X-RAY SOURCE

CLAIM OF PRIORITY

[0001] This application claims the benefit of priority to U.S. Provisional Appl. Nos. 63/122,354 filed December 7, 2020 and 63/274,367 filed November 1, 2021, each of which is incorporated in its entirety by reference herein.

BACKGROUND

Field

[0002] This application relates generally to tomography and laminography x-ray imaging systems.

Description of the Related Art

[0003] Three-dimensional (3D) x-ray imaging techniques are useful to image internal structures of objects. Typically, a tomography dataset consisting of x-ray transmission images that are collected over a large angular range (e.g., about 180 degrees; about 360 degrees), and that are subsequently reconstructed to obtain a 3D image. The large angular range is used to avoid (e.g., minimize) 3D image artifacts. A 3D x-ray imaging system comprises an x-ray source configured to illuminate an object for imaging, a position-sensitive x-ray detector configured to record transmission x-ray images, and an electromechanical system to manipulate the object with respect to the x-ray source and the position-sensitive x- ray detector.

[0004] X-ray flux incident on a region of interest of the object is inversely proportional to the square of the distance of the region of interest from the x-ray source, this distance can be referred to as the focus object distance (FOD). To achieve high throughput for 3D x-ray imaging, the FOD is selected to be small (e.g., the region of interest placed as close to the x-ray source as possible). For example, in view of the small voxel volume used to achieve the spatial resolution, placing the region of interest close to the x-ray source can be used in 3D x-ray imaging with high spatial resolution using a laboratory microfocus x-ray source. Furthermore, for 3D x-ray imaging of a small region of interest in a larger object (e.g., small regions of interest in a laterally extended planar object, examples of which include but are not limited to interconnects in semiconductor integrated circuit (IC) packages and fine structural details in a large fiber reinforced composite panel), the minimum FOD is limited by the dimensions of the object, which practically limits the achievable throughput because the object is to be rotated through 180 degrees.

[0005] However, prior art micro-x-ray computed tomography (|1XCT) and micro x-ray computed laminography (|1XCL) systems have numerous limitations. For example, FIGs. 1A and IB schematically illustrate conventional tomography and laminography configurations, respectively, of a laterally extended object (e.g., printed circuit board; wafer) where the region of interest (ROI) is at or near the center of the object. The x-ray source emits an x-ray beam (denoted by a horizontal dashed line) and the thickness of the object in FIGs. 1A and IB in a direction perpendicular to the page can be equal to or smaller than the object’s dimension along the x-ray beam (e.g., such that there is sufficient room between the x-ray source and the x-ray detector for rotating the object about the rotation axis). As seen in FIG. 1 A, for tomography, the rotation axis is substantially parallel to the surface normal of the object and is substantially perpendicular to the x-ray beam. As seen in FIG. IB, for laminography, the rotation axis is substantially parallel to the surface normal of the object and is tilted from a direction substantially perpendicular to the x-ray beam by an angle 0. FIGs. 1A and IB show that such conventional tomography and laminography configurations are not well suited to imaging defects in planes parallel to the surface of the laterally extended objects (e.g., semiconductor IC packages) because the transmitted x-ray spectrum in the tomography /laminography dataset varies with the angle of the x-ray beam axis with respect to the object. As a result, the reconstructed images (e.g., computed tomography or CT images) suffer from radiation hardening and photon starvation artifacts and introduces a dependence of the fidelity of reconstructed features on their orientation with respect to the object rotation axis. The resolution and image quality of reconstructed images in planes parallel to the surface of the laterally extended object are typically worse than in the direction along the surface normal. In addition, neither technique is optimized to achieve a small FOD due to physical interference of the object and the x-ray source. Improving image resolution by reducing x-ray source size with high flux, which can be desirable for many applications, is severely limited with such prior art XCT and XCL systems and methods and higher depth resolution along the surface normal of such extended and/or planar objects is particularly challenging to achieve. SUMMARY

[0006] In certain implementations, a three-dimensional x-ray imaging system is configured to generate a transmission image of a region of interest in an object. The system comprises at least one position-sensitive x-ray detector comprising at least one active element. The system further comprises an x-ray source comprising an x-ray transmissive vacuum window having an outer surface. The x-ray source is configured to produce diverging x-rays, at least some of the diverging x-rays emerging from the vacuum window and propagating along an x-ray propagation axis extending from the x-ray source, through the region of interest of the object, to the at least one active element of the at least one position-sensitive x-ray detector. The diverging x-rays have propagation paths within an angular divergence angle greater than 1 degree centered on the x-ray propagation axis. The x-ray propagation axis is at a first angle with respect to the outer surface of the vacuum window, the first angle in a range of 3 degrees to 45 degrees. The system further comprises at least one sample motion stage configured to rotate the object about a rotation axis and configured such that the rotation axis has a second angle relative to the x-ray propagation axis, the second angle in a range of 45 degrees to 90 degrees. The system further comprises a sample mount on the at least one sample motion stage. The sample mount is configured to hold the object and comprises a first portion in the propagation paths of at least some of the diverging x-rays propagating through the object to the at least one position-sensitive x-ray detector. The first portion has an x-ray transmission greater than 30% for x-rays having energies greater than 50% of a maximum x-ray energy of an x-ray spectrum of the diverging x-rays.

[0007] In certain implementations, a three-dimensional x-ray imaging system comprises at least one position-sensitive x-ray detector. The system further comprises an x-ray source comprising an x-ray transmissive vacuum window having an outer surface. The x-ray source is configured to produce diverging x-rays, at least some of the diverging x-rays emerging from the vacuum window and propagating along an x-ray propagation axis extending from the x-ray source. The diverging x-rays propagate through a region of interest of an object to the at least one position-sensitive x-ray detector and have an angular divergence angle greater than 1 degree centered on the x-ray propagation axis. The x-ray propagation axis is at a first angle with respect to the outer surface of the vacuum window, the first angle in a range of 3 degrees to 45 degrees. The system further comprises at least one sample motion stage configured to rotate the object about a rotation axis and configured to adjust the rotation axis to have a second angle relative to the x-ray propagation axis, the at least one sample motion stage having a non-systematic angular wobble less than 5 microradians

BRIEF DESCRIPTION OF THE DRAWINGS

[0008] FIGs. 1A and IB schematically illustrate conventional tomography and laminography configurations, respectively, of a laterally extended object where the region of interest (RO I) is at or near the center of the object.

[0009] FIG. 2 schematically illustrates an example x-ray 3D imaging system compatible with certain implementations described herein.

[0010] FIG. 3A schematically illustrate a cross-sectional view of an x-ray spot generated by an electron beam impinging at least one x-ray target in accordance with certain implementations described herein.

[0011] FIGs. 3B and 3C schematically illustrate top views of two example configurations the electron beam and the at least one x-ray target of FIG. 3A in accordance with certain implementations described herein.

[0012] FIG. 4 schematically illustrates another example system comprising at least one aperture in accordance with certain implementations described herein.

[0013] FIGs. 5A and 5B schematically illustrate example systems in which the sample stage and the sample mount are configured to hold and rotate the object in accordance with certain implementations described herein.

[0014] FIGs. 6A and 6B schematically illustrate two examples of a system in which the at least one position-sensitive x-ray detector comprises a first position-sensitive x-ray detector and a second position-sensitive x-ray detector in accordance with certain implementations described herein.

[0015] FIG. 7 schematically illustrates an example system configured to perform multi-contrast x-ray imaging using Talbot interferometry or Talbot-Lau interferometry in accordance with certain implementations described herein.

[0016] FIG. 8 schematically illustrates an example system compatible with generating a translation laminography image in accordance with certain implementations described herein.

DETAILED DESCRIPTION [0017] In certain implementations, a 3D x-ray imaging system enables imaging of an ROI with a very small FOD in a large object to reduce laminographic dataset collection time (e.g., to increase the imaging data collection speed). In certain implementations, the system also provides improved image quality (e.g., fidelity) and higher image resolution in planes parallel to the surface of a laterally extended object, which can be important for many applications, such as metrology, inspection, failure analysis, and process development of semiconductor IC packages (e.g., as solder bumps and Cu interconnects). The x-ray source can be configured to achieve the small FOD and for improving spatial resolution. Certain implementations are configured to use the measurement geometry to “compress” the electron beam focus in one dimension which can allow the use of an asymmetric larger, and therefore higher power, focus which after projection becomes symmetric or almost symmetric which can be desirable to have isotropic spatial resolution. Certain implementations are configured to have an x-ray source comprising an x-ray generating material with a thickness configured to achieve high spatial resolution in a direction substantially perpendicular to the surface of a laterally extended object being analyzed. Additionally, certain implementations comprise additional components and/or methods for implementing several modes of imaging contrast, including Talbot interferometry for obtaining absorption, phase, and darkfield (scattering) contrast, darkfield (scattering) contrast only, and enhanced absorption contrast.

[0018] FIG. 2 schematically illustrates an example x-ray 3D imaging system 5 compatible with certain implementations described herein. The system 5 comprises an x-ray source 20 and at least one position-sensitive x-ray detector 50 comprising at least one active element 52. The x-ray source 20 comprises an x-ray transmissive vacuum window 29 having an outer surface 27, and the x-ray source 20 is configured to produce diverging x-rays. At least some of the diverging x-rays 60 emerge from the vacuum window 29 and propagate along an x-ray propagation axis 10 extending from the x-ray source 20, through a region of interest 31 of the object 30, to the at least one active element 52 of the at least one position- sensitive x- ray detector 50. The diverging x-rays 60 that impinge the at least one active element 52 have propagation paths within an angular divergence angle 12 greater than 1 degree centered on the x-ray propagation axis 10. The x-ray propagation axis 10 is at a first angle 11 with respect to the outer surface 27 of the vacuum window 29, the first angle 11 in a range less than or equal to 45 degrees, (e.g., less than or equal to 30 degrees; in a range of 3 degrees to 45 degrees; between 5 to 30 degrees; less than 3 degrees).

[0019] In certain implementations, the system 5 further comprises at least one sample motion stage 80 (e.g., motorized and computer-controlled; comprising an electromechanical system). The at least one sample motion stage 80 is configured to rotate the object 30 about a rotation axis 19. The sample motion stage 80 is configured such that the rotation axis 19 has a second angle 16 relative to the x-ray propagation axis 10, the second angle 16 in a range greater than or equal to 45 degrees (e.g., in a range of 45 degrees to 90 degrees). In certain other implementations, the second angle 16 is less than 45 degrees. The second angle 16 of certain implementations can be in a range greater than or equal to 45 degrees and the rotation axis 19 can be at a third angle relative to a surface normal of the outer surface 27 of the vacuum window 29, the third angle in a range less than 45 degrees (e.g., less than 30 degrees). In certain implementations, the system 5 comprises a mechanism configured to vary the third angle. For example, the mechanism can comprise at least one tilt stage (e.g., goniometer; electromechanical motion driver; rotary motor; stepper motor; motor with encoder; linear motion driver with worm drive) configured to tilt the x-ray source 20 relative to the rotation axis 19 and/or the rotation axis 19 relative to the x-ray source 20.

[0020] In certain implementations, the system 5 further comprises a sample mount 85 on the at least one sample motion stage 80 and configured to hold the object 30. The sample mount 85 comprises a first portion 86 in the propagation paths of at least some of the diverging x-rays 60 propagating through the object 30 to the at least one position-sensitive x-ray detector 50. The first portion 86 has an x-ray transmission greater than 30% (e.g., greater than 50%) for x-rays having energies greater than 50% of a maximum x-ray energy of an x-ray spectrum of the diverging x-rays 60.

[0021] The example system 5 of FIG. 2 is configured to image a region-of-interest (ROI) 31 in a large or laterally extended object 30 (e.g., positioned to be substantially parallel to the outer surface 27 of the vacuum window 29) so as to minimize the FOD between the ROI 31 and the x-ray source 20. For example, for imaging a ROI 31 in a large three-dimensional object 30, the object 30 can be placed close to the x-ray source 20 (e.g., at a distance less than 70 millimeters between the outer surface 27 of the vacuum window 29 and the surface 32 of the object 30) and centered to the rotation axis 19 of the at least one sample motion stage 80. A three-dimensional (3D) image dataset of the ROI 31 can be collected by recording a series of x-ray transmission images of the diverging x-rays 60 that are transmitted through the ROI 31 of the object 30 to the at least one active element 52 of the at least one position-sensitive x-ray detector 50, with the object 30 rotated about the rotation axis 19 over an angular range (e.g., between 180 and 360 degrees). A computed laminography dataset can be reconstructed using a known laminography reconstruction method, to obtain a 3D image of the ROI 31. For another example, for imaging a ROI 31 in a planar object 30 (e.g., solder bumps and/or interconnects in a semiconductor IC package), the object 30 can be positioned so that the surface 32 of the object 30 closer to the ROI 31 faces the vacuum window 29. For a large/planar object 30, a small angle 14 between the outer surface 27 of the vacuum window 29 and the surface 32 of the object 30 can be used to place the ROI 31 close to the x-ray source 20 to increase x-ray flux on the ROI 31 and thus increase imaging throughput. In another example, the surface 32 of the object 30 faces away from the outer surface 27 of the vacuum window 29 (e.g., to reduce or minimize a radiation dose to the ROI 31).

X-ray source

[0022] As schematically illustrated by FIG. 2, in certain implementations, the x-ray source 20 comprises a vacuum chamber 21 containing a vacuum region 23 and an electron beam source 22 in the vacuum region 23. The x-ray source 20 further comprises electron optics 25 (e.g., electrodes) configured to direct at least some electrons from the electron beam source 22 into an electron beam 24 focused at the at least one x-ray target 28. For example, the electron beam source 22 and the electron optics 25 are configured to generate the focused electron beam 24 and to bombard the at least one x-ray target 28 with the focused electron beam 24 with a selectable maximum focused electron energy at the at least one x-tray target 28 in a range from 10 kVp to 250 kVp. In certain implementations, the vacuum chamber 21 comprises a vacuum sealed tube containing the electron beam source 22, electron optics 25, and the at least one x-ray target 28. In contrast to open-tube x-ray sources, the x-ray source 20 of certain implementations is not actively pumped.

[0023] The at least one x-ray target 28 is within the vacuum region 23 and configured to generate the diverging x-rays 60 in response to bombardment by the focused electron beam 24. The at least one x-ray target 28 comprises at least one x-ray generating material selected for its x-ray spectral production properties (e.g., characteristic x-ray energy) and/or other properties (e.g., atomic number Z; electron density) that affect the x-ray production capability of the at least one x-ray generating material. The at least one x-ray generating material can have a sufficiently high thermal conductivity to dissipate heat generated by the bombardment by electron beams 24 with high power. Examples of x-ray generating materials include but are not limited to: Cr, Fe, Co, Ni, Cu, W, Rh, Mo, Au, Pt, Ag, SrBe, LaBe, and CeBe. As shown schematically by the insert of FIG. 2, the at least one x-ray target 28 can be affixed to (e.g., integrated with; a component of; in contact with) the vacuum window 29, the vacuum window 29 separating the vacuum region 23 from a non-vacuum region outside the x-ray source 20. The thickness of the at least one x-ray generating material along a direction substantially perpendicular to the outer surface 27 of the vacuum window 29 can be in a range of 0.1 micron to 15 microns (e.g., 0.1 micron to 10 microns) and the thickness of the vacuum window 29 in the direction substantially perpendicular to the outer surface 27 of the vacuum window 29 can be in a range of 0.05 millimeter to 3 millimeters. As described herein, the thickness of the at least one x-ray generating material can be configured to optimize for high spatial resolution (e.g., by minimizing electron beam scatter inside material) and/or for high system throughput (e.g., maximizing electron energy deposition inside the at least one x-ray generating material). For example, the thickness of the at least one x-ray generating material can be less than twice the image resolution along the rotation axis 19. In certain implementations, the at least one x-ray generating material has a plurality of regions that can be bombarded by the electron beam 24 (e.g., by translating the electron beam focus), each region having a corresponding thickness along a direction substantially perpendicular to the outer surface 27 of the vacuum window 29. The electron beam 24 can be directed by the electron optics 25 to bombard a selected region with a corresponding thickness that provides a selected tradeoff between throughput and resolution.

[0024] In certain implementations, the vacuum window 29 consists essentially of atomic elements having atomic numbers (Z) less than 14 and is substantially transmissive to higher energy x-rays generated by the at least one x-ray generating material. For example, the vacuum window 29 can have a sufficiently high thermal conductivity to provide a thermal conduit to prevent thermal damage (e.g., melting) of the at least one x-ray generating material (e.g., one or more materials selected from the group consisting of: beryllium, diamond, boron carbide, silicon carbide, aluminum, and beryllium oxide (BeO)). The vacuum window 29 can further provide a sufficiently electrically conductive path to dissipate electric charge from the at least one x-ray generating material and/or the vacuum window 29. In certain implementations, the vacuum window 29 is configured to have an x-ray transmission such that more than 50% of the x-rays generated by the at least one x-ray source 28 having energies greater than one-half the selected maximum focused electron energy are transmitted through the vacuum window 29. In certain implementations, the diverging x-rays 60 emitted from the outer surface 27 of the vacuum window 29 are not obstructed by the x-ray source 20 along the x-ray propagation axis 10. While the x-ray source 20 emits x-rays into a solid angle of 4n, FIG. 2 schematically illustrates only the diverging x-rays 60 propagating along the x-ray propagation axis 10 within the angular divergence angle 12 to the at least one active element 52 of the at least one position-sensitive x-ray detector 50 (e.g., the x-rays contributing to image formation), with the other diverging x-rays generated by the at least one x-ray target 28 and emitted in other directions from the outer surface 27 of the vacuum window 29 not illustrated in FIG. 2.

[0025] In certain implementations, the system 5 further comprises a thermal cooling mechanism configured to reduce heating of the object 30 by heat produced by the x-ray source 20. For example, the thermal cooling mechanism can comprise an infrared (IR) reflective material (e.g., a thin IR reflective and highly x-ray transmissive film or layer, an example of which is aluminized mylar) between the vacuum window 29 and the object 30. The IR reflective material is configured to reflect heat generated by the x-ray source 20 (e.g., due to power of the electron beam being converted to heat in the at least one x-ray target 28) from reaching the object 30 and the sample mount 85 (e.g., directing the thermal energy away from the object 30 and the sample mount 85 to reduce or minimize heat transport to the object 30 and/or the sample mount 85). In this way, the IR reflective material can protect the object 30 and the sample mount 85 from changes in temperature of the sample that could otherwise cause thermal expansion that could deleteriously affect the accuracy of ROI selection and/or 3D volume reconstruction fidelity. The IR reflective material is sufficiently thin (e.g., thickness less than 1500 microns; thickness less than 100 microns) so as to not substantially impair the positioning of the object 30 close to the electron beam focus of the x-ray source 20.

[0026] In certain implementations, the x-ray source 20 comprises a grounded anode transmission x-ray source (e.g., with the vacuum housing electrically grounded), examples of which include but are not limited to: DAGE BrightHawk® x-ray source available from Nordson Corporation of Westlake, Ohio; L10711-03 microfocus x-ray source available from Hamamatsu Photonics K.K. of Hamamatsu City, Japan; Excillum Nanotube N1 and N2 x-ray sources available from Excillum Corporation of Kista Sweden; X-ray Worx GmbH of Garbsen, Germany; x-ray sources available from COMET Technologies of San Jose, California). These example x-ray sources 20 can be configured to have an x-ray source point integrated with the vacuum window 29 and to have an object 30 placed close to the x-ray source 20 to reduce (e.g., minimize) the FOD and therefore to increase (e.g., maximize) the x-ray flux at the object 30. Due to the electrical and mechanical constraints, the x-ray source 20 can have a large flat face which is the terminus of the vacuum envelope and is co-planar with the vacuum window 29 but cannot be made smaller without interfering with the quality of the electron beam focus. For previously-existing x-ray tomography and laminography imaging techniques utilizing such x-ray sources 20, this large flat face has restricted the ability to place a large and/or planar object 30 close to the x-ray source 20 and being able to rotate the object 30 (e.g., up to 180 degrees) around a rotation axis 19 substantially perpendicular to the large flat face. Certain implementations described herein advantageously circumvent this major drawback of previously-existing x-ray imaging systems.

[0027] In certain implementations, the x-ray source 20 is configured to have a small x-ray spot size (e.g., having a dimension of less than 7 microns in at least one lateral direction substantially parallel to the outer surface 27 of the vacuum window 29) while generating sufficient x-ray flux to facilitate sufficiently short image collection times. In general, the x-ray spot size is approximately equal to a convolution of the focused electron beam spot size (e.g., radius) at the at least one x-ray target 28 and the size (e.g., radius) of the x-ray generation volume inside the at least one x-ray target 28 due to scattering of the electrons inside the at least one x-ray target 28. Thus, larger focused electron beam spot sizes can facilitate higher electron beam powers, with concomitant higher x-ray flux and shorter image acquisition times, at the expense of lower spatial resolutions, and smaller focused electron beam spot sizes can facilitate higher spatial resolutions at the expense of lower x-ray flux and longer image acquisition times. In addition, since a large fraction (e.g., about 99%) of the incident power from the focused electron beam 24 is converted into heat in the at least one x-ray target 28, it can be desirable to limit the incident electron beam power, which typically decreases linearly with the x-ray spot dimension.

[0028] In certain implementations, higher spatial resolution of x-ray transmission images in the direction of the plane containing the surface normal of the outer surface 27 of the vacuum window 29 and the rotation axis 19 is provided by reducing a thickness / of the at least one x-ray generating material of the at least one x-ray target 28, which reduces the effective x-ray source size 5. For example, the thickness / of the at least one x-ray generating material along a direction substantially perpendicular to the outer surface 27 of the vacuum window 29 can be in a range of 0.1 micron to 15 microns. FIG. 3A schematically illustrate a cross-sectional view of an x-ray spot generated by an electron beam 24 impinging at least one x-ray target 28 in accordance with certain implementations described herein. FIGs. 3B and 3C schematically illustrate top views of two example configurations the electron beam 24 and the at least one x-ray target 28 of FIG. 3A in accordance with certain implementations described herein. As schematically illustrated by FIG. 3A, the x-ray spot size viewed along the x-ray propagation axis 10 can be smaller than the width W (e.g., diameter) of the electron beam 24 on the x-ray target 28. For an x-ray generating material with a thickness /, the full-width-at- half maximum (FWHM) effective width s of the x-ray spot viewed along the x-ray propagation axis 10 can be approximately less than t/2 (FIG. 3A is not to scale). In certain implementations, the at least one x-ray generating material comprises a thin high Z material layer (e.g., thickness / in a range of 0.1 micron to 3 microns) on or inside of a low Z material substrate (e.g., vacuum window 29) to achieve a small x-ray spot size (e.g., less than 5 microns) in the cross-sectional plane of FIG. 3 A along the x-ray propagating axis 10 with angles smaller than 30 degrees with respect to the outer surface 27 of the vacuum window 29. The FWHM effective width 5 of the x-ray spot size in the cross-sectional plane can be approximately equal to s = {(t/2) ² + [ VV-sin(Z/)] ² }° \ where t is the thickness of the high Z material, and W is the FWHM width of the electron beam size in the cross-sectional plane. For example, with / = 1 micron, 9 = 10 degrees, and IV = 1 micron, the FWHM effective width s of the x-ray spot size in the cross-sectional plane is 0.53 micron, which is smaller than W. Thus, the effective x-ray source size in the cross-sectional plane along the x-ray propagation axis 10 can be compressed as compared to the width of the electron beam 24 in the cross-sectional plane. [0029] With the effective x-ray spot size in the cross-sectional plane substantially smaller than the electron beam width W, certain implementations can further achieve a small x-ray spot size in a direction substantially perpendicular to the cross-sectional plane of FIG. 3 A. For example, as schematically illustrated by FIG. 3B, the electron beam 24 can be focused to be compressed in the direction substantially perpendicular to the cross-sectional plane. A focused electron beam 24 having an elongated (e.g., rectangular) shape or footprint at the x-ray target 28 can have a long dimension (e.g., FHWM width IV) in the cross-sectional plane of FIG. 3A and a short dimension (e.g., FWHM width w) in a direction (e.g., in a plane containing the x-ray propagation axis 10 and the surface normal of the outer surface 27 of the vacuum window 29) substantially perpendicular to the cross-sectional plane of FIG. 3A, the short dimension smaller than the long dimension.

[0030] For another example, as schematically illustrated by FIG. 3C, the width d of the high Z material of the at least one x-ray generating material in the direction substantially perpendicular to the cross-sectional plane of FIG. 3A can be smaller than the FWHM width w of the focused electron beam 24 in the direction substantially perpendicular to the cross- sectional plane of FIG. 3A. Since the at least one x-ray generating material generates x-rays more efficiently than does the vacuum window 29 (e.g., since x-ray production efficiency is approximately proportional to the mean atomic number of the material), the portions of the electron beam 24 that do not impinge the at least one x-ray generating material do not efficiently generate x-rays and do not substantially contribute to the x-ray spot size, thereby limiting the x-ray spot size to the width d in the direction substantially perpendicular to the cross-sectional plane of FIG. 3A. In certain implementations, the width d of the at least one x-ray generating material is in a range of 0.1 micron to 5 microns.

[0031] When viewed along the x-ray propagation axis 10 (e.g., the direction from the at least one position-sensitive x-ray detector 50), and taking into account the take-off angle between the outer surface 27 and the x-ray propagation axis 10, the x-ray spot of FIGs. 3B and 3C can appear square or circular at the at least one position-sensitive x-ray detector 50. For example, at a take-off angle of 10 degrees, an electron beam 24 having a rectangular focus with a 5: 1 aspect ratio can appear substantially symmetric. Since the electron beam 24 is elongated and impinges a larger area than if the electron beam 24 were narrowly focused in both directions, a higher electron power can be used to increase the x-ray flux (e.g., to achieve a higher x-ray brightness) and thus reduce image collection times while maintaining spatial resolution. For example, an electron beam 24 with the 5:1 aspect ratio can provide up to a five-fold increase of the apparent power density. Further reducing the take-off angle in conjunction with a higher aspect ratio focused electron beam can facilitate further improvements of the apparent power density. Further reducing the take-off angle in conjunction with a higher aspect ratio focused electron beam can facilitate further improvements of the apparent power density. Certain implementations provide a higher spatial resolution in the cross-sectional plane of FIG. 3 A than in the orthogonal direction to the cross- sectional plane. For many applications, high depth resolution (e.g., in a direction substantially perpendicular to the surface 32 of a laterally extended object 30) is more important than the lateral resolution (e.g., imaging delamination of the solder bumps or stress-induced cracks in solder bumps parallel to the surface in semiconductor packages).

Aperture

[0032] FIG. 4 schematically illustrates another example system 5 comprising at least one aperture 70 in accordance with certain implementations described herein. In certain implementations, the at least one aperture 70 comprises at least one orifice 72 (e.g., slit; having a width less than 100 microns) in at least one solid material (e.g., plate), the at least one orifice 72 positioned on the x-ray propagation axis 10 and between the vacuum window 29 and the object 30 (e.g., downstream of the vacuum window 29 and upstream from the object 30). The at least one aperture 70 is configured to not attenuate the diverging x-rays 60 propagating along the x-ray propagating axis 10 within the angular divergence angle 12 (e.g., the x-rays used for imaging) from reaching the ROI 31 and/or the at least one position-sensitive x-ray detector 50 but to attenuate at least some x-rays emitted from the vacuum window 29 in other directions and/or scattered x-rays (e.g., the x-rays not used for imaging) from reaching the ROI 31 and/or the at least one position-sensitive x-ray detector 50. In certain implementations, the at least one solid material of the at least one aperture 70 has a sufficiently high Z (e.g., W; Au), sufficiently high electron density, and a substantially small thickness such that the at least one aperture 70 is configured to attenuate x-rays without substantially limiting the FOD. In certain implementations, the at least one aperture 70 is configured to attenuate the amount of extraneous x-ray flux outside the angular divergence angle 12 emitted by the x-ray source 20 reaching the object 30. By attenuating this extraneous x-ray flux, the at least one aperture 70 can reduce a deleterious background contribution in the image from the extraneous x-ray flux and/or can reduce the detrimental x-ray dosage to the object 30 from the extraneous x-ray flux that does not contribute to the imaging. The edges of the at least one orifice 72 of the at least one aperture 70 can define the angular divergence angle 12 by only allowing x-rays within the at least one orifice 72 to propagate further along the x-ray propagation axis 10. In certain implementations, the distance between the one aperture 70 to the vacuum window 29 is configured (e.g., a distance in a range from 0.3 millimeter to 5 millimeters) to achieve a small FOD between the x-ray source point and the ROI 31.

Sample motion stage and sample mount

[0033] In certain implementations, the at least one sample motion stage 80 is configured to move the object 30 relative to the x-ray source 20 and/or the at least one positionsensitive x-ray detector 50. In certain implementations, the at least one sample motion stage 80 comprises at least one linear motion substage 82 configured to controllably adjust a position of the object 30 (e.g., along substantially perpendicular x-, y-, and z-directions) and at least one rotational motion substage 84 configured to controllably adjust an orientation of the object

30 (e.g., rotating the object 30 about the rotation axis 19). For example, the at least one linear motion substage 82 can comprise one, two, or three electromechanical linear motion driver (e.g., linear motor; stepper motor; motor with encoder; piezoelectric motor; rotary motor with screw) configured to move the object 30 such that the ROI 31 is at a selected position along the x-ray propagation axis 10 and the at least one rotational motion substage 84 can comprise at least one electromechanical motion driver (e.g., rotary motor; stepper motor; motor with encoder; linear motion driver with worm drive) configured to rotate the object 30 and the ROI

31 about the rotation axis 19.

[0034] In certain implementations, as schematically illustrated by FIG. 2, a laterally extended object 30 can be mounted on the at least one sample motion stage 80, such that a surface 32 of the object 30 parallel to a long dimension of the object 30 is tilted at an angle 0 (e.g., in a range of 1 degree to 30 degrees) with respect to the x-ray propagation axis 10. In certain implementations, the at least one rotational motion substage 84 is further configured to controllably adjust the angle 0 and the at least one linear motion substage 82 is further configured to linearly translate the object 30 and/or the at least one rotational motion substage 84 such that the ROI 31 is positioned on the rotation axis 19, as well as on the x-ray propagation axis 10. In certain implementations, the at least one sample motion stage 80 is configured to controllably adjust the distance between the rotation axis 19 and the x-ray spot (e.g., the electron beam focus).

[0035] In certain implementations, the sample mount 85 is configured to hold the object 30 while the object 30 is irradiated by the x-rays 60 such that the x-rays 60 are transmitted through the ROI 31 to the at least one position-sensitive x-ray detector 50. The sample mount 85 is configured such that the x-rays 60 minimally interact with (e.g., are minimally scattered and/or absorbed by) solid components of the at least one sample motion stage 80 (e.g., the at least one linear motion substage 82 and the at least one rotational motion substage 84). The sample mount 85 is configured to reduce (e.g., minimize) the portion of the diverging x-rays 60 that interact with solid portions of the at least one sample motion stage 80 as the object 30 is rotated around the rotation axis 19.

[0036] In certain implementations, the at least one sample motion stage 80 and the sample mount 85 are configured to hold and rotate the object 30 without compromising throughput. For example, since throughput for microfocus transmission x-ray computed laminography is inversely proportional to the square of the focus-to-object distance (FOD), high throughput can be achieved using a small FOD (e.g., having the object 30 as close as possible to the x-ray source 20).

[0037] FIGs. 5A and 5B schematically illustrate example systems 5 in which the at least one sample motion stage 80 and the sample mount 85 are configured to hold and rotate the object 30 in accordance with certain implementations described herein. In the example system 5 of FIG. 5A, the object 30 is between the x-ray source 20 and the at least one sample motion stage 80. With the at least one linear motion substage 82 and the at least one rotational motion substage 84 on an opposite side of the object 30 from the at least one x-ray source 20, the at least one sample motion stage 80 does not impede the x-rays 60 reaching the object 60. However, as shown in FIG. 5 A, after having propagated through the ROI 31, the x-rays 60 propagate through at least a portion of the sample mount 85 before reaching the at least one position-sensitive x-ray detector 50. In the example system 5 of FIG. 5B, the x-ray source 20 and the at least one sample motion stage 80 are on the same side of the object 30 and the x-rays 60 propagate through at least a portion of the sample mount 85 before reaching the object 30 (e.g., the sample mount 85 can limit the closest approach of the x-ray source 20 to the object 30). While FIG. 5A shows an example implementation in which the x-ray source 20 is above the object 30 and the at least one sample motion stage 80, in other implementations, the x-ray source 20, the object 30, and the at least one sample motion stage 80 can have any orientation while retaining the same relative positioning to one another. While FIG. 5B shows an example implementation in which the x-ray source 20 is below the object 30, in other implementations, the x-ray source 20, the object 30, and the at least one sample motion stage 80 can have any orientation while retaining the same relative positioning to one another.

[0038] In certain implementations, the sample mount 85 is configured to offset the object 30 from the at least one sample stage 80 so that the at least one sample stage 80 (e.g., the at least one linear motion substage 82 and the at least one rotational motion substage 84) is not in the imaging field-of-view of the at least one position-sensitive x-ray detector 50 (e.g., reduce, avoid, or minimize x-ray scattering and/or absorption that would deleteriously affect the image reconstruction fidelity). For example, the sample mount 85 can offset the object 30 from the at least one sample stage 80 by a distance that is greater than 50 millimeters (e.g., greater than 100 millimeters; in a range of 100 millimeters to 500 millimeters; in a range of 100 millimeters to 200 millimeters). The sample mount 85 of certain implementations comprises a first portion 86 configured to be impinged by at least a portion of the x-rays 60 as the object 30 and the sample mount 85 are rotated about the rotation axis 19 and a second portion 87 that mechanically couples the first portion 86 to the at least one motion substage (e.g., the at least one linear motion substage 82 and/or the at least one rotational motion substage 84). The first portion 86 and the second portion 87 are configured to offset the ROI 31 of the object 30 from the at least one motion substage such that the diverging x-rays 60 do not impinge the at least one motion substage or the second portion 87 (e.g., as the object 30 and the sample mount 85 are rotated about the rotation axis 19).

[0039] In certain implementations, the first portion 86 is comprised essentially of low Z elements (e.g., atomic elements having atomic numbers less than 14) and/or thin materials (e.g., thickness along the rotation axis 19 less than 10 millimeters). In certain implementations, the first portion 86 has an x-ray transmission greater than 50% for x-rays having energies greater than 50% of the maximum x-ray energy of the x-ray spectrum of the x-rays 60 (e.g., the x-rays emitted by the x-ray source 20). Certain such implementations concurrently provide a sufficiently high throughput with a sufficiently small amount of radiation damage to the object 30 (e.g., since the x-rays do not have to be transmitted through absorptive material of the at least one sample motion stage 80, the x-ray flux irradiating the object 30 can be kept sufficiently low to avoid radiation damage while providing sufficiently high amounts of detected x-rays for high throughput imaging). For example, the first portion 86 can comprise a carbon fiber or quartz plate (e.g., having a projected thickness along the x-ray propagation axis 10 less than or equal to 2 millimeters). The second portion 87 is mechanically coupled to the first portion 86 and to the at least one linear motion substage 82 and/or the at least one rotational motion substage 84. In certain implementations, the second portion 87 is comprised essentially of the same low Z elements and/or thin materials as is the first portion 86 (e.g., low Z rod or hollow tube, such as a carbon fiber or quartz tube having a projected thickness along the x-ray propagation axis 10 less than or equal to 2 millimeters), while in certain other implementations, the second portion 87 comprises any solid material (e.g., regardless of the x-ray absorption and/or scattering of the solid material). In certain implementations, the second portion 87 is part of the at least one linear motion substage 82 and/or the at least one rotational motion substage 84.

[0040] For example, as schematically illustrated by FIG. 5A, the first portion 86 and the second portion 87 extend along the rotation axis 19 and can be configured such that for all laminography angles of interest and for all rotational angles of interest, the x-rays 60 do not impinge the at least one linear motion substage 82 and/or the at least one rotational motion substage 84. For the at least one sample motion stage 80 having a maximum dimension (e.g., radius) R from the rotation axis 19 and along a direction substantially perpendicular to the rotation axis 19, the first and second portions 86, 87 can be configured to hold the object 30 a distance z along the rotation axis 19 from the at least one linear motion substage 82 and/or the at least one rotational motion substage 84 such that the envelope of x-rays 60 does not impinge portions of the at least one sample motion stage 80 that would scatter and/or absorb the x-rays 60 (e.g., portions comprising at least one element having an atomic number Z greater than 14; the at least one linear motion substage 82; the at least one rotational motion substage 84).

[0041] For another example, as schematically illustrated by FIG. 5B, the first portion 86 is configured to hold (e.g., clamp) the sides and/or edges of the object 30 and the second portion 87 mechanically couples the first portion 86 to the at least one sample motion stage 80 (not shown in FIG. 5B). The at least one sample motion stage 80 of FIG. 5B further comprises a clear aperture region 88 (e.g., a region at least partially bounded by the second portion 87) configured to have the x-ray source 20 extending at least partially therethrough. Certain such implementations enable the x-ray source 20 to be placed arbitrarily close to a face of the object 30, thereby providing a high throughput while rigidly mounting the object 30. An example second portion 87 compatible with certain implementations described herein is a large aperture, ultra-high-precision, air-bearing rotary stage, available from PI (Physik Instrumente) of Auburn, Massachusetts.

[0042] Image reconstruction fidelity is dependent on precise rotation of the object 30 during measurements, and uncontrolled motions of the object 30 can create deviations of the actual recorded projection data from what a laminographic reconstruction algorithm would expect. As a result, these uncontrolled motions can create a blurring in the back-projected data that degrades the resolution and contrast in the reconstructed volume. In certain implementations, the at least one sample motion stage 80 reduces (e.g., avoids; minimizes) deviations from pure rotations that cause translation and/or orientation changes of the object 30 within the image field-of-view. The at least one sample motion stage 80 can have a sufficiently low non-systematic angular wobble (e.g., uncontrolled angular motion of the rotation axis 19 as a function of rotation about the rotation axis 19), sufficiently low radial runout (e.g., uncontrolled translation of the rotation axis 19 as a function of rotation about the rotation axis 19 resulting in lateral movement of the object 30 substantially perpendicular to the rotation axis 19), and/or sufficiently low axial runout (e.g., uncontrolled axial movement of the object 30 substantially parallel to the rotation axis 19) during rotation of the object 30 about the rotation axis 19 such that uncontrolled motion of the object 30 is less than one-fifth of the system resolution (e.g., less than 0.1 micron uncontrolled motion for a system resolution of 0.5 micron). For example, for an object 30 positioned a distance L above the at least one rotational motion substage 84 of the at least one sample motion stage 80 and an image resolution (e.g., detector resolution divided by image magnification) of 5, a non-systematic angular wobble of co (e.g., less than 100 nanoradians; less than 200 nanoradians; less than 1 microradian; less than 5 microradians) can result in a radial runout of R = coL < 5/5 (e.g., less than 5/3; less than 5/2; less than 1 micron; less than 0.5 micron; less than 200 nanometers; less than 100 nanometers) and/or an axial runout A < 5/5 (e.g., less than 5/3; less than 5/2; less than 1 micron; less than 0.5 micron; less than 200 nanometers; less than 100 nanometers). In certain implementations, the at least one sample motion stage 80 has a non-systematic angular wobble (e.g., error) less than 5 microradians (e.g., less than 1 microradian), a radial runout repeatability better than 1000 nanometers, and an axial runout repeatability better than 1000 nanometers. In certain implementations, the system 5 further comprises a metrology system configured to measure an angular wobble of the at least one sample motion stage 80 with an accuracy better than less than 5 microradians (e.g., less than 1 microradian), to measure a radial runout of the at least one sample motion stage 80 with an accuracy better than 1000 nanometers, and/or to measure an axial runout of the at least one sample motion stage 80 with an accuracy better than 1000 nanometers.

[0043] In certain implementations, the at least one rotational motion substage 84 of the at least one sample motion stage 80 can comprise an air-bearing rotary stage (e.g., A-62X or A-688 rotary stage available from PI (Physik Instrumente of Auburn, Massachusetts; ABRX00, ABRX150, or ABRX250 rotary stage available from Aerotech, Inc. of Pittsburgh, Pennsylvania) having a wobble angle less than 5 microradians (e.g., less than 1 microradian; less than 200 nanoradians) and radial and axial runout less than 100 nanometers. The position of the object 30 over the angular range (e.g., 360 degrees) of rotation about the rotation axis 19 can be accurate to better than one-half of the resolution of the system.

Position-sensitive x-ray detector

[0044] In certain implementations, the at least one position-sensitive x-ray detector 50 is configured to record images of the x-rays 60 received after transmitting through the ROI 31. Examples of the at least one position-sensitive x-ray detector 50 include but are not limited to: photon counting detectors (e.g., comprising silicon, CdTe, and/or CdZnTe and configured to directly convert x-rays to electrons with or without energy discrimination; Eiger ASICs and Pilatus ASICs available from Dectris of Baden-Daettwil, Switzerland); flat panel detectors (FPD) comprising a scintillator material (e.g., CdWCU, CsI, Gd2O2S, LSO, GAGG, and/or LYSO; Shad-o-Box HS detectors available from Teledyne Dalsa of Waterloo Canada; 2315N detectors available from Varex Imaging of Salt Lake City, Utah; Athena detectors and Onyx detectors available from Nordson Corporation of Westlake, Ohio; 1412HR detectors available from Spectrum Logic Corporation of Boulder, Colorado); fiber optic plates and CMOS or CCD detectors; a scintillator material (e.g., CdWO4, CsI, Gd2O2S, LSO, GAGG, and/or LYSO) and objective configured to magnify an image onto a CMOS or CCD detector. In certain implementations, the at least one position-sensitive x-ray detector 50 comprises a plurality of active elements 52 (e.g., pixels) having lateral dimensions (e.g., along a surface of the detector 50) less than 70 microns (e.g., less than 50 microns).

[0045] In certain implementations, the at least one position-sensitive x-ray detector 50 is configured to receive and image x-rays 60 transmitted through the object 30, including the ROI 31, the x-rays 60 having a predetermined range of energies (e.g., the x-ray spectrum) which facilitates (e.g., optimize) sufficient image contrast to discern features of interest in the ROI 31 and/or reduces imaging collection times. For example, the predetermined x-ray spectrum can be generated by selecting the focused electron energy and/or the at least one x-ray generating material of the at least one x-ray target 28, such that the generated x-rays 60 in the predetermined x-ray spectrum have a sufficiently large x-ray flux to facilitate the image contrast and/or the imaging collection times. For x-ray imaging using absorption contrast, the predetermined x-ray spectrum can include energies at which the object 30 has an x-ray transmission in a range of 5% to 85% (e.g., in a range of 8% to 30%). This range of x-ray transmission can provide an advantageous trade-off between image contrast (which favors lower energy x-rays) and transmission through the object 30 (which favors higher energy x-rays).

[0046] For another example, the at least one position- sensitive x-ray detector 50 can be configured to have at least one energy threshold for detecting x-rays (e.g., the at least one position-sensitive x-ray detector 50 can be configured to reject and/or suppress detection of x-rays having energies below a first energy threshold and/or energies above a second energy threshold). For example, the at least one energy threshold can comprise a threshold cut-off x-ray energy, the at least one position-sensitive x-ray detector 50 configured to only image x-rays having energies below the threshold cut-off x-ray energy. The threshold cut-off x-ray energy of certain implementations corresponds to x-rays for which the object 30 has an x-ray transmission less than 85% (e.g., less than 50%). For example, the at least one positionsensitive x-ray detector 50 can comprise a photon counting detector configured to select at least one threshold cut-off x-ray energy (e.g., to controllably adjust the threshold cut-off x-ray energy). The photon counting detector can be further configured to collect energy-dependent x-ray transmission images (e.g., using a plurality of operator-selectable energy windows to reduce noise, image artifacts, and/or to provide material differentiation). For another example, the at least one position-sensitive x-ray detector 50 can comprise a combination of scintillating screens and materials configured to only image x-rays below the threshold cut-off x-ray energy.

[0047] FIGs. 6A and 6B schematically illustrate two examples of a system 5 in which the at least one position-sensitive x-ray detector 50 comprises a first position-sensitive x-ray detector 54 and a second position-sensitive x-ray detector 56 in accordance with certain implementations described herein. The second position-sensitive x-ray detector 56 can be configured to provide gain sensitivity to a different portion of the x-ray spectrum than obtained from the first position-sensitive x-ray detector 54, to increase overall throughput, and/or to provide measurements with a different spatial resolution from that of the first position-sensitive x-ray detector 54. For example, the first and second position-sensitive x-ray detectors 54, 56 can have different scintillating materials from one another and/or different scintillator thicknesses from one another.

[0048] For example, as schematically illustrated by FIG. 6A, the first detector 54 can be configured to absorb and detect a first spectral portion of the x-rays 60 transmitted through the ROI 31 and the second detector 56 can be configured to absorb and detect a second spectral portion of the x-rays 60 transmitted through the ROI 31 and not absorbed by the first detector 54. The first detector 54 can be configured (e.g., optimized) for high resolution and can transmit at least some of the x-ray flux received from the ROI 31, and the second detector 56 can be positioned behind the first detector 54 (see, e.g., FIG. 6A) and configured to detect at least some of the x-ray flux transmitted through the first detector 56. For another example, as schematically illustrated by FIG. 6B, a first spectral portion of the x-rays 60 propagating along the x-ray propagation axis 10 can be absorbed by a scintillator screen 55 of the first detector 54 and a second spectral portion of the x-rays 60 propagating along the x-ray propagation axis 10 can be transmitted by the scintillator screen 55 to impinge the second detector 56. The x-rays absorbed by the scintillator screen 55 can generate scintillation photons (e.g., visible light photons) that are reflected by a mirror 57 and imaged by an objective lens 58 onto a position-sensitive photon detector 59. The material and thickness of the mirror 57 can be selected to have a high transmission of the x-rays 60 that are transmitted through the object 30. [0049] While FIGs. 6A and 6B schematically illustrate configurations in which the two detectors 54, 56 are positioned to detect x-rays 60 propagating along the same direction as one another, in certain other implementations, the two detectors 54, 56 are positioned to collect x-rays propagating from the at least one x-ray source 20 along different directions from one another (e.g., different directions at angles less than 45 degrees relative to the outer surface 27 of the vacuum window 29). In certain implementations, the two detectors 54, 56 are used simultaneously with one another, while in certain other implementations, the two detectors 54, 56 are used separately (e.g., sequentially) from one another. In certain implementations, the two detectors 54, 56 are configured to have different pixel resolutions at the object 30 (e.g., approximately equal to the pixel size of the detector divided by its geometric image magnification). Combining the outputs of the two detectors 54, 56 in certain implementations can increase an overall detection efficiency of the system 5, and can give access to a broader range of object spatial frequencies, therefore improving throughput and reconstruction quality. In certain implementations, the second detector 56 is configured (e.g., optimized) to be sensitive to a different portion of the x-ray spectrum of the x-rays 60, which can allow correction for beam hardening and/or material identification.

[0050] FIG. 7 schematically illustrates an example system 5 configured to perform multi-contrast x-ray imaging using Talbot interferometry or Talbot-Lau interferometry in accordance with certain implementations described herein. The system 5 can be configured to provide high resolution and sensitivity and unique imaging capabilities (e.g., absorption, phase, and darkfield image contrast in 2D and 3D; dark-field; enhanced absorption contrast imaging) for a wide range of applications. In certain implementations, the system 5 is configured to collect a 3D imaging dataset using Talbot-Lau interferometry, darkfield contrast, and enhanced absorption contrast, and to reconstruct the dataset to obtain 3D images of the object 30 and/or the ROI 31 in the object 30. In certain implementations, as schematically illustrated by FIG. 7, the system 5 further comprises at least one sample motion stage 80 and a sample mount 85 (see, e.g., FIG. 5A) configured to reduce (e.g., minimize) interactions of the portion of the diverging x-rays 60 propagating along the x-ray propagation axis 10 with solid portions of the at least one sample motion stage 80.

[0051] As schematically illustrated by FIG. 7, the system 5 comprises a first grating G1 (e.g., a phase grating) configured to generate a Talbot self-image interference pattern at a first position along the x-ray propagation axis 10 and a second grating G2 (e.g., an analyzer grating) positioned at a second position along the x-ray propagation axis 10. The first grating G1 and the second grating G2 are configured to be compatible with Talbot interferometry such that the Talbot pattern is imaged indirectly by the at least one position-sensitive x-ray detector 50. In certain other implementations, the second grating G2 can be omitted and the at least one position-sensitive x-ray detector 50 can have active elements 52 with spatial resolutions (e.g., sizes in lateral directions substantially perpendicular to the x-ray propagation axis 10) sufficiently small (e.g., smaller than or equal to one-half of the pitch of the second grating G2) to be compatible with Talbot interferometry such that the Talbot pattern is imaged directly by the at least one position-sensitive x-ray detector 50. In certain implementations, the system 5 further comprises a source grating and is configured to perform Talbot-Lau interferometry. In certain other implementations, the x-ray source 20 comprises a plurality of x-ray targets 28 in a regular array in one or two dimensions, the geometric parameters of the plurality of x-ray targets 28, first grating Gl, and second grating G2 are configured to satisfy the Talbot-Lau interferometer conditions. Various configurations of the x-ray source 20, and the first and second gratings Gl, G2 are disclosed in U.S. Pat. Nos. 9,719,947 and 10,349,908, each of which is incorporated in its entirety by reference herein.

[0052] In certain implementations, the first grating Gl comprises an absorption grating. For example, the one or both of the first grating Gl and the second grating G2 can comprise an array of patterned one-dimensional or two-dimensional x-ray substantially absorptive (e.g., absorption greater than 50%) structures having widths in a range of 0.5 micron to 20 microns and spaced from one another by substantially non-absorptive (e.g., absorption less than 50%) gaps having widths in a range of 0.5 micron to 20 microns. In addition to using a technique such as phase stepping for tri-contrast imaging (e.g., absorption, phase, and scattering), the system 5 of certain implementations can be configured to obtain only darkfield (e.g., scattering) contrast imaging by configuring the pitch, the distances from the x-ray source 20, and the alignments of the first and second gratings, such that the x-rays transmitted through the openings of the first (e.g., upstream) grating Gl are incident on absorbing portions of the second (e.g., downstream) grating G2. For example, the first grating Gl and the second grating G2 can be placed along the x-ray propagation axis 10 between the at least one x-ray source 20 and the at least one position-sensitive x-ray detector 50 (e.g., the first grating Gl closer to the at least one x-ray source 20 than to the at least one position- selective x-ray detector 50) such that the substantially non- absorptive structures of the second grating G2 are aligned with (e.g., in the shadows of) the substantially absorptive structures of the first grating G1 and that the substantially absorptive structures of the second grating G2 are aligned with the substantially non-absorptive structures of the first grating Gl. In such a configuration, in the absence of an object 30, no x-rays would be expected to be transmitted through both the first grating Gl and the second grating G2, but in the presence of scattering features of an object 30, at least some of the scattered x-rays are transmitted through the second grating G2, leading to imaging of the features in the object 30 responsible for the scattered x-rays. In certain implementations, an enhanced absorption contrast image can be obtained by displacing the relative alignment of the first and second gratings by one-half the pitch from the configuration used in the darkfield imaging, such that the x-rays scattered by the object 30 are reduced by the absorbing structures of the second grating G2. In certain implementations, instead of having a second grating G2, a first set of the active elements 52 (e.g., pixels) of the at least one position-sensitive x-ray detector 50 are aligned with (e.g., in the shadows of) the substantially absorptive structures of the first grating Gl and a second set of the active elements 52 of the at least one positionsensitive x-ray detector 50 are aligned with the substantially non-absorptive structures of the first grating Gl. In such a configuration, when the object 30 is placed along the x-ray propagation axis 10, the x-ray counts recorded by the second set of active elements 52 can be used to generate absorption contrast images while the x-ray counts recorded by the first set of active elements 52 can be used to generate scattered/darkfield and/or refraction images.

[0053] In certain implementations in which semiconductor IC packages are to be imaged in 3D, the system 5 is configured to obtain x-ray transmission images with the x-ray propagation axis 10 at a small angle (e.g., in a range less than 45 degrees) with respect to the surface normal of the surface 32 of the semiconductor chip. For example, a rotation laminography over a large angular range (e.g., 180 degrees to 630 degrees) or a limited angle translation laminography over a finite angular range (e.g., ± 30 degrees) can be performed. The 3D image(s) can be combined with the laminography 3D image obtained with the x-ray propagation axis 10 at a large angle (e.g., greater than 60 degrees) with respect to the surface normal of the surface 32 of the semiconductor chip to generate a 3D image. FIG. 8 schematically illustrates an example system 5 compatible with generating a translation laminography image in accordance with certain implementations described herein. The system 5 comprises an additional x-ray detector 90 and at least one detector stage 92 configured to translate the detector 90 and the object 30 with respect to the x-ray source 20. In certain implementations, the at least one detector stage 92 comprises the at least one sample motion stage 80. For example, the detector 90 and the object 30 can be moved in proportion in the same direction (e.g., along a line from the x-ray source 20 through the ROI 31 to the center of the detector 90). In certain implementations, the system 5 of FIG. 8 is configured to achieve higher spatial resolution and/or better image clarity for features extending in a direction substantially parallel to the surface normal of the semiconductor chip (e.g., side walls of copper interconnects).

[0054] In certain implementations, the system 5 further comprises at least one motion mechanism configured to vary a geometric magnification of an image of the region of interest of the object generated by the at least one position-sensitive detector. For example, the at least one motion mechanism can comprise at least one first motion stage (e.g., linear motion stage; electromechanical linear motion driver; linear motor; stepper motor; motor with encoder; piezoelectric motor; rotary motor with screw) configured to move the x-ray source 20 relative to the object 30, at least one second motion stage (e.g., linear motion stage; electromechanical linear motion driver; linear motor; stepper motor; motor with encoder; piezoelectric motor; rotary motor with screw) configured to move the at least one positionsensitive detector 50 relative to the object 30, and/or at least one third motion stage (e.g., linear motion stage; ; electromechanical linear motion driver; linear motor; stepper motor; motor with encoder; piezoelectric motor; rotary motor with screw; the at least one linear motion substage 82) configured to move the object 30 relative to the x-ray source 20 and/or the at least one position-sensitive detector 50.

[0055] Although commonly used terms are used to describe the systems and methods of certain implementations for ease of understanding, these terms are used herein to have their broadest reasonable interpretations. Although various aspects of the disclosure are described with regard to illustrative examples and implementations, the disclosed examples and implementations should not be construed as limiting. Conditional language, such as “can,” “could,” “might,” or “may,” unless specifically stated otherwise, or otherwise understood within the context as used, is generally intended to convey that certain implementations include, while other implementations do not include, certain features, elements, and/or steps. Thus, such conditional language is not generally intended to imply that features, elements, and/or steps are in any way required for one or more implementations. In particular, the terms “comprises” and “comprising” should be interpreted as referring to elements, components, or steps in a non-exclusive manner, indicating that the referenced elements, components, or steps may be present, or utilized, or combined with other elements, components, or steps that are not expressly referenced.

[0056] Conjunctive language such as the phrase “at least one of X, Y, and Z,” unless specifically stated otherwise, is to be understood within the context used in general to convey that an item, term, etc. may be either X, Y, or Z. Thus, such conjunctive language is not generally intended to imply that certain implementations require the presence of at least one of X, at least one of Y, and at least one of Z.

[0057] Language of degree, as used herein, such as the terms “approximately,” “about,” “generally,” and “substantially,” represent a value, amount, or characteristic close to the stated value, amount, or characteristic that still performs a desired function or achieves a desired result. For example, the terms “approximately,” “about,” “generally,” and “substantially” may refer to an amount that is within ± 10% of, within ± 5% of, within ± 2% of, within ± 1% of, or within ± 0.1% of the stated amount. As another example, the terms “generally parallel” and “substantially parallel” refer to a value, amount, or characteristic that departs from exactly parallel by ± 10 degrees, by ± 5 degrees, by ± 2 degrees, by ± 1 degree, or by ± 0.1 degree, and the terms “generally perpendicular” and “substantially perpendicular” refer to a value, amount, or characteristic that departs from exactly perpendicular by ± 10 degrees, by ± 5 degrees, by ± 2 degrees, by ± 1 degree, or by ± 0.1 degree. The ranges disclosed herein also encompass any and all overlap, sub-ranges, and combinations thereof. Language such as “up to,” “at least,” “greater than,” less than,” “between,” and the like includes the number recited. As used herein, the meaning of “a,” “an,” and “said” includes plural reference unless the context clearly dictates otherwise. While the structures and/or methods are discussed herein in terms of elements labeled by ordinal adjectives (e.g., first, second, etc.), the ordinal adjectives are used merely as labels to distinguish one element from another, and the ordinal adjectives are not used to denote an order of these elements or of their use. [0058] Various configurations have been described above. It is to be appreciated that the implementations disclosed herein are not mutually exclusive and may be combined with one another in various arrangements. Although this invention has been described with reference to these specific configurations, the descriptions are intended to be illustrative of the invention and are not intended to be limiting. Various modifications and applications may occur to 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 making up the method/process may be performed in any suitable sequence and are not necessarily limited to any particular disclosed sequence. Features or elements from various implementations and examples discussed above may be combined with one another to produce alternative configurations compatible with implementations disclosed herein. Various aspects and advantages of the implementations have been described where appropriate. It is to be understood that not necessarily all such aspects or advantages may be achieved in accordance with any particular implementation. Thus, for example, it should be recognized that the various implementations may be carried out in a manner that achieves or optimizes one advantage or group of advantages as taught herein without necessarily achieving other aspects or advantages as may be taught or suggested herein.