System and method for approximating X-ray intensities for a sample measured by an X-ray detection system

A computer system for approximating one or more X-ray intensities for a sample measured by an X-ray detection system with at least one collimator having a given angular range, a crystal monochromator and an X-ray detector, the computer system comprising:

• an interface adapted to receive one or more measured intensities from the detection system at respective one or more diffraction angles;
• a sample simulation module adapted to compute, for the respective one or more diffraction angles, one or more simulated sample intensities from an X-ray fluorescence sample model with initial sample model parameters indicating a sample composition and/or layer thickness of one or more sample layers;
• a correction module adapted to apply a collimator correction to the one or more simulated sample intensities for the respective one or more diffraction angles by:
• determining, for each of the one or more diffraction angles, an integral over an energy range allowed by the angular range of the at least one collimator, wherein the integral is computed over a product of a multiplication of the respective simulated sample intensity with an approximation function approximating a triangular shaped profile representing a relative intensity distribution in the angular range caused by an angular tolerance of the crystal monochromator defined by a divergence of the at least one collimator, the determined integral representing a corrected simulated sample intensity;
• determining a mathematical distance between the one or more corrected simulated sample intensities and corresponding one or more measured intensities;
• adjusting the sample model parameters regarding the sample composition and/or the layer thickness and repeating the determining operations and the adjusting operation until a change of the distance falls below a minimal distance change;
• and
• the interface further adapted to provide the sample model parameters regarding the sample composition and/or the layer thickness associated with the corrected simulated intensities as approximated concentration values of respective components contained in the measured sample and/or the layer thickness of the measured sample.

A computer program product for approximating one or more X-ray intensities for a sample measured by an X-ray detection system with at least one collimator having a given angular range, a crystal monochromator and an X-ray detector, the computer program product being tangibly embodied on a non-transitory computer-readable storage medium and comprising instructions that, when executed by at least one computing device, are configured to cause the at least one computing device to:

• receive one or more measured intensities from the X-ray detection system at respective one or more diffraction angles;
• compute, for the respective one or more diffraction angles, one or more simulated sample intensities from an X-ray fluorescence sample model with initial sample model parameters indicating a sample composition and/or layer thickness of one or more sample layers;
• apply a collimator correction to the one or more simulated sample intensities for the respective one or more diffraction angles by:
• determining, for each of the one or more diffraction angles, an integral over an energy range allowed by the angular range of the at least one collimator, wherein the integral is computed over a multiplicative product of a respective simulated sample intensity and an approximation function approximating a triangular shaped profile representing a relative intensity distribution in the angular range caused by an angular tolerance of the crystal monochromator defined by a divergence of the at least one collimator, the determined integral representing a corrected simulated sample intensity;
• determining a mathematical distance between the one or more corrected simulated sample intensities and corresponding one or more measured intensities;
• adjusting the sample model parameters regarding the sample composition and/or the layer thickness and repeating the determining operations and the adjusting operation until a change of the distance falls below a minimal distance change;
• and
• provide the sample model parameters regarding the sample composition and/or the layer thickness associated with the corrected simulated intensities as approximated concentration values of respective components contained in the measured sample and/or the layer thickness of the measured sample.