Computed Tomography Methods and Computed Tomography X-ray Microscopy Systems

Abstract

A high-resolution computed tomography technique employs a "computationally centered" rotation axis to keep the region of interest (ROI) at the center of the detector's field of view at all angles. The system calibrates mechanical and optical misalignments by capturing projections of the object at multiple locations. The resulting geometric model, including stage runout and thermal drift corrections, is then applied to the sample of interest. Each projected view is associated with specific positioning parameters to ensure accurate data registration for the reconstructed image. By using a virtual rotation axis and a geometric descriptor for each view, this method produces superior resolution and fewer artifacts compared to tomography created by misaligned systems, and involves less labor than conventional physical alignment techniques.

Description

Technical Field

[0001] X-ray microscopy is an imaging technique that allows visualization of the internal structure of a sample without the need for destructive sectioning. It uses X-rays to create high-resolution images or projections of the sample. These images can be used to study a wide range of materials, from biological tissues to geological samples and man-made materials. X-ray microscopy offers significantly higher resolution than classical computed tomography (CT), and when needed, its penetration depth is considerably greater than that of conventional optical microscopes.

[0002] In X-ray microscopy, a sample is irradiated by an X-ray beam, and the transmitted X-rays are captured to form a projection. The X-ray beam is typically generated by a synchrotron radiation source or a laboratory X-ray source. The beam is then modulated to suppress unwanted energy or wavelengths of radiation to ensure high-quality imaging in many cases. As the X-ray beam passes through the sample, its intensity is modulated according to the sample's internal structure and composition. This modulated beam is then detected by a detector system, which converts the X-rays into an analyzable image.

[0003] Tomographic reconstruction converts collected X-ray projections into a three-dimensional representation of the sample. The reconstruction process involves mathematical algorithms. The most commonly used reconstruction algorithms belong to a class of reconstruction techniques called analytical reconstruction. Their goal is to find a closed-form solution to the problem of reconstructing the internal structure of an object from its projections. The most common analytical method is filtered backprojection (FBP). First, the projections are processed in the frequency or spatial domain using a high-pass filter (usually a ramp filter). Then, each filtered projection is “painted” back onto the imaging plane as if each data point were emitted back in the shape of the original beam. These backprojections from all angles are summed to produce a reconstructed volume that approximates the internal structure of the object. The filtering and backprojection operations together contribute to a more accurate and less blurred reconstruction of the original object. One type of filtered backprojection is the FDK algorithm. It is commonly used in X-ray microtomography systems because it reduces artifacts associated with the typical cone-shaped beam characteristic of laboratory X-ray sources. See Feldkamp, ​​LA, Davis, LC and Kress, JW (1984), Practical Cone-Beam Algorithms, Journal of the Optical Society of America, Vol. 1, pp. 612-619.

[0004] In X-ray microtomography systems, accurate tomographic reconstruction depends on proper system alignment, mechanical stability, and calibration. These factors ensure that the projected data accurately represents the object, minimizing errors introduced by the system itself.

[0005] Physical alignment determines the geometric relationship between the X-ray source, the object, and the detector. First, physical alignment is achieved through time-consuming and delicate alignment steps performed by a skilled operator. Misalignment leads to distortion or offset in the projected data, resulting in errors in the reconstructed image. Mechanical stability is also crucial for the object's rotational mechanisms, as deviations such as wobbling or hysteresis during rotation can introduce artifacts into the projection, thus reducing reconstruction quality.

[0006] Calibration addresses these deficiencies by characterizing the system geometry, including source location, detector alignment, and rotation axis. This allows for corrections during reconstruction to compensate for mechanical or alignment errors, thereby improving accuracy.

[0007] In addition to or replacing physical alignment systems, misalignment can be estimated and attempted to be compensated for in reconstruction, which typically provides better reconstructed image quality compared to reconstruction using incorrectly estimated geometry. Advanced reconstruction frameworks or algorithms are available to address complex challenges in image reconstruction. Some of these algorithms can dynamically adjust system-specific biases between projected views, including mechanical misalignment, rotation axis errors, and nonlinearities, based on calibration or projection-specific data. Other algorithms can handle projections at different resolutions or scales to optimize for specific imaging objectives, such as resolving fine details while preserving a broader structural background. Summary of the Invention

[0008] Reconstruction can be complicated by the fact that regions far from the object's axis of rotation (RA) are likely to be observed less frequently during tomography. Therefore, the reconstruction quality of these regions tends to be worse than that of regions closer to the RA (see Zeng Gengsheng, Lawrence). Medical Image Reconstruction Volume 530, Heidelberg: Springer Publishers, 2001 (Zeng, Gengsheng Lawrence). Medical image reconstruction (Vol. 530. Heidelberg: Springer, 2001). However, for misaligned systems, the RA may not be located in the center of the captured projected image, in which case the region of interest (ROI) deviates from the optimal reconstruction area. In worse cases (which can often occur with high-resolution systems and small fields of view (FOV), the RA of a misaligned system may not even appear in the projected image. In this case, the ROI will shift in and out of the optimal reconstruction area during tomography, resulting in a further deterioration in the quality of the reconstructed image.

[0009] Typically, achieving high-quality, high-resolution tomography faces three types of challenges: (1) reliably moving the ROI back to the center of the detector FOV for each projection; (2) accurately estimating the system geometry, which includes the source location, detector location, detector orientation, and potential optical distortions in the detector subsystem; and (3) characterizing the different estimated offsets of each individual projection view so that complex reconstruction algorithms can compensate for the different estimated offsets of each individual projection view.

[0010] Generally, according to one aspect, the present invention relates to a method for performing computed tomography using an X-ray microscope system. The method includes: loading a high-contrast calibration object onto a stage subsystem to measure and determine at least one of translational and orientation positioning parameters by estimating positioning parameters to compensate for stage runout, source drift, and source and / or detector misalignment; positioning the object of interest on the stage subsystem within an X-ray beam between an X-ray source subsystem and a detector; storing the positioning parameters in a metadata set for each view of the object of interest; and reconstructing a three-dimensional representation of the object of interest from the metadata of each view and the associated X-ray projection by incorporating the positioning parameters into the tomographic reconstruction.

[0011] The method may also include defining a virtual rotation axis by selecting a position near the center of the detector's field of view that remains substantially stationary relative to the detector within a range of rotation angles.

[0012] Compensating for detector misalignment can involve estimating nine degrees of freedom of the source and detector geometry. These nine degrees of freedom include the three translational offsets of the source subsystem and the detector, as well as the yaw, pitch, and roll angles of the detector. These nine degrees of freedom are used as global parameters that do not change with the rotation angle of the object of interest.

[0013] The optical distortion introduced by the two-stage detection subsystem can be modeled and corrected, where the distortion is calculated as a polynomial function of radial and tangential displacements in the detector plane and used as a global parameter that does not change with the rotation angle of the object of interest.

[0014] The positioning parameters for each projection angle are typically estimated by positioning one or more small steel microspheres or grid samples with high-contrast angles at multiple locations in the detector's field of view and fitting a geometric model that takes into account stage runout, to produce angle-dependent positioning parameters.

[0015] For example, global misalignment is preferably estimated by placing high-contrast calibration objects (e.g., microspheres for nine degrees of freedom and a mesh for distortion). In specific examples, the sample, source, and detector are all moved to multiple locations, but this is typically performed only at one angle (e.g., θ=0).

[0016] Stage runout is preferably estimated by placing a high-contrast object (microsphere) on the computational center rotation axis (C-RA) or rotation axis (if present in the field of view) and tracking it at different angles (such as possibly from -180 to 180 degrees in 1-degree increments).

[0017] The thermal drift of the source arises from temperature changes. This is also estimated by tracking the position of a high-contrast calibrated object as a function of the source temperature, which is measured by a temperature sensor implemented in the source. In this case, the source temperature at the same time is stored as a positioning parameter for each view.

[0018] The reconstructed 3D representation preferably implements at least one reconstruction algorithm that uses positioning parameters.

[0019] In addition, storing positioning parameters in the metadata set of each view can also involve recording time-related drift measurements and associating these measurements with the corresponding projected views.

[0020] Typically, according to another aspect, the present invention features a computed tomography X-ray microscopy system configured for high-resolution tomographic imaging under computational center conditions. The system includes: an X-ray source subsystem for generating an X-ray beam; a detector subsystem for capturing projection data; and an object stage subsystem having a physical axis of rotation for rotating an object of interest within the X-ray beam to generate projection data. At least one processor stores instructions, when executed, to cause the system to capture multiple calibrated projections at different locations, fit a misaligned geometric model, and reposition the object of interest at each angular location during scanning, such that the virtual axis of rotation remains substantially at the center of the field of view of the detector subsystem.

[0021] The above and other features of the invention (including various novel construction details and combinations of parts), as well as other advantages, will now be described in more detail with reference to the accompanying drawings, which are pointed out in the claims. It should be understood that the specific methods and apparatus embodying the invention are shown by way of illustration rather than as a limitation thereof. The principles and features of the invention may be used in various and many embodiments without departing from the scope of the invention. Attached Figure Description

[0022] In the accompanying drawings, reference numerals refer to the same parts in different views. The drawings are not necessarily drawn to scale; the focus is on illustrating the principles of the invention. In the accompanying drawings:

[0023] Figure 1 This is a schematic diagram of an X-ray microscope (XRM) system, which includes an X-ray microscope, a computer, and several subsystems, such as an X-ray source subsystem, an object stage subsystem, a detector subsystem, and a stabilization platform or base.

[0024] Figure 2 This is a flowchart illustrating a method for high-resolution computed tomography using a rotation axis at a computation center;

[0025] Figure 3 This schematically illustrates the geometry estimation used to create high-quality reconstructions, showing how to estimate source and detector misalignment and optical distortion; and

[0026] Figure 4 This demonstrates how to form the rotation axis of the computation center through coordinate transformation. Detailed Implementation

[0027] The invention will now be described more fully below with reference to the accompanying drawings, which illustrate illustrative embodiments of the invention. However, the invention may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.

[0028] As used herein, the term “and / or” includes any and all combinations of one or more of the associated listed items. Furthermore, all conjunctions used should be understood in the broadest possible sense. Therefore, unless the context explicitly requires it, the word “or” should be understood to have the definition of logical “or” rather than logical “exclusive OR”. Additionally, the singular forms and the articles “a,” “an,” and “the” are intended to also include the plural forms unless otherwise explicitly stated. It will be further understood that, when used in this specification, the terms includes, comprises, including, and / or comprising specify the presence of the stated features, integers, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. Furthermore, it will be understood that when an element (including components or subsystems) is referred to and / or shown as connected to or coupled to another element, it may be directly connected to or coupled to another element, or there may be intermediate elements present.

[0029] It will be understood that although terms such as “first” and “second” are used herein to describe various elements, these elements should not be limited by these terms. These terms are used only to distinguish one element from another. Therefore, an element discussed below may be referred to as a second element, and similarly, a second element may be referred to as a first element, without departing from the teachings of the invention.

[0030] Unless otherwise defined, all terms used herein (including technical and scientific terms) shall have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It will be further understood that terms such as those defined in common dictionaries shall be interpreted as having a meaning consistent with their meaning in the context of the relevant field, and shall not be interpreted in an idealized or overly formal sense unless expressly defined herein.

[0031] Figure 1 This is a schematic diagram of an X-ray microscope (XRM) system 200 to which the present invention can be applied.

[0032] The XRM system 200 typically includes an X-ray microscope 205 and a computer 210.

[0033] The illustrated X-ray microscope 205 is an X-ray CT system and includes several subsystems. An X-ray source subsystem 102 generates a multicolor or possibly monochromatic X-ray beam 103. An object stage subsystem 110, with an object holder 112, holds and positions the sample or object of interest 114 within the beam, allowing scanning of the object of interest 114 within stationary beams 103, 105. A detector subsystem 118 detects the beam 105 modulated by the object of interest 114. A base (such as a platform or optical stage 107) provides a stable foundation for the microscope system 200 and its subsystems.

[0034] Typically, the object stage subsystem 110 has the capability to position and rotate the object of interest 114 within the beam 103. Therefore, the object stage subsystem 110 will typically include a compound linear stage and a rotary stage. The illustrated example has a precision triaxial compound stage 150 that translates and positions the object of interest 114 very precisely, but only within a relatively small range of travel, along the x, y, and z axes. This allows the area of ​​the object of interest 114 to lie within the beam 103 / 105. The triaxial compound stage 150 is mounted on an θ stage 152, which rotates the triaxial compound stage 150, and thus the object of interest 114, about the y-axis within the beam. The θ stage 152 is in turn mounted on a base 107. Thus, with this arrangement, the reference frame or coordinate system of the triaxial compound stage 150 is associated with the reference frame or coordinate system 10 of the microscope system 200 via the current angular position of the θ stage 152.

[0035] In the example, a five-axis compensated stage as described in U.S. Patent No. 7,535,193 (the entire contents of which are incorporated herein by reference) is used as stage 110.

[0036] In this system, the lateral position ( Figure 1The motor encoder readings (x-axis and z-axis) need to be accurate, or more accurate / precise than the resolution of the imaging system. For high-magnification systems, this means <500 nm, otherwise it will affect the reconstructed resolution.

[0037] In some embodiments, the source subsystem 102 is typically a synchrotron X-ray radiation source or a “laboratory X-ray source”.

[0038] As used herein, “laboratory X-ray source” refers to any suitable X-ray source that is not a synchrotron X-ray radiation source. Laboratory X-ray source 102 can be an X-ray tube in which electrons are accelerated in a vacuum by an electric field and injected into a metallic target, emitting X-rays as they decelerate within the metal. Typically, such sources produce a continuous spectrum of background X-rays combined with intensity spikes at specific energies, originating from the characteristic lines of the selected target, depending on the type of metallic target used.

[0039] In one example, source subsystem 102 is a rotating anode type or microfocusing source with a tungsten target. Target materials including molybdenum, gold, platinum, silver, or copper can also be used. A transmission target configuration is preferred, in which the electron beam strikes a thin target from its back side. X-rays emitted from the other side of the target serve as beam 103.

[0040] The X-ray beam generated by source subsystem 102 is typically modulated to suppress unwanted radiation energy or wavelengths. For example, energy filters (designed to select the desired X-ray energy range (bandwidth)) held in filter wheel 160 are used to eliminate or attenuate undesired wavelengths present in the beam. These energy filters typically include an "air" filter corresponding to no filter, as well as a set of low-energy filters for filtering out lower-energy X-rays and high-energy filters for filtering out higher-energy X-rays.

[0041] When object 114 is exposed to X-ray beam 103, X-ray photons propagating through object 114 of interest form a modulated beam 105, which is received by detector subsystem 118. In some other examples, an image is formed on detector subsystem 118 of microscope system 200 using an objective lens.

[0042] Typically, a magnified projection image of object 114 is formed on detector subsystem 118. The magnification of the X-ray stage is inversely proportional to the distance from the source to the object 202 and the distance from the source to the detector 204.

[0043] To achieve high resolution, embodiments of the X-ray CT system 200 further utilize a very high-resolution two-stage detector 124-1 of the detector subsystem 118, possibly combined to locate the object of interest 114 close to the X-ray source system 102. The high-resolution detector 124-1 includes a scintillator combined with a microscope objective and tube lens to provide additional optical magnification in the range of 2x to 100x or more, in addition to the X-ray magnification. The scintillator converts the X-rays into an optical image that can be detected by a camera and further magnified. An example is described in U.S. Patent No. 7,297,959, the entire contents of which are incorporated herein by reference.

[0044] Other detectors are typically included as part of detector subsystem 118. For example, detector subsystem 118 may include lower-resolution detectors 124-2. In the example, this could be a flat panel detector and a camera or a detector with a low-magnification microscope objective. A configuration of one, two, or even more detectors 124 is possible for detector subsystem 118.

[0045] Preferably, two or more detectors 124-1, 124-2 are mounted on the turret 122 of the detector subsystem 118, such that they can rotate alternately into the path of the modulated beam 105 from the object of interest 114.

[0046] Typically, the source subsystem 102 and the detector subsystem 118 are mounted on their respective z-axis stages. For example, in the illustrated example, the source subsystem 102 is mounted to the base 107 via the source stage 154, and the detector subsystem 118 is mounted to the base 107 via the detector stage 156. In practice, the source stage 154 and detector stage 156 are low-precision, high-travel stages that allow the source subsystem 102 and detector subsystem 118 to move into place (typically very close to the object) during scanning and then retract to allow the object to be removed from the object holder 112 of the object stage subsystem 110, a new object to be loaded onto the object holder 112 of the object stage subsystem 110, and / or the object to be repositioned on the object holder 112 of the object stage subsystem 110.

[0047] The operation of the microscope system 200 and the scanning of the object 114 are controlled by a computer 210, which typically includes an image processor 220, a controller 222 and a memory 224.

[0048] Computer 210 includes one or more processors 260 and their data storage resources, such as disks or solid-state drives and dynamic memory (MEM). Processor 260 executes operating system 262 and various applications running on that operating system 262 to allow the user to control and operate microscope system 200. Specifically, scan control application 252 executes on operating system 262 to control XRM microscope 205 to perform scans of object of interest 114. Reconstruction application 250 then reconstructs the resulting projections into a volumetric representation of object of interest 114. Preferably, reconstruction application 250 has the capability to perform reconstruction at each projection during the scan by incorporating positioning parameters and magnification variations caused by relative movement between source subsystem 102, object of interest 114, and detector subsystem 118.

[0049] Controller 222 allows computer 210 to control and manage components in X-ray CT microscope 200 under software control. The controller may be a separate computer system suitable for handling real-time operation or an application program running on processor 260. For this purpose, source subsystem 102 includes a control interface 130 that allows it to be controlled and monitored by controller 222. In particular, X-ray source system 102 includes a temperature sensor 136 that allows controller 222 to track the temperature of the source and save this information as parameter information for each projection. Similarly, object stage subsystem 110 and detector subsystem 118 have respective control interfaces 132 and 134 that allow computer 210 to control and monitor them via controller 222.

[0050] In order to configure the microscope system 200 to scan the object of interest 114 and adjust other parameters (such as geometric magnification), the scan control application 252 adjusts the source-to-object distance 202 and the source-to-detector distance 204 by operating the source stage 154 and the detector stage 156 respectively to achieve the desired scan settings.

[0051] Specifically, the source stage 154 and detector stage 156 include their respective motor encoder systems or other actuator systems, which allow the computer 210 to position the corresponding X-ray source subsystem 102 and detector subsystem 118 to designated locations via control interfaces 130 and 134 through the controller 222. Furthermore, the source stage 154 and detector stage 156 send signals of their actual positions to the controller 222.

[0052] Then, the scan control application 252 operates the object stage subsystem 110 via controller 222 and control interfaces 130, 132, 134 to perform a CT scan. Typically, the object stage subsystem 110 positions the object by controlling the θ stage 152 to rotate the object around a Y-axis orthogonal to the optical axes of the X-ray beams 103, 105, and / or positions the object of interest 114 in the x, y, z axes using the x, y, z precision composite stage 150. The scan control application 252 saves the scan 270 of projection data from the detector subsystem 118 along with the positions of the X-ray source subsystem 102, the detector subsystem 118, and, most importantly, the positions of the x, y, z stages and the θ stage 152 of the composite stage 150. This information is saved to memory 224. More specifically, the scan data 270 includes records generated by the detector subsystem 118 for each projection (projection 1, projection 2, ...). Each of these records includes a spatially resolved image and also includes associated metadata about the stage position. Therefore, metadata 1, metadata 2… include the x, y, and z positions of the composite stage 150 and the θ stage 152 associated with each projection 1, projection 2… Furthermore, preferably, the metadata also includes the source temperature measured by the temperature detector of the X-ray source system 102 and read by the controller 222.

[0053] The scan data 270 will also include acquisition parameters, such as the X-ray source voltage settings that help determine the X-ray energy spectrum, and the exposure time and number of frames on the X-ray source subsystem 102. Other settings, such as the field of view of the X-ray beam 103 incident on the object of interest 114, the number of X-ray projection images created for the object of interest 114, and the selected detectors 124-1, 124-2, are also stored in the scan data 270. Typically, acquisition parameters include X-ray source voltage, X-ray source filtering, camera exposure time, number of frames, and total number of projections. In addition, the source-to-object distance 202 and the source-to-detector distance 204 are typically stored.

[0054] In some embodiments, the computer subsystem 102 employs or creates a "virtual axis of rotation" to keep the region of interest (ROI) of the object of interest at the center of the field of view of the detector 124 at each angle of the tomographic scan. Specifically, if the axis of rotation in the world coordinate system is However, the desired virtual axis is located at The system then uses the three-axis stage of the stage subsystem (which may include linear stages on the rotary stage, if available) to reposition the object of interest according to the following formula: , in It is along The rotation matrix of the position. .

[0055] like Figure 4 As illustrated, since real-world platforms are not infinitely precise, they usually retain small offsets. However, once measured, this offset is recorded in the scan data in the metadata for each projection so that numerical compensation is performed in the reconstruction performed by the reconstruction application 250 by combining positioning parameters and varying magnification, generating a calculated center condition that effectively “locks” the ROI to the center of the detector’s field of view.

[0056] Figure 2 This is a flowchart describing a high-resolution computed tomography method using a central rotation axis according to the present invention.

[0057] In step 310, the system uses a known grid sample, such as a precision datum or test map, to estimate and correct for potential optical distortions within the probe path. The grid sample provides regularly spaced features whose true locations are known in advance. By capturing one or more projections of this grid in the detector's field of view, the system can compare the measured locations of the grid features with their known ideal locations. Any deviations are then fitted to a distortion model—typically a polynomial function describing radial or tangential distortion in a lens or camera subsystem. More specifically, distortion models are particularly helpful when using high-resolution detectors 124-1 (including scintillators, microscope objectives, and tube lenses). The distortion model will cover the optical chain, especially when using high optical magnification. These polynomial coefficients are stored as part of detector calibration. Subsequently, when the system acquires tomographic data, the calculated distortion model is used to remap the image signal to ensure that each probe point is placed in its true location on the virtual imaging plane. This preliminary correction reduces errors that could interfere with subsequent geometry estimation and reconstruction. This is in Figure 3 The right side is shown schematically.

[0058] In step 315, a small, high-contrast object (such as a steel microsphere) is loaded into the object holder 112 and aligned at or near the system's physical rotation axis (the axis of the θ stage 152 of the object stage subsystem 110) to provide a reliable calibration reference. Because a sphere appears as a well-defined, bright feature in X-ray projection, it is well-suited for probing minute deviations in the system geometry.

[0059] While small steel spheres are effective calibration objects due to their well-defined, high-contrast edges, other configurations can be used, provided they have well-defined shapes that allow for high-precision and accurate resolution of their positions when imaged from any angle. For example, a multi-sphere phantom containing multiple microspheres at different known locations provides a broader spatial distribution of reference, aiding in the detection and correction of local distortions. Precision-manufactured metallic patterns, such as periodic wire grids or checkerboard patterns (see: Zhang Zhengyou, "A Flexible New Camera Calibration Technique"), can also be used. IEEE Transactions on Pattern Analysis and Machine Intelligence Volume 22, Issue 11 (2002): pp. 1330-1334 (Zhang, Zhengyou. "A flexible new technique for camera calibration.") IEEE Transactions on pattern analysis and machines intelligence 22.11 (2002): 1330-1334.), circular calibration plate (see: Heikkily, Gianni and Ollie Silver, “A Four-Step Camera Calibration Procedure Including Implicit Image Correction”), IEEE Computer Society Computer Vision and Pattern Recognition Identifying Conference Proceedings , IEEE, 1997 (Heikkila, Janne, and Olli Silvén. "A four-step camera calibration procedure with implicit image correction." Proceedings of IEEE computer society conference on computer vision and pattern recognition IEEE, 1997) and jigsaw puzzle (see: Steldinger, Peer, Niels Schönherr and Justus Bierman, "Jigsaw Puzzle: A Novel Camera Calibration Pattern with Position Encoding"). arXiv preprint arXiv :2409.20127 (2024) (Steldinger, Peer, Nils Schönherr, and Justus Biermann. "PuzzleBoard: A New Camera Calibration Pattern with Position Encoding." arXiv preprint arXiv: 2409.20127 (2024)), to name a few, can also be used as calibration standards, especially if they include sharp boundaries or regular patterns that can simplify feature localization in each projection. Certain grid or datum targets, while typically used for distortion correction, can be reused to estimate system geometry by precisely identifying the intersections of the grid in the detector plane. These alternatives provide the flexibility to match calibration objects to the specific resolution and field-of-view requirements of a given X-ray microscope system.

[0060] The high-contrast object is carefully mounted on the object stage subsystem 110, as close as possible to the center of the rotation axis in the world coordinate system of the microscope system 205. In practice, the operator can iteratively adjust the position of the microsphere using the x, y, z linear stages of the composite stage 150 and the θ stage 152 (or as described in U.S. Patent No. 7,535,193) until the initial projection of the system shows the sphere approximately at the center of the field of view. This initial positioning is crucial for subsequent geometry estimation: even slight misalignment introduces errors into the data propagated through tomography. By starting from the well-defined position of the high-contrast object in the coordinate system, the subsequent calibration steps and geometry fitting process accurately capture system misalignments, including beamline divergence, detector orientation, and optical distortion, which are then compensated for during tomographic reconstruction. This... Figure 3 The left side is shown graphically, illustrating spherical objects with different source and detector positions.

[0061] exist Figure 2 In step 320, and continue to refer to Figure 3 On the left side, the high-contrast object (such as a steel microsphere), along with the X-ray source subsystem 102 and detector subsystem 118, are systematically moved through a small group of different positions by the control system of the computer subsystem 210 to capture multiple projected images of the high-contrast object. Since the position of the rotation axis of the θ stage 152 may not perfectly coincide with the optical axis or field center of the selected detector 124, these movements help to expose any global misalignments in the system geometry and allow calibration procedures to detect them. Typically, this step occurs when the θ stage 152 is at a set angle (such as θ=0).

[0062] Furthermore, stage runout is estimated by continuously imaging a high-contrast object on or within the FOV of the computation center and tracking it at different angles (e.g., from -180 to 180, in 1-degree increments). At each location, the high-contrast object is positioned slightly differently relative to the source subsystem 102 and detector 124. The system records the resulting X-ray projections, which highlight the high-contrast edges of the object, making it easier to identify the precise coordinates of the sphere in each projection. These data points provide a deep understanding of stage runout. By capturing these projections at several carefully selected locations, the geometry is accurately estimated in subsequent fitting steps performed by the computer subsystem 210, ensuring that the final tomographic reconstruction takes into account system misalignment, particularly stage runout.

[0063] Furthermore, the thermal drift of source 102 arises from temperature changes. This is also estimated by tracking the position of a high-contrast object (e.g., a steel microsphere) as a function of the source temperature, and read by the temperature detector integrated in source 102 by controller 222.

[0064] In summary, source / detector translational / rotational misalignment (9 degrees of freedom) and lens distortion are “global” misalignments, the same for all rotation angles and temperatures. On the other hand, stage runout and source (thermal) drift can depend on rotation angles and / or temperature changes during scanning.

[0065] In step 325, the computer subsystem 210 identifies the position of each high-contrast object (e.g., a steel microsphere) in the captured projection and then uses these position measurements to fit a geometric model describing the mechanical and optical distortions of the system. This can be done, for example, using an autodifferentiable language such as PyTorch (see Paszke, Adam et al., "PyTorch: An Imperative, High-Performance Deep Learning Library"). Advances in Neural Information Processing Systems Volume 32 (2019)), Jax (see Bradbury, James et al., "Jax: Automatic Differentiation and xla"), Astrophysics source code library (2021): ascl-2111) and TensorFlow (Abadi, Martín et al., "TensorFlow: Systems for Large-Scale Machine Learning"), 12th The USENIX Operating System Design and Implementation Workshop (OSDI 16)The method implemented in 2016 uses a voxel-driven forward projector (Kachelriess, Marc, Michael Knaup, and Olivier Bockenbach, "Ultra-high-speed parallel-beam and cone-beam backprojection using Cell general-purpose hardware," *Medical Physics*, Vol. 34, No. 4 (2007)), but other estimation methods can also be used. The core task is to track the precise center point of the object (sphere) in each projected image captured in step 320. By precisely measuring the position where the object (sphere) appears in each projected image, the system can correlate these positions with known or measured displacements of the rotating stage 152 of the source subsystem 102, detector 124, and stage subsystem 110. In other words, the computer subsystem 210 determines the degree of offset of the small, high-contrast object (sphere) relative to the nominal center of detector 124 in the image plane, and how this offset is correlated with the physical movement applied by the system. With these data points, a fitting routine (typically implemented in a differentiable framework such as PyTorch or TensorFlow) executed by computer subsystem 210 estimates a complete set of system parameters—such as source location, detector orientation, and optical distortion polynomials—aligning the positions of all recorded high-contrast objects (spheres) in a self-consistent geometric model. Thus, even if the rotation axis is off-center or the detector plane is tilted, computer subsystem 210 obtains corrected geometric parameters that accurately describe the real-world positions of source subsystem 102, object 114, and detector 124 in each projected view. This step creates estimated geometric parameters that correlate the original image of the calibrated object with a mathematically precise representation of the actual configuration of the X-ray microscope.

[0066] It should be noted that even when the ROI is placed on a virtual axis of rotation, an X-ray microscope may still remain misaligned in other ways. These misalignments can be modeled using nine degrees of freedom, including three translational offsets each for the source and detector, as well as the detector's yaw, pitch, and roll angles. In a two-stage detection system using objectives for additional magnification, optical distortions (typically radial or tangential) can further offset the apparent position of features in each projection. Since these distortions are independent of the source-to-object or source-to-detector distance, the system can estimate them by fitting a polynomial function to the apparent distortion fields at multiple calibration locations.

[0067] For a two-stage detection system, the projector model includes an additional mapping from the scintillator plane to the visible light detector plane. The system uses differentiable methods (e.g., implemented in frameworks such as PyTorch or TensorFlow) to jointly optimize the coefficients of the geometric degrees of freedom and the distortion polynomial. This helps to isolate purely geometric misalignments (e.g., beamlines not parallel to the stage guides) from lens-driven distortions.

[0068] In step 330, the high-contrast calibration object / sphere is removed (or set aside) and replaced with the actual object of interest to be imaged. Using the geometry or positioning parameters extracted in the preceding calibration steps, the system ensures that the object of interest is always positioned at or near the optimal imaging region of detector 124. Specifically, at each angular location of the tomographic scan, computer subsystem 210 applies corrective motion instructions derived from the virtual rotation axis creation and geometry fitting process. In practice, this might mean slightly moving the object along the xyz linear stage to account for jitter or misalignment, keeping the region of interest centered in the field of view. Because the system now has an accurate model of the positions of the source and detector (and any lens distortion), each projection is captured under effective “computational center” conditions, where the rotation axis appears to remain stable in the detector’s image space. This approach maximizes resolution and minimizes artifacts, particularly in the regions of object of interest 114 that could drift out of the detector’s optimal imaging region if only the uncorrected raw physical rotation axis were used.

[0069] Although linear and rotating stages have precise encoders, small but consistent "runouts" can cause the sample to deviate from a predictable offset at each projection angle. Furthermore, thermal effects and electron beam instabilities can cause minute drifts in the X-ray source position during longer scans. The system addresses these issues by recording reference scans of high-contrast objects / spheres, registering them with longer scans to calculate any transient displacements, and then compensating for these offsets in the final reconstruction.

[0070] In step 335, computer subsystem 210 continuously tracks and records the precise position of the linear and rotating stage during the tomographic scan of the object of interest. This tracking involves reading encoder values ​​(or other position sensor values) for each axis at each projection angle and storing the positioning parameters as metadata with each projection. Since the previously determined geometric corrections include compensation for runout and other misalignments, the recorded positioning parameters serve two purposes: first, to verify that the object of interest is continuously re-centered as planned; and second, to provide an accurate record of the stage's physical position for each projection at the precise time of image capture. These metadata positioning parameters become part of the final scan dataset 270 and are directly fed into the reconstruction algorithm, ensuring that each view is associated with information describing how the object of interest 114 is positioned relative to the source subsystem 102 and detector 124.

[0071] In step 340, computer subsystem 210 uses the positioning parameters recorded in the metadata of each projection to create an accurate reconstruction setup for each view, and then performs the actual volumetric reconstruction (e.g., using filtered backprojection). Because real-world misalignment and thermal drift cause the rotation axis to deviate from a perfect circular trajectory, each projection ultimately has its own unique relationship between the source subsystem 102, the object of interest, and the detector 124. Therefore, instead of relying on a single global model, the system compiles an accurate geometric description as positioning parameters for each captured projection. This description typically includes parameters such as the relative position of the source, the orientation of the detector, and any offsets introduced by stage movement, enabling the reconstruction algorithm to account for every minute shift in the data.

[0072] Once these positioning parameters are assigned to each view, the reconstruction routine (typically a filtered back projection (FBP) or a more advanced iterative algorithm) processes the entire projection set. By incorporating corrected geometry on a view-by-view basis, artifacts and blurring caused by mechanical defects are minimized in the final 3D volume. In effect, each image is correctly registered in the “computational center” space, thus the reconstructed volume reveals the object of interest with significantly improved resolution and less distortion.

[0073] Because each projection may have slight deviations from the ideal geometry, the system develops a geometry description for each view, which includes up to twelve parameters (e.g., source location, detector location, detector orientation, and net sample offset). Then, a so-called "universal reconstructor" (e.g., Kachelriess, Marc, Michael Knaup, and Olivier Bockenbach's "Ultra-High-Speed ​​Parallel-Beam and Cone-Beam Backprojection Using Cell Universal Hardware") is used. Medical Physics (Vol. 34, No. 4 (2007): 1474-1486) processes the geometry of each of these views, whether using filtered backprojection or more complex iterative algorithms, to produce a final 3D volume with minimized artifacts. By not assuming a strictly circular scan path, the method adapts to the imperfections of the real world, thus producing superior resolution, especially for misaligned systems or scans performed over long periods of time.

[0074] Although this workflow was demonstrated using a cone-beam, two-stage detector X-ray system, the same principles can be applied to direct flat-panel detectors and even parallel-beam geometries. In parallel-beam or C-arm systems, the geometry description for each view can be adjusted by omitting source point localization or by adjusting known geometric constraints. Similarly, if the system lacks a second-stage optical magnification, simply set the distortion model to units and eliminate polynomial lens terms.

[0075] Although the invention has been specifically shown and described with reference to its preferred embodiments, those skilled in the art will understand that various changes in form and detail may be made therein without departing from the scope of the invention as covered by the appended claims.

Claims

1. A method of performing computed tomography using an X-ray microscope system, characterized by, The method includes: A high-contrast calibration object is loaded into the stage subsystem to measure and determine at least one of the translational and orientation positioning parameters by estimating the positioning parameters, in order to compensate for stage runout, source drift, and source and / or detector misalignment. Position the object of interest on the stage subsystem within the X-ray beam between the X-ray source subsystem and the detector; The positioning parameters are stored in a metadata set for each view of the object of interest; and By incorporating the positioning parameters into the tomographic reconstruction, a three-dimensional representation of the object of interest is reconstructed from the metadata of each view and the associated X-ray projection.

2. The method of claim 1 further comprises defining a virtual rotation axis by selecting a position near the center of the detector's field of view, the position remaining substantially stationary relative to the detector within a range of rotation angles.

3. The method of claim 1, wherein, Compensating for detector misalignment involves estimating nine degrees of freedom for the source and detector geometry. These nine degrees of freedom include three translational offsets in the source subsystem and the detector, as well as the detector's yaw, pitch, and roll angles. These nine degrees of freedom are used as global parameters that do not change with the rotation angle of the object of interest.

4. The method of claim 1, further comprising modeling and correcting optical distortions introduced by the two-stage detection subsystem, wherein, The distortion is calculated as a polynomial function of radial and tangential displacements in the detector plane, and the distortion is used as a global parameter that does not change with the rotation angle of the object of interest.

5. The method of claim 1, wherein, The positioning parameters for each projection angle are estimated by positioning the high-contrast calibration object at multiple locations in the detector's field of view and fitting a geometric model that takes into account stage runout.

6. The method of claim 1, wherein, The positioning parameters based on the source temperature are saved during the scan.

7. The method according to claim 1, wherein, Reconstructing the three-dimensional representation includes implementing at least one reconstruction algorithm that uses the translation and orientation positioning parameters.

8. The method according to claim 1, wherein, The step of storing the positioning parameters in the metadata set of each view also includes recording time-related drift measurements and associating the drift measurements with the corresponding projected view.

9. A computed tomography X-ray microscopy system configured for high-resolution computed tomography imaging under computing center conditions, the system comprising: X-ray source subsystem used to generate X-ray beams; A detector subsystem for capturing projection data; An object stage subsystem having a physical axis of rotation, the object stage subsystem being used to rotate an object of interest in the X-ray beam to generate the projection data; as well as At least one processor storing instructions, when executed, causes the system to capture multiple calibration projections at different locations, fit misaligned geometric models, and reposition the object of interest at each angular location during scanning, such that the virtual rotation axis remains substantially at the center of the field of view of the detector subsystem.

10. The system of claim 9, wherein, The misaligned geometric model comprises at least nine degrees of freedom, including three translational offsets of both the X-ray source subsystem and the detector subsystem, and three directional offsets of the detector subsystem, and the nine degrees of freedom are used as global parameters that do not change with the rotation angle of the object of interest.

11. The system of claim 9, wherein, The detector subsystem includes a two-stage detector with a scintillator and an optical magnifying lens, wherein at least one processor is configured to estimate and compensate for optical distortions generated in the second stage of the detector.

12. The system of claim 9, wherein, The object stage subsystem is further configured with xyz linear stages stacked on the physical rotation axis to allow repositioning of the object of interest such that the virtual rotation axis remains within the high-resolution portion of the detector's field of view.

13. The system of claim 9, wherein, The at least one processor is configured to record runout data for each projection angle, wherein the runout data represents a predictable lateral displacement of the object of interest caused by a defect in the physical axis of rotation.

14. The system of claim 9, wherein, The at least one processor is configured to apply a geometric descriptor for each view to each captured projection, such that each view is associated with specific translation and orientation parameters used to generate a 3D reconstruction of the object of interest.

15. The system of claim 9, wherein, The system also includes a reference calibration object, and the at least one processor is programmed to acquire a calibration scan of the reference calibration object to derive the misaligned geometric model before scanning the object of interest.

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