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Topic: Mie theory

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In the News (Mon 24 Jun 19)

Although Mie theory provides an exact mathematical solution to the problem of scattering of electromagnetic waves from an homogeneous sphere, it does not provide any insight into the physical processes involved in scattering.
The Debye series is essentially a reformulation of Mie theory allowing the separation of contributions due to specific ray paths.
False colour maps showing scattered intensity as a function of scattering angle and of (a) the refractive index of the sphere, (b) the radius of the sphere or (c) the wavelength of the light.
www.philiplaven.com /mieplot.htm   (2051 words)

 Mie Theory
The complete solution to this important problem was first discovered by the physicist Mie and the subject is called Mie theory in his honor.
In depth discussions of Mie theory are presented in,, and.
The final property provided by Mie is the particle phase function, which describes the angular dependence of the scattering.
dust.ess.uci.edu /facts/rt/node46.html   (0 words)

  Mie Scattering
Although these theories are restricted to the case of a perfect sphere, the results have provided insight into the scattering and absorption properties for a wide variety of pigment systems, including non-spherical pigments.
The optical theories applied in the present study describe the light scattering properties of an isolated spherical particle and therefore cannot be applied to systems in which the particles are crowded together and near-field interactions between particles are significant.
The mathematics of Mie theory is straightforward but tedious, requiring the computation of a potentially large number of series expansions.
www.lrsm.upenn.edu /~frenchrh/mie_scattering.htm   (768 words)

  Micromeritics - Products - Particle Size - Saturn Digisizer
Mie theory describes characteristics of the scattering pattern (light intensity versus scattering angle, among other things) produced by the interaction of a plane wavefront of monochromatic light with a spherical, isotropic particle suspended in a medium of known optical properties.
Mie theory predicts the intensity vs. angle relationship as a function of the size for spherical scattering particles provided that other system variables are known and held constant.
Mie theory provides the fundamental light scattered by an individual particle is a function of the scattering pattern produced by spherical particles of a specific size.
www.micromeritics.com /products/saturn_digisizer_techniques_overview.aspx   (872 words)

 ipedia.com: Mie theory Article   (Site not responding. Last check: )
The Mie theory also called Lorenz Mie Theory is a complete mathematical-physical theory of the scattering of electromagnetic radiation by spherical particles, developed by Gustav Mie in 1908.
The Mie theory is very important in meteorological optics, where diameter-to-wavelength ratios of the order of unity and larger are characteristic of many problems regarding haze and cloud scattering.
Mie theory or Lorenz Mie Theory is named after German physicist Gustav Mie (1868 Rostock - 1957 Freiburg im Breisgau) and Danish physicist Ludvig Lorenz (1829-1891) who independendtly developed the theory of electromagnetic plane wave scattering by a dielectric sphere.
www.ipedia.com /mie_theory.html   (410 words)

 IRIS software features
For a given scattering angle it calculates the Mie scattered intensity(1) which depends on the droplet diameter, wavelength of light and the complex refractive indices(2) of the droplet and surrounding medium.
The accuracy of Mie theory is in contrast to the ability to represent colours of natural phenomena.
In contrast to rigorous Mie theory, colour representation involves empiricism and approximations and its perception is to a greater or lesser extent subjective.
www.atoptics.co.uk /droplets/irishwk.htm   (964 words)

 MIE Course Offerings
Theories of stress and strain; failure criteria; energy methods; torsion of non-circular shafts; asymmetrical bending of straight beams; shear center, curved beams; beams on elastic foundations; thick-wall cylinder.
Prerequisites: MIE 313 and 375 or consent of instructor.
Prerequisite: MIE 379 or equivalent or consent of instructor; MIE 477 corequisite.
www.ecs.umass.edu /mie/undergrad/courses.htm   (4336 words)

 Blue Sky and Rayleigh Scattering
Mie scattering is not strongly wavelength dependent and produces the almost white glare around the sun when a lot of particulate material is present in the air.
As a qualitative examination of sky brightness and the saturation of the blue sky color, measurements of the color of the sky photograph were made from a computer monitor using Adobe Illustrator's color tools.
As you approach the sun's direction, the Mie scattering accounts for a larger fraction of the total light, and the Mie scattered light is essentially white.
hyperphysics.phy-astr.gsu.edu /hbase/atmos/blusky.html   (703 words)

 Analysis of the ASTM Round-Robin Test on Particle Size Distribution of Portland Cement: Phase I
Mie theory, which describes scattering by homogeneous spheres of arbitrary size, is the most rigorous scattering model available, and is used in many commercial instruments.
Mie theory has been applied with mixed success to the analysis of fine powders with diameters from several 100s of micrometers down to several tenths of micrometers.
An accurate representation of the "true" size distribution by Mie scattering is dependent on a knowledge of the complex refractive index, and will be impacted by the degree of asymmetry present in the particles and the dispersion procedure used to prepare the test sample.
ciks.cbt.nist.gov /~garbocz/nist6883/node3.htm   (1394 words)

 Manual for the LSA system
The Lorenz-Mie theory (LMT) was proposed independently by the two physicists G. Mie in 1908 and the Dane Lorenz in 1890.
Lorenz version, of the theory for light scattered from a particle in a plane wave, gives equations that are very close to the equations that are commonly used today.
Of particular interest is the theory for the light scattered from a spherical particle placed in a Gaussian beam.
hhbconsult.homepage.dk /Basic.html   (1153 words)

 Interpretation of Particle Size Reported by Different Analytical Techniques - Supplier Data from Mic
An example of the former is the particle’s sedimentation velocity in a fluid, and of the latter is the pattern of light scattered by the particle.
Another reason for using the sphere as the reference shape in some cases is because the theory describing the behavior of a particle under certain conditions, or describing the results of an interaction with a particle has only been solved rigorously for spherical particles.
A condition of using this theory is that the refractive index of the sample material be known.
www.azom.com /details.asp?ArticleID=3202   (2784 words)

 Characterizing Particles - Cover Story - Ceramic Industry
The two theories widely applied for interpreting the results of this technique are the Mie and Fraunhofer theories, both of which almost always assume a spherical particle shape.
The Mie theory is considered to be an exact solution and includes all interactions between the laser light and the particle (diffraction, reflection, absorption and refraction) but requires knowledge of the complex refractive index of the particles under analysis.
At this point, no theory exists that enables laser light scattering instruments to determine the shape of the particles under analysis, so shape would have to be assumed prior to the size analysis.
www.ceramicindustry.com /CDA/Articles/Cover_Story/4e21794e43729010VgnVCM100000f932a8c0____   (1744 words)

 Measuring particle size using modern laser diffraction techniques
Mie Theory provides a more rigorous solution for the calculation of particle size distributions from light scattering data.
Mie Theory allows for primary scattering from the surface of the particle, with the intensity predicted by the refractive index difference between the particle and the dispersion medium.
Mie Theory, which is able to predict effectively the fall off in scattering efficiency, gives appropriate weighting to the fine sizes and hence correctly predicts the overall particle size distribution.
www.chemie.de /articles/e/61205   (1694 words)

 Mie Theory Approximation
Since Mie theory is often used as an approximation to cell scattering, it is useful to know how accurate this approximation is. Since Mie theory assumes a homogeneous sphere with a fixed index of refraction, a suitable choice for n could be the volume average index, n
Figure 4.21: Comparison of FDTD and Mie theory scattering patterns for an inhomogeneous cell and a homogeneous sphere with volume averaged index of refraction.
However, because the cross section of the FDTD and average index Mie approximation are approximately equal, this method may be used to predict total tissue scattering.
www.nmr.mgh.harvard.edu /~adunn/papers/dissertation/node51.html   (392 words)

 AERI and HSRL Derived Optical Depth
The spread in AERI microwindow data as the optical depth increases is due to the index of refraction of ice spectral dependence, and will be compared to Mie theory for the statistical ensemble of points for the cases listed in Table 3.
It will be shown that this size is consistent with Mie theory for the set of cirrus data cases given in Table 3.
Data given in Table 4 was spectrally compared to Mie theory, assuming spherical ice particles, where the index of refraction for ice was taken from Warren (1984).
lidar.ssec.wisc.edu /papers/dhd_thes/node25.htm   (3259 words)

 CoulterCounter.com - Mie Theory
The Mie theory is a rigorous solution for the scattering intensity from a spherical, homogeneous, isotropic and non-magnetic particle of any diameter d in a non-absorbing medium.
The general characteristics are that the location of the first intensity minimum is closer to the axis and the peak intensity is greater for a large particle (the solid line in Figure 1) as compared with that of a smaller particle (the dashed line in Figure 1).
Because of the complicity of the formulation, it was impossible to apply the Mie theory in laser diffraction experiments before computers and microelectronics had enough computation power and speed.
www.beckman.com /coultercounter/homepage_tech_mie.jsp   (240 words)

 Ocean 590 Abstracts
Calculated from Mie theory and ADA using n=1.05, PSD at 1 m in East Sound on 04 August 1998 (gamma = -3.2), as well as a gamma of —2 and -4.
Potential explanations for this discrepancy are that the slopes from the PSD were not accurate in that we may have been missing some of the larger cells not sampled by the Coulter counter or the chosen indices of refraction may have been inappropriate.
Input and output for Mie theory and equations for the anomalous diffraction approximation.
www.ocean.washington.edu /courses/oc590/abstracts/mcleroy-etheridge.html   (1081 words)

 Use of Mie theory to analyze experimental data to identify infrared properties of fused quartz containing bubbles.
Use of Mie theory to analyze experimental data to identify infrared properties of fused quartz containing bubbles.
A modified two-flux approximation is suggested for the calculation of directional-hemispherical transmittance and reflectance of a refracting and scattering medium.
Leonid Dombrovsky, Jaona Randrianalisoa, Dominique Baillis, and Laurent Pilon, "Use of Mie theory to analyze experimental data to identify infrared properties of fused quartz containing bubbles." (2005).
repositories.cdlib.org /postprints/1647   (203 words)

 MIE Scattering   (Site not responding. Last check: )
The MIE formulation for the scattering of light from a spherical particle is an exact calculation of the far-field scattering.
In principle, the MIE formulation may be used for all particle sizes and wavelengths.
In practice, MIE theory fills the gap between simple theories like Rayleigh scattering for particles small compared to wavelength and geometric optics for structures large compared to the wavelength of interest.
my.execpc.com /~rkbrandt/scattering_mie.html   (226 words)

In general such a question is difficult to answer, as the error depends on shape and composition of the particles, and also on the scattering matrix element and range in scattering angles that is of interest.
Next, the difference between the Mie and RDG phase function is calculated, and finally the average over all scattering angles is calculated.
In the forward scattering directions AD theory performs very well, but for instance in the back scattering directions AD theory is known to perform poorly.
staff.science.uva.nl /~alfons/rdg-vs-mie/rdg.html   (1256 words)

 Ocean 590 Abstracts
Inputs to the Mie code were derived from Coulter Multisizer II particle size distribution (PSD) between 1 and 60 (m and spectrophotometric data.
Both methods for calculating a, b, and c from Mie theory underestimated the magnitude of a, b, and c compared to AC-9 data taken in situ.
The spectral shape of the difference spectrum of the AC-9 absorption spectrum and Mie theory derived absorption spectra suggested that the calculated ap neglected to account for adequate absorption by particles larger than 60 (m.
www.ocean.washington.edu /courses/oc590/abstracts/weiss.html   (768 words)

 Glory formation, Debye theory & surface waves
Simple diffraction theory fails to explain the glory or the positions of its rings.
Mie theory - formulated at a fundamental level from Maxwell's equations of electromagnetism - says only what happens and not how.
Fortunately, a reformulation of Mie theory made by Peter Debye, reveals more.
www.atoptics.co.uk /droplets/glofeat.htm   (392 words)

 Pharmaceutical Actives - Rapid Refractive Index Determination For Pharmaceutical Actives - Supplier
However, this can often be a difficult requirement to meet, as Mie Theory requires users to specify the refractive index (RI) of the material under study.
The laser diffraction results obtained using Mie Theory with RI values of 1.54 and 1.555 are shown in figure 5 along with that reported using the Fraunhofer approximation.
The use of Mie Theory is vital when using laser diffraction if accurate fine particle measurements are to be made.
www.azom.com /details.asp?ArticleID=2825   (1182 words)

 Particle Size Analysis Problem Solved With Breakthrough Technology - Supplier Data By Micromeritics
College textbooks such as Born and Wolf's "Principles of Optics" derive the equations dealing with the propagation and scattering of light beginning with Maxwell's equations which are the fundamental equations dealing with the properties of electromagnetic fields.
The primary difference between the two theories is that Fraunhofer is based on the action of light diffracting around the particles and Mie adds the effects of tile refraction of light through the particles and the absorption (or reflection) of light by the particles.
Micromeritics has developed techniques for easily determining the effective refractive index that make Mie analysis so easy to use that many customers are using it for all their analyses.
www.azonano.com /Details.asp?ArticleID=1481   (1796 words)

 Appendix B   (Site not responding. Last check: )
The scattering efficiency factor is calculated using Mie theory.
The Mie theory calculations are based on a FORTRAN computer code written by W. Lentz which calculates the efficiency factor for spherical particles.
The main purpose served by the IDL Mie code is to find the mean value of the lognormal distribution using SSM/I data.
www.geo.mtu.edu /volcanoes/research/djdelene/public_html/LARS/ssmi/thesis/appendix_B.html   (405 words)

 CILAS Laser Particle Size Analyzer -- Mie Theory
For smaller particles, it is appropriate to use Mie Theory.
The Mie model takes into account both diffraction and diffusion of the light around the particle in its medium.
To use the Mie model, it is necessary to know the complex refractive index of both the sample and the medium.
www.cilasus.com /theory/fmie.html   (0 words)

 Computing the Scattering Properties of Participating Media using Lorenz-Mie Theory
Our theory is based on a robust generalization of the Lorenz-Mie theory.
Our generalized theory is capable of handling both absorbing host media and non-spherical particles, which significantly extends the classes of media and materials that can be modeled.
We use the theory to compute optical properties for different types of ice and ocean water, and we derive a novel appearance model for milk parameterized by the fat and protein contents.
graphics.ucsd.edu /~henrik/papers/lorenz_mie_theory   (0 words)

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