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by Gregory Hallock Smith,
Hardbound, 6 by 9 inches, 524 pages,

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About Practical Computer-Aided Lens Design

The introduction of the computer revolutionized the way lenses (optical systems) are designed and evaluated. Gone is the drudgery of the past. Gone are the arcane methods. Today the process of designing lenses is more direct, much faster, and infinitely easier.

The advent of the personal computer and affordable optical design software has extended this revolution. These latest advances allow more people to design lenses than ever before.

Practical Computer-Aided Lens Design tells how to design and evaluate lenses using computers. The approach is general and fundamental, and is not limited to one specific software program. Thus, this book should be useful for many years to come.

If you are interested in lenses, lens design can also be an exciting and creative experience, and an attempt has been made to convey this feeling to the reader.

Three groups of readers are intended:

  • College students studying optics
  • Non-optical scientists and engineers who wish to design optics using programs like ZEMAX® , OSLO® , CODE V®, and SYNOPSYSTM.

Features in this book:

  1. Optical design concepts and techniques are explained
  2. Many design examples are worked and the results discussed
  3. The latest computer-aided methods are used
  4. A practical and intuitive approach is emphasized
  5. Hardbound, 6 by 9 inches, 524 pages

Read a sample chapter: “The Cooke Triplet and Tessar Lenses” in PDF.

From a Review in the Optical Society of America's
Optics and Photonics News

An engineering professor of mine once made a distinction between “computer-aided”design and “computer-ated”design. His point, of course, was that the computer can be used as a tool in the creative idea phase of a design, as well as to assist with the computational grunt work needed to bring a project to completion. Reflecting the author's years of industrial experience, Gregory H. Smith's Practical Computer-Aided Lens Design does an excellent job of covering both aspects of the lens design process.

The first 12 chapters cover the standard textbook topics of ray tracing, aberrations, diffraction, modulation transfer function and radiometry, all of which are needed for a conceptual understanding of the design types that follow. The writing is clear and well-organized. The topics are all covered from the point of view of the experienced lens designer. As a result, Smith also includes material not typically found in other texts, such as his discussion of the cosine-fourth law (Sec. A.9.5), and how to design around it (“... strong negative power in the front and rear elements and positive power in the middle...”).

The next four chapters introduce specifics of lens design principles. Chapter 13, on merit functions, is a useful gem, detailing practical Zemax (and sometimes Oslo and Code V) listings on program usage. Also included in these chapters are design hints such as “Perhaps the most valuable aberration-control operands address longitudinal color, spherical aberration, coma, and distortion”(p. 176) and “Throughout the practice of lens design, glass selection is often the most subtle issue of all”(p. 193).

Smith also covers practical aspects of specific design architectures such as doublets, the Cooke triplet, the double Gauss, and Cassegrain and Schmidt telescopes. Covered in the final seven chapters, these examples—or engineering case studies—are an excellent way for the beginner to quickly master the important aspects of a design. So if you are learning lens design as an undergraduate or graduate student, or don't yet have the years of experience which went into writing this book, you will find Practical Computer-Aided Lens Design a valuable investment.

Need Software?

  • ZEMAX® lens design program, the one used in this book, is available for sale from Focus Software at
  • CODE V® lens design program is available for lease from Optical Research Associates at
  • OSLO LT® is available at as a free download (4MB) and is full-featured except that it limits the user to 10 surfaces.
  • SYNOPSYS® lens design program (SYNthesis of OPtical SYStems) is a powerful Windows lens design program with a downloadable trial version available at
    This is a full-featured version, with nothing left out. It will run for 180 days, after which you are encouraged to register with OSD. If you need more than 180 days, you may download the latest version from their website and reinstall it.

About The Author:
Gregory Hallock Smith is an optical engineer and lens designer. He first became interested in optics and astronomy in 1954 at age 13. In 1972, he received his Ph.D. from the Optical Sciences Center, University of Arizona. Since that time, he has held optical engineering positions at several major corporations and research institutions. His experience ranges over such areas as photographic techniques, astronomical instruments, image intensifiers, optics for military and NASA spacecraft, and optics education.

Dr. Smith is now an independent optical design consultant. Recently he designed all the camera lenses for JPL's next Mars missions. These two identical spacecraft will be launched separately in mid-2003, and they will land using big airbags in different Martian locations in early 2004. Each is a six-wheeled robotic rover vehicle, and each carries a total of 10 CCD cameras of five various types. There are two narrow-angle color panoramic cameras, two wide-angle navigation cameras, one macro close-up camera on a movable arm, four 180-degree fisheye hazard-avoidance cameras, and one sun sensor camera (that uses the same lens type as the navigation cameras). It is planned that each rover will spend at least three months exploring the Martian surface doing geologic and atmospheric studies, including looking for signs of past or present liquid water, and even life.

What Others Say:
In the 'good old days', an aspiring designer would apprentice himself to a master designer and be guided by the sure hand of experience. Not only would the student learn the tools of the trade, but clever and often invaluable lessons in problem solving as well.

Now, as then, there are countless blind alleys confronting the novice. The easy availability of high-speed personal computers and user-friendly software (something we old-timers didn't have!) only let him back himself into corners more quickly. One of the questions I always ask a perplexed new designer is, "are you sure that what you're trying to do is possible? ". There is also the predictable result that arbitrarily devised designs will be more complicated and costly than necessary.

Fortunately, while not everyone has privilege of an apprenticeship to a master, or even the luxury of helpful conversations with a pro, everyone can benefit from Dr. Smith's excellent guide to methods of computer-aided optical design. Avoid needless frustration born of ignorance! Learn a disciplined approach to optical design by reading the book, then bolt ahead with your newfound knowledge!

R. A. Buchroeder, PhD
Optical Design Service
Tucson, AZ

The best optical designs are the product of equal parts of art and science. Although many books cover the science aspect well, few books integrate the art and process of optical design with the underlying theories. Practical Computer-Aided Lens Design finds that magical balance between technical depth and accessible discussion of the journey from concept to finished optical design. The integration of modern computer optimization with classical qualitative and quantitative analysis makes this book an essential part of any optical designers library, from novice to expert.

Dr. Kenneth E. Moore
President of Focus Software, Inc. and author of the ZEMAX® Optical Design Program.

While primarily a bible for the lens designer, Practical Computer-Aided Lens Design by Gregory Hallock Smith serves also as a handbook for the optical systems engineer and as a source of historical and useful information for the technically minded photographer and astronomer. It is rare to find such widespread utility in a single technical book.

Don Nicholson
Associate Director, Mount Wilson Institute

If you are in consulting business or work for a small company, finances are very important to develop an optical system. Though there are a number of optical design software packages, some free, some are affordable on a personal basis and the others with expert systems available at a cost. Having an optical design package does not make one an expert lens designer. It is the intimate knowledge of Optical Science combined with a design tool at an affordable cost has a better chance of success. Gregory Hallock Smith's Practical Computer Aided Lens Design makes an attempt to reach that goal. There is a wealth of practical and useful information available to an optical scientist. Dr. Smith cleverly showed how to combine optics theory with a design tool to produce a practical design inexpensively

R. Reddy Chirra
President Optical Society of Southern California

Table of Contents:

Part A Optical Concepts and Techniques

A.1 Introduction

A.2 A Brief History of Lens Design
  A.2.1 Two Approaches to Optical Design
  A.2.2 Analytical Design Methods
  A.2.3 Numerical Evaluation Methods
  A.2.4 Optical Design Using Computer-Aided Numerical Optimization

A.3 Light and Imaging Systems
  A.3.1 The Nature of Light
  A.3.2 Spectral Regions
  A.3.3 Objects, Light Rays, and Wavefronts
  A.3.4 Images and Imaging Systems
  A.3.5 The Optical Axis
  A.3.6 Stops and Pupils
  A.3.7 Marginal and Chief Rays
  A.3.8 Perfect Imagery
  A.3.9 Causes of Image Quality Degradation
  A.3.10 The Point Spread Function
  A.3.11 Image Motion
  A.3.12 Stray Light
  A.3.13 Focal and Afocal Systems
  A.3.14 Fast and Slow Lenses and Detectors
  A.3.15 Coordinate Systems and Sign Conventions
  A.3.16 Optical Prescriptions
  A.3.17 Aspheric Surfaces
  A.3.18 Thin Lenses
  A.3.19 The Pinhole Camera Example

A.4 First-Order, Paraxial, and Gaussian Optics
  A.4.1 Snell's Law to First Order
  A.4.2 Paraxial Optics
  A.4.3 Usefulness of Paraxial Optics
  A.4.4 Principal Planes and Cardinal Points
  A.4.5 Collinear Mapping and Gaussian Optics
  A.4.6 Where First-Order Optics Do Not Work
  A.4.7 Paraxial Properties of Surfaces

A.5 First-Order Ray Tracing
  A.5.1 Recursion Formulas for Surfaces
  A.5.2 Transfer Equation
  A.5.3 Refraction Equation
  A.5.4 Recursion Formulas for Thin Lenses
  A.5.5 Reduced Thickness
  A.5.6 The Lagrange Invariant
  A.5.7 Physical Significance of the Lagrange Invariant
  A.5.8 First-Order Ray Trace Used to Design a Projector

A.6 Basic Optical Analysis
  A.6.1 Gaussian and True Entrance Pupils
  A.6.2 Effective Refracting Surface
  A.6.3 Zones
  A.6.4 Bending a Lens
  A.6.5 Tangential and Sagittal Planes
  A.6.6 Back Focal Length and Effective Focal Length
  A.6.7 Telephoto and Retrofocus Lenses
  A.6.8 BFL, EFL, and Aberrations
  A.6.9 Sign Conventions for Aberrations
  A.6.10 Three Basic Analytical Tools
  A.6.11 Layout
  A.6.12 Spot Diagram
  A.6.13 Filling the Lens with Rays
  A.6.14 Transverse Ray-Intercept Ray Fan Plot
  A.6.15 Example of a Ray Fan Plot
  A.6.16 Use of Ray Fan Plots

A.7 On-Axis Geometrical Aberrations
  A.7.1 Plane Surfaces
  A.7.2 Correcting Versus Controlling Aberrations
  A.7.3 Undercorrected Spherical Aberration at Paraxial Focus
  A.7.4 Undercorrected Spherical Aberration at Best Focus
  A.7.5 Overcorrected Spherical Aberration at Paraxial Focus
  A.7.6 Third-Order Spherical Aberration Controlled at Paraxial Focus
  A.7.7 Third-Order Spherical Aberration Controlled at Best Focus
  A.7.8 Third- and Fifth-Order Spherical Aberration Controlled at Paraxial Focus
  A.7.9 Third- and Fifth-Order Spherical Aberration Controlled at Best Focus
  A.7.10 A Perfect Monochromatic On-Axis Lens
  A.7.11 A Defocused Perfect Lens
  A.7.12 Balancing Aberrations in Multi-Element Lenses
  A.7.13 Longitudinal Chromatic Aberration
  A.7.14 Other Chromatic Aberrations
  A.7.15 Defocus with an On-Axis Paraboloidal Mirror

A.8 Off-Axis Geometrical Aberrations
  A.8.1 Lateral Chromatic Aberration
  A.8.2 Field Curvature
  A.8.3 Coma
  A.8.4 Astigmatism and Field Curvature
  A.8.5 Distortion
  A.8.6 Higher-Order Off-Axis Aberrations

A.9 Analytical Relationships for Imagery
  A.9.1 Petzval Surface and Petzval Sum
  A.9.2 Aberration Dependence on Aperture and Field
  A.9.3 Use of Symmetry in Controlling Transverse Aberrations
  A.9.4 Effect of a Stop Shift
  A.9.5 Vignetting and the Cosine-Fourth Law

A.10 Optical Glass
  A.10.1 Index of Refraction
  A.10.2 Dispersion
  A.10.3 Crown and Flint Glasses
  A.10.4 Partial Dispersion
  A.10.5 Glass Maps
  A.10.6 Ultraviolet and Infrared Glasses
  A.10.7 Glass Selection
  A.10.8 Melt Sheets
  A.10.9 Non-Optical Glass Considerations
  A.10.10 Glass Manufacturers
  A.10.11 Mirror Substrate Materials

A.11 Wavefronts and Diffraction
  A.11.1 Diffraction by Aperture Edges
  A.11.2 Geometrical Wavefronts
  A.11.3 Aberrations Measured by Optical Path Differences
  A.11.4 Specifying the Amount of OPD Aberrations
  A.11.5 OPD Ray Fan Plots
  A.11.6 The Diffraction-Limited PSF
  A.11.7 Diffraction Plus Aberrations
  A.11.8 OPD Plots for Chromatic Aberrations
  A.11.9 Full Width at Half Power
  A.11.10 Diffraction-Limited Resolution
  A.11.11 Strehl Ratio and the Quarter-Wave Rule
  A.11.12 Scaling the Lens
  A.11.13 The Lyot Stop
  A.11.14 A Lyot Stop Plus a Field Lens

A.12 Modulation Transfer Function
  A.12.1 Frequency Response
  A.12.2 Fourier Analysis
  A.12.3 Measuring MTF
  A.12.4 Calculating the Diffraction MTF by Autocorrelation
  A.12.5 Calculating the Diffraction MTF by Fourier Transforms
  A.12.6 Consequences for Optical Design
  A.12.7 MTF in the Presence of Aberrations
  A.12.8 Minimum Detectable Modulation and Limiting Resolving Power
  A.12.9 Spurious Resolution
  A.12.10 Nyquist Frequency

A.13 The Merit Function
  A.13.1 The Merit Function as a Measure of Optical Performance
  A.13.2 The Constituents of the Merit Function
  A.13.3 Optimization Operands and Damped Least-Squares
  A.13.4 Weighting Operands and Lagrange Multipliers
  A.13.5 Weighting Fields and Wavelengths
  A.13.6 Built-in Operands and Default Merit Functions
  A.13.7 Optimizing with RMS Spot Size
  A.13.8 Optimizing with OPD Errors
  A.13.9 Optimizing with Modulation Transfer Function
  A.13.10 Optimizing with User-Selected and User-Defined Operands
  A.13.11 Examples of User-Selected and User-Defined Optimization Operands
  A.13.12 Longitudinal Color
  A.13.13 Lateral Color
  A.13.14 Spherical Aberration
  A.13.15 Tangential Coma
  A.13.16 Sagittal Coma
  A.13.17 Astigmatism
  A.13.18 Field Curvature
  A.13.19 Distortion
  A.13.20 Using Both Special Aberration Operands and Vignetting Factors
  A.13.21 The DMFS Operand
  A.13.22 Solves

A.14 Finding a Starting Design
  A.14.1 Determining System Requirements
  A.14.2 Determining the Number of Effective System Variables
  A.14.3 Controlling Optical Properties
  A.14.4 Following the Literature
  A.14.5 Attending Meetings

A.15 Optimization Techniques
  A.15.1 Local Minima and Global Optimization
  A.15.2 Entering the Starting Design
  A.15.3 How to Derive a Rough Starting Design
  A.15.4 Optimizing in Stages
  A.15.5 Early Optimizations
  A.15.6 Intermediate Optimizations
  A.15.7 Locating the Image Surface
  A.15.8 Final Optimizations
  A.15.9 Potential Problem Areas and Suggestions

A.16 Fabrication Errors and Tolerancing
  A.16.1 Types of Fabrication Errors
  A.16.2 Compensators
  A.16.3 Measures of Performance during Tolerancing
  A.16.4 Error Budget
  A.16.5 Sensitivity Analysis
  A.16.6 Iterating to Find the Final Tolerances
  A.16.7 Reoptimization for Known Fabrication Errors
  A.16.8 Test Plate Fit
  A.16.9 Recent Advances

Part B Design Examples

B.1 Achromatic and Apochromatic Doublets
  B.1.1 Achromatization 219
  B.1.2 F/5 Achromatic Doublet with BK7 and F2 Glasses
  B.1.3 F/15 Achromatic Doublet with BK7 and F2 Glasses
  B.1.4 Telescope Exit Pupils
  B.1.5 Color Curves for an Achromat
  B.1.6 Glass Selection and Color Curves for an Apochromat
  B.1.7 F/15 Apochromatic Doublet with SSK3 and KzFSN4 Glasses
  B.1.8 F/15 Apochromatic Doublet with Crystal Fluorite and SK11 Glass

B.2 The Wollaston Landscape Lens
  B.2.1 The Singlet Lens with the Stop at the Lens
  B.2.2 The Landscape Lens Optimized Polychromatically
  B.2.3 The Landscape Lens with No Coma and Flat Tangential Field
  B.2.4 The Landscape Lens with Mechanical Vignetting

B.3 The Cooke Triplet and Tessar Lenses
  B.3.1 Lens Specifications
  B.3.2 Degrees of Freedom
  B.3.3 Glass Selection
  B.3.4 Flattening the Field
  B.3.5 Vignetting
  B.3.6 Starting Design and Early Optimizations
  B.3.7 Intermediate Optimizations
  B.3.8 Final Optimizations Using Spot Size
  B.3.9 Final Optimizations Using OPD Errors
  B.3.10 The Tessar Lens

B.4 The Double-Gauss Lens
  B.4.1 Lens Specifications
  B.4.2 Multiple Configurations
  B.4.3 Vignetting Factors
  B.4.4 Gaussian Quadrature
  B.4.5 Starting Design and Early Optimizations
  B.4.6 Intermediate Optimizations
  B.4.7 Final Optimizations
  B.4.8 Final Results
  B.4.9 Comparison with Star Photos

B.5 Cassegrain Telescopes
  B.5.1 The Reflecting Telescope
  B.5.2 Types of Cassegrain Telescopes
  B.5.3 System Specifications
  B.5.4 The Classical Cassegrain
  B.5.5 The Ritchey-Chretien
  B.5.6 Refractive Field Correctors
  B.5.7 The Classical Cassegrain with Field Corrector
  B.5.8 The Ritchey-Chretien with Field Corrector

B.6 Schmidt Telescopes
  B.6.1 The Schmidt Approach
  B.6.2 System Specifications
  B.6.3 Optimizing the Classical Schmidt
  B.6.4 Evaluating the Classical Schmidt
  B.6.5 Ghost Images
  B.6.6 The Achromatic Schmidt

B.7 Tolerancing Example
  B.7.1 Tolerancing a Tessar
  B.7.2 Specifying the Tolerances
  B.7.3 Sensitivity Analysis
  B.7.4 Overall Performance
  B.7.5 Monte Carlo Statistical Analysis