HIGH-THROUGH 3D X-RAY IMAGING SYSTEM USING A TRANSMISSION X-RAY SOURCE

Abstract

Three-dimensional X-ray imaging system (5) configured to generate a transmission image of a region of interest (31) in an object (30), the system (5) comprising: at least one position-sensitive X-ray detector (50) comprising at least one active element (52); an X-ray source (20) comprising an X-ray-transparent vacuum window (29) with an outer surface (27), wherein the outer surface (27) is located at a distance of less than 70 millimeters from the region of interest (31), wherein the X-ray source (20) comprises at least one X-ray target (28) configured for bombardment with an electron beam (24) to produce diverging X-rays (60), wherein the diverging X-rays (60) extend from an X-ray focal spot having a width in a cross-sectional plane, the cross-sectional plane comprising the electron beam (24) and an X-ray propagation axis (10) extending from the X-ray focal spot through the 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), wherein at least some of the diverging X-rays (60) exit the vacuum window (29) and propagate along the X-ray propagation axis (10), wherein the diverging X-rays (60) are received by the at least one active element (52) and have propagation paths within a divergence angle (12) centered on the X-ray propagation axis (10) of more than 1 degree, wherein the X-ray propagation axis (10) forms a first angle (11) with the outer surface (27) of the vacuum window (29), wherein the first angle (11) is in a range of 3 degrees to 45 degrees, wherein the X-ray focal spot has an effective width in the cross-sectional plane along the X-ray propagation axis (10), wherein the effective width is less than the width; at least one sample movement stage (80) configured to rotate the object (30) about a rotation axis (19) and configured such that the rotation axis (19) has a second angle (16) relative to the X-ray propagation axis (10), the second angle (16) being in a range of 45 degrees to 90 degrees; and a sample holder (85) on the at least one sample movement table (80), wherein the sample holder (85) is configured to hold the object (30), the sample holder (85) comprising a first section (86) in the propagation paths of at least some of the diverging X-rays (60) that propagate through the object (30) to the at least one position-sensitive X-ray detector (50), wherein the first section (86) has an X-ray transmission of more than 30% for X-rays with energies of more than 50% of a maximum X-ray energy of an X-ray spectrum of the diverging X-rays (60), wherein the system (5) further comprises a thermal cooling mechanism configured to reduce the heating of the object (30) by the heat generated by the X-ray source (20), wherein the thermal cooling mechanism comprises an infrared (IR) reflective material between the vacuum window (29) and the object (30), wherein the IR reflective material has a thickness of less than 1,500 micrometers and is configured to reflect the heat generated by the X-ray source (20) so that it does not reach the object (30) and the sample holder (85).

Description

CLAIMING PRIORITY

[0001] This patent application claims priority over the preliminary US patent applications Nos. 63 / 122,354, filed on December 7, 2020, and 63 / 274,367, filed on November 1, 2021, each of which is incorporated herein in its entirety by reference. BACKGROUND Technical area

[0002] This application generally concerns tomography and laminography X-ray imaging systems. Description of the state of the art

[0003] Three-dimensional (3D) X-ray imaging techniques are useful for visualizing the internal structures of objects. Typically, a tomography dataset consists of X-ray transmission images acquired over a wide angular range (e.g., about 180 degrees; about 360 degrees) and subsequently reconstructed to obtain a 3D image. The wide angular range is used to avoid (e.g., minimize) 3D image artifacts. A 3D X-ray imaging system includes 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 for manipulating the object relative to the X-ray source and the position-sensitive X-ray detector.

[0004] The 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, where this distance can be referred to as the focus object distance (FOD). To achieve high throughput for 3D X-ray imaging, the FOD is chosen to be small (e.g., the region of interest is placed as close as possible to the X-ray source). For example, given the small voxel volume used to achieve 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 microfocus X-ray source for laboratory purposes. Furthermore, for 3D X-ray imaging of a small region of interest within a larger object (e.g.,small regions of interest in a laterally extending planar object, examples of which include connections in packages of integrated semiconductor circuits (ICs) and fine structural details in a large fiber-reinforced composite sheet, but are not limited to these) the minimum FOD is limited by the dimensions of the object, which limits the achievable throughput in practice, as the object is to be rotated 180 degrees.

[0005] However, state-of-the-art micro-X-ray computed tomography (µXCT) and micro-X-ray computed laminography (µXCL) systems have numerous limitations. For example, Fig. 1A and Fig. 1B Schematic representation of conventional tomography or laminography configurations of a laterally extending object (e.g., printed circuit; wafer), where the region of interest (ROI) is located in or near the center of the object. The X-ray source emits an X-ray beam (indicated by a horizontal dashed line), and the thickness of the object is shown in Fig. 1A and Fig. 1B in a direction perpendicular to the side can be equal to or less than the dimension of the object along the X-ray beam (e.g., such that there is sufficient space between the X-ray source and the X-ray detector for the object to rotate about the axis of rotation). As in Fig. As can be seen in Figure 1A, the rotation axis for tomography is essentially parallel to the surface normal of the object and essentially perpendicular to the X-ray beam. As shown in Fig. As can be seen in Figure 1B, the axis of rotation for laminography is essentially parallel to the surface normal of the object and inclined from a direction essentially perpendicular to the X-ray beam by an angle β. Fig. 1A and Fig. Figure 1B shows that such conventional tomography and laminography configurations are not well suited for imaging defects in planes parallel to the surface of laterally extending 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 relative to the object. Therefore, the reconstructed images (e.g., computed tomography or CT images) are affected by hardening and photon attenuation artifacts and introduce a dependence of the accuracy of reconstructed features on their orientation relative to the object's rotation axis. The resolution and image quality of reconstructed images in planes parallel to the surface of the laterally extending object are typically worse than in the direction along the surface normal.Furthermore, none of the techniques are optimized for achieving low FOD due to physical interferences between the object and the X-ray source. Improving image resolution by reducing the size of a high-flow X-ray source, which may be desirable for many applications, is severely limited with such state-of-the-art XCT and XCL systems and methods, and achieving higher depth resolution along the surface normals of such wide and / or planar objects is particularly difficult.

[0006] From DE 10 2013 013 344 A1, a three-dimensional X-ray imaging system for generating a transmission image of a region of interest in an object is known. The described system comprises at least one X-ray detector for spatially resolved acquisition of images of the rotating object or a detection area of ​​the X-ray detector for acquiring X-ray images. DE 10 2013 013 344 A1 is particularly concerned with enabling high-resolution X-ray tomographic detection of plate-shaped elements with structured surfaces. For this purpose, the X-ray detector is first positioned at a distance next to the object holder such that the region of interest is completely imaged on the X-ray detector.By moving the object holder and / or the carrier along the z-axis, which is aligned perpendicular to the x- and y-axes, the distance between the surface of the object to be irradiated and the X-ray focus can be minimized, thereby increasing the resolution of the area of ​​the object to be examined.

[0007] From JP 2003 32 96 16 A, an X-ray CT scanner comprising a eucentric table whose axis of rotation can be tilted to any desired position is known. The object to be examined is placed on the table, and an X-ray source and a two-dimensional detector are arranged on it. To enable magnification of a section of the object under investigation, the height of the eucentric table is changed, thereby altering the distance between the X-ray source and the object being examined.

[0008] From WO 2009 / 12 19 32 A2, a rotating apparatus is known which, in particular, comprises a rotating table and a rotating platform with a recess arranged around the axis of rotation. The object to be examined is preferably arranged on the rotating platform by means of a holder. Additionally, it is possible to tilt the sample axis. The disclosed device can be used for examining an object using computed tomography (CT), wherein the axis of rotation is perpendicular to the beam direction (axis tilt angle equal to 0 degrees), as well as for examinations using laminography with transmitted light. Advantages of the apparatus are said to include high object positioning accuracy, the reproducibility of settings, and the possibility of viewing the objects to be examined from all rotation angles around the axis of rotation. SUMMARY

[0009] The invention relates to a three-dimensional X-ray imaging system according to independent claim 1. The dependent claims relate to preferred embodiments of the X-ray imaging system according to the invention.

[0010] In certain implementations, a three-dimensional X-ray imaging system is configured to generate a transmission image of a region of interest within an object. The system includes at least one position-sensitive X-ray detector, which comprises at least one active element. The system further includes an X-ray source comprising an X-ray-transparent vacuum window with an outer surface. The outer surface is positioned at a distance of less than 70 millimeters from the region of interest of the object.The X-ray source comprises at least one X-ray target configured for bombardment with an electron beam to produce diverging X-rays, wherein the diverging X-rays extend from an X-ray focal spot having a width in a cross-sectional plane, the cross-sectional plane comprising the electron beam and an X-ray propagation axis extending from the X-ray focal spot 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, wherein at least some of the diverging X-rays exit the vacuum window and propagate along an X-ray propagation axis, the diverging X-rays being received by the at least one active element.The diverging X-rays exhibit propagation paths within a divergence angle of more than 1 degree centered on the X-ray propagation axis. The X-ray propagation axis forms a first angle with the outer surface of the vacuum window, the first angle being in a range of 3 degrees to 45 degrees, wherein the X-ray focal spot has an effective width in the cross-sectional plane along the X-ray propagation axis, the effective width being less than the width. The system further comprises at least one sample movement stage configured to rotate the object about a rotation axis, configured such that the rotation axis has a second angle relative to the X-ray propagation axis, the second angle being in a range of 45 degrees to 90 degrees. The system further comprises a sample holder on the at least one sample movement stage.The sample holder is configured to hold the object and includes a first section in the propagation paths of at least some of the diverging X-rays that propagate through the object to the at least one position-sensitive X-ray detector. This first section exhibits an X-ray transmission of more than 30% for X-rays with energies exceeding 50% of the maximum X-ray energy of an X-ray spectrum of the diverging X-rays. The system further includes a thermal cooling mechanism configured to reduce the heating of the object by the heat generated by the X-ray source. wherein the thermal cooling mechanism comprises an infrared (IR) reflective material between the vacuum window and the object, wherein the IR reflective material has a thickness of less than 1,500 micrometers and is configured to reflect the heat generated by the X-ray source so that it does not reach the object and the sample holding. BRIEF DESCRIPTION OF THE DRAWINGS Fig. 1A and Fig. Figure 1B schematically illustrates conventional tomography or laminography configurations of a laterally extending object, with the region of interest (ROI) located in or near the center of the object. Fig. Figure 2 schematically illustrates an exemplary X-ray 3D imaging system that is compatible with certain implementations described herein. Fig. Figure 3A schematically illustrates a cross-sectional view of an X-ray focal spot produced by an electron beam according to certain implementations described herein, which strikes at least one X-ray target. Fig. 3B and Fig. Figure 3C schematically illustrates top views of two exemplary configurations of the electron beam and the at least one X-ray target of Fig. 3A according to certain implementations described herein. Fig. Figure 4 schematically illustrates another exemplary system according to certain implementations described herein, which includes at least one aperture. Fig. 5A and Fig. Figure 5B schematically illustrates exemplary systems according to certain implementations described herein, in which the sample stage and sample holder are configured to hold and rotate the object. Fig. 6A and Fig. Figure 6B schematically illustrates two examples of a system according to certain implementations described herein, 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. Fig. Figure 7 schematically illustrates an exemplary system according to certain implementations described herein, configured to perform multi-contrast X-ray imaging using Talbot interferometry or Talbot-Lau interferometry. Fig. Figure 8 schematically illustrates an exemplary system according to certain implementations described herein, which is compatible with generating a translational laminography image. DETAILED DESCRIPTION

[0011] In certain implementations, a 3D X-ray imaging system enables imaging of a region of interest (ROI) with very low field of view (FOD) within a large object, reducing the acquisition time for laminographic datasets (e.g., to increase the acquisition rate of imaging data). 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 extending object, which can be important for many applications such as metrology, inspection, failure analysis, and process development of semiconductor IC packages (e.g., solder beads and copper connections). The X-ray source can be configured to achieve low FOD and improve 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 more powerful focus that becomes symmetric or nearly symmetric after projection, which can be desirable for isotropic spatial resolution. Certain implementations are configured to feature an X-ray source that incorporates 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 extending object under analysis.Furthermore, certain implementations include additional components and / or methods for implementing multiple modes of imaging contrast, including Talbot interferometry to obtain absorption, phase and darkfield (scattering) contrast, darkfield (scattering) contrast only, and enhanced absorption contrast.

[0012] Fig. Figure 2 schematically illustrates an exemplary X-ray 3D imaging system 5 that is 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, which includes at least one active element 52. The X-ray source 20 comprises an X-ray-transparent 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 exit the vacuum window 29 and propagate along an X-ray propagation axis 10, which extends 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 incident on the at least one active element 52 exhibit propagation paths within a divergence angle 12 of more than 1 degree centered on the X-ray propagation axis 10. The X-ray propagation axis 10 is located at a first angle 11 with respect to the outer surface 27 of the vacuum window 29, the first angle 11 being in a range of 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 and 30 degrees; less than 3 degrees).

[0013] In certain implementations, the system 5 further comprises at least one sample movement stage 80 (e.g., motorized and computer-controlled; comprising an electromechanical system). The at least one sample movement stage 80 is configured to rotate the object 30 about a rotation axis 19. The sample movement 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 being in a range of more 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 of more 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 being in a range of less than 45 degrees (e.g., less than 30 degrees). In certain implementations, the system 5 includes a mechanism configured to vary the third angle. For example, the mechanism can include at least one tilting table (e.g., goniometer; electromechanical motion driver; rotary motor; stepper motor; encoder motor; worm gear linear motion driver) configured to tilt the X-ray source 20 toward the rotation axis 19 and / or the rotation axis 19 relative to the X-ray source 20.

[0014] In certain implementations, the system 5 further comprises a sample holder 85 on the at least one sample movement stage 80 and is configured to hold the object 30. The sample holder 85 includes a first section 86 in the propagation paths of at least some of the diverging X-rays 60 that propagate through the object 30 to the at least one position-sensitive X-ray detector 50. The first section 86 has an X-ray transmission of more than 30% (e.g., more than 50%) for X-rays with energies greater than 50% of the maximum X-ray energy of an X-ray spectrum of the diverging X-rays 60.

[0015] The exemplary System 5 of Fig. 2 is configured for imaging a region of interest (ROI) 31 in a large or laterally extending object 30 (e.g., positioned so that it is substantially parallel to the outer surface 27 of the vacuum window 29) to minimize the field of view (FOD) between the ROI 31 and the X-ray source 20. For example, to image an 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 of less than 70 millimeters between the outer surface 27 of the vacuum window 29 and the surface 32 of the object 30) and centered on 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 acquired by recording a series of X-ray transmission images of the diverging X-rays 60 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, wherein the object 30 is rotated about the axis of rotation 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. As another example, the object 30 can be positioned for imaging a ROI 31 in a planar object 30 (e.g. solder beads and / or connections in a semiconductor IC package) such that the surface 32 of the object 30 is closer to the ROI 31 and 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 position the ROI 31 close to the X-ray source 20, thereby increasing the X-ray flux on the ROI 31 and thus increasing the 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 the radiation dose to the ROI 31). X-ray source

[0016] As schematically through Fig. As illustrated in Figure 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 within 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 on 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 at a selectable maximum focused electron energy at the at least one X-ray target 28 in a range from 10 kVp to 250 kVp.In certain implementations, the vacuum chamber 21 comprises a vacuum-tight tube containing the electron beam source 22, the electron optics 25, and the at least one X-ray target 28. Unlike open-tube X-ray sources, the X-ray source 20 in certain implementations is not actively pumped.

[0017] The at least one X-ray target 28 is located within the vacuum region 23 and is 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, which, due to its X-ray spectral production properties (e.g., characteristic X-ray energy) and / or other properties (e.g., atomic number Z; electron density), influences the X-ray-generating capability of the at least one X-ray-generating material. The at least one X-ray-generating material may have sufficiently high thermal conductivity to dissipate heat generated by bombardment by high-power electron beams 24. Examples of X-ray-generating materials include, but are not limited to: Cr, Fe, Co, Ni, Cu, W, Rh, Mo, Au, Pt, Ag, SrB6, LaB6, and CeB6.As schematically illustrated by the enlargement of . Fig. As shown in Figure 2, the at least one X-ray target 28 can be attached to (e.g., integrated with; a component thereof; 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 micrometers to 15 micrometers (e.g., 0.1 micrometers to 10 micrometers), 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 millimeters to 3 millimeters. As described herein, the thickness of the at least one X-ray-generating material can be adjusted to optimize high spatial resolution (e.g.,The system may be configured by minimizing electron beam scattering within the material and / or by maximizing electron energy deposition within the at least one X-ray generating material. For example, the thickness of the at least one X-ray generating material may 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 shifting 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, which provides a selected compromise between throughput and resolution.

[0018] In certain implementations, the vacuum window 29 consists essentially of elements with an atomic number (Z) of less than 14 and is essentially transparent to higher-energy X-rays generated by the at least one X-ray-generating material. For example, the vacuum window 29 may have sufficiently high thermal conductivity 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 may further provide a sufficiently electrically conductive path to dissipate electrical 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 exhibit X-ray transmission such that more than 50% of the X-rays generated by the at least one X-ray source 28 with energies exceeding 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. The X-ray source 20 emits X-rays in a solid angle of 4π; illustrated. Fig. 2 schematically only the diverging X-rays 60 that propagate along the X-ray propagation axis 10 within the 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 imaging), wherein the other diverging X-rays, which are 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, are shown in Fig. 2 are not illustrated.

[0019] In certain implementations, the system 5 further includes a thermal cooling mechanism configured to reduce the heating of the object 30 by the heat generated by the X-ray source 20. For example, the thermal cooling mechanism may include an infrared (IR) reflective material (e.g., a thin IR-reflective and highly X-ray-transparent film or layer, with aluminized Mylar being an example) between the vacuum window 29 and the object 30. The IR-reflective material is configured to reflect the heat generated by the X-ray source 20 (e.g., due to the power of the electron beam being converted into heat in the one or more X-ray targets 28) so that it does not reach the object 30 and the sample holder 85 (e.g.,The IR-reflective material directs thermal energy away from the object 30 and the sample holder 85 to reduce or minimize heat transfer to the object 30 and / or the sample holder 85. In this way, the IR-reflective material can protect the object 30 and the sample holder 85 from temperature changes in the sample that could otherwise cause thermal expansion, potentially affecting the accuracy of the ROI selection and / or the accuracy of the 3D volume reconstruction. The IR-reflective material is sufficiently thin (e.g., less than 1,500 micrometers thick; less than 100 micrometers thick) so as not to significantly impair the positioning of the object 30 near the electron beam focus of the X-ray source 20.

[0020] In certain implementations, the X-ray source 20 comprises a grounded anode transmission X-ray source (e.g., with an electrically grounded vacuum enclosure), with examples including, but not limited to, the DAGE BrightHawk. ®X-ray source available from Nordson Corporation, Westlake, Ohio; L10711-03 microfocus X-ray source available from Hamamatsu Photonics KK, Hamamatsu City, Japan; Excillum Nanotube N1 and N2 X-ray sources available from Excillum Corporation, Kista, Sweden; X-ray Worx GmbH, Garbsen, Germany; X-ray sources available from COMET Technologies, San Jose, California. These exemplary X-ray sources 20 can be configured to have an X-ray source point integrated into the vacuum window 29 and to have an object 30 placed close to the X-ray source 20 in order to reduce (e.g., minimize) the FOD and thus increase (e.g., maximize) the X-ray flux at the object 30.Due to electrical and mechanical limitations, the X-ray source 20 can have a large flat surface that forms the boundary of the vacuum shell and is coplanar with the vacuum window 29, but cannot be made smaller without disturbing the quality of the electron beam focus. For previously existing X-ray tomography and laminography imaging techniques using such X-ray sources 20, this large flat surface has limited the ability to position a large and / or planar object 30 close to the X-ray source 20 and to rotate the object 30 (e.g., up to 180 degrees) about a rotation axis 19 substantially perpendicular to the large flat surface. Certain implementations described herein advantageously circumvent this important limitation of previously existing X-ray imaging systems.

[0021] In certain implementations, the X-ray source 20 is configured to have a small X-ray focal spot size (e.g., with a dimension of less than 7 micrometers in at least one lateral direction substantially parallel to the outer surface 27 of the vacuum window 29) while simultaneously generating sufficient X-ray flux to enable sufficiently short image acquisition times. Generally, the X-ray focal spot size is approximately equal to a convolution of the focal spot size of the focused electron beam (e.g., radius) at the at least one X-ray target 28 and the size (e.g., radius) of the X-ray beam generation volume within the at least one X-ray target 28 due to electron scattering within the at least one X-ray target 28.Thus, larger focal spot sizes of the focused electron beam can facilitate higher electron beam powers with simultaneously higher X-ray flux and shorter image acquisition times at the expense of lower spatial resolutions, and smaller focal spot sizes of the focused electron beam can facilitate higher spatial resolutions at the expense of lower X-ray flux and longer image acquisition times. Since, in addition, a large proportion (e.g., about 99%) of the incident power of the focused electron beam 24 is converted into heat in the at least one X-ray target 28, it may be desirable to limit the power of the incident electron beam, which typically decreases linearly with the X-ray focal spot size.

[0022] 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 axis of rotation 19 is provided by reducing the thickness t of the X-ray-generating material of the at least one X-ray target 28, thereby reducing the effective X-ray source size s. For example, the thickness t of the X-ray-generating material along a direction substantially perpendicular to the outer surface 27 of the vacuum window 29 can be in a range from 0.1 micrometers to 15 micrometers. Fig. Figure 3A schematically illustrates a cross-sectional view of an X-ray focal spot produced by an electron beam 24 according to certain implementations described herein, which strikes at least one X-ray target 28. Fig. 3B and Fig. Figure 3C schematically illustrates top views of two exemplary configurations of the electron beam 24 and the at least one X-ray target 28 of Fig. 3A according to certain implementations described herein. As schematically shown by Fig. As illustrated in Figure 3A, the X-ray focal spot size considered 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-emitting material with a thickness t, the effective width s, as the full width at half maximum (FWHM), of the X-ray focal spot 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 layer of a high Z material (e.g., thickness t in the range of 0.1 micrometers to 3 micrometers) on or within a substrate of a low Z material (e.g., vacuum window 29) to achieve a small X-ray focal spot size (e.g., less than 5 micrometers) in the cross-sectional plane of Fig. 3A along the X-ray propagation axis 10 with angles of less than 30 degrees with respect to the outer surface 27 of the vacuum window 29. The effective FWHM width s of the X-ray focal spot size in the cross-sectional plane can be approximately equal to s = {(t / 2) 2 + [W·sin(θ)] 2} 0,5Let t be the thickness of the high-Z material and W the FWHM width of the electron beam size in the cross-sectional plane. For example, at t = 1 micrometer, θ = 10 degrees, and W = 1 micrometer, the effective FWHM width s of the X-ray focal spot size in the cross-sectional plane is 0.53 micrometers, which is smaller than W. Thus, the effective X-ray source size in the cross-sectional plane can be compressed along the X-ray propagation axis 10 compared to the width of the electron beam 24 in the cross-sectional plane.

[0023] Since the effective X-ray focal spot size in the cross-sectional plane is significantly smaller than the electron beam width W, certain implementations can further achieve a smaller X-ray focal spot size in a direction essentially perpendicular to the cross-sectional plane. Fig. 3A is reached. As schematically shown, for example, in Fig. As illustrated in Figure 3B, the electron beam 24 can be focused to be compressed in the direction that is essentially perpendicular to the cross-sectional plane. A focused electron beam 24 with an elongated (e.g., rectangular) shape or base at the X-ray target 28 can have a long dimension (e.g., FHWM width W) in the cross-sectional plane of Fig. 3A and a short dimension (e.g. FWHM width w) in one 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. exhibit 3A, where the short dimension is smaller than the long dimension.

[0024] For another example, how schematically by Fig. As illustrated in Figure 3C, the width d of the material with high Z of the material generating at least one X-ray can be in the direction substantially perpendicular to the cross-sectional plane of Fig. 3A less 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-producing material produces X-rays more efficiently than the vacuum window 29 (e.g., because the X-ray production efficiency is approximately proportional to the mean atomic number of the material), the sections of the electron beam 24 that do not strike the at least one X-ray-producing material do not produce X-rays efficiently and do not contribute substantially to the X-ray focal spot size, thus reducing the X-ray focal spot size to the width d in the direction substantially perpendicular to the cross-sectional plane of Fig. 3A is limited. In certain implementations, the width d of the material generating at least one X-ray is in a range of 0.1 micrometers to 5 micrometers.

[0025] 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 exit angle between the outer surface 27 and the X-ray propagation axis 10, the X-ray focal spot of Fig. 3B and Fig. 3C at which at least one position-sensitive X-ray detector 50 appears square or circular. For example, at an exit angle of 10 degrees, an electron beam 24 with a rectangular focal point and an aspect ratio of 5:1 can appear essentially symmetrical. Because the electron beam 24 is elongated and strikes a larger area than if the electron beam 24 were tightly focused in both directions, a higher electron power can be used to increase the X-ray flux (e.g., to achieve higher X-ray brightness) and to reduce image acquisition times while maintaining spatial resolution. For example, an electron beam 24 with an aspect ratio of 5:1 can provide up to a fivefold increase in apparent power density.Further reduction of the exit angle, in conjunction with a focused electron beam with a higher aspect ratio, can facilitate further improvements in apparent power density. Certain implementations provide higher spatial resolution in the cross-sectional plane. Fig. 3A as in the orthogonal direction to the cross-sectional plane. For many applications, high depth resolution (e.g., in a direction essentially perpendicular to the surface 32 of a laterally extending object 30) is more important than lateral resolution (e.g., in imaging delamination of solder beads or stress-induced cracks in solder beads parallel to the surface in semiconductor packages). Aperture

[0026] Fig. Figure 4 schematically illustrates another exemplary system 5 according to certain implementations described herein, comprising at least one aperture 70. In certain implementations, the at least one aperture 70 comprises at least one opening 72 (e.g., a slit; with a width of less than 100 micrometers) in at least one solid material (e.g., a plate), wherein the at least one opening 72 is 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 of the object 30). The at least one aperture 70 is not designed to attenuate the diverging X-rays 60 propagating along the X-ray propagation axis 10 within the divergence angle 12 (e.g.,The aperture 70 is configured not only to prevent the X-rays used for imaging from reaching the ROI 31 and / or the at least one position-sensitive X-ray detector 50, but also 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 aperture 70 has a sufficiently high Z (e.g., W; Au), a sufficiently high electron density, and a substantially small thickness such that the aperture 70 is configured to attenuate the X-rays without substantially limiting the FOD.In certain implementations, the at least one aperture 70 is configured to attenuate the amount of stray X-ray flux emitted by the X-ray source 20 outside the divergence angle 12 to prevent it from reaching the object 30. By attenuating this stray X-ray flux, the at least one aperture 70 can reduce a detrimental background contribution of the stray X-ray flux in the image and / or can reduce the adverse X-ray dose to the object 30 from the stray X-ray flux that does not contribute to imaging. The edges of the at least one aperture 72 of the at least one aperture 70 can define the divergence angle 12 by allowing further propagation only of the X-rays within the at least one aperture 72 along the X-ray propagation axis 10. In certain implementations, the distance between the one aperture 70 and the vacuum window 29 is adjusted to achieve a low field of view (FOD) between the X-ray source point and the region of interest (ROI) 31 (e.g.,a distance configured in a range of 0.3 millimeters to 5 millimeters). Sample movement table and sample holder

[0027] 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 position-sensitive X-ray detector 50. In certain implementations, the at least one sample motion stage 80 comprises at least one linear motion sub-stage 82 configured to controllably adjust the position of the object 30 (e.g., along the substantially perpendicular x, y, and z directions) and at least one rotary motion sub-stage 84 configured to controllably adjust the orientation of the object 30 (e.g., rotating the object 30 about the rotation axis 19). For example, the at least one linear motion sub-stage 82 may include one, two, or three electromechanical linear motion drivers (e.g.,comprising linear motor; stepper motor; motor with position encoder; piezoelectric motor; rotary motor with screw) configured to move the object 30 such that the ROI 31 is located at a selected position along the X-ray propagation axis 10, and the at least one rotary motion indexing table 84 may include at least one electromechanical motion driver (e.g. rotary motor; stepper motor; motor with position encoder; linear motion driver with worm drive) configured to rotate the object 30 and the ROI 31 about the rotation axis 19.

[0028] In certain implementations, such as schematically by Fig. As illustrated in Figure 2, a laterally extending object 30 can be mounted on the at least one sample movement stage 80 such that a surface 32 of the object 30 is inclined parallel to a long dimension of the object 30 at an angle β (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 rotary movement sub-stage 84 is further configured to controllably adjust the angle β, and the at least one linear movement sub-stage 82 is further configured to linearly displace the object 30 and / or the at least one rotary movement sub-stage 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, at least one sample movement stage 80 is used for controllable adjustment of the distance between the rotation axis 19 and the X-ray focal spot (e.g.configured with the focus of the electron beam.

[0029] In certain implementations, the sample holder 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 holder 85 is configured such that the X-rays 60 interact minimally with fixed components of the at least one sample motion stage 80 (e.g., the at least one linear motion sub-stage 82 and the at least one rotary motion sub-stage 84) (e.g., are minimally scattered and / or absorbed by them). The sample holder 85 is configured to reduce (e.g., minimize) the portion of the diverging X-rays 60 that interact with fixed sections of the at least one sample motion stage 80 while the object 30 is rotated about the axis of rotation 19.

[0030] In certain implementations, the at least one sample movement stage 80 and the sample holder 85 are configured to hold and rotate the object 30 without degrading the throughput. For example, since the throughput for laminography calculated using microfocus transmission X-rays is inversely proportional to the square of the focus-to-object distance (FOD), a high throughput can be achieved using a small FOD (e.g., if the object 30 is as close as possible to the X-ray source 20).

[0031] Fig. 5A and Fig. Figure 5B schematically illustrates exemplary systems 5 according to certain implementations described herein, in which the at least one sample movement stage 80 and the sample holder 85 are configured to hold and rotate the object 30. In the exemplary system 5 of Fig. In 5A, the object 30 is located between the X-ray source 20 and the at least one sample movement stage 80. With the at least one linear movement sub-stage 82 and the at least one rotary movement sub-stage 84 on one side of the object 30 opposite the at least one X-ray source 20, the at least one sample movement stage 80 does not obstruct the X-rays 60 reaching the object 60. However, the X-rays 60 propagate, as shown in Fig. 5A shows that after propagating through the ROI 31, the X-rays pass through at least one section of the sample holder 85 before reaching the at least one position-sensitive X-ray detector 50. In the exemplary system 5 of Fig. 5B the X-ray source 20 and the at least one sample movement stage 80 are located on the same side of the object 30 and the X-rays 60 propagate through at least one section of the sample holder 85 before reaching the object 30 (e.g., the sample holder 85 may limit the closest approach of the X-ray source 20 to the object 30). Fig. Figure 5A shows an exemplary implementation in which the X-ray source 20 is located above the object 30 and the at least one sample movement stage 80. In other implementations, the X-ray source 20, the object 30, and the at least one sample movement stage 80 can have any orientation while maintaining the same relative positioning to each other. Fig. Figure 5B shows an exemplary implementation in which the X-ray source 20 is located below the object 30. In other implementations, the X-ray source 20, the object 30 and the at least one sample movement stage 80 can have any orientation while maintaining the same relative positioning to each other.

[0032] In certain implementations, the sample holder 85 is configured to displace the object 30 from the at least one sample stage 80 such that the at least one sample stage 80 (e.g., the at least one linear motion sub-stage 82 and the at least one rotary motion sub-stage 84) is not located in the imaging field of view of the at least one position-sensitive X-ray detector 50 (e.g., to reduce, avoid, or minimize X-ray scattering and / or absorption, which would adversely affect the accuracy of the image reconstruction). For example, the sample holder 85 can displace the object 30 from the at least one sample stage 80 by a distance 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 holder 85 of certain implementations comprises a first section 86, configured such that at least a portion of the X-rays 60 strike it when the object 30 and the sample holder 85 are rotated about the axis of rotation 19, and a second section 87, which mechanically couples the first section 86 to the at least one motion sub-table (e.g., the at least one linear motion sub-table 82 and / or the at least one rotary motion sub-table 84). The first section 86 and the second section 87 are configured to displace the ROI 31 of the object 30 from the at least one motion sub-table such that the diverging X-rays 60 do not strike the at least one motion sub-table or the second section 87 (e.g., while the object 30 and the sample holder 85 are rotated about the axis of rotation 19).

[0033] In certain implementations, the first section 86 essentially comprises elements with low Z (e.g., elements with an atomic number of less than 14) and / or thin materials (e.g., thickness along the rotational axis 19 of less than 10 millimeters). In certain implementations, the first section 86 exhibits an X-ray transmission of more than 50% for X-rays with energies exceeding 50% of the maximum X-ray energy of the X-ray spectrum of X-rays 60 (e.g., the X-rays emitted by the X-ray source 20). Certain such implementations simultaneously provide a sufficiently high throughput with a sufficiently low amount of radiation damage to the object 30 (e.g.,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, since the X-rays do not need to be transmitted through absorbing material of the at least one sample motion stage 80. For example, the first section 86 can comprise a carbon fiber or quartz plate (e.g., with a projected thickness along the X-ray propagation axis 10 of less than or equal to 2 millimeters). The second section 87 is mechanically coupled to the first section 86 and to the at least one linear motion sub-stage 82 and / or the at least one rotary motion sub-stage 84. In certain implementations, the second section 87 essentially comprises the same low-Z and / or thin-material elements as the first section 86 (e.g.,a rod with a low Z or a hollow tube, such as a carbon fiber or a quartz tube with a projected thickness along the X-ray propagation axis 10 of less than or equal to 2 millimeters), while the second section 87 in certain other implementations comprises any solid material (e.g., regardless of the X-ray absorption and / or scattering of the solid material). In certain implementations, the second section 87 is part of the at least one linear motion sub-table 82 and / or the at least one rotary motion sub-table 84.

[0034] For example, schematically by Fig. As illustrated in Figure 5A, the first section 86 and the second section 87 extend along the axis of rotation 19 and can be configured such that the X-rays 60 do not strike the at least one linear motion sub-stage 82 and / or the at least one rotary motion sub-stage 84 at all laminography angles of interest and at all rotation angles of interest. For the at least one sample motion stage 80 with a maximum dimension (e.g.,The first and second sections 86, 87 can be configured to hold the object 30 at a distance z along the axis of rotation 19 from the at least one linear motion sub-table 82 and / or the at least one rotary motion sub-table 84, such that the envelope of X-rays 60 does not strike sections of the at least one sample motion table 80 that would scatter and / or absorb the X-rays 60 (e.g., sections comprising at least one element with an atomic number Z greater than 14; the at least one linear motion sub-table 82; the at least one rotary motion sub-table 84).

[0035] For another example, how schematically by Fig. As illustrated in Figure 5B, the first section 86 is configured to hold (e.g., clamp) the sides and / or edges of the object 30, and the second section 87 mechanically couples the first section 86 to the at least one sample movement table 80 (in Fig. 5B not shown). The at least one sample movement table 80 of Fig. 5B further comprises a clear aperture region 88 (e.g., a region bounded at least partially by the second section 87) configured such that the X-ray source 20 extends at least partially through it. Certain such implementations allow the X-ray source 20 to be positioned arbitrarily close to a face of the object 30, thus providing high throughput while the object 30 is rigidly mounted. An exemplary second section 87 compatible with certain implementations described herein is an ultra-high-precision, large-aperture air-cushion rotary stage available from PI (Physik Instrumente), Auburn, Massachusetts.

[0036] The accuracy of the image reconstruction depends on the precise rotation of the object 30 during the measurements, and uncontrolled movements of the object 30 can produce deviations of the actually recorded projection data from those that a laminographic reconstruction algorithm would expect. As a result, these uncontrolled movements can create a blurring of the back-projected data, which 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 displacement and / or orientation changes of the object 30 within the image field of view. The at least one sample motion stage 80 can introduce a sufficiently low non-systematic angular wobble (e.g.,uncontrolled angular movement of the rotation axis 19 depending on the rotation about the rotation axis 19), a sufficiently low out-of-roundness (e.g., uncontrolled displacement of the rotation axis 19 depending on the rotation about the rotation axis 19, resulting in a lateral movement of the object 30 essentially perpendicular to the rotation axis 19) and / or a sufficiently low axial out-of-roundness (e.g., uncontrolled axial movement of the object 30 essentially parallel to the rotation axis 19) such that the uncontrolled movement of the object 30 is less than one-fifth of the system resolution (e.g., less than 0.1 micrometers of uncontrolled movement at a system resolution of 0.5 micrometers). For example, with an object 30 positioned at a distance L above the at least one rotary motion sub-stage 84 of the at least one sample motion stage 80, and an image resolution (e.g.,Detector resolution divided by image magnification) of δ can lead to a non-systematic angular wobble of ω (e.g., less than 100 nanoradians; less than 200 nanoradians; less than 1 microradian; less than 5 microradians) to a radial out-of-roundness of R = ωL < δ / 5 (e.g., less than δ / 3; less than δ / 2; less than 1 micrometer; less than 0.5 micrometers; less than 200 nanometers; less than 100 nanometers) and / or to an axial out-of-roundness A < δ / 5 (e.g., less than δ / 3; less than δ / 2; less than 1 micrometer; less than 0.5 micrometers; less than 200 nanometers; less than 100 nanometers). In certain implementations, the at least one sample motion stage 80 exhibits a non-systematic angular wobble (e.g., error) of less than 5 microradians (e.g., less than 1 microradian), a repeatability of radial out-of-roundness of better than 1000 nanometers, and a repeatability of axial out-of-roundness of better than 1000 nanometers.In certain implementations, the system 5 further includes a measurement system configured to measure an angular wobble of the at least one sample movement table 80 with an accuracy of better than less than 5 microradians (e.g. less than 1 microradian) in order to measure a radial out-of-roundness of the at least one sample movement table 80 with an accuracy of better than 1000 nanometers and / or to measure an axial out-of-roundness of the at least one sample movement table 80 with an accuracy of better than 1000 nanometers.

[0037] In certain implementations, the at least one rotary motion substage 84 of the at least one sample motion stage 80 may comprise an air cushion rotary stage (e.g., A-62X or A-688 rotary stage, available from PI (Physik Instrumente), Auburn, Massachusetts; ABRX00, ABRX150, or ABRX250 rotary stage, available from Aerotech, Inc., Pittsburgh, Pennsylvania) with a wobble angle of less than 5 microradians (e.g., less than 1 microradian; less than 200 nanoradians) and radial and axial out-of-roundness of 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 may exhibit an accuracy of better than half the resolution of the system. Position-sensitive X-ray detector

[0038] 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 transmission 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 into electrons with or without energy discrimination; Eiger ASICs and Pilatus ASICs, available from Dectris, Baden-Dättwil, Switzerland); flat panel detectors (FPDs) comprising a scintillator material (e.g.,CdWO4, CsI, Gd2O2S, LSO, GAGG and / or LYSO; Shad-o-Box HS detectors, available from Teledyne Dalsa, Waterloo, Canada; 2315N detectors, available from Varex Imaging, Salt Lake City, Utah; Athena and Onyx detectors, available from Nordson Corporation, Westlake, Ohio; 1412HR detectors, available from Spectrum Logic Corporation, Boulder, Colorado; fiber optic plates and CMOS or CCD detectors; a scintillator material (e.g., CdWO4, CsI, Gd2O2S, LSO, GAGG and / or LYSO) and a lens 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) of less than 70 micrometers (e.g. less than 50 micrometers).

[0039] 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, wherein the X-rays 60 have a predetermined range of energies (e.g., the X-ray spectrum), which facilitates (e.g., optimizes) sufficient image contrast to detect features of interest in the ROI 31 and / or reduce image acquisition times. For example, the predetermined X-ray spectrum can be generated by selecting the focused electron energy and / or the 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 high X-ray flux to facilitate image contrast and / or image acquisition times.For X-ray imaging using absorption contrast, the predetermined X-ray spectrum can include energies at which the object 30 exhibits 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 compromise between image contrast (preferring lower-energy X-rays) and transmission through the object 30 (preferring higher-energy X-rays).

[0040] As a further 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 the detection of X-rays with energies below a first energy threshold and / or energies above a second energy threshold). For example, the at least one energy threshold can include a threshold cutoff X-ray energy, wherein the at least one position-sensitive X-ray detector 50 is configured to image only X-rays with energies below the threshold cutoff X-ray energy. The threshold cutoff X-ray energy of certain implementations corresponds to X-rays for which the object 30 has an X-ray transmission of less than 85% (e.g., less than 50%).For example, the at least one position-sensitive X-ray detector 50 can include a photon-counting detector configured to select at least one threshold cutoff X-ray energy (e.g., to controllably adjust the threshold cutoff X-ray energy). The photon-counting detector can further be configured to acquire energy-dependent X-ray transmission images (e.g., using a variety of operator-selectable energy windows to reduce noise, image artifacts, and / or provide material discrimination). As another example, the at least one position-sensitive X-ray detector 50 can include a combination of scintillation screens and materials configured to image only X-rays below the threshold cutoff X-ray energy.

[0041] Fig. 6A and Fig. Figure 6B schematically illustrates two examples of a system 5 according to certain implementations described herein, 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. The second position-sensitive X-ray detector 56 may be configured to provide an amplification sensitivity for a different portion of the X-ray spectrum than that obtained from the first position-sensitive X-ray detector 54 in order to increase the overall throughput, and / or to provide measurements with a different spatial resolution than that of the first position-sensitive X-ray detector 54. For example, the first and second position-sensitive X-ray detectors 54, 56 may have different scintillation materials and / or different scintillator thicknesses.

[0042] For example, schematically by Fig. As illustrated in Figure 6A, the first detector 54 can be configured to absorb and detect a first spectral component 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 component of the X-rays 60 that are 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 a portion of the X-ray flux received by the ROI 31, and the second detector 56 can be positioned downstream of the first detector 54 (see, e.g., Figure 6A). Fig. 6A) and be configured to detect at least a portion of the X-ray flux transmitted through the first detector 56. In another example, as schematically shown in Fig. As illustrated in Figure 6B, a first spectral component 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 component of the X-rays 60 propagating along the X-ray propagation axis 10 can be transmitted through the scintillator screen 55 to reach the second detector 56. The X-rays absorbed by the scintillator screen 55 can generate scintillation photons (e.g., photons of visible light), which are reflected by a mirror 57 and focused by an objective lens 58 onto a position-sensitive photon detector 59. The material and thickness of the mirror 57 can be selected to provide high transmission of the X-rays 60 transmitted through the object 30.

[0043] While Fig. 6A and Fig. Figure 6B schematically illustrates configurations in which the two detectors 54, 56 are positioned to detect X-rays 60 propagating in the same direction as the others. In certain other implementations, the two detectors 54, 56 are positioned to detect X-rays propagating from the at least one X-ray source 20 in different directions from each other (e.g., different directions at angles of 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, while in certain other implementations, the two detectors 54, 56 are used separately (e.g., sequentially). In certain implementations, the two detectors 54, 56 are used to exhibit different pixel resolutions on the object 30 (e.g.,The outputs of the two detectors 54 and 56 are configured to be approximately equal to the pixel size of the detector divided by its geometric image magnification. Combining the outputs of the two detectors 54 and 56 in certain implementations can increase the overall detection efficiency of the system 5 and can provide access to a wider range of spatial frequencies of the object, thereby improving throughput and reconstruction quality. In certain implementations, the second detector 56 is configured (e.g., optimized) with sensitivity to a different fraction of the X-ray spectrum of the X-ray beams 60, which can allow for correction for beam hardness and / or material identification.

[0044] Fig. Figure 7 schematically illustrates an exemplary System 5 according to certain implementations described herein, configured to perform multi-contrast X-ray imaging using Talbot interferometry or Talbot-Lau interferometry. The System 5 can be configured to provide high resolution and sensitivity and unique imaging capabilities (e.g., absorption, phase, and dark-field contrast imaging 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 acquire a 3D imaging dataset using Talbot-Lau interferometry, dark-field contrast, and enhanced absorption contrast, and to reconstruct the dataset to obtain 3D images of Object 30 and / or the ROI 31 within Object 30. In certain implementations, as schematically shown by Fig. As illustrated in Figure 7, the system 5 further comprises at least one sample movement table 80 and one sample holder 85 (see, for example, Figure 7). Fig. 5A), which are configured to reduce (e.g. minimize) interactions of the part of the diverging X-rays 60 that propagates along the X-ray propagation axis 10 with fixed sections of the at least one sample movement stage 80.

[0045] As schematically through Fig. As illustrated in Figure 7, the system 5 comprises a first grating G1 (e.g., a phase grating) configured to generate a Talbot self-imaging 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 indirectly imaged 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, which are essentially perpendicular to the X-ray propagation axis 10, are sufficiently small (e.g., less than or equal to half the spacing of the second grating G2) to be compatible with Talbot interferometry, so that the Talbot pattern is directly imaged 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, wherein the geometric parameters of the plurality of X-ray targets 28, a first grating G1, and a second grating G2 are configured to satisfy the conditions of the Talbot-Lau interferometer.Various configurations of the X-ray source 20 and the first and second gratings G1, G2 are disclosed in US patents Nos. 9,719,947 and 10,349,908, each of which is incorporated herein by reference in its entirety.

[0046] In certain implementations, the first grating G1 comprises an absorption grating. For example, one or both of the first grating G1 and the second grating G2 may comprise an array of patterned one-dimensional or two-dimensional X-rays essentially absorbing (e.g., absorption greater than 50%) structures with widths in the range of 0.5 micrometers to 20 micrometers, separated from each other by essentially non-absorbing (e.g., absorption less than 50%) gaps with widths in the range of 0.5 micrometers to 20 micrometers. In addition to using a technique such as phase-shifting for triple-contrast imaging (e.g., absorption, phase, and scattering), the system may, in five certain implementations, be used to obtain dark-field-only contrast imaging (e.g.,Scattering) can be configured by configuring the slope, the distances from the X-ray source 20, and the orientations of the first and second gratings such that the X-rays transmitted through the openings of the first (e.g., upstream) grating G1 strike absorbing sections of the second (e.g., downstream) grating G2. For example, the first grating G1 and the second grating G2 can be positioned 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., with the first grating G1 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 essentially non-absorbing structures of the second grating G2 are located at the (e.g.,in the shadows of the essentially absorbing structures of the first grating G1, and the essentially absorbing structures of the second grating G2 are aligned with the essentially non-absorbing structures of the first grating G1. In such a configuration, it would be expected that in the absence of an object 30, no X-rays would be transmitted through either the first grating G1 or the second grating G2, but that in the presence of scattering features of an object 30, at least some of the scattered X-rays would be transmitted through the second grating G2, resulting in an imaging representation of the features in the object 30 that are responsible for the scattered X-rays.In certain implementations, an improved absorption contrast image can be obtained by shifting the relative orientation of the first and second gratings by half the slope from the configuration used in dark-field 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 a second grating G2, a first set of active elements 52 (e.g., pixels) of the at least one position-sensitive X-ray detector 50 is aligned with the substantially absorbing structures of the first grating G1 (e.g., in the shadows of the object), and a second set of active elements 52 of the at least one position-sensitive X-ray detector 50 is aligned with the substantially non-absorbing structures of the first grating G1.If, in such a configuration, 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 scattering / darkfield and / or refraction images.

[0047] In certain implementations where semiconductor IC packages are to be 3D-imagined, 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 of less than 45 degrees) relative to the surface normal of surface 32 of the semiconductor chip. For example, rotational laminography can be performed over a large angular range (e.g., 180 degrees to 630 degrees) or translational laminography with a limited angle over a restricted angular range (e.g., ±30 degrees). The 3D image(s) can be combined with the laminographic 3D image obtained with the X-ray propagation axis 10 at a large angle (e.g., greater than 60 degrees) relative to the surface normal of surface 32 of the semiconductor chip to generate a 3D image. Fig. Figure 8 schematically illustrates an exemplary system 5 according to certain implementations described herein, which is compatible with generating a translational laminography image. The system 5 comprises an additional X-ray detector 90 and at least one detector stage 92 configured to move the detector 90 and the object 30 relative to the X-ray source 20. In certain implementations, the at least one detector stage 92 includes the at least one sample movement stage 80. For example, the detector 90 and the object 30 can be moved proportionally 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 is Fig.8 configured to achieve higher spatial resolution and / or better image clarity for features that extend in one direction substantially parallel to the surface normal of the semiconductor chip (e.g., sidewalls of copper compounds).

[0048] In certain implementations, the system 5 further comprises at least one motion mechanism configured to vary the 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 may 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, and at least one second motion stage (e.g.,linear motion stage; electromechanical linear motion driver; linear motor; stepper motor; motor with position encoder; piezoelectric motor; rotary motor with screw), configured to move the at least one position-sensitive 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 position encoder; piezoelectric motor, rotary motor with screw; the at least one linear motion sub-stage 82), configured to move the object 30 relative to the X-ray source 20 and / or the at least one position-sensitive detector 50.

[0049] Although commonly used terms are employed to describe the systems and procedures of certain implementations for ease of understanding, these terms are used herein in their broadest reasonable interpretation. Although various aspects of the disclosure are described with respect to illustrative examples and implementations, the disclosed examples and implementations should not be interpreted as restrictive. Conditional formulations such as "may," "could," "would," or "would like" are, unless specifically stated otherwise or understood differently in the context in which they are used, generally intended to indicate that certain implementations might include certain features, elements, and / or steps, while other implementations do not.Therefore, such conditional formulations should generally not imply that features, elements, and / or steps are required in any way for one or more implementations. In particular, the terms "includes" and "comprehensive" should be interpreted as not referring exclusively to elements, components, or steps, thereby indicating that the mentioned elements, components, or steps may be present or used, or combined with other elements, components, or steps not explicitly referenced.

[0050] Subjunctive formulations, such as the expression "at least one of X, Y, and Z," should, unless specifically stated otherwise, be understood in the context used to generally convey that an object, concept, etc., can be either X, Y, or Z. Thus, such subjunctive formulations should generally not imply that certain implementations require the presence of at least one of X, at least one of Y, and at least one of Z.

[0051] Qualitative formulations, such as those used herein, like the terms "approximately," "about," "generally," and "essentially," represent a value, quantity, or property close to the stated value, quantity, or property that nevertheless performs a desired function or achieves a desired result. For example, the terms "approximately," "about," "generally," and "essentially" may refer to a quantity that is within ±10%, within ±5%, within ±2%, within ±1%, or within ±0.1% of the stated quantity. As another example, the terms "generally parallel" and "essentially parallel" refer to a value, quantity, or property that is...which deviates from exactly parallel by ± 10 degrees, ± 5 degrees, ± 2 degrees, ± 1 degree, or ± 0.1 degrees, and the terms "generally perpendicular" and "essentially perpendicular" refer to a value, quantity, or property that deviates from exactly perpendicular by ± 10 degrees, ± 5 degrees, ± 2 degrees, ± 1 degree, or ± 0.1 degrees. The ranges disclosed herein also include any and all overlaps, subranges, and combinations thereof. Phrases such as "up to," "at least," "greater than," "less than," "between," and the like include the specified number. As used herein, the meanings of "a," "an," and "the" include a reference to the plural unless the context clearly requires otherwise. While the structures and / or procedures discussed herein relate to elements designated by ordinal numbers (e.g., first, second, etc.),) are marked, the ordinal numbers are used only as labels to distinguish elements from one another and are not used to indicate an order of these elements or their use.

[0052] Various configurations have been described above. It is understood that the implementations disclosed herein are not mutually exclusive and can be combined in various arrangements. Although this invention has been described with reference to these specific configurations, the descriptions are intended to illustrate the invention and are not to be understood as limiting. Many modifications and applications will occur to the person skilled in the art without departing from the true spirit and scope of the invention. For example, in any method or process disclosed herein, the actions or operations that constitute the method / process can be carried out in any suitable sequence and are not necessarily limited to any specific disclosed sequence.Features or elements from the various implementations and examples discussed above can be combined to create alternative configurations compatible with the implementations disclosed herein. Various aspects and advantages of the implementations are described where appropriate. It is understood that not all such aspects or advantages can necessarily be achieved according to any given implementation. Thus, for example, it must be acknowledged that the various implementations can be executed in a manner that achieves or optimizes one or more advantages according to the teachings herein, without necessarily achieving other aspects or advantages that may be taught or suggested herein.

Claims

[1] Three-dimensional X-ray imaging system (5) configured to produce a transmission image of a region of interest (31) in an object (30), the system (5) comprising: at least one position-sensitive X-ray detector (50) comprising at least one active element (52); an X-ray source (20) comprising an X-ray-transparent vacuum window (29) with an outer surface (27), wherein the outer surface (27) is located at a distance of less than 70 millimeters from the region of interest (31), wherein the X-ray source (20) comprises at least one X-ray target (28) configured for bombardment with an electron beam (24) to produce diverging X-rays (60), wherein the diverging X-rays (60) extend from an X-ray focal spot having a width in a cross-sectional plane, the cross-sectional plane comprising the electron beam (24) and an X-ray propagation axis (10) extending from the X-ray focal spot through the 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), wherein at least some of the diverging X-rays (60) exit the vacuum window (29) and propagate along the X-ray propagation axis (10), wherein the diverging X-rays (60) are received by the at least one active element (52) and have propagation paths within a divergence angle (12) centered on the X-ray propagation axis (10) of more than 1 degree, wherein the X-ray propagation axis (10) forms a first angle (11) with the outer surface (27) of the vacuum window (29), wherein the first angle (11) is in a range of 3 degrees to 45 degrees, wherein the X-ray focal spot has an effective width in the cross-sectional plane along the X-ray propagation axis (10), wherein the effective width is less than the width; at least one sample movement stage (80) configured to rotate the object (30) about a rotation axis (19) and configured such that the rotation axis (19) has a second angle (16) relative to the X-ray propagation axis (10), the second angle (16) being in a range of 45 degrees to 90 degrees; and a sample holder (85) on the at least one sample movement table (80), wherein the sample holder (85) is configured to hold the object (30), the sample holder (85) comprising a first section (86) in the propagation paths of at least some of the diverging X-rays (60) that propagate through the object (30) to the at least one position-sensitive X-ray detector (50), wherein the first section (86) has an X-ray transmission of more than 30% for X-rays with energies of more than 50% of a maximum X-ray energy of an X-ray spectrum of the diverging X-rays (60), wherein the system (5) further comprises a thermal cooling mechanism configured to reduce the heating of the object (30) by the heat generated by the X-ray source (20), wherein the thermal cooling mechanism comprises an infrared (IR) reflective material between the vacuum window (29) and the object (30), wherein the IR reflective material has a thickness of less than 1,500 micrometers and is configured to reflect the heat generated by the X-ray source (20) so that it does not reach the object (30) and the sample holder (85). [2] System (5) according to claim 1, wherein the second angle (16) is in a range of more than or equal to 45 degrees and the axis of rotation (19) is at a third angle relative to a surface normal of the outer surface (27) of the vacuum window (29), wherein the third angle is in a range of less than 30 degrees. [3] System (5) according to claim 2, further comprising a mechanism configured to vary the third angle. [4] System (5) according to claim 1, wherein the diverging X-rays (60) do not cross the at least one sample movement table (80). [5] System (5) according to claim 1, wherein the first section (86) consists essentially of elements having an atomic number of less than 14. [6] System (5) according to claim 1, wherein the sample holder (85) further comprises a second section which mechanically couples the first section (86) to the at least one sample movement table (80), wherein the first section (86) and the second section are configured to displace the region of interest (31) of the object (30) from the at least one sample movement table (80) such that the diverging X-rays (60) do not strike the at least one sample movement table (80) or the second section. [7] System (5) according to claim 1, wherein the at least one sample movement stage (80) has a non-systematic angular wobble of less than 5 microradians, a radial out-of-roundness of less than 500 nanometers and an axial out-of-roundness of less than 500 nanometers. [8] System (5) according to claim 1, wherein the at least one sample movement stage (80) has a non-systematic angular wobble error of less than 5 microradians, a repeatability of the radial out-of-roundness of less than 1000 nanometers and a repeatability of the axial out-of-roundness of less than 1000 nanometers. [9] System (5) according to claim 1, further comprising a measurement system configured to measure an angular wobble of the at least one sample movement table (80) with an accuracy of better than 1 microradian, in order to measure a radial out-of-roundness accuracy of the at least one sample movement table (80) with an accuracy of better than 1000 nanometers and / or to measure an axial out-of-roundness of the at least one sample movement table (80) with an accuracy of better than 1000 nanometers. [10] System (5) according to claim 1, wherein the first angle (11) of the X-ray propagation axis (10) with respect to the outer surface (27) of the vacuum window (29) is less than 30 degrees, less than 5 degrees or less than 3 degrees. [11] System (5) according to claim 1, wherein the X-ray source (20) further comprises: a vacuum chamber containing a vacuum region (23), wherein the vacuum chamber includes the vacuum window (29), the vacuum window (29) separating the vacuum region (23) from a non-vacuum region outside the X-ray source (20) and being in contact with the at least one X-ray target (28); an electron beam source (22) in the vacuum region (23); and Electron optics (25) configured to direct at least some electrons from the electron beam source (22) into the electron beam (24) focused on the at least one X-ray target (28), wherein the focused electron beam (24) has a maximum focused electron energy at the at least one X-ray target (28) in a range of 10 kVp to 250 kVp, wherein the at least one X-ray target (28) is configured to generate the diverging X-rays (60) in response to bombardment by the focused electron beam (24). [12] System (5) according to claim 11, wherein the at least one X-ray target (28) comprises at least one X-ray generating material selected from the group consisting of: Cr, Fe, Co, Ni, Cu, W, Rh, Mo, Au, Pt, Ag, SrB6, LaB6, GdB6 and CeB6. [13] System (5) according to claim 12, wherein the at least one X-ray generating material has a plurality of regions which can be bombarded by the focused electron beam (24), each region having a corresponding thickness along a direction substantially perpendicular to the outer surface (27) of the vacuum window (29) and providing a different compromise between throughput and resolution. [14] System (5) according to claim 12, wherein the at least one X-ray generating material is attached to the vacuum window (29) and has a thickness in the range of 0.1 micrometers to 15 micrometers along a direction substantially perpendicular to the outer surface (27) of the vacuum window (29), and wherein the vacuum window (29) has a thickness in the range of 0.05 micrometers to 3 micrometers along the direction substantially perpendicular to the outer surface (27) of the vacuum window (29). [15] System (5) according to claim 11, wherein the vacuum window (29) consists substantially of a material selected from the group consisting of: beryllium, diamond, boron carbide, silicon carbide, aluminum and beryllium oxide (BeO). [16] System (5) according to claim 11, wherein the focused electron beam (24) has a focal spot size with a dimension of less than 7 micrometers in at least one lateral direction substantially parallel to the outer surface (27) of the vacuum window (29). [17] System (5) according to claim 11, wherein the focused electron beam (24) at the at least one X-ray target (28) has a focal spot shape with a first dimension in a plane that includes the X-ray propagation axis (10) and the surface normal of the outer surface (27) of the vacuum window (29), and a second dimension in a second lateral direction along the at least one X-ray target (28) and substantially perpendicular to the first lateral direction, wherein the first dimension is larger than the second dimension. [18] System (5) according to claim 1, wherein the at least one position-sensitive X-ray detector (50) comprises silicon, CdTe and / or CdZnTe and is configured to directly convert X-rays into electrons. [19] System (5) according to claim 1, wherein the at least one position-sensitive X-ray detector (50) has at least one energy threshold for detecting X-rays, wherein the at least one position-sensitive X-ray detector (50) is configured to reject and / or suppress the detection of X-rays with energies below a first energy threshold and / or energies above a second energy threshold. [20] System (5) according to claim 1, wherein the at least one position-sensitive X-ray detector (50) comprises a scintillator material selected from the group consisting of: CdWO4, CsI, Gd2O2S, LSO, GAGG and LYSO. [21] System (5) according to claim 20, wherein the at least one position-sensitive X-ray detector (50) further comprises a lens and a CMOS or CCD detector, wherein the lens is configured to magnify an image of the scintillator material onto the CMOS or CCD detector. [22] System (5) according to claim 1, wherein the at least one position-sensitive X-ray detector (50) comprises a first detector configured to absorb and detect a first spectral component of the X-rays transmitted through the region of interest (31), and a second detector configured to absorb and detect a second spectral component of the X-rays transmitted through the region of interest (31) and the first detector. [23] System (5) according to claim 1, further comprising a first grating at a first position along the X-ray propagation axis (10), wherein the first grating comprises an absorption grating or a phase grating. [24] System (5) according to claim 23, wherein the at least one position-sensitive X-ray detector (50) is configured to record a Talbot pattern formed by the first grating. [25] System (5) according to claim 23, wherein the first grating, a second grating and the at least one position-sensitive X-ray detector (50) are configured to record a dark-field contrast image. [26] System (5) according to claim 1, further comprising at least one aperture (70) comprising at least one opening (72) in at least one solid material, wherein the at least one opening (72) is positioned on the X-ray propagation axis (10) and between the vacuum window (29) and the object (30), wherein the at least one aperture (70) is not configured to attenuate the diverging X-rays (60) propagating along the X-ray propagation axis (10) within the divergence angle (12) to prevent them from reaching the region of interest (31) and / or the at least one position-sensitive X-ray detector (50), while simultaneously attenuating at least some X-rays emitted from the vacuum window (29) in other directions and / or scattered X-rays to prevent them from reaching the region of interest (31) and / or the at least one position-sensitive X-ray detector. [27] System (5) according to claim 1, wherein the at least one sample movement table (80) comprises an air cushion rotary table. [28] System (5) according to claim 1, further comprising at least one movement mechanism configured to vary a geometric magnification of an image of the region of interest (31) of the object (30) generated by the at least one position-sensitive detector. [29] System (5) according to claim 1, wherein the at least one sample movement table (80) has a non-systematic angular wobble of less than 5 microradians. [30] System (5) according to claim 29, further comprising a sample holder (85) on the at least one sample movement table (80) configured to hold the object (30), wherein the sample holder (85) comprises a first section (86) configured such that 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) strike it, wherein the first section (86) substantially comprises elements having an atomic number of less than 14 and / or having a thickness of less than 10 millimeters along the axis of rotation (19). [31] System (5) according to claim 29, wherein the at least one sample movement table (80) comprises an air cushion rotary table. [32] System (5) according to claim 1, further comprising: at least one movement mechanism for varying a geometric magnification of an image of the region of interest (31) of the object (30) generated by the at least one position-sensitive detector (50). [33] System (5) according to claim 32, wherein the at least one movement mechanism is configured to move the X-ray source (20) and / or the at least one position-sensitive detector (50) relative to the object (30). [34] System (5) according to claim 1, wherein the width has a full width at half maximum (FWHM) W in the cross-sectional plane, wherein the X-ray target (28) has a thickness t along a direction that is substantially perpendicular to the outer surface (27) of the vacuum window (29), and the effective width has an effective full width at half maximum (FWHM) s in the cross-sectional plane that is substantially equal to s = {(t / 2) 2 + [W·sin(θ)] 2} 0,5 is, where the first angle is. [35] System (5) according to claim 1, wherein the effective width is less than 5 micrometers.

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