# Explaining What We Do: Gentle Introduction to Optical Design and Lens Design

What is optical design? How does it connect with other areas of optics, optical systems, and optical engineering? How do you do it?

## What Is Optics?

Optics is a branch of physics: the science of light. Optics is concerned with all aspects of the behavior of light and thus covers a lot of territory. Questions that range from "Why is the sky blue?" to "Why does a magnifying glass make things look bigger?" to "How does a laser work?" are all the proper domain of the science of optics.

Although we usually think of visible light when we say "optics," visible light is simply a narrow band of the electromagnetic spectrum, which ranges in wavelength from very short (e.g., X-rays) to medium (e.g., green light) to very long. Optics can help us with these other wavelength regions, but most of our discussion here will focus on the important and familiar visible spectrum (i.e., the colors of the rainbow, from violet light with wavelengths near 400 nm [nanometer, one-billionth of a meter] to red light near 700 nm). For comparison, X-ray wavelengths are in the nanometer range, while radio waves range from centimeters to meters in wavelength.

One interesting fact about light is that it acts sometimes like a wave, other times more like a stream of very fast particles or quanta called photons. This wave/particle duality remains one of the mysteries of nature, but in practice we emphasize and use whichever aspect makes our calculations easier! In lasers and detectors, quantum effects are especially important, but in optical design, wave or "physical" optics tends to dominate.

Under the right circumstances, we can further simplify our calculations with the additional concept of light rays. Rather than thinking about waves propagating through space, we think about lines that are normal to the waves (i.e., traveling in the direction of the advancing wave front), and we call these lines light rays or simply rays. The behavior of these rays can be modeled by some relatively simple equations (remember Snell's Law?), and much of optical design is therefore based on rays. This is called geometrical optics (don't worry, we still keep track of quantum and physical optics effects when needed to get the right answers!).

## What do Optical Engineers do?

Optical engineers make use of optics to solve problems and to design and build devices that make light do something useful. This requires them to understand and apply the science of optics in substantial detail, in order to know what is physically possible to achieve. But they also must know what is practical in terms of available technology, materials, costs, design methods, etc.

Optical engineers work in all areas of optics, using different techniques to design lasers, build telescopes, create fiber optics communication systems, and much more.

As with other fields of engineering, computers are important to many (perhaps most) optical engineers. Computers are used with instruments, for simulation, in design, and for many other applications. Engineers often use general computer tools such as spreadsheets and programming languages, and they also make frequent use of specialized software designed specifically for their field.

## Lenses and Lens Designers

So what is a lens? You might think this is a simple question -- just a curved piece of clear glass or plastic, right?

Well, right -- this is one type of lens, and the most common type at that (most eyeglass and contact lenses are this type).

To a lens designer, though, a lens is a more general device, basically any system that tries to collect and distribute light in a specifically desired way.

This is closer to what we think of when we discuss interchangeable "lenses" for a 35 mm SLR (single lens reflex) camera (e.g., normal, wide angle, telephoto, zoom). If you cut one open (don't try this at home, kids!), you'd find that such a camera lens contains a number of single "lenses" of different shapes and sizes. We refer to these as lens elements, and the complete lens is more generally called an optical system.

With this terminology, the lens designer today is more often called an optical designer, though the older term is still widely used, along with such whimsical descriptive names as "ray bender." It is increasingly common today for "lens designer" to be but one of a number of titles worn by an optical engineering generalist (who may or may not have a specific optics background -- many people doing lens design today are physicists or other types of engineers by original training).

With this background, a lens (or optical system) can actually contain any number and combination of lens elements, mirrors, prisms, rotating polygon scanners, filters, diffraction gratings, holographic elements, and other sorts of optical components. The designer also has to think about what sort of light source will be used with the lens (light bulbs, LEDs, lasers, stars, the sun, etc.). Also important is the type of "detector" (detectors are devices that react to light, such as film, photodetectors, CCD arrays, or the unsurpassed human eyeball). Systems for infrared (IR) and ultraviolet (UV) light expand the number and types of sources and detectors we consider, but the principles are the same, and lens designers work frequently with IR and UV systems as well as with visible light (special materials are often required for IR/UV work since normal optical glass doesn't work well outside the visible spectrum).

So the modern lens designer may work on "lenses" that are a long way from your bifocals or pocket 35 mm camera (although the compact lens in a pocket camera can represent some clever design and cost-effective engineering). If a system uses light in some way (including any system that uses laser beams), lens design is almost certainly involved. Some examples:

• Microscopes, telescopes, binoculars
• Camera lenses of all kinds (photo, movie, video, zoom, etc.)
• Slide, movie, overhead, and video projectors
• Laser printers, office copiers, fax machines, microfilm readers
• Endoscopes for minimally invasive surgery
• Laser-based optical readers for CD and CD-ROM
• Product code laser scanners in supermarkets
• Ultra-precise projector lenses used in making integrated circuits
• The Hubble Space Telescope (and its retrofitted repair optics)
• And many, many more...

Band structure for a 2D hexagonal lattice of air holes

The Hubble Space Telescope is perhaps the most famous space-based optical system, and several engineers at Optical Research Associates (ORA® was acquired by Synopsys) actually worked on the design and other aspects of the repair optics (ORA even won a NASA award for this and other space-related work).

## How to Design a Lens

Now that we know what a lens is, how do you design one? The full details are a bit beyond the scope of this "gentle introduction," but we can outline the typical steps.

• Problem definition - Other engineers or disciplines may define the requirements and boundaries of the design problem, but it is up to the lens designer to translate these into detailed optical specifications such as field of view and focal length. Your performance spec should be here also -- a detailed description of how good an image the lens must form (there are various types of optical evaluation used for this purpose). There may be many requirements to meet, some of them contradictory in terms of how you approach the design (e.g., large aperture and light weight are usually opposing requirements that lead to tradeoffs and compromises).
• Pre-design - Once the basic factors are set, there are decisions to be made, such as reflecting vs. refracting? Number of elements? Overall size? Pre-design often involves paper and pencil sketching, including rough graphical ray tracing, with thin lenses standing in for real lenses. There are some graphical software tools that can really help in this stage, especially when pre-design tradeoffs ("what-ifs") are needed, as they often are.

• Starting point selection - Concept moves toward reality here, often with the help of an existing solution for a similar situation (books, patents, and your own company's previous work are rich sources here). Software comes into play here, since access to a database of existing designs can really speed up the selection process. Graphical and approximate methods can also be used to create a starting point "from scratch," if necessary.

• Initial analysis - It helps to have a baseline analysis of the starting point so you can gauge improvement versus the spec. Aberration analysis may not be part of the spec, but it will probably be useful in the design process, especially in selecting variables for optimization.

• Optimization - Once you define a set of variables (parameters such as curvature, thickness, index of refraction, etc. that the program can change to try to improve performance), an error function (measure of optical quality, zero typically implying "perfection"), and constraints (boundary values that restrict possible configurations), you are ready to optimize the lens. Numerical methods are used to alter the variables in systematic ways that attempt to minimize the error function while honoring all constraints. Sometimes it goes smoothly, more often it doesn't, so changes are necessary, injecting designer guidance to resolve conflicts (though some software is pretty smart about many types of optimization problems, no program is yet fully automatic, if only because some requirements and esthetic judgments may remain in the designer's head and not in the error function).

• Final analysis - After optimizing the lens, you need to see if it is actually doing what the original spec says it should do (optimization error functions may not correlate perfectly with specifications such as MTF or encircled energy). If it's not quite there, you may have to go back for some more optimization (perhaps adding variables or changing constraints). You may even have to find a different starting point in some cases.

• Prepare for Fabrication - If the lens design meets its requirements, you will still have more work to do to prepare for fabrication. See "The Rest of the Story" (below) for a bit more on this subject.

## Optical Design Software

Model, analyze, optimize, and provide fabrication support for the development of optical systems with CODE V optical design software.

What does this leave out? A lot of the "hard parts" of the design process, in fact. Incomplete or changing specifications. Conflicting requirements. Dead-end solution attempts. Unrealistic schedules. Computer crashes. Nobody said it was easy!

## Overcoming Obstacles: Aberrations

Aberrations remained in comfortable obscurity up until the Hubble Space Telescope's (HST) well-known problem. The fabrication defect made spherical aberration temporarily famous (or perhaps infamous?). In geometrical terms, the concept of aberration is pretty simple. Rays from a zero-dimension point object (like a distant star) imaged through a perfect lens will all focus to a single zero-dimension image point (in reality, diffraction effects result in a small but finite size even for aberration-free imaging). If these rays go anywhere else, that is aberration.

Aberration can be expressed in various ways, most of which start out by tracing a number of rays through the lens to see where they go. The ray distribution can be plotted as a scatter plot (we call this a spot diagram), or cross-sections of ray position data can be plotted (ray trace or "rim ray" curves). To those trained in the art, the shapes and sizes of the resulting patterns can tell things about the amount and forms of aberrations that are present, and with this information, you can plan to correct or reduce the aberrations in various ways. Aberration theory breaks down aberration into components (terms of polynomials, actually), and can even assign "blame" for aberration to specific surfaces in the lens (a strongly curved or badly made surface can contribute major amounts of aberration, but surface contribution information at least gives a clue how to proceed).

Spherical aberration (SA) is perhaps the simplest to understand, since it depends only on distance from the optical axis. Most optical surfaces are sections of spheres, since these are the easiest surface shapes to make . For a simple spherical-surface lens or mirror, rays at different heights on the surface are not bent to the same degree, so they focus at slightly different distances along the axis; this is SA. With simple lenses, you can reduce SA by choosing the right lens form ("lens bending", as we say in the trade). With mirrors (as in the HST), you can correct it by making the mirror a slightly non-spherical conic section (but you have to create the CORRECT conic shape, which was HST's problem -- they built it perfectly against the wrong test standard!). Of course there are OTHER aberrations too, and their interactions may prevent you from making a correction you would like (the old lump-in-the-rug effect -- correct in one place and it pops up in another). This can make lens design a bit challenging (and leads to the next subject of optimization).

The Hubble also illustrates the GOOD thing about aberrations: if you know what they are in detail, you can often correct them (especially with a big enough budget!). If the optics are bending the light in the wrong way, elements can be reshaped or other elements added to cancel out the aberration, similar to the way that glasses correct myopic vision (although myopia is not exactly an aberration -- the myopic eye actually has the wrong focal length, so an additional lens is needed to allow it to focus on the retina).

## How Deep Is My Valley? (Optimization)

Optimization is such an important subject in optical design that we need to say more about it, even though it was briefly described under How to Design a Lens. Remember that the goal of optimization is to take a starting lens of some sort and change it to improve its performance (the starting lens should have a suitable number of optical surfaces of suitable types, since optimization can change only the values of the parameters, not the number or types of surfaces). Since optics is very precise (distances of micrometers can make a big difference), we need to closely determine the values of all our variables at each step of the optimization.

Let's consider local optimization first. What does "local" mean? If you have a lens model, an error function is something that correlates with its image performance, like spot size or RMS wavefront error -- smaller is better. As variables are changed, the lens changes, ray trace values change, and the error function takes on new values. If you could plot these out, you would create a map of the hills and valleys of error function space (in anywhere from one to 99 dimensions or more, depending on your variables). In the admittedly silly sketch above, vertical distance represents the error function value (lower is better), and horizontal position represents ONE of the variables in the lens (for example, it could be the curvature of the front surface).

Since smaller is better, your goal is to find the lowest possible point on this map -- the Death Valley of Error Function Land (EFL). Local optimization finds the lowest near-by region in the EFL, so if you are lucky (or smart) in choosing your starting point, you will do well (by analogy, starting in Los Angeles might let you reach Death Valley using local optimization, but starting in New York would not -- you'd probably end up somewhere in New Jersey). Does this analogy help? Maybe not, but the point is, with local optimization, your choice of starting point is very important. (In our picture, local optimization will NOT get you to the lowest point -- it will roll you into one of the valleys to the right or left of the "You are here" starting point).

Now consider global optimization. This is an algorithm that somehow looks at the entire map of Error Function Land and (eventually) locates the lowest point regardless of where you started. Even if you start in Florida, global optimization will eventually get you to Death Valley, though depending on the methods used, it might take a really long time to actually get there, and you might be told about a lot of other low places along the way, some of which might be low enough for your purposes. Silly analogy? Maybe, but the point to remember here is that global optimization considers the whole of "error function space," so your actual starting point is much less critical. (In our picture, global optimization should take you to the desired low point).

## The Rest of the Story

This would not be such a gentle (nor brief) introduction if we actually told you the rest of the story here. There is necessarily much we have left out:

• Illumination analysis
• Preparation for fabrication
• Integration with optical testing
• Analysis of manufacturing error effects (this is called tolerancing)
• Environmental effects (especially thermal)
• Mounts and baffles
• Stray light

Software can help with almost all of these problems, although the designer remains essential in identifying problems and priorities. Even with all of this, it is still a challenge to turn it all to practice and produce lenses that meet all the requirements in actual use. If you are interested in optical design tools, the Optical Solutions Group at Synopsys offers several software solutions to help you achieve your objectives. For help choosing which optical design software is best for your application, visit our Choosing An Optical Design Software Solution page.

## Learning More

There are some excellent sources of information about optics, most of them on paper in books and periodicals. This list is just a starting point -- we will add to it over time and we welcome suggestions. In particular, if you know of educational optics resources on the internet, please let us know (send e-mail to optics@synopsys.com).

### Basics

• Molecular Expressions' "Optical Microscopy Primer" on Light and Color
This site contains a lot of fascinating information on microscopy, from the basic optics of microscopes to advanced applications and sample images. It's worth a look for the excellent explanations, graphics, and some interactive Java tutorials on refraction, reflection, and other optical topics. It includes details on many subjects only briefly mentioned here, including diffraction, polarization, and interference. A fantastic web site! Open this site in a new window.

• Eyewitness: Light by David Burnie (Dorling Kindersley, 1992)
Part of the "Eyewitness Science" Series, nominally for children, beautifully illustrated with excellent explanations.

• Optics by E. Hecht and A. Zajac (Addison-Wesley, 1974)
A good text at the undergraduate physics level.

### Optical Engineering and Design

• Lens Design Fundamentals by Rudolf Kingslake (Academic Press, 1978)
Covers fundamentals needed by working designers.

• Elements of Modern Optical Design by Donald O'Shea (Wiley-Interscience, 1985)
Excellent college-level text with good explanations and a practical orientation.

• Modern Optical Engineering by Warren Smith (Second Edition, McGraw-Hill, 1990)
The standard desk reference and learning tool for optical engineering.

### Periodicals

• Optics and Photonics News (monthly, by subscription, Optica, Washington, DC)

News and technical articles (the monthly column "Light Touch" covers "everyday optics" for the non-professional).

### Other Resources

• Optics4birding.com This is part of a site dedicated to bird watching, where quality optics are very important for viewing and photography. The optics pages discuss a lot of basic optical concepts with a useful approach that is geared toward the importance of these concepts to the actual use of the optics. Click on "All About Optics."

• Also see our Optics For Kids resource page.