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3D Reflection from a Mirror
Expressions for the direction of the reflected
ray and points on the reflected beam path.
January 2021
Index
Overview ........................................................................................................ 3
Reflection from a Surface, in Local Coordinates ............................................ 4
Defining Global Coordinate System and Rotation Conventions .................... 6
Calculating a Reflected Ray's Global Coordinates ........................................ 8
- Rotation Matrices ...................................................................................... 9
- Rotation Order Matters, Since Rotations do not Commute ....................... 11
- Steps of the Procedure .............................................................................. 13
Selected Cases of Rotating a Mounted Mirror
- Example 1: Mount Adjusters Used to Tune both Pitch and Yaw ................ 14
- Example 2: Post Rotation Used for Yaw, Mount Adjuster for Pitch ............ 29
Page 2 -
Tracing the Reflected Beam Path
Each mirror in a setup has its own,
independently adjustable, angular orientation.
The beam path depends on each mirror's
orientation.
Defining a fixed (global) coordinate system for
the setup is useful for tracing the beam path
through the setup. Figure 1. The beam path reflected
by these two mirrors depends on
However, it is simplest to calculate the direction their orientations with respect to one
of the reflected beam when working in the local another.
coordinate system of the reflective surface.
Therefore, both local and global coordinate systems are often used, and it is
necessary to convert between them.
Page 3 -
Pdf INFO
Title: 3D Reflection from a Mirror
Subject: 3D rotation matrices used to calculate the direction and the path of a vector reflected from a mirror. Examples included.
Keywords: 3D, reflection matrix, pitch and yaw rotation matrices, reflected vector, reflection from a mirror, matrix algebra, mirror matrices, beam walk, steering mirrors, mirror separation, points on reflected vector, direction of reflected vector,
Author: Thorlabs
Creator: Microsoft® PowerPoint® for Office 365
Producer: Microsoft® PowerPoint® for Office 365
CreationDate: Wed Jan 6 13:54:42 2021
ModDate: Tue Apr 6 19:14:32 2021
Tagged: yes
Form: none
Pages: 40
Encrypted: no
Page size: 720 x 405 pts (rotated 0 degrees)
File size: 717655 bytes
Optimized: yes
PDF version: 1.7
