Lens optimization
Optical design is partly a science because ray paths and wavefront structure can be very accurately calculated anywhere along the propagation path through the lens. Glass and coating optical properties can be measured and modeled with sufficient precision for use in lenses. If tolerances are included during the design, parts can usually be manufactured accurately enough that the resulting lens assembly performs acceptably close to the paper design.
Optical design is also partly an art, though, as the multi-dimensional design space within which a constrained lens design is free to roam is literally beyond human imagination if more than a few construction parameters are free to vary. The number, type and placement of optical elements are partly driven by physical requirements, but are also often based on previous similar designs obtained from published data, patents and textbooks. Skill and intuition in lens design are acquired over years of experience spanning hundreds to thousands of different lens design projects, preferably leading to additional experiences (and headaches) dealing with fabricating and aligning systems.
As an example of the complexity of lens-design space, a simple two-element air-spaced lens has nine variables (four radii of curvature, two thicknesses, one airspace thickness, and two glass types). Even for this simplest case, the design space is thus nine-dimensional, and local or global solutions within this space can at least be imagined as smaller or larger bubbles in a sponge-like 9-D foam-scape. A complex multi-configuration lens corrected over a wide spectral band and field of view, at multiple zoomed focal lengths and over a realistic temperature range, can have an extremely complex design volume, having over a hundred dimensions.
Lens optimization techniques that can navigate this multi-dimensional space and proceed to local minima have been studied since the 1940s, beginning with early work by James G. Baker, and later by D. Feder,[1] Wynne,[2] Glatzel, D. Grey[3] and others. Prior to the advent of digital computers, lens design was an agonizingly slow hand-calculation process requiring high-precision trigonometric and logarithmic tables, reams of paper, plotting 2-D cuts through the multi-dimensional space, and significant patience and understudying from previous masters. Tracing a single ray through a given lens surface could take more than an hour of painstaking calculations and checks, and a lens designer could not design more than a very few complex, high-performance anastigmatic objectives in an entire lifetime.
Modern desktop computers can now raytrace tens to hundreds of millions of rays per second through a lens, and perform hundreds to thousands of optimization cycles per second, rapidly exploring the n-dimensional design volume including hill-climbing in and out of local minima in the search for the best solution.
However, even with lightning-fast optimizers, seasoned experience is still needed to guide solution trajectories through unacceptably shallow local minima and achieve the desired performance requirements. Experience in the mechanical and physical properties of glass, metals, optical coatings and bonding materials is also needed, especially in systems required to give high sustained performance over wide temperature ranges and harsh environmental conditions.