What???!!! No Perfect Lenses???
All real lenses possess aberrations – unavoidable behavior of the lens that results in the failure to create an absolutely perfect image. Aberrations can be minimized, balanced, or compensated, but they cannot be eliminated for all imaging scenarios because they are inherent to a lens working over a reasonable field of view. The most common way to minimize the aberrations of a single spherical lens element is through bending of the lens. The most familiar occurrence of this is when the only option you have is to purchase a plano-convex lens to use in a preliminary demonstration on some sort of optical bench with a grouchy boss looking over your shoulder. The orientation of that lens is VERY important. Placing the curved side on the long conjugate side of the lens will minimize the aberrations of the lens, but is clearly not an optimum solution. (See below.) Additional means of impacting aberrations are glass selection to define the index of refraction and the spectral dispersion, defining the element thickness, and balancing the spherical curves on each surface. Additionally, it is sometimes feasible to utilize an aspheric surface on one or both surfaces of an element. However, unless the lens is to be used at a very limited range of field positions, this is rarely a good idea for a single lens. We’ll return to the lens bending process and its impact on various aberrations in a future article.
Most people are familiar with modern camera lenses and recognize that multiple elements are necessary to achieve good imaging performance. This is true in cameras and projectors, as well as nearly all forms of optical instrumentation. The multiple lens elements permit the balancing of the aberrations contributed by each of the individual lens elements. Modern lenses are very often zoom lenses and are often comprised of 10 to 20 individual elements with at least two groups of lens elements that must move in perfect synchronism. Often, one or more of these lens elements are aspheric in order to reduce the overall number of lens elements while improving the aberration control. These elements are commonly made of various glasses with differing index of refraction and dispersions in order to balance the chromatic (color-based) aberrations. All of these aberrations vary as a function of field angle, aperture, spectral content, or most often, a complex combination of these.
Experience Counts - Big Time!
It is small wonder that modern lens design has improved significantly due to the power of ever-faster computers and complex software. Even so, the lens design process is hardly one of plugging in plates of glass and popping out a lens; though, with proper knowledge and skill, along with enough optimization cycles, this can occasionally be accomplished. The usual method is to draw upon past experience and start with a lens form that is appropriate for the goals being pursued. I utilize a data base of over 30,000 lens forms that I am able to search using a variety of selected parameters to find likely starting points. Once an appropriate starting point has been identified, the construction of a merit function is required to guide the optimization. The merit function is a complex listing of multiple performance and construction parameters that identifies to the software where to push on the lens parameters as well as how hard to push. The merit function will almost always be modified as the optimization progresses. There is no “one size fits all” version of the merit function! It is the lens designer’s job to observe the progress of the optimization and make appropriate changes to the merit function to guide the optimization process. In optimizing a 15 element lens, it is not uncommon for there to be several hundred terms in the merit function in order to control and guide the optimization of 30 to 80 lens variables simultaneously. Depending on the convergence speed and performance criteria, this process can still take hours on a very fast computer. This is multiplied when a zoom system is being designed, since each zoom position becomes an “additional lens”. Nevertheless, all parameters except lens group positions and imaging conditions must stay linked during the optimization process for these multiple configurations of the zoom lens. For instance, lens element shapes and thicknesses must remain consistent for all of the various “lenses” or configurations of the zoom positions. In summary, lens design is a relatively complicated process requiring a significant investment of effort and knowledge to become successful.
But What About Reflecting, Instead of Bending the Rays?
Mirrored surfaces can be combined with refractive elements to alter the layout of the lens system for purposes of packaging or performance. Reflective surfaces, however, are prone to increased aberrations at even moderate fields of view, and are therefore best utilized in systems such as telescopes where the angular field of view is quite small.
Just When You Thought You Were Done.....
Once the design is complete, the job is not finished. There is no factory in the world that can build a perfect lens; therefore, the lens must be toleranced so that it is both manufacturable and performs adequately. The implication is that no lens will perform as well as the “perfect” design that the computer spits out. Manufacturing errors will degrade the performance of the system, and it is the lens designer’s job to manage the as-manufactured performance statistics against the costs of manufacturing. This is generally a trade space that is dependent on the volumes anticipated. Precision glass molding is capable of producing very accurate glass aspheres as well as spherical surfaces, but the tooling costs of this process are very high compared to a simple grind and polish of spherical surfaces. However, cycle times of molding are a small fraction of grinding and polishing, and in high volume result in a lower cost assembly. Use of plastic lens elements or glass will affect the cost of the assembly in a significant way. In high volume, the piece price of a plastic lens assembly is usually much lower than an equivalent glass system due to the precision replication of surfaces possible with molding and the relatively short cycle times. Added to this value is the fact that it is generally no more expensive to mold an aspheric lens than a spherical lens, and the asphere will often outperform the glass component, and in many cases can replace two glass spherical elements.
Are We There Yet?
Once the tolerancing of the lens assembly is complete, the barrel must be designed to ensure that these tolerances of spacing; element tilt and decenter; as well as lens group tilt and decenter are maintained both in assembly, and in use should there be moving components. Finally, the lens coatings must be specified. The coating engineer must design the coating layer stack to account for the range of angles of incidence on the surface as well as the type of glass or material on both sides of the coating stack. Usually, this task is left to the engineer within the coating facility, for not only does the design of the stack have to be established, but tolerances, material behavior, adhesion, and method of deposition have to be managed.
The process of designing a manufacturable lens assembly is a multifaceted effort. A professor once told me that lens design was as much art as science. While I am not sure that I agree with the statement, the experience and skill of the designer does play a very significant part in the successful outcome of the design of multielement lens systems. In future articles I will address some of the characteristics of several challenging lens design forms, as well as some of the general topics outlined in the introductory paragraphs.