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  • Ilmumisaeg: 19-Dec-2017
  • Kirjastus: CRC Press Inc
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Handbook of Optical Design, Third Edition covers the fundamental principles of geometric optics and their application to lens design in one volume. It incorporates classic aspects of lens design along with important modern methods, tools, and instruments, including contemporary astronomical telescopes, Gaussian beams, and computer lens design. Written by respected researchers, the book has been extensively classroom-tested and developed in their lens design courses.

This well-illustrated handbook clearly and concisely explains the intricacies of optical system design and evaluation. It also discusses component selection, optimization, and integration for the development of effective optical apparatus. The authors analyze the performance of a wide range of optical materials, components, and systems, from simple magnifiers to complex lenses used in photography, ophthalmology, telescopes, microscopes, and projection systems. Throughout, the book includes a wealth of design examples, illustrations, and equations, most of which are derived from basic principles. Appendices supply additional background information.

Whats New in This Edition





Improved figures, including 32 now in color Updates throughout, reflecting advances in the field New material on Buchdahl high-order aberrations Expanded and improved coverage of the calculation of wavefront aberrations based on optical path An updated list of optical materials in the appendix A clearer, more detailed description of primary aberrations References to important new publications Optical system design examples updated to include newly available glasses 25 new design examples

This comprehensive book combines basic theory and practical details for the design of optical systems. It is an invaluable reference for optical students as well as scientists and engineers working with optical instrumentation.

Arvustused

"An excellent update to an excellent book. A comprehensive handbook on optical design and geometrical optics that covers the basic theory as well as practical details." James C. Wyant, College of Optical Sciences, University of Arizona, USA

"Even with modern 'easy-to-use' lens design software and global optimization, the understanding of aberration theory is essential to finding high-performing cost-effective design solutions. This book not only teaches the students the basics of aberration theory but adds in the needed understanding of higher order aberrations for modern optical systems. The chapter on wavefront aberrations and Zernike polynomials has been greatly improved and follows a notation becoming a standard in the industry." Dr. Julie L. Bentley, University of Rochester, New York, USA

"This is a new edition of a book that has been used in the course of lens design by the authors for many years. So it covers many aspects of optics taking in the progress in the individual field. Also the authors are trying to make the students of the course changing the order of materials as well as adding new ones."Kyoji Nariai, National Astronomical Observatory of Japan, Mitaka, Tokyo

Praise for Previous Editions

"Many helpful references are given at the end of each chapter and the appendices, and these have been expanded from the first edition. Overall, the changes made in this edition have enhanced the book's value as an important reference for the optics community." Optics and Photonics News, Feb. 2006

" the book makes liberal use of figures and diagrams, and covers both the basic principles of geometrical optics as well as their application to lens design. this book is recommended for academic libraries with active programs in optical engineering, and certainly for libraries owning well-used copies of the first edition." E-Streams, Vol. 7, No. 5, May 2004

"I found the book to be well presented and easy to read. For those interested in optical systems, this is a useful book to have on hand." The Physicist, Vol. 41, No. 2, March/April 2004

"Not only the basic theory is treated in this book, but many practical details for the design of important optical systems are given. [ A] book which is important and helpful and should not be missed in any optical laboratory." Optik-International Journal for Light and Electron Optics, Vol. 115, No. 10, 2004 "An excellent update to an excellent book. A comprehensive handbook on optical design and geometrical optics that covers the basic theory as well as practical details." James C. Wyant, College of Optical Sciences, University of Arizona, USA

"Even with modern 'easy-to-use' lens design software and global optimization, the understanding of aberration theory is essential to finding high-performing cost-effective design solutions. This book not only teaches the students the basics of aberration theory but adds in the needed understanding of higher order aberrations for modern optical systems. The chapter on wavefront aberrations and Zernike polynomials has been greatly improved and follows a notation becoming a standard in the industry."Dr. Julie L. Bentley, University of Rochester, New York, USA

"This is a new edition of a book that has been used in the course of lens design by the authors for many years. So it covers many aspects of optics taking in the progress in the individual field. Also the authors are trying to make the students of the course changing the order of materials as well as adding new ones."Kyoji Nariai, National Astronomical Observatory of Japan, Mitaka, Tokyo

Praise for Previous Editions







"Many helpful references are given at the end of each chapter and the appendices, and these have been expanded from the first edition. Overall, the changes made in this edition have enhanced the book's value as an important reference for the optics community."Optics and Photonics News, Feb. 2006



" the book makes liberal use of figures and diagrams, and covers both the basic principles of geometrical optics as well as their application to lens design. this book is recommended for academic libraries with active programs in optical engineering, and certainly for libraries owning well-used copies of the first edition."

E-Streams, Vol. 7, No. 5, May 2004"I found the book to be well presented and easy to read. For those interested in optical systems, this is a useful book to have on hand."The Physicist, Vol. 41, No. 2, March/April 2004

"Not only the basic theory is treated in this book, but many practical details for the design of important optical systems are given. [ A] book which is important and helpful and should not be missed in any optical laboratory."Optik-International Journal for Light and Electron Optics, Vol. 115, No. 10, 2004

Preface to the Third Edition xv
Preface to the Second Edition xvii
Preface to the First Edition xix
Chapter 1 Geometrical Optics Principles
1(34)
1.1 Wave Nature of Light and Fermat's Principle
1(7)
1.1.1 Gradient Index of Refraction
7(1)
1.2 Reflection and Refraction Laws
8(3)
1.2.1 Reflection Laws
8(1)
1.2.2 Refraction Laws
9(1)
1.2.3 Vectorial Form of Refraction Laws
10(1)
1.3 Basic Meridional Ray Tracing Equations
11(5)
1.3.1 Meridional Ray Tracing by the L-U Method
15(1)
1.3.2 Meridional Ray Tracing by the Q-U Method
15(1)
1.4 Gaussian or First-Order Optics
16(4)
1.4.1 Paraxial Ray Tracing by y-nu Method and Matrix Ray Tracing
19(1)
1.5 Image Formation
20(2)
1.6 Stop, Pupils, and Principal Ray
22(4)
1.6.1 Telecentric Systems
25(1)
1.7 Delano's Relation
26(1)
1.8 Optical Sine Theorem
27(2)
1.9 Lagrange Invariant
29(2)
1.10 Herschel Invariant and Image Magnifications
31(4)
References
33(2)
Chapter 2 Thin Lenses and Spherical Mirrors
35(8)
2.1 Thin Lenses
35(3)
2.2 Formulas for Image Formation with Thin Lenses
38(1)
2.3 Nodal Points of a Thin Lens
39(2)
2.4 Image Formation with Converging Lenses
41(1)
2.5 Image Formation with Diverging Lenses
42(1)
References
42(1)
Chapter 3 Systems of Several Lenses and Thick Lenses
43(22)
3.1 Focal Length and Power of a Lens System
43(2)
3.2 Image Formation with Thick Lenses or Systems of Lenses
45(1)
3.3 Cardinal Points
46(3)
3.4 Image Formation with a Tilted or Curved Object
49(2)
3.5 Thick Lenses
51(3)
3.6 Systems of Thin Lenses
54(1)
3.7 The Lagrange Invariant in a System of Thin Lenses
55(2)
3.8 Effect of Object or Stop Shifting
57(2)
3.8.1 Shifting the Stop
57(1)
3.8.2 Shifting Object and Image Planes
58(1)
3.9 The Delano y - y Diagram
59(6)
3.9.1 A Shift of the Stop
62(1)
3.9.2 A Shift of the Object and Image
62(1)
References
63(2)
Chapter 4 Chromatic Aberrations
65(24)
4.1 Introduction
65(1)
4.2 Axial Chromatic Aberration
66(9)
4.2.1 Axial Chromatic Aberration of a Thin Lens
68(1)
4.2.2 Achromatic Doublet
69(2)
4.2.3 Achromatic Doublet with Separated Elements
71(1)
4.2.4 Axial Chromatic Aberration Correction with One Glass
72(2)
4.2.5 Spherochromatism
74(1)
4.3 Conrady's D-d Method of Achromatization
75(2)
4.4 Secondary Color Aberration
77(2)
4.4.1 Apochromatic Triplet
78(1)
4.5 Magnification Chromatic Aberration
79(10)
4.5.1 Stop Shift Equations for Chromatic Aberrations
82(1)
4.5.2 Correction of the Magnification Chromatic Aberration
83(1)
4.5.3 Magnification Chromatic Aberration Correction with One Glass
84(3)
References
87(2)
Chapter 5 Spherical Aberration
89(28)
5.1 Spherical Aberration Calculation
89(4)
5.2 Primary Spherical Aberration
93(9)
5.2.1 Spherical Aberration of a Thin Lens
96(4)
5.2.2 A System of Thin Lenses
100(1)
5.2.3 Spherical Aberration for a Plane-Parallel Plate in Converging Light
101(1)
5.3 Aspherical Surfaces
102(1)
5.4 Spherical Aberration of Aspherical Surfaces
102(1)
5.5 Surfaces without Spherical Aberration
103(3)
5.5.1 Refractive Spherical Surfaces
103(1)
5.5.2 Reflective Conic Surfaces
104(1)
5.5.3 Descartes' Ovoid
105(1)
5.6 Aberration Polynomial for Spherical Aberration
106(5)
5.6.1 Caustic
108(3)
5.7 High-Order Spherical Aberration
111(3)
5.7.1 Aberration Balancing
113(1)
5.8 Spherical Aberration Correction with Gradient Index
114(3)
References
116(1)
Chapter 6 Monochromatic Off-Axis Aberrations
117(42)
6.1 Introduction
117(7)
6.1.1 Introduction to Off-Axis Aberrations
118(1)
6.1.2 Oblique Rays
119(4)
6.1.3 Off-Axis Aberrations Definitions
123(1)
6.2 Petzval Curvature
124(2)
6.3 Coma
126(5)
6.3.1 Offense against the Sine Condition
126(2)
6.3.2 Coma Contribution of Each Surface
128(2)
6.3.3 Coma in a Single Thin Lens
130(1)
6.4 Astigmatism
131(12)
6.4.1 Coddington Equations
133(1)
6.4.1.1 Tangential Image
133(1)
6.4.1.2 Sagittal Image
134(1)
6.4.1.3 General Expression
135(1)
6.4.2 Relations between Petzval Curvature and Astigmatism
136(3)
6.4.3 Comatic and Astigmatic Images
139(4)
6.5 Aplanatic Surfaces
143(2)
6.5.1 Aplanatic Refractive Spherical Surfaces
144(1)
6.5.2 Aplanatic Wassermann-Wolf Surfaces
145(1)
6.6 Distortion
145(3)
6.7 Off-Axis Aberrations in Aspherical Surfaces
148(3)
6.8 The Symmetrical Principle and the Bow-Sutton Conditions
151(1)
6.9 Stop Shift Equations
152(3)
6.10 Aberrations of the Pupil
155(4)
References
156(3)
Chapter 7 Aberration Polynomials and High-Order Aberrations
159(40)
7.1 Wavefronts in an Optical System
159(1)
7.2 Ray Aberrations and Wavefront Aberrations
159(2)
7.3 Wavefront Aberration Polynomial
161(14)
7.3.1 H. H. Hopkins Wavefront Aberration Polynomial for Centered Systems
163(2)
7.3.2 Kingslake Wavefront Aberration Polynomial for Centered Systems
165(2)
7.3.3 Seidel Wavefront Aberration Polynomial for Centered Systems
167(1)
7.3.4 High-Order Buchdahl Aberration Polynomials for Centered Systems
168(5)
7.3.5 Wavefront Aberration Polynomials for Noncentered and Asymmetric Systems
173(2)
7.4 Zernike Polynomials
175(5)
7.5 Fitting of Wavefront Deformations to a Polynomial
180(1)
7.6 Wavefront Representation by an Array of Gaussians
181(3)
7.7 Wavefront Aberrations in Refractive Surfaces
184(7)
7.7.1 Analysis of the Optical Path Difference Equation
186(5)
7.8 Wavefront Aberrations in Reflective Surfaces
191(4)
7.9 Aldis Theorem
195(4)
References
195(4)
Chapter 8 Computer Evaluation of Optical Systems
199(30)
8.1 Transverse Aberration Polynomials
199(7)
8.1.1 Axial, Tangential, and Sagittal Plots
200(1)
8.1.1.1 Axial Plots
201(1)
8.1.1.2 Tangential Plots
202(2)
8.1.1.3 Sagittal Plots
204(2)
8.2 Transverse Aberrations with H. H. Hopkins, Seidel, and Buchdahl Coefficients
206(4)
8.2.1 Transverse Aberrations and Ray Plots with Buchdahl Coefficients
206(1)
8.2.1.1 Spherical Aberration
206(1)
8.2.1.2 Coma
207(1)
8.2.1.3 Astigmatism
207(1)
8.2.1.4 Distortion
208(2)
8.3 Meridional Ray Tracing and Stop Position Analysis
210(1)
8.4 Spot Diagram
211(5)
8.4.1 Geometrical Spot Size
212(4)
8.4.2 Radial Energy Distribution
216(1)
8.5 Wavefront Deformation
216(6)
8.5.1 Calculation from Transverse Aberrations Data
217(1)
8.5.2 Direct Calculation of the Optical Path
217(3)
8.5.3 Conrady's Method to Compute Wavefront Deformations
220(2)
8.6 Point and Line Spread Function
222(2)
8.7 Optical Transfer Function
224(2)
8.7.1 Geometrical Optical Transfer Function
224(2)
8.8 Tolerance to Aberrations
226(3)
8.8.1 Curvature and Thickness Tolerances
226(1)
References
227(2)
Chapter 9 Diffraction in Optical Systems
229(24)
9.1 Huygens-Fresnel Theory
229(1)
9.2 Fresnel Diffraction
229(4)
9.3 Fraunhofer Diffraction
233(5)
9.3.1 Circular Aperture
235(2)
9.3.2 Annular Aperture
237(1)
9.4 Diffraction Images with Aberrations
238(1)
9.5 Strehl Ratio
239(2)
9.6 Optical Transfer Function
241(4)
9.6.1 OTF and Strehl Ratio
245(1)
9.7 Resolution Criteria
245(2)
9.8 Gaussian Beams
247(6)
9.8.1 Focusing and Collimating a Gaussian Beam
249(1)
References
250(3)
Chapter 10 Prisms
253(20)
10.1 Tunnel Diagram
253(1)
10.2 Deflecting a Light Beam
253(3)
10.3 Transforming an Image
256(1)
10.4 Deflecting and Transforming Prisms
257(4)
10.4.1 Deflecting Prisms
257(4)
10.4.2 Retroreflecting Systems
261(1)
10.5 Nondeflecting Transforming Prisms
261(4)
10.5.1 Inverting and Reverting Prisms
261(2)
10.5.2 Rotating Prisms
263(2)
10.6 Beam-Splitting Prisms
265(1)
10.7 Chromatic Dispersing Prisms
266(4)
10.7.1 Equilateral Prism
266(2)
10.7.2 Constant-Deviation Prism
268(1)
10.7.3 Nondeflecting Chromatic Dispersing Prism
269(1)
10.8 Nonimaging Prisms
270(3)
References
271(2)
Chapter 11 Basic Optical Systems and Simple Photographic Lenses
273(46)
11.1 Optical Systems Diversity
273(2)
11.2 Magnifiers and Single Imaging Lens
275(8)
11.2.1 Magnifiers
275(3)
11.2.2 Biocular Magnifiers
278(2)
11.2.3 Single Imaging Lens
280(3)
11.3 Landscape Lenses
283(2)
11.4 Periscopic Lens
285(2)
11.5 Achromatic Landscape Lens
287(3)
11.6 Doublets
290(8)
11.6.1 Nonaplanatic Doublet
290(4)
11.6.2 Air-Spaced Doublet
294(3)
11.6.3 Cemented Aplanatic Doublet
297(1)
11.6.4 Apochromatic Lenses
298(1)
11.7 Laser Light Collimators
298(1)
11.8 Spherical and Paraboloidal Mirrors
299(12)
11.8.1 Off-Axis Aberrations of Spherical Mirrors
302(1)
11.8.1.1 Spherical Aberration
302(1)
11.8.1.2 Coma
302(1)
11.8.1.3 Astigmatism
303(1)
11.8.1.4 Petzval Curvature
303(1)
11.8.2 Concave Spherical Mirror
303(1)
11.8.2.1 Spherical Aberration
303(1)
11.8.2.2 Coma
304(1)
11.8.2.3 Astigmatism
304(1)
11.8.2.4 Petzval Curvature
305(1)
11.8.3 Concave Paraboloidal Mirror
306(1)
11.8.3.1 Spherical Aberration
306(1)
11.8.3.2 Coma
307(1)
11.8.3.3 Astigmatism
308(1)
11.8.4 Convex Spherical Mirror
309(2)
11.9 Some Catoptric and Catadioptric Systems
311(3)
11.9.1 Mangin Mirror
311(1)
11.9.2 Dyson System
312(1)
11.9.3 Offner System
313(1)
11.10 F-Theta Lenses
314(1)
11.11 Fresnel Lenses and Gabor Plates
314(5)
References
316(3)
Chapter 12 Complex Photographic Lenses
319(26)
12.1 Introduction
319(1)
12.1.1 Main Parameters in Photographic Lenses
319(1)
12.2 Asymmetrical Systems
320(11)
12.2.1 Petzval Lens
320(1)
12.2.2 Telephoto Lens
321(3)
12.2.3 Cooke Triplet
324(6)
12.2.4 Tessar Lens
330(1)
12.3 Symmetrical Anastigmat Systems
331(5)
12.3.1 Dagor Lens
331(2)
12.3.2 Dialyte Lens
333(1)
12.3.3 Double Gauss Lens
333(3)
12.4 Varifocal and Zoom Lenses
336(9)
References
341(4)
Chapter 13 The Human Eye and Ophthalmic Lenses
345(16)
13.1 The Human Eye
345(3)
13.1.1 Eye Aberrations
347(1)
13.2 Ophthalmic Lenses
348(3)
13.2.1 Ophthalmic Lens Magnifying Power
350(1)
13.3 Ophthalmic Lens Design
351(4)
13.3.1 Tscherning Ellipses
353(2)
13.3.2 Aspheric Ophthalmic Lenses
355(1)
13.4 Prismatic Lenses
355(2)
13.5 Spherocylindrical Lenses
357(4)
References
359(2)
Chapter 14 Astronomical Telescopes
361(40)
14.1 Resolution and Light-Gathering Power
361(3)
14.1.1 Diffraction Effects and Atmospheric Turbulence
361(1)
14.1.2 Visual Limit Magnitude of a Telescope
362(1)
14.1.3 Photographic and CCD Limit Magnitude of a Telescope
363(1)
14.2 Reflecting Two-Mirror Cameras and Telescopes
364(5)
14.2.1 First-Order Design of Two-Mirror Systems
365(3)
14.2.2 Two-Mirror Telescope Light Shields
368(1)
14.3 Catadioptric Cameras
369(9)
14.3.1 Schmidt Camera
369(3)
14.3.2 Bouwers Camera
372(2)
14.3.3 Bouwers-Maksutov Camera
374(1)
14.3.4 Anastigmatic Concentric Schmidt-Cassegrain Cameras
375(1)
14.3.5 Flat-Field Anastigmatic Schmidt-Cassegrain Cameras
376(2)
14.4 Astronomical Telescopes
378(13)
14.4.1 Newton Telescope
378(1)
14.4.2 Cassegrain Telescope
379(1)
14.4.2.1 Spherical Aberration
379(1)
14.4.2.2 Coma
380(1)
14.4.2.3 Astigmatism
380(1)
14.4.2.4 Petzval Curvature
381(1)
14.4.2.5 Distortion
381(1)
14.4.3 Ritchey-Chretien Telescope
382(4)
14.4.4 Dall-Kirham Telescope
386(2)
14.4.5 Gregory Telescope
388(1)
14.4.6 Schmidt-Cassegrain Telescope
388(1)
14.4.7 Maksutov-Cassegrain Telescope
389(1)
14.4.8 Coude and Nasmyth Focus Configurations
390(1)
14.5 Field Correctors
391(4)
14.5.1 Single-Field Flattener
391(2)
14.5.2 Ross Corrector
393(1)
14.5.3 Wynne Corrector
393(1)
14.5.4 Aspheric Correctors
393(2)
14.6 Multiple-Mirror Telescopes
395(1)
14.7 Active and Adaptive Optics
396(5)
References
398(3)
Chapter 15 Visual Systems and Afocal Systems
401(28)
15.1 Visual Optical Systems
401(3)
15.1.1 Exit Pupil Location in Visual Optical Systems
401(1)
15.1.2 Optical Models of the Human Eye
402(2)
15.2 Basic Telescopic System
404(2)
15.3 Afocal Systems
406(3)
15.3.1 Two-Mirror Afocal Systems
408(1)
15.4 Visual and Terrestrial Telescopes
409(7)
15.4.1 Galilean Telescopes
411(3)
15.4.2 Terrestrial Telescope with Erecting Eyepiece
414(1)
15.4.3 Terrestrial Telescope with Erecting Prisms
415(1)
15.5 Telescope Eyepieces
416(7)
15.5.1 Huygens and Ramsden Eyepieces
418(2)
15.5.2 Kellner Eyepiece
420(1)
15.5.3 Symmetrical or Plossl Eyepiece
420(2)
15.5.4 Orthoscopic Eyepiece
422(1)
15.5.5 Erfle Eyepiece
422(1)
15.6 Relays and Periscopes
423(6)
15.6.1 Indirect Ophthalmoscope
425(1)
15.6.2 Endoscopes
426(2)
References
428(1)
Chapter 16 Microscopes
429(22)
16.1 Compound Microscope
429(5)
16.1.1 Microscope Aperture and Resolving Power
432(2)
16.2 Microscope Objectives
434(8)
16.2.1 Low-Power Objectives
438(1)
16.2.2 Lister Objectives
438(1)
16.2.3 Amici Objectives
439(1)
16.2.4 Oil Immersion Objectives
439(1)
16.2.5 Other Types of Objectives
440(1)
16.2.6 Reflecting Objectives
441(1)
16.2.7 Compact Disc Objectives
441(1)
16.3 Microscope Eyepieces
442(4)
16.3.1 Huygens Eyepieces
443(2)
16.3.2 Wide-Field Eyepieces
445(1)
16.4 Microscope Illuminators
446(5)
References
448(3)
Chapter 17 Projection Systems
451(14)
17.1 Image Projectors
451(1)
17.2 Main Projector Components
452(5)
17.2.1 Lamp
452(1)
17.2.2 Condenser
453(2)
17.2.3 Projection Lens
455(2)
17.3 Coherence Effects in Projectors
457(1)
17.4 Anamorphic Projection
458(2)
17.5 Slide and Movie Projectors
460(1)
17.6 Overhead Projectors
460(1)
17.7 Profile Projectors
460(1)
17.8 Television Projectors
461(1)
17.9 LCD Computer and Home Theater Projectors
462(3)
References
464(1)
Chapter 18 Lens Design Optimization
465(24)
18.1 Basic Principles
465(1)
18.2 Optimization Methods
466(1)
18.3 Glatzel Adaptive Method
467(1)
18.4 Constrained Damped Least-Squares Optimization Method
468(8)
18.4.1 Linearization of the Problem
469(1)
18.4.2 Use of the Lagrange Multipliers
470(3)
18.4.3 Matrix Representation
473(1)
18.4.4 Numerical Calculation of Matrix Solution
474(1)
18.4.5 Use of the Weight Factors
475(1)
18.5 Merit Function and Boundary Conditions
476(5)
18.5.1 Merit Function
476(1)
18.5.1.1 Color Averaging
477(2)
18.5.1.2 Field Averaging
479(1)
18.5.1.3 Distortion
480(1)
18.5.2 Boundary Conditions
480(1)
18.5.2.1 Axial Optical Thickness
480(1)
18.5.2.2 Edge Optical Thickness
481(1)
18.5.2.3 Average Lens Thickness
481(1)
18.6 Modern Trends in Optical Design
481(1)
18.6.1 Global Optimization and Simulated Annealing
481(1)
18.7 Flowchart for a Lens Optimization Program
482(1)
18.8 Practical Tips for the Use of Lens Evaluation Programs
482(3)
18.8.1 Curvature, Thickness, and Separation Sign Conventions
482(2)
18.8.2 Curvature or Radii of Curvature Specification
484(1)
18.8.3 Thickness and Separation Specification
484(1)
18.8.4 Some Useful Tricks
484(1)
18.9 Some Commercial Lens Design Programs
485(4)
References
486(3)
Appendix 1 Notation and Primary Aberration Coefficients Summary 489(8)
Appendix 2 Mathematical Representation of Optical Surfaces 497(10)
Appendix 3 Optical Materials 507(6)
Appendix 4 Exact Ray Tracing of Skew Rays 513(18)
Appendix 5 General Bibliography on Lens Design 531(2)
Index 533
Daniel Malacara-Hernández is a professor and researcher at Centro de Investigaciones en Optica in Leon, Mexico.

Zacarías Malacara-Hernández is a researcher at Centro de Investigaciones en Optica in Leon, Mexico.