Photoelastic Experiments Andrew Pskowski Arif Patel Alex Sheppard Andrew Christie

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

Elliptical Polarization Want to eliminate After some algebra

Elliptical Polarization Squaring and adding a 1 and a 2 are half the sides of a rectangle which the ellipse is circumscribes in

Circular Polarization  a 1 =a 2 =a (rectangle now square) ,  Quarter plate causes this change

Right Handed  Right Handed-viewing from source light waves travel clockwise

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

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.  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.

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.  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.

Birefringence 1 st principal stress direction 2nd principal stress direction 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. 1 st principal stress direction

Polariscope Light Source First Polarizer Second Polarizer Specimen observer

Picture of our setup Front view Top view

No Polarized FilterPolarized Filter Experimental Pictures

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  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

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  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

No Polarized FilterPolarized Filter Processing Images Determine Centers, Diameters Extract Forces

Method Used  Create an Ideal Particle Image D = 12; w = 1.05

Finding Position and Diameter  Search for minimum difference between ideal particle and real particle  Use least squares fitting and convolution  Search for minimum difference between ideal particle and real particle  Use least squares fitting and convolution

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  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

Processed Image

References  Born,Max and Emil Wolf. Principles of Optics. Cambridge: Cambridge University Press,  ity/history.php ity/history.php   cking/ChiTrack.php cking/ChiTrack.php  Born,Max and Emil Wolf. Principles of Optics. Cambridge: Cambridge University Press,  ity/history.php ity/history.php   cking/ChiTrack.php cking/ChiTrack.php