chapter 3, Sensitivities and Tolerances

from: Matrix Methods for Optical Layout

Author(s): Gerhard Kloos

Published: 21 August 2007

Chapter DOI: http://dx.doi.org/10.1117/3.737850.ch3

Chapter Page Count: 5 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

3.1 Cascading Misaligned Systems
3.2 Axial Misalignment
3.3 Beam Pointing Error

Excerpt

The analysis of the sensitivity of an optical system with respect to misadjustment is an important part of the optical design. The matrix method provides useful tools to study tilt, decentering, defocusing, and beam pointing error in a systematic way.

We will start with a simple example and consider the surface in Fig. 3.1 that separates two media with different indices of refraction. The surface is slightly tilted at an angle γ. From Eq. (1.17), we know how the situation without tilt is described by a matrix. The question is now how this relation has to be modified to incorporate the effect of tilt.

Starting with the linearized form of the law of refraction, we find from Fig. 3.1 that

Solving this equation for β⁽²⁾ and taking into account that the distance of the ray is not changed in the reference plane, this can be expressed as follows: