Recent Advances in EDXRF Research CEAR

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Recent Advances in EDXRF Research _at_CEAR

• Weijun Guo, Robin P. Gardner, and Fusheng Li
• Center for Engineering Applications of
  Radioisotopes (CEAR)
• Nuclear Engineering Department
• North Carolina State University
• Raleigh, NC 27695-7909
• Sep 5, 2006

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OUTLINE

• Introduction
• Spectrum Correction for Pulse Pile-Up Distortion
• The Monte Carlo Library Least-Squares (MCLLS)
  Approach
• Experimental Results for Alloys
• Discussion, Conclusions, and Future Work

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INTRODUCTION

• EDXRF has always had the two problems of (1)
  measuring X-ray intensity and (2)
  dealing with non-linear response.
• The present MCLLS approach provides the means for
  a practical very accurate solution to both of
  these problems thus providing a practical very
  accurate solution to the EDXRF inverse problem.

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SPECTRUM CORRECTION FOR PULSE PILE-UP DISTORTION

• High counting rates cause pulse pile-up spectral
  distortion and changes in the statistics.
• The Monte Carlo code CEARPPU can be used off-line
  to correct for both of these things.
• References
• 1. R.P. Gardner and S.H. Lee, Monte Carlo
  Simulation of Pulse Pile Up, Denver X-Ray
  Conference, Advances in X-Ray Analysis CD ROM,
  ICDD, Newtown Square, PA, pp. 941-950 (1999).
• 2. R.P. Gardner, W. Guo, and F. Li, A Monte
  Carlo Code for Simulation of Pulse Pile-Up
  Spectral Distortion in Pulse-Height Measurement,
  53rd Denver X-Ray Conference (2004).
• 3. Weijun Guo, S.H. Lee, and R.P. Gardner, The
  Monte Carlo Approach MCPUT for Correcting Pile-Up
  Distorted Pulse-Height Spectra, Nuclear
  Instruments and Methods A, 531, pp. 520-529
  (2004).

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THE MONTE CARLO LIBRARY LEAST-SQUARES (MCLLS)
APPROACH

• General Approach
• The CEARXRF Monte Carlo Code
• Detector Response Functions
• Library Least-Squares (LLS) Analysis

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GENERAL APPROACH

• 1. The Monte Carlo Code CEARXRF is used with an
  Elemental Composition Estimate to Generate
  Elemental Library Spectra and Differential
  Operators.
• 2. The Library Least-Squares (LLS) Method is used
  with the Generated Libraries on the Experimental
  Spectrum to Obtain the Calculated Elemental
  Composition.
• 3. If Calculated and Estimated Spectra are too
  far Apart Iterate Step 2 by Using Differential
  Operators to Update the Elemental Libraries. (In
  rare cases Step 1 is needed.)
• REFERENCE Weijun Guo, Robin P. Gardner, and
  Andrew C. Todd, Using the Monte Carlo - Library
  Least-Squares (MCLLS) Approach for the in vivo
  XRF Measurement of lead in Bone, Nuclear
  Instruments and Methods in Physics Research A,
  516, pp. 586-593, 2004.

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GENERAL PROCEDURE of MCLLS
EDXRF Measurement
XRFQual XRAYQuery Qualitative Analysis
MCLLS (slower)
Initial Compositional Assumption
CEARXRF(Updated Soon to Ver.5) Monte Carlo
Simulation
MCDOLLS (Faster)
GEDRF/Si(Li)DRF Detector Response Function
XLLS Quantitative Library Least-Squares Analysis
DiffOper Taylor-Series Expansion on Library
Spectra
Happy?
Update Composition Assumption
Update Composition Assumption
Completed!
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XRFQUAL XRFQUERY GUI PACKAGE

• XRFQual XRayQuery
• XRFQual Qualitative analysis of XRF measured
  spectrum
• Energy Calibration
• Composition Identification
• XRayQuery
• Interactive tool for X-ray physics, such as
  characteristic x-ray line energy, yield, etc.

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THE CEARXRF MONTE CARLO CODE (CEARXRF)

• A Specific Purpose Monte Carlo Code under
  Development since before 1975 - first benchmarked
  with the Sherman Equations (in that process two
  typos were found in the Sherman tertiary
  equations).
• Variance Reduction Methods include Use of
  Detector Response Functions (DRFs) for Si(Li)
  detector and GE Detector.
• All the pertinent physics has been added over the
  years including differential operators and a
  complete geometry treatment.
• The code has been extensively benchmarked.

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MAIN FEATURES OF CEARXRF

• CEARXRF is a specific purpose Monte Carlo code
  for modeling the complete spectral response of
  energy-dispersive X-ray fluorescence (EDXRF)
  spectrometers, developed by CEAR since 1977.
  Current Version is 4.
• The CEARXRF code has man features that make it
  suitable for a variety of applications. They
  include (1) multiple-element EDXRF simulation
  (Z1-94), (2) complete EDXRF pulse-height
  spectrum calculation, (3) a variety of excitation
  modes, (4) polarized photon transport modeling,
  (5) complete K and L XRF simulation, (6) detailed
  XRF emission physics, (7) Doppler effect modeling
  in Compton scattering, (8) general geometry
  modeling, (9) spectroscopy analysis with the
  MCLLS approach, (10) correlated sampling for
  density and composition perturbation calculation,
  (11) detector response function Si(Li) and
  low-energy photon germanium detectors, (12) phton
  cross sections adapted from MCNP (Briesmeister,
  1997) and latest atomic data, (13) optimized
  variance reduction techniques for EDXRF modeling,
  (14) differential operator technique, and (15)
  graphical interface to display simulation results
  on the fly, (16) Coincidence spectra

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CEARXRF DEVELOPMENT-FUTURE VERSION 5

• Rewrite the program by Fortran 90/95, upgraded
  from Fortran 77.
• Geometry part of CEARXRF will be compatible with
  MCNP5 and users can use VisEdt to view and modify
  the input file.
• Update the cross section library in CEARXRF with
  newest data available. And ENDF/B6 libraries will
  be used directly to make it easier for future
  updates.
• Coincidence part of CEARXRF will be updated based
  on previous work.
• XFCT(X-Ray Fluorescence Computed Tomography)
  simulation application by CEARXRF

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DETECTOR RESPONSE FUNCTIONS

• Detector Response Functions (DRFs), R(E,E),
• are pdfs that give the pulse-height
  distribution E as a function of the incident
  energy E.
• DRFs are very effective variance reduction
  methods.
• They can be obtained by semi-empirical or Monte
  Carlo approaches that use approximations.
• They provide the accuracy required for the MCLLS
  approach.

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SIMULATED FLUX SPECTRUM AFTER DRF GE DETECTOR
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MONTE CARLO LIBRARY SPECTRA(AFTER DRF) GE
DETECTOR
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ILLUSTRATION OF FLUX POINTS AFTER DRF Si(Li)
DETECTOR
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LIBRARY SPECTRA (AFTER DRF) BACKGROUND NOISE
SI(LI) DETECTOR
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LIBRARY LEAST-SQUARES ANALYSIS

• The Library Least-Squares (LLS) approach was
  originally derived and used by Salmon1 in 1961
  for gamma rays from radioisotopes.
• It is the most fundamental approach to the
  inverse spectral analysis problem, it uses all
  the spectral data and gives the best accuracy,
  and it automatically provides estimates of
  goodness of fit and statistics.
• 1Salmon, L., 1961, Analysis of Gamma-Ray
  Scintillation Spectra by the Method of Least
  Squares, Nuclear Instruments and Methods, 14,
  pp. 193-199.
  
  

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DIFFERENTIAL OPERATOR (DOLLS)

• If the fitted results from MCLLS are far from the
  previous results, a new run is required.
  Simulation based on a better guess is
  performed. CEARXRF can be executed again. But it
  is very time consuming (maybe 3-4 hours to run
  1E8 histories) compared to Differential Operator,
  which provides a faster and also accurate way
  (3-10minues).

Before DO
After DO
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EXPERIMENTAL ARRANGEMENT
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EXPERIMENTAL RESULTS FOR ALLOYS

• Stainless Steel (SS304) - excited by Cd-109
• Aluminum Alloys (AA7178 AA3004) Standards
  provided by Alcoa for some research on thickness
  gauges excited by Cd-109 and Fe -55.

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STAINLESS STEEL 304 (SS304) QUALITATIVE ANALYSIS
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STAINLESS STEEL 304 (SS304) EXPERIMENTAL FITTED
DATA
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TABLE 1. SS304 FIT RESULTS
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ALUMINUM ALLOY 7178 (AA7178) EXPERIMENTAL AND FIT
SPECTRA
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TABLE 2. AA7178 FIT RESULTS
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ALUMINUM ALLOY 3004 (AA3004) EXPERIMENTAL FIT
SPECTRA
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TABLE 3. AA3004 FIT RESULTS
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Fe-55 EXCITATION OF Al
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DISCUSSION, CONCLUSIONS, AND FUTURE WORK - PM

• Results indicate the approach is accurate.
• The CEARXRF code and a DRF for the detector
  provide all that is needed for the inverse
  problem.
• The GUI that has been developed and Differential
  Operators added to CEARXRF makes the approach
  practical.
• Now we need to develop the approach for all
  commercial analyzers including those with X-Ray
  machines and Secondary fluorescers.

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DISCUSSION, CONCLUSIONS, AND FUTURE WORK - AM

• For Routine XRF Sample Analysis the Advantages of
  this Approach are
• Use of CEARPPU makes all the data available with
  known Poisson statistics.
• Use of MCLLS corrects for all matrix effects
  including tertiary and beyond. It will be easy
  to include other refinements as necessary.
• Use of LLS avoids all problems with intensity
  measurement and gives statistical estimates of
  results automatically.
• An error analysis of existing FP approaches will
  be made.

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ACKNOWLEDGEMENT

• The authors acknowledge two grants by the
  National Institute of Environmental Health of the
  NIH for providing the opportunity for optimizing
  the XRF approaches for the in vivo measurement
  of lead in bone.