Method and apparatus for using non-linear spectral fitting procedures on gamma-ray spectral data
First Claim
1. A method for decomposing a gamma ray spectrum representative of an unknown material in order to determine the respective gamma ray contribution of each constituent postulated to constitute said material, comprising:
- measuring gamma rays of said unknown material by detecting and counting the gamma rays issued from said material;
forming an energy spectrum of said measured gamma rays;
establishing a composite spectrum constructed of individual standard spectra of said postulated constituents and comprising elemental yields being representative of the fraction of the corresponding constituents in said composite spectrum;
determining the best fit between said measured spectrum and said composite spectrum by simultaneously varying at least two parameters from a set of parameters which describe the transformation of the measured and composite spectra from channel numbers to each spectrum'"'"'s physical domain, said parameter set containing gain, offset, resolution, resolution degradation, background subtraction and non-linear gain parameters; and
determining from the best fit and a best composite spectrum associated with said best fit the relative fractions of the gamma ray spectra associated with the corresponding constituents of said material or one or more of the parameters describing the spectral transformation from channel numbers to the physical domain.
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Abstract
A method and an apparatus for decomposing a gamma spectrum representative of an unknown material for determining the contribution of each constituent postulated to constitute the material, wherein an energy spectrum of the gamma rays issued from the material is formed, as well as a composite spectrum made up of individual standard spectra of the postulated constituents and comprising elemental yields being representative of the proportion of the corresponding constituents; the best fit between the measured spectrum and the composite spectrum is determined by modifying simultaneously at least one elemental yield and at least one parameter representative of the conditions under which the measured spectrum and the composite spectrum have been obtained. The best fit may be based on any non linear least squares search for a global minimum of X2 =(S Y-U)T W(S Y-U), where "U" is a matrix representing the measured spectrum, "S" is a matrix representing the composite spectrum, "Y" is a matrix representative of the elemental yields and "W" is a weight matrix. The non linear fitting method used may be e.g. a gradient search or the Marquardt method.
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Citations
41 Claims
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1. A method for decomposing a gamma ray spectrum representative of an unknown material in order to determine the respective gamma ray contribution of each constituent postulated to constitute said material, comprising:
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measuring gamma rays of said unknown material by detecting and counting the gamma rays issued from said material; forming an energy spectrum of said measured gamma rays; establishing a composite spectrum constructed of individual standard spectra of said postulated constituents and comprising elemental yields being representative of the fraction of the corresponding constituents in said composite spectrum; determining the best fit between said measured spectrum and said composite spectrum by simultaneously varying at least two parameters from a set of parameters which describe the transformation of the measured and composite spectra from channel numbers to each spectrum'"'"'s physical domain, said parameter set containing gain, offset, resolution, resolution degradation, background subtraction and non-linear gain parameters; and determining from the best fit and a best composite spectrum associated with said best fit the relative fractions of the gamma ray spectra associated with the corresponding constituents of said material or one or more of the parameters describing the spectral transformation from channel numbers to the physical domain. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)
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13. A method for decomposing a gamma ray spectrum representative of an unknown material in order to determine the respective gamma ray contribution of each constituent postulated to constitute said material, comprising;
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measuring gamma rays of said unknown material by detecting and counting the gamma rays issued from said material; forming an energy spectrum of said measured gamma rays; establishing a composite spectrum constructed of individual standard spectra of said postulated constituents and comprising elemental yields being representative of the fraction of the corresponding constituents in said composite spectrum; determining the best fit between said measured spectrum and said composite spectrum by simultaneously varying at least one elemental yield and at least one parameter from a set of parameters which describe the transformation of the measured and composite spectra from channel numbers to each spectrum'"'"'s physical domain, said parameter set containing gain, offset, resolution, resolution degradation, background subtraction and non-linear gain; and determining from the best fit and a best composite spectrum associated with said best fit, the relative fractions of the gamma ray spectra associated with the corresponding constituents of said material or one or more of the parameters describing the spectral transformation from channel numbers to the physical domain. - View Dependent Claims (14, 15, 16, 17, 18, 19, 20, 21, 22)
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23. An apparatus for decomposing a gamma ray spectrum representative of an unknown material in order to determine the respective gamma ray contribution of each constituent postulated to constitute said material, comprising;
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means for measuring gamma rays of said unknown material by detecting and counting the gamma rays issued of said material; means for forming an energy spectrum of said measured gamma rays; means for establishing a composite spectrum constructed of elemental standard spectra of said postulated constituents and comprising elemental yields being representative of the fraction of the corresponding constituent in said composite spectrum; means for determining the best fit between said measured spectrum and said composite spectrum by simultaneously varying at least two parameters from a set of parameters which describe the transformation of the measured and composite spectra from channel numbers to each spectrum'"'"'s physical domain, said parameter set containing gain, offset, resolution, resolution degradation, background subtraction and non-linear gain parameters; and means for determining from the best fit and a best composite spectrum associated with said best fit, the relative fractions of the gamma ray spectra associated with the corresponding constituents of said material or one or more of the parameters describing the spectral transformation from channel numbers to the physical domain. - View Dependent Claims (24, 25, 26, 27, 28, 29, 30, 31)
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32. An apparatus for decomposing a gamma ray spectrum representative of an unknown material in order to determine the respective gamma ray contribution of each constituent postulated to constitute said material, comprising:
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means for measuring gamma rays of said unknown material by detecting and counting the gamma rays issued of said material; means for forming an energy spectrum of said measured gamma rays; means for establishing a composite spectrum constructed of elemental standard spectra of said postulated constituents and comprising elemental yields being representative of the fraction of the corresponding constituent in said composite spectrum; means for determining the best fit between said measured spectrum and said composite spectrum by simultaneously varying at least one elemental yield and at least one parameter from a set of parameters which describe the transformation of the measured and composite spectra from channel numbers to each spectrum'"'"'s physical domain, said parameter set containing gain, offset, resolution, resolution degradation, background subtraction and non-linear gain parameters; and determining from the best fit and a best composite spectrum associated with said best fit, the relative fractions of the gamma ray spectra associated with the corresponding constituents of said material or one or more of the parameters describing the spectral transformation from channel numbers to the physical domain. - View Dependent Claims (33, 34, 35, 36, 37, 38)
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39. A method for decomposing a gamma ray spectrum representative of an unknown material in order to determine the respective gamma ray contribution of each constituent postulate to constitute said material, comprising:
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measuring gamma rays of said unknown material by detecting and counting the gamma rays issued from said material; forming an energy spectrum and a background energy spectrum of said measured gamma rays; establishing a composite spectrum constructed of individual standard spectra of said postulated constituents and comprising elemental yields being representative of the fraction of the corresponding constituents in said composite spectrum; determining the best fit between said measured spectrum, said background specrum and said composite spectrum by simultaneously varying at least two parameters from a set of parameters which describe the transformation of the measured, background and composite spectra from channel numbers to each spectrum'"'"'s physical domain, said parameter set containing gain, offset, resolution, resolution degradation, BSF, element yields and non-linear gain parameters; and determining from the best fit and an associated best composite spectrum the relative fractions of the gamma ray spectra associated with the corresponding elemental constituents of said material or one or more of the parameters describing the spectral transformation from channel numbers to the physical domain. - View Dependent Claims (40, 41)
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Specification