The Precessions™ process polishes complex surfaces from the ground state preserving the ground-in form, and subsequently rectifies measured form errors. Our first paper introduced the technology and focused on the novel tooling. In this paper we describe the unique CNC machine tools and how they operate in polishing and correcting form. Experimental results demonstrate both the ‘2D’ and ‘2½D’ form-correction modes, as applied to aspheres with rotationally-symmetric target-form.
©2006 Optical Society of America
The case for using aspheres in optical systems was presented briefly in our first paper , and rests predominantly on the additional degrees of freedom that they provide the optical designer. As a generalization, aspheres can provide superior system-performance and/or lower mass and smaller package-size, compared with solutions using all spherical surfaces. In certain cases (the classical reflecting telescope being the most obvious example), an asphere is almost mandatory.
Several approaches to automated polishing of aspheres were overviewed in . These can be divided into two generic types. First are techniques which distribute controlled simultaneous removal over a large area of the part, such as the Steward Observatory stressed lap  and the Zeiss flexible linear polisher . Second are local removal techniques such as the Itek small-tool polisher , Magnetorheological Finishing Process (‘MRF’) ™ developed by the Centre for Optical Manufacturing in Rochester NY, with QED , and fluid-jet polishing .
In  and references therein, we described the novel local-removal tooling for the Precessions process, which uses an inflated, bulged, spinning bonnet. The bonnet is usually covered with a standard polishing ‘cloth’ (e.g. Polyurethane, Multitex ™ etc.), and the process typically operates in the presence of a re-circulated standard slurry (e.g. cerium oxide). As the bonnet is advanced towards the part, the contact-spot diameter increases, creating a material removal function (“influence function”) of variable size. The spin-axis of the bonnet can be orientated either along the local normal to the part’s surface, or it can precess about the local normal. The characteristic ‘W’ influence function delivered by the former case was shown, alongside a family of rotationally symmetrical near-Gaussian influence functions of differing sizes for the latter. The paper demonstrated how this tooling can achieve excellent texture on glass, at least down to the Ra~0.5nm noise-floor of the Wyko RST500 ™ texture interferometer used for the tests. Results were also included illustrating the inherent linearity of response of the process.
It is now timely in this second paper to describe how the motion of a polishing bonnet relative to the part is implemented in a machine tool of novel design, and how these machines are used both to polish ground surfaces preserving form, and to correct measured errors on rotational parts. This paper focuses on the smallest machine, of 200mm capacity. Subsequent papers in preparation will consider larger machines, specialized tooling, and the complex cases of non-axially-symmetric surfaces such as off-axis conics, and free-form surfaces.
2. The family of machine tools
The machine tools are designed to polish flat, spherical, aspheric and, whilst outside the scope of this paper, free-form surfaces. In order to position the centre of the bonnet’s contact-spot anywhere on the surface of the part, and to orient the axis of rotation of the bonnet with respect to the local-normal to the part, multiple CNC (computer numerically controlled) axes are required. With this in view, the machines utilize seven CNC axes of motion, as follows:
- X,Y,Z coordinates, to address the required location on the part
- Two axes of inclination of the tool (designated A and B) to follow the local surface slope of the part and impose the precession angle in different directions if required.
- Rotation of the part (‘C’ axis) to impose rotational symmetry, if required
- Rotation of the tool (‘H’ axis tool-spindle) to generate high surface-speed at the bonnet-part interface and so create the influence function
In addition, the air-pressure that inflates the bonnet is also controlled (effectively an eighth axis of CNC). At present, the air-pressure is not varied during a polishing run, but can be modified e.g. to optimize texture or removal-rate on different substrate materials. Typical values would be 1-3 Bar. Notably, there is no force feedback loop to maintain constant contact-force between bonnet and part; the machines operate entirely on a positional basis.
Of particular note is that the A and B axes mechanically constitute a ‘virtual pivot’ i.e. they intersect at a point in space that is the centre of curvature of the bonnet’s functional surface. A and B angular motions then impose no offsets in X, Y and Z, simplifying numerical control.
The machines are constructed along the lines of diamond turning or grinding machines, but positional tolerances are not as stringent due to the compliant rather than hard nature of the tool. X, Y and Z axes are mechanically referenced to a Granitan ™ or Polyquartzite ™ casting that provides overall mechanical stability and damping. The part on an IRP200 ™ machine (Fig. 1) is mounted on the horizontal C axis using a Schunk chuck and standard fixturing.
The virtual pivot assembly (Fig. 2) carries the H axis tool-spindle. All moving parts use precision rolling-element bearings. Metal fabrications utilize stainless steel throughout, in order to avoid corrosion associated with polishing slurries.
All power and CNC equipment is mounted in a hinged enclosure to rear of the machine, and the operating area is enclosed and interlocked to conform to health and safety legislation. Finally, local control of the machine is through a pod either separate or mounted off the machine enclosure. The 200mm machines are built with either Fanuc or Bosch CNC controllers by Zeeko Ltd and (under subcontract) by Satis-Loh.
3. Preparing for polishing and choice of tooling
The part on the 200mm machines will typically be waxed into a fixture that fits the Schunk chuck of the machine. During waxing, the part is clocked to a tolerance of a few microns runout, which, with experience, is a simple, reliable and fast procedure.
The most critical aspect of controlling the process is to maintain the prescribed influence function imposed on the part. The first stage in controlling spot-size is to true-in the surface of the cloth on the bonnet at or near to its operating pressure. This is achieved by mounting a single-point cutter in the Schunk chuck in place of the part. X, Y and Z are adjusted to bring the truing-tool into contact with the bonnet. The H axis is driven to spin the bonnet and the A and B virtual pivot motions then true-in the cloth to be both spherical and concentric with the virtual pivot.
The next stage is to detect ‘touch-on’ with the part. The machine incorporates a transducer to sense the local Z position of first-contact, with a sensitivity of ~2µm. Establishing first contact effectively sets the ‘zero-point’ for the local coordinate system in subsequent operations. The bonnet is then advanced towards the part by a local Z offset Δz in order to create the spot-size. Using cord geometry, the full spot-size (not FWHM) delivered by a compressed spherical membrane on a flat surface is given by:
S=(2RΔz-Δz2)1/2, which reduces to S~(2RΔz)1/2 for small Δz
Where S=spot-radius, R=bonnet radius of curvature, and Δz the linear compression of the bonnet to create the spot-size required.
A given spot-size may be produced by a larger bonnet-radius with smaller compression, or vice versa. Volumetric removal-rate tends to vary as the spot-area i.e. with S2, and so is proportional to ~RΔz. Therefore, for a given spot-size and removal-rate, a smaller bonnetradius will require larger Δz. This is useful in desensitizing process-variability against machine Δz positioning errors. The upper limit on spot-size with a particular bonnet is imposed by the tendency of the bonnet to ‘pop’ i.e. invert if compressed too far. These factors lead to a family of bonnets; currently R=20, 40, 80, 160, 320, 480mm. On the IRP200 ™ machine only the first three can be used; the larger bonnets are for larger machines.
A realistic target is to maintain process consistency at the ~95% level. Taking a mechanical setting accuracy of ~5µm orthogonal to the local surface, the corresponding minimum allowable value of Δz~100µm. For the smallest (i.e. R=20mm) bonnet, this translates to a spot-size on the order of 4mm diameter. Global X, Y errors translate into local z errors on sloping surfaces but, as the machines can attack complete hemispheres, the X, Y and Z setting accuracy requirement is the same in all three axes.
Maintaining a constant and predictable removal rate also requires control of the polishing slurry. Bulk slurry is re-circulated from a tank providing i) active temperature control and ii) mechanical agitation to prevent settling. Slurry is delivered through a pair of flexible nozzles to the region of the polishing bonnet. The slurry handling system collects the slurry and it is gravity fed back to the tank. The slurry temperature may be set optimally for certain glass types. However, there are benefits where possible in maintaining the slurry at the same temperature as the metrology laboratory used to measure form. In this case, the time required for the part and its fixturing to reach thermal equilibrium prior to testing is minimized.
4. Polishing to preserve aspheric form
The input-quality for the machines (used in the optics sector) is often a surface precisionground to the aspheric profile by, to give one example, a Satis-Loh G2 ™ grinder. The first stage of processing is then to polish the ground surface preserving the aspheric form. This can be interpreted as removing most of the sub-surface damage, then spatial filtering the surface, removing the parasitic high frequency terms whilst leaving the required low frequency ones.
In the 2D case, this is performed by rotating the part (at speeds up to ~2000 rpm). The bonnet then makes many diametric traverses (effectively, creating repetitive spiral tool-paths). In general, any local Gaussian removal process conducting a spiral tool-path overlapping the centre tends to dig a hole around the centre of the part. This is because most of the time the Gaussian removal spot acts simply on one side of the centre of the part. However, once the spot encroaches the central zone of the part and then overlaps centre, it removes material on both sides of centre simultaneously. It is empirically well established that this ‘doublecounting’ effect can be mitigated by “synchronous polishing” with a W influence function. This is conveniently provided by a pole-down rotating tool, for which the surface-speed increases radially from zero at the centre to maximum at the edge of the tool. In the ‘pure’ case, the C and H axes are driven at the same speed and in the same direction. In practice, we have found that the C and H axes should be run at very slightly different speeds. This has two advantages. First, it averages out the effects of any residual non-uniformity in the polishing bonnet or cloth. Second, it regains some relative motion between tool and part as the tool passes over the exact centre, avoiding texture defects at centre that can otherwise occur.
5. The method to rectify 2D form errors
For form-corrective polishing, the influence function should ideally be mathematically wellbehaved (such as a near-Gaussian profile) rather than the W of a poll-down tool. This is achieved by cantering the bonnet over at an angle to the local normal to the part (the precession angle; typically 10–15°. This is shown in Figs. 3 and 4. By repeating the polishing cycle with the precession angle orientated in four polar directions around the local normal (0°, 90°, 180°, 270°), the summed influence profile is very close to Gaussian; examples previously being presented . To rectify form-errors, information defining the influence function (or a family of influence functions representing a range of different spot sizes) is required. This information may be obtained by polishing witness spot(s) on a sample of the glass to be used. Alternatively, they may be interpolated from previous results on the same or a different glasstype. For this latter case, the software provides for a ‘moderation factor’ to scale the removal rate appropriately. This feature is also useful if, for example, the slurry has been changed.
Fresh influence functions may be measured as 2D profiles with a profilometer such as a Taylor Hobson Form Talysurf ™. Alternatively, 3D data from an interferometer can be used, providing that the slopes within the profile are within the dynamic range limitations imposed by the instrument.
To provide information on the surface of the part in order to control form, any two out of the following three data-sets are required:
- The target form of the surface (e.g. provided by a numerical ray-tracing program)
- The measured form of the surface, e.g. from an interferometer or profilometer
- The surface form-error (i.e. 1 minus 2 above)
The machine polishes in 2D mode correcting the radial form-error by using a spiral toolpath, where the following parameters can be varied:
- Ring-spacing of the spiral
- Polishing spot-size for each ring
- Dwell-time for each ring (effectively, the C axis speed for that ring)
In order to correct the established form-error, a numerical optimization is performed by the Precessions ™ software, usually run on an off-line PC with a typical execution time up to a few minutes. The principal function within the optimizer is to vary the dwell-time for each ring, scale the influence function according to the dwell time, and then numerically integrate the scaled influence functions for each ring over the part. If required, the optimizer can also be set by the user to vary the ring-spacing, and/or the spot-size for the each ring. The integrated influence functions provide a prediction of the removal profile. By comparison with the measured form, the new error-profile is calculated. The numerical optimization is then iterated. The cost function can be numerically weighted (under user-control) to reflect the relative importance of residual height-error and slope-errors.
The output of the optimizer is a map of influence function size and dwell-time for the radial position of each spiral zone on the part. Influence function size is converted into the Z off-set with respect to tool touch-on, which will appropriately compress the polishing bonnet to create the desired spot-size. Dwell time is converted into C axis speed for execution by the CNC controller.
6. Experimental results for 2D form control
The selected pre-ground aspheric part had a nominal diameter of 70mm, a very short radius of curvature of approximately 44.4mm, and the material was SLAH66. The aspheric departure from the base sphere was about 1mm, and 165 µm from the best-fit sphere. The clear aperture for this part was 61mm.
Figure 5 shows the profile of the part directly off the grinder, as measured using a Taylor Hobson PGI 1240 Form Talysurf ™. Figure 6 follows pre-polishing using a bonnet pressure of 1.3bar with standard Grey Rock ™ polyurethane, and Cerox 1663 ™ re-circulated slurry. Two runs, interrupted by visual inspection, gave a total polishing time of ~100 mins.
As can be seen, the profile has been preserved; a specular surface-finish achieved, and effectively subject to a spatial filter corresponding to the spot size used. The central peak in the ground part has been converted to a wider trough. This is beneficial, as subsequent formcorrection using a precessed tool and Gaussian influence function is subject to the central “double counting” anomaly. With the depressed centre, the depth of material to be removed from centre is minimised, mitigating the effect. Creating a low centre in earlier processes is therefore a useful strategy.
Results of three form correction runs are shown in Figures 7, 8, and 9 respectively. Note that Fig. 9 is shown relative to the design radius, and Fig. 10 is the same data with the radiusterm removed (albeit, inadvertently slightly cropped laterally).
7. Extension to achieving axial symmetry, with potential for non-rotational errors
The 2D form-correction optimization operates in the radial direction and so can take no account of non-rotational errors. The next refinement implemented recently - which we call 2½D - is to modulate the C axis rotation speed continuously during each rotation, in a similar fashion to a ‘phase locked loop’. When the original idea was described , the approach was to separate the radial form-error term from the azimuthal rotational-error component and optimise them independently. In practice, it has been found better to perform a single generalised optimisation of C axis speed to minimise both error components simultaneously.
2½D can rectify non-symmetric input-errors in a part. However, in the context of this paper it is more important in circumventing non-symmetric errors that can creep in during successive process iterations with small-tool polishing, mainly due to residual run-out from part-fixturing. This has proved particularly important when striving for the ultimate final form.
With this in view, the technique has been demonstrated on a Cassegrain mirror of near parabolic form, with a base radius of approximately 300mm. The clear aperture was a nominal 180mm, and the central hole 60mm. The blank was supplied after pre-polishing on another machine, and the required final form specification was λ/8 peak-to-valley (λ632.8nm). This tolerance had not previously been achieved with only the simple 2D process.
Two polishing runs (polyurethane pad and cerium oxide slurry) were conducted on the Zeeko machine to correct absolute base-radius first, using metrology feedback from a Form Talysurf ™ profilometer. 3D form (Fig. 11) was then measured on a Zygo interferometer in double-pass auto-collimation off a reference flat, in order to provide input data for formcontrol runs using the 2½D process. Form-errors over the clear aperture were 1.4 λ peak-tovalley, and 0.14λ rms (~1λ excluding the edge). Non-rotational terms were present, albeit minor.
Eight 2½D polishing runs were required and 3 hours total machine time, in order to achieve the form specification, and the final result is shown in Fig. 12. The resulting surface form-error was 0.12λ peak-to-valley and 0.015λ rms (after removing a small focus term).
We have described the operation of the Precessions™ process and the novel CNC machines on which it runs. The technology exploits familiar attributes of standard polishing cloths and slurries, but applied by a novel automated platform embodying advanced numerical optimization and CNC techniques. The accumulated wealth of craft know-how can thus be redeployed in this new context, short-circuiting process-optimization for particular materials. Experimental results have illustrated pre-polishing and 2D form-control. These provide a practical manufacturing solution particularly for surfaces such as severe aspheres measured profilometrically, where no null lens is available. We have also introduced 2½D, and reported on its success achieving diffraction-limited form for the first time by Precessions processing. This requires 3D metrology using e.g. an interferometer or multiple profilometric scans. The ability both to polish precision ground surfaces, and control form down to the optical diffraction limit, is unprecedented in a unified approach on a commercial CNC machine tool.
We acknowledge funding for this work from the UK Particle Physics and Astronomy Research Council, Basic Technology Initiative, Ministry of Defence, and Dept. of Trade and Industry. The late Dr. R.G. Bingham played an important role in the formative stages of this work and his contribution is specially acknowledged. We also thank Prof. S-W Kim for his work on the process at an early stage in its development while he was in the UK.
References and links
1. D. D. Walker, D. Brooks, A. King, R. Freeman, R. Morton, G. McCavana, and S-W Kim, “The ‘Precessions’ tooling for polishing and figuring flat, spherical and aspheric surfaces,” Opt. Express 11, 958–964 (2003). [CrossRef] [PubMed]
2. H. M. Martin, D. S. Andersen, J. R. P. Angel, R. H. Nagel, S. C. West, and R. S. Young, “Progress in the stressed-lap polishing of a 1.8m f/1 mirror,” in Advanced Technology Optical Telescopes IV ed. L.D. Barr, Proc. SPIE1236, 682–690, (1990). [CrossRef]
3. T. Korhonen and T. Lappalainen “Computer controlled figuring and testing,” in Advanced Technology Optical Telescopes IVL. Barr, ed., Proc. SPIE1236, 691–695 (1990). [CrossRef]
4. R. A. Jones “Fabrication of a large, thin, off-axis aspheric mirror,” Opt. Eng. 33, 4067–4075 (1994). [CrossRef]
5. V. W. Kordonski, D. Golini, P. Dumas, S. J. Hogan, and S. D. Jacobs, “Magnetorheological-suspensionbased finishing technology,” J. M. Sater, ed., Proc. SPIE 3326, 527–535 (1998). [CrossRef]
6. O. W. Fähnle, H. van Brug, and H. Frankena, “Fluid jet polishing of optical surfaces,” Appl. Opt. 37, 6771–6773 (1998). [CrossRef]
7. D. D. Walker, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, D. Brooks, and A. King, “The first aspheric form and texture results from a production machine embodying the precession process,” in Optical Manufacturing and Testing IV, H.P. Stahl, ed., Proc. SPIE4451, 267–276 (2001). [CrossRef]