivery system utilizing a first pair of matched targets and optics. The system of FIGURE 37A includes electron emitter 1010, target 1020 and optics system 1030. Target 1020 may include multiple microstructures 1022 and 1024. In some instances, other components may be included in the x-ray system of FIGURE 37A, such as for example one or more mounts and positioning devices.

[00233] Optics system 1030 may include multiple focusing optics 1032 and 1034. Each matched optic and target material may be chosen for a particular application such that the x-ray flux is optimized for x-ray spectra optimal for the application. X-rays collected by optics 1032 are focused to a point 1080. In some instances, the plurality of optics includes two quadric surface profiles

[00234] FIGURE 37B illustrates the x-ray beam delivery system utilizing a second pair of matched target microstructures and optics. The system of FIGURE 37B includes the same components of as that of FIGURE 37A. In operation, electron-beam 1015 bombards target microstructure 1024 rather than 1022. Target microstructure 1024 is matched with optics 1034. X-rays collected by optics 1034 are focused to the same point 1080 as the system of FIGURE 37A so that both optics 1032 and 1034 are parfocal. As shown, the parfocal optics focus the x- ray spot onto the same position when each optic is placed in the path of the x-rays.

[00235] One or more mechanisms can be sued for moving the optics, the target, and the electron beam to provide different x-ray spectra. The mechanism may ensure the optics are parfocal and that different targets can be bombarded with electron beams to create different x-ray spectra.

[00236] The x-ray source (consisting of an electron emitter and a target having microstructures) can be used with a matching optic in several types of systems. Though FIGURES 38 describes fluorescence, the x-ray source and optics described herein can be used with other systems as well.

[00237] FIGURE 38 illustrates an x-ray source and optic for use in spectroscopy. The x-ray source and optic includes x-rays 1040 generated by target microstructure 1024. X-rays having an energy of interest are collected by optics 3810, a paraboloid mirror lens. Central stop 3812 blocks x-rays that would otherwise propagate without having been reflected by the quadric surface.

[00238] The collected x-rays are reflected by optic 3810, and the reflected x-rays 3815 are incident on a two-bounce monochromator. X-rays 3815 are first diffracted by crystal 3820, and the diffracted x-rays 3825 are directed to and diffracted again by a second crystal 3830. In some instances, other monochromators can be used, such as for example a channel cut, or a four-bounce monochromator. The monochromatized beam 3835 diffracted by the second crystal 3830 is received by a second optic 3840, also a paraboloid mirror lens. Optic 3840 focuses the monochromatized beam 3835 onto sample 3850. Fluorescence x-rays 3855 are then detected by a detector, such as a high efficiency SDD detector.

[00239] FIGURE 39 illustrates a method for providing a matched target and optic from a plurality of pairs of matched targets and optics. First, an x-ray system is initialized at step 3910. Initializing may include powering on the system, performing calibration, and other preliminary functions that enable the x-ray system to operate. A selection of a matched target material and optic pair is received at step 3920. In some instances, each of multiple target materials may be matched to a particular optic.

[00240] Once a selection is received, a target region and electron beam are aligned at step 3930. The motion is relative and may involve one or several of the components moving. The optic is positioned into the emitted x-ray path at step 3940 to collect x-rays at a low take-off angle. The optic may be positioned such that it collects the maximum flux of the x-ray energy(ies) of interest. In some instances, this is one of the characteristic x-ray lines of the selected target material. The optic may then provide a collimated or focused beam.

[00241] An electron beam is produced and strikes the selected target microstructure at step 3950 and generates x-rays. The generated x-rays are collected and focused or collimated by the matching optic at step 3960.

[00242] With this application, several embodiments of the invention, including the best mode contemplated by the inventors, have been disclosed. It will be recognized that, while specific embodiments may be presented, elements discussed in detail only for some embodiments may also be applied to others. Also, details and various elements described as prior art may also be applied to various embodiments of the invention. [00243] While specific materials, designs, configurations and fabrication steps have been set forth to describe this invention and the preferred embodiments, such descriptions are not intended to be limiting. Modifications and changes may be apparent to those skilled in the art, and it is intended that this invention be limited only by the scope of the appended claims.