Single-point diamond turning (SPDT) of optical surfaces has historically been especially useful for producing aspheric and diffractive surfaces for the IR spectral region. Wavelengths in the IR spectral region are longer than those of the visible region, which means that surface roughness specifications are not as stringent as for visible components. Over recent years, however, the stability of the SPDT machines and their control systems have improved, allowing the production of surfaces that in many cases meet even the demands for optical elements used in the visible spectrum. Aspheric and Diffractive Elements
Although spherical surfaces are easiest to manufacture, especially in large volume, such lenses suffer from spherical aberration. Eliminating spherical aberration for a single element requires an aspheric surface, which is easy to design but not to manufacture using conventional manufacturing methods. SPDT technology, however, can easily generate aspheres. The appropriate mathematical function of the asphere must simply be loaded into the control system for the diamond tool to follow as it cuts across the surface.
Refractive index changes with wavelength, so a lens covering a given spectral band suffers from longitudinal chromatic aberration. Conventionally, optical designers correct chromatic aberration with two elements: a positive low-dispersion front element and a negative, high-dispersion rear element. Such an arrangement is known as an achromat.
SPDT provides us with an alternative solution to chromatic aberration. Using SPDT, we can put a diffractive phase profile on one of the two surfaces of a single element. This phase profile acts as a grating and, if properly proportioned, sends the light in the desired direction.1 To keep things in perspective, remember that the depth of the phase profile at the zone transition is only d = λ/(n-1), with λ being the wavelength, and n the index of refraction. For a silicon lens (n = 3.425) used in the mid-IR region (λ = 4 µm), for example, the maximum depth d = 1.65 µm. Superimposing such a diffractive structure on an aspheric surface yields an achromatic singlet whose spherical and chromatic aberrations are corrected. Such a lens is also called a hybrid.
The side chosen for the diffractive aspheric surface is usually the second one of the lens, which faces the inside of the housing, because it is better protected from the environment. The chromatic correction for both achromatic doublets and diffractive aspherics is restricted to just two wavelengths. The deviation of the third wavelength is called the secondary spectrum, and is sufficiently small for our optimally designed hybrid that we can consider the element to be diffraction limited.
Use caution when considering the use of diffractive elements. Not all computer design programs use the same mathematical expressions, so take care when specifying the details of the blazed grating structure to the manufacturer. The number of required zones, the minimum spacing of the zones at the edge of the lens, the tool radius, the diffraction efficiency, the surface roughness, and the direction of the profile have to be clearly identified to obtain the expected results. SPDT Advantages
Figure 1. Diamond turning can produce "snap together" opto-mechanical components with integrated mounting features leading to a complete system (top), such as this Cassegrain objective (bottom).
The SPDT process can provide mechanical as well as optical advantages. Because of the built-in precision of the machine, the registration of the mechanical and optical axes is automatically achieved. This allows us to build "snap-together" devices that can eliminate any additional adjustments of the elements (see Figure 1). In this example, the optical mirror surface is part of the mechanical structure (aluminum), and the two are machined in the same setup. Achieving the necessary optical surface quality requires properly adjusting the tool shape, tool feed rate, and spindle rpm.
Figure 2. The layout of this three-mirror anastigmat demonstrates the design freedom offered by SPDT technology.
We can apply this principle of mechanical and optical integration to many other configurations.2 Consider a modern three-mirror anastigmat consisting of two segments (see Figure 2) and produced by SPDT. Producing such a system the conventional way would require individually manufacturing the reflecting elements from glass, then mounting them into a suitable mechanical structure. The upper part of the assembly includes a flat mirror intended as an aid for an alignment process called "squaring on," in which, with the aid of an autocollimator, we can use the mirror to establish the perpendicularity of the system to its optical axis. Finding the focal position of such a system is then a relatively easy task. If the mounting screws and positioning pins of the assembly consist of the same material as the mirror components, temperature changes only introduce scaling effects; the optical integrity will be maintained.
Figure 3. Highly magnified (2,750X) phase profile of a nickel-plated mold pin shows a grating structure with a 12-mm pitch and a 4-mm depth. The profile was generated with a 5 mm split-radius diamond tool.
Micro-optics encompass lenses 2 mm or less in diameter. Manufacturers can apply diamond machining to mold inserts (mold pins) with surprisingly tiny lens features (see Figure 3). The size of the pin can of course be larger than 2 mm.
We can judge the limitation of SPDT as a process for machining diffractive micro-optics lens profiles by the simple expression
where ∆γ is the minimum radial spacing of the Fresnel steps at the edge of the diffractive lens, λ is the wavelength, and f /# is the relative aperture. A relative aperture of f /4 leads to a minimum radial spacing of 4 µm for the visible spectrum, 32 µm for the mid-wave-IR region (MWIR, 3 to 5 µm), and 80 µm for the long-wave-IR region (LWIR, 8 to 12 µm). Diamond turning can produce components with grating spacings of 2.6 µm and profile depths of 1.3 µm.3
Figure 4. Free-form shaping offers a method for producing non-rotationally-symmetric structures with SPDT.
Generating a non-rotationally symmetrical optical surface with SPDT is possible with multi-axis machining systems. Such systems permit 3-D flycutting for freeform shaping. Each small cusp-shaped area segment is generated following a programmed tool positioning sequence (see Figure 4). In our example, the swing radius of the tool is much larger than the tool radius. If we choose the radii to be equal, the small, scallop-shaped surface segments will be symmetrical. In most cases, this machining method is used for the fabrication of lens and mirror molds.
For cases in which SPDT is not appropriate, we can replace the tool with a properly shaped grinding wheel. One reason for doing so would be if the material to be machined were not diamond-turnable, such as steel for example. The grinding wheel method can achieve high surface-shape accuracy and surface quality, suitable for imaging optics in the visible spectrum. Other applications are in the field of illumination, in which the shape of the optical elements can be very complex; in such cases, figure is less important than finish. SPDT Limits
There are always limitations for any manufacturing process, and SPDT is no exception. According to Lord Rayleigh's criterion, if the optical path difference (OPD) of a system is less than or equal to λ/4 under consideration, the performance will be indistinguishable from being perfect.
We can calculate rms OPD from peak-to-valley (p-v) OPD using
For a single surface, this equates to an rms figure error of about 45 nm (0.045 µm) for the visible spectrum, 286 nm (0.286 µm) for the MWIR region, and 714 nm (0.714 µm) for the LWIR region. Clearly, the specifications for IR optical components are much less demanding than those for shorter-wavelength optics. State-of-the-art diamond turning machines can achieve visible-component specifications, however (see Figure 5).
Figure 5. Metrology data for SPDT-fabricated flat aluminum disk, 75 mm in diameter with a 12.5-mm radius of curvature over a 10-mm aperture in the disk center (inset) shows 15-nm form accuracy (0.015 mm rms) of the flat section, or outer area (top), and 24-nm form accuracy (0.024 mm rms) of spherical section, or center area (bottom). The disk was produced on a system operating at 1000 RPM with a 4-mm cut depth, a 0.508-mm tool radius, and a feed rate of 5 mm/min = 5 mm/revolution.
We express total integrated scatter (TIS) of a surface as TIS = (4πδ/λ)2, where δ is rms surface roughness. This relation verifies that for longer wavelengths (for example, in the IR region), we can relax the roughness specifications. On the other hand, it also states how demanding the requirement gets when optical surfaces are to be diamond turned for the visible spectrum. The surface roughness of the part shown in figure 2 was measured to be 2.8 nm rms. That translates to 0.4% TIS, which renders the part suitable for use in the visible spectrum.
The theoretical surface configuration of a diamond-turned surface resembles the profile of a grating. The spacing of this "grating" equals the feed of the cutting tool, and the periodic structure is cusp-shaped. Because of material deformation and other influences, this ideal profile can never be achieved, but the model serves well in the analysis of the optical behavior of such a surface.
For vertical viewing, the grating equation simplifies to
where fr is the tool feed per revolution and θm is the diffraction angle of the mth order. If the feed fr approaches λ, the diffraction effect is no longer present. The equation also shows that the effect is minimized for the longer wavelengths.
Remember, a diffraction pattern always lies in a plane perpendicular to the grooves. In the case of SPDT on a lathe, the grooves consist of complete spirals; therefore, the diffracted energy spreads in a conical pattern. Flycutting creates arc-segments, which form a more directional stray radiation pattern. Although the available data differs, all information indicates that these diffractive scatter effects are usually small enough (less than 1%) to be considered negligible for most cases.4,5 We can, furthermore, improve surface roughness by slowing down the feed rate of the finishing pass. Halving the feed rate reduces the value of the p-v height of the cusp by a factor of four.
For completeness, note that we can calculate the rms-roughness of a diamond-turned surface using
where RT is the tool radius.
SPDT is not a perfect solution. As already mentioned, there are materials that cannot be diamond turned, for example, iron, steel, glass, silicon carbide, and tungsten. For applications in the UV region, surface requirements cannot be met and post-polishing is required. For compatible materials, however, diamond-turning technology continues to improve. There are, of course, many more applications suitable for SPDT, but the material presented here indicates clearly how powerful and cost-effective this technology can be if fully exploited. oe
1. M. Riedl, Optical Design Fundamentals for Infrared Systems, Second Edition, SPIE Press (2001).
2. D. Korsch, Reflective Optics, Academic Press (1991).
3. C. Londono, Design and Fabrication of Surface Relief Diffractive Optical Elements, or Kinoforms, with Examples for Optical Athermalization, Tufts University, Boston, MA (1992).
4. J. Stover, Optical Scattering, Second Edition, SPIE Press (1995).
5. R. Kimmel, Proc. SPIE 508, p. 97 (1984).
Max Riedl serves as technical adviser to Precitech Inc., Keene, NH.