The present invention relates to a method for calibrating an X-ray fluorescence spectrometer. The invention also relates to a method for measuring the composition of a sample by the use of an X-ray fluorescence spectrometer, which measurement method comprises such a calibration in an initial step.

X-ray fluorescence spectroscopy is in general used to analyse the composition of matter, more specifically the contents of different elements in a sample. The sample is radiated with high-energy radiation, such as X-rays or gamma rays, from a radiation source. One example of such a radiation source is a radiation tube, which is arranged to accelerate electrons from a cathode towards an anode, using a known potential difference of about 10-100 keV. The electron impact will generate X-ray radiation, both a relatively specific part due to photoelectrical interaction with the anode material and a radiation part with relatively wide wave- length distribution as a result of bremsstrahlung.

As the radiation emitted from the radiation source impacts the sample, it in turn emits radiation of different origins. For all elements contained in the sample, a respective characteristic pattern of photoelectrical^ induced radiation will result, in the form of a respective characteristic spectral line pattern. Apart from this photoelectric radiation, there will also be a background radiation component, which is due to scattering within the sample.

The radiation emitted by the sample is then measured by a detector of a spectrometer. Such spectrometer detector will detect radiation within a particular wavelength interval, but will also be prone to detecting radiation of neighbouring wavelengths, to a varying degree depending on the particular design of the spectrometer and its detector (line overlapping).

When using such a setup for analysing a sample, the goal is to detect the relative amounts of different elements in the sample based on the intensity of the different photoelectric radiation peaks emitted therefrom. For elements present in the sample in larger proportions, this can be done with relatively high precision and accuracy. However, for elements with lower proportions, or even trace elements, the presence of the background radiation component will severely affect the measurement precision and accuracy.

In order to improve precision and accuracy, it has been proposed to carefully measure the background component radiated from the sample. However, such measurements are time consuming. For trace elements, careful background radiation measurements are very important for being able to correctly determine proportions of such elements. Typically, background radiation will be measured on both sides of a particular photoelectric peak for a particular element.

Hence, it would be desirable to be able to precisely calibrate a piece of X-ray spectrometry equipment in a precise and quick way. Furthermore, it would be desirable to be able to then perform accurate and precise measurements of low-proportion component elements in a sample in a less time-consuming way than what has previously been possible.

SE 0600946-8 describes a method in which a sample is investigated using spectrometry.

In the article "Application of J. E. Fernandez algorithms in the evaluation of X-ray intensities measured on fused glass discs for a set of international standards and a proposed calibra- tion procedure", J Malmqvist; X-RAY SPECTROMETRY; X-Ray Spectrom 2001;30:83-92, a method is described in which calibration is performed using a known standard sample.

The present invention solves the above described problems. J. E. Fernandez, who is referred to in the said article, has developed a mathematical model allowing one to, given a set of particular characteristics concerning a combination of a radiation source and a spectrometer, calculate an expected detected radiation across a specified wavelength interval from a sample of known composition. This mathematical model is based upon the current knowledge of the physics relevant to the above described type of spectroscopy, which is detailed enough to provide reliable results. The Fernandez model is one example of such mathematical models, which are all ultimately based upon the standard model of physics.

The present invention relies on the use of such a mathematical model. However, since such models as such can be devised by those knowledgeable in the relevant physics, and since the example constituted by Fernandez' model is available, these models are not described in closer detail herein than what is necessary in order to understand the present invention. In the following, they are simply referred to as "models". Hence, the invention relates to a method for calibrating a piece of measurement equipment for spectrometric measurement of constituent elements in a material sample, which piece of equipment comprises a source of radiation and a spectrometer detector, which method comprises, for different respective wavelength intervals, measuring the radiation intensity emitted from a number of known samples, each with a respective known proportion of a particular respective element, as well as calculating a respective expected detected radiation intensity across the same wavelength interval of each of said samples using a mathematical model, which method is characterised in that the method furthermore comprises the steps a) given a set of a plurality of different such samples, and for a particular background wavelength interval not comprising a spectral line of any element present to a meas- urable extent in the sample, determining a background relationship between measured and calculated radiation intensities; b) for each of the samples used in step a) and said background wavelength interval, calculating a respective relative difference between the calculated radiation intensity and a corresponding measured intensity calculated using said background relationship; and c) for a set of at least two different samples comprising the same certain element, and for a particular element wavelength interval comprising a spectral line of the certain element, determining an element relationship between measured radiation intensities and calculated radiation intensities for the certain element, which calculated background radiation intensities have first each been corrected using said difference for the particular sample in question; wherein the hence determined element relationship is used as calibration constant for the certain element in question. Furthermore, the invention relates to a system for measuring the composition of a material sample using a piece of measurement equipment for spectrometric measurement of constituent elements in such a material sample, which piece of equipment comprises a source of radiation and a spectrometer detector, which system is arranged to receive meas- urement values from the said spectrometer detector of the radiation intensity emitted from a number of known samples, each with a respective known proportion of a particular respective element, and for different respective wavelength intervals, as well as to calculate a respective expected detected radiation intensity across the same wavelength interval of each of said samples using a mathematical model, which system is characterised in that the system is arranged to, given a plurality different such samples, and for a particular background wavelength interval not comprising a spectral line of any element present to a measurable extent in the sample, determine a background relationship between measured and calculated radiation intensities; for each of the samples in said set and said background wavelength interval, calculate a respective relative difference between the calculated radi- ation intensity and a corresponding measured intensity calculated using said background relationship; and, for a set of at least two different samples comprising the same certain element, and for a particular element wavelength interval comprising a spectral line of the certain element, determine an element relationship between measured radiation intensities and calculated radiation intensities for the certain element, which calculated radiation intensities have first each been corrected using said difference for the particular sample in question, and in that the system is arranged to use the hence determined element relationship as calibration constant for the certain element in question during subsequent measurement on an unknown sample using the said piece of equipment. The invention also relates to a computer software product arranged to be executed on a piece of hardware, such as a system according to the invention, and arranged to perform a method according to the present invention.

In the following, the invention will be described in detail, with reference to exemplifying embodiments of the invention and to the enclosed drawings, wherein: Figure la is a flowchart illustrating a calibration method according to the present invention; Figure lb is a continuation of the flowchart of figure la, further showing a subsequent measurement part of the same method;

Figure 2 is a schematic overview of a setup with which a method according to the present invention can be used, wherein a system 100 according to the present invention is a part of said setup; and

Figures 3a and 3b are respective diagrams showing experimental results of a run-through of a method according to the present invention. Below, the following variables and relationships will be used to describe various exemplifying embodiments of the present invention: n = a basic element (such as a metal or sulphur).

B _x = background point x

λ _η = wavelength interval comprising characteristic photoelectric spectrum line for basic element n.

λ _Β = wavelength interval for background point x, not comprising any characteristic photoelectric spectrum line for any basic element being present, or at least not expected to be present in measurable quantities, in a sample for which the background point in question is selected, preferably not for any basic element.

T _m = measured intensity.

T _c = calculated intensity.

T _m (l) = k _λ ■ T _c (λ) + Ι _λ linear relation describing the relation between measured and calculated intensity for the element or background point corresponding to wavelength interval λ.

IB _c (λ) = calculated background intensity for wavelength interval λ.

/P _c (/l) = calculated photoelectric intensity for wavelength interval λ.

T _c (λ) = IB _c (λ) + IP _c (λ).

IS _c (λ) = component in calculated background intensity for waveguide interval λ which is due to primary radiation scattering in a material sample. component in calculated background intensity for waveguide interval λ which is

due to intensity additions from overlapping spectral lines.

Measured intensity for the wavelength λ as translated into calculated

intensity using the linear relationship as determined during calibra

tion. One example is the "background relationship" described below.

relative deviation for calculated intensity obtained when

measured intensity is translated to calculated intensity via the linear relationship T _m (X) = as determined during calibration for the wavelength interval λ.

s _pn = known standard sample with known proportion p of element n.

s _p = known standard sample with known element distribution p.

s _u = unknown sample.

s _a = assumed composition of unknown sample, in terms of the relative proportions of a set of elements in the sample.

Figure 1 illustrates a method according to the present invention for calibrating a piece of measurement equipment for spectrometric measurement of constituent elements in a material sample, which method will now be discussed in detail. The piece of equipment comprises a source of radiation and a spectrometer detector. Preferably, the source of radiation is a radiation tube, preferably using rhodium as the anode material. The spectrometer and its detector may be of any suitable type. Since such equipment is as such conventional and well-known, it is not described in detail herein.

As will be detailed in the following, the calibration method according to the present inven- tion comprises, for different respective wavelength intervals λ, measuring the radiation intensity emitted from a number of known samples s _pn , each with a respective known proportion p of a particular respective element n, as well as calculating a respective expected detected radiation intensity across the same wavelength interval λ of each of said samples using a particular selected mathematical model. Thus, in a first step, the said mathematical model is selected for calculating an expected detected radiation intensity by the spectrometer detector across a particular wavelength interval λ, which radiation is emitted from a particular sample as a result of subjection of the sample to certain high-energy radiation from the radiation source. The high-energy ra- diation is preferably X-ray radiation. Preferably, input parameters to the mathematical model comprise characteristics of the radiation source, such as radiation wavelength distribution; sample composition in terms of basic element proportions; spectrometer detector characteristics, such as spectrometer and spectrometer detector geometry; and wavelength detection interval. Such a model can be selected based on current knowledge about electromagnetic radiation, photoelectric effect, etc. One example of such a model is the one developed by J. E. Fernandez and referred to in the above mentioned article. For instance, the model may take into consideration the geometry and anode material of the radiation source; the geometry of the sample and the sample chamber; as well as the geometry and specifications of the spectrometer and its detector.

The present calibration method is based upon the use of calibration standard samples of known and accurate composition with respect to basic element proportions. Such calibration samples are also well-known as such. In a next step, the calibration method is commenced.

In a next step, one sample s _pn at a time is subjected to high-energy radiation of known (such as calculated) characteristics, and the radiation intensity T _m ( λ) emitted from the sample Spn in question is measured for a number of respective wavelength intervals λ. These wave- length intervals preferably comprise at least one wavelength interval λ _η comprising a respective characteristic photoelectric spectrum line of one respective element n contained, to a known proportion p, in the sample s _pn in question. The said wavelength intervals also preferably comprise at least one, preferably several different, wavelength intervals λ _Β for a respective background point, not comprising such a characteristic photoelectric spectrum line for any of the elements n used in the calibration, preferably not comprising such a spectrum line for any element. It is realized that these measurements also can be performed later during the calibration method, as needed. However, it is preferred that all measurements on the known standards s _P n are made at the offset of the calibration method, and that the method thereafter only comprises calculation steps. This provides for an efficient method, in which an initial measuring step can be proceeded by a calculation step using a high-performance computer. Preferably, the measurement on each known standard s _pn are made in parallel in the above described piece of equipment. Then, a first calibration sequence is initiated in order to, given a set of a plurality of different samples s _pn , and for a particular background wavelength interval λ _Β not comprising a spectral line of any element which is substantially present to a measurable extent in the sample, determine a background relationship (in terms of between measured and

calculated radiation intensities.

Hence, in this first calibration sequence an optimal linear relationship is determined between measured and calculated intensities for at least one of the above described background points B _x . Output variables for this calibration step comprise, for each such background point Βχ, regression constants describing a relationship between meas-

ured and calculated intensities across the background wavelength interval

Furthermore, it is preferred that an optimal fine-tuned wavelength

interval λ _Β constitutes an output variable of this calibration step, in the preferred case in which the interval is varied as described below during the calibration.

Hence, in a first step of said first calibration sequence, a background point B _x is selected, together with a corresponding wavelength interval comprising the background point B _x

in question.

In a next step, a sample s _pn is selected, and the intensity is calculated using the

selected mathematical model for the particular sample s _pn in question and the selected background point B _x . This step is repeated using a plurality of different samples s _pn , preferably having a different respective known proportion p of one and the same basic element. Preferably, more than three different samples s _pn , with different proportions p and/or elements n, are used, such as at least 10 different samples s _pn , preferably with at least two different elements n.

In a next step, a regression analysis is performed, with the aim of finding an optimal relationship, preferably a linear relationship, between measured and calculated intensities for the background point λ _Βχ wavelength interval currently considered:

Such regression analysis may be conventional as such, for instance using

least square means. Output variables from the regression analysis comprise regression constants (a background regression constant representing a linear relationship between

measured and calculated radiation intensities) and Ι _λ . Note that the intensity

was measured in the above described measurement step.

For each considered background point B _x , it is preferred that such regression constants are determined for several different wavelength intervals λ _Βχ , all comprising the background point B _x . Then, in a next step, the wavelength interval λ _Βχ , in other words the pair of lower and upper wavelength limits, associated with the highest correlation between measured and calculated radiation intensities is selected as the wavelength interval λ _Βχ for the background point B _x in question to be used throughout the rest of the method. Preferably, at least ten different intervals are tested. According to one preferred embodiment, a "try all possibilities" approach is used, across a selection of potential lower and upper wavelength interval limits in the vicinity of the background point B _x , and the best combination is then selected. However, it is also possible to use a more elaborate iterative goal-seeking approach to numerically find the optimal interval limits. Since no additional measurement is needed, and since these tests can be performed in full using only calculations, and without having to perform any additional measurements, the fine-tuning of the wavelength interval λ _Β can be performed quickly. These steps are repeated for at least one background point B _x , preferably for at least two background points.

Thereafter, for at least one background point B _x (preferably the same background point or background points as used in the above described first calibration sequence) and all samples s _P n used in the first calibration sequence, a second calibration sequence is performed, according to the following. In this second calibration sequence, a respective relative difference is calculated between the calculated radiation intensity and a corresponding

measured intensity calculated using the background relationship determined in the first calibration sequence.

Hence, in this second calibration sequence, the measured intensity for the

background point wavelength interval and sample combination in question is translated into a corresponding calculated intensity , using the previously established re-

Thereafter, the relative difference, for each considered background point and for each

considered sample s _pn , between the calculated intensity and the translated intensity, is cal-

In a third calibration sequence, an optimal, preferably linear, relationship is determined between measured T _m and corrected calculated T _mc intensities for each calibrated basic element n, preferably along with a corresponding optimal wavelength interval comprising a

respective photoelectric spectral line for each such element n.

According to the invention, in this third calibration sequence, for a set of at least two different samples s _pn comprising the same certain element n, and for a particular element wavelength interval λ _η comprising a spectral line of the certain element n, an element relationship (in terms of is determined between measured radiation intensities and

calculated radiation intensities for the said certain element n, which calculated background radiation intensities have first each been corrected using the above described calculated relative difference for the particular sample s _pn in question.

Hence, in next subsequent steps, a respective element n, a background point B _x a wave- length interval λ _η comprising a spectral line for the element n, and a sample s _pn are selected.

In a next step, the intensity for the wavelength interval λ _η is calculated, using

the selected mathematical model. The calculated intensity T _c is corrected, within the domain of the selected mathematical model, in the sense that the component of the

calculated background intensity T _c constituted by primary radiation scattered by the sample Spn currently used is corrected using the difference previously calculated with respect to the background point B _x currently used: —

Hence, the correction of the calculated radia¬

tion intensities is not performed with respect to spectrometer detector measurement er- rors resulting from line overlaps. In this preferred case, the selected mathematical model is hence used to calculate a respective background radiation component IB _C of the various radiation intensities as a sum of radiation due to scattering in the sample IS _C and spectral line overlap IO _c as detected by the spectrometer detector.

A respective corrected intensity T _c is calculated in this way for at least two samples s _pn comprising different proportions of one and the same element n, preferably for all samples s _pn used in the second calibration sequence comprising known proportions of the element n in question currently considered in the second calibration sequence.

In a next step, a regression analysis is performed for the element n in question, with the aim of determining an optimal linear relationship between measured and corrected calculated intensities Note that k _Xn is an element regression constant

representing a linear relationship between measured radiation intensities and corrected calculated radiation intensities. This regression analysis is, again, performed in a suitable way, such as using least mean squares, and is preferably performed for a number of different values for the wavelength interval λ _η , in a way which may be similar to the above described determination of an optimal value for the respective background points intervals λ _Β . Hence, the pair of lower and upper wavelength limits associated with the highest correlation between measured and corrected calculated intensities is selected as the wavelength interval λ _η for the element n in question to be used throughout the rest of the method. Preferably, at least ten different intervals are tested. According to one preferred embodiment, a "try all possibilities" approach is used, across a selection of potential lower and upper wavelength interval limits in the vicinity of the element n spectral line, and the best combination (the one yielding the highest correlation) is then selected. However, it would also be possible to use a more elaborate goal-seeking approach, in order to numerically find the optimal interval limits.

Such calibration analysis is performed for all elements n that are to be measured in subsequent measuring steps of unknown samples s _u , and preferably for more than one background point Βχ for each element n.

In the preferred case that several such background points B _x are used, it is preferred that the difference D is calculated as a weighted sum of the differences D _Bx for each such background point are the weight fac

tors. Then, different sets of such weight factors are tried, and the set resulting in the highest correlation between measured and corrected calculated intensities is selected for each element n. This set of weight factors is then used for the calculation in the third calibration sequence for that element n.

Hence, the first and second calibration sequences are preferably performed for several different background wavelength intervals resulting in one respective difference

for each such background wavelength interval and each used sample s _pn . Then,

the third calibration sequence is preferably performed using several different relative weight allocations for the said different background wavelength intervals λ _Βι , [...], λ _Βχ , and the above described element relationship is determined for the particular relative weight allocation for which the correlation between the measured and corrected radiation intensities is the highest. In a particularly preferred embodiment, the radiation source is a radiation tube, and, in the first calibration sequence, the background wavelength interval λ _Β comprises a peak of the Rayleigh or Compton scattered radiation from the sample of a characteristic line of the anode material of the source of radiation. Preferably, two different background points λ _Β and λ _Β are used, preferably represented by non-overlapping respective wavelength intervals not comprising any photoelectric line of any element, and one of the background points preferably comprises a peak of such Rayleigh radiation, while the other one comprises a peak of such Compton radiation. This makes it possible to measure over a relatively short time period in the initial measuring step of the samples s _pn , and still to obtain measurement values with acceptable statistical accuracy.

The determined calibration constants are stored, as applica

ble, for use in subsequent measurement steps.

After the above described calibration sequences, the hence determined element relation- ship, in terms of preferably in combination with the determined background

relation, in terms of and/or the determined optimal wavelength intervals and/or λ _η , may be used as calibration constants for each considered respective element n in a preferred method according to the invention for measuring the composition of an unknown sample s _u . The method steps of this preferred aspect of the invention is described in the following (see figure lb).

Like is the case for the above described calibration sequences, the measurement on sample s _u is performed using a piece of measurement equipment for spectrometric measurement of constituent elements in a material sample, which piece of equipment comprises a source of radiation and a spectrometer detector. More specifically, the measurement method comprises first performing a calibration method according to the above described, which calibration is performed with the same piece of equipment and then performing said measurement using a respective element relationship, in terms of as calibration constant for each one of a number of elements n.

In general, the measurement method comprises measuring the radiation intensity of the unknown sample s _u , for at least one of the at least one background wavelength intervals λ _Βχ used in the above described first calibration sequence, preferably the respective optimal background wavelength interval λ _Βχ determined in that respective sequence run- through, and for at least two elements (in other words, at least two respective wavelength intervals λn) used in the above described third calibration step.

In the following, a particularly preferred such measurement method is described in detail.

Hence, in a first step of a first measurement sequence, a particular element ni, [...], ΠΝ dis- tribution pi, [...], pw of the sample s _u is assumed. This first element fraction p _n is derived from the relative measured intensity of the element. The relative measured intensity is calculated as the element measured intensity of the current sample divided by the measured intensity corresponding to the calculated 100% intensity of the element (this calculated intensity is converted to a measured intensity via the element calibration constants).

In a next step, a particular background point is selected. This background point λ _Βχ is

selected from the background point or points already used in the above described first calibration sequence. In a next step, the radiation intensity is measured for the selected background

point and the sample

In a next method step, the radiation intensity is calculated using the same se

lected mathematical model as used in the calibration sequences. In a next method step, the measured radiation intensity is translated to calcu

lated intensity using the above described relation

Hence, a corresponding calculated radiation intensity results,

by calculation using the background relationship (in terms of as determined

for the particular background point λ _Β in question in the above described first calibration sequence.

In a next step a relative difference between the calculated radiation intensity

and the corresponding corrected measured intensity is calculated.

Preferably, a relative difference is calculated according to I

This first measurement sequence is performed for at least one background point pref erably for all background points used in the above described calibration sequences.

After this first measurement sequence, a high precision measure of the background radiation error is hence known, for the particular sample s _u and the particular measurement equipment used. In a subsequent second measurement sequence, the respective radiation intensity for each analysed element n is measured. It is realised that this measurement

can be performed beforehand, for instance in connection to the measurement of the background points in the first measurement sequence, preferably using a parallel measure

ment.

In a next step of the second measurement sequence, a particular element n is selected.

In a next step, the radiation intensity for element n is calculated, and the result is corrected using the calculated difference

Hence, preferably, it is the component in the cal¬

culated background intensity constituted by primary radiation scattered by the sample which is corrected, and additions from line overlap are not corrected for. Hence, r _C ' (A _n , s _u ) constitutes an expected detected radiation intensity as corrected using the difference for the background point In case several background points were used, as

described above with weight factors it is preferred that the same weight factors are used for the calculated difference D in this step as described above.

In a next step, a calculated radiation intensity ) is determined corresponding to

the measured radiation intensity This is preferably performed using the element

relationship, in terms of as determined during the third calibration sequence

as described above:

In a next step, a difference is calculated between the corrected calculated radiation intensity and the corresponding translated measured radiation intensity

In a next step, a derivative for the calculated intensity with respect to the assumed

proportion p of the currently considered element n is calculated. Preferably, this derivative is independent of the background radiation in the selected mathematical model.

In a next step, the assumed element distribution of the sample s _u is

modified, preferably in dependence of the said calculated derivative and prefera

bly according to

y &

These second measurement sequence steps are performed for all considered elements n. Then, in a next step, the method iterates back to the step in the second measurement sequence in which an element n is selected, now using the modified element distribution The iteration is then repeated until the distribution is stable for all analysed ele

ments n. The final distribution is the element distribution determined by the method at this finishing point.

The invention furthermore relates to a system 100, illustrated in figure 2, for measuring the composition of a material sample 210 of the above described kind, arranged in a measuring chamber 200, using the above-described piece of measurement equipment for spectromet- ric measurement of constituent elements in such a material sample. The piece of equipment comprises a radiation source 201 and a spectrometer detector 202, as described above. The equipment is controlled by a per se conventional control device 203. Such a system 100 is preferably connected to the piece of equipment, or at least to the spectrometer detector 202, and arranged to receive measurement values from the spectrometer detector 202 over an electric interface 102, preferably a standard interface, such as a digital data interface. Preferably, the system 100 is arranged both to perform the calibration step sequences described above, as well as the measurement step sequences described above. Preferably, the system comprises a user interface, such as in the form of a screen/keyboard interface 320 and/or an API (Application Programming Interface) 101 in order to output calibration- and measurement results, and to receive parameter input. An API 101 is, for instance, arranged to communicate with a server 310. The invention also relates to a computer software product arranged to be used for calibrating the above-described piece of measurement equipment. The software product is executable on a piece of hardware, such as on the said system 100, which is connected to said piece of measurement equipment and arranged to receive measurement values from the said spectrometer detector of the said radiation intensity. Preferably, such a software prod- uct is arranged to implement all the above described functionality in terms of calibration and measurement steps, and preferably also to operate the said user interface 320 and/or API 101.

The present invention allows for precise and quick calibration of a piece of X-ray spectrom- etry equipment, and also for subsequent measurement in a corresponding precise and quick manner of low-proportion component elements in a sample. In particular, the method allows such precise calibration and measurement to be performed using initial measurement and subsequent calculations, which admits the use of parallel measurements across several channels and use of high-speed computing circuitry.

In the following, an example is described, in which a mathematical model-based piece of software called MSXRF was used with a setup similar to the one illustrated in figure 2 to perform parts of a method according to the present invention. Hence, radiation intensities of Molybdenum (Mo) and scatter from a Rhodium (Rh) tube were measured for 26 geological standards. The standards contained very low concentrations of Mo, 0.094-15.5 ppm. The standards were prepared as beads containing 50% weight of standard material and 50% of cellulose. Intensities of both Rayleigh scatter and Compton scatter by the sample of the Rh k-alpha tube line were measured. For the instrument used, the Compton scattered peak coincided with a Th line (L2-G1, 0.653 A. This line was used for the MSXRF calls as a line within the window is required by MSXRF).

Optimum MSXRF wavelength window widths were determined in accordance with the above described, and intensity-intensity calibration lines were produced for three meas- ured intensities. Data of measured and calculated intensities produced during the calibration was transferred to a file which was imported to Excel for further calculations.

The results for Mo using conventional algorithms, not using the background point correction according to the present invention, was analysed in Excel. The standard deviation of the calculated Mo intensities from the calibration line was 3.5%. Using the intensity/concentration derivatives calculated during calibration and the calculated intensities for Mo, the resulting standard deviation of the concentrations from the certified concentrations was 9.0 ppm.

The calculated background concentrations for Mo (overlap intensities excluded) were now adjusted using the relative deviations from their calibration line of Rh_r and Rh_c for the corresponding standards. A slide control was included in the Excel sheet to be able to interactively find the optimum division of the correction between Rh_r and Rh_c. In this case, the best result was achieved when 30% of the Rh_r deviation and 70% of the Rh_c deviation was used. Regression calculations were performed to find a relation (calibration line) be- tween the adjusted calculated Mo intensities and the measured Mo intensities. Using this method, the standard deviation of the calculated intensities of Mo for the 26 standards from the calibration line was reduced to 1.2%. The standard deviation of the corresponding Mo concentrations from the certified values was 3.0 ppm. During the measurements of the Mo intensities, around 60,000 pulses were captured for each sample. This means that the standard deviation of the intensity measurements due to the stochastics of the photon production was around 0.4%. The number of pulses captured for Rh_r, around 250,000 pulses and for Rh_c, around 500,000 pulses, was high enough to give just neligible contribution to the Mo intensity deviation. A longer Mo intensity meas- urement would reduce the 1.2% intensity deviation to some extent.

Table 1 shows the results for the different standards before and after correction. Namely, Table 1 shows the relative difference of the calculated intensity from the calibration line and this difference converted to ppm using the calculated intensity per cone derivative of the standard. The concentration deviations listed are the deviations for the standard material ("the sample") so the deviation calculated for the measured bead has been multiplied with 2 (the dilution factor).

Standard de3.5% 9.0 1.2% 3.0 viation

Figures 3a and 3b show the measured/calculated intensity correlation before and after the Mo calculated background intensities had been adjusted using the deviations of Rh_r and Rh_c, respectively.

Above, preferred embodiments have been described. However, it is apparent to the skilled person that many modifications can be made to the disclosed embodiments without departing from the basic idea of the invention. For instance, the order and timing of measurements can be another one than as described above, both for the calibration sequences and the measurement sequences, as long as the measured values are available when to be used in the various method steps.

Furthermore, the method can use other types of measurement equipment so long as the calibration principles described herein are used. For instance, instead of a radiation tube, another type of high energy radiation source can be employed.

Although a quite detailed description of preferred algorithm steps have been described above, it is realized that the detailed implementation may differ in details as long as the principles as claimed are used.

Furthermore, it is realized that a calibration according to the present invention can be performed first, followed by several measurements according to the above on several different samples, preferably samples containing overlapping element compositions, preferably sam- pies prepared for measurement in the same way as the samples used during calibration.

Hence, the invention is not limited to the described embodiments, but can be varied within the scope of the enclosed claims. C L A I M S

1. Method for calibrating a piece of measurement equipment for spectrometric measurement of constituent elements in a material sample (210), which piece of equipment comprises a source of radiation (201) and a spectrometer detector (202), which method comprises, for different respective wavelength intervals (λ), measuring the radiation intensity emitted from a number of known samples (s _pn ), each with a respective known proportion (p) of a particular respective element (n), as well as calculating a respective expected detected radiation intensity across the same wavelength interval (λ) of each of said samples using a mathematical model, c h a r a c t e r i s e d i n that the method furthermore comprises the steps

a) given a set of a plurality of different such samples (s _pn ), and for a particular background wavelength interval (λ _Βχ ) not comprising a spectral line of any element present to a measurable extent in the sample, determining a background relationship between measured and calculated radiation intensities;

b) for each of the samples (s _pn ) used in step a) and said background wavelength interval (λ _Βχ ), calculating a respective relative difference between

the calculated radiation intensity and a corresponding measured intensity calculated using said background relationship;

c) for a set of at least two different samples (s _pn ) comprising the same certain element (n), and for a particular element wavelength interval (λ _η ) comprising a spectral line of the certain element (n), determining an element relationship between measured radiation intensities and calculated radiation intensities for the certain element (n), which calculated background radiation intensities have first each been corrected using said difference for the particular sample

[s _pn ) in question;

wherein the hence determined element relationship is used as calibration constant for the certain element (n) in question. 2. Method according to claim 1, c h a r a c t e r i s e d i n that, in step a), the determination of the background relationship comprises calculating a background regression constant representing a linear relationship between measured and calculated

radiation intensities, and in that, in step b), said measured intensities are corrected using said background regression constant

3. Method according to claim 1 or 2, c h a r a c t e r i s e d i n that, in step c), the determination of the element relationship comprises calculating an element regression constant representing a linear relationship between measured radiation intensities

and corrected calculated radiation intensities.

4. Method according to any one of the preceding claims, c h a r a c t e r i s e d i n that step a) is performed several times, wherein the background wavelength interval used for the calculation of the radiation intensities from the samples is modified to be

different for different performances of step a), and in that the background relationship is determined for the particular modified background wavelength interval for which the

correlation between measured and calculated radiation intensities is the highest.

5. Method according to any one of the preceding claims, c h a r a c t e r i s e d i n that, in step c), the correction of the calculated radiation intensities is not performed with respect to spectrometer detector measurement errors resulting from line overlaps.

6. Method according to any one of the preceding claims, c h a r a c t e r i s e d i n that step c) is performed several times, wherein the element wavelength interval (λ _η ) used for the calculation of the radiation intensities from the samples is modified to be different for different performances of step c), and in that the element relationship is determined for the particular modified element wavelength interval (λ _η ) for which the correlation between measured and corrected calculated radiation intensities is the highest. 7. Method according to any one of the preceding claims, c h a r a c t e r i s e d i n that steps a) and b) are performed for several different background wavelength inter- vals resulting in one respective difference for each such back

ground wavelength interval and each used sample, in that step c) is performed using several different relative weight allocations (yi,...yivi) for the said different background wavelength intervals _Μ and in that the element relationship is determined for the relative weight allocation for which the correlation between the measured and corrected

radiation intensities is the highest.

8. Method according to any one of the preceding claims, c h a r a c t e r i s e d i n that the model is used to calculate a background radiation component of the

various radiation intensities as a sum of radiation due to scattering in the sample (210) and spectral line overlap as detected by the spectrometer detector

(202).

9. Method according to any one of the preceding claims, c h a r a c t e r i s e d i n that the source of radiation (201) is a radiation tube, and in that, in step a), the background wavelength interval comprises a peak of the Rayleigh or Compton radiation

from the sample (210) of a characteristic line of the anode material of the source of radiation (201). 10. Method for measuring the composition of an unknown sample (210, s _u ) using a piece of measurement equipment for spectrometric measurement of constituent elements in a material sample (210), which piece of equipment comprises a source of radiation (201) and a spectrometer detector (202), c h a r a c t e r i s e d i n that the method comprises first performing a calibration method according to any one of the preceding claims of said piece of equipment and then performing said measurement using a respective element relationship as calibration constant for each one of a number of elements (n).

11. Method according to claim 10, c h a r a c t e r i s e d i n that the method comprises measuring, for at least one of the at least one background wavelength interval used in step a) and for at least two element wavelength intervals (λ _η ) used in step c),

the radiation intensity of the unknown sample (210, s _u ), wherein the method comprises the sub steps i) assuming a particular element distribution of the sample

(210);

ii) for at least one particular of said background wavelength intervals used in step a), calculating the radiation intensity using the model and correcting the calculated radiation intensity using the background relationship determined in step a), and calculating an difference between the calculated radia

tion intensity and the calculated intensity corresponding to the measured intensity;

iii) for each of the elements of said distribution and for the cor

responding element wavelength interval (λ _η ), calculate an expected detected radiation intensity as corrected using the said difference determine a

calculated radiation intensity corresponding to the measured radiation intensity, and calculate a difference between the said corrected calculated radiation intensity and the said corresponding calculated radiation intensity; and iv) modify the assumed element distribution and iterate back to

step i).

12. Method according to claim 10 or 11, c h a r a c t e r i s e d i n that, in step ii), the correction of the calculated radiation intensity is not performed with respect to spectrometer detector measurement errors resulting from line overlaps.

13. Method according to any one of claims 10-12, c h a r a c t e r i s e d i n that, in step iii), for each element (n) in said element distribution the derivative of the calculated radiation intensity with respect to the contents of the element (n) in question is calculated, in that, in step iv), the assumed element distribution

is modified based upon the said derivative, and in that the iteration in step iv) is

performed until the assumed element distribution stabilizes.

14. System (100) for measuring the composition of a material sample using

a piece of measurement equipment for spectrometric measurement of constituent elements in such a material sample which piece of equipment comprises a source

of radiation (201) and a spectrometer detector (202), which system (100) is arranged to