chapter 4, Anamorphic Optics

from: Matrix Methods for Optical Layout

Author(s): Gerhard Kloos

Published: 21 August 2007

Chapter DOI: http://dx.doi.org/10.1117/3.737850.ch4

Chapter Page Count: 17 pages

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Front Matter

1. An Introduction to Tools and Concepts

2. Optical Components

3. Sensitivities and Tolerances

4. Anamorphic Optics

5. Optical Systems

6. Outlook

Back Matter

Preview

Chapter Contents

4.1 Two Alternative Matrix Representations
4.2 Orthogonal and Nonorthogonal Anamorphic Descriptions
4.3 Cascading
4.4 Rotation of an Anamorphic Component with Respect to the Optical Axis
4.4.1 Rotation of an “orthogonal” system
4.4.2 Rotation of a “nonorthogonal” system
4.5 Examples
4.5.1 Rotated anamorphic thin lens
4.5.2 Rotated thin cylindrical lens
4.5.3 Cascading two rotated thin cylindrical lenses
4.5.4 Cascading two rotated thin anamorphic lenses
4.5.5 “Quadrupole” lens
4.5.6 Telescope built by cylindrical lenses
4.5.7 Anamorphic collimation lens
4.6 Imaging Condition
4.7 Incorporating Sensitivities and Tolerances in the Analysis

Excerpt

Most of the examples treated until now featured symmetry with respect to the optical axis and it was sufficient to consider a projection onto the y-z plane to find the system matrix. But there are many optical systems that are not symmetric with respect to the optical axis. In those cases, it is necessary to use an extended form of the matrix method.

4.1 Two Alternative Matrix Representations

The generalization is straightforward and leads to a 4 × 4 matrix description. There are two ways to state the corresponding matrices, namely,

The second form has the advantage that algebraic commutation relations are fulfilled between the matrices A, B, C, and D and that it allows for a generalization of the determinant relation known from 2 × 2 ray matrices with determinant 1 (Siegman, 1986, p. 618).

The first form reduces to the following partitioned matrix if there is no coupling between the two orthogonal planes:

In the case of rotation symmetry, M and N would be equal. In the case of some illumination devices such as headlamps, for example, they can be rather different.

http://dx.doi.org/10.1117/3.737850.ch4

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