Optics: measuring and testing – By polarized light examination – With polariscopes
Reexamination Certificate
2001-09-19
2004-04-13
Font, Frank G. (Department: 2877)
Optics: measuring and testing
By polarized light examination
With polariscopes
C356S369000, C356S367000
Reexamination Certificate
active
06721051
ABSTRACT:
TECHNICAL FIELD
The present invention relates generally to particle characterization; and more particularly to an apparatus and non-intrusive methods for characterizing particles based on scattering matrix elements measurements made using elliptically polarized radiation, and methods of compiling a database of theoretical data for use therein.
BACKGROUND OF THE INVENTION
In many modern materials and manufacturing processes such as printers, copiers, fluidized bed reactors, powder coating machines, ceramic coatings, etc, small particles play a significant role. The control, streamlining and overall efficiency of many of these modern processes may be significantly improved if the particles involved in the processes are able to be precisely characterized. Determining whether particles resulting from a manufacturing process are spheroids as intended, for example, or whether the resulting particles actually agglomerated during the process may be critical to the overall success/efficiency of the process. These modern processes may be further enhanced by the ability to characterize particles such that the presence of undesirable particles and their respective adverse effects may be minimized. Examples of these processes include the fabrication of solid-state devices wherein the presence of sub-micron size contaminants in a fabrication area can have an enormous detrimental impact on the devices, metallurgical manufacturing wherein airborne dust particles create a significant fire and explosion hazard, and combustion chambers wherein a failure to burn soot particles including agglomerates allows their escape into the environment.
Recent advances in diverse disciplines, such as biological, pharmaceutical, environmental, and combustion systems as well as atmospheric and oceanographic remote sensing have created a much wider range of applications of and need for better characterization of particles in general. One of the most often used methods to characterize these particles includes optical diagnostics in which the particles are subjected to incident electromagnetic waves from a radiation source, and their responses or the scattered radiation are recorded. By comparing the recorded response against responses of previously physically measured particles, some characteristics of the particles may be estimated. These estimates, however, are only as accurate as the physically measured data which itself is difficult to accurately obtain at these small particle sizes. Although generally effective in confirming the presence of known or expected particle types, these methods of characterization are significantly limited and certainly may not be used to characterize unknown particle types and/or unexpected particles resulting from agglomeration during a process or the like.
Thus, as demonstrated by the limitations and disadvantages of the prior art methods of characterizing particles, there is a need identified for an improved more robust method of characterizing particles and mixtures of particles of any size, shape, and size and/or shape distribution without a reliance on measured data which is often unavailable, inaccurate, or incomplete for the particles being characterized.
SUMMARY OF THE INVENTION
The present invention meets these needs by providing a non-intrusive method of characterizing particles or particle systems through inverse analysis of experimental data based on measurements using elliptically polarized radiation. A database of theoretical absorption and scattering data sets for particles is compiled. Optimum settings for an experimental test to gather an experimental absorption and scattering data set are determined and the experimental test is conducted. The experimental absorption and scattering data set is then compared to the theoretical absorption and scattering data sets of the database of theoretical absorption and scattering data sets in order to determine an absorption and scattering data set which differs the least from the experimental absorption and scattering data set in order to characterize the particles.
The particles referred to throughout the present application are herein defined to include fine particles and/or agglomerates of any size, size distribution, and shape. More specifically, the fine particles may include homogeneous spheres, radially inhomogeneous spheres, homogeneous cylinders, radially inhomogeneous cylinders, oblate spheroids, prolate spheroids, and/or ellipsoids, hollow particles, nanostructures, and nanocrystals, and the agglomerates may include irregular shaped structures, fractal-like agglomerates, fluffy or compact agglomerates, and hollow particles.
In accordance with a first aspect of the present invention, the step of compiling the database of theoretical absorption and scattering data sets for the particles may include the steps of calculating an interaction of a theoretical incident planar wave having a wavelength (&lgr;) on each monomer of the particle having a diameter (d) and a complex index of refraction (m=n−ik), and interactions of portions of the theoretical incident planar wave scattered by each remaining monomer of the particle using Maxwell's equations as is known in the art. The diameter (d) of each monomer may be an effective diameter based on a volume of the monomer. For irregular shaped particles, the particle may be divided into volumes which are themselves converted into effective spherical diameters. For the remaining particles types, the monomer diameter may be made equivalent to the size of the small spheres which make up the agglomerate or the like. The calculated interactions may then be summed for each monomer of the particle and a distribution of the theoretical incident planar wave scattered by the particle and an absorption of the theoretical incident planar wave by the particle determined. The method may further comprise the step of determining scattering matrix elements for the particle based on the determined distribution of the theoretical incident planar wave scattered by the particle and the determined absorption of the theoretical incident planar wave by the particle.
In accordance with another aspect of the present invention, the step of compiling the database of theoretical absorption and scattering data sets for the particles preferably includes the additional step of repeating the aforementioned steps of calculating an interaction of a theoretical incident planar wave and interactions of portions of the theoretical incident planar wave, summing the calculated interactions, determining a distribution of the theoretical incident planar wave scattered by the particles and an absorption of the theoretical incident planar wave by the particles, and determining scattering matrix elements for every possible combination of wavelength (&lgr;), and particle characteristic including diameter (d), complex index of refraction (n), and absorption index (k). For particles which include fractal agglomerates, the aforementioned steps are further repeated for every possible combination of fractal dimension D
f
and prefactor K
f
.
In accordance with still another aspect of the present invention, the step of determining optimum settings for the experimental test to gather the experimental absorption and scattering data set further includes the step of estimating characteristics of the particles being characterized. The estimated characteristics of the particles being characterized may include data obtained from a transmission electron microscope, a scanning electron microscope, or an atomic force microscope, for example. A wavelength of a theoretical elliptically polarized radiation is selected based on the estimated characteristics of the particles being characterized and a theoretical set of polarizers and retarders are selected based on the selected wavelength. The step of determining optimum settings may further include the step of selecting an orientation for optical axes of the polarizers and retarders in the theoretical set.
Utilizing the selected theoretical set of polarizers and retarders, a
Manickavasagam Sivakumar
Mengüç M. Pinar
Font Frank G.
King & Schickli PLLC
Lauchman Layla
Synergetic Technologies, Inc.
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