Semiflexible tools remove ripples

Nov. 1, 2002
Spherical glass optics are almost always ground and polished by a rigid tool of approximately the same spherical shape as the surface to be figured...

Spherical glass optics are almost always ground and polished by a rigid tool of approximately the same spherical shape as the surface to be figured (with plano optics merely a special case with the sphere's radius equal to infinity). The process works because any one section of a sphere is identical in shape to another. No technique of such simplicity is available for the fabrication of aspheres, however.

A paraboloid was ground from glass using a rigid tool, which left many high-frequency features (left). The surface was then ground further with a five-segment ring lap, reducing the high-frequency error (center). Subsequent grinding with a flexible-plate tool virtually eliminated the remaining high-frequency error and at the same time further figured the surface (right).
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Aspheres can be automatically fabricated by magenetorheological finishing, as developed by QED (Rochester, NY); however, the equipment is expensive and suited to high-volume production. The more usual technique for small quantities is to hand-figure aspheres by polishing with a rigid tool, interferometrically checking surface figure at intervals. But high-frequency surface ripples are formed in the process that are difficult to polish out.

One solution is to replace the standard rigid polishing tool with a semiflexible tool. Although such a technique is not new, most of the knowledge has been empirical and proprietary, according to Jim Burge, an assistant professor at the University of Arizona's Optical Sciences Center (OSC; Tucson, AZ). He and two other OSC researchers, Michael Tuell and Bill Anderson, are optimizing the process using engineering mechanics analysis, reducing the optimization method to rules that can be widely applied.1 The group has also developed a new type of tool that uses separated rings.

Analytic approach

In the analysis, there are essentially two regimes of interest: the low-order bending defined by the aspheric misfit, and the high-order surface errors, according to Tuell. "Given the diameter of the tool, its radius of curvature, its thickness and basic material parameters, we can calculate the required bending to make the tool fit the surface at a given point on the surface with a specific vertex radius of curvature, conic constant, and higher-order aspheric deformation terms," he says.

The bending of the plate to fit the surface causes internal stresses and strains, which translate to a varying pressure distribution at the tool/optic interface. If large slopes are evident in this distribution, there is the possibility of creating local trenches, which does not help to smooth the surface. Careful modeling is necessary to predict the pressure distribution under the tool for a specific tool action, notes Tuell. The resulting model includes the effects of transverse shear, as well as partial contact, where the plate might not bend enough to completely fit the surface feature, so the polishing surface bridges a gap.2 "The basic result of the bridging model is that we can calculate the appropriate plate thickness to allow high-frequency errors to be preferentially polished over low frequencies, ultimately smoothing the surface," says Tuell.

There are several potential ways the tool could be used, and the tool action itself can modify the aspheric misfit and therefore the pressure distribution. "With so many variables, it can be difficult to know what to do and understand what the simulation is showing you," says Tuell. "A master optician who is familiar with semiflexible tools should be involved with the tool-design process."

Controlling the pressure distribution is key to the success of the tool. This is accomplished by varying the plate thickness and material. The interface layer is also an important factor. For grinding, metal tiles are typically used, while polishing uses polishing pads, pitch, or a combination of the two, says Tuell. The compressive stiffness of the interface material is critical to the smoothing properties of the tool.

A 17-in.-diameter f/0.52 convex paraboloid was produced at the OSC with conventional and semiflexible tooling (see figure). The use of a flexible ring lap and a flexible plate smoothed the paraboloid, greatly reducing high-frequency errors induced by the conventional tool. In addition, the semiflexible tools brought the surface very close to its final figure.


  1. M. T. Tuell et al., Optical Eng. (July 2002).
  2. P. K. Mehta et al., Proc. SPIE 3786 (1999).

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