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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 -

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

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