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Title: Using geometric algebra to understand pattern rotations in multiple mirror optical systems

Abstract

Geometric Algebra (GA) is a new formulation of Clifford Algebra that includes vector analysis without notation changes. Most applications of Ga have been in theoretical physics, but GA is also a very good analysis tool for engineering. As an example, the authors use GA to study pattern rotation in optical systems with multiple mirror reflections. The common ways to analyze pattern rotations are to use rotation matrices or optical ray trace codes, but these are often inconvenient. The authors use GA to develop a simple expression for pattern rotation that is useful for designing or tolerancing pattern rotations in a multiple mirror optical system by inspection. Pattern rotation is used in many optical engineering systems, but it is not normally covered in optical system engineering texts. Pattern rotation is important in optical systems such as: (1) the 192 beam National ignition Facility (NIF), which uses square laser beams in close packed arrays to cut costs; (2) visual optical systems, which use pattern rotation to present the image to the observer in the appropriate orientation, and (3) the UR90 unstable ring resonator, which uses pattern rotation to fill a rectangular laser gain region and provide a filled-in laser output beam.

Authors:
;
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Assistant Secretary for Human Resources and Administration, Washington, DC (United States)
OSTI Identifier:
468622
Report Number(s):
LA-UR-97-721
ON: DE97005051; TRN: 97:010303
DOE Contract Number:  
AC02-94CE50390
Resource Type:
Technical Report
Resource Relation:
Other Information: PBD: [1997]
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION; 99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; OPTICAL SYSTEMS; ICF DEVICES; ALGEBRA; LASERS; BEAM OPTICS; VECTORS; MIRRORS

Citation Formats

Hanlon, J, and Ziock, H. Using geometric algebra to understand pattern rotations in multiple mirror optical systems. United States: N. p., 1997. Web. doi:10.2172/468622.
Hanlon, J, & Ziock, H. Using geometric algebra to understand pattern rotations in multiple mirror optical systems. United States. https://doi.org/10.2172/468622
Hanlon, J, and Ziock, H. 1997. "Using geometric algebra to understand pattern rotations in multiple mirror optical systems". United States. https://doi.org/10.2172/468622. https://www.osti.gov/servlets/purl/468622.
@article{osti_468622,
title = {Using geometric algebra to understand pattern rotations in multiple mirror optical systems},
author = {Hanlon, J and Ziock, H},
abstractNote = {Geometric Algebra (GA) is a new formulation of Clifford Algebra that includes vector analysis without notation changes. Most applications of Ga have been in theoretical physics, but GA is also a very good analysis tool for engineering. As an example, the authors use GA to study pattern rotation in optical systems with multiple mirror reflections. The common ways to analyze pattern rotations are to use rotation matrices or optical ray trace codes, but these are often inconvenient. The authors use GA to develop a simple expression for pattern rotation that is useful for designing or tolerancing pattern rotations in a multiple mirror optical system by inspection. Pattern rotation is used in many optical engineering systems, but it is not normally covered in optical system engineering texts. Pattern rotation is important in optical systems such as: (1) the 192 beam National ignition Facility (NIF), which uses square laser beams in close packed arrays to cut costs; (2) visual optical systems, which use pattern rotation to present the image to the observer in the appropriate orientation, and (3) the UR90 unstable ring resonator, which uses pattern rotation to fill a rectangular laser gain region and provide a filled-in laser output beam.},
doi = {10.2172/468622},
url = {https://www.osti.gov/biblio/468622}, journal = {},
number = ,
volume = ,
place = {United States},
year = {1997},
month = {5}
}