Photoelastic Experiments

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Photoelastic Experiments
Andrew Pskowski Arif Patel Alex Sheppard Andrew
Christie
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Elliptical Polarization

• E-electric vector however can also be regarded as
  light vector
• phase increase
• variable part of phase factor
• Curve which is described by end point of light
  vector
• where and are coordinates

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Elliptical Polarization

• Want to eliminate

• After some algebra

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Elliptical Polarization

• Squaring and adding

• a1 and a2 are half the sides of a rectangle which
  the ellipse is circumscribes in

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Circular Polarization

• a1a2a (rectangle now square)
• ,
• Quarter plate causes this change

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Right Handed

• Right Handed-viewing from source light waves
  travel clockwise

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Left Handed

• Left Handed-viewing from source light waves
  travel counter-clockwise

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Photoelasticity

• It an experimental method used to study the
  stress distribution in a model.
• It involves inducing birefringence on the
  material being studied.
• Our experiment uses 2D photoelasticity.

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Birefringence

• It is the splitting of a ray of light into two
  rays when it passes through a material.
• It is a property of certain transparent
  materials.
• It occurs when the material is stressed.
• It creates fringes or stress patterns.

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Birefringence

• Each point of interest has a principal stress
  direction. This is where the only stresses
  present are normal stresses.
• Polarized light transmitted through a
  birefringent material splits into two light rays,
  each traveling at different velocities parallel
  to one of the two principal stress directions.

2nd principal stress direction
1st principal stress direction
1st principal stress direction
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Polariscope
Light Source
Specimen
observer
First Polarizer
Second Polarizer
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Picture of our setup
Top view
Front view
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Experimental Pictures
No Polarized Filter
Polarized Filter
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Image Processing

• Can be low or high level
• Our task is fairly low level because it requires
  very rigidly defined input
• Low level processing typically uses filtering or
  morphological operations
• Filtering can be in spatial or frequency domain

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Filtering

• Edge detection is a common filtering task
• Sobel operator is commonly used here
• Based on central difference approximation
• Template matching is also based on filters

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Processing Images
No Polarized Filter
Polarized Filter
Determine Centers, Diameters
Extract Forces
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Method Used

• Create an Ideal Particle Image

D 12 w 1.05
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Finding Position and Diameter

• Search for minimum difference between ideal
  particle and real particle
• Use least squares fitting and convolution

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Coloring Particles Based on Force

• Use the location of particles from the
  non-polarized images
• Average the intensity inside of each particle
  from the polarized image
• Create a new image with
• Color the each particle with the average
  intensity

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Processed Image
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References

• Born,Max and Emil Wolf. Principles of Optics.
  Cambridge Cambridge University Press, 1999.
• http//www.doitpoms.ac.uk/tlplib/photoelasticity/h
  istory.php
• http//en.wikipedia.org/wiki/Photoelasticity
• http//gibbs.engr.ccny.cuny.edu/technical/Tracking
  /ChiTrack.php