Sample Characterization via Maximum Likelihood Spectral Decomposition
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing methods for characterizing samples using X and/or gamma spectrometry face inaccuracies due to measurement errors, particularly photon noise and imperfections in the spectrometer, which affect the estimation of characteristic thicknesses in calibration material decomposition.
Innovation Solution
A method that estimates characteristic thicknesses by calculating a likelihood function from measured energy spectra and calibration spectra, using a maximum likelihood criterion, without relying on theoretical models, and accounts for measurement noise modeled by a Poisson distribution.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional linear combination methods are used to estimate characteristic thicknesses, then the measurement process is simple, but measurement errors from photon noise and spectrometer imperfections significantly reduce accuracy
Solution Approach 1:
The patent transforms the measurement approach by changing from direct linear combination of attenuation coefficients to a likelihood function based method. The key parameter change is using the ratio of measured spectra to reference spectra, which cancels out many systematic errors. The likelihood function incorporates Poisson statistics to properly account for photon noise, fundamentally changing how measurement parameters are processed to achieve higher accuracy.
Solution Approach 2:
The patent replaces the traditional mechanical/physical measurement approach (direct attenuation measurement and linear combination) with a statistical information processing approach. By using likelihood functions and maximum likelihood estimation, the system substitutes direct physical measurement with statistical inference, which better handles the inherent noise in photon counting measurements.
2Measurement precision
If maximum likelihood estimation with Poisson distribution is used, then measurement accuracy improves, but computational complexity increases
Solution Approach 1:
The patent performs preliminary actions by pre-calculating reference spectra for known thicknesses of calibration materials and storing them. This pre-computation allows the actual measurement to focus only on comparing the measured spectrum against these pre-prepared references using the likelihood function, significantly reducing the computational burden during the actual characterization process.
Solution Approach 2:
The patent creates copies of reference spectra for different thicknesses of calibration materials and uses these copies for comparison with the measured spectrum. Instead of performing complex iterative calculations, the system compares the measured data against pre-generated spectral copies, making the maximum likelihood estimation computationally feasible while maintaining accuracy.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach provides accurate estimation of characteristic thicknesses, reducing measurement errors and improving the accuracy of sample characterization without the need for high-quality modeling of the detection chain.
Implementation Method 1
The analysis beam 209 is attenuated by crossing the sample according to the Beer-Lambert law: SECH(E)=S0(E)exp(−βECH*L)
Implementation Method 2
a detector 203 able to count a number of received photons, for each energy channel of a plurality
Data Source
AI summary
A method is provided for characterizing a sample, by estimating a plurality of characteristic thicknesses, each being associated with a calibration material. The method includes acquiring an energy spectrum transmitted through the sample, located in an X and/or gamma spectral band; for each spectrum of a plurality of calibration spectra, calculating a likelihood from said calibration spectrum, and from the spectrum transmitted through the sample, each calibration spectrum corresponding to the energy spectrum transmitted through a stack of gauge blocks, each formed of a known thickness of a calibration material; and estimating the characteristic thicknesses associated with the sample according to the criterion of maximum likelihood.