Spectral image analysis by integral constraint fitting

Abstract

And carrying out spectral image analysis through integral constraint fitting. Systems or techniques are provided for facilitating spectral image analysis through integral constraint fitting. In various embodiments, the system may access spectral images of a sample acquired by a scientific instrument, pixels of these spectral images respectively corresponding to an energy spectrum. In various aspects, a system may fit a function to an energy spectrum in a pixel-by-pixel manner, the function including a plurality of terms that are added and combined, where a first term of the plurality of terms represents a fine structure of the energy spectrum, and where an integral associated with the first term is constrained to zero. In various cases, the system may segment a spectral image by material based on a first term.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims the benefit of and priority to co-pending European patent application (serial number 24164816.1) filed on March 20, 2024, entitled “Spectral image analysis by integral constrained fitting”, the entire contents of which are incorporated herein by reference. Background Art

[0003] Various scientific instruments can acquire spectral images of a sample. Analysis of the spectral images can be facilitated by fitting a function to the energy spectrum represented by the spectral images. Summary of the Invention

[0004] The following presents a summary of the invention to provide a basic understanding of one or more embodiments. This summary is not intended to identify key or important elements, or to delineate any scope of a particular embodiment or any scope of the claims. Its sole purpose is to present concepts in a simplified form as a prelude to a more detailed description that will be presented later. In one or more embodiments herein, an apparatus, system, computer-implemented method, device, or computer program product that facilitates spectral image analysis by integral constrained fitting is described.

[0005] According to one or more embodiments, a system is provided. The system may include a non-transitory computer-readable memory that can store computer-executable components. The system may also include a processor that can be operably coupled to the non-transitory computer-readable memory and can execute the computer-executable components stored in the non-transitory computer-readable memory. In various embodiments, the computer-executable component may include an access component that can access spectral images of samples collected by a scientific instrument, the pixels of these spectral images corresponding to energy spectra respectively. In various aspects, the computer-executable component may include a fitting component that fits a function to the energy spectrum in a pixel-by-pixel manner, the function including multiple terms in an additive combination, wherein the first term of the multiple terms represents the fine structure of the energy spectrum, and wherein the integral associated with the first term is constrained to zero. In various cases, the computer-executable component may include an execution component that can segment the spectral image by material based on the first term.

[0006] According to one or more embodiments, a computer-implemented method is provided. In various embodiments, the computer-implemented method may include accessing, via a device operably coupled to a processor, a spectral image of a sample acquired by a scientific instrument, wherein pixels of the spectral image correspond to an energy spectrum; fitting, via the device, a function to the energy spectrum in a pixel-by-pixel manner, the function comprising additively combined multinomials, wherein a first term of the multinomials represents a fine structure of the energy spectrum, and wherein an integral associated with the first term is constrained to zero; and segmenting, via the device, the spectral image by material based on the first term.

[0007] According to one or more embodiments, a computer program product is provided for facilitating spectral image analysis by integral constrained fitting. In various embodiments, the computer program product may include a non-transitory computer-readable memory having program instructions embodied therein. In various aspects, the program instructions are executable by a processor to enable the processor to access a spectral image of a sample acquired by an electron energy loss microscope, wherein pixels of the spectral image correspond to an energy loss spectrum; fit a function to the energy loss spectrum in a pixel-by-pixel manner, wherein the function includes a fine structure term and wherein the integral associated with the fine structure term is constrained to be zero; and segment the spectral image based on the fine structure term (rather than based on the remainder of the function). BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Various embodiments will be readily understood by the following detailed description in conjunction with the accompanying drawings. For ease of description, identical reference numerals denote identical structural elements. The drawings illustrate embodiments by way of example and not by way of limitation. These drawings are not necessarily drawn to scale.

[0009] Figure 1 An exemplary non-limiting block diagram of a scientific instrument module is shown, according to various embodiments described herein.

[0010] Figure 2 An exemplary non-limiting flow chart of a computer-implemented method according to various embodiments described herein is shown.

[0011] Figure 3 A block diagram is shown of an exemplary non-limiting system for facilitating spectral image analysis via integral constrained fitting according to one or more embodiments described herein.

[0012] Figure 4 An exemplary non-limiting block diagram of a spectral image is shown according to one or more embodiments described herein.

[0013] Figure 5 A block diagram is shown of an exemplary non-limiting system including a fitting function that includes a background term, an atomic cross section term, and a fine structure term, and that facilitates spectral image analysis via integral constrained fitting according to one or more embodiments described herein.

[0014] Figure 6-13 An example non-limiting block diagram of a fit function and its components is shown according to one or more embodiments described herein.

[0015] Figure 14 A block diagram is shown of an exemplary non-limiting system including a segmentation mask for facilitating spectral image analysis via integral constrained fitting according to one or more embodiments described herein.

[0016] Figure 15 An exemplary non-limiting block diagram illustrating how a segmentation mask may be generated according to one or more embodiments described herein is shown.

[0017] Figures 16 to 23 Exemplary non-limiting simulation results are shown according to one or more embodiments described herein.

[0018] Figure 24 An exemplary non-limiting block diagram of a graphical user interface that may be used to implement some or all of the methods or techniques disclosed herein, according to various embodiments described herein, is shown.

[0019] Figure 25 An exemplary, non-limiting block diagram of a computing device that can perform some or all of the methods or techniques disclosed herein according to various embodiments described herein is shown.

[0020] Figure 26 An exemplary, non-limiting block diagram of a scientific instrument support system that can perform some or all of the methods or techniques disclosed herein according to various embodiments described herein is shown.

[0021] Figure 27 A block diagram depicts an exemplary non-limiting operating environment that can facilitate one or more embodiments described herein.

[0022] Figure 28 An exemplary networking environment is shown that is operable to perform various implementations described herein. DETAILED DESCRIPTION

[0023] The following detailed description is illustrative only and is not intended to limit the embodiments and / or the application or uses of the embodiments. In addition, there is no intention to be bound by any express or implied information presented in the previous background or summary sections or detailed description sections.

[0024] One or more embodiments will now be described with reference to the accompanying drawings, wherein like reference numerals are used throughout to refer to like elements. In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a more thorough understanding of one or more embodiments. However, it will be apparent that in various circumstances, one or more embodiments may be practiced without these specific details.

[0025] The various operations may be described as a plurality of discrete actions or operations in a manner that is most helpful in understanding the subject matter disclosed herein. However, the order described should not be interpreted as implying that these operations must be dependent on the order. In particular, these operations may be performed in an order different from the order presented. The described operations may be performed in an order different from the described embodiment. Various additional operations may be performed, or the described operations may be omitted in additional embodiments.

[0026] Although some elements may be referred to in the singular (e.g., "processing device"), any appropriate element may be represented by multiple instances of that element, and vice versa. For example, a set of operations described as being performed by a processing device may be implemented as different ones of those operations being performed by different processing devices. As used herein, the phrase "based on" should be understood to mean "based at least in part on," unless otherwise specified.

[0027] A scientific instrument (e.g., a mass spectrometer, a charged particle microscope) can be any suitable computerized device capable of acquiring or generating electronic measurements (e.g., capable of acquiring or generating spectral images or composition spectra) in a scientific, laboratory, research, or clinical operating environment. To facilitate acquiring or generating such electronic measurements, a scientific instrument can utilize a complex arrangement of actuatable components (e.g., ion sources, ion lenses, heaters, coolers, fluid valves, fluid pumps, circuit switches, sample stages, apertures), sensors (e.g., ion detectors, voltmeters, thermistors, potentiometers, manometers), or consumables (e.g., carrier fluids, calibrants, filters).

[0028] Various scientific instruments (e.g., electron energy loss microscopes) can acquire spectral images of samples. A spectral image can be an array of pixels depicting the sample, but rather than each pixel representing a corresponding intensity value (e.g., a measured Hounsfield unit), each pixel can represent a corresponding energy spectrum. In other words, each pixel can have multiple measured intensities, or counts, distributed over a series of defined energy intervals. In other words, a scientific instrument that generates a spectral image of a sample can be thought of as counting, for each defined energy interval, the number of charged particles (e.g., electrons) belonging to that interval that strike the sample at each pixel. Such spectra can be analyzed to determine or reveal information about the sample (e.g., the electronic structure of the compounds in the sample).

[0029] Analysis of a spectral image can be facilitated by fitting a function to the energy spectrum represented by the pixels of the spectral image. In particular, the energy spectrum of a pixel can be modeled as an additive or multiplicative combination of background, atomic cross section, and fine structure. The background can be represented by one or more monotonically decaying power-law functions. The atomic cross section can be represented by one or more random functions that represent the probability that a given incident excitation (e.g., a charged particle beam) will scatter in a given manner upon collision with a given type of atom. The fine structure can be represented by a spline composed of any suitable basis functions (e.g., polynomial or rectangular functions). Note that the background can be considered as a meaningless or uninformative component of the energy spectrum. Furthermore, while the fitted coefficients (e.g., amplitude) of the atomic cross section can represent meaningful or informative properties of the sample (e.g., the abundance of a compound in the sample), the overall shape of the atomic cross section may be known (e.g., any charged particle beam properties used by the scientific instrument to acquire the spectral image can be controllably selected, and it is understood how these charged particle beam properties can be used to calculate (up to a scaling factor) the random atomic cross section function for the desired atoms). Therefore, in certain situations or contexts, the atomic cross sections can be considered as less meaningful or less informative components of the spectrum. In contrast, the fine structure can be considered unknown and, therefore, the most meaningful or informative component of the spectrum. In fact, the fine structure can be considered to carry or convey information about the electronic structure of the sample (e.g., the influence of surrounding atoms or compounds). In other words, the purpose or goal of the fitting function to identify the energy spectra of spectral images can be to discover or obtain the specific characteristics or shape of the fine structure of those spectra. Therefore, once the energy spectra of the spectral images are fitted, the fine structure of these spectra (rather than the background and atomic cross sections) can be used to perform any suitable downstream analysis of the spectral images, such as image classification or image segmentation (e.g., determining the electronic structure or compounds at different locations in the sample).

[0030] Unfortunately, as recognized by the inventors of the various embodiments described herein, existing techniques for modeling the fine structure of energy spectra suffer from various shortcomings.

[0031] First, the basis functions used for fine structure modeling can take various input parameters as parameters. An example of such an argument is the energy window (also known as the energy width). The inventors have realized that the prior art is overly sensitive to the choice of energy window. That is, the inventors have realized that changes in the selected or chosen energy window can lead to corresponding changes in the obtained fine structure and, therefore, to corresponding changes in downstream image classification or image segmentation. However, such downstream changes should not occur (e.g., different energy windows should lead to the same or similar downstream results). Therefore, the prior art can be considered unstable with respect to the selected energy window.

[0032] Secondly, except being overly sensitive to the selection of energy window, the inventor also realizes that prior art generally has the problem that downstream analysis precision is not enough.In particular, the inventor realizes that, when obtaining fine structure by prior art, no matter the downstream results, image classification or image segmentation results obtained from those fine structures are generally not as good as they could or should reach the precision (for example, measuring electronic structure is generally incorrect; Many pixels are generally misclassified or mis-segmented). In addition, since atomic cross section and fine structure fit energy spectrum simultaneously, it can be considered that atomic cross section and fine structure are interdependent (for example, the fitting value of atomic cross section depends on the fitting value of fine structure, and vice versa). Therefore, since the fine structure of prior art is generally inaccurate, the fitting amplitude of the atomic cross section calculated by prior art is also generally inaccurate, which may cause the chemical abundance of determination to be too high, too low or inaccurate. Therefore, prior art can be considered as not reliable enough.

[0033] Therefore, it would be best to have a system or technology that improves one or more of these technical problems.

[0034] Various embodiments described herein can address one or more of these technical issues. In one or more embodiments, systems, computer-implemented methods, apparatus, or computer program products are described herein that facilitate spectral image analysis through integral constrained fitting. Specifically, as described above, the energy spectrum of a spectral image pixel can be fitted using a function consisting of three distinct terms: background, atomic cross-section, and fine structure. That is, each pixel can be considered to have its own background, its own atomic cross-section, and its own fine structure. Also as described above, downstream analyses (e.g., image classification and image segmentation) can be performed based on the fine structure of these pixels rather than on background and atomic cross-section. Currently, when implementing existing techniques, these downstream analyses exhibit excessive energy window sensitivity (e.g., image classification or segmentation can vary significantly depending on the choice of energy window) and excessively low accuracy (e.g., many misclassified or missegmented pixels). The inventors recognized that by constraining one or more integrals related to the fine structure of the spectral image pixels, the energy window sensitivity can be reduced and the accuracy of the downstream analysis improved. Specifically, the inventors recognized that, during the fitting process, the fine structure of the pixel can be represented not only by a spline, but also by a spline associated with an integral constrained to zero that is related to energy (or energy loss). In other words, the weighted integral of the spline can be constrained to zero. The inventors have experimentally verified that imposing this zero-integral constraint on the fine structure can both reduce the sensitivity of the energy window and improve the accuracy of downstream analysis. In other words, imposing this zero-integral constraint allows the fine structure of the resulting spectral image to better represent or convey information about the electronic structure or compounds in the sample.

[0035] The various embodiments described herein can be viewed as computerized tools (e.g., any suitable combination of computer-executable hardware or computer-executable software) that facilitate analyzing spectral images by integral constrained fitting. In various aspects, such computerized tools can include an access component, a fitting component, or an execution component.

[0036] In various embodiments, there may be a scientific instrument. In various aspects, the scientific instrument can be any suitable computerized device capable of electronically acquiring or generating a spectral image of any suitable sample (e.g., a thin layer sample). As a non-limiting example, the scientific instrument can be an energy loss electron microscope.

[0037] In any case, the spectral image can be a three-dimensional array, where two dimensions of the array represent pixels that collectively describe or illustrate the sample, and the third dimension of the array represents the pixel-by-pixel energy spectrum recorded by the scientific instrument. As a non-limiting example, for any suitable positive integers x, y, and z, the spectral image can be an x×y×z array. In this case, the spectral image can be considered to be composed of a total of xy pixels, and each of these pixels can be considered to have a corresponding distribution in a z energy interval (for example, the size of these z energy intervals can be adjusted according to any suitable electron volt (eV) resolution supported by the detector of the scientific instrument to achieve any suitable level of energy loss granularity). In other words, each pixel can be considered to represent or define a unique two-dimensional location on the sample, and the scientific instrument can count or measure the number of incident ions (e.g., electrons) emitted by the scientific instrument that belong to each z energy interval and that impact the sample at the unique two-dimensional location.

[0038] In various cases, it may be necessary to segment or otherwise analyze a spectral image, for example to determine how much of a chemical element or compound is present at which locations in a sample. In various cases, the computer tools described herein can facilitate such segmentation or analysis.

[0039] In various embodiments, an access component of a computerized tool can electronically access the spectral image. For example, the access component can receive, retrieve, or otherwise obtain the spectral image from any suitable centralized or decentralized data structure (e.g., a graph data structure, a relational data structure, a hybrid data structure). As a non-limiting example, the access component can receive, retrieve, or obtain the spectral image from the scientific instrument itself. In any case, the access component can be considered a conduit through which other components of the computerized tool can electronically interact with (e.g., read, write, edit, copy, manipulate) the spectral image.

[0040] In various embodiments, a fitting component of a computerized tool can electronically fit a function to an energy spectrum represented or conveyed by a spectral image on a pixel-by-pixel basis. In various aspects, the function can include a background term, an atomic cross-section term, and a fine structure term. In various cases, the fine structure term can be integrally constrained to zero, as described herein.

[0041] More specifically, consider a given pixel of a spectral image. In various cases, the given pixel can have a given energy spectrum. Continuing with the example above, where the spectral image is an x×y×z array, the given energy spectrum can be the distribution of ion counts or intensities at z energy intervals. In other words, the given energy spectrum can be viewed as a sequence of z tuples, each tuple being a different energy interval and a corresponding count or intensity. In various aspects, a fitting component can fit a function (e.g., by any suitable fitting technique, such as least squares (LSS)) to such a sequence of tuples, where the incident energy (or energy loss) can be viewed as the independent variable of the function, and the counts or intensities can be viewed as the dependent variable of the function. Now, in various cases, the function can be an additive combination of three different terms: a background term, an atomic cross section term, and a fine structure term.

[0042] In various cases, the background term can be any suitable number of monotonically decaying power-law functions (e.g., a single monotonically decaying power-law function or the sum of multiple monotonically decaying power-law functions), including any suitable number of first fitting coefficients. In some cases, the multiple first fitting coefficients can be exponents of the monotonically decaying power-law functions. In some cases, each first fitting coefficient can be a scaling factor that is multiplied by the monotonically decaying power-law function.

[0043] In various aspects, the atomic cross-section term can be any suitable number of random atomic cross-section probability functions (e.g., can be a single random atomic cross-section probability function, or can be the sum of multiple random atomic cross-section probability functions), including any suitable number of second fitting coefficients. In various cases, the second fitting coefficients can be scaling factors multiplied by the random atomic cross-section probability functions.

[0044] In various cases, the fine structure term can be a spline with any suitable basis function, which includes any appropriate number of third fitting coefficients. In various cases, the basis function can be a polynomial of any order or degree (e.g., a zero-order or constant polynomial, a first-order or linear polynomial, a second-order or quadratic polynomial, a third-order or cubic polynomial), and the third fitting coefficient can be a scaling factor multiplied by the corresponding term or corresponding basis function of such a basis function. In this case, the values ​​of adjacent polynomials of the spline can be forced to agree on the first-order derivative at their respective boundaries. In other cases, the basis function can be any suitable non-polynomial function, such as a rectangular function (e.g., the difference between Heaviside step functions) or a trigonometric function (e.g., based on an absolute value function), each of which can be multiplied by one of the third fitting coefficients. Regardless of which basis function is selected for the spline, the spline can be defined piecewise within any suitable interval. In some cases, such intervals can be linearly spaced or equidistantly spaced. In other cases, such intervals can be quadratically spaced (e.g., so that each consecutive interval is proportional to the square of the previous interval).

[0045] In some cases, the atomic cross section term and the fine structure term can be convolved with the low-loss (or equivalently, high-energy) portion of a given energy spectrum. More specifically, the various z energy intervals spanned by a given energy spectrum can be considered to form the low-loss (or high-energy) region of the given energy spectrum. As a non-limiting example, any interval covering or spanning from 0 eV loss to 200 eV loss can be considered to collectively form the low-loss (or high-energy) region of the given energy spectrum. Note that interesting electronic activity (e.g., the K-edge appearing in an electron energy loss spectrum) typically occurs in energy bands or intervals where the loss exceeds 200 eV. Therefore, any counts or intensities measured in the low-loss region of a given energy spectrum (e.g., measured before the 200 eV loss) can be convolved with the atomic cross section term and the fine structure term. This convolution can help to reduce or otherwise control sample thickness effects in the fitting function.

[0046] In any case, the fitting component can fit a function to a given energy spectrum (e.g., via LSS). This fitting can be viewed as identifying which specific values ​​of the first, second, and third fitting coefficients result in an error metric (e.g., the sum of squared errors) between the given energy spectrum and the function being minimized or approximately minimized (e.g., below any suitable threshold). At this point, the function can be considered to be a very good match to the given energy spectrum. However, during this fitting process, the integral of the fine structure term with respect to energy (or energy loss) can be constrained to be zero. In other words, fitting the function to a given energy spectrum can be viewed as identifying specific values ​​of the first, second, and third fitting coefficients that not only result in minimizing the error metric, but also result in the integral associated with the fine structure term being as close to zero as possible (e.g., within the range of any suitable critical threshold being zero).

[0047] In various embodiments, the execution component of the computerized tool can electronically perform any suitable downstream analysis on the spectral image based on the fitting fine structure term identified by the fitting component. In other words, the execution component can perform such downstream analysis without considering the fitting background term or the fitting atomic cross section term of the spectral image. As a non-limiting example, the execution component can calculate or generate a segmentation mask for the spectral image by applying any suitable clustering algorithm (e.g., K-means clustering) to the fine structure term of the fitting, or by executing any suitable trained machine learning segmenter (e.g., deep learning neural network). In either case, the segmentation mask can be considered to represent that each pixel of the spectral image belongs to one of two or more defined categories (e.g., two or more defined categories can represent two or more defined compounds or oxidation states known to be present in the sample, and the segmentation mask can represent which pixels of the spectral image are composed of which defined compounds or oxidation states). In various aspects, the execution component can visually present the segmentation mask on any suitable computer screen or display. In various cases, the execution component can electronically transmit the segmentation mask to any suitable computing device.

[0048] Note that the present inventors have experimentally demonstrated that this segmentation mask can be considered to have higher accuracy or reliability than other possible methods and is less sensitive to the choice of energy window because the integral of the spectral image is constrained to zero. In other words, if the fitted fine structure term of the spectral image is identified without constraining its integral to zero, the accuracy of the segmentation mask will be lower (e.g., there will be more misclassified pixels) and will vary more with the choice of energy window.

[0049] Therefore, the computerized tool described herein can be viewed as providing an improved analysis of the spectral image, and the computerized tool described herein can achieve this improvement by imposing a zero-integral constraint on the fine structure term of the fit.

[0050] The various embodiments described herein can be used to solve inherently highly technical problems (e.g., facilitating spectral image analysis via integral constrained fitting) using hardware or software. They are not purely conceptual and cannot be implemented as a series of human mental activities. Furthermore, portions of the implementation process can be performed by specialized computers (e.g., electron energy loss microscopes) to perform the specified operations related to spectral imaging.

[0051] For example, such prescribed operations may include: accessing, by a device operably coupled to a processor, a spectral image of a sample acquired by a scientific instrument, wherein pixels of the spectral image correspond to an energy spectrum; fitting, by the device, a function to the energy spectrum in a pixel-by-pixel manner, the function comprising additively combined multiple terms, wherein a first term of the multiple terms represents a fine structure of the energy spectrum, and wherein an integral associated with the first term is constrained to be zero; and segmenting, by the device, the spectral image by material based on the first term. In various aspects, the multiple terms may further include a second term representing a monotonically decaying background of the energy spectrum and a third term representing an atomic cross section of the energy spectrum.

[0052] Such prescribed operations are inherently computerized. In fact, a scientific instrument (such as an electron energy loss microscope) is a high-tech computerized device that includes specific computerized hardware (e.g., temperature sensors, pressure sensors, voltage sensors, ion beam emitters, ion focusing mirrors, mass analyzers, ion detectors, beam apertures, and fluid valves). Without a computer, the scientific instrument and the operations performed by it cannot be implemented in any reasonable or feasible manner by the human mind or by humans using pen and paper. Furthermore, a spectral image is a specific type of pixel array in which each pixel has its own measured energy spectrum or distribution (rather than its own Hounsfield unit value). Without a computer, the human brain cannot generate or acquire a spectral image, nor can humans generate or acquire a spectral image in any reasonable or feasible manner using pen and paper. Furthermore, the segmentation of a spectral image is inherently a computerized task in which each pixel of the spectral image is classified into one of two or more defined categories, thereby generating a segmentation mask that shows which pixels of the spectral image belong to which category. It makes no sense to discuss the computerized task of image segmentation outside of a computing environment.

[0053] Furthermore, various embodiments described herein can integrate various teachings related to spectral image analysis into practical applications through integral constrained fitting. As described above, when a spectral image of a sample is acquired, each pixel in the spectral image has its own energy spectrum. As described above, each energy spectrum can be fitted using a function consisting of three distinct terms: a background term, an atomic cross-section term, and a fine structure term. The background term can be well modeled by one or more monotonically decaying power-law functions; therefore, it can be considered to have a known shape or behavior and, therefore, is not a meaningful quantity. Similarly, the atomic cross-section term can be well modeled by a known random or probabilistic function, up to a scale factor or amplitude, depending on which specific atoms are of interest to the modeler; therefore, the atomic cross-section term can also be considered to have a known shape or behavior and, therefore, is not a meaningful quantity. However, the fine structure term can be modeled as a spline of any suitable basis function (e.g., polynomial, rectangular, or triangular basis functions) and can be considered to be any compositional information remaining in the acquired or represented spectral image spectrum after accounting for the background and atomic cross-section terms. In other words, the fine structure term can be considered to have an unknown shape or behavior and, therefore, is a meaningful quantity. In other words, the fine structure term can be considered the most information-rich component in the energy spectrum of the spectral image, and this most information-rich component can be used to determine how much of a compound is depicted in the spectral image. Unfortunately, the present inventors have recognized that existing techniques result in such downstream measurements being overly sensitive or unstable (e.g., having large variability depending on the choice of energy window) and overly unreliable or imprecise (e.g., prone to misclassification or missegmentation).

[0054] The various embodiments described herein contribute to improving one or more of these technical issues. Specifically, as described above, the various embodiments described herein may involve fitting a function to the energy spectrum of a spectral image, where the function consists of a background term, an atomic cross-section term, and a fine structure term. However, rather than performing or executing such fitting in an unconstrained manner, the various embodiments described herein can implement or execute such fitting while imposing a zero-integral constraint on the fine structure term. That is, specific values ​​of any fitting coefficients included in the background term, the atomic cross-section term, and the fine structure term can be identified that not only minimize the error metric between the energy spectrum and the function, but also constrain the integral of the fine structure term with respect to the incident energy or energy loss to zero (e.g., within any appropriate critical threshold of zero). The present inventors have conducted various experiments to confirm or verify that such a zero-integral constraint results in less sensitive or unstable downstream analysis (e.g., less variation between different energy windows) and also makes such downstream analysis more accurate or reliable (e.g., fewer misclassified or missegmented pixels). Therefore, compared to the prior art, the various embodiments described herein can be considered to be better or improved techniques for fitting or identifying the fine structure of the energy spectrum of a spectral image. For at least these reasons, the various embodiments described herein can be viewed as concrete, tangible technical improvements in the field of spectral imaging.Thus, the various embodiments described herein certainly qualify as useful and practical applications of computers.

[0055] Furthermore, various embodiments described herein can control real-world tangible devices based on the disclosed teachings. For example, various embodiments described herein can electronically activate, deactivate, or otherwise drive real-world hardware (e.g., ion beam emitters, ion focusing lenses, and fluid valves / pumps) of real-world scientific instruments (e.g., electron energy loss microscopes), perform real-world analysis on real-world data collected by these real-world scientific instruments (e.g., calculate segmentation masks for energy loss spectrum images), and electronically present the results of such real-world analysis on a real-world computer screen (e.g., the calculated segmentation masks can be visually presented for easy viewing by a user or technician).

[0056] Figure 1 An exemplary non-limiting block diagram of a scientific instrument module 102 is shown, according to various embodiments described herein.

[0057] In various embodiments, the scientific instrument module 102 may be implemented by circuitry (e.g., including electrical or optical components) such as a programmed computing device. The logical components of the scientific instrument module 102 may be included in a single computing device, or may be distributed across multiple computing devices that communicate with each other as appropriate. Figure 25 and Figure 27Examples of computing devices that can implement the scientific instrument module 102, either alone or in combination, are discussed and reference is made to Figure 26 and Figure 28 Examples of systems or networks that interconnect computing devices in the scientific instrument module 102 may be implemented across one or more computing devices are discussed.

[0058] The scientific instrument module 102 may include a first logic component 104, a second logic component 106, and a third logic component 108. As used herein, the term "logic component" may include a device that performs a set of operations associated with logic. For example, any of the logic elements included in the scientific instrument module 102 may be implemented by one or more computing devices that are programmed with instructions to cause one or more processing devices of the computing devices to perform an associated set of operations. In certain embodiments, the logic elements may include one or more non-transitory computer-readable media having instructions thereon that, when executed by one or more processing devices of the one or more computing devices, cause the one or more computing devices to perform an associated set of operations. As used herein, the term "module" may refer to a collection of one or more logic elements that, together, perform a function associated with the module. Different logic elements in a module may take the same form or may take different forms. For example, some logic elements in a module may be implemented by a programmed general-purpose processing device, while other logic elements in the module may be implemented by an application-specific integrated circuit (ASIC). In another example, different logic elements in a module may be associated with different instruction sets executed by one or more processing devices. A module may omit one or more logic elements depicted in the associated figures; for example, when the module is to perform a subset of the operations discussed herein with reference to the module, the module may include a subset of the logic elements depicted in the associated figures.

[0059] In various embodiments, there may be a scientific instrument corresponding to the scientific instrument module 102. In various aspects, the scientific instrument can be any suitable computerized device that can electronically measure some scientifically relevant, clinically relevant or research-related characteristics, properties or attributes of an analytical sample (e.g., a collection of known or unknown mixtures, compounds or substances). As a non-limiting example, the scientific instrument can be a mass spectrometer operably coupled to a gas chromatograph or a liquid chromatograph. In this case, the scientific instrument can measure or determine the ion spectrum (e.g., relative ion abundance as a function of mass-to-charge ratio) of the analytical sample. As another non-limiting example, the scientific instrument can be a scanning electron microscope. In this case, the scientific instrument can measure or determine the surface morphology of the analytical sample. Another non-limiting example is that the scientific instrument can be a transmission electron microscope. In this case, the scientific instrument can measure or determine the internal structural details of the analytical sample. As a more general non-limiting example, the scientific instrument can be any suitable type of charged particle microscope (e.g., certain types of microscopes can use non-electron ion beams to collect images).

[0060] In various embodiments, the first logic component 104 can access a spectral image collected or otherwise generated by a scientific instrument. In various aspects, the spectral image can be any suitable pixel array, wherein each pixel can include its own energy spectrum. As a non-limiting example, the scientific instrument can be an electron energy loss microscope, and the spectral image can be an electron energy loss spectroscopy (EELS) image, wherein each pixel can contain a series of measurement counts or measurement intensity values ​​within a defined energy loss interval or band. In other words, each pixel can represent a corresponding two-dimensional position on the analysis sample, and each pixel can represent the number of electrons emitted by the scientific instrument, belonging to each defined energy loss interval or band, and striking the analysis sample at the corresponding two-dimensional position during a scan performed by the scientific instrument.

[0061] In various embodiments, the second logic component 106 can fit a function to the energy spectrum represented or conveyed by the spectral image in a pixel-by-pixel manner. In various aspects, the function may include multiple terms that are additively combined. In particular, the function may be the sum of a background term, an atomic cross-section term, and a fine structure term. In various cases, the background term may consist of a power-law decay function that is multiplicatively scaled according to its respective fitting coefficients. In various cases, the atomic cross-section term may consist of a random or probabilistic cross-section function that is multiplicatively scaled according to its respective fitting coefficients. In various aspects, the fine structure term may consist of a spline in which each component (e.g., a constant, a linear term, a quadratic term, a cubic term) is multiplicatively scaled according to its respective fitting coefficients, or it may consist of the sum of step functions that are multiplicatively scaled according to their respective fitting coefficients. In some cases, the atomic cross-section term and the fine structure term may be convolved with a low-loss portion of the spectral image energy spectrum. In various cases, as described herein, the integral of the fine structure term may be constrained to zero during fitting. In various aspects, such integral constraints can allow the ultimately determined, obtained, or fitted fine structure term to more correctly, accurately, or reliably represent any meaningful or desirable information contained or conveyed by the spectral image energy spectrum about the analyzed sample.

[0062] In various embodiments, the third logic component 108 can segment the spectral image by material, element, compound, or any other suitable physical or chemical property based on the final determined, derived, or fitted fine structure term (rather than based on a background term or an atomic cross-section term). In some aspects, such segmentation can be facilitated by applying any suitable unsupervised clustering technique (e.g., K-means clustering) to the final determined, derived, or fitted fine structure term for the spectral image pixels. In other aspects, such segmentation can be achieved by executing any suitable trained machine learning model (e.g., a deep learning neural network) on the final determined, derived, or fitted fine structure term for the spectral image pixels. In some cases, such segmentation can be performed by analyzing the scalar output of the final determined, derived, or fitted fine structure term. In other cases, such segmentation can also be performed by analyzing the fit coefficients of the final determined, derived, or fitted fine structure term. In either case, because the fine structure term is integrally constrained to zero, the segmentation may be more accurate or more reliable than otherwise.

[0063] Thus, the scientific instrument module 102 can facilitate spectral image analysis through integral constrained fitting.

[0064] Figure 2 is an exemplary, non-limiting flowchart of a computer-implemented method 200 according to various embodiments described herein. The operations of the computer-implemented method 200 may be used in any suitable environment to perform any suitable operations (e.g., may be performed by a computer program). Figure 1 、 Figure 24 、 Figure 25 、 Figure 26 、 Figure 27 and Figure 28 Executed by or used in conjunction with any of the various modules, computing devices, or graphical user interfaces described herein. Figure 2 In the illustrations, operations are each shown once in a particular order, but the operations may be reordered or repeated as needed and appropriate (e.g., different operations may be performed in parallel where appropriate).

[0065] In various aspects, act 202 may include performing a first operation of accessing, via a device operatively coupled to the processor, a spectral image of a sample acquired by a scientific instrument, wherein pixels of the spectral image respectively correspond to energy spectra. In various cases, first logic component 104 may perform or otherwise facilitate act 202.

[0066] In various cases, act 204 may include performing a second operation of fitting, by the device, a function to the energy spectrum in a pixel-by-pixel manner, the function comprising additively combined multinomials, wherein a first term of the multinomials represents a fine structure of the energy spectrum and an integral associated with the first term is constrained to be zero. In various cases, second logic component 106 may perform or otherwise facilitate act 204.

[0067] In various aspects, act 206 can include segmenting, by the device, the spectral image by material based on the first term. In various cases, third logic component 108 can perform or otherwise facilitate act 206.

[0068] Thus, the computer-implemented method 200 can facilitate spectral image analysis through integral constrained fitting.

[0069] Figure 3 A block diagram is shown of an exemplary non-limiting system 306 that can facilitate spectral image analysis via integral constrained fitting according to one or more embodiments described herein.

[0070] In various embodiments, there may be a scientific instrument 302. In various aspects, the scientific instrument 302 can be as described above. That is, the scientific instrument 302 can be any suitable computerized device capable of electronically measuring any suitable scientifically relevant, clinically relevant, or research-related characteristic, property, or property of any suitable analytical sample. Specifically, the scientific instrument 302 can be an electron energy loss microscope. In this case, the scientific instrument 302 can utilize its component hardware (e.g., electron source, anode, condenser, condenser aperture, scanning coil, objective lens, objective aperture, deflector, condenser, stigmator, electron detector, X-ray detector, and drivable sample stage) to electronically generate or acquire a spectral image 304 of any given analytical sample.

[0071] In various embodiments, the spectral image 304 can be in any suitable format, size, or dimension. More specifically, the spectral image 304 can be an array of pixels, where each pixel can contain a corresponding energy loss spectrum. Figure 4 Non-limiting aspects are described.

[0072] Figure 4 An exemplary non-limiting block diagram 400 of a spectral image 304 is shown, according to one or more embodiments described herein.

[0073] In various aspects, the spectral image 304 may include a plurality of pixels 402. In various cases, as shown, the plurality of pixels 402 may include s pixels, any suitable positive integer s: pixel 402(1) to pixel 402(s). In various cases, the plurality of pixels 402 may be arranged in any suitable layout or organizational format. As a non-limiting example, the plurality of pixels 402 may be arranged in a linear array (e.g., in an x×y array, where xy=s, any suitable positive integers x and y).

[0074] In various aspects, each of the plurality of pixels 402 can include a corresponding energy loss spectrum. Specifically, the scientific instrument 302 can be configured to scan a given analytical sample by irradiating the given analytical sample with an incident electron beam (or any other suitable charged particle beam). Thus, the given analytical sample may be struck or impacted by electrons (or other charged particles) from the incident beam. When the scientific instrument 302 emits an electron (or other charged particle), the electron (or other charged particle) may initially have a known amount of energy. Furthermore, when the electron (or other charged particle) strikes or impacts the given analytical sample, the electron (or other charged particle) may pass through the given analytical sample, thereby losing or dissipating some energy. The amount of energy lost or dissipated by the electron (or other charged particle) depends on the physical or chemical properties or characteristics of the given analytical sample (e.g., thickness, material composition, elemental concentration), regardless of whether the electron (or other charged particle) strikes, impacts, or passes through the given analytical sample. In various cases, the scientific instrument 302 can be configured to record the number and energy loss of incident electrons (or other charged particles) that strike, hit, or pass through an analysis sample. In particular, there can be a total of t disjoint (e.g., non-overlapping) energy loss intervals or bands, where t is any suitable positive integer (e.g., a first energy loss interval or band can represent energy loss from 0 eV to slightly below a first eV value; a second energy loss interval or band can represent energy loss from the first eV value to slightly below a second eV value greater than the first eV value; and a third energy loss interval or band can represent energy loss from the second eV value to slightly below a third eV value greater than the second eV value). In various cases, the scientific instrument 302 can be configured to count or measure how many incident electrons belonging to corresponding intervals or bands in the t energy loss intervals or bands strike, hit, or pass through corresponding physical locations on a given analysis sample.

[0075] As a non-limiting example, pixel 402(1) may include an energy loss spectrum 404(1). In various aspects, energy loss spectrum 404(1) may include energy loss counts for each of t energy loss intervals or bands. For example, energy loss spectrum 404(1) may include energy loss counts 404(1)(1), which may be a scalar whose magnitude represents or is otherwise proportional to the number of incident electrons (or other charged particles) belonging to the first energy loss interval or band that strike, impinge, or pass through a given analysis sample at any particular location represented or depicted by pixel 402(1). As another example, energy loss spectrum 404(1) may include energy loss counts 404(1)(t), which may be a scalar whose magnitude represents or is otherwise proportional to the number of incident electrons (or other charged particles) belonging to the tth energy loss interval or band that strike, impinge, or pass through a given analysis sample at any particular location represented or depicted by pixel 402(1). Thus, the energy loss spectrum 404(1) can be viewed as a sequence of interval count tuples of incident electrons (or other charged particles) striking, impinging on, or passing through the analysis sample at any location represented or depicted by pixel 402(1).

[0076] As another non-limiting example, pixel 402(s) may include an energy loss spectrum 404(s). In various aspects, energy loss spectrum 404(s) may include energy loss counts for each of t energy loss intervals or bands. For example, energy loss spectrum 404(s) may include energy loss counts 404(s)(1), which may be a scalar whose magnitude represents or is otherwise proportional to the number of incident electrons (or other charged particles) belonging to the first energy loss interval or band that strike, impinge, or pass through a given analysis sample at any particular location represented or depicted by pixel 402(s). As another example, energy loss spectrum 404(s) may include energy loss counts 404(s)(t), which may be a scalar whose magnitude represents or is otherwise proportional to the number of incident electrons (or other charged particles) belonging to the tth energy loss interval or band that strike, impinge, or pass through a given analysis sample at any particular location represented or depicted by pixel 402(s). Thus, the energy loss spectrum 404(s) can be viewed as a sequence of interval count tuples of incident electrons (or other charged particles) that strike, impinge on, or pass through the analysis sample at any location represented or depicted by pixel 402(s).

[0077] review Figure 3, system 306 can be electronically integrated with spectral image 304 or with scientific instrument 302 (e.g., via any suitable wired or wireless electronic connection). In various cases, it may be necessary to segment or otherwise analyze spectral image 304, for example, to determine how much of a chemical element or compound is located where in the analysis sample. In various cases, system 306 can facilitate such segmentation or analysis as described herein.

[0078] In various aspects, the system 306 may include a processor 308 (e.g., a computer processing unit, a microprocessor) and a non-transitory computer-readable memory 310 that is operatively or operably or communicatively connected or coupled to the processor 308. The non-transitory computer-readable memory 310 may store computer-executable instructions that, when executed by the processor 308, may cause the processor 308 or other components of the system 306 (e.g., an access component 312, a fitting component 314, an execution component 316) to perform one or more actions. In various embodiments, the non-transitory computer-readable memory 310 may store the computer-executable components (e.g., the access component 312, the fitting component 314, the execution component 316), and the processor 308 may execute the computer-executable components.

[0079] In various embodiments, system 306 may include an access component 312. In various aspects, access component 312 may electronically access scientific instrument 302. That is, access component 312 may electronically communicate with or otherwise electronically interact with scientific instrument 302 (e.g., send electronic instructions or commands to it, receive electronic data from it). Thus, access component 312 may be considered an agent or conduit through which other components of system 306 may interact with, communicate with, or otherwise operate on scientific instrument 302. In various cases, access component 312 may electronically access spectral image 304. That is, access component 312 may electronically receive, retrieve, or otherwise electronically obtain spectral image 304 from any suitable electronic source or database (not shown). As a non-limiting example, access component 312 may electronically receive, retrieve, or otherwise obtain spectral image 304 from scientific instrument 302. In any case, access component 312 may be considered an agent or conduit through which other components of system 306 may interact with, communicate with, or otherwise operate on spectral image 304. However, these are merely non-limiting examples. In other cases, access component 312 may be omitted, and any other component of system 306 may communicate or interact directly with scientific instrument 302 or spectral image 304 .

[0080] In various embodiments, the system 306 can include a fitting component 314. In various aspects, as described herein, the fitting component 314 can fit a polynomial function to the energy loss spectrum of the spectral image 304, where certain terms of the polynomial function can represent the fine structure of the energy loss spectrum of the spectral image 304 and can be integrally constrained to zero.

[0081] In various embodiments, system 306 can include an execution component 316. In various cases, execution component 316 can segment or otherwise analyze spectral image 304 based on the fine structure fitted by the fitting component, rather than based on the entirety of the energy loss spectrum of spectral image 304, as described herein.

[0082] Figure 5 A block diagram is shown of an exemplary non-limiting system including a fitting function that includes a background term, an atomic cross section term, and a fine structure term, and that can facilitate spectral image analysis through integral constrained fitting according to one or more embodiments described herein.

[0083] In various embodiments, the fitting component 314 can electronically fit a function 502 to the energy loss spectrum of the spectral image 304 in a pixel-by-pixel manner. In various aspects, the function 502 can include a background term 504, an atomic cross section term 506, and a fine structure term 508. Figures 6 to 13 Various non-limiting aspects are described.

[0084] Figure 6-13 An exemplary non-limiting block diagram of function 502 and its components is shown, according to one or more embodiments described herein.

[0085] First, consider Figure 6 In various embodiments, function 502 can be viewed as a function that maps real-valued scalars to other real-valued scalars (e.g., it can be viewed as a function from In various aspects, energy loss (e.g., measured in eV) can be considered or treated as the independent variable of function 502. In various cases, count (e.g., measured in the number of incident electrons or other charged particles) or intensity (e.g., measured in arbitrary units) can be considered or treated as the dependent variable of function 502. In various cases, function 502 can be an additive combination (e.g., a sum) of background term 504, atomic cross section term 506, and fine structure term 508.

[0086] In various aspects, the background term 504 can include one or more power-law functions 602, which can utilize one or more fitting coefficients 604. In fact, when the edges (e.g., K-edges, L-edges) that it depicts are not considered, the energy loss spectrum can be expected to decay monotonically or exponentially with increasing energy loss, and this decay can be modeled or represented by a power-law function with a negative exponent. As a non-limiting example, the background term 504 can be represented as follows:

[0087]

[0088] Where E may represent energy loss, B(E) may represent the background term 504, k may represent the summation exponent, l may represent the total cardinality of one or more power law functions 602, and r k can represent the kth index, may represent the kth of one or more power law functions 602, and C back_k may represent the kth of one or more fitting coefficients 604. Note that in some cases, r k Can be known or selected ab initio or a priori constants. For example, the following situation may occur: l = 4 and r1 = 1, r2 = 2.33, r3 = 3.67 and r4 = 5. In this case, one or more fitting coefficients 604 (e.g., C back_k ) can be viewed as multiplicatively scaling the corresponding function in the one or more power law functions 602. However, in other cases, r k Instead, they may be considered as additional coefficients to the one or more fitting coefficients 604. In this case, some of the one or more fitting coefficients 604 (e.g., C back_k ) can be considered as multiplicatively scaling the corresponding function in the one or more power law functions 602, while the remaining coefficients in the one or more fitting coefficients 604 (e.g., r k ) can be considered as the exponent of each of the one or more power-law functions 602. In various cases, any suitable inequality constraints can be imposed on the background term 504 to ensure the non-negativity, monotonically decreasing, and convexity of the background term 504. In any case, the background term 504 can be considered as a meaningless or uninformative component of the function 502 because the background term 504 already has a known format or shape (e.g., a negative power-law function).

[0089] In various aspects, the atomic cross-section term 506 may include one or more material-based probability functions 606, which may utilize one or more fitting coefficients 608. In various cases, the one or more material-based probability functions 606 may be any suitable random functions that describe the probabilities or likelihoods of various atomic events (e.g., scattering, absorption, emission) occurring when an incident electron (or other charged particle) beam collides with one or more given or respective atoms. For example, the one or more material-based probability functions 606 may include or otherwise be based on any suitable hydrogen wave function or any suitable Hartree-Slater central field function. In other cases, the one or more material-based probability functions 606 may be derived from the generalized oscillator strength, the collection angle, and the accelerating voltage. As a non-limiting example, the atomic cross-section term 506 (at least with respect to the inner shell of a given atom) may be expressed as follows:

[0090]

[0091] where σ atomic (E) may represent the atomic cross-section term 506, k may represent the summation index, n may represent the total cardinality of one or more material-based probability functions 606 (e.g., n may represent the total number of different types of atoms that are meaningful), C atomic_k may represent the kth of one or more fitting coefficients 608, where may represent the kth of one or more material-based probability functions 606. In various cases, a0 may represent the Bohr radius, β may represent the collection angle, R may represent the Rydberg energy, T may represent the effective incident energy, θ may represent the integration variable, and θ E (E) can represent the characteristic angle. In each case, also, Can represent momentum And the generalized oscillator strength of the inner electron shell of the kth atom can be expressed as follows:

[0092]

[0093] where Z inner_k It can represent the cardinality of the free electrons at rest in the electron shell of the kth atom, where |i> can represent the initial state, where |p> can represent the final state, where E p can represent the energy transfer between |i> and |p>, where Σ p can be expressed as the sum of all desired final states |p>, where l can be the summation index, where can be the position of the lth electron in the inner shell of the kth atom, where δ(*) can represent the Dirac delta function. For small collection angles, the generalized oscillator strength can be approximated as a constant and can therefore be derived from the integral of θ. This may produce the following results:

[0094]

[0095] Note that the generalized oscillator strength can be approximated by its value at the origin, which is why Can be replaced by Additionally, note that one or more of the fitting coefficients 608 (e.g., C atomic_k ) can be considered as multiplicatively scaling the corresponding function in the one or more material-based probability functions 606. In various cases, any appropriate inequality constraints can be imposed on the atomic cross section term 506 to ensure that the one or more fitting coefficients 608 are non-negative. In any case, like the background term 504, the atomic cross section term 506 can be considered as a less meaningful or less informative component of the function 502 because, for any given material of interest, the atomic cross section term 506 already has a well-known format or shape (however, the one or more fitting coefficients 608 can be considered to be at least partially meaningful or desirable once fitted because they can represent elemental abundances).

[0096] In various aspects, the fine structure term 508 can be a spline including one or more basis functions 610, which can utilize one or more fitting coefficients 612. In various cases, the one or more basis functions 610 can be any suitable mathematical function, and the one or more fitting coefficients 612 can multiplicatively scale a corresponding one of the basis functions 610, or a portion thereof.

[0097] As a non-limiting example, one or more basis functions 610 may take the form of basis splines (B-splines) of any suitable order, defined as piecewise polynomials over various energy loss intervals. In this case, the fine structure term 508 may be expressed as follows:

[0098]

[0099] Where F(E) can represent the fine structure term 508; E∈[E0,E max ]with E0 representing the starting point of the energy window in which the fine structure term 508 is defined, and E max represents its end (for example, E0 can be regarded as the starting energy loss of the K-edge, as shown in a given energy loss spectrum); E h >E h-1 For all positive integers 0 <h≤h max ;h maxcan be considered as the total number of nodes, E h Indicates that a spline is defined on the seam; B h can represent the hth B-spline; and C fine_h can represent the hth of one or more fitting coefficients 612. In this case, any suitable equality constraints may be present to ensure the continuity of the B-spline (up to any suitable number of derivatives) (e.g., for any suitable positive integer n of degree n B-spline, it is guaranteed that the intersection between any adjacent intervals of fine structure terms 508 has matching values ​​and matching derivatives up to the (m-1)th derivative). In some cases, the spacing of the B-spline can be linear. That is, the start and end points of such intervals can be linear or equidistant, so that all such intervals have equal length. However, in other cases, the spacing of the fine structure terms 508 can have any other suitable spacing, such as quadratic spacing. In the case of quadratic spacing, the square roots of the start and end points of such intervals can be linear or equidistant, so that the intervals become progressively longer. It should be understood that the one or more basis functions 610 can take the form of B-splines of any suitable order. As a non-limiting example, each of the one or more basis functions 610 can be a quadratic B-spline. However, this is merely a non-limiting example. In other cases, each of the one or more basis functions 610 may take the form of any suitable higher order B-spline (eg, cubic, quartic, quintic) or any suitable lower order B-spline (eg, linear).

[0100] While the various embodiments described above refer to the fine structure term 508 being a spline, it should be understood that these are merely non-limiting examples. In various embodiments, the fine structure term 508 (and the resulting one or more basis functions 610) may take or exhibit any other suitable form.

[0101] As a non-limiting example, one or more basis functions 610 may instead take the form of rectangular functions, each defined within a corresponding energy loss interval. In this case, the fine structure term 508 may be represented as follows:

[0102]

[0103] Where H(·) can represent the Heaviside step function, E h =E h-1 +ΔE may be a node as described above, where E0 may be the starting point of the K-edge energy loss shown in a given energy loss spectrum, ΔE may represent any suitable energy step, and C fine_h may represent the hth of one or more fitting coefficients 612. Note that the result h maxΔE can be considered as the energy window or energy width of the fine structure term 508. As another non-limiting example, one or more basis functions 610 can instead take the form of trigonometric functions. As yet another non-limiting example, one or more basis functions 610 can instead take the form of trigonometric functions (e.g., cosine functions oscillating at different frequencies, such as used in a cosine transform).

[0104] Regardless of the specific mathematical form that the one or more basis functions 610 take or exhibit, the fine structure term 508 can be viewed as capturing any energy loss spectroscopy activity or behavior not collectively captured by the background term 504 and the atomic cross section term 506 .

[0105] In some cases, function 502 may be an additive combination of background term 504, atomic cross section term 506, and fine structure term 508. That is, the following may occur:

[0106] I(E)=B(E)+σ atomic (E)+F(E)

[0107] where I(E) may represent function 502. However, in other cases, the atomic cross section term 506 and the fine structure term 508 may be convolved with the low-loss region of any given energy loss spectrum prior to such additive combination. That is, the following may occur:

[0108] I(E)=B(E)+L(E)*[σ atomic (E)+F(E)]

[0109] Wherein L(E) can represent a low-loss region of a given energy-loss spectrum, and (*) can represent a mathematical convolution operation. In other words, a given energy-loss spectrum can be considered to have a starting energy loss at the K-edge, and the portion of the given energy-loss spectrum extending from 0 eV energy loss to the starting energy loss value can be considered to be L. However, this is merely a non-limiting example. In various cases, L does not have to extend to the starting point of the K-edge (e.g., L can stop before the K-edge or at any suitable energy loss value before it). In various cases, it can be considered that convolving the atomic cross-section term 506 and the fine structure term 508 (but not the background term 504) with this low-loss region helps to reduce the occurrence of unnecessary artifacts due to irregularities in the sample thickness.

[0110] In any case, unlike the background term 504 and the atomic cross section term 506, the fine structure term 508 can be viewed as representing or containing the most informative or meaningful portion of any given energy loss spectrum (although elemental abundances are sometimes considered meaningful but can be inferred from the atomic cross section term 506).

[0111] In various aspects, given an energy loss spectrum for any pixel of the spectral image 304, the fitting component 314 can electronically fit the function 502 to the energy loss spectrum. In other words, the fitting component 314 can electronically calculate, electronically determine, or otherwise electronically identify any values ​​of the one or more fitting coefficients 604, the one or more fitting coefficients 608, and the one or more fitting coefficients 612 that closely match or resemble the energy loss spectrum for the given pixel. In other words, the fitting component 314 can electronically calculate or approximate any values ​​of the one or more fitting coefficients 604, the one or more fitting coefficients 608, and the one or more fitting coefficients 612 that minimize the error between the function 502 and the energy loss spectrum (e.g., to below any suitable threshold error value). In various cases, the fitting component 314 can accomplish this by implementing any suitable curve fitting technique. As a non-limiting example, fitting component 314 can utilize a least squares (LSS) technique to identify which values ​​of one or more fitting coefficients 604, one or more fitting coefficients 608, and one or more fitting coefficients 612 best match or fit function 502 to the energy loss spectrum. In various cases, fitting component 314 can utilize any suitable software package or platform (e.g., quadratic programming such as the Quadprog Python package) to facilitate such fitting.

[0112] In various embodiments, the fitting component 314 can impose a zero integral constraint on the fine structure term 508 during such fitting. That is, the fitting component 314 can electronically calculate, determine, or otherwise identify any values ​​of the one or more fitting coefficients 604, the one or more fitting coefficients 608, and the one or more fitting coefficients 612 that not only closely match or closely resemble the energy loss spectrum of the given pixel, but also cause the integral associated with the fine structure term 508 to be as close to zero as possible (e.g., within any suitable critical threshold of zero).

[0113] In some cases, such an integral may be applied solely to the fine structure term 508. That is, the fitting component 314 may apply the following equation when fitting the function 502 to the energy loss spectrum of a given pixel:

[0114]

[0115] Among them E max can be any energy loss value high enough to include the desired edge present in the energy loss spectrum for a given pixel (e.g., E max ≥1300eV). Note that if another edge in the energy loss spectrum for a given pixel follows any desired edge, then E maxIt can be chosen to be large enough to encompass the desired edge while being smaller than the starting energy loss of another edge.

[0116] However, in other cases, such an integral may be applied to some constant multiple of the fine structure term 508. That is, the fitting component 314 may apply the following equation when fitting the function 502 to the energy loss spectrum of a given pixel:

[0117]

[0118] where C may represent any suitable constant.

[0119] However, in other cases, such integration can be applied to any suitable complex function including the fine structure term 508. That is, the fitting component 314 can apply the following equation when fitting the function 502 to the energy loss spectrum of a given pixel:

[0120]

[0121] where D(E) can represent any suitable function of E.

[0122] Please note that in some cases, E max In any of the above integral constraints, ∞ can be replaced by ∞, and E0 can be replaced by 0 in any of the above integral constraints.

[0123] As a specific, non-limiting example of how the integral constraint may be applied, consider the following discussion. Bethe's summation rule can be thought of as stating that when a system receives momentum When , the sum of all the energies transferred in the internal excitation modes can be equal to the energy transferred to the stationary Z free electron. That is,

[0124]

[0125] in It can be considered as the generalized oscillator strength of all electron shells. In various cases, only the inner electrons may be of interest. Therefore, it can be expressed as follows:

[0126]

[0127] in It can represent the generalized oscillator strength of the inner electron shell, and Z inner can be the number of free electrons in the inner electron shell. For example, for the K shell, Z inner = 2. Now, as mentioned above, the atomic cross section of the inner electron shell can be expressed as follows:

[0128]

[0129] a0 is the Bohr radius, R is the Rydberg energy, β is the collection angle, T is the effective incident energy, and θ E (E) is the characteristic angle. Except for the generalized oscillator strength, moving all the factors dependent on E to the left and combining with the energy loss, the following result can be obtained:

[0130]

[0131] Since is a constant as shown above, and also since is also a constant, therefore is also a constant. This means that if one cross-section is known to be accurate, then all other measured cross-sections should have the same value as this cross-section. Now, in all aspects, the cross-section of an atom can be used to calculate a free atom, while a more general cross-section can be used to calculate an atom that is not free due to environmental interactions. In various cases, the objective or purpose of fitting can be to collect or include such environmental interactions through the fine structure term 508. Now, representing the general cross-section σ(E) (not necessarily of an atom) as the sum of the atomic cross-sections of the corresponding elements (e.g., σ A (E)) and the fine structure (e.g., σ(E) = σ A (E) + F(E)), and bearing in mind the above insights, the corresponding integral equality can be obtained. The equations for these corresponding integrals are as follows:

[0132]

[0133] Subtracting from each side gives the following result:

[0134]

[0135] In various cases, the fine structure term 508 can be defined as the energy window E ∈ [E0, E max , otherwise it can be zero (e.g., when E < E0 before the desired edge or E > E max after the desired edge, F(E) = 0). Therefore, the focus can be placed on the energy window. That is:

[0136]

[0137] In other words, the following situation occurs: where In any case, this expression can be viewed as a constraint on the integral associated with or otherwise related to the fine structure term 508 (e.g., on the integral of F(E) with respect to E). In various cases, the fitting component 314 can impose this integral constraint when fitting the function 502 to the energy loss spectrum of the spectral image 304. In other words, the fitting component 314 can identify which specific values ​​of the one or more fitting coefficients 604, the one or more fitting coefficients 608, and the one or more fitting coefficients 612 will not only minimize the error (e.g., LSS) between the function 502 and any given energy loss spectrum for any given pixel, but also that the expression falls within any suitable critical threshold of 0. In other words, during such a fit, the fine structure term 508 may be integrally constrained to zero.

[0138] In various cases, the above zero-integral constraint formula can be considered to apply to incident electrons described as plane waves. In various aspects, similar integral constraints can be derived for incident electrons of any suitable type or description. As a non-limiting example, assume that a converging incident electron beam is used. In this case, the following zero-integral constraint can be derived:

[0139]

[0140] Where Q(θ) can be considered as a correction factor that takes into account the convergence angle of the incident electron beam. Specifically, Q(θ) can be obtained by the following formula:

[0141]

[0142] in in Where α is the convergence angle or convergence half-angle, and β is the collection angle or collection half-angle. For any other type of incident electron beam, any other derivation of this zero-integral constraint can be appropriately implemented.

[0143] In any case, function 502 can be an additive combination of background term 504, atomic cross section term 506, and fine structure term 508, and fitting component 314 can electronically fit a corresponding version or instance of function 502 to the energy spectrum of each pixel in spectral image 304. In any case, fitting component 314 can derive a total of s different or unique fitted versions of function 502 and each pixel of spectral image 304. Figure 7-13 Various non-limiting details regarding such fitting are shown.

[0144] In all respects, as shown in the figure, Figure 7A curve 702 is depicted. In various cases, curve 702 can be viewed as a graphical representation of an energy loss spectrum measured or recorded for any given pixel of spectral image 304. As shown, the independent variable of curve 702 (e.g., displayed on the abscissa axis) can be energy loss, and the dependent variable of curve 702 (e.g., displayed on the ordinate axis) can be counts or intensity. In various cases, as shown, a K-edge appears in curve 702 starting at or near energy loss value E0. In various aspects, it can be desirable to determine which specific values ​​of one or more fit coefficients 604, one or more fit coefficients 608, and one or more fit coefficients 612 result in function 502 matching or otherwise fitting to curve 702.

[0145] Now, Figure 8 Curve 802 is depicted. In various aspects, curve 802 can be viewed as a graphical representation of background term 504 after fitting function 502 to curve 702 as described herein. As can be seen, curve 802 decays monotonically and, therefore, explains or accounts for certain portions of curve 702, but curve 802 does not account for the K-edge of curve 702.

[0146] Next, Figure 9 Curve 902 is depicted. In various cases, curve 902 can be viewed as a graphical representation of atomic cross section 506 after fitting function 502 to curve 702 as described herein. As can be seen, curve 902 can exhibit a sharp increase consistent with the K-edge of curve 702, but curve 902 does not take into account the most meaningful or informative activity or behavior of the K-edge of curve 702.

[0147] at last, Figure 10 Curve 1002 is depicted. In various aspects, curve 1002 can be viewed as a graphical representation of fine structure term 508 after fitting function 502 to curve 702 as described herein. As can be seen, curve 1002 can be viewed as capturing or accounting for the most meaningful or informative activities or behaviors of the K-edges of curve 702. In other words, curves 802 and 902 can be viewed as capturing a known or less informative portion of curve 702, while curve 1002 can be viewed as capturing the remaining portion of curve 702.

[0148] picture Figures 7 to 10 Reproductions are shown to help illustrate the various embodiments described herein. However, Figure 11-13 The experimental data of the simulated world and the real world obtained by the present inventors are depicted.

[0149] in particular, Figure 11Curve 1102 and curve 1104 are shown. Curve 1102 depicts a computer simulated energy loss spectrum. Curve 1104 depicts the fitted, final, or resulting form of fine structure term 508 after fitting it to curve 1102 as described herein.

[0150] Likewise, Figure 12 Curve 1202, curve 1204, curve 1206, and curve 1208 are shown. Curve 1202 depicts a real-world energy loss spectrum recorded by a real-world electron energy loss microscope. Curve 1204 depicts a simulated version of background term 504. Curve 1206 depicts a simulated version of atomic cross section term 506. Curve 1208 depicts a simulated version of fine structure term 508.

[0151] As described herein, the fine structure term 508 can be integrally constrained to zero. In various aspects, such integral constraints can result in the fine structure term 508 being at least partially negative (e.g., less than zero) while at least partially positive (e.g., greater than zero). Without such integral constraints, the fine structure term 508 may instead be entirely positive. The foregoing is presented in a non-limiting manner. Figure 13 middle.

[0152] in particular, Figure 13 Graph 1302 and graph 1304 are included. Graph 1302 now includes curve 1306, curve 1308, curve 1310, and curve 1312. Curve 1306 depicts a real-world energy loss spectrum recorded by a real-world electron energy loss microscope. In other words, curve 1306 can be considered to show the silicon K-edge. Curve 1308 depicts the fitted, final, or resulting form of the background term 504 after being fitted to curve 1306 as described herein. Curve 1310 depicts the fitted, final, or resulting form of the atomic cross-section term 506 (silicon atoms) after being fitted to curve 1306 as described herein. Curve 1312 depicts the fitted, final, or resulting form of the fine structure term 508 after being fitted to curve 1306 (e.g., a spline of a rectangular function). However, curve 1312 is generated without the zero integral constraint described herein. As shown, all portions of curve 1312 are greater than or equal to zero. In other words, no portion of curve 1312 is negative.

[0153] Now, graph 1304 includes curve 1306, curve 1314, curve 1316, and curve 1318. Curve 1314 depicts another fitted, final, or resulting form of background term 504 after being fitted to curve 1306 as described herein. Curve 1316 depicts another fitted, final, or resulting form of atomic cross-section term 506 (silicon atoms) after being fitted to curve 1306 as described herein. Curve 1318 depicts another fitted, final, or resulting form of fine structure term 508 after being fitted to curve 1306 (e.g., a spline of a rectangular function). However, curve 1318 is generated without the zero integral constraint described herein. As shown, the implementation of this zero integral constraint results in the heights of curves 1314 and 1316 being different from the heights of curves 1308 and 1310, and the implementation of this zero integral constraint also results in at least a portion of curve 1318 being less than zero. This helps demonstrate that implementing the zero integral constraint as described herein can significantly change any final, resulting, or fitted version of the obtained fine structure term 508.

[0154] It should be understood that Figure 7-13 These are non-limiting examples only and are not necessarily drawn to scale. In some cases, function 502 may be entirely or predominantly positive, or entirely or predominantly negative, without the integration constraints described herein. In any case, when the integration constraints described herein are implemented, fine structure term 508 may be significantly different (in fact, significantly more accurate) than when they are not implemented.

[0155] In any case, the fitting component 314 can generate a total of s functions 502 and a different or unique fitted version for each pixel of the spectral image 304 .

[0156] Figure 14 A block diagram is shown of an exemplary non-limiting system including a segmentation mask that can facilitate spectral image analysis via integral constrained fitting according to one or more embodiments described herein.

[0157] In various embodiments, the execution component 316 can electronically generate the segmentation mask 1402 based on a fitted pixel-by-pixel version of the fine structure term 508 rather than based on the entirety of the fitted pixel-by-pixel version of the function 502 . Figure 15 Non-limiting aspects are described.

[0158] Figure 15 An exemplary, non-limiting block diagram illustrating how a segmentation mask 1402 may be generated according to one or more embodiments described herein is shown.

[0159] In various aspects, as described above, fitting component 314 can generate a respective fitted version of function 502 for each pixel of spectral image 304. In various cases, each fitted version of function 502 can be considered to include a respective fitted version of fine structure term 508. In various cases, the respective fitted version of fine structure term 508 can be referred to as a plurality of fitted fine structure terms 1502.

[0160] Specifically, because the spectral image 304 may include s pixels, the plurality of fitted fine structure terms 1502 may include s fitted fine structure terms: fitted fine structure term 1502(1) through fitted fine structure term 1502(s). In various aspects, the fitted fine structure term 1502(1) may be considered to be any version of the fine structure term 508 that the fitting component 314 has calculated for the pixel 402(1). In other words, the fitting component 314 may calculate a first version of the background term 504 (e.g., a first combination of specific values ​​of one or more fitting coefficients 604), a first version of the atomic cross section term 506 (e.g., a first combination of specific values ​​of one or more fitting coefficients 608), and a first version of the fine structure term 508 (e.g., a first combination of specific values ​​of one or more fitting coefficients 612) based on the energy loss spectrum 404(1) of the pixel 402(1). In various cases, the first version of the fine structure term 508 may be referred to as the fitted fine structure term 1502(1). Thus, the fitted fine structure term 1502(1) can be considered to convey any meaningful or informative electronic activity present in the energy loss spectrum 404(1). Similarly, the fitted fine structure term 1502(s) can be considered to be any version of the fine structure term 508 that the fitting component 314 has calculated for the pixel 402(s). That is, the fitting component 314 can calculate the sth version of the background term 504 (e.g., the sth combination of specific values ​​of one or more fitting coefficients 604), the sth version of the atomic cross section term 506 (e.g., the sth combination of specific values ​​of one or more fitting coefficients 608), and the sth version of the fine structure term 508 (e.g., the sth combination of specific values ​​of one or more fitting coefficients 612) based on the energy loss spectrum 404(s) of the pixel 402(s). In various cases, the sth version of the fine structure term 508 can be referred to as the fitted fine structure term 1502(s). Thus, the fitted fine structure term 1502(s) can be considered to convey any meaningful or informative electronic activity present in the energy loss spectrum 404(s). ).

[0161] In various aspects, the execution component 316 can electronically generate the segmentation mask 1402 based on the plurality of fitted fine structure terms 1502 .

[0162] As a non-limiting example, the execution component 316 can apply any suitable unsupervised clustering technique (e.g., K-means clustering in combination with principal component analysis (PCA)) to the plurality of fitted fine structure terms 1502. It should be understood that any data formatting or pre-processing steps can be performed before or during such clustering (e.g., normalizing the amplitude and energy axes of the plurality of fitted fine structure terms 1502; centering the plurality of fitted fine structure terms 1502 by subtracting the mean count or mean intensity). In any case, such clustering can allow the execution component 316 to separate the plurality of fitted fine structure terms 1502, thereby dividing the plurality of pixels 402 into two or more clusters, wherein the fitted fine structure terms of any given cluster can be considered to be more similar in value to each other than to the fitted fine structure terms of some different cluster. Because the fitted fine structure term for any given pixel can be considered to convey meaningful or informative electronic behavior for any portion of the analysis sample represented by that pixel, any two pixels in the same cluster can be considered to represent portions of the analysis sample that exhibit the same or similar electronic behavior and, therefore, have the same or similar material composition. Conversely, any two pixels in different clusters can be considered to represent portions of the analysis sample that exhibit different electronic behavior and, therefore, have different material compositions. In various aspects, each of the two or more clusters identified by execution component 316 can be assigned a unique label (e.g., Cluster 1, Cluster 2, Cluster 3), and segmentation mask 1402 can be a matrix indicating to which cluster the corresponding pixel of spectral image 304 is assigned. For example, assuming again that the plurality of pixels 402 are arranged in an x×y linear array, where xy=s. In this case, segmentation mask 1402 can be an x×y array, where, for row a and column b, the (a, b)th element of segmentation mask 1402 can represent the cluster label assigned to the (a, b)th pixel of the plurality of pixels 402. Therefore, segmentation mask 1402 can be viewed as a visual representation of which pixels in spectral image 304 are determined to belong to the same or different clusters, and thus to be composed of the same or different substances or concentrations of substances. In fact, the fitted fine structure term for any given pixel can be viewed as representing the electronic environment surrounding the desired element at any location represented by that pixel. In other words, the fitted fine structure can indicate which compound the desired element belongs to at the location represented by that pixel.

[0163] As another non-limiting example, rather than using unsupervised clustering, the execution component 316 can execute any suitable machine learning model that has been trained or configured to perform segmentation on the plurality of fitted fine structure terms 1502. Such execution can cause the machine learning model to generate a segmentation mask 1402 as an output.

[0164] In particular, a machine learning model can exhibit any suitable internal architecture, such as a deep learning neural network internal architecture. Indeed, a machine learning model may have an input layer, one or more hidden layers, and an output layer. In various cases, any of these layers can be coupled together via any suitable inter-neuron or inter-layer connections, such as forward connections, skip connections, or recurrent connections. Furthermore, in various cases, any of these layers can be any suitable type of neural network layer having any suitable learnable or trainable internal parameters. For example, any of the input layer, one or more hidden layers, or the output layer can be a convolutional layer, and the learnable or trainable parameters of the convolutional layer can be convolution kernels. As another example, any of the input layer, one or more hidden layers, or the output layer can be a dense layer, and its learnable or trainable parameters can be weight matrices or bias values. As yet another example, any of the input layer, one or more hidden layers, or the output layer can be a batch normalization layer, and its learnable or trainable parameters can be shift factors or scaling factors. As another example, any such input layer, one or more hidden layers, or output layer may be a long short-term memory (LSTM) layer, whose learnable or trainable parameters may be an input state weight matrix or a hidden state weight matrix. Furthermore, in various cases, any of such layers may be any suitable type of neural network layer with any suitable fixed or non-trainable internal parameters. For example, any of such input layer, one or more hidden layers, or output layer may be a nonlinear layer, a padding layer, a pooling layer, or a cascade layer.

[0165] Regardless of its specific internal architecture, the machine learning model can be trained (e.g., in a supervised manner using true segmentation masks, in an unsupervised manner without using true segmentation masks, or in a reinforced learning manner using any suitable reward or penalty strategy) to receive as input the fitted fine structure terms and generate as output a segmentation mask based on these fitted fine structure terms. Thus, the execution component 316 can execute the machine learning model on the plurality of fitted fine structure terms 1502, and such execution can produce the segmentation mask 1402. More specifically, the execution component 316 can feed the plurality of fitted fine structure terms 1502 to an input layer of the machine learning model, the plurality of fitted fine structure terms 1502 can complete a forward pass through one or more hidden layers of the machine learning model, and the output layer of the machine learning model can compute the segmentation mask 1402 based on the activation maps or feature maps generated by the one or more hidden layers.

[0166] In any case, the segmentation mask 1402 can indicate which pixels of the spectral image 304 belong to which of two or more defined classes, where these defined classes can be considered to represent different or unique material compositions.

[0167] In some embodiments, the execution component 316 can generate the segmentation mask 1402 based on the plurality of fitted fine structure terms 1502 as a whole. However, in other embodiments, the execution component 316 can generate the segmentation mask 1402 based only on the fit coefficients of the plurality of fitted fine structure terms 1502. That is, each of the plurality of fitted fine structure terms 1502 can be considered to have a corresponding value of one or more fit coefficients 612, and the execution component 316 can perform clustering or machine learning model execution on the corresponding values ​​of the one or more fit coefficients 612 (e.g., in this case, the remaining portion of each of the plurality of fitted fine structure terms 1502 can be ignored or discarded). The inventors have discovered that by clustering or otherwise analyzing the fit coefficients of the plurality of fitted fine structure terms 1502, acceptable segmentation accuracy can be achieved in a shorter time and with less computational resource consumption.

[0168] In various aspects, the execution component 316 can electronically transmit the segmentation mask 1402 to any suitable computing device. In various cases, the execution component 316 can electronically render or display the segmentation mask 1402 on any suitable computer screen.

[0169] Although the disclosure herein primarily describes execution component 316 as generating a segmentation mask 1402 for spectral image 304, this is provided as a non-limiting example for ease of explanation. In various other embodiments, execution component 316 may perform any other suitable downstream analysis on spectral image 304, and such analysis may be based on the plurality of fitted fine structure terms 1502 (or their fitted coefficients, or any subset of such fitted coefficients) rather than the raw energy spectrum of spectral image 304. As a non-limiting example, execution component 316 may classify spectral image 304 based on the plurality of fitted fine structure terms 1502. As another non-limiting example, execution component 316 may explicitly calculate any suitable material composition of the analysis sample depicted by spectral image 304 based on the plurality of fitted fine structure terms 1502. Various other non-limiting examples of such downstream analysis may include: phase analysis; mobility mapping; or oxidation state mapping.

[0170] In order to demonstrate the various technical advantages of the various embodiments described herein, the present inventors conducted various experiments, some of which are shown in Figures 16 to 23 Shown in.

[0171] Figure 16A block diagram of sample 1600 analyzed according to various embodiments described herein is depicted. Sample 1600 comprises four regions: region 1602, region 1604, region 1606, and region 1608. Region 1602 is composed of Al4O6. Region 1604 is composed of Cu4O2. Region 1606 is composed of Si2O4. Region 1608 is composed of Sr1Ti1O3. In addition, each of the four regions has a continuously varying thickness, increasing from 0.2 times the mean free path to 1.5 times in 25 steps. A spectral image of sample 1600 was simulated, and the fine structure was fitted to the energy loss spectrum of the spectral image as described herein.

[0172] Figure 17 Shown is a segmentation mask 1700 obtained from fitting the fine structure as described herein. In particular, the segmentation mask 1700 is obtained by K-means clustering. Figure 17 Different shades of color can be considered to represent different material compositions. As shown, segmentation mask 1700 shows with very high accuracy which parts of sample 1600 are composed of the same material. In fact, only two pixels (for example, one in area 1602 and the other in area 1606) are misclassified or incorrectly segmented.

[0173] Figure 18 A scatter plot 1800 generated by PCA based on the data used for the K-means clustering described above is shown. As shown, the obtained fitted fine structure is neatly divided into four distinct tight clusters (e.g., one cluster for each substance).

[0174] Now, Figure 19 The segmentation mask 1900 obtained from only the final or resulting fitting coefficients of those fitting fine structures is shown. As described above, the segmentation mask 1900 is obtained by K-means clustering, Figure 19 The different shades of color in the image can represent different material components. As shown in the figure, the segmentation mask 1900 shows which parts of the sample 1600 are composed of the same material as each other, with a slightly lower accuracy, but still acceptable. Figure 17 In comparison, there are more misclassified or missegmented pixels, but the level of segmentation accuracy shown is still sufficient.

[0175] Figure 20 A scatter plot 2000 is shown, generated by PCA based on the data used for the above K-means clustering. As shown, the final or resulting fitting coefficients obtained for the fitted fine structure are still neatly divided into four different clusters (e.g., one cluster for each substance), although Figure 18Compared to the ensemble, these clusters are slightly less compact. Note that clustering only the coefficients of the fitted fine structure terms requires less time and computational resources (e.g., memory, processing power) than clustering all fitted fine structure terms. However, as these experimental results show, acceptable segmentation accuracy can still be achieved despite the reduction in time and computational resources.

[0176] Now, Figure 21 1 shows a segmentation mask 2100 obtained from a spectral image of sample 1600 by prior art techniques. In particular, such prior art techniques do not involve the integral-constrained fine structure fitting described herein. As described above, the segmentation mask 2100 is obtained by K-means clustering. Figure 21 Different shades of color in the image may represent different material compositions. As can be seen, segmentation mask 2100 is highly inaccurate (e.g., it does not reliably or correctly indicate which parts of sample 1600 are composed of the same material as one another). In fact, segmentation mask 2100 demonstrates that prior art techniques are significantly affected or otherwise biased by variations in material composition and thickness across sample 1600.

[0177] Figure 22 A scatter plot 2200 is shown, generated by PCA based on the data used for the K-means clustering described above. As shown, the fine structure of the fit obtained by the prior art does not neatly or tightly separate into four distinct clusters. This again illustrates the inability of the prior art to handle the compositional and geometric diversity of sample 1600.

[0178] Figure 23 Shown are graphs 2302, 2304, and 2306 obtained during various additional experiments performed by the inventors.

[0179] Specifically, a 5000 energy loss spectrum of the silicon K-edge in an amorphous Si3N4 sample was obtained while keeping the illumination area unchanged. A parallel electron beam was used to maximize the irradiation area, thereby minimizing electron beam damage and contamination. In one case, the 5000 energy loss spectrum was fitted using the zero integral constraint described in this article. In another case, the 5000 energy loss spectrum was fitted without using the zero integral constraint described in this article. In both cases, the fine structure term was considered to be the sum of 125 rectangular functions (e.g., h max=125) and ΔE=4eV, resulting in an energy window of 500eV. The inventors found that when the element abundances were estimated using a combination of the fitting coefficients of the atomic cross section and the fine structure without integral constraints, the resulting abundance values ​​(represented by number 2308 in graph 2302) were widely distributed. In contrast, when the element abundances were estimated using the fitting coefficients of the atomic cross section and the fine structure with integral constraints, the resulting abundance values ​​(represented by number 2310 in graph 2302) were more tightly distributed. In other words, the fine structure with integral constraints can make element abundance determinations more accurate. The reason is that function 502 can have a very large number of fitting coefficients (e.g., 604, 608, 612), and specific values ​​need to be determined. Such a large number of parameters may lead to overfitting and noise sensitivity. However, the zero integral constraint described herein can be considered to help reduce the possibility of such overfitting and noise sensitivity.

[0180] The inventors conducted more tests to investigate how the precision or accuracy of element abundances varies with the energy window. For these tests, the same 5000 energy loss spectra were used, but the energy window was varied in steps of 60 eV, from a low of 60 eV to a high of 540 eV. Again, in one case, the energy loss spectra were fitted using the integration constraints described herein and the resulting element abundances were obtained; in another case, no integration constraints were used. Graph 2304 shows the average measured abundance of silicon as a function of the energy window, with and without integration constraints. As shown, in the absence of integration constraints, the average measured abundance changes significantly (e.g., by 25%) as the energy window changes. In contrast, in the absence of integration constraints, the average measured abundance changes only slightly (e.g., by 6%) as the energy window changes. Graph 2306 shows the standard deviation of the measured abundance of silicon as a function of the energy window, with and without integration constraints. As shown, the standard deviation in the absence of integration constraints almost quadruples as the energy window changes. In contrast, the standard deviation in the case of the integral constraint only slightly increases with the change of the energy window. These experimental results demonstrate that the zero-integration constraint described in this paper can significantly improve the accuracy and precision of downstream analysis of energy loss spectra.

[0181] Thus, the various embodiments described herein may be viewed as facilitating improved spectral image analysis by implementing integral constrained fitting of fine structure.

[0182] The scientific instrument systems, methods, or techniques disclosed herein may include interaction with a human user (e.g., via a Figure 26 The user's local computing device 2620 discussed above. These interactions may include providing information to the user (e.g., about scientific instruments such as Figure 26information about the operation of a scientific instrument such as a scientific instrument 2610, information about samples being analyzed or other tests or measurements being performed by the scientific instrument, information retrieved from a local or remote database, or other information) or provide the user with the option of inputting commands (e.g., controlling a scientific instrument such as Figure 26 In some embodiments, these interactions may be performed via a graphical user interface (GUI) that includes a display device (e.g., a graphical user interface, such as a display device, such as a display device, such as a display device, such as a display device, such as a display device, and ... Figure 25 2510) that provides output to the user and / or prompts the user to provide input (e.g., via the display device 2510 discussed herein). Figure 25 Other I / O devices 2512 discussed include one or more input devices such as a keyboard, mouse, trackpad, or touch screen. The scientific instrument systems, methods, or techniques disclosed herein may include any GUI suitable for interacting with a user.

[0183] Figure 24 An exemplary graphical user interface 2400 (hereinafter referred to as "GUI 2400") is depicted that can be used to perform some or all of the supporting methods or techniques disclosed herein, according to various embodiments. In various aspects, GUI 2400 can be provided on a scientific instrument support system (e.g., as described herein with reference to Figure 26 The computing device of the scientific instrument support system 2600 discussed herein (e.g., Figure 25 Any suitable electronic display (e.g., the computing device 2500 discussed herein) Figure 25 2510) and the user or technician may use any suitable input device (e.g., Figure 25 The user interface 2400 may interact with the GUI 2400 using any of the other I / O devices 2512 discussed herein and input technologies (e.g., cursor movement, motion capture, facial recognition, gesture detection, voice recognition, button activation).

[0184] GUI 2400 may include a data display area 2402 , a data analysis area 2404 , a scientific instrument control area 2406 , and a settings area 2408 . Figure 24 The specific number and arrangement of regions shown in is illustrative only, and any number and arrangement of regions (including any desired features) may be included in other embodiments of GUI 2400.

[0185] The data display area 2402 may display data generated by a scientific instrument (e.g., Figure 26 Data generated by the scientific instrument discussed 2610).

[0186] Data analysis area 2404 can display any suitable data analysis results (e.g., the results of analyzing the data shown in data display area 2402 or other data). In some embodiments, data display area 2402 and data analysis area 2404 can be combined in GUI 2400 (e.g., including data output from a scientific instrument and some analysis of the data in a common graph or area).

[0187] The scientific instrument control area 2406 may include options that allow a user or technician to control the scientific instrument (e.g., Figure 26 For example, the scientific instrument control area 2406 may include configurable parameters that control the operation of such a scientific instrument (e.g., a configurable parameter that controls the voltage or current of the scientific instrument, a configurable parameter that controls the internal temperature of the scientific instrument, or a configurable parameter that controls the flow rate of a fluid in the scientific instrument).

[0188] The settings area 2408 may include options that allow the user or technician to control any features or functions of the GUI 2400 (or other GUIs) or to perform common computational operations with respect to the data display area 2402 and the data analysis area 2404 (e.g., saving data on a storage device such as that described herein). Figure 25 The storage device 2504 discussed, sends data to another user, tags the data).

[0189] As described above, the scientific instrument module 102 may be implemented by one or more computing devices. Figure 25 is a block diagram of a computing device 2500 that can execute some or all of the scientific instrument support methods or techniques disclosed herein, according to various embodiments. In certain embodiments, the scientific instrument module 102 can be implemented by a single instance of the computing device 2500 or multiple instances of the computing device 2500. In addition, as described below, the computing device 2500 (or multiple instances thereof) that implements the scientific instrument module 102 can be Figure 26 A portion of one or more of a scientific instrument 2610, a user local computing device 2620, a service local computing device 2630, or a remote computing device 2640.

[0190] The computing device 2500 is shown as having multiple components, but any one or more of these components may be omitted or duplicated depending on the application and settings. In some embodiments, some or all of the components included in the computing device 2500 may be attached to one or more motherboards and enclosed in a housing (e.g., comprising plastic, metal, or other materials). In some embodiments, some of these components may be manufactured on a single system on a chip (SoC) (e.g., the SoC may include one or more instances of the processing device 2502 and one or more instances of the storage device 2504). Additionally, in various embodiments, the computing device 2500 may omit the processor. Figure 25 The computing device 2500 may include one or more of the components shown, but may include interface circuitry (not shown) for coupling to one or more omitted components using any suitable interface (e.g., a universal serial bus (USB) interface, a high-definition multimedia interface (HDMI) interface, a controller area network (CAN) interface, a serial peripheral interface (SPI) interface, an Ethernet interface, a wireless interface, or any other suitable interface). For example, the computing device 2500 may omit the display device 2510, but may include display device interface circuitry (e.g., a connector and driver circuitry) to which the display device 2510 may be coupled.

[0191] The computing device 2500 may include a processing device 2502 (e.g., one or more processing devices). As used herein, the term "processing device" may refer to any device or portion of a device that processes electronic data from a register or memory to convert the electronic data into other electronic data that can be stored in the register or memory. The processing device 2502 may include one or more digital signal processors (DSPs), application-specific integrated circuits (ASICs), central processing units (CPUs), graphics processing units (GPUs), cryptographic processors (specialized processors that execute cryptographic algorithms in hardware), server processors, or any other suitable processing devices.

[0192] The computing device 2500 may include a storage device 2504 (e.g., one or more storage devices). The storage device 2504 may include one or more memory devices, such as random access memory (RAM) (e.g., static RAM (SRAM) devices, magnetic RAM (MRAM) devices, dynamic RAM (DRAM) devices, resistive RAM (RRAM) devices, or conductive bridging RAM (CBRAM) devices), hard drive-based memory devices, solid-state memory devices, network drives, cloud drives, or any combination of memory devices. In some embodiments, the storage device 2504 may include memory that shares a die with the processing device 2502. In such embodiments, the memory may be used as a cache memory and may include, for example, embedded dynamic random access memory (eDRAM) or spin-transfer torque magnetic random access memory (STT-MRAM). In some embodiments, the storage device 2504 may include a non-transitory computer-readable medium having instructions thereon that, when executed by one or more processing devices (e.g., processing device 2502), cause the computing device 2500 to perform any appropriate method or portion of the methods disclosed herein.

[0193] The computing device 2500 may include an interface device 2506 (e.g., one or more instances of the interface device 2506). The interface device 2506 may include one or more communication chips, connectors, or other hardware and software to manage communications between the computing device 2500 and other computing devices. For example, the interface device 2506 may include circuitry for managing wireless communications for transmitting data to and from the computing device 2500. The term "wireless" and its derivatives may be used to describe circuits, devices, systems, methods, techniques, and communications channels that can transmit data through a non-solid medium using modulated electromagnetic radiation. The term does not imply that the associated device does not contain any wires, although in some embodiments, it may not. The circuitry included in the interface device 2506 for managing wireless communications may implement any of a variety of wireless standards or protocols, including, but not limited to, Institute of Electrical and Electronics Engineers (IEEE) standards, including Wi-Fi (IEEE 802.11 series), IEEE 802.16 standards (e.g., IEEE 802.16-2005 amendment), Long Term Evolution (LTE) project, and any amendments, updates, and / or revisions (e.g., LTE-Advanced project, Ultra Mobile Broadband (UMB) project (also known as "3GPP2"). In some embodiments, the circuitry included in the interface device 2506 for managing wireless communications may operate in accordance with Global System for Mobile Communications (GSM), General Packet Radio Service (GPRS), Universal Mobile Telecommunications System (UMTS), High Speed ​​Packet Access (HSPA), Evolved HSPA (E-HSPA), or LTE networks. In some embodiments, the circuitry included in the interface device 2506 for managing wireless communications may operate in accordance with Enhanced Data for GSM Evolution (EDGE), GSM EDGE Radio Access Network (GERAN), Universal Terrestrial Radio Access Network (UTRAN), or Evolved UTRAN (E-UTRAN). In certain embodiments, the circuitry included in the interface device 2506 for managing wireless communications may operate in accordance with Code Division Multiple Access (CDMA), Time Division Multiple Access (TDMA), Digital Enhanced Cordless Telecommunications (DECT), Evolution-Data Optimized (EV-DO) and its derivatives, as well as any other wireless protocols designated as 3G, 4G, 5G, and higher. In certain embodiments, the interface device 2506 may include one or more antennas (e.g., one or more antenna arrays) to receive and / or transmit wireless communications.

[0194] In certain embodiments, interface device 2506 may include a circuit for managing wired communication, such as electrical communication protocol, optical communication protocol or any other suitable communication protocol. For example, interface device 2506 may include a circuit for supporting communication according to Ethernet technology. In certain embodiments, interface device 2506 may support both wireless and wired communication, or may support multiple wired communication protocols or multiple wireless communication protocols. For example, a first group of circuits of interface device 2506 may be dedicated to short-range wireless communication such as Wi-Fi or Bluetooth, and a second group of circuits of interface device 2506 may be dedicated to long-range wireless communication such as global positioning system (GPS), EDGE, GPRS, CDMA, WiMAX, LTE, EV-DO etc. In certain embodiments, a first group of circuits of interface device 2506 may be dedicated to wireless communication, and a second group of circuits of interface device 2506 may be dedicated to wired communication.

[0195] Computing device 2500 may include battery / power circuitry 2508. Battery / power circuitry 2508 may include one or more energy storage devices (e.g., batteries or capacitors) or circuitry for coupling components of computing device 2500 to an energy source separate from computing device 2500 (e.g., AC line power).

[0196] Computing device 2500 may include a display device 2510 (e.g., multiple display devices). Display device 2510 may include any visual indicator, such as a heads-up display, a computer monitor, a projector, a touch screen display, a liquid crystal display (LCD), a light-emitting diode display, or a flat panel display.

[0197] The computing device 2500 may include other input / output (I / O) devices 2512. For example, the other I / O devices 2512 may include one or more audio output devices (e.g., speakers, headphones, earbuds, alarms), one or more audio input devices (e.g., microphones or microphone arrays), a positioning device (e.g., a GPS device that communicates with a satellite-based system to receive the location of the computing device 2500), an audio codec, a video codec, a printer, sensors (e.g., thermocouples or other temperature sensors, humidity sensors, pressure sensors, vibration sensors, accelerometers, gyroscopes), an image capture device such as a camera, a keyboard, a cursor control device such as a mouse, stylus, trackball, or touchpad, a barcode reader, a Quick Response (QR) code reader, or a Radio Frequency Identification (RFID) reader.

[0198] The computing device 2500 may have any suitable form factor suitable for its applications and settings, such as a handheld or mobile computing device (e.g., a cell phone, a smartphone, a mobile internet device, a tablet computer, a laptop computer, a netbook computer, an ultrabook computer, a personal digital assistant (PDA), an ultra-mobile personal computer), a desktop computing device, or a server computing device or other networked computing component.

[0199] One or more computing devices implementing any scientific instrument module, method, or technique disclosed herein may be part of a scientific instrument support system. Figure 26 26 is a block diagram of an exemplary scientific instrument support system 2600 in which some or all of the scientific instrument support methods disclosed herein may be implemented, according to various embodiments. The scientific instrument modules, methods, or techniques disclosed herein (e.g., scientific instrument module 102, computer-implemented method 200, system 306) may be implemented by one or more scientific instruments 2610, a user local computing device 2620, a service local computing device 2630, or a remote computing device 2640 of the scientific instrument support system 2600.

[0200] Any of the scientific instrument 2610, the user local computing device 2620, the service local computing device 2630, or the remote computing device 2640 may include any implementation of the computing device 2500, and any of the scientific instrument 2610, the user local computing device 2620, the service local computing device 2630, or the remote computing device 2640 may take the form of any appropriate implementation of the implementation of the computing device 2500.

[0201] Scientific instrument 2610, user local computing device 2620, service local computing device 2630, or remote computing device 2640 may each include a processing device 2602, a storage device 2604, and an interface device 2606. Processing device 2602 may take any suitable form, including any form of processing device 2502, and processing devices 2602 included in different devices among scientific instrument 2610, user local computing device 2620, service local computing device 2630, or remote computing device 2640 may take the same form or different forms. Storage device 2604 may take any suitable form, including any form of storage device 2504, and storage devices 2604 included in different devices among scientific instrument 2610, user local computing device 2620, service local computing device 2630, or remote computing device 2640 may take the same form or different forms. The interface device 2606 can take any suitable form, including any form of the interface device 2506, and the interface devices 2606 included in different devices in the scientific instrument 2610, the user local computing device 2620, the service local computing device 2630 or the remote computing device 2640 can take the same form or different forms.

[0202] The scientific instrument 2610, the user local computing device 2620, the service local computing device 2630, and the remote computing device 2640 can communicate with other elements of the scientific instrument support system 2600 via a communication path 2608. The communication path 2608 can communicatively couple the interface device 2606 of different ones of the elements of the scientific instrument support system 2600, as shown, and can be a wired or wireless communication path (e.g., according to any of the communication technologies discussed herein with reference to the interface device 2506). Figure 26 The particular scientific instrument support system 2600 depicted in FIG2 includes a communication path between each pair of devices among the scientific instrument 2610, the user local computing device 2620, the service local computing device 2630, and the remote computing device 2640, but this "fully connected" embodiment is merely illustrative, and in various embodiments, various of the communication paths 2608 may not be present. For example, in some embodiments, the service local computing device 2630 may lack a direct communication path 2608 between its interface device 2606 and the interface device 2606 of the scientific instrument 2610, and may instead communicate with the scientific instrument 2610 via the communication path 2608 between the service local computing device 2630 and the user local computing device 2620, as well as the communication path 2608 between the user local computing device 2620 and the scientific instrument 2610.

[0203] Scientific instrument 2610 may include any suitable scientific instrument, such as scientific instrument 302 .

[0204] The user-local computing device 2620 can be a computing device local to the user of the scientific instrument 2610 (e.g., according to any embodiment of the computing device 2500). In some embodiments, the user-local computing device 2620 can also be local to the scientific instrument 2610, but this is not necessarily the case; for example, the user-local computing device 2620 located in the user's home or office can be remote from the scientific instrument 2610 but in communication with the scientific instrument such that the user can use the user-local computing device 2620 to control and / or access data from the scientific instrument 2610. In some embodiments, the user-local computing device 2620 can be a laptop, smartphone, or tablet device. In some embodiments, the user-local computing device 2620 can be a portable computing device.

[0205] The service local computing device 2630 can be a computing device local to the entity serving the scientific instrument 2610 (e.g., according to any embodiment of the computing device 2500). For example, the service local computing device 2630 can be a device local to the manufacturer of the scientific instrument 2610 or a third-party service company. In some embodiments, the service local computing device 2630 can communicate with the scientific instrument 2610, the user local computing device 2620, or the remote computing device 2640 (e.g., via a direct communication path 2608 or via multiple "indirect" communication paths 2608, as described above) to receive data regarding the operation of the scientific instrument 2610, the user local computing device 2620, or the remote computing device 2640 (e.g., self-test results of the scientific instrument 2610, calibration coefficients used by the scientific instrument 2610, measurements of sensors associated with the scientific instrument 2610). In some embodiments, the service local computing device 2630 can communicate with the scientific instrument 2610, the user local computing device 2620, or the remote computing device 2640 (e.g., via a direct communication path 2608 or via multiple "indirect" communication paths 2608, as described above) to transfer data to the scientific instrument 2610, the user local computing device 2620, or the remote computing device 2640 (e.g., to update programming instructions (such as firmware) in the scientific instrument 2610 to initiate execution of a test or calibration sequence in the scientific instrument 2610, to update programming instructions (such as software) in the user local computing device 2620 or the remote computing device 2640). A user of the scientific instrument 2610 can utilize the scientific instrument 2610 or the user local computing device 2620 to communicate with the service local computing device 2630 to report a problem with the scientific instrument 2610 or the user local computing device 2620, to request a technician visit to improve the operation of the scientific instrument 2610, to order consumables or replacement parts associated with the scientific instrument 2610, or for other purposes.

[0206] Remote computing device 2640 can be a computing device remote from scientific instrument 2610 or user local computing device 2620 (e.g., according to any of the embodiments of computing device 2500 discussed herein). In some embodiments, remote computing device 2640 can be included in a data center or other large-scale server environment. In some embodiments, remote computing device 2640 can include network attached storage (e.g., as part of storage device 2604). Remote computing device 2640 can store data generated by scientific instrument 2610, perform analysis of data generated by scientific instrument 2610 (e.g., according to programmed instructions), facilitate communication between user local computing device 2620 and scientific instrument 2610, or facilitate communication between service local computing device 2630 and scientific instrument 2610.

[0207] In some embodiments, the Figure 26 In addition, in certain embodiments, there may be one or more elements of the scientific instrument support system 2600 shown in FIG. Figure 26 26. The scientific instrument support system 2600 may include multiple of the various elements of the scientific instrument support system 2600. For example, the scientific instrument support system 2600 may include multiple user-local computing devices 2620 (e.g., different user-local computing devices 2620 associated with different users or located in different locations). In another example, the scientific instrument support system 2600 may include multiple scientific instruments 2610, all of which communicate with a service local computing device 2630 and / or a remote computing device 2640; in such an embodiment, the service local computing device 2630 may monitor these multiple scientific instruments 2610, and the service local computing device 2630 may cause updates or other information to be "broadcasted" to the multiple scientific instruments 2610 simultaneously. The different scientific instruments 2610 in the scientific instrument support system 2600 may be located near each other (e.g., in the same room) or far away from each other (e.g., on different floors of a building, in different buildings, in different cities, etc.). In some embodiments, the scientific instrument 2610 can be connected to an Internet of Things (IoT) stack that allows command and control of the scientific instrument 2610 through web-based applications, virtual or augmented reality applications, mobile applications, or desktop applications. Any of these applications can be accessed by a user operating a user-local computing device 2620 that communicates with the scientific instrument 2610 through an intermediary remote computing device 2640. In some embodiments, the scientific instrument 2610 can be sold by a manufacturer along with one or more associated user-local computing devices 2620 as part of a local scientific instrument computing unit 2612.

[0208] In some embodiments, the different scientific instruments 2610 included in the scientific instrument support system 2600 can be different types of scientific instruments 2610; for example, one scientific instrument 2610 can be a mass spectrometer, while another scientific instrument 2610 can be a chromatograph or an autosampler. In some such embodiments, the remote computing device 2640 or the user's local computing device 2620 can combine data from the different types of scientific instruments 2610 included in the scientific instrument support system 2600.

[0209] In various cases, the machine learning algorithm or model can be implemented in any suitable manner to facilitate any suitable aspect described herein. To facilitate some of the above-mentioned machine learning aspects of the various embodiments, consider the following discussion of artificial intelligence (AI). The various embodiments described herein can employ artificial intelligence to facilitate the automation of one or more features or functionalities. These components can employ various AI-based schemes to execute the various embodiments / examples disclosed herein. In order to provide or assist in the numerous determinations described herein (e.g., determining, ascertaining, inferring, calculating, predicting, prognosing, estimating, deriving, forecasting, detecting, calculating), the components described herein can examine all or a subset of the data to which they are granted access rights, and can provide a method for reasoning or determining the state of a system or environment from a set of observations such as those captured via events or data. For example, determinations can be employed to identify a specific context or action, or a probability distribution of a state can be generated. These determinations can be probabilistic; that is, a probability distribution of a state of interest is calculated based on a consideration of data and events. Determination can also refer to the techniques employed to compose a higher-level event from a set of events or data.

[0210] Such determination can result in constructing new events or actions from a set of observed events or stored event data, regardless of whether the events are closely related in time and whether the events and data come from one or several event and data sources. The components disclosed herein can employ various classification (explicitly trained (e.g., via training data) as well as implicitly trained (e.g., via observed behavior, preferences, historical information, receiving external information, etc.)) schemes or systems (e.g., support vector machines, neural networks, expert systems, Bayesian belief networks, fuzzy logic, data fusion engines, etc.) in connection with performing automatic or determined actions related to the claimed subject matter. Thus, the classification scheme or system can be used to automatically learn and perform multiple functions, actions, or determinations.

[0211] The classifier can take the input attribute vector z=(z1,z2,z3,z4,z n) is mapped to the confidence that the input belongs to a certain class, such as f(z) = confidence(class). This classification can use probabilistic or statistical-based analysis (for example, taking into account the utility and cost of the analysis) to determine the action to be automatically performed. Support vector machines (SVM) can be an example of a classifier that can be used. SVM operates by finding a hypersurface in the space of possible inputs, where the hypersurface attempts to separate triggering criteria from non-triggering events. Intuitively, this makes the classification correct for test data that is close to but not the same as the training data. Other directed and non-directed model classification methods include, for example, naive Bayes, Bayesian networks, decision trees, neural networks, fuzzy logic models, or probabilistic classification models that provide different independent patterns, any of which can be used. The classification used in this article also includes statistical regression for developing priority models.

[0212] To provide additional context for the various embodiments described herein, Figure 27 The following discussion is intended to provide a brief, general description of a suitable computing environment 2700 in which various embodiments of the embodiments described herein may be implemented. Although the embodiments have been described above in the general context of computer-executable instructions that may be executed on one or more computers, those skilled in the art will recognize that the embodiments may also be implemented in conjunction with other program modules or as a combination of hardware and software.

[0213] Generally, program modules include routines, programs, components, data structures, etc. that perform particular tasks or implement particular abstract data types. Moreover, those skilled in the art will appreciate that the methods of the present invention can be practiced with other computer system configurations, including single-processor or multi-processor computer systems, minicomputers, mainframe computers, Internet of Things (IoT) devices, distributed computing systems, as well as personal computers, handheld computing devices, microprocessor-based or programmable consumer electronics, etc., each of which can be operatively coupled to one or more associated devices.

[0214] The embodiments shown herein can also be practiced in distributed computing environments where certain tasks are performed by remote processing devices that are linked through a communications network.In a distributed computing environment, program modules may be located in both local and remote memory storage devices.

[0215] Computing devices typically include various media, which may include computer-readable storage media, machine-readable storage media, or communication media, as used herein differently, as shown below. A computer-readable storage medium or machine-readable storage medium can be any available storage medium that can be accessed by a computer, and includes volatile and non-volatile media, removable and non-removable media. By way of example and not limitation, a computer-readable storage medium or machine-readable storage medium can be implemented in conjunction with any method or technology for storing information, such as computer-readable or machine-readable instructions, program modules, structured data, or unstructured data.

[0216] Computer-readable storage media may include, but are not limited to, random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, compact disc read-only memory (CD-ROM), digital versatile disc (DVD), Blu-ray disc (BD) or other optical disc storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, solid-state drives or other solid-state storage devices, or other tangible or non-transitory media that can be used to store the desired information. In this regard, the terms "tangible" or "non-transitory" as applied to storage, memory, or computer-readable media herein should be understood as excluding only the propagation of transient signals themselves as a modifier and not as a disclaimer of all standard storage, memory, or computer-readable media that are not merely propagation of transient signals themselves.

[0217] Computer-readable storage media can be accessed by one or more local or remote computing devices, eg, via access requests, queries, or other data retrieval protocols, for various operations regarding the information stored by the media.

[0218] Communication media typically embodies computer-readable instructions, data structures, program modules, or other structured or unstructured data in a data signal (such as a modulated data signal, such as a carrier wave or other transport mechanism), and includes any information delivery or transmission media. The term "modulated data signal" or signal refers to a signal whose one or more characteristics are set or changed so as to encode information in one or more signals. By way of example, and not limitation, communication media include wired media (such as a wired network or direct-wired connection) and wireless media (such as acoustic, RF, infrared, and other wireless media).

[0219] Reference again Figure 27, an exemplary environment 2700 for implementing various embodiments of aspects described herein includes a computer 2702 including a processing unit 2704, a system memory 2706, and a system bus 2708. The system bus 2708 couples system components including, but not limited to, the system memory 2706 to the processing unit 2704. The processing unit 2704 can be any of a variety of commercially available processors. Dual microprocessors and other multi-processor architectures can also be used as the processing unit 2704.

[0220] The system bus 2708 can be any of several types of bus structures and can further be interconnected with a memory bus (with or without a memory controller), a peripheral bus, and a local bus using any of a variety of commercially available bus architectures. The system memory 2706 includes ROM 2710 and RAM 2712. A basic input / output system (BIOS) containing the basic routines that help transfer information between elements within the computer 2702, such as during startup, can be stored in a nonvolatile memory such as ROM, erasable programmable read-only memory (EPROM), or EEPROM. RAM 2712 can also include high-speed RAM, such as static RAM for caching data.

[0221] Computer 2702 also includes an internal hard disk drive (HDD) 2714 (e.g., EIDE, SATA) and may include one or more external storage devices 2716 (e.g., a magnetic floppy disk drive (FDD) 2716, a memory stick or flash drive reader, a memory card reader, etc.). As well as a drive 2720, such as a solid-state drive, an optical drive, which can read or write to a disk 2722 (e.g., a CD-ROM disk, a DVD, a BD, etc.). Alternatively, if a solid-state drive is involved, the disk 2722 is not included unless provided separately. Although the internal HDD 2714 is shown as being located within the computer 2702, the internal HDD 2714 can also be configured for external use in a suitable chassis (not shown). In addition, although not shown in environment 2700, a solid-state drive (SSD) can be used to supplement or replace the HDD 2714. The HDD 2714, external storage device 2716, and drive 2720 can be connected to the system bus 2708 via an HDD interface 2724, an external storage interface 2726, and a drive interface 2728, respectively. The interface 2724 for an external drive implementation may include at least one or both of Universal Serial Bus (USB) and Institute of Electrical and Electronics Engineers (IEEE) 1394 interface technologies. Other external drive connection technologies are also contemplated by the embodiments described herein.

[0222] The drives and their associated computer-readable storage media provide non-volatile storage of data, data structures, computer-executable instructions, and the like. For the computer 2702, the drives and storage media accommodate the storage of any data in a suitable digital format. Although the above description of computer-readable storage media refers to corresponding types of storage devices, those skilled in the art will appreciate that other types of storage media (whether currently existing or developed in the future) that can be read by a computer may also be used in the exemplary operating environment, and further, any such storage media may contain computer-executable instructions for performing the methods described herein.

[0223] A number of program modules may be stored in the drives and RAM 2712, including an operating system 2730, one or more applications 2732, other program modules 2734, and program data 2736. All or portions of the operating system, applications, modules, or data may also be cached in RAM 2712. The systems and methods described herein may be implemented using various commercially available operating systems or combinations of operating systems.

[0224] Computer 2702 may optionally include emulation technology. For example, a virtual machine hypervisor (not shown) or other intermediary may emulate the hardware environment for operating system 2730, and the emulated hardware may optionally be different from the hardware of the operating system. Figure 27 . In this embodiment, operating system 2730 may include one of multiple virtual machines (VMs) hosted at computer 2702. In addition, operating system 2730 may provide a runtime environment for application 2732, such as a Java runtime environment or a .NET framework. A runtime environment is a consistent execution environment that allows application 2732 to run on any operating system that includes a runtime environment. Similarly, operating system 2730 may support containers, and application 2732 may be in the form of containers, which are lightweight, independent, executable software packages that include, for example, the application's code, runtime, system tools, system libraries, and settings.

[0225] Furthermore, computer 2702 may be equipped with a security module, such as a Trusted Processing Module (TPM). For example, using a TPM, a boot component hashes the next boot component in time and waits for the hash to match a security value before loading the next boot component. This process can be performed at any layer in the code execution stack of computer 2702, for example, at the application execution level or the operating system (OS) kernel level, thereby achieving security for code execution at any level.

[0226] A user may enter commands and information into the computer 2702 through one or more wired / wireless input devices, such as a keyboard 2738, a touch screen 2740, and a pointing device such as a mouse 2742. Other input devices (not shown) may include a microphone, an infrared (IR) remote control, a radio frequency (RF) remote control, or other remote control, a joystick, a virtual reality controller or headset, a game controller, a stylus, an image input device (e.g., a camera), a gesture sensor input device, a visual movement sensor input device, an emotion or facial detection device, a biometric input device (e.g., a fingerprint or iris scanner), and the like. These and other input devices are typically connected to the processing unit 2704 through an input device interface 2744, which may be coupled to the system bus 2708, but may also be connected through other interfaces, such as a parallel port, an IEEE 1394 serial port, a game port, a USB port, an IR port, a memory card, a memory card, a memory card reader ... Interface, etc.

[0227] A monitor 2746 or other type of display device may also be connected to the system bus 2708 via an interface, such as a video adapter 2748. In addition to the monitor 2746, computers typically include other peripheral output devices (not shown), such as speakers, printers, and the like.

[0228] Computer 2702 can operate in a network environment, using logical connections to one or more remote computers (such as remote computer 2750) via wired or wireless communications. Remote computer 2750 can be a workstation, server computer, router, personal computer, portable computer, microprocessor-based entertainment device, peer device, or other common network node, and typically includes many or all of the elements described with respect to computer 2702, but only memory / storage device 2752 is shown for simplicity. The depicted logical connections include wired / wireless connections to a local area network (LAN) 2754 or a larger network (e.g., wide area network (WAN) 2756). Such LAN and WAN networking environments are common in offices and companies and facilitate the establishment of enterprise-wide computer networks (e.g., intranets), all of which can be connected to a global communication network (e.g., the Internet).

[0229] When used in a LAN networking environment, the computer 2702 can be connected to the local network 2754 through a wired or wireless communication network interface or adapter 2758. The adapter 2758 can facilitate wired or wireless communication with the LAN 2754, which can also include a wireless access point (AP) provided thereon for communicating with the adapter 2758 in a wireless mode.

[0230] When used in a WAN networking environment, the computer 2702 can include a modem 2760 or can be connected to a communication server on the WAN 2756 by other means to establish communications over the WAN 2756, such as over the Internet. The modem 2760 can be internal or external, wired or wireless, and can be connected to the system bus 2708 via the input device interface 2744. In a networked environment, program modules shown relative to the computer 2702 or portions thereof can be stored in the remote memory / storage device 2752. It should be understood that the network connections shown are exemplary and other means of establishing a communications link between the computers can be used.

[0231] When used in a LAN or WAN networking environment, computer 2702 can access cloud storage systems or other network-based storage systems, in addition to or as an alternative to external storage devices 2716 as described above, such as, but not limited to, network virtual machines that provide one or more aspects of storage or processing of information. Generally, a connection between computer 2702 and a cloud storage system can be established via LAN 2754 or WAN 2756, for example, via adapter 2758 or modem 2760, respectively. When computer 2702 is connected to an associated cloud storage system, external storage interface 2726 can manage the storage provided by the cloud storage system with the aid of adapter 2758 or modem 2760, as it would other types of external storage. For example, external storage interface 2726 can be configured to provide access to cloud storage sources as if those sources were physically connected to computer 2702.

[0232] Computer 2702 is operable to communicate with any wireless device or entity that operates in a wireless communication manner, such as printers, scanners, desktop or portable computers, portable data assistants, communication satellites, any device or location associated with a wirelessly detectable tag (e.g., information kiosks, newsstands, store shelves, etc.), and telephones. This may include Wireless Fidelity (Wi-Fi) and Wireless technology. Therefore, the communication can be a predefined structure like traditional networks or an ad hoc communication between at least two devices.

[0233] Figure 28is a schematic block diagram of an exemplary computing environment 2800 with which the disclosed subject matter can interact. The exemplary computing environment 2800 includes one or more clients 2810. Clients 2810 can be hardware or software (e.g., threads, processes, computing devices). The exemplary computing environment 2800 also includes one or more servers 2830. Servers 2830 can also be hardware or software (e.g., threads, processes, computing devices). For example, servers 2830 can accommodate threads to perform transformations by employing one or more embodiments described herein. One possible communication between clients 2810 and servers 2830 can take the form of data packets suitable for transmission between two or more computer processes. The exemplary computing environment 2800 includes a communication framework 2850 that can be used to facilitate communication between clients 2810 and servers 2830. Clients 2810 are operably connected to one or more client data repositories 2820 that can be used to store information local to the clients 2810. Similarly, servers 2830 are operably connected to one or more server data repositories 2840 that can be used to store information local to the servers 2830.

[0234] Various embodiments can be systems, methods, devices or computer program products at any possible level of technical detail integration. A computer program product can include a computer-readable storage medium (or medium) having computer-readable program instructions thereon for causing a processor to execute various aspects of the various embodiments. A computer-readable storage medium can be a tangible device that can retain and store instructions for use by an instruction execution device. A computer-readable storage medium can be, for example, but not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device or any suitable combination of the foregoing. A non-exhaustive list of more specific examples of computer-readable storage media can also include the following: a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanical encoding device (such as a punched card or a raised structure in a groove with instructions recorded thereon) and any suitable combination of the foregoing. Computer-readable storage media as used herein should not be construed as transient signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through waveguides or other transmission media (e.g., light pulses transmitted through fiber optic cables), or electrical signals transmitted through wires.

[0235] Computer-readable program instructions as herein described can be downloaded to corresponding computing / processing equipment from computer-readable storage media or downloaded to external computers or external storage devices via a network (for example, the Internet, local area network, wide area network or wireless network).The network may include copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computers or edge servers.Network adapter cards or network interfaces in each computing / processing equipment receive computer-readable program instructions from the network, and forward computer-readable program instructions to be stored in the computer-readable storage media in the corresponding computing / processing equipment.The computer-readable program instructions for performing the operation of various embodiments can be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-related instructions, microcode, firmware instructions, state setting data, configuration data of integrated circuits, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​(for example, Smalltalk, C++ etc.) and procedural programming languages ​​(for example " C " programming language or similar programming languages). Computer readable program instructions can be performed entirely on the user's computer, partially on the user's computer, performed as an independent software package, partially on the user's computer, partially on a remote computer, or entirely on a remote computer or server. In the latter case, the remote computer can be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or can be connected to an external computer (for example, using an Internet service provider through the Internet). In certain embodiments, the electronic circuit comprises, for example, a programmable logic circuit, a field programmable gate array (FPGA), or a programmable logic array (PLA), and the electronic circuit can be personalized by utilizing the state information of the computer readable program instructions, thereby executing the computer readable program instructions, to perform various aspects.

[0236] Various aspects are described herein with reference to the flow chart explanation or block diagram according to the method, device (system) and computer program product of various embodiments.Should be understood that the combination of each frame in flow chart illustration or block diagram and flow chart illustration or the frame in block diagram can be realized by computer-readable program instructions.These computer-readable program instructions can be provided to the processor of general-purpose computer, special-purpose computer or other programmable data processing equipment to produce machine, so that the instruction executed via the processor of computer or other programmable data processing equipment creates the device for implementing the function / action specified in one or more frames of flow chart or block diagram.These computer-readable program instructions can also be stored in computer-readable storage medium, and this computer-readable storage medium can guide computer, programmable data processing equipment or other equipment to run in a special way, and the computer-readable storage medium stored with instruction comprises manufacturing product, and this manufacturing product comprises the instruction of each aspect of the function / action specified in one or more frames of implementation flow chart or block diagram.Computer-readable program instructions can also be loaded onto computer, other programmable data processing equipment or other equipment so that on computer, other programmable equipment or other equipment, perform a series of operation actions, thereby produce the process implemented by computer, so that the instruction executed on computer, other programmable equipment or other equipment is implemented in the function / action specified in one or more frames of flow chart or block diagram.

[0237] The flow chart and block diagram in the figure show the architecture, functionality and operation of the possible implementation of the system, method and computer program product according to various embodiments.In this regard, each frame in the flow chart or block diagram can represent a module, segment or partial instruction, which comprises one or more executable instructions for implementing a specified logical function.In some alternative embodiments, the function marked in the frame can not occur in the order marked in the figure.For example, two frames shown continuously can actually be performed substantially simultaneously, or can sometimes be performed in the opposite order, depending on the function involved.It should also be noted that each frame in the block diagram or flow chart and the combination of frames in the block diagram or flow chart can be realized by a dedicated hardware system that performs a specified function or action or performs a combination of dedicated hardware and computer instructions.

[0238] Although the subject matter has been described above in the general context of computer-executable instructions of a computer program product running on a computer, those skilled in the art will recognize that the present disclosure may also or may be implemented in combination with other program modules. Typically, a program module includes routines, programs, components, data structures, etc. that perform specific tasks or implement specific abstract data types. In addition, those skilled in the art will recognize that various aspects can be practiced using other computer system configurations, including single-processor or multi-processor computer systems, small computing devices, mainframe computers, and computers, handheld computing devices (e.g., PDAs, phones), microprocessor-based or programmable consumer or industrial electronics, etc. The various aspects shown can also be practiced in a distributed computing environment, where tasks are performed by remote processing devices connected via a communication network. However, some aspects of the present disclosure (if not all aspects) can be practiced on a stand-alone computer. In a distributed computing environment, program modules can be located in both a local memory storage device and a remote memory storage device.

[0239] The terms "component", "system", "platform", "interface" and the like used in this application may refer to or include computer-related entities or entities related to an operating machine having one or more specific functions. The entities disclosed herein may be hardware, a combination of hardware and software, software, or software in execution. For example, a component may be, but is not limited to, a process, a processor, an object, an executable program, a thread of execution, a program, or a computer running on a processor. As an example, both an application running on a server and a server may be components. One or more components may reside within a process or thread of execution, and a component may be located on a single computer or distributed between two or more computers. In another example, corresponding components may be executed from various computer-readable media having various data structures stored thereon. These components may communicate via local or remote processes, such as according to signals having one or more data packets (for example, data from one component interacts with another component in a local system, a distributed system, or interacts with other systems via a network such as the Internet). As another example, a component may be a device having specific functionality provided by mechanical parts operated by electrical or electronic circuits, which are operated by software or firmware applications executed by a processor. In this case, the processor may be inside or outside the device and may execute at least a portion of the software or firmware application. As yet another example, a component can be a device that provides specific functionality through electronic components without mechanical parts, where the electronic components may include a processor or other device for executing software or firmware that at least partially imparts the functionality to the electronic components. In one aspect, the component can emulate the electronic components via, for example, a virtual machine within a cloud computing system.

[0240] In addition, the term "or" is intended to mean an inclusive "or" rather than an exclusive "or". That is, unless specified otherwise, or clear from the context, "X employs A or B" is intended to mean any natural inclusive permutation. That is, if X employs A; X employs B; or X employs both A and B, then "X employs A or B" is satisfied under any of the foregoing examples. As used herein, the term "and / or" is intended to have the same meaning as "or". In addition, unless specified otherwise, or clear from the context to refer to a singular form, the articles "a" and "an" as used in the subject specification and the accompanying drawings should generally be interpreted to mean "one or more". As used herein, the terms "example" or "exemplary" are used to mean serving as an example, instance, or illustration. For the avoidance of doubt, the subject matter disclosed herein is not limited to such examples. In addition, any aspect or design described herein as "example" or "exemplary" is not necessarily to be construed as preferred or advantageous over other aspects or designs, nor is it meant to exclude equivalent exemplary structures and techniques known to those of ordinary skill in the art.

[0241] The content disclosed herein describes non-limiting examples. For ease of description or explanation, the various parts disclosed herein use the terms "each," "each," or "all" when discussing various examples. The usage of terms such as "each," "each," or "all" is not restrictive. In other words, when the content disclosed herein provides a description of "each," "all," or "all" applicable to a particular object or component, it should be understood that this is only a non-limiting example, and it should also be understood that in various other examples, such a description may be applicable to less than "each," "all," or "all" of the particular object or component.

[0242] As used in this subject specification, the term "processor" may refer to substantially any computational processing unit or device, including but not limited to a single-core processor; a single processor with software multi-threaded execution capabilities; a multi-core processor; a multi-core processor with software multi-threaded execution capabilities; a multi-core processor with hardware multi-threading technology; a parallel platform; and a parallel platform with distributed shared memory. In addition, a processor may refer to an integrated circuit, an application-specific integrated circuit (ASIC), a digital signal processor (DSP), a field-programmable gate array (FPGA), a programmable logic controller (PLC), a complex programmable logic device (CPLD), discrete gate or transistor logic components, discrete hardware components, or any combination thereof, designed to perform the functions described herein. In addition, the processor may utilize nanoscale architectures, such as (but not limited to) molecular and quantum dot-based transistors, switches, and gates to optimize space usage or enhance the performance of the user device. The processor may also be implemented as a combination of computational processing units. In this disclosure, terms such as "repository," "storage device," "data repository," "data storage device," "database," and substantially any other information storage component related to the operation and functionality of the component are used to refer to a "memory component," an entity embodied in "memory," or a component that includes memory. It should be understood that the memory and / or memory components can be volatile memory or non-volatile memory, or can include both volatile memory and non-volatile memory. By way of illustration and not limitation, non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable ROM (EEPROM), flash memory, or non-volatile random access memory (RAM) (e.g., ferroelectric RAM (FeRAM)). Volatile memory can include RAM, which can, for example, act as external cache memory. By way of example and not limitation, RAM takes many forms, such as synchronous RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), direct Rambus RAM (DRRAM), direct Rambus dynamic RAM (DRDRAM), and Rambus dynamic RAM (RDRAM). In addition, the memory components of the systems or computer-implemented methods disclosed herein are intended to include, but are not limited to, these and any other suitable types of memory.

[0243] The foregoing includes only examples of systems and computer-implemented methods. Of course, it is not possible to describe every conceivable combination of components or computer-implemented methods for purposes of describing the present disclosure, but many further combinations and permutations of the present disclosure are possible. Furthermore, with respect to the use of the terms "including," "having," "having," and the like in the detailed description, claims, appendices, and drawings, these terms are intended to be inclusive in a manner similar to that in which the term "comprising" is interpreted when used as a transitional word in a claim.

[0244] The descriptions of various embodiments have been presented for illustrative purposes, but are not intended to be exhaustive or limited to the embodiments disclosed herein. Many modifications and variations are apparent without departing from the scope and spirit of the described embodiments. The terminology used herein was chosen to best explain the principles of the embodiments, practical applications, or technical improvements over commercially available technologies, or to enable others of ordinary skill in the art to understand the embodiments disclosed herein.

[0245] Various non-limiting aspects are described in the following examples.

[0246] Example 1: A system may include: a processor that executes computer-executable components stored in a non-transitory computer-readable memory, wherein the computer-executable components include: an access component that can access a spectral image of a sample collected by a scientific instrument, wherein pixels of the spectral image correspond to an energy spectrum, respectively; a fitting component that can fit a function to the energy spectrum in a pixel-by-pixel manner, wherein the function includes multiple terms that are additively combined, and the first term of the multiple terms represents a fine structure of the energy spectrum, and wherein the integral associated with the first term is constrained to be zero; and an execution component that can segment the spectral image by material based on the first term.

[0247] Example 2: The system of any of the preceding examples may be implemented, wherein the multiple terms may further include a second term representing a monotonically decaying background of the energy spectrum and a third term representing an atomic cross section of the energy spectrum.

[0248] Example 3: The system of any of the preceding examples may be implemented, wherein the first and third terms may be convolved with a low-loss portion of the energy spectrum.

[0249] Example 4: The system of any of the preceding examples may be implemented, wherein the first term may include a spline whose basis functions are quadratic polynomials computed at intervals spaced apart by a power of two.

[0250] Example 5: The system of any of the preceding examples may be implemented, wherein the first term may include a spline whose basis functions are rectangular functions or trigonometric functions.

[0251] Example 6: A system of any of the preceding examples may be implemented, wherein the execution component may segment the spectral image by applying K-means clustering to the first item of the corresponding pixels of the spectral image or by executing a trained machine learning model on the first item of the corresponding pixels of the spectral image.

[0252] Example 7: A system can implement any of the preceding examples, wherein the execution component can segment the spectral image by applying K-means clustering to the fitting coefficients of the first term corresponding to the pixels of the spectral image or by executing a trained machine learning model on the fitting coefficients of the first term corresponding to the pixels of the spectral image.

[0253] Example 8: The system of any of the preceding examples may be implemented, wherein the scientific instrument may be an electron energy loss microscope.

[0254] In various embodiments, any one or more combinations of Examples 1 to 8 may be implemented.

[0255] Example 9: A computer-implemented method may include accessing, by a device operably coupled to a processor, a spectral image of a sample acquired by a scientific instrument, wherein pixels of the spectral image correspond respectively to an energy spectrum; fitting, by the device, a function to the energy spectrum in a pixel-by-pixel manner, the function comprising multiple terms in an additive combination, wherein a first term of the multiple terms represents a fine structure of the energy spectrum, and wherein an integral associated with the first term is constrained to be zero; and segmenting, by the device, the spectral image by material based on the first term.

[0256] Example 10: The computer-implemented method of any of the preceding examples may be implemented, wherein the plurality of terms may further include a second term representing a monotonically decaying background of the energy spectrum and a third term representing an atomic cross section of the energy spectrum.

[0257] Example 11: The computer-implemented method of any of the preceding examples may be implemented, wherein the first term and the third term may be convolved with a low-loss portion of the energy spectrum.

[0258] Example 12: The computer-implemented method of any of the preceding examples may be implemented, wherein the first term may include a spline whose basis functions are quadratic polynomials computed at intervals spaced apart by a power of two.

[0259] Example 13: The computer-implemented method of any of the preceding examples may be implemented, wherein the first term may include a spline whose basis functions are rectangular functions or trigonometric functions.

[0260] Example 14: A computer-implemented method of any of the preceding examples may be implemented, wherein segmentation of the spectral image may be based on: applying K-means clustering to the first item of the corresponding pixels of the spectral image by the device; or executing a trained machine learning model on the first item of the corresponding pixels of the spectral image by the device.

[0261] Example 15: A computer-implemented method of any of the preceding examples may be implemented, wherein segmentation of the spectral image may be based on: applying K-means clustering to the fitting coefficients of the first term of the corresponding pixels of the spectral image by the device; or executing a trained machine learning model on the fitting coefficients of the first term of the corresponding pixels of the spectral image by the device.

[0262] Example 16: The computer-implemented method of any of the preceding examples may be implemented, wherein the scientific instrument is an electron energy loss microscope.

[0263] In various embodiments, any one or more combinations of Examples 9 to 16 may be implemented.

[0264] Example 17: A computer program product for facilitating spectral image analysis via integral constrained fitting may include a non-transitory computer-readable memory containing program instructions. In various aspects, the program instructions are executable by a processor to enable the processor to: access a spectral image of a sample acquired by an electron energy loss microscope, wherein pixels of the spectral image correspond to an energy loss spectrum; fit a function to the energy loss spectrum in a pixel-by-pixel manner, wherein the function includes a fine structure term and wherein the integral associated with the fine structure term is constrained to be zero; and segment the spectral image based on the fine structure term (rather than based on the residue of the function).

[0265] Example 18: The computer program product of any of the preceding examples may be implemented, wherein the remainder of the function may include a monotonically decaying background term and an atomic cross section term additively combined with a fine structure term.

[0266] Example 19: A computer program product that can implement any of the preceding examples, wherein the fine structure term and the atomic cross section term (but not the monotonically decaying background term) can be convolved with the low-loss portion of the energy-loss spectrum.

[0267] Example 20: The computer program product of any of the preceding examples may be implemented, wherein the fine structure term may include a spline whose basis functions are: quadratic polynomials computed at intervals spaced a power of two; rectangular functions; or trigonometric functions.

[0268] In various embodiments, any one or more combinations of Examples 17 to 20 may be implemented.

[0269] In various embodiments, any one or more combinations of Examples 1 to 20 may be implemented.

Claims

1. A system comprising: a processor that executes computer-executable components stored in a non-transitory computer-readable memory, wherein the computer-executable components include: An access component accesses spectral images of samples collected by a scientific instrument, where pixels of the spectral images correspond to energy spectra respectively. a fitting component that fits a function to the energy spectrum in a pixel-by-pixel manner, the function comprising additively combined polynomials, wherein a first term of the polynomials represents a fine structure of the energy spectrum, and wherein an integral associated with the first term is constrained to zero; and An execution component is provided that segments the spectral image by material based on the first term. 2 . The system of claim 1 , wherein the plurality of terms further comprises a second term representing a monotonic decay background of the energy spectrum and a third term representing an atomic cross section of the energy spectrum.

3. The system of claim 2, wherein the first term and the third term are convolved with a low-loss portion of the energy spectrum.

4. The system of claim 1, wherein the first term comprises a spline whose basis functions are quadratic polynomials computed at intervals spaced apart by a power of two. The system of claim 1 , wherein the first term comprises a spline whose basis functions are rectangular functions or trigonometric functions. 6 . The system of claim 1 , wherein the executing component can segment the spectral image by applying K-means clustering to the first items of the corresponding pixels of the spectral image or by executing a trained machine learning model on the first items of the corresponding pixels of the spectral image.

7. The system of claim 1 , wherein the execution component can segment the spectral image by applying K-means clustering to the fitting coefficients of the first terms of the corresponding pixels of the spectral image or by executing a trained machine learning model on the fitting coefficients of the first terms of the corresponding pixels of the spectral image.

8. The system of claim 1, wherein the scientific instrument is an electron energy loss microscope.

9. A computer-implemented method, comprising: accessing, by a device operatively coupled to the processor, a spectral image of the sample acquired by the scientific instrument, wherein pixels of the spectral image respectively correspond to an energy spectrum; fitting, by the device, a function to the energy spectrum in a pixel-by-pixel manner, wherein the function comprises additively combined multinomials, wherein a first term of the multinomials represents a fine structure of the energy spectrum, and wherein an integral associated with the first term is constrained to zero; as well as The spectral image is segmented by material based on the first item by the device.

10. The computer-implemented method of claim 9, wherein the plurality of terms further comprises a second term representing a monotonic decay background of the energy spectrum and a third term representing an atomic cross section of the energy spectrum.

11. The computer-implemented method of claim 10, wherein the first term and the third term are convolved with a low-loss portion of the energy spectrum.

12. The computer-implemented method of claim 9, wherein the first term comprises a spline whose basis functions are quadratic polynomials computed at intervals spaced apart by a power of two.

13. The computer-implemented method of claim 9, wherein the first term comprises a spline whose basis functions are rectangular functions or trigonometric functions.

14. The computer-implemented method of claim 9, wherein segmenting the spectral image is based on: applying, by the device, K-means clustering to the first term of the corresponding pixels of the spectral image; or The trained machine learning model is executed by the device on the first term of the corresponding pixel of the spectral image.

15. The computer-implemented method of claim 9, wherein segmenting the spectral image is based on: Applying, by the device, K-means clustering to the fitting coefficients of the first term for corresponding pixels of the spectral image; or The trained machine learning model is executed by the device on the fitted coefficients of the first term for corresponding pixels in the spectral image.

16. The computer-implemented method of claim 9, wherein the scientific instrument is an electron energy loss microscope.

17. A computer program product for facilitating spectral image analysis by integral constrained fitting, the computer program product comprising a non-transitory computer readable memory having program instructions embodied therein, the program instructions being executable by a processor to cause the processor to: accessing a sample spectrum image acquired by an electron energy loss microscope, wherein pixels of the spectrum image correspond to energy spectra respectively; fitting a function to the energy loss spectrum in a pixel-by-pixel manner, the function including a fine structure term, wherein the integral associated with the fine structure term is constrained to zero; and Segment the spectral image based on the fine structure term (rather than based on the remainder of the function).

18. The computer program product of claim 17, wherein: The remainder of the function may include a monotonically decaying background term and an atomic cross section term additively combined with the fine structure term.

19. The computer program product of claim 18, wherein the fine structure term and the atomic cross section term (but not the monotonically decaying background term) are convolved with the low-loss portion of the energy-loss spectrum.

20. The computer program product of claim 17, wherein the fine structure terms comprise splines whose basis functions are: quadratic polynomials computed at intervals spaced a power of two; rectangular functions; or trigonometric functions.

Images