Optics: measuring and testing – By dispersed light spectroscopy
Reexamination Certificate
1997-07-11
2001-03-06
Font, Frank G. (Department: 2877)
Optics: measuring and testing
By dispersed light spectroscopy
C356S323000, C356S213000, C356S222000
Reexamination Certificate
active
06198531
ABSTRACT:
BACKGROUND OF THE INVENTION
The present invention relates to spectroscopy analysis systems. More particularly, the invention relates to improvements in the compression of data carried by light so that information about the light may be obtained.
Light conveys information through data. When light interacts with matter, for example, it carries away information about the physical and chemical properties of the matter. A property of the light, for example its intensity, may be measured and interpreted to provide information about the matter with which it interacted. That is, the data carried by the light through its intensity may be measured to derive information about the matter. Similarly, in optical communications systems, light data is manipulated to convey information over an optical transmission medium, for example fiber optic cable. The data is measured when the light signal is received to derive information.
In general, a simple measurement of light intensity is difficult to convert to information because it likely contains interfering data. That is, several factors may contribute to the intensity of light, even in a relatively restricted wavelength range. It is often impossible to adequately measure the data relating to one of these factors since the contribution of the other factors is unknown.
It is possible, however, to derive information from light. An estimate may be obtained, for example, by separating light from several samples into wavelength bands and performing a multiple linear regression of the intensity of these bands against the results of conventional measurements of the desired information for each sample. For example, a polymer sample may be illuminated so that light from the polymer carries information such as the sample's ethylene content. Light from each of several samples may be directed to a series of bandpass filters which separate predetermined wavelength bands from the light. Light detectors following the bandpass filters measure the intensity of each light band. If the ethylene content of each polymer sample is measured using conventional means, a multiple linear regression of ten measured bandpass intensities against the measured ethylene content for each sample may produce an equation such as:
y=a
0
+a
1
w
1
+a
2
w
2
+ . . . +a
10
w
10
(Equation 1)
where y is ethylene content, a
n
are constants determined by the regression analysis, and w
n
is light intensity for each wavelength band.
Equation 1 may be used to estimate ethylene content of subsequent samples of the same polymer type. Depending on the circumstances, however, the estimate may be unacceptably inaccurate since factors other than ethylene may affect the intensity of the wavelength bands. These other factors may not change from one sample to the next in a manner consistent with ethylene.
A more accurate estimate may be obtained by compressing the data carried by the light into principal components. To obtain the principal components, spectroscopic data is collected for a variety of samples of the same type of light, for example from illuminated samples of the same type of polymer. For example, the light samples may be spread into their wavelength spectra by a spectrograph so that the magnitude of each light sample at each wavelength may be measured. This data is then pooled and subjected to a linear-algebraic process known as singular value decomposition (SVD). SVD is at the heart of principal component analysis, which should be well understood in this art. Briefly, principal component analysis is a dimension reduction technique which takes m spectra with n independent variables and constructs a new set of eigenvectors that are linear combinations of the original variables. The eigenvectors may be considered a new set of plotting axes. The primary axis, termed the first principal component, is the vector which describes most of the data variability. Subsequent principal components describe successively less sample variability, until only noise is described by the higher order principal components.
Typically, the principal components are determined as normalized vectors. Thus, each component of a light sample may be expressed as x
n
z
n
, where x
n
is a scalar multiplier and z
n
is the normalized component vector for the n
th
component. That is, z
n
is a vector in a multi-dimensional space where each wavelength is a dimension. As should be well understood, normalization determines values for a component at each wavelength so that the component maintains it shape and so that the length of the principal component vector is equal to one. Thus, each normalized component vector has a shape and a magnitude so that the components may be used as the basic building blocks of all light samples having those principal components. Accordingly, each light sample may be described in the following format by the combination of the normalized principal components multiplied by the appropriate scalar multipliers:
x
1
z
1
+x
2
z
2
+ . . . +x
n
z
n
.
The scalar multipliers x
n
may be considered the “magnitudes” of the principal components in a given light sample when the principal components are understood to have a standardized magnitude as provided by normalization.
Because the principal components are orthogonal, they may be used in a relatively straightforward mathematical procedure to decompose a light sample into the component magnitudes which accurately describe the data in the original sample. Since the original light sample may also be considered a vector in the multi-dimensional wavelength space, the dot product of the original signal vector with a principal component vector is the magnitude of the original signal in the direction of the normalized component vector. That is, it is the magnitude of the normalized principal component present in the original signal. This is analogous to breaking a vector in a three dimensional Cartesian space into its X, Y and Z components. The dot product of the three-dimensional vector with each axis vector, assuming each axis vector has a magnitude of 1, gives the magnitude of the three dimensional vector in each of the three directions. The dot product of the original signal and some other vector that is not perpendicular to the other three dimensions provides redundant data, since this magnitude is already contributed by two or more of the orthogonal axes.
Because the principal components are orthogonal, or perpendicular, to each other, the dot, or direct, product of any principal component with any other principal component is zero. Physically, this means that the components do not interfere with each other. If data is altered to change the magnitude of one component in the original light signal, the other components remain unchanged. In the analogous Cartesian example, reduction of the X component of the three dimensional vector does not affect the magnitudes of the Y and Z components.
Principal component analysis provides the fewest orthogonal components that can accurately describe the data carried by the light samples. Thus, in a mathematical sense, the principal components are components of the original light that do not interfere with each other and that represent the most compact description of the entire data carried by the light. Physically, each principal component is a light signal that forms a part of the original light signal. Each has a shape over some wavelength range within the original wavelength range. Summing the principal components produces the original signal, provided each component has the proper magnitude.
The principal components comprise a compression of the data carried by the total light signal. In a physical sense, the shape and wavelength range of the principal components describe what data is in the total light signal while the magnitude of each component describes how much of that data is there. If several light samples contain the same types of data, but in differing amounts, then a single set of principal components may be used to exactly describe (except fo
Booksh Karl S.
Myrick Michael L.
Nelson Matthew P.
Font Frank G.
Nelson Mullins Riley & Scarborough LLP
Ratliff Reginald A.
University of South Carolina
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