12 Dec 2006
Aspheres allow designers to build smaller, lighter and simpler optical systems, and can be found in everyday products. Edwin Diaz provides a back-to-basics guide to the technology.
You may not realize it, but aspherical lenses are found in a wide variety of products. Examples include compact disc players, digital cameras, virtual-reality helmets, professional movie cameras, surgical lasers, bar-code laser scanners and endoscopes.
An aspherical lens, or asphere, is essentially any lens that is not spherical – in other words, its surface is not a constant distance from a central point. This unique shape allows the lens to deliver much better optical performance and image quality than traditional spherical lenses.
Optical designers benefit from the fact that aspheres can correct aberrations using fewer elements than was previously possible with conventional spherical optics. This leads to systems with reduced weight, size and complexity; and fewer alignment requirements and shorter assembly times. Designing with aspheres also results in an optical system that is less susceptible to tolerance variations that can affect imaging performance.
Advantages of aspheres
Aspheres are often found in applications that require an element to focus or collimate light. For such applications, designers tend to use low f-number or fast lenses because the focused spot size of a diffraction-limited lens decreases in direct proportion to its f-number. However, a single spherical lens with a low f-number suffers from spherical aberration (see figure 1), which degrades its focusing performance. By changing the lens to an asphere, spherical aberration can be eliminated (see figure 2) and a diffraction-limited focused spot can be achieved.
In systems that use spherical lenses only, additional elements are often added to compensate for aberrations. A single asphere can take the place of two or more spherical elements in many optical devices, such as night-vision goggles, since it focuses light more precisely. Replacing large sets of spherical lenses with an asphere makes the goggles smaller and lighter, while also enhancing image quality and resolution. Another example is zoom lenses, which can sometimes contain more than 10 optical elements. Aspheres can produce similar or better zoom performance with far fewer elements, which reduces the overall size of the optical system as well as production costs.
An optical system that uses fewer elements also minimizes the number of alignment steps required during assembly. If one uses more elements to correct aberrations than necessary, then the stack up of tolerances can decrease performance. Another advantage of using fewer elements is that it reduces the number of surfaces and corresponding number of antreflection coatings. Loose manufacturing tolerances during assembly or thermal and mechanical shock to the lens after it has been assembled are generally more of a problem for a system with more elements.
Using aspheric surfaces is nothing new. Astronomers using reflective telescopes realized long ago that parabolic mirrors (a specific type of aspheric mirror) produce better images than spherical mirrors. The rays that strike the edge of a spherical mirror focus at a different spot from rays striking the mirror's centre. Parabolic mirrors do not suffer from such deviation and produce better image quality in telescopes with lower f-numbers.
Although various techniques exist to combat aberrations in an optical design that uses spherical surfaces, none matches the imaging performance and flexibility that aspheres provide. One technique used to reduce aberrations in spherical lenses is to increase the f-number of the lens. This however reduces the amount of light that reaches the image, which leads to a trade off between light collection and image quality.
By using aspheres it is possible to design high-throughput (low f-number) lenses while at the same time maintaining good image quality. For this reason, aspheres are increasingly used in low-light imaging applications such as fluorescence microscopy where, to minimize surface reflections, glass absorption and autofluorescence, imaging lenses are designed with as few elements as possible.
Aspheres can have much shorter focal lengths than similarly sized spherical lenses. Single spherical lenses are limited to f-numbers of one or greater. Because aspheres can be manufactured to have larger numerical apertures (NA), and hence lower f-numbers, they are especially useful for collimating laser-diode beams and coupling light into and out of optical fibres.
Collimating a laser beam exiting a fibre requires the NA of the collimating lens to be larger than that of the fibre to capture all of the available light. Prior to the use of aspheric lenses, only ball lenses could provide higher NAs. Ball lenses, however, suffer from significant spherical aberration. Laser-diode manufacturers continue to incorporate aspheres into their laser-diode modules because of their improved light collection and focusing performance.
Aspheres can also be used to correct aberrations that increase with image height (see figure 3). An aspheric surface can exert considerable control and correction on off-axis rays, which reduces aberrations such as field curvature, astigmatism and distortion.
Today's optical software allows designers significant freedom to use aspheric terms on as many surfaces as needed to get an optimal design. The software can easily and quickly produce a result for an asphere that will improve a lens design. Designers should be cautious, however, to ensure that any aspheres can be manufactured at a reasonable cost. Two aspheric surfaces can, in some cases, provide sufficient performance: one near the stop to correct for spherical aberration and one away from the stop to correct for field-dependent aberrations. By adding appropriate constraints during the design phase, a designer can quickly turn a difficult part into an easy-to-manufacture, cost-effective solution.
Machine, mould or turn?
A designer must provide all of the specifications to allow an asphere to be manufactured. Simply providing the aspheric coefficients from the optical-design software is not enough. Most, if not all, asphere manufacturing facilities require a lens drawing that lists not only the aspheric coefficients but also the aspheric equation used and a sag table to ensure that there is no ambiguity in how the asphere is being specified.
Due to advances in aspheric manufacturing technology, many glasses and crystalline materials today can be used to make aspheres. These lenses can be manufactured for wavelengths ranging from the ultraviolet to the infrared. Single-point diamond turning is routinely used to rapidly produce precision aspheric optics in metals, plastics and crystals.
Glass aspheres are typically compression-moulded or machined using computer-controlled grinding and polishing equipment. Both types can be purchased as off-the-shelf products.
Common glass materials used as substrates for off-the-shelf aspheres include BK7 and fused silica.
An application may require a lower- or higher-dispersion glass to reduce chromatic aberrations. In such cases, a custom asphere will be needed. Custom-moulded aspheres will have comparatively higher tooling costs but will make most sense in applications requiring several thousands of lenses. Machined aspheres are used in low- to mid-volume applications such as large-aperture telescopes, high-end camera lenses and microscope objectives. Moulded aspheres are used primarily in commercial optics such as digital cameras and laser-diode focusing assemblies.
Machined aspheres can generally be made larger than their moulded counterparts. Parts ranging from 15 to 200 mm and larger can be readily machined –aspheres as large as 800 mm in diameter have been manufactured.
In contrast, moulded asphere diameters tend to be between 1 and 25 mm. Making a mould 200 mm in diameter would not be possible – as the lens cools it shrinks causing deformation. Moulded aspheres, on the other hand, can have smaller vertex radii of curvatures, which enables them to have larger NAs. The NAs of commercially available moulded aspheres can range anywhere from 0.15 to 0.8, although larger NAs are possible in custom-made lenses. The fundamental limitation is how small a radius one can cut into the mould.
For a machined asphere, two functions determine how difficult it will be to manufacture: the magnitude of the departure from a spherical shape and how quickly the aspheric departure changes with distance from the optical axis. In general, higher refractive index and softer glasses reduce production costs. The higher index allows the vertex radius of curvature to be longer for the same amount of bending, which enables the aspheric departure to be reduced with the same impact on the transmitted wavefront. In the case of moulded aspheres, it is best to use glasses with low transformation temperatures and low coefficients of thermal expansion to minimize shrinkage as the lens cools.
With the advent of magnetorheological finishing (MRF), it is now possible to take a diamond-turned, moulded or machined asphere and adjust its aspheric profile. In MRF, the polishing tool is a fluid that changes viscosity depending on the strength of the applied magnetic field. This technique can even turn a polished sphere into an asphere fairly quickly.
Aspheres offer various advantages for reducing the complexity, weight and size of optical systems. These advantages, coupled with significant advances in asphere manufacturing, make designing with aspheres both practical and cost effective. Aspheres have been, and will continue to be, incorporated into a broad range of consumer and industrial products.
• This article originally appeared in the December 2006 issue of Optics & Laser Europe magazine.