Jump to Content
Your Recent History
View Cart
SUBSCRIPTIONS & PRICING
GENERAL INFORMATION
chapter 1, An Introduction to Tools and Concepts
Table of Contents
- 6. Outlook
Chapter Contents
- 1.1 Matrix Method
- 1.2 Basic Elements
- 1.2.1 Propagation in a homogeneous medium
- 1.2.2 Refraction at the boundary of two media
- 1.2.3 Reflection at a surface
- 1.3 Comparison of Matrix Representations Used in the Literature
- 1.4 Building up a Lens
- 1.5 Cardinal Elements
- 1.6 Using Matrices for Optical-Layout Purposes
- 1.7 Lens Doublet
- 1.8 Decomposition of Matrices and System Synthesis
- 1.9 Central Theorem of First-Order Ray Tracing
- 1.10 Aperture Stop and Field Stop
- 1.11 Lagrange Invariant
- 1.11.1 Derivation using the matrix method
- 1.11.2 Application to optical design
- 1.12 Petzval Radius
- 1.13 Delano Diagram
- 1.14 Phase Space
- 1.15 An Alternative Paraxial Calculation Method
- 1.16 Gaussian Brackets
Excerpt
1.1 Matrix Method
Ray-transfer matrices is one of the possibile methods to describe optical systems in the paraxial approximation. It is widely used for first-order layout and for the purpose of analyzing optical systems (Gerrard and Burch, 1975). The reason why the paraxial approximation is often used in the first phase of a design or of an optical analysis becomes obvious if we have a look at the law of refraction in vectorial form as follows:
is the vector of the ray incident on the interface with the normal 
. This interface separates two homogeneous media with indices of refraction n1 and n2. The refracted ray is described by the vector 
. For optical-layout purposes, we need an explicit expression of this ray in terms of the other quantities because we have to trace the ray through the optical system. Using vector algebra, Eq. (1.1) can be rewritten in the following way: 
It would be a precious tool for analyzing optical instruments if the approximated description would also allow for cascading subsystems to describe a compound system. The method of ray-transfer matrices provides this advantage and cascading of subsystems is performed by matrix multiplication.
Another aspect, which might be sometimes underestimated, is that paraxial descriptions, and especially the matrix method, provide a convenient shorthand notation to communicate and discuss ideas to other optical designers.
©2007 Society of Photo-Optical Instrumentation Engineers
PURCHASE CHAPTER ($US12)
SPIE Digital Library
This Publication
Google Scholar
PubMed