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Corner Cube Retroreflector
Introduction
This tutorial model shows how to simulate the reflection of a bundle of rays at a corner cube retroreflector using the Geometrical Optics interface.
A corner cube retroreflector is used to reflect rays so that the reflected rays are antiparallel to the incident rays, regardless of the angle of incidence. A basic corner cube retroreflector consists of three orthogonal reflecting surfaces.
Model Definition
1000 rays are released into the corner cube retroreflector with a conical distribution. The geometry, shown in Figure 1, is imported as a built-in Part from the Part Library for the Ray Optics Module. The initial and final directions of the rays are used to confirm that the initial and final trajectories are parallel, regardless of the angle of incidence.
Figure 1: Geometry of a typical corner cube retroreflector.
Results and Discussion
Figure 2 shows the ray trajectories as they propagate through the geometry. The color expression corresponds to the ray index, which has a unique integer value for each ray. In Figure 3, the initial and final angles between each ray trajectory and the surface normal are plotted to confirm that the incident and reflected rays are parallel.
Figure 2: Ray trajectories in the corner cube retroreflector.
Figure 3: Acute angle of incidence for the reflected rays as a function of the initial angle between the released rays and the surface normal.
Application Library path: Ray_Optics_Module/Tutorials/corner_cube_retroreflector
Modeling Instructions
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  3D.
2
In the Select Physics tree, select Optics>Ray Optics>Geometrical Optics (gop).
3
Click Add.
4
Click  Study.
5
In the Select Study tree, select Preset Studies for Selected Physics Interfaces>Ray Tracing.
6
Click  Done.
Geometry 1
1
In the Model Builder window, under Component 1 (comp1) click Geometry 1.
2
In the Settings window for Geometry, locate the Units section.
3
From the Length unit list, choose mm.
Part Libraries
1
In the Home toolbar, click  Windows and choose Part Libraries.
2
In the Part Libraries window, select Ray Optics Module>3D>Retroreflectors>corner_cube_retroreflector_3d in the tree.
3
Click  Add to Geometry.
Geometry 1
Corner Cube Retroreflector 1 (pi1)
1
In the Model Builder window, under Component 1 (comp1)>Geometry 1 click Corner Cube Retroreflector 1 (pi1).
2
In the Settings window for Part Instance, locate the Input Parameters section.
3
In the table, enter the following settings:
Name
Expression
Value
Description
niy
1
1
Incident ray direction, y component
niz
1
1
Incident ray direction, z component
Geometrical Optics (gop)
1
In the Model Builder window, under Component 1 (comp1) click Geometrical Optics (gop).
2
In the Settings window for Geometrical Optics, locate the Ray Release and Propagation section.
3
In the Maximum number of secondary rays text field, type 0.
Medium Properties 1
1
In the Model Builder window, under Component 1 (comp1)>Geometrical Optics (gop) click Medium Properties 1.
2
In the Settings window for Medium Properties, locate the Medium Properties section.
3
From the n list, choose User defined. In the associated text field, type 1.5.
Mirror 1
1
In the Physics toolbar, click  Boundaries and choose Mirror.
2
Select Boundaries 5–7 only.
Wall 1
1
In the Physics toolbar, click  Boundaries and choose Wall.
2
Select Boundary 2 only.
Release from Grid 1
1
In the Physics toolbar, click  Global and choose Release from Grid.
2
In the Settings window for Release from Grid, locate the Initial Coordinates section.
3
In the qx,0 text field, type -22/sqrt(3).
4
In the qy,0 text field, type -22/sqrt(3)-5.
5
In the qz,0 text field, type -22/sqrt(3)+5.
6
Locate the Ray Direction Vector section. From the Ray direction vector list, choose Conical.
7
In the Nw text field, type 1000.
8
Specify the r vector as
1
x
1.3
y
1
z
9
In the α text field, type pi/18.
Study 1
Step 1: Ray Tracing
1
In the Model Builder window, under Study 1 click Step 1: Ray Tracing.
2
In the Settings window for Ray Tracing, locate the Study Settings section.
3
From the Time-step specification list, choose Specify maximum path length.
4
From the Length unit list, choose mm.
5
Click  Range.
6
In the Range dialog box, type 0.2 in the Step text field.
7
In the Stop text field, type 70.
8
Click Replace.
9
In the Home toolbar, click  Compute.
Results
Ray Trajectories (gop)
In the Model Builder window, expand the Ray Trajectories (gop) node.
Color Expression 1
1
In the Model Builder window, expand the Results>Ray Trajectories (gop)>Ray Trajectories 1 node, then click Color Expression 1.
2
In the Settings window for Color Expression, locate the Expression section.
3
In the Expression text field, type gop.pidx.
4
Click the  Zoom Extents button in the Graphics toolbar.
5
In the Ray Trajectories (gop) toolbar, click  Plot. Compare the resulting plot to Figure 2.
Create a plot to display the angle of incidence of the reflected rays as a function of the angle of the incident rays with respect to the boundary normal. Use the at operator to get the angle of incidence at t = 0 s.
Acute Angle of Incidence
1
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
2
In the Settings window for 1D Plot Group, type Acute Angle of Incidence in the Label text field.
3
Locate the Data section. From the Dataset list, choose Ray 1.
4
From the Time selection list, choose Last.
Ray 1
1
In the Acute Angle of Incidence toolbar, click  More Plots and choose Ray.
2
In the Settings window for Ray, locate the y-Axis Data section.
3
In the Expression text field, type gop.phii.
4
Locate the x-Axis Data section. From the Parameter list, choose Expression.
5
In the Expression text field, type at(0,gop.phii).
Acute Angle of Incidence
1
In the Model Builder window, click Acute Angle of Incidence.
2
In the Settings window for 1D Plot Group, click to expand the Title section.
3
From the Title type list, choose None.
4
Click the  Zoom Extents button in the Graphics toolbar.
5
In the Acute Angle of Incidence toolbar, click  Plot. Compare the resulting plot to Figure 3.