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UNDER CONSTRUCTION
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UNDER CONSTRUCTION, work
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Reflection photoelasticity method
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Reflection photoelasticity method
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## 1.Overview
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## 1.Overview
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In some special cases, the light source of the polariscope can not be placed on the back of the granular sample. For example, when air table is used to float the particles or the driving motors of the base are placed beneath the sample. Reflective photoelasticity is utilized here using the reflective polariscope. (fig) The major difference of the polariscope comparing to that used in the transmission polariscope is that the polarization of the polarizer covering the light source and the analyzer covering the camera lens are the same.
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In some cases, the light source of the polariscope can not be placed on the back of the granular sample. For example, when air table is used to float the particles or the driving motors of the base are placed beneath the sample. Reflective photoelasticity is utilized here using the reflective polariscope. (fig) The major difference of the polariscope comparing to that used in the transmission polariscope is that the polarization of the polarizer covering the light source and the analyzer covering the camera lens are the same.
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... | @@ -116,28 +116,29 @@ Note: how to think of the reflected light go through the particle has different |
... | @@ -116,28 +116,29 @@ Note: how to think of the reflected light go through the particle has different |
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The whole problem has reflection symmetry so the final result would not be fundamentally different. proof?
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The whole problem has reflection symmetry so the final result would not be fundamentally different. proof?
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## 3. Implementation of the reflective photoelasticimetry
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## 3. Implementation of the reflective photoelasticimetry
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There are two ways to implement the reflective photoelasticimetry. One is by using particles with reflective bases. The other is by putting particles on mirror. Using particles with reflective bases can be achieved by paiting particles using.... The advantage is that it can be used on air tables ...
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There are two ways to implement the reflective photoelasticimetry. One is by using particles with reflective bases. The other is by putting particles on mirror.
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### 3.1. Paint on particles
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### 3.1. Particles with reflective base
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Duke reflective setup: base as mirror, particle are mirrored
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This method requires to make one side of the particles reflective. This is usually achieved by coating a layer of reflective material. Note the reflective layer can not be harder than the material so that the elastic property of the particle would not change after coating. Current technique involves painting the particles using the mirror effect powders (link to be added, citation to be added).
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Advantages:
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1. The particles can be used on a air table where a mirror table can not be used.
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Disadvantages:
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1. The reflective light intensity is sensitive to the tilting angle of the particle if the light source is not very uniform. (Fig) This problem introduces non-negligible errors in the stress estimations (both for qualitative $`G^2`$ method and the quantitative inverse problem solver). This problem can be overcomed by rescaling the light intensity using a non polarized image.
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2. The reflection ratio for the powders is usually not as good as a commercial mirror, creating larger noise to signal ratio in the detection of photoelastic patterns. (Calibration?)
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### 3.2. Mirror base
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### 3.2. Mirror base
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mirror base has the advatange that no additional process needs to be done on particles. So the transparent photo-elastic particles used in other experiments can be used on this setup. No more purchase/cast of particles particular for this geometry is needed. Also, the tilting of the particles will not be a problem. The disadvantage is that the reflection of the particle height makes the detection of the particle boundaries really hard. (fig) Also for the base-driven uniform shear system, the split between strips or rings will leave a dark line inside the photo-elastic response pattern, introducing errors in the stress estimations.
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In this method, the particles are transparent but they are put on a big mirror.
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Advantage:
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1. No need for coating the particles so the particles used for this experiment can also used in other experiments with non-reflective polariscopes.
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Mirror also provides a higher reflection ratio R than painted particles (check?)
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2. Particle tilting will not cause light inhomogeneity.
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3. The reflection ratio is better so the signal-to-noise ratio is better.
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Disadvantage:
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1. For particles that is not directly beneath camera, the mirror image of their boundaries will be recorded, which reduces the accuracy of the boundary detection and thus the center detection. (Fig)
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2. For base-driven experiments to apply internal shear (cite), the split between bottom slats or bottom rings will cause discontinuous photo elastic fringes, increasing errors in the stress estimations.
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### 3.3. Example implementations
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### 3.3. Example implementations
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#### 3.3.1 Biaxial experiment with air-table (cite)
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## 4. Common issues with the reflective photoelascimetry
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#### 3.3.2 Couette shear experiment with mirror bottom. (Cite)
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### 4.1. Non-uniform light distribution
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#### 4.1.1. Sensitivity to tilting
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When using the reflective photoelasticity. Small titling of the particles may cause a non-negligible change of the light intensity reflected by that particle. (fig) Since all the stress solver (either the qualitative $G^2$ method or the quantitative inverse solver method) depends on the intensity value, this issue will introduce errors for the stress estimations. However, this issue can be resolved by renormalize the light intensity by divide the polarized image to a pure light image. Fig. show a calibration result for particle with different tilting angle (light intensity).
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#### 4.1.2. Light source
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### 4.2. Signal to noise ratio: non perfect reflection: comparing to other kinds of imagings.
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Current technology using mirror effect powders to paint the base of the particle to create the reflection of light. However, the reflection ratio is much smaller than a real mirror. So the signal to noise ratio may be smaller than the experiments using the transparent particles. However, the
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## 5. References
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## 4. References
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[1]: Griffiths, David J. (2007), Introduction to Electrodynamics, 3rd Edition; Pearson Education
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[1]: Griffiths, David J. (2007), Introduction to Electrodynamics, 3rd Edition; Pearson Education
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[<go back to home](https://git-xen.lmgc.univ-montp2.fr/PhotoElasticity/Main/wikis/home) |
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[<go back to home](https://git-xen.lmgc.univ-montp2.fr/PhotoElasticity/Main/wikis/home) |
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