CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] Patent Application is a Continuation-in-Part of U.S. Patent Application 15/431,786, filed Feb. 14, 2017, which in turn is a Continuation-in-Part of U.S. Patent Application 15/269,855, filed Sept. 19, 2016 now issued as US 9,570,265, and is also a Continuation-in-Part of U.S. Patent Application 15/166,274, filed May 27, 2016, all of which are hereby incorporated by reference in their entirety. Additionally, U.S. Patent Application 15/269,855 is a Contmuation-in-Part of U.S. Patent Application 14/544,191, filed Dec. 5, 2014 and now issued as U.S. Patent 9,449,781, which is hereby incorporated by reference in its entirety, and which claims the benefit of U.S. Provisional Patent Application Nos.61/912,478, filed on Dec. 5, 2013, 61/912,486, filed on Dec. 5, 2013, 61/946,475, filed on Feb. 28, 2014, and 62/008,856, filed on Jun. 6, 2014, all of which are incorporated herein by reference in their entirety. Application 15/269,855 is also a Continuation-in-Part of U.S. Patent Application 14/636,994, filed Mar. 3, 2015 and now issued as U.S. Patent 9,448,190, which is hereby incorporated by reference in its entirety, and which in turn claims the benefit of U.S. Provisional Patent Application Nos. 62/008,856, filed June 6, 2014; 62/086,132, filed Dec. 1, 2014, and 62/117,062, filed Feb. 17, 2015, all of which are incorporated herein by reference in their entirety.

BACKGROUND

[0002] Meas irement of the x-ray absorption properties of a material near the ionization energy can reveal information about the chemical state of the elements of interest within a sample, revealing information such as oxidation state and coordination number. [0003] X-ray absorption spectroscopy (XAS) measures the fraction of x-rays absorbed by an object as a function of x-ray energy over a predetermined narrow energy range. It is often carried out at synchrotron light sources because of their high brightness and energy tunability. Unfortvmately, synchrotron based x-ray absorption spectroscopy systems have numerous accessibility limitations, such as long wait times to obtain proposal-based access, limited measurement time granted per user group, and logistic issues including the need for travel and shipment of special experiment.

[0004] Small laboratory-based x-ray absorption spectroscopy systems wottld provide easy access and full control, however the performance of laboratory XAS systems has been largely limited by a combination of many factors, including low brightness and flux of laboratory x- ray sources, low efficiency of the x-ray optic used, and low diffraction efficiency of the crystal analyzer associated with the vise of high index reflections required for high energy resolution measurements due to the typically large x-ray source sizes of laboratory sources. Those limitations result in unacceptably long acquisition times (-tens of hours) and/or poor energy resolution. As a result, there are few laboratory systems in use.

[0005] There is a need for a laboratory x-ray absorption spectroscopy system with high throughput that circumvents the limitations of prior laboratory XAS systems.

SUMMARY

[0006] The present technology, roughly described, is an x-ray absorption spectrometer usable with a compact x-ray source to measure x-ray transmission with high throughput, high spatial, and high spectral resolution. In some instances, the spectrometer includes an optical x-ray optic system which achromatically focuses x-rays emerging from the x-ray source to preserve the brightness of the x-ray source, also serves as a low-pass filter with a predetenriined high-energy cut-off for the x-rays. One major advantage of the use of an x-ray optical system serving as low-pass focusing reflector is that the energy of the electrons of the x-ray source can be substantially higher than the predetermined high-energy cut-off, increasing the x-ray production efficiency to achieve high source brightness. This x-ray optical system can provide a point or a line focus that serves as the virtual source for x-rays in a spectrometer comprising of a crystal analyzer.

[0007] In some instances, a method for x-ray absorption spectroscopy by an x-ray optical system includes collecting x-rays received from a first x-ray source through an x-ray optical system. The x-ray optical system has low-pass spectral filter properties such that x-rays above a cut-off energy are reduced. A focused x-ray beam is produced by the x-ray optical system with a focus at a predetermined focal plane downstream of the x-ray optical system. The focused x-ray beam passes through a sample to be analyzed. The focused x-ray beam acts as a secondary source of diverging x-rays located at the focal plane. The diverging x-rays from the secondary source are received by an x-ray spectrometer having an x-ray wavelength dispersive element and an analyzer to analyze the spectrum of the dispersed x-rays.

BRIEF DESCRIPTION OF THE DRAWINGS

[0008] FIG. 1 illustrates a block diagram of an exemplary x-ray spectrometer system 200.

[0009] FIG. 2 illustrates an x-ray radiation spectrum.

[0010] FIG. 3 illustrates a portion of a target comprising three x-ray generating structures, each having a different x-ray generating material, as may be used in some embodiments of the invention.

[0011] FIG. 4A illustrates a cross section schematic view of an x-ray source and an optical system comprising an ellipsoidal optical element as may be used in some embodiments of the invention.

[0012] FIG. 4B illustrates a perspective schematic view of a portion of the x-ray source and optical system of FIG. 4A

[0013] FIG. 5A illustrates a cross section schematic view of an x-ray source and an optical system comprising a pair of paraboloidal optical elements as may be used in some embodiments of the invention.

[0014] FIG. 5B illustrates a perspective schematic view of a portion of the x-ray source and optical system of FIG. 5A

[0015] FIG. 6 illustrates a cross section schematic view of a spectrometer system using a single crystal analyzer according to the invention.

[0016] FIG. 7 illustrates a cross section schematic view of the spectrometer portion of the system illustrated in FIG. 11.

[0017] FIG. 8A illustrates a cross section schematic view of the spectrometer portion of a system similar to that illustrated in FIG. 11, but using a mosaic crystal.

[0018] FIG. 8B illustrates a schematic view of a spectrometer such as that illustrated in FIG. 13B, additionally arranged to show the related Rowland Circles.

[0019] FIG. 9 illustrates a perspective schematic view of a spectrometer system as may be used in some embodiments of the invention. [0020] FIG. 10 illustrates a perspective schematic view of a spectrometer system having multiple options for x-ray source _/ optical system _/ aperture _/ and crystal analyzer position as may e used in some embodiments of the invention.

[0021] FIG. 11 illustrates a cross section schematic view of a spectrometer system using a single crystal analyzer according to the invention.

[0022] FIG. 12A presents a portion of the steps of a method for collecting spectroscopy data according to an embodiment of the invention.

[0023] FIG. 12B presents the continuation of the steps of the method of FIG. 12A for collecting spectroscopy data according to an embodiment of the invention.

[0024] FIG. 12C presents the continuation of the steps of the method of FIGs. 12A and 12B for collecting spectroscopy data according to an embodiment of the invention.

DETAILED DESCRIPTION

[0025] Instances of the present technology include an x-ray absorption spectrometer usable with a compact x-ray source (e.g., first source) to measure x-ray transmission with high throughput, high spatial, and high spectral resolution. In some instances, the spectrometer includes an x-ray optical system which achromatically focuses x-rays emerging from the x- ray source that preserves the brightness of the x-ray source and also serves as a low-pass filter with a predetermined high-energy cut-off for the x-rays. One major advantage of the use of an x-ray optical system serving as low-pass focusing reflector is that the accelerating voltage of the electrons of the x-ray source can be substantially higher than the predetermined high- energy cut-off, increasing the x-ray production efficiency to achieve high source brightness. This optical system can provide a point or a line focus that serves as the virtual source for x- rays in a spectrometer that includes of a crystal analyzer.

[0026] The x-ray optical elements in the train may include paraboloid optics, ellipsoidal optics, polycapillary optics, or various types of Wolter optics, Kirkpatrick-Baez mirrors or multilayers suitably graded and systems comprising combinations thereof. The high collection and focusing efficiency achievable using these optical elements helps achieve high flux density in tightly focused spots.

[0027] In some embodiments, the higher brightness compact x-ray source is achieved in part through the use of novel x-ray targets used in generating x-rays from electron beam bombardment. These x-ray target configurations may include a number of microstructures of one or more selected x-ray generating materials fabricated in close thermal contact with (such as embedded in or buried in) a substrate with high thermal conductivity, such that the heat is more efficiently drawn out of the x-ray generating material. This in turn allows bombardment of the x-ray generating material with higher electron density and/or higher energy electrons, which leads to greater x-ray brightness and greater x-ray flux.

[0028] An object to be examined in transmission is placed in the x-ray beam, and an aperture is placed at the point or line of focus to selectively pass the transmitted x-rays while restricting the widely radiated x-ray fluorescence and any scattered radiatio that may exist. The object may be translated in x- and y-axes to allow a 2-D "map" of the transmission spectrum to be collected.

[0029] The aperture placed at the point or line of focus becomes the "source" (often referred to as the virtual source or second sotrrce) for a second x-ray optical system (the spectrometer) designed to disperse x-rays emerging from the aperture. This second system uses diffractive analyzer crystals to diffract x-rays of different energies onto an array detector, aligned so that different pixels of the detector correspond to different x-ray energies.

[0030] In some embodiments, an additional beam stop may be placed after the aperture to block the directly transmitted beam, but allow x-ray fluorescence emitted by the object to enter the spectrometer and be spectroscopically analyzed.

[0031] The present x-ray optical system may have several advantages. One or more optics of the x-ray optical system can be used as a low pass filter to cut out and/or reduce the energy of at least a portion of the x-rays provided by an x-ray source to provide a second source for directing at a target. Additionally, the x-ray optical system may allow selection of one of a plurality of optics. This interchangeability of sources based on a selected optic provides different spectrums that can be optimized for different tasks.

[0032] The present x-ray optical system also provides for high spatial resolution. The present system can interrogate a sample and raster scan the sample at a spatial resolution of 10 microns, for example. This degree of spatial resolution is much stronger than prior systems, which for example provide resolution at a millimeter level.

[0033] The present x-ray optical system further provides a sample holder or mount that can include multiple samples without requiring a door of the system to be opened, and wherein each sample canbe positioned at a distance from the source other than at or close to the source. In some instances, the mount can receive one or more of a plurality of samples and positions at least one sample in the focused x-ray beam for analysis. This variable sample positioning is better suited to changes in temperature and/or the environment and therefore provides for more accurate analysis of the sample. Further, the sample can be micro-fluidic, allowing x- rays to flow through samples of a different material. 1. An Exemplary Spectrometer System.

[0034] FIG. 1 illustrates a block diagram of an exemplary x-ray spectrometer system 200. The spectrometer system 200 of FIG. 1 includes an x-ray so irce 80, an x-ray optical system 3000 that includes an object 240 to be examined by x-ray transmission, a spectrometer 3700 including detector 290, signal processing electronics 292, and an analysis system 295 having a display 298.

[0035] The exemplary x-ray source 80 (e.g., first sotirce) includes a vacuum environment (typically 10 ⁶ torr or better) commonly maintained by a sealed vacuum chamber 20 or active pumping. Vacuum chamber 20 can be manufactured with sealed electrical leads 21 and 22 that pass from the negative and positive terminals of a high voltage source 10 outside the tube to the various elements inside the vacuum chamber 20. The source 80 can include mounts 30 which secure the vacuum chamber 20 in a housing 50. The housing 50 may include shielding material, such as lead, to prevent x-rays from being radiated by the source 80 in unwanted directions.

[0036] Inside vacuum chamber 20, ah electron emitter 11 is coupled through lead 21 to the negative terminal of a high voltage source 10, which serves as a cathode and generates a beam of electrons 111, for example by running a current through a filament. Any number of prior art techniques for electron beam generation maybe 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), emitters including nanostructures such as carbon nanotubes, and by use of ferroelectric materials.

[0037] A target 1100 includes a target substrate 1000 and x-ray generating structures 700, which can include one or more x-ray generating materials. Target 1100 is electrically connected to the opposite high voltage lead 22 via tar-get support 32 to be at ground or a positive voltage relative to the electron emitter 11, thus serving as an anode. The electrons 111 accelerate towards the target 1100 and collide with it at high energy, with the energy of the electrons determined by the magnitude of the accelerating voltage. The collision of the electrons 111 into the target 1100 induces several effects, including the radiation of x-rays 888, some of which exit the vacuum chamber 20 and are transmitted through a window 40 designed to be transparent to x-rays.

[0038] In some instances, there can also be an electron control mechanism 70 such as an electrostatic lens system or other system of electron optics. Control mechanism 70 can be controlled and coordinated with the electron dose and voltage provided by the electron emitter 11 by a controller 10-1 through an additional lead 27. The electron beam 111 may therefore be scanned, focused, de-focused, or otherwise directed onto target 1100, which can include one or more x-ray generating structures 700 fabricated to be in close thermal contact with a substrate 1000.

[0039] Once x-rays 888 exit the x-ray source 80, a portion of the x-rays are collected by optical system 3000. Optical system 3000 can include one or more optical systems 840 having x-ray optical elements with axial symmetry. The elements of the optical system 840 reflect x-rays at grazing angles to focus a portion 887 of the x-rays onto an aperture component 270 having one or more apertures 272. The object 240 to be examined is typically placed in a mount 244 and positioned at the focus or just before the aperture 272. The mount may allow the object 240 to be translated and/or rotated so that different portions of the object 240 are iUuminated by the x-ray beams 887, allowing different positions on the object 240 to be illuminated in a systematic scan or from several angles of incidence, with this motion controlled by a controller 246. X-rays propagating along the axis of the optical system that are not collected and focused may be blocked by a beam stop 850.

[0040] Once the focused portion of the x-rays 887 converge onto the object 240, the transmitted x-rays 888-T that also pass through the aperture 272 are collected by a spectrometer 3700. The spectrometer 3700 typically includes at least one dispersing x-ray crystal and an x-ray detector 290. The detector 290 will typically be an array detector, positioned to record tire intensity of the dispersed x-rays as a fimction of position. Additional signal processing electronics 292 and analysis system 295 correlate the intensity signals to the corresponding x-ray energy. The analysis system 295 may additionally include a display 298. The detector 290 may also include sensors and electronics that serve as an x-ray spectrometer, analyzing both the number of x-ray fluorescence photons emerging from the object 240 as well as their energy.

[0041] Additional embodiments of x-ray sources have been described in U.S. Patent Applications "X-RAY SOURCES USING LINEAR ACCUMULATION" (U.S. Patent Application 14/490,672, filed Sept. 19, 2014 and now issued as US. Patent 9,390,881), "X-RAY SOURCES USING LINEAR ACCUMULATION" (U.S. Patent Application 14/999,147, filed Apr. 1, 2016, and now issued as US. Patent 9,543,109), and "DIVERGING X-RAY SOURCES USING LINEAR ACCUMULATION" (U.S. Patent Application 15/166,274 filed May 27, 2016), all of which are hereby incorporated by reference in their entirety, along with any provisional applications to which these Patents and co-pending Patent Applications claim benefit.

[0042] Any of the target and/or source designs and configurations disclosed in the above referenced Patents and Patent Applications may be considered for use as a component in any or all of the methods or systems disclosed herein. Such variations may include active cooling systems having channels that carry liquid near or into the target to remove heat, mechanisms to rotate the anode to allow different portions to be bombarded by electrons while other recently bombarded portions cool, systems including multiple electron beams that bombard opposite sides of a target to increase x-ray brightness through linear ac vmulation, and systems that additionally use multiple anodes aligned to create an x-ray beam through linear acauntilation from several sources.

[0043] The components illustrated in the Figures are exemplary, and the various elements (microstructures, surface layers, cooling channels, etc.) are not intended to be limiting. It should also be noted that the x-ray source used for embodiments of the invention may be a microfocus, nanofocus, or rotating anode sottrce using bombardment of a solid anode target by electrons, but that the target may also include multiple x-ray generating materials, and may additionally contain regions in which the x-ray generating materials are molten or liquid. Furthermore, the x-ray source may be any x-ray source designed to use a liquid metal (such as a gallium liquid metal jet) as the anode.

2. X-ray Source Spectrum. [0044] FIG. 2 illustrates an x-ray radiation spectrum for 100 keV electron excitation with a tungsten (W) target. The broad spectrum x-ray radiation continuum 388, commonly called bremsstrahlung, is larger at lower energy and decreases at energies approaching the excitation energy of 100 keV. Characteristic lines 988 for tungsten are also illustrated.

[0045] This exemplary spectrum is modified for use in a spectroscopy system to limit the x- ray bandwidth. As discussed with respect to FIG. 1, the x-ray source 80 will typically have a window 40. This window 40 may attenuate low energy x-rays. Shown in FIG. 2 is a modified energy spectrum 488 for the x-rays that results from using an S1O2 window 100 microns thick. Some laboratory sources either come with a Be window (normally 200-300um thick) or with a diamond window (normally ~200-300um thick), which also doubles up as a target substrate in the transmission source type. The system may additionally include a filter, such as a sheet or layer of ahiminum, placed near the source or on the window to further attenuate low energy x-rays.

[0046] For a spectrometer, broad-spectrum x-rays can be used, and in some instances can be preferred, and characteristic lines 988 may make the task of interpreting the resulting spectra more difficult. It is therefore often advantageous to have the optical system collecting and focusing the x-rays designed to serve as a low-pass filter, severely attenuating any characteristic lines that may be generated and high energy bremsstrahlung background.

[0047] The optical system can include one or more x-ray optical elements in which the x-rays ilhtminates the inner surface of the element at a near-grazing angle (e.g. at angles of a few degrees or smaller). The optics may be coated with a particularly selected material, sttch that the critical angle of reflection can be exceeded for the higher energy x-rays, and the higher energy x-rays may not be efficiently reflected by the optical surface. As such, the x-ray optical system can have low-pass spectral filter properties such that x-rays above a cut-off energy are reduced as they pass through the optic system. X-rays below the cut-off energy may be focused to a predetermined focal plane.

[0048] Also in FIG. 2, a modified energy spectrum 588 that results from using a silver (Ag) coating on the interior of a capillary with a grazing angle of incidence of 3.5 mrad (0.2005 degrees), as calculated using the website

henke.lbl.gov/optical_constants/layer2.htrnl .

X-ray energies above 17.4 keV are significantly attenuated, providing 17.4 keV as a "high- energy cutoff" for reflection in this system. This arts out the strong tungsten characteristic lines at higher energy. When combined with the "high pass" filter provided by the window, the "low-pass" optical system provides a system with a predetermined x-ray "bandwidth".

[0049] The "high-energy" cutoff is well defined for a given material with a critical angle, and the attenuation of high energy x-rays prevents spurious signals from being observed athigher harmonics (e.g. twice (2x) the energy) downstream in the spectrometer. However, additional structure in the reflectivity spectrum may be observed at high energy with some materials. For some x-ray reflective optics, the reflectivity may be designed to be below 25% for all energies greater than 1.2 times the cutoff energy. For some x-ray reflective optics, the reflectivity maybe designed to be below 10% for all energies greater than 1.2 times the cutoff energy.

3. Structured X-ray Source.

[0050] The x-ray bandwidth for a given x-ray source target material and combination of window/filter and x-ray optical system may or may not provide the full range of x-ray energies needed for the measurement of the x-ray absorption spectrum of a given object to be examined. Achieving enough x-ray brightness in the spectral region of interest may be an issue, and therefore, x-ray sources includes targets having x-ray generating materials embedded into a thermally conductive substrate. X-ray source material could include one of several types of sources, including a solid continuous target or a micro-structured target.

[0051] Microstructured targets, x-ray generating materials, x-ray target materials, microstructures of different shapes, and microstructures of various materials such as those that may be used in embodiments of the present technology disclosed herein are described in US Patent Application entitled "STRUCTURED TARGETS FOR X-RAY GENERATION" (US Patent Application 14/465,816, filed Aug. 21, 2014), the disclosure of which is hereby incorporated by reference in its entirety along with any provisional Applications to which said Patent Application claims benefit.

[0052] Although the targets may be aligned to radiate x-rays vising a zero-degree take-off angle, as discussed above, some embodiments may use near-zero degree take off angles using source configurations as presented in, for example, U.S. Patent Application 15/166,274, filed May 27, 2016 by the inventors of the present Application and entitled "DIVERGING X-RAY SOURCES USING LINEAR ACCUMULATION," which is hereby incorporated by reference into the present application in its entirety.

[0053] FIG. 3 illustrates a portion of a target comprising three x-ray generating structures, each having a different x-ray generating material. By translating the target along the width direction so that the electrons 111 now bombard this second set of microstructures, a second set of x-rays 1888 are produced. If the materials of the first set 710 and second set 720 are distinct, the corresponding x-rays 1788 and 1888 generated when selected for bombardment by electrons will also have distinct spectral properties.

[0054] Various targets include different x-ray generating materials may be used in various embodiments. As illustrated in FIG. 3, multiple solid structures 740, 750 and 760 of different x- ray generating materials may be used in an anode target as well, with selection between target materials made by translation of the target under the electron beam 111 to select, for example, the third material 760, generating the corresponding x-rays 1688.

[0055] Although the physical translation of the target imder the electron beam may allow the materials to be "switched" from one to another while producing a beam that remains aligned with a single set of x-ray optics, other embodiments in which the electron beam is simply directed from one set of materials to another may also be used. This may be beneficial in cases where the different x-ray generating materials are aligned with different sets of x-ray optics, with each set of optics tuned to match the radiation spectrum of x-rays for each material. Directing the electron beam from one to the other therefore allows rapid switching between spectral sources.

4. X-ray Optical System. [0056] Once x-rays are generated by a high-brightness x-ray source, a portion of the x-rays can be collected by an optical system to be subsequently collimated and/or focused onto the object to measure the x-ray absorption and transmission.

[0057] Optical systems used in embodiments of the invention disclosed herein have been described in detail in the US Patent Application entitled "X-RAY ILLUMINATORS WITH HIGH FLUX AND HIGH FLUX DENSITY" (US Patent Application 15/431,786, filed Feb. 14, 2017) and its parent Applications (US Patent Applications 15/269,855, filed Sep. 16, 2016, and now issued as US 9,570,265, and 14/544,191, filed Dec. 5, 2014 and now issued as US 9,449,781), which are all hereby incorporated by reference in their entirety, along with the provisional Applications to which they claim benefit.

[0058] Referring to FIG. 1, the generated x-rays will diverge from the x-ray source 80, and after passing from the source through an x-ray transparent window 40, an optical system 3000 includes a set of one or more x-ray optical elements will intersect a portion of the x-rays and redirect their path of propagation.

[0059] The optical system 3000 may be a simple, single x-ray reflecting optical element with the topology of a hollow tube, or a more complex set of x-ray optics. This optical system 3000 can be mounted along the axis of brightest illumination so that a portion of the diverging x- rays 888 will reflect off the inner surface of the various optical elements. The curvatttre of the inner and/or inner and outer surface may take a number of geometric forms, but a very useful set of geometric forms for a number of optical elements are found among the quadric surfaces, and in particular, spheroids, ellipsoids, paraboloids, hyperboloids, elliptic cylinders, circular cylinders, elliptic cones, and circular cones. In some instances, at least a portion of a reflective surface of the reflective x-ray focusing optic is axially symmetric. In some embodiments, the reflective surface may be coated with a material selected for its x-ray reflective properties, including its critical angle. Such materials may include chromium, copper, rhodium, palladium, gold, silver, nickel, iridium, and platinum, among others.

[0060] These optical elements will typically be mounted such that a portion of the x-rays experience total external reflection from the inner surface, as was described above. The reflected x-rays from an individual optical element may be focused to a point or a li e _/ or collimated, or configured to produce some other diverging or converging wavefront, but for the embodiments presented here, the optical system produces a converging wavefront of x- rays 887 that comes to a focus at an aperture 272.

[0061] By placing an object 240 to be examined where it will be ilkiminated by the converging x-rays 887, a transmitted diverging x-ray wavefront 888-T is produced on the far side of the aperture 272, and may be subsequently analyzed by the spectrometer.

4.1. Optics Configurations

[0062] Optical configurations for use with the present technology can be configured as an ellipse, parabola, paraboloidal, or other shape. FIGs. 4A-5B illustrate exemplary optical reflectors.

[0063] FIG. 4A illustrates in cross section a possible optical configuration for the optical system using the form of an ellipse. An ellipse has two foci Fi and Fi such that any photons radiating from one of the foci will be reflected and converge onto the other. By configuring the inner surface of a tube-shaped optical element 3010 to have an ellipsoidal surface, and choosing the coating for the reflecting portion of the tube such that the angle of incidence for x-rays within a designated bandwidth emerging from the x-ray source is smaller than the critical angle, total external reflection is achieved. Then, at least a portion of the x-rays generated by an x-ray source placed at one of the foci will be focused to the other focus.

[0064] FIGs. 4A and 4B illustrate a portion of an embodiment of the invention utilizing such an ellipsoidal reflector 3010. An x-ray source includes x-ray generating microstructures 1700 embedded in a substrate 1000 generate x-rays 888 when bombarded by electrons 111 in a vacuum. The diverging x-rays 888 pass through a window 40 and enter the ellipsoidal optical element 3010. A portion of the x-rays experience total external reflection from the inner elliptical sttrface of a tube-like optical element 3010, and become focused x-rays 887 that converge onto an aperture 272 in an aperture component 270 after passing through the object 240 to be examined. In some embodiments, the on-axis x-rays may be blocked with a beam stop 1850, In some embodiments, as illustrated in FIG. 4A and the corresponding perspective view of FIG. 4B, the on-axis x-rays may be blocked with a beam stop 1850.

[0065] FIGs. 5A and 5B illustrate a portion of an embodiment of the invention utilizing a paraboloidal reflector 3020. An x-ray source includes x-ray generating microstructures 1700 embedded in a substrate 1000 generate x-rays 888 by linear accumulation when bombarded by electrons 111 in a vacuum. A parabola has single focus F _r such that any photons radiated from the point of focus will be reflected to form a parallel (collimated) beam. The diverging x-rays 888 pass through a window 40 and enter the first paraboloidal optical element 3020. A portion of the x-rays experience total external reflection from the inner paraboloidal surface of the tube-like optical element 3020, and become collimated x-rays 889.

[0066] Once collimated, a second optical element 3022 with a tube-shaped topology and paraboloidal inner surface, as shown in FIGs. 5A and 5B, may be aligned with the optical axis of the first optical element 3020 so that the collimated x-rays 889 are incident on the inner surface of the second optical element 3022 at angles smaller than the critical angle for the surface. The reflected x-rays then become focused x-rays 887 that converge onto an aperture 272 after passing through the object 240 to be examined.

[0067] Although the illustration shows a second paraboloidal optical element 3022 of the same size and shape as the initial paraboloidal optical element 3020, these need not be the same dimensions, but may have paraboloid surfaces with different curvature and relative focus positions.

[0068] In some embodiments, as illustrated in FIG. 5A and the corresponding perspective view of FIG. 5B, the on-axis x-rays may be blocked with a beam stop 1852, Although shown positioned between the two paraboloidal optical elements, the beam stop may be at the entrance to the first optical element 3020, or at the exit of the second optical element 3022 as well.

4.3. Other X-ray Optics. [0069] Other x-ray optical systems, such as Wolter Type I optics, cone shaped capillary optics, Kirkpatrick-Baez optics, etc. may be used as components of the optical system. Systems including filters and additional beam stops, etc. may also be used.

[0070] The optical elements described above may be fabricated of any number of optical materials, including glass, silica, quartz, BK7, silicon (Si), Ultra-low expansion glass (ULE™), Zerodur™ or other materials.

^' [0071] The reflective coatings used for the various optical elements used in embodiments of the invention as described above may be of a single elemental material, to take advantage of the total external reflection for angles of incidence smaller than the critical angle, and preferably may be of higher mass density material (greater than 2.5 g/cm ³ ) at least 25 run thick. Materials such as gold (Au), silver (Ag), platinum (Pt), etc. may be used as single-material coatings for these optical elements.

[0072] The reflective coatings may also be multilayer coatings, with alternating periodic layers of two or more materials, that provide constructive interference in reflection for certain x-ray wavelengths. The reflection efficiency depends on the wavelength and angle of incidence of the x-rays as well as the thickness of the alternating layers and number of layers, so this has limited use as a broadband reflector, but may be used if specific wavelengths are desired. A multilayer could also be depth graded and so the energy bandwidth could be "reasonably large," such as for example 20-25% bandwidth has already been demonstrated for hard x-rays.

[0073] Combinations that may be used for multilayer reflectors may be tungsten/carbon (W/C), tungsten/silicon (W/Si), tungsten/tungsten silicide (W/WS12), molybdenum/silicon (Mo/Si), nickel/carbon (Ni/C), chromium/scand vm (Cr/Sc), lanthanum/boron carbide (La BiC), tungsten/boron carbide (W/B4C), and tantalum/silicon (Ta/Si), nickel/boron carbide (Ni//B4C), and alummtun/ahtmina (AI/AI2O3), among others. The surface may also be a compound coating that includes an alloy or mixture of several materials.

[0074] Other optical elements, such as Fresnel Zone Plates, cylindrical Wolter optics, Wolter Type II optics, Kirkpatrick-Baez mirrors, Wolter Type III optics, Montel optics, diffraction gratings, crystal mirrors using Bragg diffraction, hole-array lenses, multi-prism or "alligator" lenses, rolled x-ray prism lenses, "lobster eye" optics, micro channel plate optics, or other x- ray optical elements may be used or combined with those already described to form compound optical systems for embodiments of the invention that direct x-rays in specific ways that will be known to those skilled in the art.

5.0 Basic Spectrometer.

[0075] FIGs. 6-9 illustrate schematic cross-section views and a perspective view the elements of a spectrometer system that may be used in some embodiments of the invention. Turning to FIG. 6, the x-ray target 1100 includes a substrate 1000 and x-ray generating material 1700 bombarded by electrons 111 in a vacuum. As drawn, the x-rays 888 emerge at a non-zero takeoff angle relative to the surface, but other alignments using a zero-degree take-off angle may be used as well.

[0076] The x-rays 888 that diverge from the x-ray source pass through the window 40 in the vacuum chamber, and are collected by an optical system. In the example of FIGs. 6-9, the optical system includes a single ellipsoidal capillary optic 3010 and a beam stop 1854. This single optic 3010 has an inner surface that reflects x-rays at near-grazing angles and focuses them onto the aperture 272 in the aperture component 270. An object 240 to be examined is positioned before the aperture component 270, arid the x-rays passing through the aperture 272 are those that have been transmitted through the object 240.

[0077] The aperture 272 will typically be a small hole of a diameter comparable to the size of the focused spot produced by the x-ray optical system. Aperture diameters of 5 to 25 microns maybe typical in some embodiments of the invention. In some embodiments of the invention, the aperture may include a slit, in some instances generally oriented horizontally. The size of the aperture will generally be designed to correspond to the expected size and dimensions of the focused x-ray beam. The aperture component itself may include a piece of metal (e.g. molybdenum or platinum) having a thiclcness shorter man the depth of focus for the optical system (e.g. on the order of 20 microns thick). [0078] On the far side of the aperture component 270, the x-rays emerge from the focus and are again diverging x-rays 888-T. The geometry will generally be an annulus of x-rays, as defined by the exemplary x-ray optic 3010. As shown, the aperture 272 serves as the point of origin for the x-rays entering the spectrometer 3700. Additional aperture(s) may also be used within the spectrometer to further block scattered x-rays.

[0079] In the spectrometer, the cone of x-rays 888-T will fall onto the surface of a diffracting crystal analyzer 3710, which will diffract x-rays of different wavelengths λι, λι, h$ ΛΊ, etc. (shown as ray bundles 887- A, 887-B, 887-C, and 887-D etc., respectively) to different points on an array detector 290. As shown in FIG. 5 and, in more detail in FIG. 6, the crystal analyzer will act as a Bragg diffraction element, reflecting the x-rays if the correct conditions of wavelength and angle of incidence are met. X-rays that are not diffracted 899 are typically transmitted through the crystal analyzer, and may be absorbed by a beam stop (not shown) or by the crystal, or by the crystal's mount.

[0080] In some instances, multiple crystals can be used in the x-ray spectrometer. When more than one crystal is used, each of the crystals may be selected based on monochromaticity requirements.

[0081] The crystal analyzer 3700 may be positioned -250 mm away from the aperture 272, and will typically have a width of about 1 cm. and a length smaller than 5 cm., but other dimensions may be used. The crystal analyzer 3700 may include a single planar Bragg crystal, but in practice, the crystal analyzer may be a thin crystal curved in the sagittal direction. This allows the x-rays diverging in the directions perpendicular to the direction of propagation to be collected and focused onto the detector 290, while allowing the x-rays to be diffracted by wavelength along the direction of propagation. For some embodiments, a bending radius between 50 and 200 mm may be used. Such configurations are sometimes called a von Hamos Spectrometer.

[0082] Curved crystal analyzers such as those made from thin wafers of single crystal silicon with (111) and (220) planes parallel to the surface may be used in some embodiments of the invention. Single crystal silicon analyzers may be grown onto a curved substrate or bent and glued to a similarly shaped substrate. [0083] In some instances, crystal analyzers can include graphite, highly oriented pyrolytic graphite (HOPG), or highly annealed pyrolytic graphite (HAPG). These embodiments may be produced by growing a graphite layer (e.g., 5 and 200 microns thick) onto a trved substrate.

[0084] FIGs. 8A and 8B illustrate a spectrometer 3730 using a crystal analyzer in the form of - a mosaic crystal 3733. in the mosaic crystal 3733, the crystal analyzer includes an ensemble of micro-crystals at varied angles throughout the material, each as small as a few hundred nanometers or as large as several microns, held with a backing 3734, typically made of metal. Transmitted x-rays that were not diffracted by the micro-crystal at the surface may still be diffracted from another micro-crystal positioned deeper within the mosaic.

[0085] Although the entire spectrum of x-rays transmitted through the object 240 will be present at all points of the transmitted annulus of x-rays 888-T, dispersion is achieved because the diverging cone has a variety of angles of incidence on the crystal analyzer, and therefore for at least some angle of incidence, x-rays of a particular energy within the designated x-ray bandwidth may be reflected. However, all other wavelengths at the same angle of incidence will not be diffracted, and will be partially or completely absorbed by the crystal analyzer shown as transmitted x-rays 899 in FIGs. 5 and 6).

[0086] FIG. 8B illustrates the relationship for which additional collection of x-rays may occur. The origin (the aperture in this case), the diffracting crystal, and the point of convergence at the detector all fall along the Rowland Circles 808-A and 808-D for the corresponding wavelengths. Although other micro-crystals are present in the mosaic crystal, only those that He along the Rowland Circle and have the correct orientation will diffract x-rays to converge to the same position at the detector 290. X-rays of varying wavelengths distributed throughout the diverging beam 888-T have a better chance of encountering a properly positioned and oriented micro-crystal, increasing the number of x-rays directed towards the detector. Use of mosaic crystals can collect as much as 30 times the amount of x-rays that a single crystal diffraction element can produce.

[0087] FIG. 8B includes the elements of FIG. 8A, but additionaUy shows the Rowland Circles 808-A and 808-D for the two x-ray wavelengths, and also only illustrates representative micro- crystals on the mosaic crystal contributing to the diffraction for the two wavelengths. Although micro-crystals with "random" orientations are illustrated in FIG.8A to dramatically illustrate the mosaic non-uniformity, most mosaic crystals will be more closely aligned with the Bragg angles at the angles of incidence for which they are designed.

[0088] FIG 9 illustrates a schematic perspective view of a system using a curved crystal analyzer having a mosaic crystal that distributes the spectrum along one axis, while focusing x-rays in the other (sagittal) axis. As noted before, it should be clear that the drawings presented here are not illustrated to scale, but have been created to better point out how the invention is to be made and used.

[0089] For more on crystal or multilayer reflectors, see James H. Underwood, "Multilayers and Crystals", Section 4.1 of the X-ray Data Booklet, which may be downloaded at: xdb.lbl.gov/Section4/Sec_4-l.pdf, and which is hereby incorporated by reference.

5.2. Detectors.

[0090] The detector 290 typically includes a 2-D pixel array 294, in which one axis is significantly longer than the other. A 2048 x 256 pixel array may be typically used, although a detector with at least 128 pixels along the long axis (the dispersive direction) may be preferred. For some configurations where the beam cross sections are smaller and the distances are shorter, fewer pixels may be used. Also, if a portion of the beam is to be blocked, fewer pixels may be used. The long axis will be aligned along the direction of x-ray propagation, and the dispersion of x-rays by wavelength will occur along that axis. The short axis will be aligned with the sagittal direction. The diffracted x-rays may not form a perfect spot, and so detection using multiple pixels may provide a higher collection efficiency.

[0091] The detector may be any one of a number of x-ray array detectors, such as a CCD array, a CMOS or S-CMOS detector, a flat panel sensor, or any one or more position sensitive x-ray array detectors known in the art that converts x-ray intensity to an electronic signal, inclttding 1-D line and 2-D array detectors. Such examples of position-sensitive detectors include linear detectors, position-sensitive array detectors, pin diodes, proportional counters, spectrometers, photodiode detectors, scintiUator-type and gas-filled array detectors, etc.

[0092] Energy resolving pixel array detectors may also be used. In these detectors, each pixel also provides information on the energy of x-rays detected, and may be especially useful when the object produces significant fluorescence. Also known as energy resolving x-ray spectrometer, such a detector uses a semiconductor device to measure the energy of the detected x-ray photons. The silicon PIN photodiode (Si-PIN) is a simple and low cost class of EDS spectrometer that typically has the lowest performance in terms of energy resolution. Energy resolving pixel array spectrometers are available and may be used in some embodiments of the invention.

[0093] Another type of detector, known as a pixel array microcalorimeter spectrometer, uses typically a superconductor circuit to measure change of the electric response from absorption of an x-ray photon.

[0094] In some instances, the spectrometer may include a mechanism, such as a shielding component, that prevents undesired x-rays from being detected. For example, at least one x- ray shielding component can be implemented that prevents x-rays not-dispersed by the wavelength dispersive component from arriving at the detector.

[0095] Additional configurations may involve additional filters (e.g. thin foils containing the appropriate element(s)) along the beam path before the detector to preferentially attenuate some unwanted x-rays from arriving at the spectrometer, reducing the background due to the detection of the x-rays scattered from the object or redtice total x-ray flux entering the spectrometer to avoid satLiration. Multiple spectrometers of the same type or combination of two or more types can be used simultaneously or interchangeable to utilize their respective strength individually or collectively.

[0096] Other detector geometries and arrangements may be known to those skilled in the art. For more on x-ray detectors, see Albert C. Thompson,

"X-Ray Detectors", Section 4.5 of the X-ray Data Booklet, which may be downloaded at: xdb.lbl.gov/Section4/Sec_4-5.pdf which is also hereby incorporated by reference. 5.3. Options and Versatility.

[0097] As discussed above, a single x-ray generating material combined with a selected coating for an x-ray optic may provide a limited bandwidth for an x-ray optical system that avoids unwanted characteristic lines and provides a particular region of an absorption spectrum for an object to be investigated. However, any given x-ray generating material with any given optical coating will generally not provide the full spectral range needed to characterize an object in transmission.

[0098] FIG 10 provides a schematic illustration of a spectrometer system having a diversity of options built into the system. The target 1102 includes a substrate 1002 and two (or more) different types of x-ray generating materials 1702 and 1704. The mount 34 upon which the target is secured not only connects to the electrical lead 32, but also has a controller 36 that allows physical motion in a lateral direction for the selection of the material to be bombarded by electrons 111.

[0099] The system of FIG. 10 also has three different optical systems 3010-A, 3010-B and 3010- C supported in a mount 3016 that allows the set of optical systems to be moved laterally to allow alignment of any of the optical systems (which may use different material coatings and filters inside to allow different x-ray bandwidths) with any of the x-ray generating targets 1702, 1704 etc. As illustrated, the rightmost x-ray generating material 1704 is being bombarded by electrons, and the left most optical system 3010-A is positioned to collect the x-rays transmitted through the window 40.

[00100] As before, the converging x-rays 887 emerging from the optical system are focused onto an aperture 272 in an aperture component 270, and also pass through the object 240 to be investigated. The resulting x-rays diverging from the aperture 272 become the "virtual origin" for the x-rays diffracted by the spectrometer 3700.

[00101] However, the aperture component 270 may have multiple openings, such as circular apertures 272 and 274 having different sizes, or slits 275 and 277 of different sizes.

[00102] As before, the spectrometer 3731 includes a mosaic crystal analyzer3733 that disperses the x-rays onto the x-ray sensor 294 of the detector 290. However, in. case the wavelength range is insufficient to span the entire spectrum in a single shot, this spectrometer 3731 also includes a mount 3740 that allows the crystal analyzer 3710, an x-ray wavelength dispersive clement, to rotate about an axis perpendicular to the direction of x-ray propagation. This allows a larger range of x-ray dispersion to be measured using a single detector.

[00103] Such a multi-source / multi optic system may be used to collect x-ray spectra in a sequence of bands. For example, a first measurement may be taken using a source/ optic combination to provide an x-ray spectrum between 4 and 5 keV; the next a different combination to provide a spectrum between 5 and 6 keV; and the next a third combination to provide a spectrum between 6 and 7 keV, etc. Rotation of the crystal about the axis may expand the range of energies collected from the same source/optic combination.

[00104] In other variations, optical systems with a variety of beam stops may be used. Beam stops may be positioned at the entrance to the optical system, at the exit of the optical elements of the optical system, or in between elements of the optical system. In some embodiments with a single condenser optic, there maybe a stop on both the entrance side and the exit side of the condenser optic, with the exit-side stop being ~ 2/3 the size of the entrance stop. These stops will both block the through-beam, and in addition, the exit stop will also block a good portion of any scattered x-rays from the condenser optic. This provides for a cleanly reflected x-ray beam.

[00105] In other variations, a number of shielding elements may be used to block or reduce unwanted x-rays from being detected. Scattering and x-ray fluorescence may occur every time x-rays encounter a component of the system. Likewise, x-rays not diffracted by the crystal analyzer will be transmitted through the analyzer, and may create additional scattered and/or fluorescence x-rays unless a suitable beam absorbing element is positioned behind the analyzer. Although these unwanted x-rays will not propagate along the principle beam-path of the system in the way that the focused x-rays propagate, they may still find their way through the system and onto a detector element unless additional shielding is installed.

[00106] In other variations, the entire system (and not just the x-ray source) may be enclosed in a vacuum chamber, removing the need for the window 40 be present to maintain the vacuum around the x-ray source. Likewise, the optical system and spectrometer may be flushed with helium gas, to reduce scattering in the system.

5.4. X-ray Emission Spectroscopy (XES).

[00107] Another embodiment adapted to detect the spectrum of x-ray fluorescence for use in x-ray emission spectroscopy (XES) is shown in FIG. 11. The embodiment of FIG. 11 is similar to the configuration illustrated in FIG. 6, except the object 240-F emits x-ray fluorescence 877. This fluorescence will generally be emitted in all directions from the object 240-F. Therefore, to block the x-rays 888-T directly transmitted through the object 240-F, a beam stop 254 is positioned after the aperture component 270, and only the x-ray fluorescence 877 emerging from the object 240-F around the beam stop 254 propagates onward to the crystal analyzer 3710. The crystal analyzer 3710 then disperses the fluorescence according to wavelength, with x-rays 877- A, 877-B, 877-C, 877-D, etc. of different wavelengths directed to different positions on the detector sensor 294.

6.0 Methods of Spectroscopic Data Gathering.

[00108] The process steps to measure the transmission spectrum of an object according to an embodiment are represented in FIGs. 12A, 12B, and 12C, and are described below.

[00109] In the first step 4610 an object to be examined is selected, and the x-ray spectral range over which transmission information is desired is selected. The object may be any type of object, as long as a significant number of detectable x-rays are transmitted through the object.

[00110] In the next step 4620, an x-ray target that will produce x-rays in the spectral range when bombarded by electrons is selected. This may include a target with any number of x- ray generating materials that have been mentioned in the Patent Applications cited above, including tungsten, molybdenum, copper, rhodium, etc. The target may include a single x- ray generating material, or multiple x-ray generating materials, and may function in the x-ray source as a static or as a rotating anode. [00111] In the next step 4630, a reflective x-ray focusing optic or optical system is selected that has a particular high-energy cutof f . This may arise from the material of the optic itself, reflective coating that have been applied to the optic or optical elements, or filters that are a part of the optical system.

[00112] The focusing optic will be designed to collect x-rays and focus them to a particular focal plane, and so in the next step 4640, the position in space where this focus plane will occur will be determined. This may be set by simply placing the optic into a predetermined position, or may require some alignment and adjustment of the position of the optic and the target within x-ray source, as noted in step 4660. Before this step is carried out, however, a decision step 4644 occurs, in which a decision is made as to whether an aperture or slit in the focal plane should be used. If the decision is yes, then a step 4650 in which the aperture or slit is positioned in the focal plane is carried out before the subsequent alignment step 4660.

[00113] Once the position of the x-rays in the focal plane (or the location of the aperture/slit) has been determined, the crystal analyzer is aligned to collect x-rays emerging from the focal plane (or aperture/slit, if used) and disperse them. The crystal analyzer may be any analyzer as described previously, including a single crystal structure, a mosaic crystal, etc.

[00114] In the next step 4680, the x-ray detector, generally a 2-D array detector as described above, will be placed to detect the x-rays dispersed by the crystal analyzer. This step will typically complete the alignment phase of the method, and the method proceeds to the steps shown in FIG. 12B, with the handoff desigxrated by the circled X in the figures.

[00115] Referring now to FIG. 12B, in the next step 4810, the electrons bombard the target and x-rays are generated.

[00116] In the next step 4820, the transmission x-ray spectrum of the instrument (without the object in the optical path) is recorded. This serves as the reference data against which the subsequent measurements will be made.

[00117] In the following steps, the object will be positioned to be illmninated by x-rays. A decision 4822 to use or not use a shutter to block the beam made, and, if positive, the shutter is used to block the beam in step 4830, and in the next step 4840 the object may be positioned without the x-rays illuminating the object. Once positioned, the next step 4850 imb locks the x-ray beam, allowing the object to be illuminated by the x-rays. If the shutter is not xised, then in step 4844 the object may be positioned while the x-rays beam is still on.

[00118] Once the x-rays illuminate the object, in the next step 4860 the x-rays transmitted through the object and then dispersed by the spectrometer are detected by the detector sensor and recorded.

[00119] Now that an x-ray transmission for the system with and without the object have been recorded, in the next step 4870 the two results may be compared, and the results of the comparison may be used to calculate the transmission spectrum of the object in the following step 4880. From the transmission results, the absorption spectrum of the object may also be inferred.

[00120] The transmission spectrum so generated represents the spectrum of the object at a single point of illumination in the object for a single x-ray bandwidth range (selected by the choice of optic and target in the previous steps). The method then proceeds to the next steps, represented by the circled Ύ in the FIGs. 12B and 12C, in which alternative variations of the data may be collected.

[00121] In the next step 4882, it is determined whether information about additional points in the object need be collected; i.e. is there a "scan" of the object desired that forms a "map" of the spectral properties of the object. If so, the new position coordinates for the object are provided in the next step 4885, and the path of control proceeds to the position marked with a circled B in FIG. 12C and back to FIG. 12B, where the process of steps 4822 4844, 4830, 4840, 4850, 4860, 4870, 4880 and 4882 are repeated in a loop until the entire desired areal dataset for the object has been completed.

[00122] If the dataset is complete, the next step 4888 determined whether the data collected will be a 2-D dataset (representing, for example, a planar "map" of the object) or if a 3-D representation of the object for analysis, using algorithms related to, for example, laminography or tomography, may be required. If 3-D data for this energy range is desired, the process determined i the next step 4892 whether in fact the 3-D data collection is complete. If not, the settings for a different relative rotational orientation for the object relative to the x-rays are determined in the next step 4895, and control proceeds to the position marked with a Girded B in FIG. 12C and back to FIG. 12B, where the process of steps 48224844, 4830, 4840, 4850, 4860, 4870, 4880, 4882, 4885, 4888, 4892, and 4895 are repeated in a loop until the entire desired 3-D dataset for the object has been completed.

[00123] Once the 2-D and/or 3-D data collection has been completed, in the next step 4900 it is determined whether additional inf onnation for a different x-ray spectral range is required. If the collected dataset is adequate, the process ends. Data collection is complete.

[00124] If, on the other hand, additional spectral data is required, in the next step 4950 a new spectral range is determined, and control passes through the path marked with the circled A in FIG. 12C and back to FIG. 12A, where the process beginning with step 4620 repeats using the new spectral range.

[00125] Variations on the method described above may also be put into practice. For example, instead of first executing a loop of data collection in x- and y-dimensions at a fixed rotation position, and then changing the rotation setting to collect additional data, ^" embodiments in which the object is rotated while the x- and y-position settings remain fixed may also be executed. Rotation of the object around the z-axis may also provide additional information that can be used in image tomosynthesis. Likewise, data for various spectral ranges may be collected with or without the completion of 2-D or 3-D scans.

7. Limitations and Extensions.

[00126] 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 being in the prior art may also be applied to various embodiments of the invention.

[00127] While specific materials, designs, configurations and fabrication steps have been set forth to desaibe 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. [00128] Elements as shown in the drawings are meant to illustrate the functioning of various embodiments of the invention, and should not be assumed to have been drawn in proportion or to scale. Likewise, any single figure should not be construed as being an illustration showing all elements of any particular embodiment of the invention.