System and method for improving the measurement of peak intensity in pulse height spectra obtained by wavelength dispersive x-ray fluorescence spectrometer

Abstract

A system (100), method and computer program product for estimating peak intensity in a pulse height spectrum obtained by a wavelength dispersive x-ray fluorescence spectrometer is disclosed. The pulse height spectrum (212) is obtained from a sample (202) by a multi-channel analyzer (205) of the wavelength dispersive x-ray fluorescence spectrometer (200). A model generator (120) generates a pulse height spectrum model (112) by creating a plurality of diffraction order profiles with predefined profile shapes at photon energy positions corresponding to corresponding diffraction orders of a monochromator (203) of the spectrometer (200). For each created diffraction order profile where the corresponding photon energy is above the edge energy of the detector material of the detector, a corresponding escape profile is added. A model adjustment module (130) uses a fitting algorithm (FA1) to adjust pulse height to energy mapping parameters and a contribution area of ​​each diffraction order profile set of the pulse height spectrum model to minimize the difference between the pulse height spectrum model (112) and the measured pulse height spectrum (212). The intensity module (140) provides the contribution area of ​​the first-order profile set as the intensity (EI1) of energy to be determined by the wavelength dispersive X-ray fluorescence spectrometer (200).

Description

Technical Field

[0001] The present invention relates generally to wavelength dispersive x-ray fluorescence spectrometry and, more particularly, to separating analytically relevant information from multiple signals contained in a pulse height spectrum of a multi-channel analyzer used by a wavelength dispersive x-ray fluorescence spectrometer. Background Art

[0002] In wavelength-dispersive X-ray fluorescence spectrometry, an X-ray tube generates polychromatic radiation consisting of characteristic lines and bremsstrahlung. This radiation is directed onto the sample to be analyzed. This radiation generates polychromatic X-ray fluorescence and scattered radiation in the sample. In a wavelength-dispersive X-ray fluorescence spectrometer, the radiation emitted by the sample is analyzed by measuring the radiation reflected by the spectrometer's monochromator (usually a crystal) at various diffraction angles θ using a goniometer. This technique is based on Bragg's law.

[0003] nλ=2dsinθ,(F1)

[0004] where n is the diffraction order, λ is the wavelength and d is the lattice plane distance of the monochromator.

[0005] If n=1, only a single wavelength (the analytical signal) can reach the detector. However, the diffraction order can be higher than one, allowing shorter wavelengths (higher energy) to reach the detector as well:

[0006]

[0007] in ...or E2=2E1, E3=3E1, ...

[0008] Therefore, x-ray photons with an energy multiple of the analysis signal E1 reach the detector.

[0009] When a photon strikes the detector of a spectrometer, it is ultimately converted into an electrical pulse, where the pulse height is proportional to the photon's energy. However, following the initial absorption of the x-ray photon, the detector material itself produces fluorescent radiation that can escape the detector and, therefore, reduce the pulse height recorded (measured) by the detector. This is called scattering and results in additional peaks at lower energies in the pulse height spectrum.

[0010] Additionally, if a second x-ray photon of the same energy strikes the detector before it finishes registering the first, the pulses partially or fully add and produce a feature in the pulse height spectrum that is centered at twice the original energy and is called pile-up.

[0011] Additional influences can further complicate the pulse height spectrum and interfere with the determination of the analytical signal. The detector itself can add background noise, the crystal can increase its fluorescence signal, and detector aging can cause changes in peak shape and position in the spectrum.

[0012] In the pulse height spectrum of the sample obtained by the multichannel analyzer of the spectrometer, the measured peak is generated by multiple overlapping signal components from different diffraction orders related to the structure of the monochromator. In other words, there is a problem in deriving the correct intensity of the analytical signal from the measured pulse height spectrum. Existing methods generally use a fixed integration region to estimate the intensity of the first-order peak from the measured pulse height spectrum. However, due to the superposition of contributions from higher diffraction orders within this fixed integration region, the problem of separating such contributions from the intensity of the first-order peak can lead to inaccurate estimates. Summary of the Invention

[0013] Therefore, there is a need for systems and methods that provide the intensity of an analytical signal at an energy to be determined by wavelength dispersive X-ray fluorescence spectrometry.

[0014] Embodiments of the present invention, as claimed in the independent claims, comprise computer-implemented methods, computer systems, and computer program products for estimating the peak intensity of a pulse height spectrum obtained by a wavelength-dispersive X-ray fluorescence spectrometer—in particular, determining the contribution of the first diffraction order in the obtained pulse height spectrum. It should be noted that in some embodiments, the computer system can be an integrated component of the wavelength-dispersive X-ray fluorescence spectrometer. In other embodiments, the computer system is communicatively coupled to the wavelength-dispersive X-ray fluorescence spectrometer.

[0015] In one aspect, this is achieved when a computer program product is executed by a computer system to perform the computer-implemented method. Initially, the computer system receives a pulse height spectrum obtained from a sample by a multi-channel analyzer (MCA) of a wavelength dispersive X-ray fluorescence spectrometer. Digital interfaces suitable for receiving pulse height spectra from the MCA by a computer system are well known. The received pulse height spectrum contains multiple peaks, which generally reflect the superposition of different signal components from different diffraction orders, as described in the background section. In the context of the present disclosure, the term "peak" refers to a portion of the measured pulse height spectrum near a local maximum of the measurement graph (i.e., a portion of the corresponding measured graph).

[0016] The computer system's model generator generates a pulse height spectrum model (PHSM). To distinguish measured peaks from local maxima in the PHSM, this disclosure uses the term "profile" to refer to components that contribute to the composition of the PHSM. Components can also have local maxima similar to peaks, but other component shapes are possible. The PHSM includes at least two different types of profiles: diffraction order profiles and dispersion profiles.

[0017] The model generator creates a plurality of diffraction order profiles with predefined profile shapes at the photon energy positions corresponding to the corresponding diffraction orders of the monochromator of the spectrometer. For example, a Gaussian shaped profile can be used. However, alternative shapes such as a Lorentzian shape, a Voigt shape or a pseudo-Voigt shape can also be used. The photon energy position is determined by the Bragg equation and the diffraction properties of the monochromator. The model generator determines the width of the diffraction profile by using a calibrated width model that reflects the dependence of the width on the corresponding energy position and the total incoming count rate of the detector of the spectrometer. The relative position of the diffraction profile is determined by mapping its corresponding energy and pulse height to the corresponding energy value. The photons captured by the detector generate electrical pulses, from which only the pulse height is evaluated. The higher the photon energy, the higher the measured electrical pulse. The pulse height to energy mapping mentioned describes the correlation between the photon energy and the height of the corresponding electrical pulse.

[0018] Where appropriate, the model generator further adds a dispersion profile to the PHSM. This is the case for each previously created diffraction order profile where the corresponding photon energy is above the edge energy of the detector material. The corresponding dispersion profile is added to the PHSM at the position of the photon energy of the corresponding diffraction order profile attenuated by the fluorescence energy of the photons escaping from the detector material. The intensity of the dispersion profile is determined by using a calibrated dispersion intensity model that reflects the dependence of the intensity on the corresponding energy position. For gas detectors, the dispersion intensity model can also depend on the gas pressure. The dispersion profiles of higher diffraction orders typically overlap with the first-order diffraction profile.

[0019] The generated PHSM, together with the received (measured) pulse height spectrum, serves as input to a model adjustment module (MAM) for the computer system. The MAM adjusts the pulse height to energy mapping parameters and the contribution area of ​​each diffraction order profile set of the PHSM. This is achieved by using a fitting algorithm to minimize the difference between the PHSM and the measured pulse height spectrum. Furthermore, the PHSM and the measured spectrum can be weighted or Anscombe transformed. For example, certain detector regions are dominated by electronic noise and can be weighted with zero, while other regions can be weighted with one or the inverse of the error. Other weightings can also be used by those skilled in the art. As used herein, the term "diffraction order profile set" refers to all generated profiles associated with the corresponding diffraction order. For example, the superposition of a first-order diffraction profile and a pile-up profile can be referred to as a first-order profile set (if no scatter profile is generated for the first order). The superposition of a second-order scatter profile and a second-order diffraction profile can be referred to as a second-order profile set (if no other profile types are present), and so on. The pulse height to energy mapping parameters include the following two parameters: slope and offset. The contribution area of ​​a particular set of diffraction orders is the integral of the pattern resulting from the superposition of all the profiles associated with the particular diffraction order.

[0020] The intensity module of the computer system ultimately provides the contribution area of ​​the first-order profile set as the intensity at the energy to be determined (i.e., measured) by the wavelength dispersive X-ray fluorescence spectrometer. In other words, the intensity of the analytical signal in the measured pulse height spectrum corresponds to the contribution area of ​​the first-order profile set, which can be accurately determined after fitting the PHSM to the measured pulse height spectrum in the adjustment step. Typically, a least squares fitting algorithm can be used as the fitting algorithm. However, those skilled in the art can also use other appropriate fitting algorithms. In general, the intensity of the analytical signal at the energy to be determined (i.e., the contribution area of ​​the first-order profile set) is the sum of the first-order profile intensity, the dispersion profile intensity (if the first-order profile set has generated a dispersion profile), and the intensity of the pile-up profile multiplied by a correction factor. For example, a correction factor of two can be used because each pulse in the pile-up is actually based on two pulses. However, the correction factor can also be more complex. By using the correction factor to appropriately add the pile-up profile to the first-order diffraction profile set, the linearity of the detector is significantly increased (up to three times the linearity).

[0021] As described earlier, the measured pulse height spectrum can be affected by other signal components that make it difficult to analyze the measurement of signal intensity. One of these other signal component types is so-called pile-up. Therefore, the model generator can add a pile-up profile to the first-order diffraction profile. The intensity of the pile-up is determined by using a calibrated pile-up intensity model that reflects the dependence of the pile-up intensity on the corresponding energy position (of the first-order diffraction profile) and the total incoming count rate at the detector.

[0022] Another example of these other signal component types is an aging peak. Aging peaks appear in measured pulse height spectra obtained using an aged detector (particularly when using a gas detector with aged wires). In one embodiment, to account for aging peaks, the model generator may further add one or more aging profiles to the PHSM if the detector used by the spectrometer is a gas detector. Aging profiles are generated by copying the corresponding set of diffraction order profiles and shifting them by a calibrated energy offset. That is, each set of diffraction order profiles is copied and shifted by an energy offset derived from the corresponding calibrated aging model, thereby generating the corresponding set of aging profiles. In an adjustment step (i.e., during pulse height spectrum fitting), the model adjustment module proportionally adjusts the intensity of the generated set of diffraction order profiles relative to the intensity of the corresponding set of aging profiles. In other words, during fitting, an aging ratio describing the relationship between the intensity of a set of diffraction order profiles and its corresponding set of aging profiles is used as a fitting parameter.

[0023] Another type of signal component is the so-called rack contribution. In one embodiment, the model generator may add the corresponding one or more rack contribution profiles to the one or more generated profiles of the PHSM as a constant intensity value, the constant intensity value starting at the corresponding generated profile position and extending to a defined lower energy that depends on the detector type. For example, for a gas detector, this defined lower energy is zero. The constant intensity value is determined by using a calibrated rack intensity model that reflects the dependence of the intensity on the corresponding energy position. In other words, the model generator retrieves the constant intensity value for the corresponding generated profile using the calibrated rack intensity model and adds this constant value as an offset to the PHSM, the constant value starting at a defined lower energy (e.g., zero energy) up to the energy position of the maximum value of the corresponding profile.

[0024] It should be noted that the methods disclosed herein further allow for providing the contribution area of ​​any higher diffraction order profile set. In particular, the contribution area of ​​the second-order profile set can be used to improve the resolution of goniometer measurements performed by wavelength dispersive X-ray fluorescence spectrometry, as described in detail in the detailed description.

[0025] By performing pulse height spectrum fitting as described in the adjustment step, the computer system can also ensure that artifact contributions from different elements are removed from the goniometer measurements performed by the spectrometer. Furthermore, the methods described herein allow for the reduction of the effects of higher-order bremsstrahlung background from the pulse height spectrum. These effects are also described in more detail in the detailed description.

[0026] In one embodiment, a computer program product includes computer-readable instructions that, when loaded into a computer system's memory and executed by one or more processors of the computer system, enable the computer system to perform, at runtime, the method steps described herein for measuring peak intensity in a pulse height spectrum obtained by a wavelength dispersive x-ray fluorescence spectrometer. In other words, the computer program product, when loaded into the computer system, implements the various functional modules of the computer system as described herein.

[0027] Other aspects of the invention will be realized and attained by the elements and combinations particularly described in the appended claims.It should be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention described. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 A block diagram of an exemplary embodiment of a computer system for measuring the peak intensity of a pulse height spectrum obtained by a wavelength dispersive X-ray fluorescence spectrometer is included;

[0029] Figure 2 is a simplified flow chart of a computer-implemented method for measuring peak intensity in a pulse height spectrum obtained by a wavelength dispersive X-ray fluorescence spectrometer according to one embodiment;

[0030] Figure 3 shows overlapping signal contributions from different diffraction orders in the measured pulse height spectrum for the corresponding integration region;

[0031] Figure 4 showing the contributions of different signal types for specific diffraction orders in the measured pulse height spectrum;

[0032] Figure 5 shows the resulting pulse height spectrum model with diffraction order profile and escape profile;

[0033] Figure 6 shows a measured pulse height spectrum and a pulse height spectrum model with diffraction orders and escape profile after fitting according to an embodiment;

[0034] Figure 7 showing a first-order peak of a measured pulse height spectrum with a pile-up and a corresponding set of fitted first-order profiles according to an embodiment;

[0035] Figure 8 shows the generation / creation of an aging profile for a set of diffraction order profiles according to an embodiment;

[0036] Figures 9A to 9Cshows the improvement obtained when evaluating measured pulse height spectra using pulse height spectrum fitting according to an embodiment;

[0037] Figures 10A to 10D shows various steps of an example of generating a pulse height spectrum model with diffraction orders, dispersion and aging profiles according to one embodiment;

[0038] Figure 11 shows a measured pulse height spectrum and a fitted pulse height spectrum model with diffraction orders, dispersion, and aging profiles according to an embodiment;

[0039] Figure 12 shows improving the resolution of goniometer measurements by providing second order profile intensity according to an embodiment; and

[0040] Figure 13 is a diagram showing an example of a general-purpose computer device and a general-purpose mobile computer device that can be used with the techniques described herein. DETAILED DESCRIPTION

[0041] Figure 1 A block diagram of an exemplary embodiment of a computer system 100 for measuring peak intensity in a pulse height spectrum obtained by a wavelength dispersive X-ray fluorescence spectrometer 200 is included. Figure 1 The system 100 is used to measure Figure 2 1 is described in the context of a simplified flow chart of a computer-implemented method 1000 for determining peak intensities in a pulse height spectrum as shown in FIG. Figure 1 and Figure 2 The system 100 is further configured to perform the method 1000 when a corresponding computer program is loaded into a memory of the system and executed by a processing member of the system. The computer program product implements the functional modules 120, 130, 140 of the system 100.

[0042] exist Figure 1 In an exemplary embodiment of the present invention, the system 100 is communicatively coupled to the spectrometer 200. In an alternative embodiment, the computer system 100 can be an integral component of the wavelength dispersive x-ray fluorescence spectrometer 200. In both embodiments, the system 100 can receive 1100 a pulse height spectrum 212 obtained by the MCA 205 of the spectrometer 200 via an appropriate interface (not shown). The functionality of the spectrometer 200 has been largely described in the background section. Generally speaking, it is known to those skilled in the art how the spectrometer 200 can obtain the pulse height spectrum 212 from the sample 202. Nevertheless, reference is made hereinafter to Figure 1 Briefly summarize the functionality.

[0043] An x-ray tube 201 generates polychromatic radiation 201-r, containing characteristic lines and bremsstrahlung radiation, which is directed onto a sample 202 to be analyzed. This radiation produces polychromatic x-ray fluorescence and scattered radiation 202-r in the sample 202. The radiation 202-r emitted by the sample 202 is analyzed by measuring the radiation reflected by the spectrometer's monochromator 203 at various diffraction angles θ using a goniometer. This technique is based on Bragg's law. X-ray photons 203-r with energies multiples of the analysis signal reach the spectrometer's detector 204. Photons striking the detector 204 are converted into electrical pulses, where the pulse height is proportional to the photon's energy. A multichannel analyzer 205 (MCA) can then count the number of photons at the energies corresponding to the various channels of the MCA, thereby generating a pulse height spectrum 212. Additional effects that can contribute to pulse height spectroscopy have been described in the background section and will be described in more detail in the context of the figures and the corresponding detailed description. The method disclosed herein is described using diffraction angle scanning, but is also applicable to fixed diffraction angle measurements.

[0044] The system has a model generator 120 adapted to generate a pulse height spectrum model (PHSM) 112. The PHSM 112 is a model based on the various signal components that add up to form the measured curve in the measured pulse height spectrum. As previously mentioned, a pulse height spectrum typically includes at least diffraction order peaks and dispersion peaks. Thus, the model generator 120 generates a PHSM that includes at least corresponding diffraction order profiles 121 and dispersion profiles 122. In optional embodiments of the model generator, a stacking profile 123 may be further generated for a first-order diffraction profile, an aging profile 124, and / or a rack profile 125.

[0045] A plurality of diffraction order profiles 121 having predefined profile shapes are created 1210 at photon energy positions corresponding to the respective diffraction orders of the monochromator 203. The width of the diffraction profile is determined using a calibrated width model that reflects the dependence of the width on the respective energy position and the total incoming count rate of the spectrometer's detector 204. The width model to be used may depend on the type of detector. Three example width models are shown below. However, those skilled in the art may also use other models for determining the width of the diffraction profile.

[0046] With E as the energy and r as the total incoming count rate, the profile width for various detectors can be determined using a width model described by the mathematical terms T1 to T3 (other terms may also be used by those skilled in the art):

[0047] S6JAGUAR flow meter:

[0048]

[0049] S8 TIGER flow meter:

[0050]

[0051] S8 TIGER Scintillation Counter:

[0052] 0.46E+2.4(T3)

[0053] The outline width is summarized by model F3:

[0054]

[0055] Wherein w1, w2, w3 and w4 are used as calibration parameters for the profile width model F3.

[0056] The positions of the diffraction order profiles are then determined by their corresponding energies and the pulse height to energy mapping.

[0057] If the created diffraction order peaks have photon energies that are higher than the edge energy of the detector material of the detector, then typically a dispersion peak is generated by the detector material. The model generator takes this into account by adding 1220 the corresponding dispersion profile to the PHSM 112 at the location of the photon energy of the diffraction order profile that is attenuated by the fluorescence energy of the photons escaping from the detector material. In turn, the intensity of the dispersion profile is determined by using a calibrated dispersion intensity model that reflects the dependence of the intensity on the corresponding energy position. In the case of gas detectors, the dispersion intensity model may also reflect the dependence on the gas pressure of the detector. The dispersion intensity model also depends on the detector type. Some examples of dispersion intensity ratios at sea level pressure (i.e., the ratio between the intensity of the dispersion profile and the intensity of its associated diffraction order profile) that can be used by various detector types are (alternatively, other appropriate values ​​may be used depending on the respective individual detector):

[0058] S6 JAGUAR flow meter: 0.075

[0059] S8 TIGER flow meter: 0.075

[0060] S8 TIGER Scintillation Counter: 0 (i.e., no scintillation profile for this detector type)

[0061] A summary of the fugitive intensity model is given by F4:

[0062] (e1E+e2)(e3p+e4)(F4)

[0063] where e1, e2, e3, and e4 are calibration parameters for the emission intensity ratio. p is the pressure of the gas in the gas detector. For non-gas detectors, e3 = 0 and e4 = 1.

[0064] The model adjustment module 130 of the system 100 uses a fitting algorithm FA1 to adjust 1300 the pulse height to energy mapping parameters (slope and offset) and the contribution area of ​​each diffraction order profile set of the pulse height spectrum model. The fitting algorithm FA1 is adapted to minimize the difference between the pulse height spectrum model 212 and the received pulse height spectrum 112. For example, a least squares fitting algorithm may be used. Alternatively, an alternative fitting algorithm (e.g., a minimum sum method) may be used.

[0065] In general, fitting iteratively attempts to find the minimum deviation between the model (PHSM) and the observations (measured pulse height spectra). However, if the model depends nonlinearly on the parameters to be fitted, several local minima may exist. Some fitting algorithms may converge to a local minimum rather than finding the global minimum. In addition, the fitting algorithm may tend to overshoot in the first iteration, thereby deviating from the path toward the global minimum. Fitting algorithms that find the global minimum are generally slow. In one embodiment, these problems can be alleviated by selecting starting values ​​for the fitting parameters that are already close to the global minimum and by allowing the adjustment module 130 to search only in a reasonable solution space. As used herein, a reasonable solution space means no significant deviation from the previously determined pulse height to energy mapping parameters. Starting values ​​for the intensities of a set of diffraction order profiles can be obtained by integrating the pulse height spectrum between 50% and 150% (i.e., between 0.5 and 1.5 times) the corresponding diffraction order energy for the first order, between 150% and 250% for the second order, and so on. A further restriction to only use positive intensities can also be used.

[0066] In other words, the fit may use constraints on the fitting parameters regarding the diffraction orders and the dispersion profile, for example:

[0067] -Box constraints that allow only small changes to the pulse height to energy mapping parameters

[0068] - Non-negativity constraint on the contribution area of ​​the set of diffraction order profiles.

[0069] Box constraints are lower and upper bound inequality constraints that restrict the parameters to be fitted within a predetermined range. Non-negativity constraints are lower bound inequality constraints where the lower bound is zero. Figure 8 ), a box constraint can be set so that the aging ratio (ie, the ratio between the intensity of an aging profile set and the intensity of its associated diffraction order profile set) remains between 0 and 1.

[0070] The intensity module 140 of the system 100 ultimately provides 1400 the contribution area of ​​the set of first-order profiles as the intensity EI1 of the energy to be determined by the wavelength dispersive X-ray fluorescence spectrometer 200. Since the PHSM automatically knows the contribution of each signal model component, after fitting, the contribution area of ​​the set of first-order profiles is immediately known from the fitted PHSM 112, since each of the profiles of the PHSM represents an integrable function.

[0071] Figure 3 The problem of overlapping signal components from different diffraction orders in the actual measured pulse height spectrum is shown. In curve 301, the pulse height spectrum of the 1st order peak associated with the 1st order dispersion peak is shown. In order to determine the intensity of the analytical signal - in this example of a low-intensity 1st order peak, a narrow fixed integration range (interval IR1) is traditionally used, which is suitable for including both the contribution of the 1st order peak and the contribution of its dispersion peak. Curve 302 shows a 1st order peak with high intensity, where pile-up is also observed. In traditional peak evaluation methods, a wider fixed integration range IR2 can also be used to capture the contribution of pile-up to the first-order intensity. Curve 303 shows how the signal contribution of the 2nd order now overlaps with the fixed integration ranges IR1 and IR2 in two scenarios (low-intensity curve 301 and high-intensity curve 302). The 2nd order dispersion peak overlaps with the narrow fixed integration range IR1. With respect to the wider fixed integration range IR2, the 2nd order dispersion peak and the 2nd order peak completely overlap with the integration range IR2. That is, the intensity to be determined of the analytical signal (1st order contribution) is distorted by the high-order signal contribution in the fixed integration range. This often results in inaccurate measurements when using a fixed integration range.

[0072] Figure 4 Another example of a pulse height spectrum 400 is shown, having a 1st-order peak 401, a 2nd-order peak 402, and a 2nd-order scatter peak 402e. In this example, the scatter peak 402e (from the 2nd-order peak 402) overlaps with the analytical signal 401. In such a situation, it is impossible to find an integration range that excludes such interference of higher diffraction orders on the analytical signal. It should be noted that overlap with the analytical signal can even arise from diffraction orders higher than 2. For example, for the aluminum Al KA1 fluorescence line from the sample, the 1st-order peak is approximately 1.5 keV. The 2nd-order peak is at 3 keV (which is less than the edge energy of the detector material argon (Ar), 3.3 keV → no scatter peak). The 3rd-order peak is at 4.5 keV (which corresponds to the titanium Ti KA1 fluorescence line), which creates a scatter peak at 1.5 keV (4.5 keV due to the 3 keV attenuation of the Ar KA1 fluorescence energy), and therefore overlaps with the 1st-order analytical signal. Furthermore, as mentioned above, peak positions may change with signal strength, temperature, and age of the detector, resulting in additional types of potentially overlapping signal contributions.

[0073] Figure 5A generated PHSM 500 is shown with diffraction order profiles 501 to 504 and scattering profiles 501e to 504e. The example model 500 uses Gaussian-shaped profiles at positions corresponding to the photon energies of the diffraction orders of the monochromator. The highest visible diffraction order depends on the energy range of the detector and the expected interference (overlap), which is detector-specific. In the example, a scattering profile is added for each diffraction order profile. However, when generating the PHSM, the scattering profile is only added to the corresponding diffraction order profile set if the corresponding photon energy is above the edge energy of the detector material. For the example model 500, this is assumed to be the case for all diffraction order profile sets.

[0074] The scatter intensity ratio (the ratio between the intensity of the scatter profile and the intensity of the associated diffraction order profile) is determined by the scatter intensity model described above, which takes into account the energy and detector material. According to the previously disclosed calibrated width model, the profile width increases with the energy of the corresponding profile. The relative position of the profiles is determined by their corresponding energy and pulse height to energy mapping. The PHSM including diffraction order profiles and scatter profiles is considered to be a basic embodiment. However, it should be emphasized again that not every diffraction order profile set needs to include both profile types. In some cases, the scatter profile is only included in the higher order diffraction order profiles.

[0075] Figure 6 Measured pulse height spectrum 601 and pulse height spectrum model 602 (white dashed line) with diffraction order and dispersion profiles after fitting are shown. In the example, pulse height spectrum 601 has a 1st order peak, a 1st order dispersion peak, a 2nd order peak, and a 2nd order dispersion peak that partially overlaps with the 1st order peak. Fitted model 602 has been adjusted to minimize the difference between spectrum 601 and PHSM 602 by using pulse height to energy mapping parameters (slope and offset) and the contribution areas of the 1st order profile set (including the 1st order diffraction profile and the 1st order dispersion profile) and the 2nd order profile set (including the 2nd order diffraction profile and the 2nd order dispersion profile).

[0076] When generating a PHSM, profiles of other profile types may be added to the spectrum before fitting. In one embodiment, the model generator 120 may add 1230 a pileup profile to the first-order diffraction profile. The intensity of the pileup is determined using a calibrated pileup intensity model. Furthermore, the pileup intensity ratio depends on the detector type. The pileup intensity ratio is the ratio between the intensity of the pileup profile and the intensity of the first-order diffraction profile.

[0077] In the case of r as the total count rate, the following detector-dependent pile-up intensity ratios can be used when adding the pile-up profile:

[0078] S6 JAGUAR flow meter:

[0079] 1.4·10 -13 r+4.5·10 -8 +1.2·10 -5 / r(T4)

[0080] S8 TIGER flow meter:

[0081] 1.4·10 -13 r+4.5·10 -8 +1.2·10 -5 / r(T5)

[0082] S8 TIGER Scintillation Counter:

[0083] 3.5·10 -16 r+3·10 -9 +5.8·10 -2 / r(T6)

[0084] A summary of the packing strength model described by F5 is:

[0085] p1r+p2+p3 / r(F5)

[0086] Where p1, p2, and p3 are calibration parameters for the stacking intensity ratio.

[0087] Figure 7 An example of a 1st order peak in the measured pulse height spectrum 701 is shown, which shows pile-up on the falling edge of the peak. Curve 702 represents the fitted PHSM, which contains the pile-up profile in the set of 1st order profiles. Since pile-up is produced by two photons from the analytical signal, the intensity of the analytical signal is not just the sum of the intensities of the main peak and the pile-up. It is actually the sum of the main peak intensity and twice the pile-up intensity. When a wide integration range is selected, the fixed integration range method may only give an uncorrected sum. This can lead to a nonlinear response of the detector to increasing intensity. As pile-up increases with increasing intensity, the nonlinearity increases and the summation error becomes larger and larger. The pulse height spectrum fitting method disclosed in this article uses separate profiles for the 1st order diffraction profile and the pile-up profile so that the pile-up and 1st order diffraction intensities add correctly. This improves the linearity of the detector to significantly higher count rates.

[0088] Another type of profile that can be added by the model generator is for representing so-called aging peaks. Gas detectors exhibit aging effects due to aging of the wires. Thus, an aging peak is generated for each peak in the pulse height spectrum of an aging gas detector of the spectrometer. Therefore, in the case where a gas detector is used by the spectrometer, the model generator adds 1240 one or more aging profiles to the pulse height spectrum model 112 to account for aging effects. This is achieved by replicating the generated set of diffraction order profiles and shifting them by a calibrated energy offset. Figure 8 A diffraction order profile set is shown with a diffraction order profile DOP1 and an escape profile EP1. The model generator copies DOP1 and EP1 and shifts them to higher energies by a calibrated energy offset. The intensities of the diffraction order profile set (DOP1, EP1) are then scaled relative to the intensities of the corresponding shifted profiles, thereby generating shifted, rescaled aging profiles EPA1 and DOAP1. In other words, the relative intensities between the profiles of the diffraction order profile set and the corresponding aging peaks are fitted, while the offset between the original profile and the shifted aging profile is fixed. In other words, the ratio between the intensities of the shifted aging profile set and the intensities of the corresponding diffraction order profile set is adjusted by the fitting algorithm, while the shift is provided by the calibration.

[0089] 1250 can be added to PHSM 112 (see Figure 1 Another type of profile is the so-called shelf. For this profile type, a constant contribution can be added to each generated profile, extending from the corresponding profile position to a defined detector-dependent lower energy, thereby defining the shelf for the profile. The constant intensity value is determined by using a calibrated shelf intensity model. The shelf intensity ratio (i.e., the ratio between the intensity of a shelf profile and the intensity of its associated diffraction order profile) also depends on the detector type and energy E. The following terminology can be used:

[0090] S6 JAGUAR flow meter:

[0091]

[0092] S8 TIGER flow meter:

[0093]

[0094] S8 TIGER Scintillation Counter:

[0095] 0 (no rack for this detector type)

[0096] Summary of frame strength:

[0097]

[0098] where s1, s2, and s3 are calibration parameters for the rack strength ratio.

[0099] Figures 10A to 10D The steps for generating an example of a pulse height spectrum model with diffraction orders, dispersion and aging profiles are shown. Figure 10A In , the dash-dot lines indicate the energy positions used for the diffraction order profiles. Figure 10B In , the energy positions of the scatter profiles for higher diffraction orders are added and are represented by dashed lines. When a scatter profile is added to a diffraction order profile, the intensity of the diffraction order profile is reduced by the intensity of the added scatter profile, so that the intensity of the corresponding set of diffraction order profiles remains constant. Figure 10C In , the energy positions of the aging profiles are added for the set of all diffraction order profiles represented by the solid lines. Finally, in Figure 10D In , all lines are convolved with a profile shape (e.g., a Gaussian shape) to present the corresponding diffraction order, dispersion, and aging profiles (e.g., 2nd order diffraction profile DOP_10, 2nd order dispersion profile EP_10, and 2nd order aging profile AP_10). The sum of all profiles produces the pulse height spectrum model PHSM_10, which is Figure 10D Indicated by dotted lines.

[0100] Figure 11 Measured pulse height spectrum 81 and fitted pulse height spectrum model 82 are shown. Spectrum 81 was obtained using a flowmeter gas detector in which charged particles generated by incident x-ray photons are collected by a wire in the center of the detector. Over time, the wire surface degrades (aging effects), causing the peak shape in the measured pulse height spectrum to change. In this example, the 1st-order diffraction peak overlaps with the 1st-order aging peak. In addition, the 2nd-order dispersion peak also overlaps with the 1st-order aging peak. The 2nd-order peak has a strong overlap with its own aging peak. PHSM 82 is created by creating corresponding diffraction order profiles, dispersion profiles, and aging profiles and fitting the resulting diffraction order profile set to the measured pulse height spectrum 81 using the slope and offset of the pulse height to energy mapping, the contribution area of ​​the corresponding profile set, and the aging peak ratio as fitting parameters. The fitted PHSM 82 is very close to the original measured spectrum 81. Because PHSM 82 knows the contribution area of ​​the 1st-order diffraction profile set and its corresponding aging profile set exactly, the intensity of the analytical signal can be accurately determined. In the classical approach using integration regions this is not possible.

[0101] Figures 9A to 9C The improvement obtained when evaluating measured pulse height spectra using pulse height spectrum fitting according to an embodiment is shown. Figure 9AThe measured pulse height spectrum 91 dominated by the second order diffraction order contribution and the fitted PHSM 92 (dashed white line) is shown. The fixed integration range IR9 is centered on the vertical dashed line and indicates the energy of the analytical signal. The fixed integration range adds the 2nd order dispersion peak to the integration result.

[0102] Figure 9B and 9C Shown are the same goniometer scans of two samples performed by the spectrometer, where each point is the result of extracting the intensity from the pulse height spectrum using two different methods. Figure 9B In the example, the analysis signal is extracted using classical integration within the integration range IR9. Spectrum 95 is measured using a sample containing only scandium (Sc), while spectrum 96 (dashed curve) is measured using a sample containing only tantalum (Ta). Figure 9A As shown in Figure 9, the second-order Ta LA1 intensity contributes to the integration range IR9 by escaping the peak. This produces an artifact in the form of a peak in spectrum 96, where there should be no signal because Sc is not present in the sample. To simplify the visualization of curve 90, only samples containing either element are shown. Samples containing a mixture of the two elements will show the sum of the two peaks, and therefore Ta will hinder the quantification of Sc. When viewing Figure 9C When curve 90' ​​in FIG (extracted using pulse height spectral fitting), a peak corresponding only to Sc KA (curve 95') is present in the spectrum of the sample containing Sc. No artifact peaks appear in spectrum 96' of the sample containing only Ta because the contribution of the second-order peaks is completely eliminated when the pulse height spectral fitting method disclosed herein is used. Since the spectrum from the sample also contains scattered bremsstrahlung from the tube, which is continuous at all energies, the higher orders of the monochromator will always contribute intensity to integration range IR9 when the higher-order bremsstrahlung peaks are within the integration range. Therefore, using pulse height spectral fitting to separate the contribution of the higher-order bremsstrahlung peaks from the first-order intensity significantly reduces the contribution of the higher-order bremsstrahlung to the analytical signal.

[0103] In one embodiment, the strength module 140 (see Figure 1 ) is further adapted to provide 1410 (see Figure 2 ) The contribution area of ​​at least the second-order profile set is used to improve the resolution of the goniometer measurement performed by the wavelength dispersive X-ray fluorescence spectrometer 200. The energy error of the second-order profile set is smaller than the energy error of the first-order profile set, which is Figure 12 In other words, an improvement in the resolution of the spectrometer can be achieved when also taking higher orders into account - at least the second order.

[0104] Wavelength dispersive x-ray spectrometers use a monochromator to select the energy E to be analyzed by adjusting the diffraction angle θ on the monochromator according to the Bragg equation:

[0105]

[0106] where n is the diffraction order and d is the lattice plane distance. However, since the diffraction order can be any positive integer, the monochromator actually allows multiple energies to be reflected to the detector. The energy of the second order is twice that of the first order, the energy of the third order is three times that of the first order, and so on. Pulse height spectral fitting provides not only the intensity of the first order, but also the intensities of higher orders simultaneously, because the pulse height spectral model contains the collection of profiles of all corresponding separated diffraction orders. The first order and higher orders are recorded at the same diffraction angle, but correspond to different energies.

[0107] Therefore, the intensities of all orders can be plotted against the energy, e.g. Figure 12 12-IR represents the intensity obtained by the fixed integration window method. Curve 12-PH1 represents the first-order intensity obtained by using the pulse height spectrum fitting method. Curve 12-PH2 represents the second-order intensity obtained by using the pulse height spectrum fitting method. The x-axis is the energy in keV. The y-axis is the intensity expressed in arbitrary units (logarithmic scale). It can be clearly seen in curve 12-z that the 12-PH2 peaks associated with Co KA, Ni Ka, Co KB, and Ni Kb are much narrower than the corresponding 12-PH1 peaks at the same position. However, the intensity is weakened by approximately ten times.

[0108] The following describes the resolution improvement mathematically. Only typical diffraction angles 0° < θ < 90° are allowed. Measuring the same energy at different diffraction orders gives:

[0109] For the first order,

[0110]

[0111] And for the second order,

[0112]

[0113] This can be combined to give:

[0114] sin(θ2)=2sin(θ1)(F10)

[0115] Since sine is monotonically increasing in a given range of θ,

[0116] θ2>θ1. (F11)

[0117] The broadening of the peak is governed by the angular resolution of the diffractometer (monochromator crystal). The angular error Δθ can be expressed as an energy error ΔE via error propagation:

[0118] ΔE=E|cot(θ)|Δθ. (F12)

[0119] The energy errors can be calculated for first- and second-order measurements of the same energy at different diffraction angles and are:

[0120] ΔE1=E|cot(θ1)|Δθ(F13)

[0121] and

[0122] ΔE2=E|cot(θ2)|Δθ(F14).

[0123] Since |cot(θ2)| is monotonically decreasing in a given range of θ, and θ2>θ1,

[0124] |cot(θ2)|<|cot(θ1)|(F15)

[0125] And therefore

[0126] ΔE2<ΔE1. (F16)

[0127] That is, the energy error of the second order is smaller than the energy error of the first order. Therefore, the energy resolution of the second order is higher than that of the first order. Figure 1 ) can provide higher diffraction orders as input to the system 100 via the user interface in case the system should also provide intensity values ​​for higher diffraction order profile sets.

[0128] Another advantage can be the reduction of higher order intensities. Wavelength dispersive x-ray spectrometers use high power excitation sources to mitigate the intensity loss caused by the monochromatization of the analytical signal from the sample and to improve the sensitivity of low concentration elements (trace amounts). However, the sample analyst needs to determine the concentration of sample components from trace levels to very high concentrations. However, the dynamic range of the detector is limited. Typically, different fluorescence lines are used for low and high concentrations, or the generator power is reduced. Alternatively, a filter can be added between the x-ray tube and the sample. However, such changes in excitation or detection increase the measurement time. Since higher order intensities (contribution area) and first-order contribution area are determined simultaneously by the pulse height spectrum fitting method disclosed herein, such higher order intensities can be used to collect reduced intensities without changing the excitation and therefore without increasing the measurement time.

[0129] Figure 13 is a diagram showing an example of a general purpose computer device 900 and a general purpose mobile computer device 950 that can be used with the techniques described herein. In some embodiments, the computing device 900 can be used with the system 100 (see Figure 1). As previously mentioned, this computer device 900 can be implemented as an integrated component of a wavelength dispersive X-ray fluorescence spectrometer. Computing device 950 is intended to represent various forms of mobile devices, such as personal digital assistants, cellular phones, smartphones, and other similar computing devices. In the context of the present disclosure, computing device 950 may provide I / O components to enable a user to interact with computing device 950 (e.g., for selecting diffraction orders for analysis of a sample). The components shown here, their connections and relationships, and their functions are exemplary only and are not meant to limit the embodiments of the invention described and / or claimed in this document.

[0130] The computing device 900 includes a processor 902, a memory 904, a storage device 906, a high-speed interface 908 connected to the memory 904 and a high-speed expansion port 910, and a low-speed interface 912 connected to a low-speed bus 914 and the storage device 906. Each of the components 902, 904, 906, 908, 910, and 912 is interconnected using various buses and can be appropriately mounted on a common motherboard or otherwise mounted. The processor 902 can process instructions for execution within the computing device 900, including instructions stored in the memory 904 or on the storage device 906, to display graphical information of a GUI on an external input / output device such as a display 916 coupled to the high-speed interface 908. In other embodiments, multiple processors and / or multiple buses, as well as multiple memories and memory types, can be used as appropriate. In addition, multiple computing devices 900 can be connected, with each device providing a portion of the necessary operations (e.g., as a server bank, a group of blade servers, or a multi-processor system).

[0131] Memory 904 stores information within computing device 900. In one embodiment, memory 904 is one or more volatile memory units. In another embodiment, memory 904 is one or more non-volatile memory units. Memory 904 may also be another form of computer-readable medium, such as a magnetic disk or optical disk.

[0132] Storage device 906 can provide mass storage for computing device 900. In one embodiment, storage device 906 can be or include a computer-readable medium, such as a floppy disk drive, a hard disk drive, an optical disk drive, or a magnetic tape drive, a flash memory or other similar solid-state storage device, or an array of devices, including those in a storage area network or other configuration. A computer program product can be tangibly embodied in an information carrier. A computer program product can also include instructions that, when executed, perform one or more methods, such as those described above. The information carrier is a computer- or machine-readable medium, such as memory 904, storage device 906, or memory on processor 902.

[0133] The high-speed controller 908 manages bandwidth-intensive operations of the computing device 900, while the low-speed controller 912 manages less bandwidth-intensive operations. This allocation of functions is exemplary only. In one embodiment, the high-speed controller 908 is coupled to the memory 904, the display 916 (e.g., via a graphics processor or accelerator), and to the high-speed expansion port 910 that can accept various expansion cards (not shown). In the described embodiment, the low-speed controller 912 is coupled to the storage device 906 and the low-speed expansion port 914. The low-speed expansion port, which can include various communication ports (e.g., USB, Bluetooth, Ethernet, wireless Ethernet), can be coupled to one or more input / output devices, such as a keyboard, pointing device, scanner, or networking devices, such as a switch or router, for example, via a network adapter.

[0134] Computing device 900 can be implemented in a variety of different forms, as shown. For example, it can be implemented as a standard server 920, or multiple implementations in a group of such servers. It can also be implemented as part of a rack server system 924. In addition, it can be implemented in a personal computer such as laptop computer 922. Alternatively, components from computing device 900 can be combined with other components in a mobile device (not shown), such as device 950. Each of these devices can contain one or more of computing devices 900, 950, and the entire system can be composed of multiple computing devices 900, 950 communicating with each other.

[0135] The computing device 950 includes a processor 952, a memory 964, input / output devices such as a display 954, a communication interface 966, and a transceiver 968, among other components. The device 950 may also have a storage device, such as a microdrive or other device, to provide additional storage. Each of the components 950, 952, 964, 954, 966, and 968 are interconnected using various buses, and several components may be appropriately mounted on a common motherboard or otherwise.

[0136] Processor 952 can execute instructions within computing device 950, including instructions stored in memory 964. The processor can be implemented as a chipset of chips that include separate or multiple analog and digital processors. The processor can provide, for example, coordination of other components of device 950, such as control of a user interface, applications executed by device 950, and wireless communications performed by device 950.

[0137] The processor 952 can communicate with the user through a control interface 958 and a display interface 956 coupled to a display 954. The display 954 can be, for example, a TFT LCD (thin film transistor liquid crystal display) or an OLED (organic light emitting diode) display, or other appropriate display technology. The display interface 956 can include appropriate circuits for driving the display 954 to present graphics and other information to the user. The control interface 958 can receive commands from the user and convert them to be submitted to the processor 952. In addition, an external interface 962 in communication with the processor 952 can be provided to enable close range communication between the device 950 and other devices. The external interface 962 can, for example, provide wired communication in some embodiments, or provide wireless communication in other embodiments, and multiple interfaces can also be used.

[0138] Memory 964 stores information within computing device 950. Memory 964 can be implemented as one or more computer-readable media, one or more volatile memory units, or one or more non-volatile memory units. Expansion memory 984 may also be provided and connected to device 950 via expansion interface 982, which may include, for example, a SIMM (Single In-line Memory Module) card interface. This expansion memory 984 can provide additional storage space for device 950 or store applications or other information for device 950. Specifically, expansion memory 984 may include instructions for executing or supplementing the processes described above and may also include security information. Thus, for example, expansion memory 984 can serve as a security module for device 950 and can be programmed with instructions that allow for secure use of device 950. Furthermore, secure applications can be provided via a SIMM card along with additional information, such as identifying information placed on the SIMM card in a non-hackable manner.

[0139] The memory may include, for example, flash memory and / or NVRAM memory, as described below. In one embodiment, a computer program product is tangibly embodied in an information carrier. The computer program product comprises instructions that, when executed, perform one or more methods, such as those described above. The information carrier is a computer-readable medium or machine-readable medium, such as memory 964, expansion memory 984, or memory on processor 952, which may be received, for example, via transceiver 968 or external interface 962.

[0140] The device 950 can communicate wirelessly via a communication interface 966, which may include digital signal processing circuitry, if necessary. The communication interface 966 can provide communication in various modes or protocols, such as GSM voice calls, SMS, EMS or MMS messaging, CDMA, TDMA, PDC, WCDMA, CDMA2000, or GPRS. Such communication can occur, for example, via a radio frequency transceiver 968. In addition, short-range communication can occur, such as using Bluetooth, WiFi, or other such transceivers (not shown). In addition, a GPS (Global Positioning System) receiver module 980 can provide additional navigation- and location-related wireless data to the device 950, which can be used appropriately by applications running on the device 950.

[0141] Device 950 may also communicate audio using an audio codec 960 that receives voice information from a user and converts it into usable digital information. For example, in a handset of device 950, audio codec 960 may similarly generate audible sound for the user, such as through a speaker. Such sound may include sound from a voice phone call, may include recorded sound (e.g., voice messages, music files, etc.), and may also include sound generated by applications operating on device 950.

[0142] The computing device 950 can be implemented in a variety of different forms, as shown in the figure. For example, it can be implemented as a cellular phone 980. It can also be implemented as part of a smart phone 982, a personal digital assistant, or other similar mobile device.

[0143] Various embodiments of the systems and techniques described herein can be implemented in digital electronic circuitry, integrated circuitry, specially designed ASICs (application specific integrated circuits), computer hardware, firmware, software, and / or combinations thereof. These various embodiments can include implementations in one or more computer programs executable and / or interpretable on a programmable system comprising at least one programmable processor, which can be special purpose or general purpose, coupled to receive data and instructions from and send data and instructions to a storage system, at least one input device, and at least one output device.

[0144] These computer programs (also referred to as programs, software, software applications, or code) include machine instructions for a programmable processor and may be implemented in high-level procedural and / or object-oriented programming languages ​​and / or in assembly / machine language. As used herein, the terms "machine-readable medium," "computer-readable medium," and "machine-readable medium" refer to any computer program product, apparatus, and / or device (e.g., a magnetic disk, an optical disk, a memory, a programmable logic device (PLD)) for providing machine instructions and / or data to a programmable processor, including machine-readable media that receive machine instructions as a machine-readable signal. The term "machine-readable signal" refers to any signal used to provide machine instructions and / or data to a programmable processor.

[0145] To provide interaction with a user, the systems and techniques described herein can be implemented on a computer having a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to the user, and a keyboard and pointing device (e.g., a mouse or trackball) through which the user can provide input to the computer. Other types of devices can also be used to provide interaction with the user; for example, the feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form, including sound, voice, or tactile input.

[0146] The systems and techniques described herein can be implemented in a computing device that includes a back-end component (e.g., as a data server), or includes a middleware component (e.g., an application server), or includes a front-end component (e.g., a client computer with a graphical user interface or a web browser through which a user can interact with embodiments of the systems and techniques described herein), or any combination of such back-end, middleware, or front-end components. The components of the system can be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include a local area network ("LAN"), a wide area network ("WAN"), and the Internet.

[0147] Computing devices may include clients and servers. A client and server are generally remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other.

Claims

1. A computer-implemented method (1000) for estimating peak intensity in a pulse height spectrum obtained by a wavelength dispersive X-ray fluorescence spectrometer, comprising: receiving (1100) a pulse height spectrum (212) obtained from a sample (202) by a multi-channel analyzer (205) of a wavelength dispersive X-ray fluorescence spectrometer (200); A pulse height spectral model (112) having a plurality of diffraction order profile sets is generated (1200) by: creating (1210) a plurality of diffraction order profiles having predefined profile shapes at photon energy positions corresponding to respective diffraction orders of a monochromator (203) of the spectrometer (200), wherein the widths of the diffraction profiles are determined by using a calibrated width model reflecting the dependence of the widths on the respective energy positions and the total incoming count rate of a detector (204) of the spectrometer, and wherein the relative positions of the diffraction order profiles are determined by their respective energies and a pulse height to energy mapping; for created diffraction order profiles where the corresponding photon energy is above the edge energy of a detector material of the detector, adding (1220) a corresponding escape profile at positions of the photon energy of the diffraction order profile attenuated by fluorescence energy of photons escaped from the detector material, wherein the intensity of the escape profile is determined by using a calibrated escape intensity model reflecting the dependence of the intensity on the corresponding energy position; wherein a particular diffraction order profile set comprises all generated profiles associated with said corresponding diffraction order; adjusting (1300) pulse height to energy mapping parameters and contribution areas of each diffraction order profile set of the pulse height spectral model using a fitting algorithm (FA1) to minimize a difference between the pulse height spectral model (112) and a received pulse height spectrum (212); and The contribution area of ​​the first order profile set is provided (1400) as the intensity (EI1) at the energy to be determined by the wavelength dispersive X-ray fluorescence spectrometer (200).

2. The method of claim 1, wherein generating (1200) a pulse height spectrum model (112) further comprises any one of the following: adding (1230) a pile-up profile to the first order diffraction profile, wherein the intensity of the pile-up is determined by using a calibrated pile-up intensity model reflecting the dependence of the intensity on the corresponding energy position and the total incoming count rate of the detector (204); If the detector (204) is a gas detector, adding (1240) one or more aging profiles to the pulse height spectral model (112) by replicating and shifting the generated set of diffraction order profiles by a calibrated energy offset, wherein adjusting (1300) further comprises scaling the intensity of the generated set of diffraction order profiles relative to the intensity of the corresponding aging profiles; and The corresponding one or more rack contribution profiles are added (1250) to one or more generated profiles of the pulse height spectral model (112) as constant intensity values ​​starting at the corresponding generated profile positions and extending to a defined lower detector-dependent energy, wherein the constant intensity values ​​are determined by using a calibrated rack intensity model that reflects the dependence of the intensity on the corresponding energy position.

3. A method according to claim 1 or 2, wherein the fitting algorithm (FA1) is a least squares fitting algorithm, and wherein the starting value of the contribution area of ​​the diffraction order profile set is obtained by integrating the obtained pulse height spectrum (212) between 0.5 times and 1.5 times the corresponding diffraction order energy, and wherein one or more of the following constraints are set: a box constraint on the pulse height to energy mapping parameters that only allows insignificant changes of previously determined parameters, a non-negative constraint on the contribution area of ​​the diffraction order profile set.

4. The method according to any one of the preceding claims, wherein the predefined contour shape is selected from any one of the following: a Lorentz shape, a Gaussian shape, a Voigt shape, and a pseudo-Vogt shape.

5. The method of any of the preceding claims, wherein providing (1400) further comprises providing (1410) the contribution area of ​​at least a second order profile set for improving the resolution of goniometer measurements performed by the wavelength dispersive X-ray fluorescence spectrometer (200), wherein an energy error of the second order profile set is less than an energy error of the first order profile set.

6. A method according to any of the preceding claims, wherein the adjusting (1300) and providing (1400) steps remove artifact contributions of characteristic emission lines from higher orders of the pulse height spectrum (212) in a goniometer measurement performed by the spectrometer (200).

7. The method according to any of the preceding claims, wherein the adjusting (1300) and providing (1400) steps reduce the effects of higher order bremsstrahlung background from the pulse height spectrum (212).

8. The method according to any one of claims 2 to 7, wherein the intensity (EI1) at the energy to be determined is the sum of the first-order profile intensity, the stray profile intensity and the intensity of the pile-up profile multiplied by a correction factor.

9. A computer program product for estimating peak intensity in a pulse height spectrum obtained by a wavelength dispersive X-ray fluorescence spectrometer, having computer readable instructions which, when loaded into a memory of a computing device and executed by at least one processor of the computing device, cause the computing device to perform a computer-implemented method according to any one of the preceding claims.

10. A computer system (100) for estimating peak intensity in a pulse height spectrum obtained by a wavelength dispersive x-ray fluorescence spectrometer, comprising: An interface adapted to receive a pulse height spectrum (212) obtained from a sample (202) by a multi-channel analyzer (205) of a wavelength dispersive X-ray fluorescence spectrometer (200); A model generator (120) is adapted to generate a pulse height spectral model (112) having a plurality of diffraction order profile sets by: creating a plurality of diffraction order profiles having predefined profile shapes at photon energy positions corresponding to respective diffraction orders of a monochromator (203) of the spectrometer (200), wherein the width of the diffraction profiles is determined by using a calibrated width model reflecting the dependence of the width on the respective energy positions and the total incoming count rate of a detector (204) of the spectrometer, and wherein the relative positions of the diffraction order profiles are determined by their respective energies and a pulse height to energy mapping; for created diffraction order profiles where the corresponding photon energy is above the edge energy of a detector material of the detector, adding a corresponding escape profile at positions of the photon energy of the diffraction order profile attenuated by fluorescence energy of photons escaped from the detector material, wherein the intensity of the escape profile is determined by using a calibrated escape intensity model reflecting the dependence of the intensity on the corresponding energy position; wherein a particular diffraction order profile set comprises all generated profiles associated with said corresponding diffraction order; a model adjustment module (130) adapted to adjust pulse height to energy mapping parameters and contribution areas of each diffraction order profile set of the pulse height spectrum model using a fitting algorithm (FA1) to minimize a difference between the pulse height spectrum model (112) and a received pulse height spectrum (212); and An intensity module (140) adapted to provide the contribution area of ​​the first-order profile set as an intensity (EI1) of energy to be determined by the wavelength dispersive X-ray fluorescence spectrometer (200).

11. The system of claim 10, wherein the model generator (120) is further adapted to generate the pulse height spectrum model (112) by using any of: adding a pile-up profile to the first order diffraction profile, wherein the intensity of the pile-up is determined by using a calibrated pile-up intensity model reflecting the dependence of the intensity on the corresponding energy position and the total incoming count rate of the detector (204); If the detector (204) is a gas detector, adding one or more aging profiles to the pulse height spectral model (112) by replicating and shifting the generated set of diffraction order profiles by a calibrated energy offset, wherein adjusting further comprises scaling the intensity of the generated set of diffraction order profiles relative to the intensity of the corresponding aging profiles; and The corresponding one or more rack contribution profiles are added to the one or more generated profiles of the pulse height spectral model (112) as constant intensity values ​​starting at the corresponding generated profile positions and extending to a defined lower detector-dependent energy, wherein the constant intensity values ​​are determined by using a calibrated rack intensity model reflecting the dependence of the intensity on the corresponding energy position.

12. The system of claim 10 or 11, wherein the intensity module (140) is further adapted to provide the contribution area of ​​at least a second-order profile set for improving the resolution of a goniometer scan performed by the wavelength dispersive X-ray fluorescence spectrometer (200), wherein an energy error of the second-order profile set is less than an energy error of the first-order profile set.

13. The system according to any one of claims 10 to 12, wherein the adjustment module (130) and the intensity module (140) remove artifact contributions of characteristic emission lines from higher orders of the pulse height spectrum (212) in a goniometer measurement performed by the spectrometer (200) when performing the adjusting and providing steps.

14. A system according to any one of claims 10 to 13, wherein the fitting algorithm (FA1) is a least squares fitting algorithm, and wherein the starting value of the contribution area of ​​the diffraction order profile set is obtained by integrating the obtained pulse height spectrum (212) between 0.5 times and 1.5 times the corresponding diffraction order energy, and wherein one or more of the following constraints are set: a box constraint on the pulse height to energy mapping parameters that only allows insignificant changes of previously determined parameters, a non-negative constraint on the contribution area of ​​the diffraction order profile set.

15. A wavelength dispersive x-ray fluorescence spectrometer (200) comprising the computer system (100) according to any one of claims 10 to 14.

Images