An Introduction to Machining Non-Axisymmetric Optics

Existing single point diamond turning machines are capable of fabricating complex aspheric optical surfaces; however, the machine tool limits these surfaces to ones of revolution. Introducing a high speed control system, spindle position and a high bandwidth axis parallel to the spindle axis, and two additional axes enables the machining of non-axisymmetric machine surfaces.

Researchers have carried out only a limited amount of work to fabricate non-axisymmetric components with the help of diamond and other conventional tools. Early attempts at diamond machining non-axisymmetric surfaces were carried out by Douglass, who found that the control system and tool actuator prevent the generation of optical quality surfaces. Later, Meinel achieved good results while using a piezoelectric actuator to fabricate a phase corrector plate. In conventional machining, Tsao and Tomizuka machined non-circular cylindrical parts.

This article describes the single point diamond turn non-axisymmetric optical surfaces that serve as off-axis segments of large optics. The segments can be employed as off-axis mirrors or as segments for developing larger on-axis mirrors. One such example of on-axis mirror is the 10 m Keck Telescope. The article also includes the experimental setup description and its cutting results.

Non-Axisymmetric Geometry

The general conic of revolution is the parent optic considered in this experiment, selected because there is a known closed form description of the off-axis segment surface, and because it can be put into a form that makes real time implementation by a high speed controller possible. However, it is necessary to bear in mind the details of implementation at each step of the development.

The surface of an off-axis conic segment is described in cylindrical coordinates in the following equation:

where z3 is the segment sagitta, ρ is the segment center radius, φ is the angular position around the segment, and the di’s are the functions of the parent optic and the distance of the segment from the parent axis.

Gerchman has provided a detailed development of this equation and a full description of the surface.


The non-axisymmetric segment surface is machined by coordinating the motion of the tool servo (Z' axis) and machine's X and Z axes. As the machine spindle rotates the segment, tool servo motion is generated with respect to the position of the measured spindle. The separation of the Z and Z' motions is critical to attaining the proper segment surface. Hence, the resulting surface is explained in Equation 1, which is divided in two parts; one part is φ and ρ dependent while the other is dependent only on ρ.

Precalculation of the X and Z motions at each ρ value is an optimal approach to separating the equation. It is possible to generate a baseline motion for the machine slides by determining the maximum and minimum values of z3 at each ρ while considering a point half way between the values as the reference. The tool servo motion is calculated by subtracting the value of each ρ from z3 (ρ, φ). The following equation defines the tool servo motion calculated by this method:

Figure 1 shows an example of the optimal baseline based tool servo motion. In this, the tool motion is illustrated as a function of the angular position φ. The dotted line is motion at 1/4 ρ, the dashed line at 3/4 ρ, the dash-dot line at 1/2 ρ, and the solid line at ρmax. This is an example for cutting an off-axis segment of a paraboloid. It was observed that the motion looks like a decaying sinusoid, but as shown by the dotted line, is not that way towards the center of the segment.

Tool servo motion with optimum baseline subtracted. Solid line is tool motion at ρmax

Figure 1. Tool servo motion with optimum baseline subtracted. Solid line is tool motion at ρmax

Experimental Setup

The experiments were carried out using the Fast Tool Servo (FTS) on a Rank Pneumo AS G-2500. The device is a short range high bandwidth linear tool motion device that is based on a piezoelectric actuator. The position feedback, provided by an integral capacitance gauge, compensates for non-linearities in the actuator. The bandwidth of the existing device is over 1 kHz, and it has a range of 20 µm.

There are two other main components: a high voltage amplifier (HVA) and a high speed controller to fabricate the complete machining system. The HVA makes use of a low voltage signal and amplifies to a high voltage, high current drive signal for the piezoelectric actuator. However, the high speed controller combines the components together and generates a control signal for the actuator. The components of the experimental setup and the interconnections are shown in the Figure 2.

Diagram of experimental setup

Figure 2. Diagram of experimental setup

Results and Discussion

Different types of non-axisymmetric surfaces have been designed to read the viability of machining and illustrate the possible error sources. For instance, generating a decaying, once per revolution sinusoidal signal for the tool servo leads to the fabrication of a flat surface tilted with respect to the plane that is at right angle to the spindle rotation axis.

Figure 3 shows an interferogram of the tilted flat with a normal reference flat around its periphery. The inner flat is titled to make the distance between its lowest and highest point about 5 µm. The diameter of the tilted flat surface was measured to be 20 mm.

nterferogram of tilted flat surface machined with tool servo at a spindle speed of 480 rpm.

Figure 3. Interferogram of tilted flat surface machined with tool servo at a spindle speed of 480 rpm.

While machining the tilted surface under less than ideal operating conditions, two surface errors were observed. The earlier machining attempts without feedback from the capacitance gage resulted in the generation of a non-symmetric surface error. Further, the estimation of X-axis position based on X starting position and feedrate produced a coma-like surface error. Both the errors demonstrated the need for an efficient control system with required inputs.


The effectiveness of the concept was shown by the initial experiments that involved machining of non-axisymmetric optical surfaces on a diamond turning machine. The capabilities of various key components of the machining system have also been discussed in such experiments. The components feature efficient software capable of generating the proper control signal, a high speed control system with sufficient inputs, a high voltage amplifier, and the high bandwidth tool servo.

Further research work is focused on enabling the system to machine off-axis segments of aconicoid surfaces.

About Precitech

Precitech began operations in 1992, but continues the rich history of ultra-precision machine tool building dating back to 1962, when Pneumo Precision was founded. In October of 1997, the Pneumo ultra-precision machine tool division of Taylor Hobson (formerly Rank Taylor Hobson / Rank Pneumo) was merged with Precitech. The Precitech name was retained for this corporate entity and all offices and manufacturing facilities are now located at 44 Blackbrook Road in Keene, New Hampshire.

Our facility staffs approximately 100 talented individuals in a recently designed 60,000 Sq. Ft. building.

Precitech is a member of AMT (The Association of Manufacturing Technology) and has corporate affiliations with several professional societies and academic institutions such as Germany’s Research Community for Ultra Precision Technology at the Fraunhofer Institute, ASPE the American Society for Precision Engineering, and EUSPEN the European Society for Precision Engineering and Nanotechnology.

This information has been sourced, reviewed and adapted from materials provided by Precitech.

For more information on this source, please visit Precitech.


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