... | ... | @@ -6,24 +6,31 @@ Reflection photoelasticity method |
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## 1. Reflective polariscope
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Reflective polariscope can probe the photo-elastic fringes with light source and camera on same side of the granular sample. An example implementation is sketched in fig.1(a). The reflective polariscope contains 5 parts: (1) The light source (2) the ‘polarizer’ in front of the light source (3) a mirror or a effective mirror to reflect light (4) the analyzer and (5) the camera. Similar to transmissive polariscope, both the polarizer and analyzer are usually circular polarizer. It is important to point out that a dark field reflective polariscope uses same kind of circular polarizer for polarizer and analyzer, whereas the transmissive polariscope uses circular polarizers with different chirality.
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Reflective polariscope can probe the photoelastic fringes with light source and camera on same side of the photoelastic specimen. As shown in the figure below, the reflective polariscope contains 5 basic elements:
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* The light source.
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* The *Polarizer*, which is the circular polarizer (plotted as a combination of a linear polarizer and quarter-wave plate below) between the light source and photoelastic specimen.
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* The mirror to reflect light.
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* The *Analyzer*, which is the circular polarizer (plotted as a combination of a linear polarizer and quarter-wave plate below) between the camera and the photoelastic specimen.
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* The camera.
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![reflective_circular_4](uploads/9b9996db2ba507c78fd8e16f65a6144c/reflective_circular_4.png)
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Similar to the [transmissive polariscope](#), both the *Polarizer* and the *Analyzer* are usually circular polarizers. Thus the principle axis of the quarter-wave plate in figure below must form $`45^{\circ}`$ angle with the direction of polarization of the linear polarizer. It is important to point out that a dark field reflective polariscope uses same kind of circular polarizer for both the *Polarizer* and the *Analyzer* (see [Section 2](#2.-theoretical-background) for mathematical proof), whereas the transmissive polariscope uses circular polarizers with different chirality.
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## 1.1. Example experimental realizations
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![reflective_circular_4](uploads/9b9996db2ba507c78fd8e16f65a6144c/reflective_circular_4.png)
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There are two ways to implement the mirror in real granular physics experiments:
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### 1.1. Example experimental realizations
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make a list
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There are two typical ways to implement the mirror in real granular physics experiments:
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(1) by using photo-elastic particles with a reflective surface (see J. Picket et al. Or K. Daniels et al). The left figure below shows a sketch of an example experimental setup that implementing the reflective polariscope using reflective particles. (From j. Pucket et al) A typical force network recorded from the same experiment is also attached below, showing same type of fringes as observed in the transmissive polariscopes. (link to transmissive polariscope)(from pucket et al).
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(2) put transparent particles on a big mirror.
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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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![james](uploads/958f33b4b081ddc4ee59e906709a9a28/james.png)
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## 1.2. Technique for coating the particles
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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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A typical way to coat the particle is using mirror effect painting powders. 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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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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