Optical spectrometer and method of analysis

Abstract

There is described a method of optical spectroscopy for analysing a sample, the method comprising: obtaining an emission spectrum of a sample, wherein the emission spectrum of the sample comprises an emission spectrum of an analyte and one or more emission spectra of chemical entities in a background matrix; obtaining at least one stored emission spectrum of the one or more chemical entities in the background matrix; using the at least one stored emission spectrum of the one or more chemical entities in the background matrix to generate a matrix spectrum to match one or more portions of the emission spectrum of the sample; and subtracting the matrix spectrum from the emission spectrum of the sample to generate an emission spectrum of the analyte. An optical spectrometer is also described.

Description

[0001] Optical Spectrometer and Method of Analysis

[0002] Technical Field

[0003] The present invention relates to methods of optical emission spectroscopy and an optical emission spectrometer. In particular, the present invention relates to methods of analysing spectral peaks generated using a spectrometer.

[0004] Background

[0005] Optical spectroscopy is a spectroscopic technique used to determine the properties of a sample based on light emitted by the sample. To cause the sample to emit light the sample is excited. There are many ways to do this as will be understood by the person skilled in the art. The light emitted from the sample includes emissions at one or more wavelengths. The wavelength of the emitted light is indicative of the contents of the sample such as the chemical elements that are present in the sample. In general a sample will emit light at multiple wavelengths. Optical spectroscopy detects these and provides an emission spectrum from the sample.

[0006] Emission spectra may comprise a plurality of spectral peaks representing emissions from a sample. Part of the process of analysing the plurality of spectral peaks involves the identification of spectral peaks from the measurement data. Since a peak or group of peaks may represent a particular chemical element or species it is desirable to be able to distinguish peaks from each other and identify the contributions from each chemical element or species. This allows the chemical elements or species present to be determined. From the peaks it is also possible to determine the relative quantities of the chemical elements or species present in the sample.

[0007] Figure 1 is a schematic block diagram of an optical spectrometer 10. The optical spectrometer 10 is configured to perform a method of optical spectroscopy. The optical spectrometer 10 comprises a light source 1 1 , an optical arrangement 12, a detector 13, a processor 14, a memory 15, and an input / output (1 / O) unit 16. The optical spectrometer 10 may, in some embodiments, be an optical emission spectrometer.

[0008] The light source 1 1 may be a plasma source, for example an inductively coupled plasma (ICP) source. The optical arrangement 12 may comprise an echelle grating and a prism (and / or a further grating). The optical arrangement 12 may be configured to produce an echelle spectrum of the light produced by the light source 11 . The optical arrangement 12 may be configured to direct an image of the two-dimensional echelle spectrum to be formed on the detector 13.

[0009] 17294024.MDE.MDE The detector 13 may be a detector array such as a CCD (charged coupled device) array, for example. A typical detector array may have at least approximately 1024x1024 pixels (1 megapixel). The detector array may be a rectangular, or square detector array. The detector array 13 may be configured to produce spectrum values corresponding with the detected amount of light of the echelle spectrum, and configured to transfer the spectrum values to the processor 14.

[0010] The processor 14 may comprise a commercially available microprocessor and the like. The memory 15 may be a suitable semiconductor memory and may be used to install instructions to allow the processor 14 to cause the spectrometer 10 to carry out measurements and perform analysis on the measurements.

[0011] A detector array 13 on which an echelle spectrum has been imaged is shown schematically in figure 2a. The detector array 13 can record emissions detected at each pixel in the detector array. This is known as “full-frame”. The white spots shown in the full frame are the detection of light emitted from chemical elements, for example, carbon, nitrogen etc. For a quantitative measurement regions of the detector are selected. These regions are known as sub-arrays. Figure 2b shows an example sub-array. A subarray may comprise a rectangular region of pixels, that is an area of m x n pixels. In one example, a sub-array is 25 x 9 pixels.

[0012] In spectrochemical analysis by quantifying the intensity of the emissions and using specific samples called standards it is possible to infer the concentration of elements in the sample. To determine the intensity of the emission the measured intensities of spectral lines are preferably converted to single intensity values. To obtain intensity values, the subarray such as shown in figure 2b is converted into a one-dimensional array. For example, starting with the 25 x 9 pixel sub-array, the column-wise average is taken to reduce the sub-array to a one-dimensional array as shown in figure 2c, which may for example be a 25 x 1 array. Each element in the one-dimensional array corresponds to a value in wavelength such as nanometres, which is obtained by a wavelength calibration using known species and emission wavelengths.

[0013] As can be seen in figure 2c, the amount of light represented by each of the elements in the one-dimensional sub-array varies. Figure 2c shows elements near the centre of the one-dimensional array as lighter than those at the edges. As mentioned above, the elements of figure 2c are a column-wise average of a sub-array of pixels. The lighter colour in figure 2c represents a higher average amount of emission hitting the pixels in the respective column of the sub-array of figure 2b. Hence, when plotted to form an emission spectrum the data from the elements will form a peak.

[0014] 17294024.MDE.MDE In real samples there are likely to be multiple peaks. Some peaks may represent the analyte of interest and others may represent the background such as a solvent in which the sample is dissolved. In addition, argon, carbon and nitrogen lines are part of the plasma and can be found within the spectra and may also be considered to be background. Other peaks might be caused by the composition of the sample.

[0015] Figure 3 is a graph showing an example spectrum C from a sample. The horizontal axis shows wavelength in nanometres and the vertical axis shows relative intensity. The central peak falling in the grey rectangle labelled ROI is the peak of the analyte of interest. The grey rectangle ROI defines a region of interest which has been set as where the analyte is expected to be. To extract the level or intensity of the peak for the analyte from the other peaks a background level is determined. The two regions labelled BG1 and BG2 are used to define a background. The background regions may be chosen to be a certain distance in wavelength from the centre or edges of the region of interest. For example, in figure 3 the centres of the regions BG1 and BG2 are around 0.017 nm from the centre of the region of interest. An integral (or sum) is calculated across each of the background regions by integrating the area under the graph. In the greyed regions BG1 and BG2 in figure 3 the integral is provided at the centre of the regions BG1 and BG2. By linearly interpolating (see for example, line LI) across from the value at the centre of BG1 and that for BG2 and subtracting the linear interpolations values from the values in the region of interest (ROI), an intensity value can then be calculated by integrating over the width of the ROI, for example as shown in the rectangle, ROI, of figure 3. By using calibration standards linking known intensities to known concentrations, the concentration of elements, and in particular for the analyte of interest, can be determined. However, simply setting the background regions a certain distance from the region of interest and performing the linear interpolation does not result in an accurate representation of the level of the background signal through the region of interest. In particular, BG1 sits on a peak and BG2 sits just to the right of a trough. It may be better to look at the spectrum line and use minima or troughs in the spectrum to place the background regions. If it seems that the background signal is non-zero through the region of interest the level of the background spectral line through the region of interest may need to be estimated. Additionally, in setting the width of any background regions, the width may be set to produce a result having the required relative standard deviation (RSD) for the data evaluation. For example, if placed correctly, a wider background region could provide a better RSD.

[0016] As discussed in relation to the graph of figure 3 the above-described approach may not provide an accurate determination of the background. This is even more pronounced in

[0017] 17294024.MDE.MDE the graph of figure 4 where the background is complex. Curve C1 is the spectrum of the background and curve C2 is the spectrum of the background plus analyte of interest. For example, as shown in figure 4 background peaks and the analyte peak overlap so a simple interpolation, such as by straight line LI2, between background regions BG1 and BG2 and subtraction from the region of interest ROI is unlikely to provide an accurate result. In figure 4 the complexity of the background is described as having matrix-effects which includes spectral interferences neighbouring and overlapping the analyte peak.

[0018] ‘Matrix effect’ refers to the inherent signal or noise present in a sample due to its complex composition. This kind of background signal arises from the fact that different elements or chemical entities may have emissions at (almost or exactly) the same wavelength. If there are multiple emissions at almost or exactly the same wavelength and they are coming from elements that are also within the sample, this is typically called matrix. The matrix may also include peaks resulting from the plasma which may be an argon-based plasma but could also include peaks from carbon, nitrogen etc. The matrix signal which may be due to various sources can be particularly problematic in analytical methods where the analyte is present at low concentrations or where high sensitivity is required. Returning to figure 4, the task of recovering the intensity of the peak for the analyte, namely that with the ROI, is not trivial and it is desirable to provide methods for accurately and reliably doing so.

[0019] Summary of the Invention

[0020] The present invention provides a method of optical spectroscopy for analysing a sample, the method comprising: obtaining an emission spectrum of a sample, such as using an optical spectrometer, wherein the emission spectrum of the sample comprises an emission spectrum of an analyte and one or more emission spectra of chemical entities in a background matrix; obtaining at least one stored emission spectrum of the one or more chemical entities in the background matrix; using the at least one stored emission spectrum of the one or more chemical entities in the background matrix to generate a matrix spectrum to match one or more portions of the emission spectrum of the sample; and subtracting or removing the matrix spectrum from the emission spectrum of the sample to generate an emission spectrum of the analyte. The analyte is the substance, species or element of interest in the sample. The chemical entities in the background matrix may be chemical elements or compounds. The method may be incorporated into an optical spectrometer for optical emissions spectroscopy (OES), such as ICP-OES (inductively coupled plasma OES) or GD-OES (Glow discharge OES). For example, the method may

[0021] 17294024.MDE.MDE be performed by a controller of the spectrometer. Alternatively, the method may be performed in a computing system separate from the spectrometer.

[0022] Obtaining the emission spectrum of the sample may comprise measuring the emission spectrum of the sample by the optical spectrometer.

[0023] The method may further comprise calculating an intensity of the analyte emission based on an area of a peak corresponding to the emission spectrum of the analyte.

[0024] The method may further comprise quantifying the amount or concentration of analyte in the sample based on the area of the peak corresponding to the emission spectrum of the analyte. Alternatively, a relative amount of the analyte in the sample may be determined.

[0025] The step of using the at least one stored emission spectrum may further comprise offsetting and / or scaling the at least one stored emission spectrum of the one or more chemical entities in the background matrix to generate the matrix spectrum to match and / or align to the one or more portions of the emission spectrum of the sample.

[0026] The at least one stored emission spectrum is preferably at least one normalized emission spectrum.

[0027] The method may comprise: normalizing the emission spectrum of the sample; and following subtracting or removing the matrix spectrum from the emission spectrum of the sample to generate the emission spectrum of the analyte, rescaling the emission spectrum of the analyte to remove the normalization.

[0028] The step of using the at least one stored emission spectrum of the one or more chemical entities in the background matrix to generate the matrix spectrum may comprise: determining an offset and / or a scaling factor for fitting each of the respective at least one stored emission spectrum to the one or more portions of the emission spectrum of the sample, the determining comprising minimizing the difference between matrix spectrum and the emission spectrum of the sample.

[0029] The method may further comprise minimizing the offset in the step of determining the offset and the scaling factor for fitting each of the respective at least one stored emission spectrum for matching the at least one offset and scaled emission spectrum to the one or more portions of the emission spectrum of the sample.

[0030] The one or more portions of the emission spectrum of the sample to which the generated matrix spectrum are matched may comprise at least a first background region. The first background region may have wavelengths excluding a region of interest comprising the emission wavelength of the analyte. Alternatively, there may be overlap between the one or more background regions and the region of interest. As such, matching

[0031] 17294024.MDE.MDE of the matrix spectrum to the sample spectrum may continue at least partly through the region of interest.

[0032] The region of interest may comprise a wavelength window extending around the wavelength of interest, such as the (expected) peak wavelength of the analyte.

[0033] The region of interest may depend on several factors such as the width of the spectral line or the resolution of the spectrometer. In some embodiments the region of interest may extend at least 0.02nm, at least 0.05 nm or at least 0.1 nm. The width of the region of interest may also depend on other factors such as the proximity of neighbouring peaks and also to meet requirements in terms of the standard deviation of the result. The width of region of interest may also scale to become larger at higher wavelengths of interest and lower at smaller wavelengths of interest.

[0034] The one or more portions of the emission spectrum of the sample may comprise the first background region and a second background region excluding, or partially excluding, the region of interest, wherein the region of interest is at wavelengths between the first background region and the second background region.

[0035] The first background region may extend over or across a greater wavelength range than the region of interest. In some embodiments there may be multiple regions of interest.

[0036] The first background region may extend greater than the 0.1 nm, greater than 0.5nm or greater than 1 nm.

[0037] The method may further comprise applying a smoothing function to the emission spectrum of the analyte.

[0038] The method may further comprise fitting a peak function to the emission spectrum of the analyte.

[0039] According to an embodiment of the present invention, the at least one stored emission spectrum may comprise a single emission spectrum (that is, only a single emission spectrum) of the one or more chemical entities in the background matrix, excluding the analyte.

[0040] The single emission spectrum of the one or more chemical entities in the background matrix, excluding the analyte, may be collected immediately prior to, or immediately after, collecting the emission spectrum of the sample including the analyte.

[0041] The step of using the at least one stored emission spectrum of the one or more chemical entities in the background matrix to generate a matrix spectrum may comprise performing a non-linear fit of the at least one stored emission spectrum to match the one or more portions of the emission spectrum of the sample.

[0042] 17294024.MDE.MDE According to an alternative embodiment, the step of obtaining the at least one stored emission spectrum of the one or more chemical entities in the background matrix may comprise obtaining a plurality of stored emission spectra of the one or more chemical entities on the background matrix, and using the at least one stored emission spectrum of the one or more chemical entities in the background matrix to generate a matrix spectrum to match one or more portions of the emission spectrum of the sample may comprise combining the stored emission spectra of the one or more chemical entities in the background matrix to generate a matrix spectrum to match one or more portions of the emission spectrum of the sample.

[0043] The step of combining the stored emission spectra of the one or more chemical entities in the background matrix to generate a matrix spectrum to match one or more portions of the emission spectrum of the sample may comprise iteratively adding spectra to and / or removing spectra from the generated matrix spectrum to improve the match between the generated matrix spectrum and the one or more portions of the emission spectrum of the sample.

[0044] The present invention further provides an optical spectrometer for analysing a sample, the optical spectrometer comprising a detector and a controller, wherein the controller is configured to cause the optical spectrometer to perform any of the method set out herein, and the optical spectrometer is configured to measure the emission spectrum of the sample.

[0045] The optical spectrometer may further comprise a user interface and a database storing at least one emission spectrum, the optical spectrometer may be configured to receive user input for selecting the at least one stored emission spectrum from the database. In embodiments where multiple stored emission spectra are used, the spectrometer may be configured to receive user input selecting a plurality of stored emission spectra for the controller to combine to generate the background matrix.

[0046] The controller may select one or more spectra from the database of stored emissions spectra for generating the matrix spectrum.

[0047] The present invention further provides a computer-readable medium having stored thereon processor-executable instructions for performing a method comprising: obtaining an emission spectrum of a sample such as generated by an optical spectrometer, wherein the emission spectrum of the sample comprises an emission spectrum of an analyte and one or more emission spectra of chemical entities in a background matrix; obtaining stored emission spectra of the one or more chemical entities in the background matrix; combining the stored emission spectra of the one or more chemical entities in the background matrix

[0048] 17294024.MDE.MDE to generate a matrix spectrum to match one or more portions of the emission spectrum of the sample; and subtracting or removing the matrix spectrum from the emission spectrum of the sample to generate an emission spectrum of the analyte.

[0049] Brief Description of the Drawings

[0050] Embodiments of the present invention will now be described with reference to the accompanying drawings of which:

[0051] Figure 1 is a schematic block diagram of an optical spectrometer;

[0052] Figures 2a-2c are respectively diagrams of a detector array showing a spectrum incident on the array, a diagram indicating a sub-array of the detector and the conversion of data from the sub-array to a one-dimensional array;

[0053] Figure 3 is a graph showing an example of a spectrum of a sample;

[0054] Figure 4 is a graph showing an example of a spectrum of another sample, wherein the sample includes an analyte and structured or matrix background;

[0055] Figure 5 is a flow diagram of a method for removing the emission spectrum of the background matrix from a sample spectrum;

[0056] Figures 6a and 6b are schematic plots of wavelength against relative intensity for spectra of a sample “S”, matrix “M” and analyte “A”;

[0057] Figure 7a-7d are schematic graphs showing separate emission spectra for the three elements e1 , e2 and e3, how they are combined to form the matrix and the resulting analyte spectrum following removal of the matrix;

[0058] Figures 8a-8c are example sample traces using the method described herein, with figure 8a showing the collected data and matrix, figure 8b including scaling and offset to better fit the background and figure 8c the resulting analyte spectrum; and

[0059] Figure 9 shows smoothing of the analyte data of figure 8c using a neural network to provide a clean peak.

[0060] Detailed Description

[0061] Figure 5 is a flow diagram of steps of a method for removing the emission spectrum of the background matrix from a sample spectrum. The method comprises at step 510 obtaining the emission spectrum of the sample. This may include the analyte and the background matrix. At step 520 an emission spectrum or emission spectra of one or more elements or chemical species in the background matrix are obtained. These may be obtained from a database where they are stored. At step 530 the stored emission spectrum or spectra are used or combined to generate the emission spectrum for the background

[0062] 17294024.MDE.MDE matrix. The spectrum for the background matrix is generated so that it matches portions of the signal of the sample. This may be outside of a region of interest relating to the analyte or may overlap the region of interest. At step 540 the spectrum of the background matrix is subtracted from the spectrum for the sample to generate the spectrum for the analyte of interest. We now describe more detail of the methods of the present disclosure.

[0063] To obtain the matrix spectrum there are different options depending on the complexity of the background and the data available. A first embodiment is when the user has a “blank-matrix-sample” at hand and can acquire the spectrum for it or has already done so and it is stored in a database or library. The “blank-matrix-sample” may be a solvent in which the analyte is dissolved or may be a more complex background medium in which the analyte is held. If the user has access to the background matrix material and the sample comprising the analyte, then the user can acquire the matrix spectrum separately as a first spectrum measurement which may then be stored in a sample list. Preferably, the spectrum of the background matrix material is measured immediately before or after measuring the spectrum of the full sample including the analyte. In this way the two spectra are closely matched because drifts in the equipment (such as due to temperature variations) are minimized. The measurement of the spectrum of the full sample, i.e. including the analyte, may be obtained by first dissolving the analyte into the matrix and then taking the measurement to obtain a spectrum. The matrix spectrum may require fitting to the sample spectrum. After fitting, the matrix signal can then be subtracted from the sample signal to obtain the analyte spectrum. Figure 6 schematically shows plots of wavelength and relative intensity for spectra. In figure 6a the solid line labelled “S” is an example representation of the spectrum obtained for a sample, that is the analyte plus matrix. The dashed line labelled “M” in figure 6a represents the spectrum for the matrix. In figure 6b the dotted line labelled “A” is the spectrum for the analyte which has been obtained by subtracting the matrix spectrum “M” from the spectrum for the sample “S”. That is, A = S - M. To obtain a good fit between the matrix spectrum and the sample spectrum for the background regions it is preferable if the matrix spectrum undergoes a fitting process before subtraction. We describe this later in the specification.

[0064] Peak intensity, shape, and location can shift in the spectrum based upon the matrix concentration. Hence, in embodiments it is useful to have several representative spectra based on concentration. Then when performing matrix subtraction the best matching of the representative spectra can be used. The matching can be done by looking at minimum, maximum, and inflection points on each of the spectra. They may also be scaled so that

[0065] 17294024.MDE.MDE the differences are minimized. Once the fit is made, the subtraction is performed and the corrected analyte waveform is displayed.

[0066] In other situations, the background matrix may be more complex or may be unavailable. According to an alternative embodiment of the present disclosure the user generates the matrix spectrum by combining different emissions or spectra. Preferably, a database or library of previously recorded spectra is available. If the user knows the elements or species that the matrix is made up from, the user can select spectra for these elements and construct the background matrix from these emissions. Alternatively, an automatic construction of the background matrix may be made, such as by assessing peak wavelengths in the sample spectrum. In a further alternative, the background matrix is constructed by a combination of automatic and user input. For example, a spectrometer, controller or computing device could generate a first approximate background spectrum based on a user or automated selection of matrix elements or species from a database. The results of the initial spectrum may be presented to a user and the user may make adjustments to the selection of matrix elements and species to improve the generated background spectrum such that it is closer to that of the sample spectrum. This process may be iterated interactively with the user to refine the spectrum, for example, by adding and / or deleting spectra to arrive at a good match to the background matrix to the sample spectrum.

[0067] As a further illustration we now refer to figures 7a-7d which show how spectra may be combined. For example, if element e1 emits with a peak wavelength wei,i, element e2 emits with a peak wavelength we2,i, and element e3 emits with a peak wavelength wes,i and these three wavelengths are very closely aligned in wavelength, the spectrum for each of the three elements can be combined to construct the matrix as we will now describe. Figure 7a schematically shows separate emission spectra for the three elements e1 , e2 and e3. In one example, the respective wavelengths are: e1 : 198.995 nm e2 : 199.001 nm e3 : 199.005 nm

[0068] Next the three spectra are normalized as shown in figure 7b. It is almost always necessary to normalise and rescale the previous measurement because the concentrations required for a measurement will usually be different to that for the measurement that is stored in the database. At this point the peak positions remain the same in wavelength terms (for example, nanometres). At the next step, as shown in figure 7c, the emission spectra for the

[0069] 17294024.MDE.MDE elements e1 -e3 are individually rescaled in intensity to fit the background matrix. The spectra may also be shifted slightly in wavelength to better fit the background matrix. However, such shifts should be small because larger shifts may reduce the confidence level of the results. Hence, when the three rescaled spectra are added together the background matrix is recreated similarly to the curve “M” in figure 6a. The background matrix can now be subtracted from the sample spectrum such as “S” in figure 6a to produce the analyte spectrum A shown in figure 7d.

[0070] We now describe the above method using more mathematical notation for: a) a single spectrum making up the background matrix and b) multiple spectra making up the background matrix. a) Matrix acquired from a single background spectrum:

[0071] Starting with a matrix m(x), such as from spectrum “M”, in figure 6a and the full sample including analyte signal s(x), such as from spectrum “S”, with both spectra in some unknown and arbitrary concentration for x e 52Twhere 52Tdenotes the “total region” of the measurement, the method is as follows.

[0072] Both signals are normalized to the range [0,1] yielding m(x) for the matrix signal and s(x) for the sample signal. Next, the region of interest, that is, the mass or wavelength of the analyte of interest, is defined as 52(2Tand an optimization problem is defined and solved as follows: with the conditions that :

[0073] |C| < 6

[0074] X g 5 j

[0075] In other words, the task is to find a scaling factor f and a shifting signal intensity offset c for the normalized matrix signal m(x) so that it matches the normalized measured sample (analyte plus matrix) signal s(x) as best as possible without considering the region of interest 52((which is where the analyte signal is expected to be). As discussed in relation to figure 7c, the value of the shifting offset c should be as small as possible (as indicated by the < e notation). Hence, the Ac term penalizes this term such that only small drifts or no drift in wavelength is included between the acquisition of the matrix and the sample. Hence,

[0076] 17294024.MDE.MDE the optimization process is guided against including large values of c during the iteration process.

[0077] After solving, we obtain f * and c* as the optimal solution. The next step is to subtract the matched background which is given by f * • m(x + c‘) from s(x), which results in normalized spectrum for the analyte. In some embodiments, as the resulting signal may show small artifacts due to fitting tolerances and the subsequent subtraction, the analyte spectrum may be smoothed using a mathematical smoothing function or procedure. In a final step, the analyte spectrum is re-scaled back to correspond to the scaling of the spectrum of the sample spectrum by reversing the original normalisation step. The result is the analyte spectrum with background matrix removed such as shown in figures 6b and 7d.

[0078] In other embodiments the fitting may use a non-linear fitting algorithm, which maximizes the overlap of the matrix and sample on one or both sides of the analyte peak. The non-linear fitting allows adjusting both the position (x-axis) and the intensity (y-axis) simultaneously. An algorithm that can be used is the Levenberg-Marquardt algorithm. Such an algorithm can be used to iteratively minimize the distance between two curves, that is, between the matrix spectrum and the sample spectrum outside a region of interest, such as regions not including the analyte peak(s).

[0079] In matching or fitting the background matrix spectrum to the sample spectrum it is useful to consider the regions of the spectrum that are used. In figures 3 and 4 two narrow bands BG1 and BG2 are shown. In present embodiments, much larger parts, up to almost the entire spectrum are preferably used. For example, consider a spectrum of 25 pixels wide with a region of interest (ROI) of about 5 to 6 pixels. To the left and right of the ROI, about 40% of the spectrum, each side, may be used to determine the background. This amounts to about 10 pixels on each side, which covers the entire spectrum in this embodiment. Of course, if the ROI is not in the middle of the spectrum then other numbers of pixels either side may be used. Also, for spectra of other numbers of pixels, other numbers may be used in the fitting. If more pixels are present in the total spectrum such as 50 pixels then a lower percentage of the pixels may be used. b) Matrix acquired from multiple background spectra:

[0080] In this case, instead of starting with a single spectrum for the matrix, we are starting with multiple spectra or multiple individual matrix contributions which may be denoted by m ) for the interfering wavelength j = 1, of a subarray. The “full” analyte signal is again denoted by s(x). Both may be at an unknown and arbitrary concentration and include measurements across the “total region” of measurements, or in other words x e 3?T.

[0081] 17294024.MDE.MDE The method comprises normalizing all of the separate matrix signals and also the sample spectrum (which includes matrix and analyte) to the range [0,1], The normalization yields m ) (for the individual contribution of analytes to the matrix signal) and s(x) (for sample signal). Again we define a region of interest (which is the wavelength of the analyte of interest) as 52(c 52Tand the following optimization problem is defined and solved: with the conditions that:

[0082] |c| < 6

[0083] X £ 5 ] and where

[0084] In other words, the task is to find a scaling factors ) and shifting signal intensity offsets c7to construct the normalized matrix signals m)(x) so that the sum of all transformed (scaled, shifted) individual matrix spectra matches the normalized measured sample (analyte plus matrix) signal s(x) as best as possible without considering the region of interest 52((which is where the analyte signal is expected to be). Again the value of the shifting offset c should be as small as possible, and is penalized in the same way as for the single matrix spectra described above.

[0085] As before, the resulting signal may show small artifacts due to fitting tolerances and the subsequent subtraction. Hence, the reconstructed clean analyte signal can be smoothed using a mathematical smoothing function or procedure. In a final step, the analyte spectrum is re-scaled to remove the normalization.

[0086] This method using multiple background spectra is an extension of the case a) relating to the single matrix spectra. Conversely, this method b) reduces to the single matrix method if we do not have multiple spectra but only one spectrum. In this case, we can set k=1 and as result there is only matrix with the subscript j=1 .

[0087] Figures 8a-8c show example sample traces using the method described herein. Figure 8a shows the data as collected after normalization. The dashed-line curve is the measured sample spectrum (including analyte and matrix) and the solid-line curve is the spectrum for the matrix, such as obtained from a database or library. The horizontal scale is pixel number taken directly from the detector instead of wavelength and the vertical axis

[0088] 17294024.MDE.MDE is relative intensity. The analyte that it is desired to obtain a spectrum for, can be seen as the extension to the peak at around pixel number 22. It can be seen that the tops of the other peaks in the sample are higher than for the matrix. In figure 8b the optimization and scaling has been performed to better match the matrix spectrum with the sample spectrum. In figure 8b it can be seen that almost all of the peaks of the matrix spectrum now align with the peaks of the matrix in the sample spectrum, in both relative intensity and x-axis position. Again the analyte peak can still be seen at around pixel number 22. In figure 8c the optimized and rescaled matrix spectrum has been subtracted from the sample spectrum to obtain the spectrum for the analyte. The peak of the analyte signal can be clearly seen.

[0089] If required, a smoothing function or process can be applied to the spectrum. An example of a smoothed analyte peak is shown in figure 9 (solid line). In this figure the approach described in the International Patent Application published as WO 2023 / 111096 A2 has been applied to the data from figure 8c (shown as dotted line in figure 9). The approach described in WO 2023 / 111096 A2 applies a process to reconstruct a peak based on Al processing. The reconstructed peak is based on the neural network of the Al having been trained on similar peaks. As can be seen, the reconstructed peak does not include noise along the baseline which crosses the x-axis multiple times for the unsmoothed peak.

[0090] To arrive at the spectrum of the analyte to allow quantification of the analyte to be generated, the spectrum should be de-normalized by reversing the normalization that occurred at the start of this method. This may involve multiplying by a scaling factor that was previously used to normalize the sample signal received from the spectrometer.

[0091] To determine the quantity or concentration of the analyte, the area under the peak or the height of the peak may be used. The smoothed function allows easier quantification if using the area technique. However, quantification may still be produced using the unsmoothed data signal. Comparison to known standards linking an intensity to a concentration or amount of the relevant element may be needed to determine concentrations or amounts of analyte present in a sample.

[0092] The approach described herein considers a signal, the matrix signal, as the full background and optimizes it to fit a combined sample signal comprising matrix and analyte. This is different to prior approaches. Here the matrix may be constructed manually and artificially by the user. To construct the matrix the user can acquire spectra of new solutions relating to the matrix or can re-use already acquired spectra that are combined into one matrix. Regardless of the way the matrix is constructed, the approach described herein

[0093] 17294024.MDE.MDE allows for handling complex samples with structured background and significantly improves the accuracy of quantification.

[0094] The proposed method can handle samples with matrix-induced background with high precision. Other approaches rely on approximating the background and are not able to consider matrix or structured backgrounds. As a result for these prior approaches, the background corrected signal can exhibit multiple interferences which may prevent users from accurately setting the background regions for computation. For example, with reference to figures 3 and 4 the user may set the background regions BG1 and BG2 but interferences with the analyte signal result in difficulties in accurately estimating the background levels on the region of interest.

[0095] The invention can be used for method development or in big-scale measurements where a customer does not want to re-acquire the matrix. In such cases, if the user needs a more precise result, the invention allows to fine-tune the matrix signal after construction by comparing the measurement with the artificially created matrix signal.

[0096] The method can also be used within the standard addition method, that is usually used when a sample is heavily interfered by a matrix. In the standard addition method the user performs multiple measurements where the sample is spiked with the analyte of interest in different, known, concentrations. Then, the user can generate a calibration curve and go back to the original sample and determine its concentration. In such an example, the matrix matching can be used to check if the subtraction “recovers” the spike correctly.

[0097] We have discussed that the background matrix may comprise various chemical entities that are not of interest. For example, they may be included in the sample but are not the parts or species we are interested in measuring. The background may also, or instead, include chemical entities that are generated in forming the plasma such as argon ions or carbon or nitrogen. An example of the background comprising entities in the sample that are not of interest is sea water which comprises large amounts of sodium. However, analysis of sea water will more likely be looking for chemical entities indicating levels of pollution, so the amount of sodium is part of the background matrix. Similarly in blood analysis you may be interested in trace amounts of lead but there is naturally iron present which forms part of the background matrix.

[0098] The person skilled in the art will readily appreciate that various modifications and alterations may be made to the above described methods and apparatus. We have described that the method may be incorporated into an optical spectrometer, and for

[0099] 17294024.MDE.MDE example performed by a controller or microprocessor of the optical spectrometer. In embodiments, once the spectrum of the sample has been collected, the method may be performed on a computer separate from the optical spectrometer. In such a case the database or library of elements may be stored on the computer or accessed separately by the computer. Although we discuss wavelength or pixel number regarding the various spectra, alternatively frequency or wavenumber may be used. Further modifications may be made without departing from the scope of the appended claims. For example, different values and ranges may be used for the background regions and region of interest, the order of steps of methods may be changed and aspects of different embodiments may be combined.

[0100] Embodiments of the present invention are set out in the following clauses: Clause A1 . A method of optical spectroscopy for analysing a sample, the method comprising: obtaining an emission spectrum of a sample, wherein the emission spectrum of the sample comprises an emission spectrum of an analyte and one or more emission spectra of chemical entities in a background matrix; obtaining stored emission spectra of the one or more chemical entities in the background matrix; combining the stored emission spectra of the one or more chemical entities in the background matrix to generate a matrix spectrum to match one or more portions of the emission spectrum of the sample; and subtracting the matrix spectrum from the emission spectrum of the sample to generate an emission spectrum of the analyte.

[0101] Clause A2. The method of clause A1 , further comprising calculating an intensity of the analyte emission based on an area of a peak corresponding to the emission spectrum of the analyte.

[0102] Clause A3. The method of clause A1 or clause A2, further comprising quantifying the amount or concentration of analyte in the sample based on the area of the peak corresponding to the emission spectrum of the analyte.

[0103] Clause A4. The method of any of clauses A1 to A3, wherein combining the stored emission spectra further comprises offsetting and / or scaling the stored emission spectra of the one or more chemical entities in the background matrix to generate the matrix spectrum to match the one or more portions of the emission spectrum of the sample.

[0104] 17294024.MDE.MDE Clause A5. The method of any of clauses A1 to A4, wherein the stored emission spectra are normalized emission spectra.

[0105] Clause A6. The method of clause A5, further comprising: normalizing the emission spectrum of the sample; and following subtracting of the matrix spectrum from the emission spectrum of the sample to generate the emission spectrum of the analyte, rescaling the emission spectrum of the analyte to remove the normalization.

[0106] Clause A7. The method of any of clauses A1 to A6, wherein combining the stored emission spectra of the one or more chemical entities in the background matrix to generate the matrix spectrum comprises: determining an offset and a scaling factor for fitting each of the respective stored emission spectra to match to the one or more portions of the emission spectrum of the sample, the determining comprising minimizing the difference between matrix spectrum and the emission spectrum of the sample.

[0107] Clause A8. The method of clause A7, further comprising minimizing the offset in the step of determining the offset and the scaling factor for fitting each of the respective stored emission spectra for matching the combined offset and scaled emission spectra to the one or more portions of the emission spectrum of the sample.

[0108] Clause A9. The method of any of clauses A1 to A8, wherein combining the stored emission spectra of the one or more chemical entities in the background matrix to generate a matrix spectrum to match one or more portions of the emission spectrum of the sample comprises iteratively adding spectra to and / or removing spectra from the generated matrix spectrum to improve the match between the generated matrix spectrum and the one or more portions of the emission spectrum of the sample.

[0109] Clause A10. The method of any of clauses A1 to A9, wherein the one or more portions of the emission spectrum of the sample to which the generated matrix spectrum are matched comprise at least a first background region.

[0110] Clause A11 . The method of clause A10, wherein the one or more portions of the emission spectrum of the sample to which the generated matrix spectrum are matched comprise the first background region and a second background region excluding the region of interest, wherein the region of interest is at wavelengths between the first background region and the second background region.

[0111] Clause A12. The method of clause A10 or clause A11 , wherein the region of interest comprises a wavelength window extending around the wavelength of interest.

[0112] 17294024.MDE.MDE Clause A13. The method of clause A12, wherein the region of interest extends at least 0.02 nm, at least 0.05 nm or at least 0.1 nm.

[0113] Clause A14. The method of any of clauses A10 to A13, wherein the first background region extends across a greater wavelength range than the region(s) of interest.

[0114] Clause A15. The method of clause A14, wherein the first background region extends greater than 0.1 nm.

[0115] Clause A16. The method of any of clauses A1 to A15, further comprising applying a smoothing function to the emission spectrum of the analyte.

[0116] Clause A17. The method of any of clauses A1 to A16, further comprising fitting a peak function to the emission spectrum of the analyte.

[0117] Clause B18. An optical spectrometer for analysing a sample, the optical spectrometer comprising a detector and a controller, wherein the controller is configured to cause the optical spectrometer to perform the method of any of clauses A1 to A17.

[0118] Clause B19. The optical spectrometer of clause B18, further comprising a user interface and a database of stored emission spectra, the optical spectrometer configured to receive user input selecting one or more spectra from the database of stored emission spectra for the controller to combine to generate the background matrix.

[0119] Clause B20. The optical spectrometer of clause B18 or clause B19, wherein the controller selects one or more spectra from the database of stored emissions spectra for generating the matrix spectrum.

[0120] Clause C21 . A computer-readable medium having stored thereon processor-executable instructions for performing a method of any of clauses A1 to A17.

[0121] 17294024.MDE.MDE

Claims

CLAIMS:1 . A method of optical spectroscopy for analysing a sample, the method comprising: obtaining an emission spectrum of a sample, wherein the emission spectrum of the sample comprises an emission spectrum of an analyte and one or more emission spectra of chemical entities in a background matrix; obtaining at least one stored emission spectrum of the one or more chemical entities in the background matrix; using the at least one stored emission spectrum of the one or more chemical entities in the background matrix to generate a matrix spectrum to match one or more portions of the emission spectrum of the sample; and subtracting the matrix spectrum from the emission spectrum of the sample to generate an emission spectrum of the analyte.

2. The method of claim 1 , further comprising calculating an intensity of the analyte emission based on an area of a peak corresponding to the emission spectrum of the analyte.

3. The method of claim 1 or claim 2, further comprising quantifying the amount or concentration of analyte in the sample based on the area of the peak corresponding to the emission spectrum of the analyte.

4. The method of any preceding claim, wherein using the at least one stored emission spectrum further comprises offsetting and / or scaling the at least one stored emission spectrum of the one or more chemical entities in the background matrix to generate the matrix spectrum to match the one or more portions of the emission spectrum of the sample.

5. The method of any preceding claim, wherein the at least one stored emission spectrum is at least one normalized emission spectrum.

6. The method of claim 5, further comprising: normalizing the emission spectrum of the sample; and following subtracting of the matrix spectrum from the emission spectrum of the sample to generate the emission spectrum of the analyte, rescaling the emission spectrum of the analyte to remove the normalization.17294024.MDE.MDE7. The method of any preceding claim, wherein using the at least one stored emission spectrum of the one or more chemical entities in the background matrix to generate the matrix spectrum comprises: determining an offset and a scaling factor for fitting each of the respective at least one stored emission spectrum to match to the one or more portions of the emission spectrum of the sample, the determining comprising minimizing the difference between matrix spectrum and the emission spectrum of the sample.

8. The method of claim 7, further comprising minimizing the offset in the step of determining the offset and the scaling factor for fitting each of the respective at least one stored emission spectrum for matching the at least one offset and scaled emission spectrum to the one or more portions of the emission spectrum of the sample.

9. The method of any preceding claim, wherein the one or more portions of the emission spectrum of the sample to which the generated matrix spectrum are matched comprise at least a first background region.

10. The method of claim 9, wherein the one or more portions of the emission spectrum of the sample to which the generated matrix spectrum are matched comprise the first background region and a second background region excluding a region of interest, wherein the region of interest is at wavelengths between the first background region and the second background region.11 . The method of claim 9 or claim 10, wherein the region of interest comprises a wavelength window extending around the wavelength of interest.

12. The method of claim 11 , wherein the region of interest extends at least 0.02 nm, at least 0.05 nm or at least 0.1 nm.

13. The method of any of claims 9 to 12, wherein the first background region extends across a greater wavelength range than the region(s) of interest.

14. The method of claim 13, wherein the first background region extends greater than 0.1 nm.17294024.MDE.MDE15. The method of any preceding claim, further comprising applying a smoothing function to the emission spectrum of the analyte.

16. The method of any preceding claim, further comprising fitting a peak function to the emission spectrum of the analyte.

17. The method of any preceding claim, wherein the at least one stored emission spectrum comprises one emission spectrum of the one or more chemical entities in the background matrix, excluding the analyte.

18. The method of claim 17, wherein the emission spectrum of the one or more chemical entities in the background matrix, excluding the analyte, is collected immediately prior to, or immediately after, collecting the emission spectrum of the sample including the analyte.

19. The method of any preceding claim, wherein the using the at least one stored emission spectrum of the one or more chemical entities in the background matrix to generate a matrix spectrum comprises performing a non-linear fit of the at least one stored emission spectrum to match the one or more portions of the emission spectrum of the sample.

20. The method of any of claims 1 to 16, wherein obtaining at least one stored emission spectrum of the one or more chemical entities in the background matrix comprises obtaining a plurality of stored emission spectra of the one or more chemical entities on the background matrix, and using the at least one stored emission spectrum of the one or more chemical entities in the background matrix comprises combining the stored emission spectra of the one or more chemical entities in the background matrix to generate a matrix spectrum to match one or more portions of the emission spectrum of the sample.21 . The method of claim 20, wherein combining the stored emission spectra of the one or more chemical entities in the background matrix to generate a matrix spectrum to match one or more portions of the emission spectrum of the sample comprises iteratively adding spectra to and / or removing spectra from the generated matrix spectrum to improve the- 22 - match between the generated matrix spectrum and the one or more portions of the emission spectrum of the sample.

22. An optical spectrometer for analysing a sample, the optical spectrometer comprising a detector and a controller, wherein the controller is configured to cause the optical spectrometer to perform the method of any preceding claim.

23. The optical spectrometer of claim 22, further comprising a user interface and a database storing at least one emission spectrum, the optical spectrometer configured to receive user input selecting at least one stored emission spectrum from the database .

24. The optical spectrometer of claim 22 or claim 23, wherein the controller selects one or more spectra from the database of stored emissions spectra for generating the matrix spectrum.

25. A computer-readable medium having stored thereon processor-executable instructions for performing a method of any of claims 1 to 21 .

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