Systems and methods using filtered X-ray fluorescence

Abstract

An x-ray optical filter includes at least one x-ray optical mirror configured to receive a plurality of x-rays having a first x-ray spectrum, separate at least some of the received x-rays into reflected x-rays and non-reflected x-rays by multi-layer reflection or total external reflection, and form an x-ray beam including at least some of the reflected x-rays and / or at least some of the non-reflected x-rays among the reflected x-rays, wherein the first x-ray spectrum has a first intensity that is a function of energy in a predetermined solid angle range. The x-ray beam has a second x-ray spectrum, and the second x-ray spectrum has a second intensity that is a function of energy in the solid angle range, the second intensity being greater than or equal to 50% of the first intensity in a first continuous energy range that is at least 3 keV wide, and the second intensity being less than or equal to 10% of the first intensity in a second continuous energy range that is at least 100 eV wide.

Description

[0001] Priority Claim

[0002] This application claims the benefit of priority of U.S. Provisional Application No. 62 / 726,776, filed Sep. 4, 2018, and U.S. Provisional Application No. 62 / 794,281, filed Jan. 18, 2019, the entire contents of each application being incorporated herein by reference.

[0003] Field

[0004] This application generally relates to laboratory-based x-ray fluorescence analysis systems and methods. Background Art

[0005] In x-ray fluorescence (XRF) analysis using a laboratory x-ray source, the main limitation in the detection and quantification of trace elements is the background contribution due to elastic and inelastic (Compton) scattering of the incident x-rays that reach and are detected by the x-ray detector. This background contribution extends over an energy range that overlaps the energy of the x-ray fluorescence lines of interest and is a significant source of noise that reduces the signal-to-noise ratio of the x-ray detector.

[0006] In some conventional XRF systems, the background contribution is reduced by attenuating the x-rays that are incident on the sample in the energy range of the x-ray fluorescence lines of interest by transmitting the incident x-ray beam through one or more thin foil filters. However, such transmission filters tend to be effective only over a relatively narrow energy range slightly above the absorption edge of the filter material. Additionally, such transmission filters also attenuate the higher energy bremsstrahlung x-rays that reach the sample and excite the x-ray fluorescence lines, thereby reducing the desired x-ray fluorescence signal. In other conventional XRF systems, the background contribution is filtered out of the incident x-ray energy spectrum by reflecting the incident x-ray beam from a multi-layer coated surface (e.g., a mirror; a monochromator) that selectively reflects x-rays within a corresponding energy range and transmits x-rays outside the corresponding energy range. The reflected x-rays are directed to illuminate the sample, while the transmitted x-rays propagate away from the sample and the x-ray detector. Summary of the Invention

[0007] In one aspect disclosed herein, an x-ray optical filter includes at least one x-ray optical mirror. The at least one x-ray optical mirror is configured to receive a plurality of x-rays having a first x-ray spectrum, separate at least some of the received x-rays into reflected x-rays and non-reflected x-rays by multi-layer reflection or total external reflection, and form an x-ray beam that includes at least some of the reflected x-rays and / or at least some of the non-reflected x-rays among the reflected x-rays, wherein the first x-ray spectrum has a first intensity that is a function of energy in a predetermined solid angle range. The x-ray beam has a second x-ray spectrum, and the second x-ray spectrum has a second intensity that is a function of energy in this solid angle range, and the second intensity is greater than or equal to 50% of the first intensity in a first continuous energy range that is at least 3 keV wide, and the second intensity is less than or equal to 10% of the first intensity in a second continuous energy range that is at least 100 eV wide.

[0008] In another aspect disclosed herein, a method for performing x-ray fluorescence analysis is provided. The method includes receiving x-rays having a first energy spectrum and a first spatial distribution. The method further includes reflecting at least some of the received x-rays, and the reflected x-rays have a second energy spectrum and a second spatial distribution. The method further includes separating the reflected x-rays into a first portion that impinges on a sample and a second portion having a predetermined x-ray energy range by multi-layer reflection and / or total external reflection, and the first portion has a third energy spectrum, and the intensity of the third energy spectrum in the predetermined x-ray energy range is reduced compared to the second energy spectrum.

[0009] In another aspect disclosed herein, an x-ray system includes at least one first x-ray optical mirror, and the at least one first x-ray optical mirror is configured to receive at least a portion of a first x-ray beam having a first energy spectrum and reflect at least some of the x-rays in this portion of the first x-ray beam to form a second x-ray beam. The x-ray system further includes at least one second x-ray optical mirror, and the at least one second x-ray optical mirror includes at least one mosaic crystal layer, at least one depth-graded multi-layer reflector, and / or at least one grazing incidence mirror. The at least one second x-ray optical mirror is configured to receive at least some of the x-rays from the at least one first x-ray optical mirror, transmit the second x-ray beam, and reflect the reflected portion of the x-rays received from the at least one first x-ray optical mirror, and the second x-ray beam includes the transmitted portion of the x-rays received from the at least one first x-ray optical mirror. The second x-ray beam has a second energy spectrum, and the intensity of the second energy spectrum is reduced in a predetermined x-ray energy range compared to the first energy spectrum.

[0010] In another aspect disclosed herein, an x-ray system includes at least one x-ray source configured to generate x-rays. The x-ray system also includes at least one x-ray optical element configured to receive and focus at least some of the x-rays from the at least one x-ray source. The at least one x-ray optical element includes at least one substrate having a surface and at least one depth-graded multilayer coating on the surface. The at least one depth-graded multilayer coating is configured to substantially reflect x-rays having energy within a first energy range and substantially not reflect x-rays having energy within a second energy range, the second energy range not overlapping the first energy range. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 Examples of biologically important elements detectable using hard x-rays in accordance with certain embodiments described herein (from MJ Pushie et al., "Elemental and chemically specific x-ray fluorescence imaging of biological systems", Chemical Reviews 114:17 (2014): 8499-8541).

[0012] Figures 2A - 2D Schematically illustrates an example x-ray optical system in accordance with certain embodiments described herein.

[0013] Figure 3A Schematically illustrates an example x-ray optical system in accordance with certain embodiments described herein.

[0014] Figure 3B Schematically illustrates in accordance with certain embodiments described herein Figure 3A an example at least one substrate of an x-ray focusing optical element.

[0015] Figure 3C Schematically illustrates in accordance with certain embodiments described herein Figure 3A an example at least one layer of an x-ray focusing optical element.

[0016] Figure 4A Schematically illustrates an example idealized x-ray spectrum of an electron-impact x-ray source within a predetermined solid angle range, and an idealized conventional foil-filtered Au target spectrum within the solid angle range.

[0017] Figure 4BSchematically illustrates an example idealized x-ray spectrum of electrons colliding with an x-ray source within a predetermined solid angle range according to certain embodiments described herein, as well as an idealized "notch" filtered Au target x-ray spectrum within the solid angle range.

[0018] Figure 5A Shows two example x-ray spectra reflected from the downstream end of the elliptical portion of an x-ray focusing optical element at an incident angle of 16.7 milliradians (0.93 degrees) for 4.5 nm and 3 nm d spacings respectively according to certain embodiments described herein.

[0019] Figure 5B Shows two example x-ray spectra reflected from the upstream end of the elliptical portion of an x-ray focusing optical element at an incident angle of 12.5 milliradians (0.72 degrees) for 4.5 nm and 3 nm d spacings respectively according to certain embodiments described herein.

[0020] Figure 6 Shows a table of K-line x-ray fluorescence cross-sections of Fe, Cu, and Zn at four x-ray excitation energies according to certain embodiments described herein.

[0021] Figure 7 Shows the suppression of unwanted background under P and S K-line fluorescence using a 5 mm thick Si filter according to certain embodiments described herein.

[0022] Figures 8A - 8D Schematically illustrates various other examples of an x-ray optical system according to certain embodiments described herein.

[0023] Figure 9A Schematically illustrates a cross-sectional view of an example first x-ray optical element including at least one capillary according to certain embodiments described herein.

[0024] Figure 9B Schematically illustrates an example first x-ray energy spectrum of a first x-ray beam according to certain embodiments described herein.

[0025] Figure 10A Schematically illustrates an example system according to certain embodiments described herein, in which at least one second x-ray optical element includes at least one x-ray reflector.

[0026] Figure 10B Schematically illustrates according to certain embodiments described herein Figure 10A of an example second x-ray energy spectrum of a second x-ray beam.

[0027] Figure 11ASchematically illustrates an example system in accordance with certain embodiments described herein, in which at least one second x-ray optical element includes a plurality of x-ray reflectors.

[0028] Figure 11B Schematically illustrates in accordance with certain embodiments described herein Figure 11A an example second x-ray energy spectrum of a second x-ray beam.

[0029] Figure 12A Schematically illustrates an example system in accordance with certain embodiments described herein, in which at least one x-ray reflector includes at least one grazing incidence mirror.

[0030] Figure 12B Schematically illustrates in accordance with certain embodiments described herein Figure 12A an example second x-ray energy spectrum of a second x-ray beam.

[0031] Figure 13A Schematically illustrates an example system in accordance with certain embodiments described herein that includes a first x-ray reflector and a second x-ray reflector.

[0032] Figure 13B Schematically illustrates in accordance with certain embodiments described herein a second x-ray beam and an example second x-ray energy spectrum of x-rays reflected from Figure 13A a second x-ray reflector.

[0033] Figure 14 is a flowchart of an example method of performing x-ray fluorescence analysis in accordance with certain embodiments described herein. DETAILED DESCRIPTION

[0034] One example area where x-ray fluorescence (XRF) can provide information is the interaction of metals in biological systems (e.g., the role of metals in biological processes; metal-based drugs). These trace elements are typically found at concentrations of parts per million (ppm) and are spatially specific at the organ, tissue, cell, and subcellular levels. Abnormal trace element distributions in tissues are directly related to many diseases, including Alzheimer's disease, Parkinson's disease, amyotrophic lateral sclerosis (ALS), and Huntington's disease. More recent studies have also linked medical conditions such as arthritis and schizophrenia to abnormal trace element concentrations in the serum of the population, which is generating interest in the elemental distribution in diseased tissues. Additionally, promising new metal-based therapies (e.g., anti-cancer and anti-HIV) are creating a need for metal mapping capabilities to better understand the in vivo uptake of drugs and to determine targeting strategies.

[0035] XRF has previously been used for chemical analysis and elemental imaging for metal mapping in biological specimens. High-performance synchrotron-based "micro-XRF" can perform elemental analysis of biological tissues with cellular and subcellular resolution (e.g., a few microns down to 30 nm) and trace-level (e.g., below parts per million (ppm)) sensitivity and quantification. Synchrotron XRF microprobes typically use a monochromator to define the single incident x-ray energy and large synchrotron-specific optics (e.g., Kirkpatrick-Baez mirrors or KB mirrors) to focus the x-rays onto a spot size of 0.5 - 5 μm. Example synchrotron-based micro-XRF studies performed at approximately 1.6 μm resolution analyzed the intracellular localization of Pt-based anticancer chemotherapeutic compounds in cancerous and non-cancerous cells and the relationship between Pt and Zn, providing insights that Zn-related detoxification is a cause of chemoresistance. In another example study, synchrotron-based micro-XRF performed at approximately 4 μm resolution was used to determine the ratio of Co to Cu around failed hip implants, which showed that failed implants preferentially distribute Co compared to non-failed implants, and analysis of this ratio can inform implant selection. In yet another example study, the spatial density of iron-rich regions in the nails of a person diagnosed with lung cancer was mapped at approximately 2 μm resolution.

[0036] However, such micro-XRF systems require access to synchrotron facilities, which are expensive (e.g., each synchrotron facility can cost up to $1 billion), and are limited in number to only a few centers worldwide. Due to the small number of such facilities with x-ray fluorescence beamlines (e.g., each beamline can cost over $10 million), competition for access is very high. Even when approved, beam time is typically limited to a week or a few days, which is problematic as it limits the number of samples that can be analyzed and / or the ability to vary the measurement protocol (e.g., improvements to sample preparation and / or sample selection). Of course, there are also other challenges, including the logistics and associated costs of traveling to the synchrotron.

[0037] Conventional laboratory-based XRF systems that have been developed for widespread access to micro-XRF analysis are typically based on electron-bombarded laboratory x-ray sources, which produce a polychromatic x-ray spectrum that is then focused to a spot size of approximately 30 - 100 μm using polycapillary x-ray optics. Compared to synchrotron systems, such conventional systems are limited to poorer resolution and have lower sensitivity, which is problematic for elemental analysis of trace concentrations in biological applications.

[0038] Certain embodiments described herein provide a system (e.g., an x-ray fluorescence system) that includes a microstructured x-ray source that includes at least one target material (e.g., Au) embedded in a thermally conductive substrate (e.g., diamond), the x-ray source being configured to emit x-rays having an energy corresponding to one or more characteristic x-ray lines of the at least one target material. The system further includes x-ray optics positioned to receive at least a portion of the x-rays from the x-ray source. The x-ray optics includes an axially symmetric x-ray focusing optic having a depth-graded multilayer coating on an inner surface thereof (e.g., having an elliptical profile in a plane along the longitudinal axis of the x-ray optic), the depth-graded multilayer coating being configured to substantially reflect (e.g., having a reflectivity greater than 30%; having a reflectivity greater than 50%) x-rays having an energy within a first predetermined range and substantially not reflect (e.g., having a reflectivity less than 10%; having a reflectivity less than 5%) x-rays within a second predetermined range (e.g., within a range including the fluorescent lines of the elements being analyzed) and to focus the reflected x-rays onto a sample to be analyzed (e.g., a biological sample; a semiconductor sample; a geological sample).

[0039] Certain embodiments described herein provide an x-ray optic that includes at least an axially symmetric portion of a tube (e.g., a capillary) having an inner surface shaped (e.g., having an elliptical profile in a plane along the longitudinal axis of the x-ray optic) to focus (e.g., using source imaging; using source reduction; using source magnification) x-rays from an x-ray source. The inner surface of the axially symmetric portion includes at least one depth-graded multilayer coating configured to substantially reflect x-rays having an energy within a first energy range and substantially not reflect x-rays having an energy within a second energy range that does not overlap the first energy range.

[0040] Certain embodiments described herein provide an x-ray fluorescence system. The system includes at least one x-ray optical device configured to receive at least a portion of a first x-ray beam having a first energy spectrum and reflect at least some of the x-rays of the portion of the first x-ray beam to form a second x-ray beam. The second x-ray beam has a second energy spectrum. The system further includes at least one optical element (e.g., a mirror) configured to receive at least some of the x-rays of the second x-ray beam, transmit a third x-ray beam including a transmitted portion of the x-rays received from the second x-ray beam, and reflect a reflected portion of the x-rays received from the second x-ray beam. The third x-ray beam has a third energy spectrum, the intensity of which in a predetermined x-ray energy range is reduced compared to the second energy spectrum.

[0041] Certain embodiments described herein provide a method of performing x-ray fluorescence analysis. The method includes: receiving x-rays having a first energy spectrum and a first spatial distribution; and reflecting at least some of the received x-rays. The reflected x-rays have a second energy spectrum and a second spatial distribution. The method further includes: transmitting a first portion of the reflected x-rays to impinge on a sample; and reflecting a second portion of the reflected x-rays. The first portion has a third energy spectrum, the intensity of which in a predetermined x-ray energy range is reduced compared to the second energy spectrum.

[0042] Certain embodiments described herein advantageously tailor the energy spectrum of x-rays incident on a sample to maintain (e.g., substantially not affect) the intensity (e.g., flux) of x-rays having energies above the x-ray fluorescence energy range of interest while reducing (e.g., removing; excising) the intensity (e.g., flux) of x-rays within the x-ray fluorescence energy range of interest. Certain embodiments reduce the impact of scattered x-rays on the background within the x-ray fluorescence energy range by reducing the intensity of the incident x-rays within the x-ray fluorescence energy range. By maintaining the intensity of the incident x-rays having energies above the x-ray fluorescence energy range, certain embodiments maintain (e.g., substantially do not reduce) the x-ray intensity that excites x-ray fluorescence within the sample. Certain embodiments described herein utilize reflection rather than absorption to reduce the intensity of x-rays within the x-ray fluorescence energy range of interest.

[0043] Certain embodiments described herein advantageously act as a "notch filter" where x-rays within at least one predetermined energy range having a lower x-ray energy and an upper x-ray energy are substantially prevented from impinging on the sample, while x-rays outside the at least one predetermined energy range (e.g., energies above the upper x-ray energy; energies above the upper x-ray energy and x-rays below the lower x-ray energy) are allowed to propagate to impinge on the sample.

[0044] Certain embodiments described herein advantageously increase the throughput of x-ray fluorescence analysis by reducing the data acquisition time required to perform measurements with a sufficient signal-to-noise ratio. For example, the data acquisition time T can be expressed as: T ∝ B / F 2 , where B is the background influence and F is the x-ray fluorescence signal. Certain embodiments described herein reduce the background influence B by approximately 90%, while the x-ray fluorescence signal F is only reduced by approximately 10%, resulting in a reduction of the data acquisition time T by approximately 88%.

[0045] Certain embodiments described herein are configured to facilitate (e.g., improve) an x-ray fluorescence system configured for trace element mapping (e.g., in biological samples; in semiconductor samples; in geological samples). In certain such embodiments, the bremsstrahlung x-ray beam is refocused using a second parabolic optical device, and the sample is scanned to generate an elemental map of a wide range of elements. Certain embodiments described herein provide a more rapid analysis of the trace elements being analyzed and / or increased sensitivity (e.g., by improving the signal-to-noise ratio), while maintaining a desired high spatial resolution (e.g., for semiconductor applications, biomedical research, and other applications). Certain other embodiments described herein provide a more rapid analysis of the trace elements being analyzed and / or increased sensitivity (e.g., by improving the signal-to-noise ratio) in applications that do not utilize high spatial resolution (e.g., mineral exploration).

[0046] Some other embodiments are configured to determine the influence of a first x-ray fluorescence line from a first element (e.g., Hf) from the influence of a second x-ray fluorescence line from a second element (e.g., Cu), where the first x-ray fluorescence line and the second x-ray fluorescence line have similar (e.g., substantially the same) energies. For example, in a semiconductor processing application, a notch filter can be configured to remove x-rays in the energy range of 9 keV - 9.6 keV from an incident x-ray beam, and a sample containing both Cu (e.g., having a K absorption edge at about 9 keV and a Kα fluorescence line at about 8 keV) and Hf (e.g., having an L absorption edge at about 9.6 keV and an Lα fluorescence line at about 8 keV) can be analyzed by: (i) measuring a first x-ray fluorescence from the sample using a notch filter that blocks x-rays in the energy range from striking the sample; (ii) measuring a second x-ray fluorescence from the sample without the notch filter that blocks x-rays in the energy range from striking the sample, and (iii) comparing the first x-ray fluorescence and the second x-ray fluorescence. Some other embodiments described herein are configured to advantageously remove the influence of diffraction peaks from the measured x-rays. Some other embodiments described herein are configured to reduce (e.g., block; minimize) the flux of x-rays in a selected energy range striking the sample while allowing x-rays outside the selected energy range to strike the sample, thereby advantageously reducing the overall x-ray flux striking the sample (e.g., a sample that is sensitive or vulnerable to radiation doses above a predetermined threshold).

[0047] Regarding biological systems, XRF analysis is typically complex (e.g., XRF of different elements is maximized at different energies), and it may be desirable to detect multiple elements simultaneously with as high a sensitivity as possible. Some embodiments described herein generate both strong characteristic x-ray energies associated with the x-ray target material and a broad polychromatic x-ray spectrum up to the accelerating voltage of the electron beam of the x-ray source, thus enabling increased excitation.

[0048] Certain embodiments described herein provide systems and methods for x-ray fluorescence for chemical analysis and elemental imaging at subcellular resolution. As described herein, certain such embodiments may provide advantages that even exceed those provided by recently developed laboratory micro-XRF systems that incorporate microstructured x-ray sources and double-parabolic x-ray optics to achieve resolutions less than 10 μm (e.g., 8 μm) and detection sensitivities below ppm and below femtogram (absolute). This laboratory-based micro-XRF system has been applied by various researchers to a wide range of biological applications, including but not limited to: nanoparticles in tumors; trace element dysregulation in diseased calcified tissues (e.g., penile stones, kidney stones, and teeth); genetically modifying crops to improve nutrient uptake (e.g., iron); the correlation between the abnormal elemental distribution of Zr, I, Cu, and Sr in hair samples and the occurrence and development of diabetes, autism, and cancer; Parkinson's disease mouse models, and the trend towards the use of micro-XRF and inductively coupled plasma mass spectrometry (ICP-MS) technology to create quantitative mixing routine applications. Certain embodiments described herein are configured to advantageously provide imaging of biologically important elements at a resolution of 1.6 μm at a speed three times faster than that provided by the system at 8 μm resolution. Certain embodiments described herein advantageously extend the use of laboratory micro-XRF systems for imaging biologically important elements in biomedical applications and accelerate the pace of biomedical research that has been bottlenecked due to low synchrotron access.

[0049] Certain embodiments described herein are configured to provide information related to metal-binding proteins (e.g., metalloproteins) in tissue samples. Metalloproteins, which are known to account for one-third of all proteins in the human body, perform at least one step in almost every biological pathway. It is hypothesized that the dysregulation of these physiologically important metals is associated with a variety of diseases, including Menkes and Wilson's diseases, neurodegenerative diseases (such as Alzheimer's disease, Parkinson's disease, amyotrophic lateral sclerosis (ALS), Huntington's disease, autism), and autoimmune diseases, such as rheumatoid arthritis, Crohn's disease, Graves' disease, and infertility. Certain embodiments described herein are configured to provide information related to other elements that have not been previously found in biological systems but are being introduced into such systems either intentionally (e.g., pharmaceuticals, which have evolved towards inorganic-based concepts and metal nanoparticles) or unintentionally (e.g., through environmental exposure accumulation, typically as a result of modern industrial uses and pollution), and may have potential toxic effects. Certain embodiments described herein are configured to provide information related to the development of targeted and rational design methods for metal drugs (e.g., information related to the uptake of metal drugs by tumors, cells, and organelles; information related to the clearance or detoxification of such drugs; information related to the efficacy of such drugs and / or the development of resistance to such drugs).

[0050] Although the trace-level concentrations of many biologically important elements in biological samples are low (due to the small number of metal atoms in the small detection volume), certain embodiments described herein provide high-spatial-resolution imaging information with a scale resolution of multiple lengths (e.g., related to understanding the underlying biological functions of physiologically important elements and associated molecules, as well as the biological pathways of therapeutic drugs or toxic elements), such as cellular resolution for imaging tissues and organs and subcellular resolution for imaging cells. Certain embodiments described herein enable the simultaneous imaging of multiple elements at subcellular resolution and high sensitivity to provide information related to the relationship between the elements and the corresponding biomolecules (e.g., metalloproteins) and / or structural information (such as K). For example, imaging the distribution of trace elements along with phosphorus, sulfur, and potassium by certain embodiments described herein provides information related to the spatial correlation of DNA (P), protein (S), and cell shape (K).

[0051] Certain embodiments described herein provide “pre - synchrotron” screening, which can inform sample preparation and ensure efficient use of synchrotron resources, as well as select samples prior to ultra - high - resolution (e.g., 30 nm–100 nm) XRF studies. Certain embodiments described herein provide analysis of a large number of samples (e.g., samples used in many biomedical applications) to account for statistical population variance. Certain embodiments described herein provide analysis of samples that cannot be transported to other facilities (e.g., synchrotron) due to the proprietary nature of the sample, the hazardous nature of the sample, or other reasons. Certain embodiments described herein provide high penetration and experimental flexibility in accommodating various sample sizes and shapes under various conditions (e.g., within a range of flexible operating conditions, wet, cryopreserved, fixed, and / or stained; ambient; cryogenic). Certain embodiments described herein provide non - destructive x - ray fluorescence analysis that can be combined with related (e.g., follow - up or follow - on) analysis and / or imaging performed with other techniques for studying the chemical state of elements of interest, including but not limited to: infrared and Raman spectroscopy / microscopy, molecular mass spectrometry (e.g., matrix - assisted laser desorption / ionization or MALDI), secondary mass spectrometry x - ray absorption spectroscopy. Certain embodiments described herein advantageously provide other benefits, including but not limited to: simultaneous detection of many elements within the absolute detection limit and measurement of samples in their natural or near - natural state under ambient conditions. Certain embodiments described herein provide much higher spatial resolution than mass spectrometry imaging techniques (e.g., laser ablation inductively coupled plasma mass spectrometry or LA - ICP - MS), and provide sensitivity orders of magnitude higher and radiation dose lower than electron - based techniques.

[0052] Certain embodiments described herein are configured to provide elemental imaging (e.g., information about spatial distribution) of one or more biologically important elements present in tissue samples at trace and ultra - trace levels (e.g., parts per million; 0.1% or less), such as in metalloproteins. Figure 1 Examples of biologically important elements detectable with hard x - rays according to certain embodiments described herein (see MJ Pushie et al., “Elemental and chemically specific x - ray fluorescence imaging of biological systems”, Chemical Reviews 114:17 (2014):8499 - 8541) are shown. As Figure 1 shown, biologically important elements can include:

[0053] · Physiologically important elements essential for life (e.g., Na, Mg, Si, P, S, Cl, K, Ca, V, Mn, Fe, Co, Ni, Cu, Zn, Se, Br, Mo, I). For example, such an element can be a component of a protein (e.g., a metalloprotein containing Fe, Cu, and / or Zn);

[0054] · Pharmacologically active elements used as novel therapeutic and diagnostic agents (e.g., Ti, Ga, Zr, Ru, Pd, Ag, Pt, Au, Bi, Gd, Dy). For example, such an element can be a component of a cancer drug (e.g., including Pt, Au, and / or Ru); and

[0055] · Toxic or carcinogenic elements widely distributed due to modern industrial and technological activities (e.g., Al, Cr, As, Sr, Cd, Sn, Sb, Te, Ba, Hg, Tl, Pb, Po, Th, Pa, U, Np, Pu, Am).

[0056] Figures 2A - 2D Schematically illustrates various example x-ray optical systems 10 in accordance with certain embodiments described herein. Figure 2A The x-ray optical system 10 (e.g., an x-ray optical filter) includes at least one x-ray optical element 20 (e.g., a mirror). In certain embodiments, at least one x-ray optical element 20 includes at least one substrate and at least one layer on the at least one substrate. At least one x-ray optical element 20 is configured to receive a plurality of x-rays having a first x-ray spectrum (e.g., a first x-ray beam 12), and separate at least some of the received x-rays into reflected x-rays and non-reflected x-rays by multi-layer reflection (e.g., reflection satisfying Bragg reflection conditions from multi-layers and / or mosaic crystal layers) or total external reflection, wherein the first x-ray spectrum has a first intensity that is a function of energy in a predetermined solid angle range. At least one x-ray optical element 20 is further configured to form a second x-ray beam 32, which includes at least some of the reflected x-rays and / or at least some of the non-reflected x-rays among the reflected x-rays. The second x-ray beam 32 has a second x-ray spectrum, and the second intensity of the second x-ray spectrum is a function of energy in the solid angle range. The second intensity is greater than or equal to 50% of the first intensity in a first continuous energy range that is at least 3 keV wide, and the second intensity is less than or equal to 10% of the first intensity in a second continuous energy range that is at least 100 eV wide. In certain embodiments, the second intensity is greater than or equal to 50% of the first intensity in a third continuous energy range that is at least 2 keV wide, and the second continuous energy range is between the first continuous energy range and the third continuous energy range.

[0057] In certain embodiments, as shown by Figure 2BSchematically illustrated, the x-ray optical system 10 includes at least one x-ray source 40 configured to generate a first x-ray beam 12, and at least one x-ray optical element 20 is positioned to receive at least a portion of the x-rays from the at least one x-ray source 40 (e.g., at least a portion of the first x-ray beam 12). As Figure 2C and 2D Schematically illustrated, in certain embodiments, at least a portion of the second x-ray beam 32 is configured to irradiate a sample 50 (e.g., a biological sample; a semiconductor sample; a geological sample) and excite x-ray fluorescence 52 within the sample 50. The x-ray fluorescence 52 is emitted from the sample 50 and includes x-ray fluorescence lines within a predetermined x-ray energy range.

[0058] In certain embodiments, the system 10 further includes at least one x-ray detector 60 configured to detect and measure at least a portion of the x-ray fluorescence 52 emitted from the sample 50. For example, the at least one x-ray detector 60 may include an energy dispersive detector configured to detect fluorescent x-rays emitted from the sample (e.g., to generate an image indicative of the elemental distribution of the sample). As Figure 2C Schematically illustrated, the second x-ray beam 32 impinges on a first surface 54 of the sample 50, and the at least one x-ray detector 60 is positioned to receive the x-ray fluorescence 52 emitted from a second surface 56 of the sample 50 that is different from the first surface 54 (e.g., the second surface 56 faces away from the first surface 54). For another example, as Figure 2D Schematically illustrated, the second x-ray beam 32 impinges on a first surface 54 of the sample 50, and the at least one x-ray detector 60 is positioned to receive the x-ray fluorescence 52 emitted from the first surface 54 (e.g., a portion of the first surface 54 is impinged upon by the second x-ray beam 32, and the x-ray fluorescence 52 is received by the at least one x-ray detector 60 from the same portion and / or different portions of the first surface 54). Examples of x-ray detectors 60 compatible with certain embodiments described herein are disclosed in U.S. Patent Nos. 9,874,531, 9,823,203, 9,719,947, 9,594,036, 9,570,265, 9,543,109, 9,449,781, 9,448,190, and 9,390,881, the entire contents of each patent being incorporated herein by reference.

[0059] Figure 3A Schematically illustrates an example x-ray optical system 10 in accordance with certain embodiments described herein. Figure 3AAn example x-ray optical system 10 includes: an x-ray source 40 configured to emit a first x-ray beam 12; at least one x-ray optical element 20 (e.g., a mirror) configured to receive the first x-ray beam 12 and form and direct a second x-ray beam 32 to impinge on a sample 50; and at least one x-ray detector 60 configured to detect (e.g., measure) fluorescent x-rays emitted from the sample 50. In some embodiments, the system 10 is integrated with a vacuum system and is configured to provide elemental imaging of a sample (e.g., a freeze-dried tissue sample; a biological sample; a semiconductor sample; a geological sample). With respect to biological samples, the system 10 of some embodiments advantageously provides micro-XRF analysis and imaging at subcellular resolution (e.g., in the range of 0.5 μm to 2 μm; 1.5 μm; 1.6 μm; a resolution nearly an order of magnitude better than previous systems) and high sensitivity (e.g., ppm) for detecting biologically important elements (e.g., Fe, Cu, Zn, P, S) present at trace levels of concentration.

[0060] In some embodiments, the x-ray source 40 includes at least one microstructured target 42 having at least one material (e.g., Au) on or embedded in a thermally conductive substrate 44 (e.g., diamond). The at least one material of the at least one microstructured target 42 is configured to emit x-rays (e.g., a first x-ray beam 12) with an ultra-high source brightness when bombarded by electrons 46, and the first x-ray beam 12 is emitted from the x-ray source 40 through at least one window 48. The at least one material of the at least one target 42 is configured to emit x-rays having an energy higher than one or more characteristic x-ray fluorescence lines of the sample 50 to be analyzed. For example, the characteristic L line of Au is slightly higher than the K absorption edge of Zn, but not so high as to exceed the K absorption edges of Fe and Cu by too much. Thus, for the generation of x-ray fluorescence signals for these exemplary elements, the efficiency of the L line of the Au target material can be more than three times higher. The x-ray source 40 of some embodiments has a source size in the range of 5 μm to 15 μm (e.g., 8 μm; 10 μm). Exemplary parameters of the x-ray source 40 include but are not limited to: an electron beam operating acceleration voltage of 35 kV; an electron power of 30 W; a window 48 including beryllium and having a thickness of 50 μm; an electron beam coverage area (e.g., full width at half maximum) on the target of 8 μm (width) x 100 μm (length); a substrate 44 including diamond having 200 etched trenches (e.g., 4 μm deep, 1 μm thick, and 20 μm wide) extending along the long dimension of the electron beam coverage area; trenches filled with at least one material (e.g., Au) of the at least one target 42; and a first x-ray beam 12 having a take-off angle of 5° along the long dimension of the electron beam coverage area. Exemplary x-ray sources 40 compatible with some embodiments described herein are disclosed in U.S. Patent Nos. 9,874,531, 9,823,203, 9,719,947, 9,594,036, 9,570,265, 9,543,109, 9,449,781, 9,448,190, and 9,390,881, the entire contents of each patent being incorporated herein by reference.

[0061] Figure 3AExample of at least one x-ray optical element 20 includes an axially symmetric x-ray focusing optical element 70 (e.g., mirror; mirror lens) and a light stop 80. The x-ray focusing optical element 70 includes at least one substrate 72 and at least one layer 74 (e.g., depth-graded multilayer coating 90) on the at least one substrate 72, and the x-ray focusing optical element 70 is configured to efficiently collect at least some of the x-rays emitted from an x-ray source 40 (e.g., first x-ray beam 12), the collected x-rays having a specific x-ray energy (e.g., characteristic L line of Au). The x-ray focusing optical element 70 is further configured to focus the collected x-rays (e.g., second x-ray beam 32 consisting essentially of at least some of the reflected x-rays among the reflected x-rays) onto a sample 50 to be analyzed (e.g., to maximize the signal; the focused flux of these energies is increased by at least 13 times). As Figure 3A schematically illustrated in, the light stop 80 is placed on the longitudinal axis of the x-ray focusing optical element 70 (e.g., at or near the upstream end 76 of the x-ray focusing optical element 70; at or near the downstream end 78 of the x-ray focusing optical element 70; upstream of the x-ray focusing optical element 70; downstream of the x-ray focusing optical element 70). The light stop 70 is configured to prevent x-rays not reflected by the x-ray focusing optical element 70 from impinging on the sample 50. Example light stops 80 compatible with certain embodiments described herein are disclosed in U.S. Patent Nos. 9,874,531, 9,823,203, 9,719,947, 9,594,036, 9,570,265, 9,543,109, 9,449,781, 9,448,190, and 9,390,881, the entire contents of each patent being incorporated herein by reference.

[0062] Figure 3B Schematically illustrates according to certain embodiments described herein Figure 3AAn example of the x-ray focusing optical element 70 includes at least one substrate 72. The at least one substrate 72 of certain embodiments includes a single, unitary element. For example, the at least one substrate 72 may include a portion of a hollow, axially symmetric tube or pipe (e.g., a capillary) that extends along a longitudinal axis 75 and includes an inner surface 73 (e.g., a mirror surface) that extends completely around the longitudinal axis 75 (e.g., circumscribes the longitudinal axis 75; extends 360 degrees around the longitudinal axis 75). In certain other embodiments, the at least one substrate 72 includes at least a portion of a hollow, axially symmetric structure (e.g., a portion of an axially symmetric tube) that extends along the longitudinal axis 75 with an inner surface that extends only partially around the longitudinal axis 75 (e.g., less than 360 degrees; in the range of 45 degrees to 360 degrees; in the range of 45 degrees to 315 degrees; in the range of 180 degrees to 360 degrees; in the range of 90 degrees to 270 degrees). In certain embodiments, the at least one substrate 72 includes a plurality of substrate portions (e.g., 2, 3, 4, 5, 6, or more) that are separated from each other (e.g., have a gap between the substrate portions) and are distributed around the longitudinal axis 75, wherein the surface 73 of each substrate portion extends at least partially around the longitudinal axis 75 and along the longitudinal axis 75. For example, the surface 73 of the plurality of substrate portions may extend around the longitudinal axis 75 at an angle in the range of 15 degrees to 175 degrees, in the range of 30 degrees to 115 degrees, and / or in the range of 45 degrees to 85 degrees.

[0063] In certain embodiments, the surface 73 of the x-ray focusing optical element 70 is configured to focus x-rays by imaging a portion of an x-ray source 40 (e.g., a source spot on at least one microstructured target 42 that emits x-rays) at a 1:1 ratio at the sample 50. In certain other embodiments, the surface 73 of the x-ray focusing optical element 70 is configured to focus x-rays by magnifying (e.g., at least 3 times; at least 5 times; 1:3; 1:5) a portion of an x-ray source 40 (e.g., a source spot on at least one microstructured target 42 that emits x-rays) at the sample 50. In certain other embodiments, the surface 73 of the x-ray focusing optical element 70 is configured to focus x-rays by reducing (e.g., at least 3 times; at least 5 times; 3:1; 5:1) a portion of an x-ray source 40 (e.g., a source spot on at least one microstructured target 42 that emits x-rays) at the sample 50. In certain embodiments, as by Figure 3BSchematic illustration, the surface 73 has an elliptical contour shape (e.g., in a plane along the longitudinal axis), and the elliptical contour shape is configured for source reduction (e.g., the surface 73 collects and focuses x-rays from the source spot of the x-ray source 40 to produce a reduced image of the source spot). For example, the x-ray focusing optical element 70 can be configured for source reduction by at least 5 times (e.g., a 5:1 reduction ratio; the spot size is reduced by 5 times), which corresponds to a ratio of at least 5:1 between the distance from the source spot to the center of the x-ray focusing optical element 70 and the distance from the center of the x-ray focusing optical element 70 to the focus of the x-ray focusing optical element 70. In the case where the source spot size is 8 μm, the x-ray focusing optical element 70 reduces the source by at least 5 times, which produces a focused spot size equal to or less than 1.6 μm. In some other embodiments, the source reduction ratio of the x-ray focusing optical element 70 is at least 3 times (e.g., a 3:1 reduction ratio; the spot size is reduced by 3 times; the distance between the source spot and the center of the x-ray focusing optical element 70 is 100 mm and the distance between the center of the x-ray focusing optical element 70 and the focus of the x-ray focusing optical element 70 is 30 mm), so as to produce a focused spot size equal to or less than 2.7 μm for a source spot size of about 8 μm - 9 μm. In some embodiments, the axially symmetric elliptical portion of the reflective surface 73 of the x-ray focusing optical element 70 has a nearly minimum surface error (e.g., a surface error less than 200 nm) and / or a focus (e.g., point spread function) better than 3 μm for a source size of 10 μm (e.g., a focus or point spread function better than 0.6 μm).

[0064] Figure 3C Schematically illustrates an example of at least one layer 74 of the x-ray focusing optical element 70 according to certain embodiments described herein Figure 3A The at least one layer 74 includes at least one depth-graded multilayer 90 (e.g., supermirror) coated on the surface 73 of at least one substrate 70 (e.g., manufactured using atomic layer deposition (ALD) technology; manufactured using sputtering). ALD and sputtering are quite mature technologies and are widely used due to their conformal coating characteristics (e.g., when manufacturing advanced integrated circuits; when manufacturing multilayers on flat substrates for x-ray monochromators).

[0065] As Figure 3CSchematically illustrated, at least one depth-graded multi-layer 90 of certain embodiments includes a plurality of layer pairs 92 (e.g., layer pairs or bilayer pairs having high atomic number materials and low atomic number materials alternating in a direction perpendicular to the layers). The thicknesses of the layer pairs are different from each other (e.g., the spacings between successive high atomic number material layers are different from each other). For example, each layer pair 92 may include a first layer 94 (including a first material) and a second layer 96 (including a second material) (e.g., Pt / Si layer pair; Pt / B4C layer pair; Pt / Al2O3 layer pair; W / Si layer pair; W / B4C layer pair; W / Al2O3 layer pair; Mo / Si layer pair; Mo / B4C layer pair; Mo / Al2O3 layer pair; Ni / Si layer pair; Ni / B4C layer pair; Ni / Al2O3 layer pair; Cu / Si layer pair; Cu / B4C layer pair; Cu / Al2O3 layer pair). The thickness of each layer pair 92 (e.g., in a direction substantially perpendicular to the surface 73; d-spacing) is substantially constant along a direction substantially parallel to the surface 73. However, along the normal to the surface 73, the layer pairs are configured in sets or groups, where the thicknesses of the layer pairs 72 in each group are different from each other. For example, the thicknesses of the layer pairs 72 of the respective groups may increase from a first thickness (e.g., 3 nm) to a second thickness (e.g., 4.5 nm), where the layer group closer to the surface of the substrate 72 has a thinner layer thickness than the layer group farther from the surface of the substrate 72.

[0066] In Figure 3C an example depth-graded multi-layer 90, the total number of layer pairs 90 is 240, consisting of 6 sets of 40 layer pairs 92. From the first set 98a of layer pairs 92a (e.g., closest to the surface 73) to the last set 98f of layer pairs 92 (e.g., farthest from the surface 73), the thickness of the layer pairs 92 gradually increases (e.g., from 3 nm to 4.5 nm, with each set increasing by approximately 0.3 nm = 3 Å, which is approximately equal to the thickness of two atomic layers). The thickness difference between the sets 98a - 98f of layer pairs 92 is limited by the quantization nature of the atomic size and does not need to be exact. For example, the depth-graded multi-layer 90 may include 6 sets of 40 Pt / Al2O3 layer pairs or 40 W / Al2O3 layer pairs, where the d-spacing is in the range of 3 nm to 4.5 nm, and each set increases by approximately 0.3 nm. At least one depth-graded multi-layer 90 is substantially different from the multi-layers most widely used in monochromators. For example, for a monochromator, all layer pairs have the same thickness as each other. For another example, the typical number of layer pairs used in a monochromator (e.g., between 10 and 40) is at least about 3 - 4 times less than the total number of layer pairs 92 of the depth-graded multi-layer 90 (e.g., between 100 and 500; between 150 and 400; between 200 and 300).

[0067] In some embodiments, the x-ray focusing optical element 70 is further configured to reduce background effects at specific x-ray energies that are not desired (e.g., reduce by at least a factor of 12), which would otherwise obscure the trace element signal of interest. The main component of this undesired background effect is the bremsstrahlung continuum from the laboratory x-ray source 40. Previously, two conventional methods have been used to minimize the background B j,k : (i) crystal or multilayer monochromators to obtain an x-ray excitation beam with a narrow energy bandwidth, but at the cost of substantially reducing the optical flux; and (ii) spectral filters (e.g., foils) to absorb a portion of the "undesired" x-rays. However, both conventional methods have major limitations for laboratory micro-XRF, particularly for high-resolution applications with a focal spot size less than 8 μm. The monochromator method only provides limited flux because only a small portion of the x-ray spectrum is used (e.g., only one x-ray energy, such as the Au Lα energy of 9.713 keV, would be used). Additionally, there are technical challenges associated with the conflicting requirements of: (i) collecting x-rays over a large solid angle to obtain good focused x-ray flux; and (ii) the need for a highly collimated x-ray beam to be used with the monochromator, which becomes more challenging when collecting x-rays incident at multiple angles to meet requirement (i). Thus, the monochromator method is almost only performed at synchrotron facilities and no laboratory micro-XRF systems use this method.

[0068] Figure 4A Schematically illustrates (i) an example idealized first x-ray spectrum within a predetermined solid angle range of an electron-impact x-ray source 40 including an Au target 42, and the K-edge absorption energies of Fe, Cu, and Zn (at 7.11 keV, 8.98 keV, and 9.66 keV, respectively) and their corresponding Kα characteristic x-ray energies (at 6.4 keV, 8.05 keV, and 8.64 keV, respectively), and (iii) an example idealized second x-ray spectrum within that solid angle range and corresponding to the first x-ray spectrum using an absorption spectral filter, the absorption spectral filter including a 15-μm thick Cr foil, the 15-μm thick Cr foil being placed in the path of the x-rays from the x-ray source 40. The K-edge absorption energy is the minimum x-ray energy required to ionize the K-shell electrons of the corresponding element and generate characteristic K-line fluorescent x-rays. The example first x-ray spectrum contains distinct characteristic L-lines of the Au target 42 and the continuum bremsstrahlung (the main component of the background B j,k ). To reduce x-rays from the x-ray source 40 having an energy equal to the energies of the Fe, Cu, and Zn Kα lines (e.g., bremsstrahlung x-rays), the spectral absorption filter includes a filtering material having an ionization energy below that of the Fe Kα line. As Figure 4AAs shown, a 15-μm-thick Cr foil absorption spectral filter absorbs higher-energy x-rays and reduces the background portion of the second x-ray spectrum transmitted through the absorption spectral filter in a bandwidth corresponding to the x-ray energies of the Fe, Cu, and Zn Kα lines. However, the absorption spectral filter also significantly reduces useful x-ray energies above the K-edge absorption energies of these elements, resulting in an undesired reduction in the x-ray fluorescence signal F j，k of.

[0069] In contrast, Figure 4B schematically illustrates (i) an example idealized first x-ray spectrum within a predetermined solid angle range, (ii) Figure 4A the K-edge absorption energies of Fe, Cu, and Zn therein and their corresponding Kα characteristic x-ray energies, and (iii) an example idealized second x-ray spectrum within the solid angle range and corresponding to the first x-ray spectrum using an x-ray focusing optical element 70 having a depth-graded multilayer 90. The depth-graded multilayer 90 is configured to act as a "notch" filter, where the intensity of the second x-ray spectrum (e.g., the x-ray spectrum of the reflected and focused x-rays) is reduced only within a specific bandwidth relative to the first x-ray spectrum (e.g., the x-ray spectrum of the x-rays incident on the depth-graded multilayer 90), while the remaining x-ray spectrum is substantially maintained (e.g., the second x-ray spectrum is substantially equal to the first x-ray spectrum). For example, as Figure 4B schematically illustrated, only the x-ray energies in the bandwidth where the background overlaps the Fe, Cu, and Zn Kα lines in the second x-ray spectrum are reduced, while useful higher-energy x-rays (e.g., energies above the K-edge absorption energy of Zn) are effectively maintained, thereby providing optimal fluorescence excitation of the elements of interest. In certain such embodiments, while maintaining a high x-ray fluorescence signal F j，k , the background F j，k is reduced (e.g., minimized).

[0070] In certain embodiments, the x-ray focusing x-ray optical element 70 (e.g., including at least one substrate 72 and at least one layer 74 including a depth-graded multilayer 90) is configured to provide a near-optimal spectrum for the intended application. For example, applying Bragg's equation (2d·sinθ = λ), the x-rays reflected from locations on the depth-graded multilayer 90 have a spectral bandwidth of approximately 45 - 50%. The lowest x-ray energy reflected by the depth-graded multilayer 90 is given by the maximum incident angle and the maximum thickness (e.g., d-spacing) (e.g., 4.5 nm), and the maximum incident angle is at the downstream end 78 of the elliptical portion of the x-ray focusing optical element 70 (e.g., the end 78 farthest from the x-ray source 40; see Figure 3A ).

[0071] Figure 5AShows two example x-ray spectra reflected from the downstream end 78 of the elliptical portion of the x-ray focusing optical element 70 at an incident angle of 16.7 milliradians (0.93 degrees) for 4.5 nm and 3 nm d-spacing, respectively. Three fluorescence lines of Fe, Cu, and Zn at 6.4 keV, 8.05 keV, and 8.64 keV, respectively, are in the range of x-ray energies that are essentially not reflected by the elliptical portion of the x-ray focusing optical element 70. The lowest x-ray energy reflected by the set 98 of layer pairs 92 having a thickness (e.g., d-spacing) of 4.5 nm at an incident angle of 16.7 milliradians is equal to 8.86 keV, which is about 200 eV higher than the Zn Kα line energy. The x-ray energy reflected by the set 98 of layer pairs 92 having a thickness (e.g., d-spacing) of 3 nm at an incident angle of 16.7 milliradians is equal to 13 keV. Thus, the energy range of the x-rays reflected by the depth-graded multilayer 90 at the downstream end 78 of the x-ray focusing optical element 70 (as shown by the shaded region of Figure 5A is in the range between 8.86 keV and 13 keV, which includes all three strong L-lines of the Au target and also includes the bremsstrahlung continuum.

[0072] Figure 5B Shows two example x-ray spectra reflected from the upstream end 76 of the elliptical portion of the x-ray focusing optical element 70 at an incident angle of 12.5 milliradians (0.72 degrees) for 4.5 nm and 3 nm d-spacing, respectively. Three fluorescence lines of Fe, Cu, and Zn at 6.4 keV, 8.05 keV, and 8.64 keV, respectively, are in the range of x-ray energies that are essentially not reflected by the elliptical portion of the x-ray focusing optical element 70. The energy range of the x-rays reflected by the depth-graded multilayer 90 at the upstream end 76 of the x-ray focusing optical element 70 (as shown by the shaded region of Figure 5B is in the range between 11.3 keV and 17 keV, which includes two of the three strong L-lines (11.44 keV and 11.61 keV) of the Au target and also includes the bremsstrahlung continuum. The 9.71 keV L-line of Au is not in this x-ray energy range, but the downstream mirror length of only half (50%) has a large enough incident angle to satisfy the Bragg reflection condition, so the total collection angle of this line is about 50% of the total collection angle of the other two Au lines. However, the associated loss of the reflected flux of this line is not just an offset of the x-ray flux of the bremsstrahlung continuum over a wide range of 4 keV energy bandwidth. The intensity ratio of the strongest L-line of Au is about 1000 times higher than the bremsstrahlung continuum over the energy width of the line (e.g., about 4 eV), so the x-ray flux of the focused second x-ray beam 32 may contain up to 50% of the bremsstrahlung continuum. It should be noted that the lowest energy of the continuum is 8.9 keV, which is higher than the Zn Kα line energy. Thus, the continuum contributes to the background Bj,k has less impact, but contributes significantly to the fluorescence signals F of Fe, Cu, and Zn j,k .

[0073] As Figure 5A and 5B shown in Figure 4B , in some embodiments, the depth-graded multilayer 90 of the x-ray focusing optic 70 provides spectral "notch" filtering that approximates j,k shown in j,k and reduces the background B while efficiently reflecting and focusing x-rays of the following energies

[0074] : These energies are favorable (e.g., nearly optimal) for efficiently generating fluorescence signals of elements with ionization absorption edge energies below 8.9 keV. Additionally, in some embodiments, the depth-graded multilayer 90 of the x-ray focusing optic 70 advantageously increases the solid angle of collection of x-rays from the x-ray source 40 compared to a depth-graded multilayer achieved using a conventional focusing optic coated with a single high atomic number (Z) material, to increase the fluorescence signal F Figure 5A and 5B . j,k As shown in the example reflectivity spectra of

[0075] and 5B , the x-ray reflectivity of the x-ray focusing optic 70 for x-rays with energies between 5 keV - 8.9 keV can be less than 5%. As a result, the background B caused by elastic scattering of incident x-rays in the 5 keV - 8.9 keV energy range (e.g., covering the Fe, Cu, and Zn Kα fluorescence lines) can be suppressed by more than 12 times (e.g., approximately equal to the multiple of the ratio of the minimum x-ray reflectivity 60% divided by 5%). This background suppression can improve the detection of biologically important elements (e.g., Fe, Co, Cu, Zn) and other elements with characteristic x-rays in this energy range. Additionally, in some embodiments, the 16.7 mrad Bragg (incident) angle of the depth-graded multilayer 90 is approximately 2.8 times larger than the critical angle (e.g., about 6.2 mrad) of a mirror coated with a single 30 nm thick Au layer for 11.6 keV x-rays, resulting in a large solid angle collection of x-rays from the x-ray source 40. Furthermore, in some embodiments, the second x-ray spectrum reflected and focused by the x-ray focusing optic 70 includes the Au L lines and continuum, and may be nearly optimal for generating a large fluorescence cross-section and signal because these x-rays are slightly above the Zn K absorption edge but not too far above the K absorption edges of Fe and Cu.In some embodiments, the combination of an increased x-ray fluorescence signal and a reduced background provides a significant gain in the signal-to-noise ratio and the imaging speed for imaging elements of interest. For example, as described more fully herein, the fluorescence signal F is increased by maximizing the flux of x-ray energy greater than the K-edge absorption energy j,k and minimizing the background B j,k , to maximize the figure of merit (FOM) of some embodiments. In addition to examples such as Fe, Cu, and Zn (as shown in Figure 4A , 4B , 5A and 5B), many other elements can be advantageously analyzed using some of the embodiments described herein. For example, elements with characteristic fluorescence x-rays in the energy range between 5 keV and 8.9 keV (e.g., K fluorescence lines of Cr, Mn, Co, and Ni; L fluorescence lines of various rare earth elements).

[0076] Some of the embodiments described herein can be characterized by a figure of merit (FOM) that indicates the performance of a micro-XRF system. The minimum detectable limit (MDL) using x-ray fluorescence analysis is proportional to 3*F j，k / sqrt(B j，k ), i.e., MDL ~ 3F’ j，k / sqrt(B’ j，k ) = 3*F j，k *T / *sqrt(B j，k *T) = 3*sqrt(T)*F j，k / sqrt(B j，k ), where F’ j，k and F j，k are the total net counts and count rate (counts / s) of the fluorescence x-rays of element j integrated over the detector energy resolution band for a given characteristic x-ray fluorescence line k, respectively, and B’ j，k and B j，k are the total net counts and count rate (counts / s) of the background below the x-ray fluorescence signal (F j，k ) integrated over the same detector energy resolution band, respectively. Therefore, the time T required to obtain a given MDL is proportional to B j，k / F 2 j，k , which can be defined as the figure of merit (FOM):

[0077] FOM ~ F 2 j，k / B j，k (1)

[0078] Some of the embodiments described herein advantageously are at least partially based on increasing (e.g., maximizing) the x-ray fluorescence signal (F j，k) and / or reduce (e.g., minimize) the background influence (B j，k ).

[0079] The X-ray fluorescence signal (F j，k ) detected by the energy dispersive detector 60 in the X-ray micro-XRF system is approximately given by the following function:

[0080] F j，k = F * σ j，k (E) * N j * Ω * η / 4π (2)

[0081] where F is the flux of the incident focused second X-ray beam, σ j，k (E) is the X-ray fluorescence cross-section of element j for the characteristic line k with energy E, N j is the number of atoms of element j in the illuminated volume, Ω is the detector solid angle (in steradians), and η is a parameter accounting for losses, including detector detection efficiency and attenuation of the fluorescent X-rays from the production point to the detector.

[0082] When evaluating the micro-XRF system (e.g., comparing among different micro-XRF systems), N j is the element concentration to be measured and should be kept constant. The detector solid angle Ω and the loss parameter η largely depend on the detector and physics (self-attenuation), and in principle can be achieved in most micro-XRF systems. Some of the embodiments described herein advantageously are at least partially based on increasing (e.g., maximizing) the flux F of the incident focused X-ray beam and / or increasing (e.g., maximizing) the X-ray fluorescence cross-section σ j，k (E).

[0083] Regarding increasing (e.g., maximizing) the flux F of the incident focused X-ray beam, the incident focused X-ray flux F can be expressed as:

[0084] F = B * L 2 * (2NA) 2 (3)

[0085] where B is the product of the X-ray source brightness B at the sample and the brightness B defined as the number of X-rays per unit area and per unit solid angle illuminating the sample (and should not be confused with the background influence B j，k ), L is the focus size, and NA is the numerical aperture of the X-ray focusing optics (which is related to the collection solid angle). The product of L 2 and (2NA) 2 is the square of the phase space of the focused X-ray beam.

[0086] Certain embodiments described herein advantageously are based at least in part on increasing (e.g., maximizing) the x-ray source brightness B and increasing (e.g., maximizing) the collection solid angle of the x-ray focusing optic 70 for a given detector spot size L. For example, a microstructured target x-ray source 40 can be used to achieve high source brightness (see, e.g., U.S. Patent Nos. 9,874,531, 9,823,203, 9,719,947, 9,594,036, 9,570,265, 9,543,109, 9,449,781, 9,448,190, and 9,390,881, the entire contents of each application being incorporated herein by reference), the microstructured target x-ray source including micron-sized metal targets 42 on or embedded in an anode substrate 44 (e.g., diamond). The brightness B of the electron bombardment x-ray source 40 is proportional to the electron power density on the anode, which can be limited by anode melting and thus the heat dissipation characteristics of the anode. Due to the excellent thermal properties of diamond, whose thermal conductivity at room temperature is five times that of Au, certain embodiments described herein advantageously load the anode within a spot (e.g., 8-10 μm spot size) with an electron power density substantially higher than that used for a bulk metal anode as used in a conventional source. Other benefits of the microstructured anode include: (i) a high temperature gradient between the micron-sized metal target 42 and the surrounding diamond substrate 44 due to the difference in the energy deposition rate (proportional to the mass density) of the incident electrons in the metal material of the target 42 (having a higher mass density) and in the diamond substrate 44 (having a lower mass density), and / or (ii) the small-sized microstructured target 42 having a maximum contact between the microstructured target 42 and the diamond substrate 44. The microstructured x-ray source 40 also enables the use of one or more metal materials for the target 42 that have optimal x-ray spectral characteristics for the intended application (e.g., Au) and / or that otherwise would be impractical to use.

[0087] Regarding increasing (e.g., maximizing) the x-ray fluorescence cross section σ j，k (E), the x-ray fluorescence cross section σ j，k (E) is equal to the product of the ionization cross section and the fluorescence yield of the characteristic line, which is constant for a given element. The ionization cross section depends largely on the energy of the incident x-ray beam E and is proportional to (E - E j，k ) - 3, and thus so is the x-ray fluorescence cross section, i.e.:

[0088] σ j，k (E) ~ (E - E j，k ) -3 (4)

[0089] Where E j，k is the photon ionization energy of element j that is used to generate characteristic line k.

[0090] Certain embodiments described herein advantageously are at least partially based on selecting the x-ray energy of an excitation beam to increase (e.g., maximize) the quantity (E - E j，k ). -3 . For example, the microstructured target 42 including Au can provide a nearly optimal spectrum for increasing σ j，k (E) for many elements including, but not limited to: Fe, Cu, and Zn. Figure 6 shows a table listing the x-ray fluorescence cross-sections of Fe, Cu, and Zn (used as reference examples in Figure 6 ) at the following four x-ray excitation energies: two main Au L lines (9.71 keV and 11.44 keV) and two characteristic K lines of Cu and Mo, which are target materials widely used in conventional x-ray sources. Other widely used target materials in conventional x-ray sources (such as W and Cr) may not be suitable for the intended application because the characteristic L line of W and the K line of Cr are below the K absorption edges of Cu and Zn. As Figure 6 shown, the two main Au x-ray L lines have energies higher than the K absorption edges of Fe, Cu, and Zn (e.g., three biologically important trace elements), and have a large fluorescence cross-section that is three times larger than the fluorescence cross-sections of these elements using the characteristic K lines of a Mo target x-ray source. Thus, an x-ray source with an Au microstructured target can provide significantly better spectral characteristics for generating x-ray fluorescence signals for Figure 6 the three biologically important elements in

[0091] Regarding reducing the background influence (B j,k ), the background influence B of the x-ray spectrum recorded in the micro-XRF system j,kCaused by two main factors: (i) incident x-rays scattered by the sample 50 and detected by the energy dispersive detector 60 (and having energy within the same energy bandwidth of the corresponding fluorescence signal); and (ii) incomplete charge collection of the energy dispersive detector 60, designated as the peak-to-background (P / B) ratio. Since the widely used energy dispersive detector 60 typically has a large P / B ratio (e.g., equal to 20,000), the background effect B j,k is dominated by the scattered incident x-rays of the micro-XRF system. Certain embodiments described herein advantageously reduce (e.g., minimize) B at least in part based on reducing (e.g., minimizing) the incident x-rays within the energy bandwidth of the (one or more) corresponding fluorescence signals of trace-level elements j,k , thereby achieving a large figure of merit (FOM) for bio-related trace elements. When analyzing trace elements with weak x-ray fluorescence signals (F j,k ), this reduction of B j,k can be particularly advantageous.

[0092] In certain embodiments, the focusing x-ray optical element 70 including the depth-graded multilayer 90 is configured to provide substantial improvement relative to conventional focusing x-ray optical devices (e.g., x-ray optical devices including a coating with a single Pt layer). For example, the focusing x-ray optical element 70 including the depth-graded multilayer 90 may include the following properties:

[0093] · A resolution of 1.6 μm (spot size at the focus) achieved by reducing the 8 μm source by a factor of 5;

[0094] · For a small focusing spot size of 1.6 μm, the reduction of the x-ray fluorescence signal (F j,k ) is small (e.g., reduced by a factor of 0.49). The small reduction of F j,k may be due to the following combination of factors:

[0095] ο The solid angle (NA in expression (3)) for the multilayer-coated focusing x-ray optical element to collect x-rays from the x-ray source increases by a factor of 9 because the Bragg angle reflection of the multilayer is 3 times larger than the critical angle of the single Pt coating of the conventional focusing x-ray optical element 2 ;

[0096] ο The multilayer reflectivity is 45% (η in expression (2)),

[0097] ο The focal spot size area (L in expression (3)) 2 is reduced by a factor of 25, and

[0098] ο Due to the Au L lines with larger fluorescence cross-sections for Fe, Cu, Zn, the x-ray fluorescence cross-section (σ in expression (2)) j,k(E)) increased by 3 times.

[0099] ο Multiplying these factors together results in a net change in F j,k of (9 * 0.45 * 3 / 25) = 0.49.

[0100] · By reducing (e.g., reducing by more than 12 times) the bremsstrahlung continuum within the energy range of the incident focused x-ray beam, reducing (e.g., reducing by more than 12 times) the background count rate B within the 5 keV - 8.9 keV x-ray energy range used to image Fe, Cu, and Zn j,k .

[0101] · Increasing (e.g., increasing by at least 3 times = 0.49 2 * 12) the combined net gain in the FOM (see, e.g., expression (1)), including the gain from the Au microstructured anode.

[0102] In certain embodiments, compared to other micro-XRF systems, the 3-fold net gain in the FOM (expression (1)) is produced by a combination of the following: a 3-fold increase in the relative gain of the fluorescence cross-section of the focused second x-ray beam 32; a 9-fold increase in the solid angle collection of x-rays from the x-ray source 40; a 45% multilayer reflectivity shift; a 12-fold reduction in unwanted background; and a 25-fold loss of the number of metal atoms due to an area reduction caused by 5-fold higher resolution (e.g., 5:1 reduction ratio).

[0103] The main challenge of laboratory-based micro-XRF is to image a large number of biologically important elements at trace concentrations with sufficient sensitivity and at an acceptable speed, and imaging at high resolution is even more challenging. The FOM of a laboratory-based micro-XRF system can indicate the time required to image elements at trace levels in a biological sample with sufficient detection sensitivity at high spatial resolution, which is an important measure of the performance of a laboratory-based micro-XRF system. Certain embodiments described herein can provide such an image in a shorter amount of time than conventional systems.

[0104] In certain embodiments, at large incident angles of the depth-graded multilayer 90, lower energy x-rays (e.g., up to 4 keV) can be reflected with relatively high efficiency, and these energies can be above the K absorption edges of P and S. In certain embodiments, a thin film filter (e.g., a Si film approximately 5 mm thick) is placed in the path of the focused x-ray beam to suppress the unwanted background below the fluorescence lines of P and S. Figure 7shows suppression of unwanted background under the P and S K-line fluorescence using a 5 mm thick Si filter according to certain embodiments described herein. An increase in the solid angle for collecting x-rays from the x-ray source 40 results in an increase in the flux of focused x-rays having an energy higher than the K absorption edge energies of P and S (e.g., an increase of about 5 times, which is approximately equal to 9 times multiplied by Figure 5A and 5B the reflectivity shown in). Due to a 5-fold higher resolution (e.g., 5:1 demagnification), the combined benefit of the increased collection solid angle and background suppression can offset a 25-fold loss in the number of P and S atoms in the detection area / volume. This net result (combined with its naturally higher concentration) provides sufficient fluorescence signal for imaging.

[0105] Figures 8A - 8D Schematically illustrates various other examples of an x-ray optical system 10 according to certain embodiments described herein. As Figures 8A - 8D schematically illustrated, at least one x-ray optical element 20 (e.g., a mirror) includes at least one first x-ray optical element 22 (e.g., a mirror) and at least one second x-ray optical element 24 (e.g., a mirror). At least one first x-ray optical element 22 is configured to receive at least a portion of a first x-ray beam 12 having a first energy spectrum and reflect at least some of the x-rays 26 in that portion of the first x-ray beam 12 (e.g., the x-rays 26 may have an energy spectrum that is substantially the same as or substantially different from the first energy spectrum). At least one second x-ray optical element 24 is configured to receive at least some of the x-rays 26 from at least one first x-ray optical element 22, transmit a second x-ray beam 32 that includes the transmitted (e.g., non-reflected and non-absorbed) portion of the x-rays 26 received from at least one first x-ray optical element 22, and reflect a reflected portion 34 of the x-rays 26 received from at least one x-ray optical element 22. The second x-ray beam 32 has a second energy spectrum with a reduced intensity within a predetermined x-ray energy range as compared to the first energy spectrum. As Figure 8B schematically illustrated, the x-ray optical system 10 may further include an x-ray source 40 that is configured to generate the first x-ray beam 12, and as Figure 8C and 8D schematically illustrated, the x-ray optical system 10 may further include at least one x-ray detector 60 that is configured to detect fluorescent x-rays 52 from a sample 50 (e.g., from a first surface 54 irradiated by the second x-ray beam 32 and / or from a second surface 56 opposite the first surface 54 irradiated by the second x-ray beam 32).

[0106] In some embodiments, at least one first x-ray optical element 22 includes at least one x-ray concentrator (e.g., at least one x-ray optical element configured to collect and direct x-rays), the at least one x-ray concentrator having a reflective interface region (e.g., surface) configured to receive at least some of the x-rays of the first x-ray beam 12 and reflect (e.g., at grazing incidence; total external reflection) at least some of the received x-rays 26 of the first x-ray beam 12. In some embodiments, at least one first x-ray optical element 22 is unitary (e.g., a single piece) and axially symmetric about a longitudinal axis. For example, at least one first x-ray optical element 22 may include a portion of a hollow axially symmetric tube or pipe (e.g., a capillary), the portion of the hollow axially symmetric tube or pipe (e.g., a capillary) extending along the longitudinal axis and including an inner surface (e.g., a mirror surface) that extends completely around the longitudinal axis (e.g., surrounds the longitudinal axis; extends 360 degrees around the longitudinal axis). In some other embodiments, at least one first x-ray optical element 22 includes at least a portion of a hollow axially symmetric structure (e.g., a portion of an axially symmetric tube), the at least a portion of the structure extending along the longitudinal axis with an inner surface that extends only partially around the longitudinal axis (e.g., less than 360 degrees; in the range of 45 degrees to 360 degrees; in the range of 45 degrees to 315 degrees; in the range of 180 degrees to 360 degrees; in the range of 90 degrees to 270 degrees). In some embodiments, at least one first x-ray optical element 22 includes a plurality of portions (e.g., 2, 3, 4, 5, 6, or more), which are separated from each other (e.g., have a gap between the portions) and are distributed around the longitudinal axis, wherein the surface of each portion extends at least partially around the longitudinal axis and along the longitudinal axis. For example, the surfaces of the plurality of portions may extend an angle around the longitudinal axis in the range of 15 degrees to 175 degrees, in the range of 30 degrees to 115 degrees, and / or in the range of 45 degrees to 85 degrees, respectively. In some other embodiments, at least one first x-ray optical element 22 includes a plurality of portions (e.g., a multi-capillary lens including a plurality of capillaries) positioned around the longitudinal axis.

[0107] Figure 9A A cross-sectional view schematically illustrates an example first x-ray optical element 22 including at least one capillary 120 according to some embodiments described herein. Figure 9A The capillary 120 (e.g., glass; quartz; silicon) is unitary and has an inner surface 122 that is axially symmetric about the longitudinal axis 124 of the capillary 120. In some embodiments, the inner surface 122 includes at least one metal layer (e.g., Au; Pt; Ir), the at least one metal layer being configured to facilitate reflection of x-rays by the inner surface 122 (e.g., by increasing the critical angle of total external reflection). As Figure 9ASchematic illustration. In some embodiments, the capillary 120 includes a reflective interface region (such as the inner surface 122) having a parabolic shape. In some other embodiments, the capillary 120 includes a reflective interface region having a quadratic function shape (such as parabolic; elliptical; hyperbolic) or a portion having an approximately quadratic function shape. For the shape of the reflective interface region including a focus (such as parabolic; elliptical; hyperbolic), in some embodiments, at least a portion of the x-ray source 40 is placed at the focus, while in some other embodiments, the x-ray source 40 is shifted relative to the focus. The x-ray source 40 can be placed away from the upstream end 125 of at least one capillary 120 (such as at a distance within less than 10 cm). Examples of capillary reflection optical devices 120 compatible with some embodiments described herein are disclosed in U.S. Patent Nos. 9,874,531, 9,823,203, 9,594,036, 9,570,265, 9,543,109, 9,449,781, 9,448,190, and 9,390,881, the entire content of each patent being incorporated herein by reference.

[0108] As Figure 9A Schematic illustration. At least one first x-ray optical element 22 may further include at least one light blocker 80 placed along a line coinciding with the longitudinal axis 124 of at least one capillary 120 (such as at or near the upstream end 125 of at least one capillary 120; at or near the downstream end 127 of at least one capillary 120; upstream of at least one capillary 120; downstream of at least one capillary 120). For example, as Figure 9A Schematic illustration. A first portion of the first x-ray beam 12 impinges on the inner surface 122 of the capillary 120, and the x-rays 26 are reflected by the inner surface 122 (such as to form a collimated x-ray beam), while a second portion of the first x-ray beam 12 propagates through the central region of the capillary 120 and does not impinge on the inner surface 122 of the capillary 120. At least one light blocker 80 of some embodiments includes at least one material opaque to x-rays (such as lead), and at least one light blocker 80 is configured to block (such as prevent) the contribution of the second portion of the first x-ray beam 12 to the x-rays 26. In some embodiments, the x-rays 26 form an x-ray beam having an annular cross-sectional shape in a plane perpendicular to the longitudinal axis 124.

[0109] In some embodiments, the x-ray 26 forms an x-ray beam having a beam size (e.g., outer diameter) in the range of less than 3 mm (e.g., in the range between 1 mm and 3 mm) at the downstream end 127 of at least one first x-ray optical element 22. In some embodiments, the portion of the first x-ray beam 22 received by the at least one first x-ray optical element 22 is divergent (e.g., having a first divergence angle in the range of 5 milliradians to 60 milliradians), and the x-ray 26 of some embodiments forms a collimated x-ray beam (e.g., having a second divergence angle in the range of less than two milliradians, less than 1.5 milliradians, or less than 1 milliradian). Figure 9B Schematically illustrates an example first x-ray energy spectrum of a first x-ray beam 12 (e.g., x-rays from an x-ray source 40) according to some embodiments described herein. In some embodiments, the x-ray 26 has an x-ray energy spectrum substantially the same as the first x-ray energy spectrum of the first x-ray beam 12, while in some other embodiments, the x-ray 26 has an x-ray energy spectrum different from the first x-ray energy spectrum of the first x-ray beam 12 (e.g., having a high energy cutoff due to the critical angle for total external reflection for the at least one first x-ray optical element 22).

[0110] Figure 10A Schematically illustrates an example system 10 according to some embodiments described herein, in which at least one second x-ray optical element 24 includes at least one x-ray reflector 130 (e.g., including at least one mosaic crystal layer and / or at least one depth-graded multilayer). Figure 10B Schematically illustrates according to some embodiments described herein Figure 10A of an example second x-ray energy spectrum of a second x-ray beam 32 (e.g., x-rays transmitted through the at least one x-ray reflector 130). Figure 11A Schematically illustrates an example system 10 according to some embodiments described herein, in which at least one second optical element 24 includes a plurality (e.g., two; three or more) of x-ray reflectors 130. Figure 11B Schematically illustrates according to some embodiments described herein Figure 11A of an example second x-ray energy spectrum of a second x-ray beam 32 (e.g., x-rays transmitted through the plurality of x-ray reflectors 130). Figure 12A Schematically illustrates an example system 10 according to some embodiments described herein, in which at least one x-ray reflector 130 includes at least one grazing incidence mirror. Figure 12B Schematically illustrates according to some embodiments described herein Figure 12A of an example second x-ray energy spectrum of a second x-ray beam 32 (e.g., x-rays transmitted through the at least one x-ray reflector 130). Figures 10A - 10B andFigures 11A - 11B At least one x-ray reflector 130 may include at least one mosaic crystal layer, at least one depth-graded multilayer reflector, and / or at least one grazing incidence mirror, as described herein.

[0111] At least one x-ray reflector 130 is configured to reflect a first portion 132 of the x-rays 26 having an energy within at least one predetermined energy range and transmit a second portion of the x-rays 26 having an energy outside the at least one predetermined energy range. As described herein, the transmitted second portion of the x-rays 26 serves as a second x-ray beam 32 for irradiating the sample being analyzed, and the second x-ray beam 32 is substantially composed of at least some of the non-reflected x-rays that have transmitted through at least one x-ray reflector 130.

[0112] For example, at least one x-ray reflector 130 may include at least one mosaic crystal layer on a substrate (such as silicon or glass, having a thickness in the range of 0.2 mm to 1 mm). Example materials for at least one mosaic crystal layer compatible with certain embodiments described herein include, but are not limited to, highly oriented pyrolytic graphite (HOPG) or highly aligned pyrolytic graphite (HAPG). The mosaic crystal layer includes a plurality of crystal portions (such as domains; microcrystals) that are tilted relative to each other by a mosaicity (such as a range of crystal plane orientations; a range of normal directions of the crystal planes). In certain embodiments, the mosaicity is less than three degrees. The thickness of the x-ray reflector 130 of certain embodiments including at least one mosaic crystal layer and a substrate is in the range of 0.5 mm to 3 mm, and the mosaic crystal layer includes a low atomic number material (such as carbon; silicon; quartz) such that the absorption of the x-rays 26 by the mosaic crystal layer is below a predetermined upper limit (such as less than 20%; less than 10%; less than 5%; less than 3%). In certain embodiments, at least one mosaic crystal layer is planar, while in certain other embodiments, at least one mosaic crystal layer is curved or bent (such as controllably bent to adjust the angle of incidence at which the x-rays 26 impinge on the crystal portions). In certain embodiments, at least one mosaic crystal layer is oriented such that the surface of the at least one mosaic crystal layer is within a range of 6 degrees to 20 degrees, within a range of 15 degrees to 40 degrees, within a range of 40 degrees to 50 degrees, or within a range of 40 degrees to 65 degrees relative to the x-rays 26 (such as relative to a collimated x-ray beam including the x-rays 26).

[0113] At least a first portion 132 of the x-rays 26 impinging on the mosaic crystal layer satisfies the Bragg reflection condition for at least some of the crystal portions in the crystal portion of the mosaic crystal layer. The Bragg reflection condition can be expressed as: 2d·sinθ = n·λ, where d is the interplanar spacing between the crystal planes (e.g., carbon layers) of the crystal portion, θ is the angle of incidence of the x-rays relative to the crystal planes of the crystal portion, n is the integer order of reflection, and λ is the wavelength of the incident x-rays (where the x-ray wavelength is related to the x-ray energy by the relation: E = h·c / λ, where E is the energy, h is Planck's constant, and c is the speed of light). The first portion 132 of the x-rays 26 that satisfies the Bragg reflection condition for at least some of the crystal portions in the crystal portion of the mosaic crystal layer is reflected by the mosaic crystal layer. The remaining portion of the x-rays 26 that does not satisfy the Bragg reflection condition for any of the crystal portions of the mosaic crystal layer is not reflected by the mosaic crystal layer but is transmitted through the mosaic crystal layer (e.g., with substantially no attenuation), thereby forming a second x-ray beam 32.

[0114] In certain embodiments, due to the slight misalignment among the crystal portions in the mosaic crystal layer and the small divergence angle of the incident x-rays 26, some of the x-rays 26 within a narrow wavelength range will find crystal portions that satisfy the Bragg reflection condition and will be reflected by the mosaic crystal layer so as to have no effect on the second x-ray beam 32. The mosaic crystal layer can be configured to have a mosaicity and be oriented relative to the x-rays 26 (e.g., relative to a collimated x-ray beam including the x-rays 26) to reflect x-rays having an energy range with a predetermined central value and a predetermined bandwidth (e.g., a range with a lower limit and an upper limit), thereby preventing the x-rays within the range (e.g., between the lower limit and the upper limit) from having an effect on the second x-ray beam 32.

[0115] For another example, at least one x-ray reflector 130 can include at least one depth-graded multilayer reflector, an example of which is schematically illustrated by Figure 3C The depth-graded multilayer reflector includes a substrate having a thickness in the range of 0.5 mm to 3 mm or in the range of 0.2 mm to 1 mm (e.g., including a low atomic number material such as silicon, quartz, glass, or aluminum) and a depth-graded multilayer coating on the surface of the substrate. The depth-graded multilayer reflector has an absorption of the x-rays 26 lower than a predetermined value (e.g., less than 20%; less than 10%; less than 5%; less than 3%). In certain embodiments, at least one depth-graded multilayer reflector is oriented such that the surface of the at least one depth-graded multilayer reflector is in the range of 3 degrees to 15 degrees, in the range of 10 degrees to 40 degrees, or in the range of 40 degrees to 50 degrees relative to the x-rays 26 (e.g., relative to a collimated x-ray beam including the x-rays 26).

[0116] At least one depth-graded multilayer of some embodiments includes a plurality of layer pairs (e.g., layer pairs or bilayer pairs that alternate in a direction perpendicular to the layers and include a high atomic number material and a low atomic number material). The thicknesses of the layer pairs are different from each other (e.g., the spacings between successive high atomic number material layers are different from each other). For example, each layer pair may include a first layer (including a first material) and a second layer (including a second material) (e.g., a Pt / Si layer pair; a Pt / B4C layer pair; a Pt / Al2O3 layer pair; a W / Si layer pair; a W / B4C layer pair; a W / Al2O3 layer pair; a Mo / Si layer pair; a Mo / B4C layer pair; a Mo / Al2O3 layer pair; a Ni / Si layer pair; a Ni / B4C layer pair; a Ni / Al2O3 layer pair; a Cu / Si layer pair; a Cu / B4C layer pair; a Cu / Al2O3 layer pair). The thickness of each layer pair (e.g., in a direction substantially perpendicular to the substrate surface) is substantially constant along a direction substantially parallel to the surface. However, along the normal to the substrate surface, the layer pairs are configured in sets or groups, where the thicknesses of the layer pairs in each group are different from each other. For example, the thicknesses of the layer pairs of the respective groups may increase from a first thickness to a second thickness, where the layer group closer to the substrate surface has a thinner layer thickness than the layer group farther from the substrate surface.

[0117] At least a first portion 132 of the x-rays 26 impinging on the depth-graded multilayer reflector satisfies the Bragg reflection condition (2d·sinθ = n·λ) for at least some of the layers in the depth-graded multilayer coating, where d is the spacing between the high atomic number material layers (e.g., the spacing between Pt, W, Mo, Ni, or Cu layers). The first portion 132 of the x-rays 26 that satisfies the Bragg reflection condition for at least some of the layers is reflected by the depth-graded multilayer coating. The remaining portion of the x-rays 26 that does not satisfy the Bragg reflection condition for any of the layers in the depth-graded multilayer coating is not reflected by the depth-graded multilayer coating but is transmitted through the depth-graded multilayer coating and the substrate (e.g., with substantially no attenuation), thereby forming a second x-ray beam 32.

[0118] In some embodiments, due to the variation in the thicknesses of the layers of the depth-graded multilayer coating, incident x-rays 26 in a narrow wavelength range will find layer spacings that satisfy the Bragg reflection condition and will be reflected by the depth-graded multilayer coating so as to have no effect on the second x-ray beam 32. The depth-graded multilayer reflector can be oriented relative to the x-rays 26 (e.g., relative to a collimated x-ray beam including the x-rays 26) to reflect x-rays 26 having an energy range with a predetermined central value and a predetermined bandwidth (e.g., a range with a lower limit and an upper limit), thereby preventing the x-rays 26 within the range (e.g., between the lower limit and the upper limit) from having an effect on the second x-ray beam 32.

[0119] As Figure 10BSchematic illustration. The second x-ray energy spectrum of the second x-ray beam 32 has a predetermined energy range (e.g., a "notch") in which the x-ray intensity (e.g., flux) is reduced (e.g., reduced by at least 80%; reduced by at least 90%; reduced by at least 95%) compared to the x-ray energy spectrum of the first x-ray beam 12 (e.g., by Figure 9B Schematic illustration). Additionally, the x-ray intensity (e.g., flux) of the second x-ray energy spectrum of the second x-ray beam 32 at energies below a predetermined value (e.g., 4 keV) is reduced (e.g., reduced by at least 80%; reduced by at least 90%; reduced by at least 95%) compared to the first x-ray energy spectrum of the first x-ray beam 12 (e.g., by Figure 9B Schematic illustration).

[0120] As Figure 10B Schematic illustration, the second x-ray energy spectrum has sharp edges at the upper and lower limits of the predetermined energy range. Compared to conventional transmission filters for reducing x-ray flux, some embodiments described herein provide an upper edge that is sharp enough such that the upper edge can be selected to be between the x-ray absorption edge and the x-ray fluorescence line of an element (e.g., Cu) to be analyzed using an x-ray fluorescence system (e.g., the full width at half maximum of the upper edge is less than the energy difference between the x-ray absorption edge and the x-ray fluorescence line to be analyzed).

[0121] Figure 11ASchematically illustrates an example system 10 according to certain embodiments described herein, in which at least one second x-ray optical element 24 includes a plurality (e.g., two; three or more) x-ray reflectors 130. For example, a first x-ray reflector 130a including a first substrate and at least one first layer (e.g., at least one mosaic crystal layer and / or at least one depth-graded multilayer) on the first substrate is oriented at a first angle with respect to x-rays 26 (e.g., with respect to a collimated x-ray beam including x-rays 26), and a second x-ray reflector 130b including a second substrate and at least one second layer (e.g., at least one mosaic crystal layer and / or at least one depth-graded multilayer) on the second substrate is oriented at a second angle different from the first angle with respect to x-rays 26 (e.g., with respect to a collimated x-ray beam including x-rays 26). The first x-ray reflector 130a is configured to reflect a first portion 132a of the x-rays 26, and the second x-ray reflector 130b is configured to receive at least some of the non-reflected x-rays (e.g., x-rays transmitted through the first x-ray reflector 130a) from the first x-ray reflector 130a and is configured to reflect a second portion 132b of the x-rays 26 such that the first portion 132a and the second portion 132b have no effect on the second x-ray beam 32, such that the second x-ray beam 32 consists essentially of at least some of the non-reflected x-rays (e.g., x-rays transmitted through the second x-ray reflector 130b) from the second x-ray reflector 130b.

[0122] Figure 11B Schematically illustrates according to certain embodiments described herein Figure 11A an example second x-ray energy spectrum of the second x-ray beam 32 (e.g., x-rays transmitted through two x-ray reflectors 130a, 130b). For example, the first x-ray reflector 130a may be configured to provide a first "notch" energy range including a first x-ray fluorescence line of interest, and the second x-ray reflector 130b may be configured to provide a second "notch" energy range including a second x-ray fluorescence line of interest (e.g., the Hf L α1 line at 7.9 keV and the La L β1 line at 5 keV; the Si K β1 line at 1.8 keV and the Mg K β1 line at 1.3 keV). As Figure 11BAs shown, in some embodiments, the two energy ranges of the two "notches" can be separated from each other (e.g., the upper limit of the first energy range from one of the x-ray reflectors 130 is lower than the lower limit of the second energy range from another x-ray reflector in the x-ray reflectors 130). In some other embodiments, the two energy ranges of the two "notches" can overlap with each other (e.g., the upper limits of the two energy ranges are higher than the lower limits of the two energy ranges), thereby effectively forming a larger energy range and effectively reducing the background influence within this energy range (e.g., extending from the lower limit of the first energy range to the upper limit of the second energy range).

[0123] In Figures 12A - 12B the example system of, at least one x-ray reflector 130 includes at least one grazing-incidence mirror according to certain embodiments described herein. For example, the grazing-incidence mirror can include a substrate having a thickness in the range of 0.001 mm to 0.05 mm or in the range of 0.05 mm to 0.2 mm (e.g., including low atomic number materials such as silicon, quartz, glass, or aluminum) and a coating on the surface of the substrate including one or more layers (e.g., including high atomic number materials such as Au, Ir, Pt, W, Cu, or Mo). The absorption of the grazing-incidence mirror for the x-rays 26 is lower than a predetermined value (e.g., less than 20%; less than 10%; less than 5%; less than 3%). In some embodiments, the grazing-incidence mirror is planar, while in some other embodiments, the grazing-incidence mirror is curved or bent. In some embodiments, at least one grazing-incidence mirror is oriented such that the surface of the grazing-incidence mirror is within the range of 1 degree to 10 degrees or within the range of 0.5 degree to 5 degrees with respect to the x-rays 26 (e.g., with respect to the collimated x-ray beam including the x-rays 26).

[0124] At least a first portion 132 of the x-rays 26 that impinge on the grazing-incidence mirror includes the following x-rays: the grazing incidence angles of these x-rays are less than the critical angle of total external reflection by the grazing-incidence mirror (e.g., low energy x-rays; x-rays with an energy lower than 1 keV, 3 keV, or 5 keV), and these x-rays are reflected by the grazing-incidence mirror. The remaining portion of the x-rays 26 in which the grazing incidence angle is greater than the critical angle of total external reflection (e.g., higher energy x-rays; x-rays with an energy higher than 1 keV, 3 keV, or 5 keV) are not reflected by the grazing-incidence mirror and are transmitted through the grazing-incidence mirror (e.g., with substantially no attenuation), thereby forming a second x-ray beam 32 (e.g., the second x-ray beam 32 is substantially composed of at least some of the non-reflected x-rays from at least one x-ray reflector 130).

[0125] As shown by Figure 12BSchematic illustration showing that the x-ray intensity (e.g., flux) of the second x-ray energy spectrum of the second x-ray beam 32 transmitted through the grazing-incidence mirror at energies below a predetermined “cutoff” value (e.g., 4 keV) is reduced (e.g., reduced by at least 80%; reduced by at least 90%; reduced by at least 95%) compared to the first x-ray energy spectrum of the first x-ray beam 12 (e.g., by Figure 9B Schematic illustration). In certain embodiments, the angle of incidence of the x-rays 26 on the grazing-incidence mirror (e.g., relative to the critical angle) is adjustable to adjust the predetermined “cutoff” value for a portion of the x-rays 26.

[0126] Figure 13A Schematically illustrates an example system 10 according to certain embodiments described herein. The example system includes a first x-ray reflector 130 (e.g., a first grazing-incidence mirror) and a second x-ray reflector 134 (e.g., a second grazing-incidence mirror). The second x-ray reflector 134 is configured to substantially reflect the x-rays 136 of the first portion 132 of the x-rays 26 and substantially not reflect the remainder of the first portion 132 of the x-rays 26. Figure 13B Schematically illustrates an example second x-ray energy spectrum of the second x-ray beam 32 and the x-rays 136 reflected from Figure 13A the second x-ray reflector 134.

[0127] For example, the grazing incidence angle of at least some of the x-rays 136 of the first portion 132 of the x-rays 26 impinging on the second x-ray reflector 134 (e.g., the second grazing-incidence mirror) is below the critical angle for total external reflection by the second x-ray reflector 134 (e.g., low-energy x-rays; x-rays with energy below 1 keV, 3 keV, or 5 keV) and are reflected by the second x-ray reflector 134 (e.g., the x-rays 136 are reflected twice, once by the first x-ray reflector 130 and once by the second x-ray reflector 134). The remaining x-rays of the first portion 132 of the x-rays 26 (grazing incidence angle greater than the critical angle for total external reflection by the second x-ray reflector 134) (e.g., higher-energy x-rays; x-rays with energy above 1 keV, 3 keV, or 5 keV) are not reflected by the second x-ray reflector 134 but are transmitted through the second x-ray reflector 134.

[0128] In certain embodiments, as shown by Figure 13ASchematic illustration, the first x-ray reflector 130 and the second x-ray reflector 134 can be configured such that the second x-ray beam 32 and at least some of the "doubly reflected" x-rays 136 (e.g., the x-rays in the first portion 132 of the x-rays 26 that impinge on the second x-ray reflector 134) irradiate the sample 50. In certain embodiments, the x-rays 136 impinge on a first region of the sample 50 that is the same as the second region of the sample 50 that is impinged upon by the second x-ray beam 32, while in certain other embodiments, the first region of the sample 50 that is impinged upon by the x-rays 136 is different from the second region of the sample 50 that is impinged upon by the second x-ray beam 32 (e.g., the first region partially overlaps the second region).

[0129] In certain embodiments, the first x-ray reflector 130 is configured to reflect x-rays 132 in a first energy range having a first upper limit (e.g., 4 keV, 5 keV, 6 keV), and the second x-ray reflector 134 is configured to reflect x-rays 136 in a second energy range having a second upper limit lower than the first upper limit (e.g., 2 keV, 3 keV, 4 keV). As compared to the x-ray energy spectrum of the first x-ray beam 12, the energy range between the first upper limit and the second upper limit may have a reduced x-ray intensity (e.g., flux) (e.g., reduced by at least 80%; reduced by at least 90%; reduced by at least 95%) (e.g., by Figure 9B Schematic illustration). In this way, certain embodiments are configured to perform x-ray fluorescence analysis on high atomic number elements (e.g., using the high energy portion of the x-ray energy spectrum of the second x-ray beam 32 that impinges on the sample 50) and on low atomic number elements (e.g., using the low energy portion of the x-ray energy spectrum of the "doubly reflected" x-rays 136 that impinge on the sample 50). In certain embodiments, the angle of incidence of the x-rays 26 on the first x-ray reflector 130 is adjustable, and the angle of incidence of the x-rays 132 on the second x-ray reflector 134 is adjustable (e.g., adjusted at a slightly different grazing angle with respect to the respective critical angle) in order to adjust the portion of the x-rays 26 that do not impinge on the sample 50 (e.g., the portion of the x-rays 26 that is not included in the second x-ray beam 32 or the x-rays 136; in order to excise an unwanted portion of the low energy spectrum).

[0130] Figure 14It is a flowchart of an exemplary method 200 for performing x-ray fluorescence analysis according to certain embodiments described herein. In operation block 210, method 200 includes receiving x-rays having a first energy spectrum and a first spatial distribution. In operation block 220, method 200 further includes reflecting at least some of the received x-rays, the reflected x-rays having a second energy spectrum and a second spatial distribution. In operation block 230, method 200 further includes separating the reflected x-rays into a first portion that impinges on a sample and a second portion having a predetermined x-ray energy range by means of multilayer reflection (e.g., reflection satisfying Bragg reflection conditions from a multilayer and / or mosaic crystal layer) and / or total external reflection. The first portion has a third energy spectrum, the intensity of which within the predetermined x-ray energy range is reduced as compared to the second energy spectrum. In certain embodiments, at least some of the x-rays in the first portion are configured to excite x-ray fluorescence within the sample, the x-ray fluorescence including x-ray fluorescence lines within the predetermined x-ray energy range. In certain embodiments, method 200 further includes reflecting some of the x-rays in the second portion to impinge on the sample.

[0131] Unless otherwise specifically stated or otherwise understood within the context in which it is used, conditional language such as can, could, may, or might generally is intended to convey that certain embodiments include while other embodiments do not include certain features, elements, and / or steps. Thus, such conditional language generally is not intended to imply that the features, elements, and / or steps are in any way required for one or more embodiments.

[0132] Unless otherwise specifically stated, conjunctive language such as “at least one of X, Y, and Z” should be understood within the context generally used to convey that items, terms, etc. can be X, Y, or Z. Thus, such conjunctive language generally is not intended to imply that certain embodiments require the presence of at least one of X, at least one of Y, and at least one of Z.

[0133] Degree language such as the terms “about,” “approximately,” “generally,” and “substantially” as used herein represents a value, quantity, or characteristic that is close to the stated value, quantity, or characteristic and still performs the desired function or achieves the desired result. For example, the terms “about,” “approximately,” “generally,” and “substantially” can refer to a quantity within ±10%, ±5%, ±2%, ±1%, or ±0.1% of the stated amount. As another example, the terms “generally parallel” and “substantially parallel” refer to a value, quantity, or characteristic that deviates from exact parallelism by ±10 degrees, ±5 degrees, ±2 degrees, ±1 degree, or ±0.1 degree, and the terms “generally perpendicular” and “substantially perpendicular” refer to a value, quantity, or characteristic that deviates from exact perpendicularity by ±10 degrees, ±5 degrees, ±2 degrees, ±1 degree, or ±0.1 degree.

[0134] Various configurations have been described above. Although the present invention has been described with reference to these specific configurations, the description is intended to be illustrative of the invention and not restrictive. Various modifications and applications can be envisioned by those skilled in the art without departing from the true spirit and scope of the invention. Thus, for example, in any method or process disclosed herein, the acts or operations constituting the method / process can be performed in any suitable order and need not be limited to any particular disclosed order. Features or elements from the various embodiments and examples discussed above can be combined with one another to produce alternative configurations that are compatible with the embodiments disclosed herein. The various aspects and advantages of the embodiments have been described in the appropriate places. It should be understood that not all such aspects or advantages may be achieved according to any particular embodiment. Thus, for example, it should be recognized that the various embodiments can be implemented in a manner that achieves or optimizes one advantage or a group of advantages as taught herein, without necessarily achieving other aspects or advantages as may be taught or suggested herein.

Claims

1. An X-ray optical filter includes at least one X-ray optical mirror, the at least one X-ray optical mirror being configured to receive a plurality of X-rays having a first X-ray spectrum, separate at least some of the received X-rays into reflected X-rays and non-reflected X-rays by multi-layer reflection or total external reflection, and form an X-ray beam having a second X-ray spectrum, the X-ray beam including at least some of the reflected X-rays and / or at least some of the non-reflected X-rays, wherein, The first x-ray spectrum has a first intensity that is a function of energy in a predetermined solid angle range, the x-ray beam has a second intensity that is a function of energy in the solid angle range, the second intensity is greater than or equal to 50% of the first intensity in a first continuous energy range that is at least 3 keV wide, the second intensity is less than or equal to 10% of the first intensity in a second continuous energy range that is at least 100 eV wide, and the second intensity is greater than or equal to 50% of the first intensity in a third continuous energy range that is at least 2 keV wide, the second continuous energy range being between the first continuous energy range and the third continuous energy range. Wherein, the at least one x-ray optical mirror includes a first grazing incidence mirror and a second grazing incidence mirror, and the x-ray beam consists essentially of at least some of the non-reflected x-rays from the first grazing incidence mirror and at least a portion of at least some of the reflected x-rays from the first grazing incidence mirror that are reflected from the second grazing incidence mirror and are directed to irradiate the sample.

2. The filter according to claim 1, wherein The first grazing incidence mirror includes a substrate and a coating on the surface of the substrate.

3. A method of performing x-ray fluorescence analysis, the method comprising: Receiving x-rays having a first energy spectrum and a first spatial distribution, the first energy spectrum having a first intensity that is a function of energy; Reflecting at least some of the received x-rays, the reflected x-rays having a second energy spectrum and a second spatial distribution, the second energy spectrum having a second intensity that is a function of energy; Separating the reflected x-rays into a first portion that impinges on a sample and a second portion having a predetermined x-ray energy range by means of multilayer reflection and / or total external reflection, the first portion having a third energy spectrum, the third energy spectrum having a third intensity in the predetermined x-ray energy range, the third intensity being a function of energy, the third intensity being greater than or equal to 50% of the first intensity in a first continuous energy range that is at least 3 keV wide, the third intensity being less than or equal to 10% of the first intensity in a second continuous energy range that is at least 100 eV wide, and the third intensity being greater than or equal to 50% of the first intensity in a third continuous energy range that is at least 2 keV wide, the second continuous energy range being between the first continuous energy range and the third continuous energy range; And Reflecting some of the x-rays of the second portion to impinge on the sample.

4. The method according to claim 3, wherein At least some of the x-rays of the first portion are configured to excite x-ray fluorescence within the sample, the x-ray fluorescence including x-ray fluorescence lines within the predetermined x-ray energy range.

5. An x-ray system, comprising: At least one x-ray optical mirror configured to receive a plurality of x-rays having a first x-ray spectrum and separate at least some of the received x-rays into reflected x-rays and non-reflected x-rays by multilayer reflection or total external reflection, and form an x-ray beam including at least some of the reflected x-rays and / or at least some of the non-reflected x-rays, wherein the first x-ray spectrum has a first intensity that is a function of energy in a predetermined solid angle range, the x-ray beam has a second x-ray spectrum, and the second intensity of the second x-ray spectrum is a function of energy in the solid angle range, the second intensity being greater than or equal to 50% of the first intensity in a first continuous energy range of at least 3 keV, the second intensity being less than or equal to 10% of the first intensity in a second continuous energy range of at least 100 eV, and the second intensity being greater than or equal to 50% of the first intensity in a third continuous energy range of at least 2 keV, the second continuous energy range being between the first continuous energy range and the third continuous energy range, wherein the plurality of received x-rays includes a received x-ray beam having the first x-ray spectrum, and the at least one x-ray optical mirror includes: at least one first x-ray optical mirror configured to receive at least a portion of the received x-ray beam and reflect at least some of the x-rays of that portion of the received x-ray beam to form a reflected x-ray beam; and at least one second x-ray optical mirror including at least one grazing incidence mirror, the at least one second x-ray optical mirror being configured to receive at least some x-rays from the at least one first x-ray optical mirror, transmit a transmitted x-ray beam including a transmitted portion of the x-rays received from the at least one first x-ray optical mirror, and reflect a reflected portion of the x-rays received from the at least one first x-ray optical mirror, wherein the at least one grazing incidence mirror includes a first grazing incidence mirror and a second grazing incidence mirror, the first grazing incidence mirror being configured to reflect the reflected portion of the x-rays received from the at least one first x-ray optical mirror and transmit the transmitted x-ray beam toward the sample, the second grazing incidence mirror being configured to reflect a portion of the reflected portion of the x-rays received from the at least one first x-ray optical mirror toward the sample.

6. The system according to claim 5, wherein, At least a portion of the transmitted x-ray beam is configured to irradiate a sample and excite x-ray fluorescence within the sample, the x-ray fluorescence being emitted from the sample and including x-ray fluorescence lines within a predetermined x-ray energy range.

7. The system according to claim 5, further comprising an x-ray source configured to generate the received x-ray beam.

8. The system according to claim 5, wherein, The portion of the received x-ray beam has a first divergence angle in the range of 5 milliradians to 60 milliradians.

9. The system according to claim 8, wherein, The x-rays reflected from the at least one first x-ray optical mirror have a second divergence angle in a range less than two milliradians.

10. The system according to claim 5, wherein, This portion of the received x-ray beam is divergent, and the x-rays reflected from the at least one first x-ray optical mirror are collimated.

11. The system according to claim 5, wherein, The x-rays reflected from the at least one first x-ray optical mirror have an x-ray spectrum that is substantially equal to the first x-ray spectrum within a predetermined x-ray energy range.

12. The system according to claim 5, wherein The at least one first x-ray optical mirror includes a reflective surface having a parabolic shape.

13. The system according to claim 12, further comprising at least one light blocker configured to prevent a second portion of the received x-ray beam that is not reflected by the at least one first x-ray optical mirror from contributing to the transmitted x-ray beam.

14. The system according to claim 5, wherein, The at least one grazing incidence mirror includes a substrate and a coating on a surface of the substrate, the substrate including at least one material selected from the group consisting of silicon, quartz, glass, and aluminum, and the coating including at least one material selected from the group consisting of Au, Ir, Pt, W, Cu, and Mo.

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