Peak position measurement offsets in two-dimensional optical spectra.

Abstract

A peak position measurement offset is determined in the two-dimensional optical spectrum. A plurality of peaks are identified that appear in both the spectrum obtained from the reference material under known conditions and the spectrum obtained from the sample of interest. The peak position measurement offset is determined by comparing a pattern formed by the peak positions of the identified plurality of peaks in the spectrum obtained from the sample of interest to the identified plurality of peaks in the spectrum obtained from the reference material.

Description

[Technical field]

[0001] The present disclosure relates to determining or judging peak position measurement offsets in a two-dimensional optical spectrum. [Background technology]

[0002] In Inductively Coupled Plasma Optical Emission Spectroscopy (ICP-OES), a plasma source ionizes and excites atoms in the gases that make up the plasma and / or in the sample. The light emitted by the excited atoms is collected, scattered, and directed towards a detector through a series of mirrors. After scattering, each ionized element emits a unique wavelength that occupies a unique location in the two-dimensional detector array.

[0003] The collection of all emission wavelengths (from the sample and plasma) at any one point scattered and projected onto the detector is called an "eshelogram" or "full frame". During manufacture and testing of an ICP-OES instrument, the mapping between position (expressed as x,y coordinates on the physical surface of the detector, e.g., a CCD chip), wavelength, and diffraction order is performed via a procedure called wavelength calibration. This procedure is performed with special care that the optics are thermally stabilized and that the temperature remains constant throughout the measurements required for the procedure. Intensity peaks can be identified in the spectrum, with each peak representing the signal from each unique wavelength.

[0004] The models that map positions to wavelengths and / or orders refer to these stability conditions. These stability conditions are not necessarily met during routine measurements (of a sample of interest) in terms of the environment (e.g., temperature, airflow, etc.). For example, temporary temperature fluctuations in the optical system may rotate mirrors, thereby introducing position shifts into the detector array. Thus, the models are sensitive to environmental conditions, and the mapping from positions to wavelengths and / or orders is typically inappropriate for routine measurements. In practice, drift or offsets are introduced into the positions that are compared to the models.

[0005] Existing approaches attempt to reduce drift by thermally isolating the plasma, particularly at temperatures between 5000 K and 10000 K, from the optical tank. Some ways to achieve this include physically removing the heat sink, using a different material at the torch box / optical tank interface, and using active heating and / or cooling devices at the torch box / optical tank interface. All of these entail tighter tolerances, higher material costs, and / or even more complexity.

[0006] For this reason, drift correction is considered to relocate each peak so that it can be accurately identified via its unique location on the detector. An existing technique for drift correction is described in GB 2586046. It uses peaks that appear in both the reference and sample spectra, such as from CO2. Subarrays can be defined around expected peaks and analysis can be limited to the subarray region. By carefully defining the subarray, interference from adjacent peaks can be mitigated. This allows the drift of the peak from its expected location to be calculated. The identified location of an unknown peak in the same sample spectrum can then be shifted using the determined drift. Spectral values ​​can also be interpolated within the subarray to more accurately determine or determine peak intensity values.

[0007] In practice, this approach can be implemented by choosing one peak from multiple options that are always present in a full frame. An offset is then applied linearly across the full frame, effectively canceling out the drift.

[0008] This approach becomes more difficult to implement if none of the peaks that always appear in a full frame have a clearly identifiable location in the spectrum. For example, this can occur due to saturation of the recorded intensity, interference by another peak, or excessive displacement of the full frame. In such cases, drift correction may fail. In some implementations, the measurement drift may vary depending on the selected peak. Therefore, a more robust and accurate approach to drift or offset measurement is desirable. Summary of the Invention

[0009] Against this background, there is provided a method for determining a peak position measurement offset in a two-dimensional optical spectrum according to claim 1. Also provided is a computer program for performing any of the methods disclosed herein. Further optional and / or advantageous features are defined in the dependent claims.

[0010] The disclosed approach uses significantly more information to estimate full-frame offset or drift. In existing approaches, linear offset is estimated based on the location of a single reference peak (which is a peak in both dimensions). In contrast, the disclosed approach uses a pattern formed by multiple peaks (a collection of two-dimensional peaks) to estimate drift. This may allow linear and / or nonlinear offsets to be measured. The use of a pattern may also allow distortion and / or interference effects on the peaks to be mitigated or ignored. The pattern is defined by the peak locations (although such locations need not be exact) and by a combination of approximate peak locations, and optionally together with and / or taking into account other information about the peaks (e.g., one or more of the following): the geometry (e.g., shape) formed by the peak locations, intensities (which may include relative intensities, e.g., simply ordering the peaks by intensity), and peak shapes (e.g., three-dimensional peak intensities across a two-dimensional spectrum). Additional information (other than peak locations) may form part of the pattern and / or be used to refine the pattern of peak intensities. The peak advantageously appears in both a spectrum obtained from a reference material under known conditions and a spectrum obtained from the sample of interest. A transformation or movement of the pattern (e.g., a translation, rotation, change in size, warping, or deformation) can be identified, and based on this, a measurement of drift can be deduced.

[0011] The approach according to the present disclosure can be used in a much wider range of environmental conditions (e.g., temperature) and a wider selection of sample matrices (e.g., high carbon). Additionally or alternatively, the approach can be more robust to two-dimensional image spectra, especially when a base peak can be surrounded by different sample peaks. Two-dimensional optical spectra can be obtained from an inductively coupled plasma optical emission spectroscopy (ICP-OES) instrument, although other forms of optical spectroscopy can be used instead.

[0012] The peaks are advantageously selected so that the change in the pattern formed by the peaks provides an accurate and robust measure of drift. In particular, preferably at least three peaks or at least four peaks are used (but more peaks can be used, for example at least or exactly 5, 6, 7 or more peaks). In this way, the positions of the peaks in the two-dimensional optical spectrum define a polygon, for example by connecting each peak to its two nearest neighbors. More preferably, the polygon is asymmetric (so that rotation of the polygon can be recognized). It is also advantageous that the peaks are characteristic of the plasma chemistry of the reference material and the sample material. The area enclosed by the peaks is preferably at least 10% (or more than 10%) of the spectrum.

[0013] Algorithms, such as image alignment algorithms (image registration algorithms) (e.g., phase correlation algorithms) and / or machine learning algorithms (e.g., using artificial neural networks), may be used to estimate the drift. The (filled) polygon shape may be used as a characteristic shape for image alignment. In some implementations, the offset may be determined by first estimating or measuring a peak-specific offset for each peak. An overall peak location measurement offset may then be established from the peak-specific offsets, for example, by a combination (e.g., weighted average) of the peak-specific offsets or by a further machine learning algorithm, such as a linear regression algorithm, that takes the peak-specific offsets as input.

[0014] Pre-processing of the two-dimensional optical spectral data is preferably performed prior to providing the data to image registration and / or machine learning algorithms. Various pre-processing steps may be considered, and any combination of these may be implemented, although preferred combinations are discussed herein.

[0015] For example, subarrays may be established around the peak. Each subarray (for both the reference and sample images) may be based on the respective position of the peak in the reference spectrum. Only the data within the subarray may be provided to and / or used in the algorithm used to estimate the drift. For example, pixels outside the subarray may be removed from both the sample and reference spectra. Using subarrays may help mitigate interference from adjacent peaks and / or reduce calibration costs. Removing pixels from subarrays may increase the percentage of the Regions Of Interest (ROI) for better accuracy of image registration.

[0016] One or more of the following may be used: removal of base levels, logarithmic transformation, and intensity normalization. In some implementations, each peak may be normalized with a number according to a number indicating the relative maximum value (magnitude) of the peak compared to other peaks. For example, the peaks may be normalized such that the highest peak has the lowest number, the second highest peak has the second lowest number, and so on until the smallest peak has the highest number. The numbers used may be prime numbers (particularly consecutive prime numbers).

[0017] Peak-specific offsets can be obtained in several approaches. A weighted average of these can then be taken to determine an overall offset. In particular, the weights for averaging can be based on the relative image correlation between the subarrays in the reference spectrum for the peak and the corresponding subarrays in the sample spectrum.

[0018] The determined offset may be verified. For example, image correlation may be determined between the reference spectrum and the sample spectrum before and after correction (according to the determined offset). If the correlation increases, the determined offset may be considered valid.

[0019] In some approaches, for each peak, a precise peak location is established. This can be achieved by analysis of the spectral intensity around each peak. For example, a K-means clustering algorithm on portions of the spectrum (each portion containing a single peak) can be used. Patterns can then be based on the precise peak locations.

[0020] A machine learning image alignment algorithm (preferably semi-supervised) can be trained first. In one implementation, the algorithm can be trained using, for each peak, a portion of the spectrum centered on the respective peak. The trained algorithm can then be queried to determine peak-specific offsets. For example, a polygon can be defined for all of the identified peaks by connecting adjacent peaks. The algorithm can then be trained using the portion of the spectrum centered on each peak along with the corresponding portion of the defined polygon.

[0021] The disclosure may be put into practice in many ways and a preferred embodiment may be described below, by way of example only, and with reference to the accompanying drawings. [Brief description of the drawings]

[0022] [Figure 1] 1 shows an exemplary two-dimensional optical spectrum for a reference material taken at known conditions. [Diagram 2] 2 shows the exemplary two-dimensional optical spectrum of FIG. 1 with six identified peaks connected by lines. [Diagram 3] 2 illustrates the exemplary two-dimensional optical spectrum of FIG. 1 with six identified peaks surrounded by square frames (subarrays) according to a first implementation. [Figure 4] 4 illustrates the example two-dimensional optical spectrum of FIG. 3 with additional processing to remove data outside the subarray. [Figure 5a] 5 shows a three-dimensional plot within an exemplary subarray of the spectrum shown in FIG. 4. [Figure 5b] 5b shows the three-dimensional plot of FIG. 5a with the reference level removed. [Figure 6a] A two-dimensional plot of the intensities of the subarrays in Fig. 4, with prime labels associated with each peak. [Figure 6b] We show the plot in Fig. 6a, where each intensity is normalized by its associated prime label. [Figure 7] 13 illustrates a series of initial pre-processing steps for an exemplary two-dimensional optical spectrum according to a second implementation. [Figure 8] 1 shows a series of further pre-processing steps for an exemplary two-dimensional optical spectrum. [Figure 9] 9 shows an additional pre-processing step from the output shown in FIG. [Figure 10] 10 illustrates diagrammatically the use of the output shown in FIG. 9 in training a machine learning image registration algorithm. [Figure 11] 10 illustrates diagrammatically the use of the output shown in FIG. 9 when querying a trained machine learning image alignment algorithm. [Figure 12] 12 illustrates generally the use of a query output from the process shown in FIG. 11 in a linear regression machine learning algorithm. [Figure 13] 1 illustrates a schematic depiction of an existing system for optical spectroscopy; DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0023] The disclosed approach uses a pattern formed by multiple peaks (typically three, four or more peaks). The peaks are present in both the reference spectrum or image (emission spectrum recorded while a reference material, which may be no sample or only deionized water, is fed through the sample introduction system) and the sample spectrum or image (emission spectrum recorded while a sample material containing the sample of interest is fed through the sample introduction system). Preferably, the peaks are characteristic of the plasma chemistry (i.e., the mixture of elements that are ionized in the plasma) and therefore are always present (as long as the plasma is ignited), regardless of the chemical introduced as the sample. The peaks can be distinguished from common elements (e.g., nitrogen, hydrogen, carbon) that are likely to be present in all test samples. Also, the peaks are desirably strong (intensity above a minimum threshold) and / or not easily interfered with by other sample peaks. The approximate location of such peaks in the spectrum may be known.

[0024] Referring first to Figure 1, an exemplary two-dimensional optical spectrum 10 is shown for a reference material taken under known conditions. This is a reference spectral image taken using ICP-OES in greyscale. Six peaks 20 are identified in the spectrum.

[0025] Referring now to FIG. 2, the exemplary two-dimensional optical spectrum 10 of FIG. 1 is shown having six identified peaks 20 connected by lines (each line connects the two nearest neighboring peaks). As shown, these six peaks form a polygonal shape. It is established that any three or more peaks may form the vertices of the polygonal shape, but four or more peaks are preferred. The peaks are preferably selected to form the vertices of a polygonal shape, more preferably an asymmetric polygonal shape. When a symmetric polygonal shape is used, it may be difficult to distinguish between rotation and translation of the peaks. It is also desirable that the area enclosed by the selected reference peaks (the area of ​​the polygon formed by the peaks) is greater than 10% of the area of ​​the entire spectral image ("full frame").

[0026] The pattern formed by this polygon may change between the reference and sample spectra. By processing the changes in the pattern, an estimate or measurement of drift can be made. Image registration is a useful tool for determining drift from pattern changes. The pattern uses peak positions, but may also consider (include and / or be refined by) one or more of the following: the geometric shape formed by the peak positions (e.g., the polygon discussed above), the intensity or relative intensity of the peaks, and the peak shape. By considering the pattern more generally than only the peak positions, distortions and / or interferences that affect the determination of the peak positions can be taken into account. For example, interferences may cause peaks to overlap partially or completely with the reference peaks. As a result, it may be difficult to determine the peak positions (e.g., double peaks or other more complex peak shapes may appear). Additionally or alternatively, the peak positions may appear to have shifted due to interferences rather than due to drift, as evident from changes in (relative) intensity and / or changes in the shape of the peaks. These effects may also be evident by distortions unrelated to drift. Therefore, determining drift based on pattern changes can account for these effects, for example by reducing (or ignoring) weight peaks when the pattern change is not solely in the peak position.

[0027] Two different algorithms for processing the changes are considered as examples. In the first approach, a phase correlation image alignment algorithm is used. It can determine the offset from the change in the pattern formed by the position and relative intensity of the reference peaks. In the second approach, a machine learning image alignment implementation is applied. It can use the change in the polygon shape formed by the exact location of the reference peaks to determine the offset. These two approaches are considered in more detail below.

[0028] Each approach uses a different pre-processing step to maximize the use of the respective algorithm. It will be appreciated that different pre-processing steps are possible and, in fact, different algorithms may also be applied. It will also be appreciated that, looking at changes in the pattern of peaks, the overall offset may be determined by providing peak-specific offsets from the analysis of multiple peaks combined together or by analyzing changes in one or more individual peaks, and then using these to determine the overall offset.

[0029] In a general sense, a method for determining a peak position measurement offset in a two-dimensional optical spectrum (specifically a two-dimensional optical spectrum obtained from a sample of interest) can be considered. The method includes identifying a plurality of peaks appearing in both a spectrum obtained from a reference material under known conditions and a spectrum obtained from the sample of interest, and determining a peak position measurement offset by comparing a pattern formed by the peak positions of the identified plurality of peaks in the spectrum obtained from the sample of interest with a pattern formed by the peak positions of the identified plurality of peaks in the spectrum obtained from the reference material. The method can be implemented, for example, by a controller that may form part of an optical spectrometer, or in the form of a computer program including instructions configured to perform the method when executed by a computer. The present disclosure can also provide one or more of an optical spectrum analyzer, a computer program, an optical spectrometer (e.g., an ICP-OES instrument), which may include such an optical spectrum analyzer and / or computer program or may be configured to operate according to the method.

[0030] Preferably, the identified peaks include at least three or four peaks. The positions of the identified peaks in the two-dimensional optical spectrum desirably define the vertices of a polygon (by connecting each peak to its two nearest neighbors), preferably an asymmetric polygon. Advantageously, the identified peaks are characteristic of the plasma chemistry of the reference material and the sample material. In an embodiment, the area of ​​the two-dimensional spectrum enclosed by the identified peaks (and / or the polygon defined by the peaks, e.g., as discussed above) is at least 10% (or more than 10%) of the two-dimensional optical spectrum (optionally at least 20%, 25%, 30%, 40%, 50%, 60%, 70%, 80%, or 90%).

[0031] In certain implementations, the pattern is formed by the peak positions and the (relative) intensities and / or shapes of the identified peaks.

[0032] The determining step includes establishing the comparison using an image registration algorithm (eg, a phase correlation algorithm) and / or a machine learning algorithm.

[0033] The peak position measurement offset may be determined using peak-specific offsets for each of the multiple peaks, for example, the peak-specific offsets may be combined, interpolated, or otherwise analyzed.

[0034] Two particular implementations are now described by way of example only, to which further details in the general sense discussed above are referred to again below.

[0035] Implementation example 1 This implementation is discussed with reference to seven steps and uses a phase correlation image registration algorithm.

[0036] 1) In the reference image, four or more reference peaks are selected (four is preferred, although fewer reference peaks may be used, as discussed below). Referring to FIG. 3, the exemplary two-dimensional optical spectrum of FIG. 1 is shown with six identified peaks surrounded by a square frame (subarray). The frame width or thickness in any direction from the identified peak is larger than the maximum possible drift (geometric offset of the peak position relative to the complete full-frame fixed coordinate system mapping). The minimum size of the subarray is desirably larger than the maximum drift of the image, which can ensure that the peak of the sample image is always in the subarray. The maximum size of the subarray is typically small enough to include one peak (and preferably only one) in the subarray.

[0037] Each peak is labeled with a different prime number and sorted in ascending order of relative signal strength. These prime labels start at 3. The starting point is not important, and to avoid even labels, 2 is avoided. The absolute position in the frame (pixel index in the subarray) is recorded and labeled with the assigned prime label.

[0038] 2) A newly acquired image is obtained by ICP-OES of the sample material of interest (hereafter this image is called the sample image). The reference peak in the sample image is shifted with respect to the peak in the reference image by an estimated unknown amount. In the sample image, the peak is again identified according to its absolute position (pixel index) in the reference image, regardless of the position of the reference peak in the sample image, and the subarray frame is determined.

[0039] 3) All pixels that are not within the selected subarray frame are set to zero for both the reference and sample images. This may help to avoid the computational or machine learning algorithm being misled by extra features (pixels) that do not convey relevant information. Additionally or alternatively, it may ensure that the computational algorithm or training is computationally efficient. Referring to FIG. 4, the exemplary two-dimensional optical spectrum of FIG. 3 is shown with additional processing to remove data outside the subarray (dot-square frame) according to this step.

[0040] 4) Now referring to FIG. 5a, a three-dimensional plot of the intensities in an exemplary subarray of the spectrum shown in FIG. 4 is shown. It shows a reference level, indicated by a relatively high intensity level ("bump") along the y dimension. In other words, considering each value on the y axis, the minimum level is higher than 0. Removal of this reference level is advantageous to accurately identify peaks. Therefore, the reference level is preferably removed from each pixel in the subarray by subtracting either i) the minimum intensity value across the entire subarray, or ii) the minimum intensity value across the y values ​​(rows) of the subarray. Referring to FIG. 5b, the three-dimensional plot of FIG. 5a is shown with the reference level removed by subtracting the minimum intensity value across the y values ​​(rows) of the subarray. This step may be omitted in an embodiment.

[0041] 5) A logarithmic transformation is applied to the intensities of both the reference and sample images. This step can also be omitted in embodiments.

[0042] 6) Referring now to FIG. 6a, the intensities of the subarrays of FIG. 4 are plotted in two dimensions, with a prime label associated with each peak shown. The z-axis of this figure shows the measured intensity. Each peak is then normalized according to its assigned prime label. Referring now to FIG. 6b, the plot of FIG. 6a is shown, with each intensity normalized by its associated prime label. This is performed for both the reference and sample images. This normalization removes some of the peak intensity information, but at least preserves that the peaks have different intensities, specifically their respective intensity orders. Nevertheless, by normalizing the peaks in this way, the relative weighting of the peaks is adjusted (e.g., any peaks that have a much lower intensity than other peaks are not ignored by the algorithm).

[0043] 7) Apply a phase correlation algorithm to achieve image registration between the reference image and the sample image (with unknown drift) and estimate the drift of the sample image with sub-pixel accuracy. The particular algorithm applied in this example is disclosed in Hassan Foroosh, et al., "Extension of Phase Correlation to Subpixel Registration", IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 11, NO. 3, MARCH 2002, pages 188-199, which is incorporated as if disclosed herein. For completeness, key elements of this algorithm are discussed below.

[0044] a. After pre-processing according to the above steps, a Fourier transform is applied to both the reference image and the sample image (f(x,y),f s (x',y')), frequency domain spectrum (F0(u,v),F s (u',v') is obtained. b. The power spectrum is calculated as follows:

[0045]

number

[0046] c. An inverse Fourier transform is applied to the power spectrum H(u,v) to obtain the Dirac function δ(x'-x, y'-y). d. Peaks in the Dirac function are identified using a quadratic polynomial that works by fitting eight pixels around the "peak" pixel (the one with the maximum intensity). e. Hence, the peak position (x'-x, y'-y) is obtained as the sample image drifts.

[0047] Returning to the general sense discussed above, further optional and / or advantageous features may be considered. For example, the method may further comprise establishing a respective subarray around each of the identified peaks in the spectrum obtained from the sample of interest and in the spectrum obtained from the reference material. Each subarray may be based on a respective position of each identified peak in the spectrum obtained from the reference material (or may be a subarray for each identified peak in the spectrum obtained from the sample material). The comparison is advantageously based (only) on the information in the subarray.

[0048] Optionally, the comparison uses one or more of the identified peaks with the reference level removed, with a logarithmic transformation applied, and with intensity normalization. Advantageously, each of the identified peaks is normalized according to a number indicating the relative maximum or magnitude of the respective peak compared to the other identified peaks in the two-dimensional optical spectrum. For example, the number may be provided by a set of prime numbers, and in an embodiment, the number is selected from a continuous range of prime numbers. In such latter case, each peak is normalized according to a number within a continuous range of prime numbers corresponding to the relative maximum or magnitude of the respective peak compared to the other identified peaks in the two-dimensional optical spectrum.

[0049] The determining step advantageously includes establishing the comparison using a phase correlation algorithm.

[0050] Further specific details according to a second implementation example will now be considered, again with information pertaining to such general meaning of the disclosure being provided later.

[0051] Implementation example 2 This implementation uses a machine learning image alignment algorithm and is discussed with reference to five steps.

[0052] 1) In the reference image, four or more reference peaks are selected (four is preferred, although fewer may be used, as discussed below). This identifies rough coordinates for each of the selected reference peaks. A sample image is also obtained with the reference peaks, but shifted relative to those in the reference by an estimated unknown amount.

[0053] 2) Pre-processing of the reference and sample images for the machine learning image alignment algorithm is implemented using several steps. See Fig. 7, where a series of initial pre-processing steps are shown in schematic form, and Fig. 8, where a series of further pre-processing steps are shown. This is based on a sample spectrum image 100.

[0054] The rough coordinates of the selected reference peak are used to cut (105) a small image slice from the sample image 100. The rough coordinates of the peak 115 are (x n ,y n ), the cut pieces are

[0055]

number

[0056]

number

[0057] b. K-means algorithm 116 with clusters=2 is used on the cropped image piece 110. The reference peak has a larger intensity and is therefore extracted by the K-means algorithm. To perform peak segmentation, the pixel intensity of the identified peak 122 is marked as 1 and the background pixels 121 are marked as 0. This is shown by the segmented cropped image piece 120. Again, this is performed for all peaks according to the K-means clustering step 210 also shown in FIG. 8.

[0058] c. A peak bounding box 130 is generated 125 from the peak segmentation. d. The coordinates of the bounding box center 140 are identified 135 as the exact location of the peak.

[0059] e. Using the identified coordinates, the sample image is then modified according to step 220 to connect the exact locations of the peaks, thereby forming a polygon. Pixel values ​​within the polygon 230 are marked with intensity 1, and the remainder of the sample image 240 is marked with intensity 0. This operation creates a segmented image 250 with defined (filled) polygonal regions that can be used for subsequent AI training. f. Pre-processing steps a-d are repeated on the reference spectral image.

[0060] 3) First, consider training a machine learning image alignment algorithm with reference to FIG. 9, which shows additional pre-processing steps from the sample spectral image 100 and segmented image 250 shown in FIG. 8.

[0061] a. Using the determined accurate peak locations as centers, larger pieces of the sample spectrum image for each reference peak are cut out and extracted (260). The cut out process is the same as that discussed with reference to step 3a above, but with a larger size (e.g., size=128). This may accelerate the training of the machine learning algorithm by using several small images (as many as peaks) instead of a large 2048×2048 image. The cut out pieces of the spectrum are normalized to provide raw image pieces 265 that are used for training (not for finding peaks as in step 3). In addition, the segmented image 250 is cut out and extracted (270) for each peak with the same size and same location to provide segmented cut out pieces 275. The cut out process 260 and extraction process 270 are performed for all peaks, resulting in raw image pieces 265 and segmented fragment images 275 for all peaks. In each cut out fragment image 275, filled triangles are seen. These triangles have different shapes and interior angles. They can be used as characteristic shapes for machine learning image recognition.

[0062] b. Referring now to FIG. 10, there is shown a schematic diagram of the use of the output shown in FIG. 9 in training a machine learning image alignment algorithm, specifically a U-Net model (as originally described in Ronneberger, Olaf; Fischer, Philipp; Brox, Thomas (2015) "U-Net: Convolutional Networks for Biomedical Image Segmentation", Springer, Cham.). It uses a video (m) and a fixed image (f). A U-Net model 280 is trained on a video 281 (m) and a fixed image 282 (f) based on raw image pieces 265 for the reference and sample spectral images, respectively. A spatial transformation block 285 is used to identify an "alignment field" 283 for transforming the video to predict a "shifted image" 286 that corresponds to the "fixed image" 282. The "shifted image" 286 is compared to the "fixed image" 282 to compute a loss function. Such fixed images of segmented fragments 275 and videos of segmented fragments 276 are used for semi-supervised learning to identify spatial transformations in order to arrive at a segmentation 290 of the moved image (which acts as a mask to establish areas for focus and thereby improve the accuracy of the prediction).

[0063] The U-Net model adjusts its weights to minimize the loss between the "moved" and "fixed" images. L us (f,m,φ)=L sim (f,m°φ)+λL smooth (φ) L a (f,m,s f ,s m ,φ)=L us (f,m,φ)+ΥL seg (s f ,s m °φ) During the ceremony, L sim penalizes differences in appearance, typically MSE 288, L smoothpenalizes local spatial variation,287 L us is the loss function for unsupervised learning, L seg is the segmentation loss,289, L a is the loss function for semi-supervised learning.

[0064] Each peak is trained separately since it may have a different weighting. In other words, this step is repeated for each reference peak. The U-Net model provides feature extraction and gives as its output an "alignment field" 283 that represents the drift in the x and y dimensions.

[0065] 4) Referring now to FIG. 11, there is shown generally the use of the output shown in FIG. 9 when querying a trained machine learning image alignment algorithm.

[0066] 9, a larger fragment of the sample spectral image for each reference peak is cropped and extracted (260) using a smaller size and normalized to provide raw image pieces 265. Similarly, segmented image 250 is cropped and extracted (270) for each peak having the same size and same position to provide segmented cropped pieces 275.

[0067] b. Each original image piece 265 and segmentation fragment 275 for the peaks are provided as input to a trained U-Net model 300. Using weights 310 (determined from training, as discussed above), the U-Net model 300 provides an alignment field 283 as output. A query 330 based on the position of each peak 335 is used to determine an x ​​drift 336 and a y drift 337 for the peak. This results in a set of peak-specific x and y drift estimates, an x ​​drift estimate and a y drift estimate for each peak.

[0068] 5) A linear regression algorithm can then be used to determine an overall x drift estimate and an overall y drift estimate. This is because the calculated drift for each of the peaks is likely to be different and it is desirable for the entire image to have only one drift (dx, dy). Referring now to Figure 12, there is shown a schematic of the use of the query output from the process shown in Figure 11 for six peaks in a linear regression machine learning algorithm.

[0069] An exemplary linear regression is based on the following equation:

[0070]

number

[0071] A linear regression algorithm is first trained using the query output. Then, for a given sample image, the preprocessing and querying in step 4) above are performed. The manually identified image drifts of several sample images are used as (Pred_x,Pred_y), and then the machine learning predicted drift (Peak_x_drift,Peak_y_drift)_i is calculated using the metric 350, α i , βi , b x , and b y The weights from the output of the linear regression algorithm are used to predict the final drift. In other words, the predicted drift (Peak_x_drift,Peak_y_drift)_i from the machine learning algorithm and a constant α i , β i , b x and b y is used to calculate the global drift (Pred_x,Pred_y) for the entire image, which allows the linear regression algorithm to integrate the peak-specific drift estimated from each reference peak.

[0072] Returning to the general sense of the present disclosure as considered above, further optional and / or beneficial features are considered. For example, the method may further include establishing a position for each of the identified peaks based on the intensity of the two-dimensional optical spectrum around each identified peak. For example, this may be accomplished by using a K-means clustering algorithm on portions of the two-dimensional optical spectrum (each portion typically containing a single peak). The pattern may be based on the established positions of the identified peaks.

[0073] The method advantageously further includes training a machine learning image alignment algorithm for each peak using at least a portion of the two-dimensional optical spectrum centered on each peak. A peak-specific offset can then be determined for each of the multiple peaks using the trained machine learning image alignment algorithm. The U-Net model can provide a suitable machine learning image alignment algorithm. The machine learning image alignment algorithm may be semi-supervised. For example, for all of the identified peaks, a polygon formed by connecting adjacent peaks can be defined. The machine learning image alignment algorithm can be trained by using a portion of the two-dimensional optical spectrum centered on each peak (to enable semi-supervised learning) together with a corresponding portion of the defined polygon.

[0074] In an embodiment, an overall peak location measurement offset can be established from the peak-specific offsets. Advantageously, the linear regression machine learning algorithm can be provided with the peak-specific offsets to determine the overall peak location measurement offset. Additional details in the general sense discussed above are further referenced below.

[0075] Implementation example 3 This implementation is discussed with reference to four steps and, like implementation 1, uses a phase correlation image alignment algorithm.

[0076] 1) Perform steps 1 and 2 of Implementation Example 1. 2) Remove the pixels outside the subarray from both the reference image and the sample image to obtain a trimmed (smaller size) reference image and a trimmed (smaller size) sample image. This can increase the ratio of the region of interest (ROI) for better accuracy in image alignment. For example, assuming the original full-frame image has N×N pixels, n peaks are selected as reference peaks, and n subarrays with a size of n×m pixels are selected, where n×m×m < N×N, and the resized image can be (n×m)×m pixels, m×(n×m) pixels, or (qn×m)×(qn×m), etc., where

[0077]

Number

[0078] 3) Perform one, two or more, or all of steps 4, 5, and 6 of Implementation Example 1. Any one or more of these steps can be omitted, and these steps can be performed in a different order.

[0079] 4) Apply the phase correlation algorithm to achieve image alignment between the resized reference image and the resized (with unknown drift) sample image, and estimate the drift of the sample image with sub-pixel accuracy (as considered in step 7 of Implementation Example 1, for example).

[0080] Example 4 This implementation example is considered with reference to six steps and, similar to Implementation Example 1, uses the phase correlation image alignment algorithm.

[0081] 1) Perform steps 1 and 2 of Implementation Example 1. 2) Implement one, two or more, or all of steps 4, 5, and 6 of Implementation Example 1. Any one or more of these steps can be omitted, and the steps can be implemented in a different order.

[0082] 3) Apply the phase correlation algorithm to achieve image alignment between each sub-array in the reference image and the corresponding sub-array in the sample image (with unknown drift), and estimate the drift of the sample image with sub-pixel accuracy (as considered in step 7 of Implementation Example 1, for example). For example, assuming that the original full-frame image has N×N pixels, n peaks are selected as reference peaks, and n sub-arrays with a size of m×m pixels are selected, where n×m×m < N×N, and thus n values of drift are obtained.

[0083] 4) The final drift of the sample image is calculated using the weighted drift as detailed in the following equation.

[0084]

Equation

[0085]

Equation

[0086]

Equation

[0087]

Equation

[0088] 5) Although not necessary, preferably, in step 4, w i can be set to zero (C i in the case of <C0), where C0 is the threshold of the image correlation selected by the operator. For example, C0 can be 0.95, 0.90, 0.85, 0.80, etc.

[0089] 6) Although not necessary, preferably, after the validity check is performed and the drift correction is applied, if the image correlation C' between the reference image and the sample image is less than or equal to the previous one C, the drift estimation is discarded (the drift vector is set to D~zero) before applying the drift correction.

[0090]

Number

[0091]

Number

[0092] Implementation example 5 This implementation example is considered with reference to five steps and, like Implementation Example 1, uses the phase correlation image alignment algorithm.

[0093] 1) Perform steps 1 to 7 of Implementation Example 1. Any one or more of steps 4, 5, and 6 of Implementation Example 1 can be omitted and / or those steps can be performed in a different order.

[0094] 2) If the validity check is performed and the image correlation C' between the reference image and the sample image after drift correction is less than or equal to the previous one C, the drift estimation is discarded (the drift vector is set to D~zero) before drift correction.

[0095]

number

[0096] 3) In step 2, if the validity check passes (i.e., the drift estimate is not discarded), perform steps 2 to 4 of Implementation Example 3. 4) The same validity checks as in step 2 of this implementation example are performed again. 5) In step 4, if the validity check passes (i.e., the drift estimate is not discarded), perform steps 2 to 6 of Implementation Example 4.

[0097] Referring again to the general meaning of the present disclosure as discussed above, further optional and / or advantageous features may be detailed. For example, in some embodiments, pixels outside the subarray may be removed from both the spectrum obtained from the sample of interest and the spectrum obtained from the reference material. The comparison (of the pattern formed by the peak positions of the identified peaks) is then advantageously based on the spectrum obtained from the sample of interest after removal of the pixels and the spectrum obtained from the reference material after removal of the pixels. This may increase the proportion of the ROI for better accuracy of image registration.

[0098] In some embodiments, determining the peak location measurement offset includes determining a peak-specific offset for each of the plurality of peaks. The peak location measurement offset may then be calculated by taking a weighted average of the peak-specific offsets determined for the plurality of peaks. Each weight of the weighted average is advantageously determined based on a relative correlation between a portion (subarray) of the spectrum obtained from the sample of interest corresponding to the respective peak and a portion (subarray) of the spectrum obtained from the reference material corresponding to the respective peak.

[0099] The determined peak position measurement offset may optionally be verified. This may be accomplished by comparing (i) the correlation between the spectrum obtained from the sample of interest and the spectrum obtained from the reference material, and (ii) the correlation between the corrected spectrum from the sample of interest and the spectrum obtained from the reference material. In particular, the corrected spectrum from the sample of interest may be generated by applying a correction to the spectrum obtained from the sample of interest based on the determined peak position measurement offset.

[0100] Referring to Figure 13, there is shown a schematic diagram of an existing system for optical spectroscopy, as disclosed in GB Patent No. 2586046. This system can be adapted to operate in accordance with the present disclosure.

[0101] The schematic optical spectroscopy system 400 is shown to include a light source 410, an optical device 420, a detector array 430, a processor 440, a memory 445, and an input / output (I / O) unit 450. The light source 410 may be a plasma source, such as an ICP source. The optical device 420 may include an echelle grating and a prism (and / or further gratings) to generate an echelle spectrum of the light generated by the light source 410. An image of the two-dimensional echelle spectrum is formed on the detector array 430. The detector array 430 may be, for example, a CCD (charge-coupled device) array. A typical detector array will have at least about 1024×1024 pixels (1 megapixels). The rectangular detector array may be, but is not necessarily, square. The detector array 430 may be configured to generate spectral values ​​corresponding to the detected light amount of the echelle spectrum and transfer the spectral values ​​to the processor 440. The processor 440 may be configured by a commercially available microprocessor. The memory 450 may be a suitable semiconductor memory and may be used to store instructions that enable the processor 440 to perform embodiments of the methods according to the present disclosure.

[0102] Although the embodiments according to the present disclosure are described with reference to a particular type of device and application (particularly ICP-OES), and the embodiments have particular advantages in such cases, as discussed herein, the approach according to the present disclosure may be applied to other types of devices and / or applications. In particular, the technique may be applied to other types of two-dimensional optical spectra. The particular structural, arrangement and operational details (e.g., parameters) of the process, while potentially advantageous (especially in view of known configurations and capabilities), may be significantly modified to arrive at an operational mode having similar or identical performance. Certain features may be omitted or substituted, for example, as shown herein. Each feature disclosed herein may be replaced by an alternative feature serving the same, equivalent, or similar purpose, unless otherwise specified. Thus, unless otherwise specified, each feature disclosed is merely an example of a generic series of equivalent or similar features.

[0103] In implementation example 1, many of the pre-processing steps can be avoided and / or their order can be changed. For example, only sub-array processing (steps 2 and 3 in the algorithm) may be performed, and steps 4-6 may be omitted. Any one or more of steps 4, 5, and 6 can be omitted, and the steps can be performed in a different order. Also, while prime number labels are used for improved processing, the use of prime numbers is not required. Other numeric labels can be used to indicate relative intensity patterns.

[0104] Phase correlation algorithms, U-Net model algorithms, and linear regression algorithms are just examples of a wide range of algorithms that can be used in accordance with the present disclosure. Those skilled in the art will recognize different image registration algorithms, with or without machine learning, that can be used to identify changes in patterns of peak positions (and, optionally, intensities or relative intensities). Some of these may identify peak-specific offsets that can be used to determine an overall peak position measurement offset, while others may be able to directly determine an overall peak position measurement offset. As discussed above, other algorithms can be used to make drift determinations for specific combinations of pattern changes, some of which do not require the use of image registration, but other pattern information from the peak data.

[0105] As used herein, including in the claims, the singular form of a term herein is to be construed as including the plural, and vice versa, unless the context indicates otherwise. For example, in the claims, a reference to a singular form, including "a" or "an" (such as an ion multipole device), means "one or more" (e.g., one or more ion multipole devices), unless the context indicates otherwise. Throughout the specification and claims of this disclosure, words such as "comprise," "including," "having," and "contain," as well as variations of words such as "comprising" and "comprises" or the like, mean "including, but not limited to," and are not intended to exclude other components.

[0106] The use of any and all examples or exemplary language provided herein (such as, for example, and similar language) is intended merely to better illustrate the invention and does not pose a limitation on the scope of the disclosure unless specifically claimed. No language in the specification should be construed as indicating any element not claimed as essential to the practice of the disclosure.

[0107] Any steps described herein can be performed in any order, or simultaneously, unless otherwise stated or required otherwise by context.

[0108] All aspects and / or features disclosed herein may be combined in any combination, except combinations in which at least some of such features and / or steps are mutually exclusive. There may be specific combinations of aspects that are more beneficial, such as combinations of specific pre-processing steps and specific algorithms, as described herein. In particular, preferred features of the present disclosure are applicable to all aspects of the present disclosure and may be used in any combination. Similarly, features described in non-essential combinations may be used separately (not in combination).

Claims

1. 1. A method for determining a peak position measurement offset in a two-dimensional optical spectrum, the method comprising: Identifying a plurality of peaks that appear in both a spectrum obtained from a reference material under known conditions and a spectrum obtained from a sample of interest; determining the peak position measurement offset by comparing a pattern formed by peak positions of the identified peaks in a spectrum obtained from the sample of interest with a spectrum obtained from the reference material.

2. 2. The method of claim 1, wherein the identified plurality of peaks includes at least three peaks and / or the positions of the identified plurality of peaks in the two-dimensional optical spectrum define vertices of an asymmetric polygon.

3. The method of claim 1 or 2, wherein the identified peaks are characteristic of the plasma chemistry of the reference material and the sample.

4. The method of any one of claims 1 to 3, wherein the area of ​​the spectrum enclosed by the identified peaks is at least 10% of the two-dimensional optical spectrum.

5. The method according to any one of claims 1 to 4, wherein the pattern is formed by peak positions, taking into account the intensities and / or shapes of the identified peaks.

6. The method of any one of claims 1 to 5, wherein said determining comprises using an image registration algorithm and / or a machine learning algorithm to establish said comparison.

7. The method of any one of claims 1 to 6, wherein the peak location measurement offset is determined using a peak-specific offset for each of the plurality of peaks.

8. 8. The method of claim 1, further comprising: establishing a respective subarray around each of the plurality of identified peaks in the spectrum obtained from the sample of interest and the spectrum obtained from the reference material based on a respective position of each identified peak in the spectrum obtained from the reference material, wherein the comparison is based on information in the subarray.

9. 10. The method of claim 8, further comprising removing pixels outside the subarray from both the spectrum obtained from the sample of interest and the spectrum obtained from the reference material, wherein the comparison is based on the spectrum obtained from the sample of interest after removal of the pixels and the spectrum obtained from the reference material after removal of the pixels.

10. 10. The method of claim 1, wherein the comparison uses the identified peaks with one or more of a reference level removed, a logarithmic transformation applied, and intensity normalization.

11. 11. The method according to any one of claims 1 to 10, wherein each of the identified peaks is normalized according to a number indicating the relative maximum value of the respective peak compared to other identified peaks in the two-dimensional optical spectrum.

12. 12. The method of claim 1, further comprising establishing a position for each identified peak based on an intensity of the two-dimensional optical spectrum around each identified peak, wherein the pattern is based on the established positions for the identified peaks.

13. determining the peak position measurement offset determining a peak-specific offset for each of the plurality of peaks; 13. The method of claim 1, further comprising: calculating the peak location measurement offset by taking a weighted average of the peak-specific offsets determined for the plurality of peaks, each weight being determined based on a relative correlation between a portion of a spectrum obtained from the sample of interest corresponding to the respective peak and a portion of a spectrum obtained from the reference material corresponding to the respective peak.

14. 14. The method of claim 1, further comprising: validating the determined peak position measurement offset by comparing (i) a correlation between a spectrum obtained from the sample of interest and a spectrum obtained from the reference material, and (ii) a correlation between a corrected spectrum obtained from the sample of interest and a spectrum obtained from the reference material, wherein the corrected spectrum from the sample of interest is generated by applying a correction to the spectrum obtained from the sample of interest based on the determined peak position measurement offset.

15. training a machine learning image alignment algorithm for each peak using at least a portion of the two-dimensional optical spectrum centered on each peak; 15. The method of claim 1, further comprising: determining a peak-specific offset for each of the plurality of peaks using the trained machine learning image alignment algorithm.

16. The method of claim 15 , wherein the machine learning image registration algorithm is semi-supervised.

17. 17. The method of claim 15 or 16, further comprising defining a polygon by connecting adjacent peaks for all of the identified peaks, and wherein the training of the machine learning image alignment algorithm uses the portion of the two-dimensional optical spectrum centered on each peak together with a corresponding portion of the defined polygon.

18. A computer program comprising instructions adapted to perform the method according to any one of claims 1 to 17, when the computer program is executed by a computer.

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