Modeling Depolarization and Scattering in a Complex System

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Modeling Depolarization and Scattering in a
Complex System

• Geoff Franz

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Outline

• Abstract
• Budget, Resources and Environment
• Specific Aims
• Background and Significance
• Experimental Design and Methods
• Timetable
• Summary and Questions

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Abstract

• Develop empirical models
• Particle size range 0.1-10µm
• Develop experimental index vectors
• Derive a predictive relationship

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Budget

• Optical equipment 400
• Linear polarizers, mounts, brackets, fiber optic
  light guides, filters
• Data acquisition system 1600
• DAQ board, cables, pre-amp, silicon detectors
• Sample materials 2000
• Polymer lattices, index matching fluid
• Total 4000

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Budget Justification

• Optical equipment
• Needed for the experiment
• High quality data acquisition system
• We need accurate, precise measurements
• Sample materials
• Accurately sized polymer lattices difficult to
  make, priced accordingly

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Budget Credit Hours

• Credit hours
• Experiment is straightforward
• No significant time commitment required
• 2 credit hours for Winter quarter
• Performing the experiment
• Analyzing results
• 1 credit hour for Spring quarter
• Drawing conclusions and writing final report

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Resources and Environment

• Image Microstructure Lab
• Personal computers
• Optics benches
• Necessary tools already present

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Specific Aims

• Broad, long-term objective
• Make data gathered from existing
  microgoniophotometer more interpretable
• Development of empirical models
• Scattering and depolarization models for our
  system
• Design and construction of a useful optical
  instrument

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Background and Significance

• Scattering of light studied since late 1800s
• Theoretical models already developed
• Particles much smaller than wavelength (Rayleigh)
• Particles much larger than wavelength (Mie)
• Extensive supporting evidence
• Includes polarization effects

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Background and Significance

• Single scattered light should maintain initial
  polarization1
• Multiple scattered light should lose some degree
  of polarization2
• Unsure if our system is singly or multiply
  scattered

1 - Van de Hulst, W.C., Light Scattering by Small
Particles, 1957. 2 Brosseau, C.,
Depolarization behavior of multiple scattered
light, OSA TOPS on Advances in Optical Imaging
and Photon Migration, 1996.
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Background and Significance

• If its so well studied, why bother?
• Our particles fall in between Rayleigh and Mie
• Difficult to accurately model for particles of
  this size
• Effects of depolarization often not directly
  addressed by theoretical models
• Our microgoniophotometer works on assumptions
  involving depolarization and scattering

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Background and Significance

• Gaps in literature
• Most papers on depolarization do not attempt to
  predict scattering
• Most papers on scattering do not attempt to
  predict depolarization
• Papers that do both fail to cover our entire
  range of particle sizes or deal exclusively with
  backscattering

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Experimental Design and Methods

• Hypothesis
• An empirical model can be developed that can
  predict scattering from the amount of
  depolarization for particles of sizes ranging
  from 0.1-10µm.

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Experimental Design and Methods

• Experiments
• Measure amount of scattering and depolarization
• Repeat experiment for polymer lattices of twenty
  sizes between 0.1-10µm
• Derive a predictive model for scattering from
  depolarization

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Experimental Design and Methods
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Experimental Design and Methods

• Measure relative intensities
• Fraction of polarization should decrease with
  increasing concentration
• Scattering fraction should increase along with
  concentration
• Overall intensity should decrease with increasing
  concentration

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Experimental Design and Methods

• Populate a matrix M1 with constants
• Scattering constant (ks), depolarization constant
  (kp)
• Ratio of scattering to depolarization for each
  optical path (R)
• Populate a second matrix M2 with constants
• Diameter of particles (d)
• Ratio of refractive indices of the particles and
  the liquid (r)
• Expanded terms (d2, r2, dr)

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Experimental Design and Methods

• M1 M M2
• M1 T M2
• Transform matrix T found by taking a
  pseudoinverse
• True inverse cannot be found as M1 and M2 are not
  square
• T M-1

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Experimental Design and Methods

• One transform matrix should be valid over the
  range of particle sizes
• Another transform matrix might be required if
• The shape of the relationship between the
  polarization fraction and concentration is
  dependent on concentration
• Should be a simple power law
• Easy to compute

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Timetable

• Winter Quarter
• Weeks 1-5 Setup and characterize instrument
• Weeks 5-10 Data collection
• Spring Quarter
• Weeks 1-2 Finish data collection
• Weeks 3-7 Process and analyze data
• Weeks 8-10 Prepare final report

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Conclusion

• Scattering of light well-studied
• Attempt to fill gaps in literature
• Predict scattering from depolarization
• Use model to interpret goniophotometric data

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The End

• Questions and Comments?