The title of this book originates from Michael Kidger's short courses for SPIE titled âIntermediate Optical Design.â It is a compilation of material from these courses and a number of similar ones given for Kidger Optics in Australia, Germany, Italy, Sweden, Singapore, and the UK during the 1990s. It forms the second of two volumes, the first being Fundamental Optical Design, published by SPIE Press in 2002.
These intermediate-level courses were aimed at students and practicing optical designers who already had a thorough knowledge of geometrical optics and third-order (Seidel) aberration theory. The courses continued to use the same âImperial Collegeâ nomenclature and the Sigma optical design program as their basis. They were workshops, or master classes, rather than academic discourses or promotional material for Sigma. In the interests of authenticity and continuity with the first volume, the same Sigma output format is used here for tables of lens prescriptions, aberration data, and graphics. This second volume does not review the material in the first volume; the assumption is that the reader is already familiar with it, preferably having already worked through the examples in that volume, and is able to refer back to it when needed. The connections between the two volumes are not often explicit, but rather left for the perceptive reader to discover as he or she works through these design examplesâI think this is in keeping with the intent of the courses.
While the first volume carefully avoided the subject of optimization, this volume starts with a general but wide-ranging discussion of it. As any optical designer quickly discovers, the key to this art and science (as Professor Shannon has referred to our field) is optimization. In fact, a desire to learn more about optimization probably brought many people to these courses, even some who had been designing lenses for many years. More specifically, the courses taught âlocalâ optimization, where the choice of starting design is crucial to the success of the optimized design. Michael was also interested in the more general problem of âglobalâ optimization, which he somewhat wryly described as a user inputting a series of âflat platesâ and the program finding the best possible arrangement of lens elementsâideally, the program would even decide the optimum number of plates, mirrors, diffractive elements, and so on.
The first chapter in this volume has been compiled from Michael's writings on local optimization, from several published papers as well as his course notes. This material is inevitably very closely related to the Imperial College and Sigma software that he developed and used. Unfortunately, readers of this book will not have access to Sigma, or Michael's unique ability to answer questions as they arise. They will instead be using another commercial optimization program, perhaps without supervision. Recognizing this inevitable limitation, I have attempted to rise above the trees of the Sigma program and give my interpretation of Michael's overview of the forest that is any optical design optimization program, at least one that is based on the damped least squares (DLS) method.
Included here are some design examples to illustrate certain points, such as the effects of lens diameter and thickness constraints on aberration performance. In the courses, these examples were in a separate section under the heading of âunusual or novel optical designs.â One of these is the âmonochromatic quartet,â which I was fortunate enough to find with Sigma for the International Lens Design Conference problem in 1990. Several other designers also found the same form with other local optimization programs, and the design has subsequently been rediscovered by global optimizationâfrom flat platesâbut I have been gratified to hear that such programs have not yet found a better design. Although totally impractical (which was the intention), it is a good illustration of the importance of size constraints, which is one of the key factors in the control of higher-order aberrations.
The chapter concludes with the Kingslake double-Gauss example that became a tradition of Michael's courses. This was the start of the practical work with Sigma, but in this book readers are left to apply it to whichever optical design program they are using. Naturally, the detailed lens and ray setup will be quite different from one program to another. However, the example is retained with Sigma output because this is the way it was in the courses, and it also serves to illustrate the importance of damping factor and step size on the ultimate performance of the optimized design. It is unfortunate that in most other commercial programs these numbers remain invisible to the designerâSigma was a model of transparency.
Perhaps the most important message from the first chapter, and indeed the whole book, is the role of higher-order aberration correction in most optical designs. Accordingly, the second chapter is a relatively brief discussion of Buchdahl fifth-order aberrations, with references provided for those mathematically inclined readers who want all the gory details. Over the years, after âgraduatingâ as a formal student of Michael's, I had several discussions with him about Buchdahl aberrations while I went through a phase in my career when I was enthusiastic about them. I think he remained rather skeptical, even though Sigma became one of the few commercial lens design codes that included Buchdahl's monochromatic aberration coefficients in the main program (other programs have them as reluctant extensions). This is not only because they cannot simply be attributed to individual optical surfaces, but also because they are not usually sufficiently accurate, since they are based on paraxial rays. Michael made the point that it is usually quickerâand always more accurateâto trace a limited number of finite rays, and this is indeed the more common approach in this age of very fast personal computers.
It remains useful to think about fifth- and higher-order aberrations such as oblique spherical aberration, coma, astigmatism, and field curvature, because these often dominate the lens design problem. Usually I look for them in the transverse ray aberration plots, of which there are many examples in these two books. Someone (I forget who) has defined an optical designer as one who understands transverse ray aberration curves, and so this is considered a prerequisite for the reader of this intermediate-level text. Later in my career, thanks to Abe Offner and Juan Rayces, I became a convert to Zernike coefficients, which more accurately describe and optimize higher-order aberrations. While the last version of Sigma did contain these coefficients, the original course material contains little discussion of them, so I have decided not to add that here.
The remaining chapters contain a wide range of design examples that are dominated by higher-order monochromatic and chromatic aberrations. The choice of examples partly reflects Michael's background and interest in certain design types, but it also evolved from student requests. It does not attempt to cover all design types, but rather it uses these examples to illustrate specific or generally applicable design approaches.
Many readers may find in the third chapter the most useful insights into an optical designer's thought processes, such as they are. The synthesis of starting points for optimization is the aspect of optical design that is the least written about but most importantâat least until the truly global optimization program arrives. While there have been numerous attempts to apply databases and artificial intelligence, here the approach to the challenge of the blank computer screen is to use human memory, common sense, experience, and knowledge. It involves using the (local) optimization program as a field in which to play with new ideas, discarding those that show less promise, and then refining the more promising ones to include greater accuracy and all of the required practical aspects prior to finalizing a design for manufacture. To the outsider this may seem like trial and error, but readers of this book are likely to appreciate that there is more to it than that!
Michael had a particular interest in the history and practice of photography, so the fourth chapter covers many of the classical photographic lenses. Although these will already be well known to most readers, this is a brief review, with some valuable insights and historical observations.
The fifth chapter attempts to cover a wide range of approaches to the problem of secondary spectrum correction, which is a higher-order chromatic aberration that the practicing designer will often encounter, and which can be the most stubborn imaging defect to reduce or eliminate. The most common approach has been to use anomalous glass types, and this is briefly reviewed. I have also added references to many of the published systematic methods of glass selection. Some less well known approaches using normal glasses are also described in more detail, and I have added a brief reference to the use of diffractive optics, since they are starting to be used in photographic lenses. I have also added the Schupmann medial telescope, from a prescription kindly provided by Richard Bingham. This is not often thought of as a means of secondary spectrum correction, since it avoids the problem rather than corrects it. An implicit lesson of these two volumes is that avoidance is usually better than correction! Many other catadioptric designs also use the Schupmann principle, including some described in the last chapter of Fundamental Optical Design.
Chapter 6 illustrates the wide variety of situations that an optical designer may encounter, where in this case chromatic aberrations are unimportant, but other considerations specific to lasers need to be taken into account. Even for the simplest designs the opportunity is taken to remind us of some basic aberration theory, such as the sine condition, which was covered in more detail in the first volume.
The material in Chapters 7 and 8 were in the courses combined as a section on high-numerical-aperture designs. I have separated them into two chapters here, on the basis that microscope objectives operate over a relatively small field size and broad spectral bandwidth, whereas microlithographic objectives cover a relatively large field size and narrow spectral range. No doubt this also reflects my own interest in microlithography, from where I have added a few more designsâsome my ownâwith the justification that the courses did include one of my earlier designs, and I wanted to include the substantial progress that has taken place since then.
Microlithographic objectives are the best illustration of the remarkably high and uniform performance across the image format that can be obtained by the combination of large size and complexity to ârelaxâ the optical design, a term first used by Glatzel in 1980. Essentially, this strategy simply minimizes ray incidence angles on optical surfaces. It is one of the more remarkable stories in the history of optics that such large and complex designs are now routinely produced with aberrations measured in a small number of milliwaves rms in the ultraviolet spectrum.
Another class of systems that one might more reasonably expect to find in a book on advanced optical design is zoom lenses. As a designer with little experience in this field, and one who skips over the numerous complicated papers on such lenses, I found Michael's course notes on the subject remarkably easy to understandâthis is the genius of Michael's teaching style. I have not changed the material significantly from the original, other than making the tables and graphics compatible with the rest of the book. After working with this chapter, I felt that I had sufficient understanding of zoom lenses to at least have the confidence to begin to design one.
Chapter 10 discusses some of the more basic issues involved in the design of tilted or decentered optical systems. Originally, I was not going to include this chapter, since it is specific to the particular way that Sigma treated such systems. But, there are some interesting illustrations here of apparently simple decentered systems with unusual ambiguities and challenges, which I felt made the chapter of general interest to users of all optical design programs.
The final chapter is a brief discussion of some of the practical issues involved in designing a lens that has to be manufactured within specified price and performance requirements. The original courses also included a more detailed discussion of tolerancing, using Sigma's methodology. However, I decided not to include that here, since it is rather too specific to Sigma. The user of another optical design program will generally find appropriate documentation provided with it, or may have to develop tolerancing methods for specific applications, but I considered such a discussion to be beyond the scope of this book.
I have not, for similar reasons, reproduced here other features of Sigma that were in the original course notes or program documentation. These include non-sequential raytracing, illumination system design, Gaussian beam propagation, fiber coupling, and so on.
I have also not provided a list of recommended reading, beyond the references given in each chapter, which I have expanded considerably from those given in the courses. However, mention should be made of Don O'Shea's extensive compilation of optical design papers on CD-ROM (published by SPIE). This includes, among others, all of Michael Kidger's published papers from the Proceedings of SPIE.
Many of the design examples in these two volumes were included in Sigma's optical design database. These have been converted and now form a part of the Zebase lens database. There may be subtle differences in some of these lens prescriptions, such as glass refractive index data, apertures, and fields, which the reader is encouraged to explore; perhaps the prescriptions can be improved, or starting points for new designs can be formed. This is one reason why the paraxial ray data and Seidel aberration tables have been included for many of the designs: they can be used to check the accuracy of translation of the lens prescription into other optical design programs. Study of these tables is also a good way to understand how a design is working; it is one of the more important skills of the optical designer. Of particular interest are the marginal and chief ray incidence angles (A and ABAR), showing how ârelaxedâ the design is, and the magnitude of surface aberrations and how they are cancelled within the system. This will affect the magnitude of residual higher-order aberrations and sensitivity to manufacturing errors, and is the implicit theme of these two volumesâthe simple secret, if there is one, of optical design.
I am grateful to a number of colleagues, including Brian Blandford, Tom Matsuyama, and Juan Rayces, who have read the manuscript and offered comments and constructive criticism. I am also very grateful for Tina Kidger's constant encouragement to âget it out there!â My hope is that this book retains as much as possible of Michael Kidger's original brevity and clarity, and that it will be a useful and practical resource for students of classical optical design for many years to come.
David M. Williamson
© 2004 Society of Photo-Optical Instrumentation Engineers