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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 Ex  a1 cos(  1 )


E y  a2 cos(   2 )
where Ex and E y are coordinates
Elliptical Polarization
•Want to eliminate

Ex
 cos( ) cos(1 )  sin( ) sin(1 )
a1
Ey
a2
 cos( ) cos( 2 )  sin( ) sin( 2 )
•After some algebra
Ey
Ex
sin( 2 )  sin(1 )  cos( )sin( 2  1 )
a1
a2
Ey
Ex
cos( 2 )  sin(1 )  sin( )sin( 2  1 )
a1
a2
Elliptical Polarization
•Squaring and adding
2
2
 Ex   E y 
Ex E y
2


2
cos(



)

sin
( 2  1 )
2
1
   
a1 a2
 a1   a2 
•a1 and a2 are half the sides of
a rectangle which the ellipse
is circumscribes in
Circular Polarization
 a1=a2=a (rectangle now square)
    2  1  m / 2 , m  1, 3, 5,...
Ex  E  a
2
2
y
2
 Quarter plate causes this change
Right Handed
 Right Handed-viewing from source light
waves travel clockwise
sin( )  0
Left Handed
 Left Handed-viewing from source light
waves travel counter-clockwise
sin( )  0
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.
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.
1st principal
stress direction
2nd principal stress
1st principal stress
direction
direction
Polariscope
Light Source
Specimen
observer
First Polarizer
Second Polarizer
Picture of our setup
Top view
Front view
Experimental Pictures
No Polarized Filter
Polarized Filter
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
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
Processing Images
No Polarized Filter
Determine Centers,
Diameters
Polarized Filter
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
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
Processed Image
References
 Born,Max and Emil Wolf. Principles of Optics.
Cambridge: Cambridge University Press,
1999.
 http://www.doitpoms.ac.uk/tlplib/photoelastic
ity/history.php
 http://en.wikipedia.org/wiki/Photoelasticity
 http://gibbs.engr.ccny.cuny.edu/technical/Trac
king/ChiTrack.php