The proliferation of consumer electronics with built-in optical systems has given rise to what might fairly be called the Age of the Asphere. In fact, more than 500 million aspheres were produced in 2002 alone, of which approximately 200 million were glass. We predict that when numbers are collected for 2003, about 250 million glass aspheres will turn out to have been manufactured. Indeed, the desire for compact, durable, high-performance lens systems is at a new height.
Cameras, telecommunication products, and DVD players are responsible for most of the increase. Interestingly, you cannot buy a digital camera of reasonable quality these days that does not include at least two aspheric surfaces. In 2002, more digital cameras were sold than film cameras; by the summer of 2003, more mobile phones with cameras were sold than digital cameras.
Optical designers have known for many years of the often significant performance improvements and physical space savings they could gain by using one or more non-spherical surfaces, or aspheres, in their optical designs, but issues of cost and ease of manufacture held them back. The traditional monochromatic aberrations, including spherical aberration, coma, astigmatism, and distortion, are due entirely to the fact that it is simply impossible to perfectly image light with spherical surfaces. The reason for the imperfection has to do with Snell's Law (n sin Θ = n' sin Θ'), an inherently nonlinear relationship that describes the refraction of a wavefront as it travels from one medium to another. In the small-angle, or paraxial, region, sin Θ ≈ Θ, however, and we can approximate Snell's Law as n Θ = n' Θ'. Approximations have their limits, though. In this case, aberrations represent the nonlinear difference between paraxial imagery, which assumes no aberrations, and real ray tracing using the full version of Snell's Law.
The result is that the imagery from a typical lens is often imperfect, with the residual aberrations being proportional to different orders. For instance, third-order spherical aberration is proportional to the cube of the aperture, fifth-order spherical aberration is proportional to the fifth order of the aperture, and so on. A further and direct effect of these aberrations is a residual optical path differencethe departure from perfect sphericity of the final image wavefront with respect to a best-fitting spherical reference wavefront. The ultimate purpose of an aspheric surface in a lens system is to assist in redirecting the rays to achieve a near-perfect image. We can also think of the asphere as introducing wavefront error to cancel the lack of sphericity of the wavefront.
A single glass lens element with a strong "bending" produces large amounts of spherical aberration. If we bend the lens for minimum spherical aberration, still using spherical surfaces, we can reach a solution that is significantly betterbut not perfect. To eliminate the residual aberration in the spherical lens, we need to either split the element into two or more elements with the same total power, or increase the refractive index of the glass. A simpler alternative is to change either surface into an asphere.
If we use an asphere to eliminate the spherical aberration in an otherwise all-spherical design, we can, in principle, use the other optical surface to more effectively minimize the other aberrations. Consider a plano-convex lens with spherical aberration. We could create a plano-convex element with the same focal length and an asphere on the curved surface. Now the lens would have near-perfect performance, at least on axis, monochromatically, and not including fabrication errors.
Although a designer can place aspheric surfaces on every lens surface in a given system, this often results in a lens system that is difficult to manufacture and a design whose performance improvement is not worth the increased cost. Aspheric surfaces tend to create wavefronts that beat against one another, the changes in one negating the effects of another. If, for example, we use an asphere on each side of an element, the aspheric profile on the front may get stronger than the equivalent spherical element, but the rear surface could essentially cancel most of the effect with a reverse-profile asphere. Although the lens will probably function fineat least on paperthe design will suffer from tight manufacturing and alignment tolerances, which will, in turn, increase cost. Clearly, the magnitude of asphericity will increase cost. We thus recommend that designers use aspheric surfaces only where needed to achieve system performance requirements, but not to make the manufacturer's job impossible. The designer must maintain a balance between system cost and performance at all times.
To illustrate the point of system cost versus performance, consider the performance of a Cooke triplet starting as an all-spherical design and progressing to an all-aspherical design (see figure). As the spot diagrams and modulation-transfer-function curves show, the all-aspheric design provides the best performance. Adding aspheres on only two of the six surfaces provides nearly that level of performance, without the cost of the all-asphere system. The optical designer must make engineering tradeoffs to achieve the cost and performance requirements.
A Cooke triplet shows enhanced performance as the number of aspheric surfaces increases from zero (left), to three (middle), to all (right). In many cases, however, the additional cost of fabricating six aspheric surfaces instead of two, for example, may outweigh the performance benefits. Compression Counts
The use of aspherics in lens design has been established for some time, especially the use of injection-molded polymers, including acrylic, polystyrene, and polycarbonate. Plastic lenses suffer from a variety of problems such as a large negative change in refractive index with temperature (dn/dT ), coating instabilities, and sometimes excessive surface irregularity; in addition, the available plastic lens materials offer a limited range of refractive indices. Such issues notwithstanding, plastic lenses have been used for years in producing consumer-level semiprecision optical systems; but these problems, as well as poor long-term stability, make plastic lenses unsuitable for many precision applications.
Fortunately, advances in compression-molded components have opened up the use of glass aspheres for high-volume applications. Today, almost any glass can be compression molded in a low-temperature process that yields shapes of extremely high accuracy and significantly reduced process time, enabling, in turn, the use of economical molded glass components in high-precision optical devices.1 A mold is prepared having the precise internal configuration of the desired final component. A glass preform is placed in the mold cavity and the mold and the glass preform are heated. A load is applied to the mold at temperatures at which the glass preform exhibits a viscosity of about 108 to 1010 poise, to shape the preform into conformity with the mold. A force is maintained on the mold while it is cooled to a temperature at which the glass is at a viscosity of about 1011 to 1012 poise.
Commercial compression molding processes today can readily handle glass lenses ranging from 1 to 80 mm in diameter, with typical diameters under 20 mm. The process time for a 100-mm plate of any combination of diameter lenses is usually 15 to 20 min. The residual surface irregularity on the surface of finished lenses with diameters less than 25 mm will be in the vicinity of 0.10 to 0.15 µm P-V. Note that the region of 0.10 to 0.15 µm on the surface, which is predicted for compression molding, introduces 0.1 to 0.15 waves P-V to the transmitted wavefront. This measurement is within the Rayleigh criteria for diffraction-limited performance (see table).
Precision glass aspheres can be manufactured at volume with a residual surface irregularity that is well within the diffraction limit. Despite these capabilities, glass asphere producers still face an important challengeconsumer demand has outpaced manufacturing output. Mobile phone producers are reducing production of devices with cameras due, in part, to a lack of glass aspheres. With the markets for digital cameras, mobile phone cameras, and DVD optical pick-ups experiencing double-digit growth, the shortage will continue. China alone is expected to add more than 50 million mobile-phone users annually for the next several years. New optical pick-ups for next-generation, recordable DVD machines based on blue-emitting lasers will further drive demand. Looking ahead, glass molding machine manufacturers will need to ramp up capacity even more to meet these tremendous demands.
Optical system designers are seeing their dreams come true as manufacturing methods improve and costs drop. In some cases, cost-effective optical system designs are feasible that simply were not possible several years ago. It appears that the Age of the Asphere is here to stay. oeReferences:
1. U.S. patents US4,734,118; US4,854,958; & US4,969,944.
Robert E. Fischer is president of Optics 1 Inc., Westlake Village, CA.
Dane Hileman is director of strategic growth: science and technology at Corning Inc., Corning, NY.