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Optical lens design is the science/art of calculating the various lens construction parameters (variables) that will meet or at least approach desired performance requirements while staying within required constraint values, and any cost/schedule limitations.

Construction parameters include surface types (spherical, aspheric, holographic, diffractive, etc.), and different parameters for each surface type, such as radius of curvature, thickness to the next surface, glass type, and tilt and/or decenter.

Design requirements

Performance requirements can include:

1. Optical performance (i.e., image quality) can be quantified by encircled energy, modulation transfer function, Strehl ratio, ghost reflection control, etc. and/or pupil performance (size, location, aberration control). The choice of the image quality metric is application specific.

2. Physical requirements such as weight, static volume, dynamic volume, center of gravity, and overall configuration requirements, and

3. Environmental requirements (ranges for temperature, pressure, vibration, electromagnetic shielding, etc.)

Design constraints can include realistic lens element center and edge thicknesses, minimum and/or maximum airspaces between lenses, maximum constraints on incidence and exitance angles, physically realizable glass index of refraction and dispersion properties, etc.

Manufacturing costs and delivery schedules are also a major part of optical design that must be addressed. The price of an optical glass blank of given dimensions can vary by a factor of 50 or more, depending on the size, glass type, index homogeneity quality, and availability, with BK7 usually being the cheapest. Costs for larger and/or thicker optical blanks of a given material, above 100mm to 150mm or so, usually increase faster than what would be proportional to just the increase in physical volume. This is primarily due to increased blank annealing time required to achieve acceptable index homogeneity and internal stress birefringence levels throughout the blank volume. Availability of glass blanks is driven by how frequently a particular glass type is mixed and poured by a given manufacturer, and can seriously affect manufacturing cost and schedule.

Process

Lenses can first be designed using paraxial theory to position images and pupils as desired, then real surfaces inserted and optimized. Paraxial theory can be skipped in simpler cases and the lens directly optimized using real surfaces. Lenses are first designed using average glass index of refraction and dispersion (see Abbe number) properties published in the various glass manufacturer catalogs, and though glass model calculations. However, when the actual glass batch ingredients for a desired glass type are mixed together and melted, then further mixed while molten to maximize batch homogeneity, then poured into lens blanks and annealed according to empirically determined time-temperature schedules, the finished blank optical properties usually vary slightly from catalog values. Index of refraction values can vary by as much as 0.0003 or more from catalog values, and dispersion can either remain about the same or vary slightly. These changes in index and dispersion can sometimes be enough to affect the lens focus location and imaging performance in highly corrected systems.

The glass blank pedigree, or "melt data", can be determined for a given glass batch by making small precision prisms from various locations in the batch and measuring their index of refraction on a spectrometer, typically at five or more wavelengths. Lens design programs have curve fitting routines that can fit the melt data to a selected dispersion curve, from which the index of refraction at any wavelength within the fitted wavelength range can be calculated. A re-optimization, or "melt re-comp", can then performed on the lens design using measured index of refraction data where available. When manufactured, the resulting lens performance will more closely match the desired requirements than if average glass catalog values for index of refraction were assumed.

Delivery schedules are impacted by glass and mirror blank availability and lead times to acquire, the amount of tooling a shop must fabricate prior to starting on a project, the manufacturing tolerances on the parts (tighter tolerances mean longer fab times), the complexity of any optical coatings that must be applied to the finished parts, further complexities in mounting or bonding lens elements into cells and in the overall lens system assembly, and any post-assembly alignment and quality control testing and tooling required. Tooling costs and delivery schedules can be reduced by using existing tooling at any given shop wherever possible, and by maximizing manufacturing tolerances to the extent possible.

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 tolerancing is included during the design, parts can usually be manufactured accurately enough that the resulting lens assembly performs fairly closely to the paper design.

Optical design is also partly an art, though, as the multi-dimensional design volume within which a constrained lens design is free to roam is literally beyond human imagination or comprehension if more than two to three construction parameters are free to vary. The number, type and placement of optical elements is partly driven by physical requirements, but is also often based on previous similar designs obtained from published data, patents, books, etc. Skill and intuition in lens design is 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 airspaced 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 9-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 foamscape. 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 100 dimensions or more.

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 and even 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/or harsh environmental conditions.