Opto-Mechanical Systems Design, Volume 2

Design and Analysis of Large Mirrors and Structures

Paul Yoder, Daniel Vukobratovich, Paul Yoder, Daniel Vukobratovich

• Publisher: CRC Press
• Year: 2017
• ISBN:
  9781351830942
• Edition: 4
• Topic: Physical Sciences
• Subtopic: Mechanics

Opto-Mechanical Systems Design, Fourth Edition is different in many ways from its three earlier editions: coauthor Daniel Vukobratovich has brought his broad expertise in materials, opto-mechanical design, analysis of optical instruments, large mirrors, and structures to bear throughout the book; Jan Nijenhuis has contributed a comprehensive new chapter on kinematics and applications of flexures; and several other experts in special aspects of opto-mechanics have contributed portions of other chapters. An expanded feature—a total of 110 worked-out design examples—has been added to several chapters to show how the theory, equations, and analytical methods can be applied by the reader. Finally, the extended text, new illustrations, new tables of data, and new references have warranted publication of this work in the form of two separate but closely entwined volumes.

This second volume, Design and Analysis of Large Mirrors and Structures, concentrates on the design and mounting of significantly larger optics and their structures, including a new and important topic: detailed consideration of factors affecting large mirror performance. The book details how to design and fabricate very large single-substrate, segmented, and lightweight mirrors; describes mountings for large mirrors with their optical axes in vertical, horizontal, and variable orientations; indicates how metal and composite mirrors differ from ones made of glass; explains key design aspects of optical instrument structural design; and takes a look at an emerging technology—the evolution and applications of silicon and silicon carbide in mirrors and other types of components for optical applications.

1

Factors Affecting Mirror Performance

Daniel Vukobratovich

CONTENTS

1.1 Introduction and Summary

1.2 Tolerances, Error Budgets, and Superposition

1.3 Gravity Deflections

1.4 Mirror Deformations from Shear Effects

1.5 Mirror Deformations from Mounting Effects

1.6 Mirror Deformations from Dynamic Effects

1.7 Fundamental Frequencies

1.7.1 Drumhead Frequency of a Vertical-Axis Mirror

1.7.2 Rigid Body Fundamental Frequencies of an Axisymmetric Mirror

1.7.3 Damping

1.8 Rigid Body Response to Dynamic Excitation

1.8.1 Displacement

1.8.2 Response to Random Vibration

1.8.3 Response to Mechanical Shock

1.9 Thermal Effects

1.9.1 Uniform Change in Temperature

1.9.2 Temperature Gradients

1.9.3 Anisotropy of Coefficient of Thermal Expansion

1.9.4 Bimetallic Bending Effects

References

1.1 Introduction and Summary

The most important performance specifications for a mirror are associated with the shape, that is, optical figure, and position of its reflecting surface at all operational orientations relative to gravity. Secondary specifications include cost, weight, material availability, maintainability, and technical risk. Design of a mirror and its mount involves balancing performance with these and other considerations, such as pertinent environmental influences. Simple approximate closed-form solutions are a useful means for rapidly evaluating performance during conceptual design. Following the selection of conceptual designs, more detailed analysis methods, such as the finite element method, can be used to predict performance more accurately.

In this chapter, we consider the establishment and application of tolerances on various possible errors, such as gravitational effects, mounting influences, dynamic influences, and thermal effects on mirror performance. The combined effect of these on mirror performance is represented by an error budget. Numerical examples are presented to illustrate the application of performance estimation techniques.

1.2 Tolerances, Error Budgets, and Superposition

Mirror optical performance is defined in terms of two tolerances: optical figure and position. The optical figure tolerance determines the allowable deviation from the ideal form of the mirror. The position tolerance determines the location and orientation of the mirror surface with respect to the optical axis of the optical system as well as to other components of that system. The optical figure of the mirror is influenced by the mirror material, its shape, and method of mounting, as well as environmental factors, including temperature. The mirror mounting controls the location of the mirror and is affected by dynamic effects such as mechanical shock and vibration as well as the specified service environment.

A variety of factors influence the optical figure of the mirror. Included are self-weight, excitation from vibration, temperature changes, temperature gradients, and dimensional instability. Normally, the deflections of a mirror from all such causes are small, on the order of 10⁻⁶ of the mirror diameter. These deflections then are well within the linear part of the stress–strain curve, so the mirror material functions within its linear range. It is, therefore, possible to deal with each source of deflection independently and to add all deflections together using the principle of superposition. It is also assumed that the deflections are not correlated. In this case, the overall deflection can be defined as the root-sum-square (rss) of all deflections.

If the mirror optical surface deflections are measured at a series of points, as is...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Preface to the Fourth Edition (2015)
• Preface to the Third Edition (2006)
• Preface to the Second Edition (1993)
• Preface to the First Edition (1986)
• Editors
• Contributors
• 1. Factors Affecting Mirror Performance
• 2. Large Mirror Design
• 3. Mounting Large, Horizontal-Axis Mirrors
• 4. Mounting Large, Vertical-Axis Mirrors
• 5. Mounting Large, Variable-Orientation Mirrors
• 6. Design and Mounting of Metallic Mirrors
• 7. Optical Instrument Structural Design
• 8. Emerging Mirror Technologies
• Glossary
• Units and Conversions
• Index