Peak position measurement offset 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] This disclosure relates to determining or judging the peak position measurement offset 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 gas and / or sample that make up the plasma. The light emitted by the excited atoms is focused, scattered, and guided through a series of mirrors towards a detector. After scattering, each ionized element emits a specific wavelength that occupies a unique position in the two-dimensional detector array.

[0003] The collection of all emission wavelengths (from the sample and plasma) at any given point, scattered and projected onto the detector, is called an "eschelogram" or "full frame." During the manufacture and testing of ICP-OES instruments, mapping between position (represented as x, y coordinates on the physical surface of the detector, e.g., a CCD chip) and wavelength and diffraction order is performed through a procedure called wavelength calibration. This procedure is carried out with special care to ensure that the optical system is thermally stabilized and that the temperature is kept constant throughout the measurements required for the procedure. Intensity peaks can be identified in the spectrum, and each peak represents a signal originating from its respective intrinsic wavelength.

[0004] Models that map position to wavelength and / or order refer to these stability conditions. These stability conditions are not necessarily met during routine measurements (of the sample of interest) from an environmental perspective (e.g., temperature, airflow, etc.). For example, transient temperature fluctuations in the optical system may rotate the mirrors, thereby introducing a position shift in the detector array. Therefore, the model is sensitive to environmental conditions, and mapping from position to wavelength and / or order is typically unsuitable for routine measurements. In practice, drift or offset is introduced into the position compared to the model.

[0005] Existing approaches attempt to reduce drift, particularly by thermally separating the plasma, which is at temperatures between 5000K and 10000K, from the optical tank. Several methods to achieve this include physically removing the heat sink, using different materials at the joint between the torch box and the optical tank, and using active heating and / or cooling devices at the joint between the torch box and the optical tank. All of these inevitably involve tighter tolerances, higher material costs, and / or greater complexity.

[0006] For this reason, drift correction is considered to reposition each peak so that it can be accurately identified through its respective unique position on the detector. An existing technique for drift correction is described in UK Patent No. 2586046. This uses peaks that appear in both the reference spectrum and the sample spectrum, such as CO2. A subarray can be defined around the expected peak, and the analysis can be limited to the subarray region. By carefully defining the subarray, interference from adjacent peaks can be reduced. This allows the drift of the peak from its expected position to be calculated. The identified location of an unknown peak in the same sample spectrum can then be shifted using the determined drift. Furthermore, spectral values ​​can be interpolated within the subarray to more accurately determine or judge peak intensity values.

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

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

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

[0010] The approach of this disclosure uses a considerable amount of information to estimate the full-frame offset or drift. In existing approaches, linear offset is estimated based on the position of a single reference peak (which is a peak in both dimensions). In contrast, the approach of this disclosure 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 the effects of distortion and / or interference on the peaks to be mitigated or ignored. The pattern is defined by the peak positions (however such positions do not need to be exact), by combinations of approximate peak positions, and optionally, together with and / or in consideration of other information about the peaks (e.g., one or more of the following): the geometric structure formed by the peak positions (e.g., shape), intensity (which may include relative intensity, e.g., simply ordering the peaks by intensity), and peak shape (e.g., three-dimensional peak intensity across a two-dimensional spectrum). Additional information (other than peak positions) may form part of the pattern and / or be used to refine the pattern of peak intensity. The peaks appear, advantageously, in both the spectrum obtained from a reference material under known conditions and the spectrum obtained from the sample of interest. Transformations or shifts in the pattern (e.g., translation, rotation, size changes, warping, or deformation) can be identified, and based on this, drift measurements can be estimated.

[0011] The approach described herein can be used over 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 may be more robust to two-dimensional image spectra, particularly when the reference peak may be surrounded by different sample peaks. Two-dimensional optical spectra can be obtained from inductively coupled plasma emission spectroscopy (ICP-OES) instruments, but other forms of optical spectroscopy may be used instead.

[0012] The peaks are beneficially selected such that the change in the pattern formed by the peaks provides an accurate and robust measure of drift. Specifically, preferably, at least 3 peaks or at least 4 peaks are used (however, more peaks, for example, at least or exactly 5, 6, 7 or more peaks can be used). 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 neighboring peaks. More preferably, the polygon is asymmetric (so that rotation of the polygon can be recognized). It is also advantageous for the peaks to be characteristics 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 registration algorithms (image registration algorithms) (e.g., phase correlation algorithms) and / or machine learning algorithms (e.g., using artificial neural networks), can be used to estimate the drift. The (filled) polygon shape can be used as a characteristic shape for image registration. In some implementations, the offset can be determined by first estimating or measuring a peak-specific offset for each peak. Then, an overall peak position measurement offset can 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 that takes the peak-specific offsets as input, such as a linear regression algorithm.

[0014] The preprocessing of the two-dimensional optical spectrum data is preferably performed before providing the data to an image registration and / or machine learning algorithm. Various preprocessing steps can be considered and any combination of these can be implemented, but the preferred combinations are discussed herein.

[0015] For example, sub-arrays may be established around the peaks. Each sub-array (for both the reference image and the sample image) may be based on the respective positions of the peaks in the reference spectrum. Only the data within the sub-array is provided to and / or used by the algorithm for estimating drift. For example, pixels outside the sub-array may be removed from both the sample spectrum and the reference spectrum. Using sub-arrays can help reduce interference from adjacent peaks and / or reduce calibration costs. Removing pixels from the sub-array can increase the ratio of the Regions Of Interest (ROI) for better accuracy of image alignment.

[0016] One or more of baseline removal, logarithmic transformation, and intensity normalization can be used. In some implementations, each peak can be normalized according to a number indicating the relative maximum value (size) of the peak compared to other peaks. For example, the peaks can be normalized such that the tallest peak has the lowest number, the second tallest peak has the second lowest number, and the smallest peak has the highest number, and so on. The numbers used can be prime numbers (especially consecutive prime numbers).

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

[0018] The determined offset can be verified. For example, the image correlation can 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 can be considered valid.

[0019] In some approaches, the precise peak location is established for each peak. This can be achieved by analyzing the spectral intensity around each peak. For example, a K-means clustering algorithm can be used for parts of the spectrum (each part containing a single peak). The pattern can then be obtained 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 may be trained using a portion of the spectrum centered on each peak. The trained algorithm can then be queried to determine peak-specific offsets. For example, a polygon may be defined for all identified peaks by connecting adjacent peaks. The algorithm can then be trained using portions of the spectrum centered on each peak, along with corresponding portions of the defined polygon.

[0021] This disclosure can be implemented in many ways, and preferred embodiments may be described below, merely as examples, with reference to the accompanying drawings. [Brief explanation of the drawing]

[0022] [Figure 1] An exemplary two-dimensional optical spectrum of a reference material taken under known conditions is shown. [Figure 2] Figure 1 shows an exemplary two-dimensional optical spectrum with six identified peaks connected by lines. [Figure 3] Figure 1 shows an exemplary two-dimensional optical spectrum of the first implementation, with six identified peaks enclosed by a square frame (subarray). [Figure 4] Figure 3 shows an exemplary two-dimensional optical spectrum with additional processing to remove data outside the subarray. [Figure 5a] Figure 4 shows a three-dimensional plot of an exemplary spectrum within a subarray. [Figure 5b] Figure 5a shows a three-dimensional plot with the reference level removed. [Figure 6a] Figure 4 shows a two-dimensional plot of the subarray's intensity, with prime number labels associated with each peak. [Figure 6b] Figure 6a shows a plot where each intensity is normalized by the associated prime number label. [Figure 7] A series of initial preprocessing steps for an exemplary two-dimensional optical spectrum, based on a second implementation, are shown. [Figure 8] A series of further pretreatment steps for an exemplary two-dimensional optical spectrum are shown. [Figure 9] Figure 8 shows additional preprocessing steps from the output. [Figure 10] The output shown in Figure 9 is schematically used when training a machine learning image alignment algorithm. [Figure 11] The output shown in Figure 9 is schematically used when querying a trained machine learning image alignment algorithm. [Figure 12] This diagram schematically illustrates the use of query output from the process shown in Figure 11 in a linear regression machine learning algorithm. [Figure 13] This provides a schematic description of existing systems for optical spectroscopic measurements. [Modes for carrying out the invention]

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

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

[0025] Referring here to Figure 2, an exemplary two-dimensional optical spectrum 10 from Figure 1 is shown, having six identified peaks 20 connected by lines (each line connecting two nearest adjacent peaks). As shown in the figure, these six peaks form a polygonal shape. It is established that any three or more peaks can form the vertices of a polygonal shape, but four or more peaks are preferred. It is preferable that the peaks are selected to form the vertices of a polygonal shape, more preferably an asymmetrical polygonal shape. When a symmetrical polygonal shape is used, it can be difficult to distinguish between the rotation and translation of the peaks. Also, it is 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 can vary between the reference spectrum and the sample spectrum. By processing the variation in the pattern, drift can be estimated or measured. Image registration is a useful tool for determining drift from pattern variations. The pattern uses peak positions, but one or more of the following may also be considered (may include, and / or be refined by): the geometric shape formed by the peak positions (e.g., the polygons considered above), the peak intensity or relative intensity, and the peak shape. By considering the pattern more generally than just the peak positions, distortions and / or interferences that affect the determination of peak positions can be taken into account. For example, interferences can cause peaks that partially or completely overlap with the reference peak. As a result, determining the peak position may be difficult (e.g., double peaks or other more complex peak shapes may appear). Additionally or alternatively, peak positions may appear to have shifted due to interference rather than drift, as is evident from the changes in (relative) intensity and / or changes in peak shape. These effects can also be evident from distortions unrelated to drift. Therefore, determining drift based on pattern changes can account for these effects, for example, by reducing (or ignoring) weighted peaks when pattern changes are not limited to peak locations.

[0027] Two different algorithms for handling the changes are considered as examples. The first approach uses a phase-correlated image registration algorithm, which can determine the offset from the change in the pattern formed by the position and relative intensity of the reference peaks. The second approach applies an implementation of machine learning image registration, which can use the change in the polygonal shape formed by the precise location of the reference peaks to determine the offset. These two approaches will be discussed in more detail below.

[0028] Each approach uses different preprocessing steps to make the most of its respective algorithm. It will be understood that different preprocessing steps are possible, and in fact, different algorithms may also be applied. It will also be understood that by looking at changes in peak patterns, the overall offset can be determined by providing peak-specific offsets from an 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 peak position measurement offsets in a two-dimensional optical spectrum (specifically, a two-dimensional optical spectrum obtained from a sample of interest) can be considered. This method includes identifying multiple peaks that appear in both a spectrum obtained from a reference material and a spectrum obtained from a sample of interest under known conditions, and determining the peak position measurement offsets by comparing a pattern formed by the peak positions of the identified multiple peaks in the spectrum obtained from the sample of interest with a pattern formed by the peak positions of the identified multiple peaks in the spectrum obtained from the reference material. This 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 that, when executed by a computer, includes instructions configured to carry out the method. The disclosure may also provide one or more of an optical spectral analyzer, a computer program, and an optical spectrometer (e.g., an ICP-OES instrument), which may include such an optical spectral analyzer and / or a computer program, or may be configured to operate according to the method.

[0030] Preferably, the identified peaks include at least three or four peaks. It is desirable that the positions of the identified peaks in the two-dimensional optical spectrum define the vertices of a polygon (by connecting each peak to two nearest adjacent peaks), preferably an asymmetric polygon. Advantageously, the identified peaks are plasma chemical properties of the reference material and the sample material. In embodiments, the area of ​​the two-dimensional spectrum enclosed by the identified peaks (and / or, for example, the polygon defined by the peaks as considered 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, (relative) intensities, and / or shapes of multiple identified peaks.

[0032] The decision-making step involves establishing a comparison using an image alignment algorithm (e.g., a phase correlation algorithm) and / or a machine learning algorithm.

[0033] The peak position measurement offset can be determined using peak-specific offsets for each of multiple peaks. For example, peak-specific offsets can be combined, interpolated, or analyzed in other ways.

[0034] Here, we will describe two specific implementation forms as mere examples. Further details in the general sense discussed above will be referenced again below.

[0035] Implementation Example 1 This implementation example is discussed by referring to seven steps and uses a phase-correlated image alignment algorithm.

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

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

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

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

[0040] 4) Referring now to Figure 5a, a three-dimensional plot of intensity within an exemplary subarray of the spectrum shown in Figure 4 is shown. This indicates a reference level, indicated by relatively high intensity levels ("bumps") along the y-dimension. In other words, considering each value on the y-axis, the minimum level is higher than 0. Removing this reference level is advantageous for accurately identifying peaks. Therefore, the reference level is preferably removed by subtracting from each pixel in the subarray 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 now to Figure 5b, a three-dimensional plot of Figure 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 embodiments.

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

[0042] 6) Referring to Figure 6a, the intensities of the subarray in Figure 4 are plotted in two dimensions, with a prime number label associated with each peak shown. The z-axis in this figure represents the measured intensity. Each peak is then normalized according to its assigned prime number label. Referring to Figure 6b, the plot from Figure 6a is shown, with each intensity normalized by its associated prime number label. This is performed for both the reference image and the sample image. This normalization removes some of the peak intensity information, but at least retains 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 (for example, any peak with a much lower intensity than the others is not ignored by the algorithm).

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

[0044] a. After performing the preprocessing according to the above steps, the Fourier transform is applied to both the reference image and the sample image (f0(x,y),f s (x',y')), frequency domain spectrum (F0(u,v),F s Obtain (u',v')). b. The power spectrum is calculated as follows:

[0045]

number

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

[0047] Returning to the general meaning discussed above, further optional and / or advantageous features may be considered. For example, the method may further include establishing separate subarrays around each of the identified peaks in the spectra obtained from the sample of interest and the spectra obtained from the reference material. Each subarray may be based on the respective positions of each identified peak in the spectra obtained from the reference material (or may be subarrays for each identified peak in the spectra obtained from the sample material). This comparison is advantageously based on the information (only) within the subarrays.

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

[0049] The decision-making step, to the advantage of the situation, involves establishing a comparison using a phase correlation algorithm.

[0050] Here, we will consider further specific details using a second implementation example. Again, information relating to the general meaning of this disclosure will be provided later.

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

[0052] 1) In the reference image, four or more reference peaks are selected (four are preferred, although fewer reference peaks may be used, as will be discussed below). This allows for the identification of approximate coordinates for each of the selected reference peaks. Sample images are also obtained that have reference peaks but are shifted relative to the reference by an estimated unknown amount.

[0053] 2) Preprocessing of reference and sample images for the machine learning image alignment algorithm is implemented using several steps. Refer to Figure 7, which shows a series of initial preprocessing steps in schematic form, and Figure 8, which shows a series of further preprocessing steps. This is based on the sample spectral image 100.

[0054] a. The rough coordinates of the selected reference peak are used to cut out a small image fragment (105) from the sample image 100. The rough coordinates of peak 115 are (x n ,y n If this is the case, the cut-out pieces are in the column (x dimension)

[0055]

number

[0056]

number

[0057] b. A K-means algorithm 116 with cluster=2 is used on the extruded image segment 110. The reference peak is extracted by the K-means algorithm because it has a higher intensity. To segment the peak, 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 extruded image segment 120. Again, this is done for all peaks according to the K-means clustering step 210, which is also shown in Figure 8.

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

[0059] e. Next, using the identified coordinates, the sample image is modified according to step 220 to connect the precise locations of the peaks, thereby forming a polygon. Pixel values ​​within the polygon 230 are marked with an intensity of 1, and the rest of the sample image 240 is marked with an intensity of 0. This action creates a segmented image 250 with defined (filled) polygonal regions that can be used for subsequent AI training. f. Preprocessing steps a to d are repeated for the reference spectral image.

[0060] 3) First, we consider training a machine learning image alignment algorithm, referring to Figure 9, which shows additional preprocessing steps from the sample spectral image 100 and segmented image 250 shown in Figure 8.

[0061] a. Using the determined precise peak position as the center, larger fragments of the sample spectral image for each reference peak are cut out and extracted (260). The cutting process is the same as that considered with reference to step 3a above, but with a larger size (e.g., size = 128). This can accelerate the training of the machine learning algorithm by using several smaller images (the same number as the peaks) instead of a large 2048 × 2048 image. The cut-out spectral fragments are normalized to provide original image fragments 265 that will be used for training (not to find peaks as in step 3). In addition, the segmented image 250 is cut out and extracted for each peak having the same size and position to provide segmented cut-out fragments 275 (270). The cutting process 260 and the extraction process 270 are performed for all peaks, yielding original image fragments 265 and segmented fragment images 275 for all peaks. Each cut-out fragment image 275 shows a filled triangle. These triangles have different shapes and interior angles. These can be used as characteristic shapes for machine learning image recognition.

[0062] b. Next, referring to FIG. 10, the use of the output shown in FIG. 9 in training a machine learning image alignment algorithm, specifically, a U-Net model (originally described in Ronneberger, Olaf; Fischer, Philipp; Brox, Thomas (2015) "U-Net: Convolutional Networks for Biomedical Image Segmentation", Springer, Cham.) is schematically shown. This uses a video (m) and a fixed image (f). The U-Net model 280 is trained with the video 281 (m) and the fixed image 282 (f) based on the original image patches 265 for the reference spectral image and the sample spectral image, respectively. The spatial transformation block 285 is used to identify a "registration field" 283 for transforming the video in order to predict a "shifted image" 286 corresponding to the "fixed image" 282. The "shifted image" 286 is compared with the "fixed image" 282 to calculate a loss function. Such segmented fragments of the fixed image 275 and the segmented fragments of the video 276 are used for semi-supervised learning to identify a spatial transformation in order to reach the segmentation 290 of the shifted image (functioning as a mask to establish a portion for focus and thereby increase the accuracy of the prediction).

[0063] The U-Net model adjusts its weights to minimize the loss between the "shifted" image and the "fixed" image. 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) Wherein, L sim is usually MSE 288 that penalizes appearance differences, and L smoothThis imposes a penalty on local spatial variation 287, L us This is the loss function for unsupervised learning, L seg The segmented loss is 289. L a This is the loss function for semi-supervised learning.

[0064] Each peak can have a different weight and is therefore trained separately. In other words, this step is repeated for each reference peak. The U-Net model provides feature extraction and, as its output, gives a “alignment field”283 representing the drift in the x and y dimensions.

[0065] 4) Next, referring to Figure 11, the use of the output shown in Figure 9 when querying a trained machine learning image alignment algorithm is schematically illustrated.

[0066] a. As discussed above with reference to Figure 9, larger fragments of the sample spectral image for each reference peak are cut out and extracted using a smaller size (260) and normalized to provide the original image fragment 265. Similarly, the segmented image 250 is cut out and extracted for each peak having the same size and position (270) to provide segmented cut-out fragments 275.

[0067] b. Each original image segment 265 and segmented segment 275 for each peak is provided as input to the trained U-Net model 300. By using the weights 310 (determined from training as discussed above), the U-Net model 300 gives the alignment field 283 as output. A query 330 based on the position of each peak 335 is used to determine the x-drift 336 and y-drift 337 for the peak. This yields a set of peak-specific x-drift and y-drift estimates, and the x-drift and y-drift estimates for each peak.

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

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

[0070]

number

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

[0072] As considered above, returning to the general meaning of this disclosure, further optional and / or beneficial features are considered. For example, the method may further include establishing a position for each identified peak based on the intensity of the two-dimensional optical spectrum around each identified peak. For example, this can be achieved 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 registration algorithm for each peak using at least a portion of the two-dimensional optical spectrum centered on each peak. Then, using the trained machine learning image registration algorithm, a peak-specific offset can be determined for each of the multiple peaks. The U-Net model can provide a suitable machine learning image registration algorithm. The machine learning image registration algorithm may be semi-supervised. For example, for all identified peaks, a polygon formed by connecting adjacent peaks can be defined. The machine learning image registration algorithm can be trained using the portion of the two-dimensional optical spectrum centered on each peak (to enable semi-supervised learning), along with the corresponding portion of the defined polygon.

[0074] In some embodiments, the overall peak positioning offset can be established from the peak-specific offsets. Advantageously, a linear regression machine learning algorithm may be provided with the peak-specific offsets to determine the overall peak positioning offset. Further details, in the general sense discussed above, are referenced below.

[0075] Implementation Example 3 This implementation example is discussed by referring to four steps and uses the same phase-correlated image alignment algorithm as in Implementation Example 1.

[0076] 1) Perform steps 1 and 2 of Implementation Example 1. 2) Remove the pixels outside the sub-array from both the reference image and the sample image to obtain a trimmed (smaller-sized) reference image and a trimmed (smaller-sized) 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 sub-arrays 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 those 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] Implementation Example 4 This implementation example is considered with reference to six steps and, like 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 subarray in the reference image and the corresponding subarray 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 subarrays with a size of m×m pixels are selected, where n×m×m < N×N, and thus, n values of the 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]

Number

[0085]

Number

[0086]

Number

[0087]

Number

[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) If the validation check in Step 2 is passed (i.e., the drift estimate was not discarded), then steps 2-4 of Implementation Example 3 are performed. 4) The same validation checks as in step 2 of this implementation example are performed again. 5) If the validation check in step 4 is passed (i.e., the drift estimate was not discarded), then steps 2-6 of implementation example 4 are performed.

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

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

[0099] The determined peak position measurement offset can be optionally verified. This can be achieved 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. Specifically, the corrected spectrum from the sample of interest can 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, an existing system for optical spectroscopic measurements disclosed in British Patent No. 2586046 is schematically shown. This system may be adapted to operate in accordance with the present disclosure.

[0101] The schematicly shown optical spectroscopy system 400 is shown to include a light source 410, an optical device 420, a detector array 430, a processor 440, 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 diffraction grating and a prism (and / or further diffraction gratings) to generate an echelle spectrum of light produced 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 would have at least about 10²⁴ × 10²⁴ pixels (1 megapixel). The rectangular detector array may be square, but is not necessarily required. The detector array 430 may be configured to generate spectral values ​​corresponding to the detected amount of light in the echelle spectrum and transfer the spectral values ​​to the processor 440. The processor 440 may consist of 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 method according to the present disclosure.

[0102] The embodiments described herein are described with reference to specific types of apparatus and applications (in particular ICP-OES), and while the embodiments have particular advantages in such cases as considered herein, the approaches described herein may be applicable to other types of apparatus and / or applications. In particular, this technique can be applied to other types of two-dimensional optical spectra. Specific structural, arrangement and operating details of the process (e.g., parameters) may be substantially modified to achieve operating modes having similar or identical performance, although this may be potentially advantageous (especially considering known configurations and capabilities). Certain features may be omitted or replaced, 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 general set of equivalent or similar features.

[0103] In Implementation Example 1, many of the preprocessing steps can be avoided and / or their order can be changed. For example, only the subarray 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 these steps can be performed in a different order. Also, prime number labels are used for the improved processing, but the use of prime numbers is not mandatory. Other numerical labels can be used to indicate relative intensity patterns.

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

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

[0106] Any use of any example or illustrative language provided herein (such as "for instance," "such as," "for example," and similar language) is intended merely to better illustrate the invention and, unless specifically claimed, does not imply any limitation to the scope of this disclosure. No language herein should be construed as indicating any element not claimed to be essential to the practice of this disclosure.

[0107] Any step described herein may be performed in any order or concurrently, unless otherwise stated or the context requires otherwise.

[0108] All embodiments and / or features disclosed herein can be combined in any combination, except for any combination in which at least some of such features and / or steps are mutually exclusive. There may be specific combinations of embodiments that are more beneficial, such as combinations of specific preprocessing steps and specific algorithms, as described herein. In particular, preferred features of this disclosure are applicable to all embodiments of this disclosure and can be used in any combination. Similarly, features described in non-essential combinations can be used separately (rather than in combination).

Claims

1. A method for determining the peak position measurement offset in a two-dimensional optical spectrum, wherein the method is Identifying multiple peaks that appear in both the spectrum obtained from a 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 peaks in the spectrum obtained from the sample of interest with a spectrum obtained from the reference material, Determining the peak position measurement offset is Determining a peak-specific offset for each of the aforementioned multiple peaks, A method for calculating the peak position measurement offset by taking a weighted average of the peak-specific offsets determined for the plurality of peaks, wherein each weight is determined based on the relative correlation between the portion of the spectrum obtained from the sample of interest corresponding to each peak and the portion of the spectrum obtained from the reference material corresponding to each peak.

2. A method for determining the peak position measurement offset in a two-dimensional optical spectrum, wherein the method is: Identifying multiple peaks that appear in both the spectrum obtained from a 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 peaks in the spectrum obtained from the sample of interest with a spectrum obtained from the reference material, A method for verifying the determined peak position measurement offset 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 obtained from the sample of interest and the spectrum obtained from the reference material, further comprising verifying that 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.

3. A method for determining the peak position measurement offset in a two-dimensional optical spectrum, wherein the method is: Identifying multiple peaks that appear in both the spectrum obtained from a 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 peaks in the spectrum obtained from the sample of interest with a spectrum obtained from the reference material, Using at least a portion of the two-dimensional optical spectrum centered on each peak, a machine learning image alignment algorithm is trained for each peak. A method further comprising determining a peak-specific offset for each of the plurality of peaks using the trained machine learning image alignment algorithm.

4. The method according to any one of claims 1 to 3, wherein the identified plurality of peaks include at least three peaks, and / or the positions of the identified plurality of peaks in the two-dimensional optical spectrum define the vertices of an asymmetric polygon.

5. The method according to any one of claims 1 to 3, wherein the identified plurality of peaks are characteristics of the plasma chemistry of the reference material and the sample.

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

7. The method according to any one of claims 1 to 3, wherein the pattern is formed by the peak positions, taking into consideration the intensity and / or shape of the identified plurality of peaks.

8. The method according to any one of claims 1 to 3, wherein the determination comprises establishing the comparison using an image alignment algorithm and / or a machine learning algorithm.

9. The method according to any one of claims 1 to 3, wherein the peak position measurement offset is determined using a peak-specific offset for each of the plurality of peaks.

10. The method according to any one of claims 1 to 3, further comprising establishing a 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 the position of each identified peak in the spectrum obtained from the reference material, wherein the comparison is based on information in the subarray.

11. The method according to claim 10, 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 the removal of the pixels and the spectrum obtained from the reference material after the removal of the pixels.

12. The method according to any one of claims 1 to 3, wherein the comparison uses the plurality of peaks identified in one or more of the following states: with the reference level removed, with a logarithmic transformation applied, and with intensity normalization.

13. The method according to any one of claims 1 to 3, wherein each of the identified peaks is normalized by assigning a number corresponding to the relative magnitude of each peak compared to other identified peaks in the two-dimensional optical spectrum.

14. The method according to any one of claims 1 to 3, further comprising establishing a position for each of the identified peaks based on the intensity of the two-dimensional optical spectrum around each identified peak, wherein the pattern is based on the established position for the identified peaks.

15. The method according to claim 3, wherein the machine learning image alignment algorithm is semi-supervised.

16. The method according to claim 3, further comprising defining a polygon by connecting adjacent peaks for all of the identified peaks, 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 the corresponding portion of the defined polygon.

17. A computer program comprising instructions configured to, when executed by a computer, carry out the method described in any one of claims 1 to 3.

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