... | ... | @@ -22,33 +22,31 @@ Similar to the [transmissive polariscope](#), both the *Polarizer* and the *Anal |
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There are two typical ways to implement the mirror in real granular physics experiments:
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* Using photo-elastic particles with a reflective surface. The left figure below shows a sketch of an example experimental setup using this technique. (see [*J. Puckett et al.*](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.110.058001) or [*K. E. Daniels et al.*](https://aip.scitation.org/doi/abs/10.1063/1.4983049) for more details about the experiment) A typical image recorded from this same experiment for a jammed disc packing is also attached below (from [*the PhD Thesis of J. G. Puckett*](http://nile.physics.ncsu.edu/pub/Publications/papers/Puckett-2012-thesis.pdf) ), showing same type of fringes as observed in the transmissive polariscopes.
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* Using a mirror table. Particles are then put on this table to perform experiments. This technique allows usage of transparent photoelastic particles the same way as in the transmissive polariscope case. An example implementation of the mirror table is shown in the up-right subfigure of the figure below. (see [Y. Zhao et al.](https://www.epj-conferences.org/articles/epjconf/abs/2017/09/epjconf162348/epjconf162348.html) for more details of this experiment)
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* Using a mirror table. Particles are then put on this table to perform experiments. This technique allows usage of transparent photoelastic particles the same way as in the transmissive polariscope case. An example implementation of the mirror table is shown in the up-right subfigure of the figure below. (see [*Y. Zhao et al.*](https://www.epj-conferences.org/articles/epjconf/abs/2017/09/epjconf162348/epjconf162348.html) for more details of this experiment)
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![james](uploads/958f33b4b081ddc4ee59e906709a9a28/james.png)
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### 1.2. How to make the photoelastic particles reflective?
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A typical way to create the reflective surface for photoelastic particles is to coat one side of the particles with mirror effect paint. An empirical choice that works well on
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The lower left figure shows a typical painting material (RUST-OLEUM mirror effect) that provides good reflection for the light, while attaches firmly on the vanchy PSM material. To ensure uniform coating. Usually a whole sheet of photo elastic material is painted. And the particles are cutter from the sheet afterwards. The lower right figure shows a picture of the painted psm layer after cutting of the particles (see cut section to learn how to perform the cut). The figure below also shows different angle of a particle after this coating process.
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A typical way to create the reflective surface for photoelastic particles is to coat one side of the particles with mirror effect paint. An empirical choice that works well on the [*Vishay PS-4*](http://www.vishaypg.com/micro-measurements/photo-stress-plus/category/coating/?subCategory=materials) material is the [*Rust-Oleum Mirror Effect spray*](https://www.amazon.com/Rust-Oleum-267727-Specialty-Mirror-6-Ounce/dp/B00FMRXJW2/ref=sr_1_1?ie=UTF8&qid=1544796251&sr=8-1&keywords=rust-oleum+mirror+effect) (shown in the figure below). To ensure uniform coating, it is typical to first paint a sheet of photoelastic material and then cut particles from it. The lower right figure below shows a picture of the painted [*Vishay PS-4*](http://www.vishaypg.com/micro-measurements/photo-stress-plus/category/coating/?subCategory=materials) sheet after cutting of the particles (see [here](#cuting) to learn how to cut). The figure below also shows different angles of a particle after this coating process.
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![particles](uploads/ba1713b99aba580dd47cdeb73c15cc8d/particles.png)
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## 1.3. Polarizer configuration
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### 1.3. Determine the configuration of circular polarizers
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It is very important to note that in reflective polariscope, the circular polarizer has to make its wave-plate side towards the granular sample. However sometimes it is hard to tell which side of a circular polarizer is wave-plate. A simple trick can be used to determine this: put the circular polarizer on a piece of metal. If the metal becomes black then the wave-plate side is towards the metal, otherwise the linear polarizer side is towards the metal.
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It is very important to note that in reflective polariscope, the circular polarizers used as both *Polarizer* and *Analyzer* must have their quarter-wave plate side towards the granular sample. However sometimes it is hard to tell which side of a circular polarizer is quarter-wave plate by simple looking at it. A simple trick can be used to solve this problem is: put the circular polarizer on a piece of metal (can be any metal in the lab, even your lab keys). If the metal becomes black then the wave-plate side is towards the metal, otherwise the linear polarizer side is towards the metal.
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![polarizer](uploads/5ae4ce71bf075d4694730975d4b992f0/polarizer.png)
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## 1.4. Light condition
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### 1.4. Ensure a uniform distribution of light intensity
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In experiments using photoelastic particles, it is important to keep the light intensity distribution uniform among the system. Because both empirical pressure measurement (see here for details) and the nonlinear fitting contact force measurement (see here for details) depends sensitively on the back ground light intensity. The reflective polariscope has a higher chance to suffer from the light heterogeneity. First, the reflection light intensity is sensitive to the relative position between light source, particle and camera (shown in figure below). Second, if the effective mirror is implemented using coated particles, small titing of particles may induce big change of background light intensity for that particle. This is shown in figure below. This heterogeneity can be removed by rescale the polarized image using a image taken without the analyzer (which records the background light intensity).
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In experiments using photoelastic particles, it is important to keep the light intensity distribution uniform among the system. Because both [empirical pressure measurement](#) and the [nonlinear fitting force measurement](#) depend sensitively on the background light intensity. The reflective polariscope has a higher chance to suffer from the light heterogeneity, comparing to the transmissive polariscope. First, the reflection light intensity is more sensitive to the relative position between light source, particle and camera (shown in figure below). Second, if the effective mirror is implemented using coated particles, small titing of particles may induce big change of background light intensity for that particle. This is shown in figure below. This heterogeneity can be removed by rescale the polarized image using a image taken without the analyzer (which records the background light intensity).
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![intensity_adjust](uploads/646bf87c6e83f6eb63f2a513e8582df6/intensity_adjust.png)
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![reflective_light](uploads/1837153441070c0232be07b2629e53cc/reflective_light.png)
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## 1.5. Coated particle or mirror table?
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