Data processing: measuring – calibrating – or testing – Measurement system in a specific environment – Chemical analysis
Reexamination Certificate
2001-06-01
2003-06-24
Hallacher, Craig (Department: 2853)
Data processing: measuring, calibrating, or testing
Measurement system in a specific environment
Chemical analysis
C702S194000, C702S196000
Reexamination Certificate
active
06584413
ABSTRACT:
COMPUTER PROGRAM LISTING
A computer program listing appendix has been submitted on two, identical compact discs in computer readable form, labeled “Copy
1
” and “Copy
2
”, which is a duplicate of “Copy
1
” disc. The material contained in this computer program listing appendix is herein incorporated by reference.
As a demonstration of a working implementation of the complete multivariate data analysis method, according to an embodiment of the present invention, the following software executable routines were implemented in MATLAB® language, MathWorks, Inc., Natick, Mass., and stored on a computer readable medium. Intel Math Kernel Library (MKL) and LAPACK routines (www.netlib.org) were incorporated as “mex-files”. The source code, which is supplied as a Computer Program Listing Appendix on Compact Disk, and herein is incorporated by reference, includes the following files listed in Table 1.
TABLE 1
Files Contained on Computer Program Listing Appendix
Name
Size
Date Created
axsia.m
5,230
08/08/00
mk_als.m
2,714
08/06/00
mk_autoplotsandl.m
1,800
08/07/00
mk_base.m
1,595
08/06/00
mk_cxpeig.f
2,894
07/15/00
mk_gemm.f
2,989
12/21/00
mk_ger.f
2,375
12/21/00
mk_nnls.m
3,693
08/06/00
mk_npures.m
701
08/06/00
mk_outputfiles.m
1,405
08/14/00
mk_readnoran.m
941
08/07/00
mk_varimax.m
1,694
08/06/00
FIELD OF THE INVENTION
The present invention relates generally to the field of chemical compositional analysis, and more specifically to a method and apparatus for performing multivariate spectral analysis.
BACKGROUND OF THE INVENTION
In general, multivariate spectral analysis for chemical microanalytical characterization of a sample can include: (1) determining the number of chemical species (pure elements and chemical phases or alloys) that comprise the inhomogeneous mixture being imaged; (2) extracting the spectra of these “pure” components (elements or phases); (3) quantifying the amount or concentration of each component present in the sample; and (4) mapping the spatial distribution of these components across the sample, while simultaneously preserving a high spatial resolution. Full spectrum images refer to a complete spectrum that is produced at each pixel of 2-D array of pixels (i.e., image).
Spectral data can be produced by a variety of microanalytical techniques, including: Electron Probe Microanalysis (EPMA), also called X-Ray Microanalysis (XMA) in Japan, Scanning Electron Microscopy (SEM) with attached Energy Dispersive Spectrometer (EDS), X-ray fluorescence (XRF), Electron Energy Loss spectroscopy (EELS), Particle Induced X-ray Emission (PIXE), Auger Electron Spectroscopy (AES), gamma-ray spectroscopy, Secondary Ion Mass Spectroscopy (SIMS), X-Ray Photoelectron Spectroscopy (XPS), Raman Spectroscopy, Magnetic Resonance Imaging (MRI) scans, Computerized Axial Tomography (CAT) scans, IR reflectometry, etc.
The spectral data can be generated from a spot on the sample, from a 1-D line scan, or from a 2-D rastered pattern. Other dimensions, however, can be time or temperature, for example. Hence, the spectral data can vary with time, for example, as a chemical reaction process evolves over time, or from species diffusing across an interface, or concentrations that vary with temperature as the sample heats up.
A spectrum is created by detecting radiation (e.g., photons or particles) emitted within a specified interval (window) of energy (mass, wavelength, or frequency), as a function of energy (mass, wavelength, or frequency). In other words, we measure the energy (or mass, wavelength, or frequency) of emitted photons (or particles) and then “bin” them according to their energy (mass, wavelength, or frequency). The spectrum is basically a histogram that results from this binning process. The spectrum generally includes well-defined spectral features that have a characteristic energy distribution (mass, wavelength, or frequency).
We define “spectral features” to include sharp, well-defined spectral peaks, as well as double-peaks, overlapping peaks, and less well-defined maxima.
The phrase “energy spectrum” is broadly defined to also include a “mass spectrum” (for mass spectroscopy), a “wavelength spectrum” (for wavelength dispersive analysis, WDS), a “frequency spectrum” (for Fast Fourier Transform analysis), or an “acoustic spectrum” (for sound/speech analysis).
The word “characteristic” broadly relates to a property that is typical or characteristic of a material's unique individual atomic or molecular structure. For example, in X-ray spectroscopy, “characteristic” refers to a specific electronic transition in the element's atomic structure resulting in emission of an X-ray having a well-known energy. However, in infrared spectroscopy, the characteristic property relates to vibrational transitions; and in mass spectroscopy, to the mass of fragments. Additionally, the spectrum can includes contributions from non-“characteristic” sources (e.g., continuum radiation from background or Bremsstrahlung X-radiation), which are continuous and don't have characteristic peaks or lines. Inspection of the detected spectrum allows the chemical composition to be determined by comparison of the spectral peaks with spectra measured from known elements or phases, which can found in lookup tables in data libraries, books, etc.
In electron probe microanalysis (EPMA), for example, a pre-selected small area on the surface of a solid specimen is bombarded with energetic electrons (e.g., 20 KeV electrons). The resulting emission from the sample includes a variety of particles and photons, including: backscattered primary electrons, low-energy photoelectrons, Auger electrons, and characteristic X-ray emission superimposed on a background of continuum (i.e., Bremsstrahlung) X-radiation. The X-rays emitted by the sample are counted and recorded by an X-ray detector, a crystal spectrometer, or an Energy Dispersive Spectrometer (EDS). A multi-channel EDS spectrum analyzer (e.g., with 1024 “energy” channels) is used to count the number of X-rays randomly emitted during the counting period within a single channel (i.e., a small band of energy having a width, &Dgr;E. For example, &Dgr;E can be equal to 10 eV. A 2-D “full spectrum” image is generated by scanning and rastering a focused electron beam spot across the surface of a sample, at a specified spatial resolution (e.g., 128×128 pixels). For each pixel, a multi-channel (e.g., 1024) X-ray spectrum is detected by the EDS. A full spectrum image contains, for example, a 3-D array of 128×128×1024=16.8 million data points. The measured X-ray spectrum from a single pixel can have spectral contributions integrated from not only multiple elements, but also multiple phases.
The word “sample” is not limited to representing a small, conventional specimen that would be used, for example, in a Scanning Electron Microscope. “Sample” is broadly defined to mean any surface area or volume of a material that is emitting radiation that can be detected by a detector. For example, the word “sample” can include the Earth's (or Moon's) surface, which may be emitting radiation (in response to irradiation by Sunlight) that can be detected by an array of CCD detectors located on a satellite in orbit around the Earth (or Moon). The “sample” can also include astronomical objects, such as stars and galaxies, which emit radiation detected by telescopes.
The phrase “radiation emitted by the sample” is broadly defined to include any type of photon or particle, including, but not limited to: radio waves, microwaves, visible light, infrared radiation, ultraviolet radiation, X-rays, gamma-rays, electrons, positrons, protons, neutrons, neutral particles, alpha particles, charged particles (ions), ionized atoms, ionized molecules, excited molecules. We also include in this broad definition of “radiation emitted by the sample” the emission of acoustic energy (i.e., sound waves). We also include in this broad definition of “radiation emitted by the sample” the transmission of radiation through a sample, either completely or partially, which is subse
Keenan Michael R.
Kotula Paul G.
Hallacher Craig
Mouttet Blaise
Sandia Corporation
Watson Robert D.
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