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Spie Press Book

Design and Mounting of Prisms and Small Mirrors in Optical Instruments
Author(s): Paul R. Yoder Jr.
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Book Description

This Tutorial Text examines the various ways in which prisms and small mirrors typically are designed and mounted in optical instruments. It provides analytical tools for evaluating different designs and discusses advantages and disadvantages of various techniques. The book, in part, is an outgrowth of SPIE short courses taught by the author and is a companion to his 1995 volume, 'Mounting Lenses in Optical Instruments' (SPIE PRESS Vol. TT21). The book is intended for engineers, designers, technicians, and other practitioners in the fields of optical engineering and optomechanical design.

Book Details

Date Published: 16 July 1998
Pages: 268
ISBN: 9780819429407
Volume: TT32

Table of Contents
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Preface iii
1. Introduction 1
1.1 Applications of prisms and mirrors 1
1.2 Environmental considerations 2
1.2.1 Temperature 3
1.2.2 Pressure 3
1.2.3 Vibration and shock 4
1.2.4 Other environmental conditions 5
1.3 Materials properties 6
1.3.1 Optical glasses 7
1.3.2 Optical plastics 7
1.3.3 Optical crystals 10
1.3.4 Mirrors 10
1.3.5 Materials for mechanical components 10
1.3.6 Adhesives and sealants 12
2. Attributes of the Successful Optic-to-Mount Interface 14
2.1 Mechanical constraints 14
2.2 Consequences of mounting forces 17
2.3 Cost and manufacturability 18
3. Prism Design 19
3.1 Geometric considerations 19
3.1.1 Refraction and reflection 19
3.1.2 Total internal reflection 25
3.2 Prism aberration contributions 27
3.3 Typical prism configurations 27
3.3.1 Right angle prism 28
3.3.2 Beamsplitter (beamcombiner) cube prism 28
3.3.3 Amici prism 28
3.3.4 Porro prism 28
3.3.5 Abbe version of the Porro prism 30
3.3.6 Rhomboid prism 30
3.3.7 Porro erecting system 34
3.3.8 Abbe erecting system 34
3.3.9 Penta prism 34
3.3.10 Roof penta prism 35
3.3.11 Amici/penta erecting system 35
3.3.12 Dove prism 36
3.3.13 Double Dove prism 37
3.3.14 Reversion prism 41
3.3.15 Pechan prism 41
3.3.16 Delta prism 42
3.3.17 Schmidt prism 43
3.3.18 45o Bauernfeind prism 44
3.3.19 Internally reflecting axicon prism 44
3.3.20 Cube corner prism 45
3.3.21 Biocular prism system 47
3.3.22 Dispersing prisms 48
3.3.23 Thin wedge prisms 51
3.3.24 Risley wedge system 52
3.3.25 Sliding wedge 53
3.3.26 Focus-adjusting wedge system 54
3.3.27 Anamorphic prism systems 56
4. Prism Mounting Techniques 58
4.1 Semi-kinematic mountings 58
4.2 Mechanically clamped non-kinematic mountings 62
4.3 Bonded prism mountings 68
4.3.1 General considerations 68
4.3.2 Cantilevered techniques 70
4.3.3 Double-sided support techniques 71
4.4 Flexure mounts for prisms 76
5. Estimation of Contact Stresses in Prisms 79
5.1 Compressive stress in clamped prisms 79
5.1.1 Constraint with multiple cantilevered leaf springs 79
5.1.2 Constraint with one leaf spring clamped at both ends 85
5.1.3 Contact stress with curved interfaces 86
5.1.4 Contact stress at prism locating pads 90
5.1.5 Spring-loading prisms through non-rigid pads 90
5.2 Tensile stress in the single-sided bonded interface 92
6. Small Mirror Design 95
6.1 First- and second-surface mirrors 95
6.2 Mirror aperture determination 98
6.3 Weight reduction techniques 101
6.3.1 Contoured-back configurations 101
6.3.2 Machined and built-up structural configurations 111
6.4 Metallic mirrors 115
6.5 Pellicles 121
7. Small Mirror Mounting Techniques 125
7.1 Mechanically clamped mirror mountings 125
7.2 Bonded mirror mountings 134
7.3 Multiple mirror mountings 136
7.4 Flexure mountings for mirrors 142
7.5 Center-mounts for circular-aperture mirrors 144
7.6 Mounting metal mirrors 146
7.7 Gravitational effects on small mirrors 150
8. Estimation of Contact Stresses in Small Mirrors 156
8.1 Compressive stress in axially clamped mirrors 156
8.1.1 Line contact around the mirror edge 156
8.1.2 Local area contacts on a mirror bevel 162
8.1.3 Contact stress at mirror axial locating pads 166
8.1.4 Stress in spring clips 166
8.2 Radial stresses in rim-mounted mirrors 167
8.2.1 Radial stress in a mirror at low temperature 167
8.2.2 Tangential (hoop) stress in the mount wall 168
8.2.3 Growth of radial clearance at increased temperatures 169
8.3 Bending stresses in mirrors 170
8.3.1 Causes of bending 170
8.3.2 Bending stress in the mirror 170
8.3.3 Surface sag of a bent mirror 172
8.4 Stresses in bonded mirrors 173
9. Descriptions of Hardware Examples 175
9.1 Clamped penta prism 175
9.1.1 Constraint perpendicular to the plane of reflection 175
9.1.2 Constraint in the plane of reflection 176
9.2 Bonded Porro prism erecting system for a binocular 178
9.3 Large flexure-mounted mirror assembly for a microlithography
mask projection system 181
9.4 Mounting for large prisms in the Keck II Echellette
Spectrograph/Imager (ESI) 183
9.5 Mountings for prisms in an articulated telescope 188
9.6 Mounting for the GOES telescope secondary mirror 192
9.7 Mounting for the FUSE spectrograph gratings 193
9.8 Mounting for the IRAS cryogenic beryllium mirror 197
Appendix A - Pertinent Unit Conversion Factors 201
Appendix B1 - Extreme Service Environments 202
Appendix B2 - Vibration Power Spectral Densities 203
Appendix C - Selected Mechanical Properties of Materials 204
References 241
Index 247


This tutorial text is intended to provide practitioners in the fields of optical engineering and optomechanical design with a comprehensive understanding of several different ways in which prisms and small mirrors typically are designed and mounted in optical instruments, the advantages and disadvantages of these various mounting arrangements, and some analytical tools that can be used to evaluate and compare different designs. The presentation does not include the theoretical background for these tools, but does cite the sources for the equations listed. Each section contains an illustrated discussion of the technology involved and, wherever feasible, one or more worked-out practical examples.

The text is based, in part, on short courses on Precision Optical Component Mounting Techniques offered by SPIE--The International Society for Optical Engineering, that I have had the privilege of teaching over a period of years. Techniques for mounting lenses which also are covered in those courses are discussed in another tutorial text Mounting Lenses in Optical Instruments published as TT21 in 1995 by the SPIE Press. Because of page limitations, the mirrors considered here have major dimensions no larger than about 24 in. (61 cm). Much of the material included here is applicable to any sized mirrors, but the treatment of those topics in the context of larger sized optics is not comprehensive. In depth tutorial treatment of the design and mounting of larger mirrors would make a useful future contribution by some ambitious author.

The designs discussed here are drawn from the literature, my own experiences in optical instrument design and development, and the works of colleagues. I acknowledge the contributions of others with my deepest thanks and sincerely hope that I have accurately recorded and explained the information given to me. I further acknowledge and thank Robert Ginsberg, Alson Hatheway, and Donald O'Shea who reviewed this book in its preliminary form and offered many valuable suggestions for improvements.

The mounting stress theories discussed in Chapters 5 and 8 have not previously been covered explicitly to this depth in the literature and can only be considered as approximations. These theories would benefit from further investigation and refinement based on more precise computational methods such as finite element analysis. Comments, corrections, and suggestions for improvements in the presentations of these topics or in any other portion of this book would be welcomed.

I wish for the readers of this book a deepening understanding of the technologies discussed and success in the application of the concepts, designs, and analytical techniques presented here.

Paul R. Yoder, Jr.
Norwalk, Connecticut
June 1998

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