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Lens Design Fundamentals

Second Edition

RUDOLF KINGSLAKE

R. BARRY JOHNSON

Academic Press is an imprint of Elsevier 30 Corporate Drive, Suite 400 Burlington, MA 01803, USA

The Boulevard, Langford Lane

Kidlington, Oxford, OX5 1 GB, UK

Co-published by SPIE

P.O. Box 10

Bellingham, Washington 98227-0010 USA

Tel.: þ1 360-676-3290 / Fax: þ1 360-647-1445

Email: Books@SPIE.org

SPIE ISBN: 9780819479396

SPIE Vol: PM195

No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions.

This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein).

Notices

Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary.

Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility.

To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein.

Library of Congress Cataloging-in-Publication Data

Application submitted.

ISBN: 978-0-12-374301-5

British Library Cataloguing-in-Publication Data

A catalogue record for this book is available from the British Library.

For information on all Academic Press publications visit our Web site at www.elsevierdirect.com

Printed in the United States
09	10	11	12	13	10	9	8	7	6	5	4	3	2	1

To my dearest wife Marianne Faircloth Johnson and our remarkable son Rutherford Barry Johnson for their gentle encouragement and support.

In memory of my parents, J. Ralph and Sara F. Johnson,

for their enduring tolerance of my often trying inquisitiveness.

And

In memory of Rudolf Kingslake (1903–2003),

who taught me to appreciate the beauty in well-designed lenses.

Preface to the Second Edition		ix
Preface to the First Edition		xiii
A Special Tribute to Rudolf Kingslake		xv
Chapter 1 The Work of the Lens Designer		1
1.1	Relations Between Designer and Factory	2
1.2	The Design Procedure	8
1.3	Optical Materials	11
1.4	Interpolation of Refractive Indices	16
1.5	Lens Types to be Considered	20
Chapter 2 Meridional Ray Tracing		25
2.1	Introduction	25
2.2	Graphical Ray Tracing	30
2.3	Trigonometrical Ray Tracing at a Spherical Surface	32
2.4	Some Useful Relations	37
2.5	Cemented Doublet Objective	41
2.6	Ray Tracing at a Tilted Surface	42
2.7	Ray Tracing at an Aspheric Surface	45
Chapter 3 Paraxial Rays and First-Order Optics		51
3.1	Tracing a Paraxial Ray	52
3.2	Magnification and the Lagrange Theorem	63
3.3	The Gaussian Optics of a Lens System	67
3.4	First-Order Layout of an Optical System	78
3.5	Thin-Lens Layout of Zoom Systems	87
Chapter 4 Aberration Theory		101
4.1	Introduction	101
4.2	Symmetrical Optical Systems	101
4.3	Aberration Determination Using Ray Trace Data	114
4.4	Calculation of Seidel Aberration Coefficients	128

Contents			v
Chapter 5	Chromatic Aberration		137
	5.1	Introduction	137
	5.2	Spherochromatism of a Cemented Doublet	139
	5.3	Contribution of a Single Surface to the Primary
		Chromatic Aberration	143
	5.4	Contribution of a Thin Element in a System
		to the Paraxial Chromatic Aberration	145
	5.5	Paraxial Secondary Spectrum	149
	5.6	Predesign of a Thin Three-Lens Apochromat	152
	5.7	The Separated Thin-Lens Achromat (Dialyte)	156
	5.8	Chromatic Aberration Tolerances	162
	5.9	Chromatic Aberration at Finite Aperture	163
Chapter 6	Spherical Aberration		173
	6.1	Surface Contribution Formulas	176
	6.2	Zonal Spherical Aberration	194
	6.3	Primary Spherical Aberration	197
	6.4	The Image Displacement Caused
		by a Planoparallel Plate	204
	6.5	Spherical Aberration Tolerances	206
Chapter 7 Design of a Spherically Corrected Achromat			209
	7.1	The Four-Ray Method	209
	7.2	A Thin-Lens Predesign	211
	7.3	Correction of Zonal Spherical Aberration	216
	7.4	Design of an Apochromatic Objective	220
Chapter 8	Oblique Beams		227
	8.1	Passage of an Oblique Beam through
		a Spherical Surface	227
	8.2	Tracing Oblique Meridional Rays	234
	8.3	Tracing a Skew Ray	238
	8.4	Graphical Representation of Skew-Ray
		Aberrations	243
	8.5	Ray Distribution from a Single Zone
		of a Lens	252
Chapter 9 Coma and the Sine Condition			255
	9.1	The Optical Sine Theorem	255
	9.2	The Abbe Sine Condition	256

vi		Contents
9.3 Offense Against the Sine Condition		258
9.4 Illustration of Comatic Error		266
Chapter 10 Design of Aplanatic Objectives		269
10.1	Broken-Contact Type	269
10.2	Parallel Air-Space Type	272
10.3	An Aplanatic Cemented Doublet	275
10.4	A Triple Cemented Aplanat	277
10.5	An Aplanat with a Buried Achromatizing
	Surface	280
10.6	The Matching Principle	283
Chapter 11 The Oblique Aberrations		289
11.1	Astigmatism and the Coddington Equations	289
11.2	The Petzval Theorem	297
11.3	Illustration of Astigmatic Error	306
11.4	Distortion	306
11.5	Lateral Color	313
11.6	The Symmetrical Principle	316
11.7	Computation of the Seidel Aberrations	318
Chapter 12 Lenses in Which Stop Position Is a Degree
of Freedom		323
12.1	The H0 – L Plot	323
12.2	Simple Landscape Lenses	325
12.3	A Periscopic Lens	331
12.4	Achromatic Landscape Lenses	334
12.5	Achromatic Double Lenses	339
Chapter 13 Symmetrical Double Anastigmats with Fixed Stop		351
13.1	The Design of a Dagor Lens	351
13.2	The Design of an Air-Spaced Dialyte Lens	355
13.3	A Double-Gauss–Type Lens	363
13.4	Double-Gauss Lens with Cemented Triplets	369
13.5	Double-Gauss Lens with Air-spaced Negative
	Doublets	373
Chapter 14 Unsymmetrical Photographic Objectives		379
14.1	The Petzval Portrait Lens	379
14.2	The Design of a Telephoto Lens	388
14.3	Lenses to Change Magnification	397

Contents			vii
	14.4	The Protar Lens	400
	14.5	Design of a Tessar Lens	409
	14.6	The Cooke Triplet Lens	419
Chapter 15 Mirror and Catadioptric Systems			439
	15.1	Comparison of Mirrors and Lenses	439
	15.2	Ray Tracing a Mirror System	440
	15.3	Single-Mirror Systems	442
	15.4	Single-Mirror Catadioptric Systems	447
	15.5	Two-Mirror Systems	471
	15.6	Multiple-Mirror Zoom Systems	482
	15.7	Summary	497
Chapter 16	Eyepiece Design		501
	16.1	Design of a Military-Type Eyepiece	502
	16.2	Design of an Erfle Eyepiece	506
	16.3	Design of a Galilean Viewfinder	510
Chapter 17 Automatic Lens Improvement Programs			513
	17.1	Finding a Lens Design Solution	514
	17.2	Optimization Principles	518
	17.3	Weights and Balancing Aberrations	522
	17.4	Control of Boundary Conditions	523
	17.5	Tolerances	524
	17.6	Program Limitations	525
	17.7	Lens Design Computing Development	525
	17.8	Programs and Books Useful for Automatic
		Lens Design	529
Appendix	A Selected Bibliography of Writings
	by Rudolf Kingslake		535
Index			537

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Lens Design Fundamentals

Contents