Apparatus and method

Abstract

Apparatus comprising a tool (2) for forming an aspherical surface on a material (14), and a support for supporting the material (12) for rotation about an axis, the arrangement being such that the tool (2) is restricted to movement with respect to the material (14) in two substantially linear axes transverse to each other. The apparatus may be a high-performance machine comprising a measuring arrangement (18) mounted so as to extend substantially across the surface of the material (14) and serving to measure the distance between the tool (2) and a referencing region (32) of the measuring arrangement (18) which can be in the form of a symmetrical metrology device (18), the metrology device being structurally unloaded. The apparatus is substantially symmetrical in two substantially vertical planes substantially perpendicular to and intersecting each other.

Description

This invention relates to machine tools, and in particular, grinding machine tools.

A known use of grinding machine tools is for the production of mirror segments needed to produce ground-based telescopes or extra large telescopes (ELT's). The proposed next generation of ground based telescopes or ELT's will bring about an unprecedented demand for hundreds of large off-axis mirror segments each having a diameter in the range of 1 to 2 metres. Such mirror segments will be made from glass or ceramic material and have a hexagonal shape as used, for instance, in the Hobby-Eberly telescope. At present, the manufacturing technologies for producing ultra-precise mirrors having a diameter of 1 to 2 metres are associated with processing times of hundreds of hours. Consequently, the time to manufacture hundreds, even thousands, of such mirrors for an ELT would involve many years of production.

In the late 1970's, high-precision diamond turning machines were devised to produce large optics in the 1 to 2 meter diameter range. However, these machines and subsequent machines tend to be of a very large size and weight (many tonnes).

According to a first aspect of the present invention, there is provided apparatus comprising a tool for forming an aspherical surface on a material, and a support for supporting said material for rotation about an axis, the arrangement being such that said tool is restricted to movement with respect to said material in two substantially linear axes transverse to each other.

According to a second aspect of the present invention, there is provided a method of forming an asphercial surface on a material, comprising rotating said material about an axis of rotation, moving a tool with respect to said surface, and restricting the movement of said tool to movement in two substantially linear axes transverse to each other.

Owing to these two aspects of the invention, it is possible to provide a high level of loop stiffness between a tool and the material to be worked.

Advantageously, the two substantially linear axes of tool movement are in a substantially vertical plane in which the rotational axis of the material lies.

In this way a machine tool such as a grinding machine or a diamond turning machine can have its tool limited to motions in only two axes, namely substantially vertical movement in a vertical plane and substantially horizontal movement in the vertical plane. Thus, the amount of moving parts in the machine is reduced, thereby enabling the machine to be relatively stiff.

Preferably, the loop of stiffness is a substantially quadrangular stiffness loop between the tool and the material.

Having a high level of loop stiffness in a grinding machine is extremely important in grinding ceramics and glasses rapidly whilst maintaining good form accuracy. In order to ensure that subsequent polishing operations are effective, the output quality from a fixed abrasive grinding operation must have both good form accuracy and minimal sub-surface damage, which may be caused by the abrasive grain penetration depth of the grinding tool. In order to control the abrasive penetration depth it is necessary to have control of the relative motion of the abrasive surface of the grinding tool with respect to the material, or workpiece, surface.

Loop stiffness can be divided into two categories, namely static loop stiffness and dynamic loop stiffness, both of which are, preferably, at a relatively high level. Low levels of static loop stiffness result in edge “roll-off” errors produced when the grinding wheel of the grinding tool moves out of full contact with the workpiece surface. High levels of dynamic loop stiffness are also critical to permit the control of the abrasive penetration at sufficiently high force levels to provide effective material removal rates.

An advantage of having a relatively high level of loop stiffness is that, per unit of time, there is a high output of finished product which is of good quality.

According to a third aspect of the present invention, there is provided a high-performance machine comprising a tool for working at a surface of a material, a support which supports said material, and a measuring arrangement mounted so as to extend substantially across said surface and serving to measure the distance between said tool and a referencing region of said measuring arrangement.

Owing to this aspect of the invention, a measuring arrangement can be provided on a high-performance machine tool for referencing machine motions against the measuring arrangement.

A high-performance machine tool offers a machining capability approaching a relative accuracy level of 5 parts in one million, i.e. 5 microns for a 1 metre workpiece diameter. The measuring arrangement allows the accuracy to be improved to around a relative accuracy level of 1 part in one million, i.e. 1 micron for a 1 metre workpiece.

Advantageously, the machine tool is a high-performance grinding or diamond turning machine and the measuring arrangement comprises a metrology frame which has a referencing region in the form of a mirror and which is mounted on the material support of the machine, and a laser interferometer system mounted on the high-performance tool.

In this way, the tool, such as a grinding tool or a diamond turning tool, can be moved with great accuracy without a deterioration in performance.

Preferably, the referencing mirror of the metrology frame is a low-mass straight-edge mirror and the laser interferometer system is a small independent laser interferometer mounted on a carriage unit which carries the tool. Advantageously, the laser interferometer is mounted on the upper end of an invar support beam, at the lower end of which there is an air-bearing linear variable differential transducer (LVDT) contact probe. Such an arrangement helps to compensate for any errors in the tool motion.

According to a fourth aspect of the present invention, there is provided apparatus comprising a tool for working at a surface of a material, a symmetrical metrology device, and a support upon which said metrology device is mounted, said metrology device being structurally unloaded and including a single referencing device for providing positional information of said tool with respect to said surface.

Owing to this aspect of the invention, a symmetrical metrology device with a single referencing device can be provided on a machine tool and not have any load bearing parts of the machine attached to it.

Advantageously, the metrology device is a fully symmetrical metrology frame associated with a laser interferometer system mounted on the tool which has only two axes of tool movement.

Thus, a high-accuracy feedback-controlled machine tool can be obtained in which the position of the tool relative to the material can be monitored without the need for a multi-axis interferometer system or the need for the metrology frame to protrude into the working volume.

According to a fifth aspect of the present invention, there is provided apparatus comprising a tool for working at material, said apparatus being substantially symmetrical in two substantially vertical planes substantially perpendicular to and intersecting each other.

Owing to this aspect of the invention, it is possible to provide a fully symmetrical machine tool which is structurally stable.

Not only is the machine tool symmetrical in a right-to-left direction but also in a front-to-back direction, which gives the machine tool a box-shape appearance. Such a machine tool is relatively thermally more stable and suffers less from tilt errors caused by thermal gradients when the machine is in operation.

According to a sixth aspect of the present invention, there is provided a numerically controlled machine comprising a tool and having two substantially linear axes and a rotational axis, a tool surface having a pre-determined shape, and a data processing system for generating geometric information in relation to said tool surface.

According to a seventh aspect of the present invention, there is provided a method comprising providing a predetermined shape to a surface of a tool, operating the tool surface against a material surface, and generating using a data processing system geometric information in relation to the tool surface.

Owing to these two aspects of the invention, it is possible to generate geometric information in relation to change of the shape of the tool surface.

The tool surface can be an abrasive surface of a grinding tool. The surface of the material to be shaped may be non-symmetrical such as that for a free-form optical element, such that, during the grinding operation in which the grinding surface wears in such a manner as to depart from the pre-determined shape, the contact zone between the abrasive surface of the grinding tool and the surface of the material changes to tend to produce a non-optimal contact zone. The shape of the abrasive surface is determined by a data processing system such that any change required or any error to be compensated for can be dealt with.

Advantageously, the data processing system uses Non-Uniform Rational B-Splines (NURBS) to monitor wear of the tool surface.

According to an eighth aspect of the present invention, there is provided apparatus comprising a tool having a material-contacting surface, said tool being substantially linearly movable across said apparatus, a forming device located in the substantially linear path of said tool for forming a desired cross-sectional profile on said material-contacting surface, a conditioning device having a conditioning surface for conditioning the formed material-contacting surface, and an inspecting device for determining a cross-sectional profile of said conditioning surface.

According to a ninth aspect of the present invention, there is provided a method comprising forming with a forming device a desired cross-sectional profile of a material-contacting surface of a tool arranged to move in a substantially linear path, said forming occurring in said substantially linear path, conditioning said material-contacting surface by a conditioning surface of a conditioning device, and determining with an inspection device the cross-sectional profile of said conditioning surface.

Owing to these two aspects of the invention, it is possible to determine the cross-sectional profile of the material-contacting surface by determining the cross-sectional profile of the conditioning surface.

Advantageously, the forming device is a forming wheel, the conditioning device is a dressing stick and the inspecting device is a surface-contacting probe which contacts the conditioning surface of the dressing stick. Preferably, the material-contacting surface is an abrasive surface of a grinding tool having a cup wheel which has a symmetrical toric cross-sectional profile when formed, such that the measurement of the cross-sectional profile of the conditioning surface in the one direction can be electronically transposed to give measurements in a direction substantially perpendicular to that in which the determination is taken. This has the advantage that no movement of the tool is needed in the direction perpendicular to that in which the determination is taken. This arrangement enables a machine tool which requires forming and dressing of a tool surface to have a relatively high degree of stiffness.

In order that the invention can be clearly and completely disclosed, reference will now be made, by way of example, to the following drawings in which:—

FIG. 1 is a cross-sectional perspective view of a grinding machine,

FIG. 2 is a perspective view from above and one end of the grinding machine,

FIG. 3 is a cross-section of the grinding machine in a plane at substantially a right-angle to that of FIG. 1, and

FIG. 4 is a perspective view from above and the opposite end to that of FIG. 2.

Referring to FIG. 1, a grinding machine tool 2 comprises a grinding tool piece 4 which includes a tool spindle portion 6 and a grinding cup wheel 8. The machine 2 further comprises two movement sub-systems by way of which the tool 4 is moved and a material-supporting table 12 for supporting material, or a workpiece 14, to be acted upon by the tool 4. There is a work station 16 at which an operator of the machine 2 can control the machine. The machine 2 also comprises a metrology frame unit 18 mounted from a base portion 3 of the machine 2.

In order to minimise the moving masses, the machine motions are limited to three axes, namely two stacked linear axes which carry the grinding spindle 6 over a single rotary axis of the workpiece 14 supported on the table 12. A tool carriage unit 10 in which the grinding spindle 6, which is preferably a hydrostatic oil bearing spindle, is mounted, is preferably of aluminium construction. The carriage unit 10 is itself further mounted on tube-type hydrostatic oil linear bearing rails 20 and movement of the carriage unit 10 along the rails 20 (i.e. in to and out of the page of FIG. 1) is driven by a pair of linear motors 22 mounted either side of the hydrostatic bearing rails 20. Two high performance linear encoders are employed closely positioned to the bearing rails 20. An advantage of this slideway sub-system of the carriage 10 and bearing rails 20 is that the carriage 10 can be removed and replaced with other slideway tool sub-systems, for example, a diamond turning unit. Movement along the bearing rails 20 enables the tool 4 to be moved substantially horizontally in a substantially linear path across the workpiece 14 in a substantially vertical plane of the machine 2, and in relation to a three-dimensional positioning system such movement is in the X-axis direction. The tool 4 is also movable in a substantially vertical direction in the substantially vertical plane of the machine 2, which in the three-dimensional positioning system would be movement in the Z-axis direction. Movement in the Z-axis is achieved by way of a further pair of motors 22′ (shown also in FIG. 3). To ensure safe operation of the Z-axis, and to reduce motor loading, a double-acting seal-less air counter-balance cylinder 24 is used in association with Z-axis bearing rails 20′ (see also FIG. 3) and positioned such that it acts close to the centre of gravity of the moving Z-axis mass. The movement permitted in the Z-axis is much shorter than that permitted in the X-axis. The Z-axis sub-system forms an integral part of the longer X-axis slideway sub-system which also includes an X-axis carriage unit 21 in order to minimise any cantilevers. The hydrostatic bearing rails 20 are, preferably, rectangular in cross-section, as shown, and are directly mounted onto the upper portion 23 of the main machine structure. As is the case with the X-axis sub-system, two linear motors and two encoders are employed using a symmetrical design with minimal parallax errors, i.e. Abbé Offset Error.

The substantially vertical rotary axis of the table 12 which carries the workpiece 14 is driven by a direct drive hydrostatic oil bearing unit 28 which is of a low moving mass. This direct drive hydrostatic oil bearing unit 28 has a small depth to diameter ratio to ensure the distance from the motor and an associated rotary encoder to the workpiece surface is minimised.

The grinding spindle 6 is inclined relative to the vertical and is fixed firmly in position via the carriage unit 10. The grinding wheel 8 is therefore also inclined to the same degree and uses a toric-shaped cup wheel. The cup wheel has an external diameter of approximately 325 mm and provides a grinding speed in the range of 25 to 35 m/s (25 to 35 Hz). The combined mass of the tool 4 and the Z-axis sub-system embedded within the X-axis sub-system is minimised to less than 750 Kg.

The whole machine structure is based around a substantially symmetrical box-shape. It is substantially symmetrical not only from side-to-side but also front-to-back and simple shaped castings are used to support the main active Z- and X-axis movements. In order to produce a 2 m diameter free-form optic for a large telescope, the box-shape structure is substantially 3 m in length by substantially 1.5 m in height and would weigh around 12 tons which is 10% of the total mass of some existing machines. Obviously, for the production of smaller optics a smaller box-shape structure can be used.

By having the absolute minimum number of active motions of minimal mass, namely the tool being only movable in a single substantially vertical plane of the machine 2, and the use of high stiffness bearings allows the machine 2 to have relatively high dynamic and relatively high static loop stiffness. The loop of stiffness is substantially quadrangular in form with operational forces of the grinding tool 4 being transferred upwardly and outwardly through the periphery of the machine 2 and subsequently downwardly and inwardly to beneath the workpiece 14. Having such a relatively high degree of static and dynamic loop stiffness, a relatively high output of finished work pieces having good quality can be achieved.

In having the machine 2 of relatively low mass and of a compact modular design, thermal stabilising systems have been incorporated to control the temperature of the hydrostatic bearing fluids. Motor cooling systems have been incorporated for the linear and rotary motors and, in addition, temperature control of the machine structure itself and the grinding fluid are also present. High diffusivity materials have been employed to reduce the effects of the main slow moving heat sources, i.e. the X-axis motors 22. Furthermore, the top structure 23 of the machine 2 which mounts the X-axis encoders is thermally monitored in order to independently validate thermal stability. The grating encoder scales which are measuring devices which measure the position on the linear X- and Z-axes are of low co-efficient of thermal expansion and are suitably restrained to prevent thermal creep. These grating scales are positioned symmetrically either side of the moving carriages for both the X- and Z-axes.

Referring to FIG. 2, the metrology frame unit 18 is non-load bearing and is mounted from the base portion 3 of the machine 2 and includes, on an upper substantially horizontal beam 30, a referencing region in the form of a single low mass straight edge mirror 32. Only a single mirror 32 need be used owing to the restricted movement of the tool 4 in the Z- and X-axes.

Referring to FIG. 3, the Z-axis carriage unit 10 is provided with an independent laser interferometer 34 mounted on an upper end of an invar support beam 36 which is thermally stable. The laser interferometer 34 has a short measurement path in order to minimise ambient effects. At the lower end of the invar support beam 36, a first air bearing linear variable differential transducer (LVDT) probe 38 is present. The laser interferometer 34 measures the distance to the straight edge mirror 32 when the LVDT probe 38 is brought into contact with the surface of the workpiece 14. The metrology frame unit 18 and the laser interferometer 34 therefore provide the ability of in-situ post-process measurement, owing to the measured distance being progressively across the surface of the workpiece 14 along the substantially linear path of the X-axis movement and thereby providing a profile of that surface. In a similar way to the structure of the machine 2, the metrology frame unit 18 is substantially fully symmetrical both from side-to-side and from front-to-back.

Referring to FIGS. 3 and 4, after the grinding wheel 8 is fitted onto the inclined grinding spindle 6, the abrasive surface 40 of the wheel 8 needs to be shaped into the correct cross-sectional form which is a toric cross-sectional shape. Therefore, it is necessary to machine this desired cross-sectional shape onto the abrasive surface 40. In order to impart the correct toric cross-sectional shape to the abrasive surface 40, the abrasive surface 40 is formed, or trued, against a forming or truing wheel 42. The truing wheel 42 which has an axis of rotation substantially perpendicular to the rotary axis of the workpiece 14 is shaped such that the rim of the wheel, which is preferably of diamond coated steel, is shaped to have the inverse cross-sectional shape as that to be imparted to the abrasive surface 40. In order to true the grinding wheel abrasive surface 40, the tool 4 is moved in the X-axis direction in the vertical plane to above the rim of the truing wheel 42 which is located in a position towards one end of the machine 2, as shown, and lies in the vertical plane through which the tool 4 is moved. After the truing operation, the abrasive surface 40 has the correct cross-sectional shape, but requires a further operation to condition the abrasive surface 40 such that the diamond abrasives thereon protrude beyond the bond matrix of that surface. This is to ensure that the diamond abrasives cut effectively during the grinding process. This conditioning process is conventionally known as dressing and is carried out by plunging the abrasive surface 40 of the grinding wheel 8 into a fixed dressing stick 44 which is located proximally and to one side of the truing wheel 42, and is preferably made of an abrasive ceramic compound. The tool 4 is moved in the X-axis direction after the truing operation to bring the abrasive surface 40 into contact with the top conditioning surface 46 of the dressing stick 44. Consequently, the conditioning surface 46 is shaped using the abrasive surface 40 of the grinding wheel 8 which, thus, imparts the cross-sectional shape of the abrasive surface 40 into the conditioning surface 46. Since the dressing stick 44 is located to one side of the truing wheel 42, the truing and dressing operations occur at different positions on the inclined toric-shaped abrasive surface. Once the dressing operation has been completed, the tool 4 can be used for grinding the surface of the material 14. The width of the rim of the truing wheel 42 and the width of the dressing stick 44 are the same as or greater than the width of the abrasive surface 40 of the grinding cup wheel 8.

After grinding for some time, the abrasive surface 40 wears, such that the correct toric cross-sectional shape may wear away. However, owing to the arrangement of the truing wheel 42 and the dressing stick 44 on the machine 2, the machine 2 has a system whereby wear of the abrasive surface 40 is determined by inspecting the cross-sectional shape of the conditioning surface 46. As is the case with the truing wheel 42, the conditioning surface 46 has a cross-sectional shape which is the inverse of the cross-sectional shape of the abrasive surface 40 and, thus, corresponds to the cross-sectional shape of the truing wheel 42, but transposed through substantially 90°, which is achieved by the dressing stick 44 being located to one side of the truing wheel 42. This inspection system also comprises a second air-bearing contact probe 48, shown in FIG. 3, located on the Z-axis carriage unit 10 on the opposite side of the carriage unit 10 to the first probe 38.

The dressing stick probe 48 is moved across and contacts the conditioning surface 46 by movement of the tool in the X- and Z-axes which results in measurements which give the profile of the cross-sectional shape of the abrasive surface 40. Probing of the conditioning surface 46 occurs only in the X-axis direction along a path which is substantially parallel to the linear path of the tool piece 4. Owing to the symmetrical nature of the abrasive surface 40, the measurements from the probing of the conditioning surface 46 in the X-axis direction can then be electronically transposed to measure the cross-sectional shape of the abrasive surface 40 in the Y-axis direction indicated by the arrow 50 in FIG. 4. By measuring only in the X-axis direction, there is no need for the addition of other linear motion axes to the machine 2 which can be expensive and reduces the overall stiffness of the machine 2. In conventional grinding machines, there are typically four or five motion axes and one of these is dedicated to permit the truing and dressing operations. In the machine 2, there is no dedicated axis for truing nor dressing. Thus, the machine 2 not only has a relatively high degree of stiffness but it is also of simpler construction and is therefore relatively less expensive to produce. Furthermore, the construction of the machine 2 allows it to be of relatively low mass.

The relatively low mass of the machine 2 enables an increase in the frequency of production of good quality finished workpieces 14.

The use of the rotary axis about which the workpiece 14 turns in combination with the linear motion of the tool 4 to define a surface on the workpiece 14 requires a control system and associated computer software to deal with a change in shape of the contact zone between the abrasive surface 40 and the workpiece 14 owing to wearing away of the abrasive surface 40.

Non-Uniform Rational B-Splines, commonly referred as NURBS, have become the industry standard for the representation and design, and data exchange of geometric information processed by computers. NURBS provides a unified mathematical basis for representing both analytic shapes, such as conic sections and quadric surfaces, as well as free-form entities, such as the surfaces of optical elements. A NURBS curve is defined by

$C\left(t\right)=\frac{\sum _{i=0}^nN_{i,k}\left(t\right)w_iP_i}{\sum _{i=0}^nN_{i,k}\left(t\right)w_i}$

where k is the order of basis functions, N_i,k are the B-spline basis functions, P_i are control points, and the weight w_i of P_i is the last ordinate of the homogeneous point P_i^w.

One of the key characteristics of NURBS curves is that their shapes are determined by the positions of control points. The basis functions determine how strongly control points influence the curve. A series of points, called knots vector, are used in the basis functions to partition the time into non-uniform intervals so that some control points affect the shape of the curve more strongly than others.

With the machine 2 having its toroidal shape grinding wheel, the center of curvature of the wheel is not in the wheel's rotational axis. This makes the tool path over the surface of the workpiece 14 more complex. As already mentioned, the diamond grinding wheel abrasive surface 40 will experience a substantial wear in the grinding process. Wear will induce changes of grind wheel shape and result in significant form errors on the surface of the workpiece 14, which could be an optical surface.

By using a NURBS algorithm, compensation for wheel wear can be provided. The toroidal grinding wheel shape is defined by a NURBS representation which has several control points. Changes of wheel shape due to wear of the abrasive surface 40 can be modelled by NURBS interpolation which is achieved by adjusting the control points used for defining the toroidal grinding wheel shape. Therefore the complex shape changes of the grinding wheel are presented by using relatively little data. Owing to the wheel shape changes, the tool path across the workpiece 14 will also be adjusted by NURBS interpolation to compensate for the grinding wheel wear. The NURBS data will help to maintain the motion smoothness and achieve optical surfaces with high form accuracy.

The advantages of the NURBS grinding wheel wear compensation system are that NURBS offers a way to represent complex toroidal wheel shapes while maintaining mathematical exactness and resolution independence, NURBS gives accurate control over the changes of wheel shapes (the set of control points and knots which guide the wheel shape, can be directly manipulated to control its smoothes and curvature), the grinding wheel wear compensation is numerically stable as NURBS curves and surfaces are invariant under common geometric transformations, such as translation, rotation and perspective projection, and the grinding wheel wear compensation process is fast as relatively little data is needed to represent complex wheel shape before and after wear occurs.

The machine 2 is able to grind surfaces of the workpiece 14 such as optical surfaces to a precision of 1 μm over a 1 m diameter surface, the finished surfaces having minimal sub-surface damage at depths of 2 to 5 μm. This high precision accuracy capability is the result of the relatively high motional repeatability of machine motions through thermal control, fluid film bearings, machine symmetry, minimised parallax errors, and error compensation and correction via the in-situ metrology frame unit and its associated post-process measuring system.

Plans for an ELT to be built are in place which has a 100 m diameter and will need 2000 ultra-precisely machined optical segments of 2 m diameter. With conventional grinding machines, for the production of the required free-form optics, each such segment will take around 280 hours to produce. The machine 2 is capable of producing such segments in around just 20 hours.

Claims

1. Apparatus comprising a tool for forming an aspherical surface on a material, and a support for supporting said material for rotation about an axis, the arrangement being such that said tool is restricted to movement with respect to said material in two substantially linear axes transverse to each other.

2. Apparatus according to claim 1, wherein the two substantially linear axes are in a substantially vertical plane in which the rotational axis of the material lies.

3. Apparatus according to claim 2, wherein the two substantially linear axes are constituted by a substantially vertical axis of movement in said vertical plane and a substantially horizontal axis of movement in said vertical plane.

4. Apparatus according to any preceding claim, wherein said apparatus has a relatively high stiffness loop.

5. Apparatus according to claim 4, wherein the loop of stiffness is a substantially quadrangular stiffness loop between said tool and said material.

6. Apparatus according to any preceding claim, wherein said tool is a grinding machine tool.

7. Apparatus according to claim 6 as appended to claim 4, wherein both static loop stiffness and dynamic loop stiffness are at a relatively high level.

8. Apparatus according to any preceding claim, and further comprising two movement sub-systems by way of which said tool is moved in said two substantially linear axes.

9. Apparatus according to claim 8 as appended to claim 3, wherein a first movement sub-system moves said tool vertically and a second movement sub-system moves said tool horizontally.

10. Apparatus according to claim 8 or 9, wherein the first movement sub-system is an integral part of the second movement sub-system.

11. Apparatus according to any one of claims 8 to 10, wherein the movement sub-systems are removable from said apparatus.

12. Apparatus according to any one of claims 8 to 11, wherein the movement sub-systems comprise respective pairs of associated linear motors and linear encoders for movement of said tool along respective pairs of bearing rails.

13. Apparatus according to any preceding claim wherein said tool is a high-performance machine tool further comprising a measuring arrangement mounted so as to extend substantially across a surface of said material and serving to measure the distance between said tool and a referencing region of said measuring arrangement.

14. Apparatus according to claim 13, wherein said measuring arrangement comprises a metrology frame including said referencing region, and a laser interferometer system mounted on the high-performance tool.

15. Apparatus according to claim 14, wherein said referencing region is in the form of a mirror.

16. Apparatus according to claim 15, wherein said mirror is a low-mass straight-edge mirror and the laser interferometer system is a small independent laser interferometer mounted on a carriage unit which carries the tool.

17. Apparatus according to any one of claims 14 to 16, wherein said laser interferometer is mounted on the upper end of an invar support beam, at the lower end of which there is an air-bearing linear variable differential transducer (LVDT) contact probe.

18. Apparatus according to any one of claims 14 to 17, wherein said metrology frame is a symmetrical metrology frame, and said apparatus further comprises a support upon which said metrology frame is mounted, said metrology frame being structurally unloaded.

19. Apparatus according to claim 18, wherein said symmetrical metrology frame is a fully symmetrical metrology frame.

20. Apparatus according to any one of claims 14 to 19, the arrangement being such that the metrology frame is outside of the working volume.

21. Apparatus according to any preceding claim, wherein said apparatus is substantially symmetrical in two substantially vertical planes substantially perpendicular to and intersecting each other.

22. Apparatus according to claim 21, wherein said apparatus is substantially box-shaped.

23. Apparatus according to any preceding claim, wherein said tool is a numerically controlled machine tool having a tool surface of a pre-determined shape, and a data processing system for generating geometric information in relation to said tool surface.

24. Apparatus according to claim 23 as appended to claim 6, wherein said tool surface is an abrasive surface of said grinding tool.

25. Apparatus according to claim 23 or 24, wherein said data processing system uses Non-Uniform Rational B-Splines (NURBS) to monitor wear of said tool surface.

26. Apparatus according to any one of claims 23 to 25, and further comprising a forming device located in one of said substantially linear axes for forming a desired cross-sectional profile on said tool surface, a conditioning device having a conditioning surface for conditioning the formed tool surface, and an inspecting device for determining a cross-sectional profile of said conditioning surface.

27. Apparatus according to claim 26, wherein said forming device is a forming wheel, the conditioning device is a dressing stick and the inspecting device is a surface-contacting probe which contacts the conditioning surface of the dressing stick.

28. Apparatus according to claim 26 or 27 wherein said tool comprises a cup wheel which includes said surface of said tool and which has a symmetrical toric cross-sectional profile when formed, such that said measurement of the cross-sectional profile of the conditioning surface in one direction can be electronically transposed to give measurements in a direction substantially perpendicular to that in which the determination is taken.

29. Apparatus according to any one of claims 8 to 28, wherein the combined mass of said tool and the two movement sub-systems is less than substantially 750 Kg.

30. Apparatus according to any preceding claim, wherein said material is a free-form optic.

31. Apparatus according to claim 30 as appended to claim 22, wherein for a 2 m diameter free-form optic, the box-shape structure is substantially 3 m in length by substantially 1.5 m in height and weighs substantially 12 tons.

32. Apparatus according to any preceding claim, and further comprising a thermal stabilising system for controlling the temperature of said apparatus.

33. Apparatus according to claim 32, wherein said thermal stabilising system comprises high diffusivity materials.

34. Apparatus according to claim 32 or 33 as appended to claim 12, wherein grating scales of the encoders are of low co-efficient of thermal expansion and are suitably restrained to prevent thermal creep.

35. A method of forming an asphercial surface on a material, comprising rotating said material about an axis of rotation, moving a tool with respect to said surface, and restricting the movement of said tool to movement in two substantially linear axes transverse to each other.

36. A method according to claim 35, wherein the two substantially linear axes of tool movement are in a substantially vertical plane in which the rotational axis of the material lies.

37. A method according to claim 36, wherein the two substantially linear axes are constituted by a substantially vertical axis of movement in said vertical plane and a substantially horizontal axis of movement in said vertical plane.

38. A method according to any one of claims 35 to 37, wherein said tool is a grinding machine tool.

39. A method according to any one of claims 35 to 38, wherein said moving is by way of two movement sub-systems.

40. A method according to claim 37, 38 or 39, wherein a first movement sub-system moves said tool substantially vertically and a second movement sub-system moves said tool substantially horizontally.

41. A method according to claim 40, wherein the first movement sub-system is an integral part of the second movement sub-system.

42. A method according to any one of claims 39 to 41, wherein the two movement sub-systems are removable from said tool.

43. A method according to any one of claims 35 to 42, wherein said tool is a high-performance machine tool and further comprising a measuring arrangement mounted so as to extend substantially across a surface of said material and serving to measure the distance between said tool and a referencing region of said measuring arrangement.

44. A method according to any one of claims 35 to 43 and further comprising providing a pre-determined shape to a surface of said tool, operating the tool surface against a surface of said material surface, and generating using a data processing system geometric information in relation to the tool surface.

45. A method to claim 44, wherein said data processing system uses Non-Uniform Rational B-Splines (NURBS) for monitoring wear of said tool surface.

46. A method according to claim 44 or 45, and further comprising forming with a forming device a desired cross-sectional profile of said surface of said tool arranged to move in one of said substantially linear axes, said forming occurring in one of said substantially linear axes, conditioning said surface of said tool by a conditioning surface of a conditioning device, and determining with an inspection device the cross-sectional profile of said conditioning surface.

47. A method according to claim 46, wherein said forming is by a forming wheel, the conditioning is by a dressing stick and the inspecting is by a surface-contacting probe which contacts the conditioning surface of the dressing stick.

48. A method according to claim 46 or 47, wherein said tool comprises a cup wheel which includes said surface of said tool and which has a symmetrical toric cross-sectional profile when formed, such that said measurement of the cross-sectional profile of the conditioning surface in one direction can be electronically transposed to give measurements in a direction substantially perpendicular to that in which the determination is taken.

49. A method according to any one of claims 35 to 48, and further comprising a thermally stabilising tool.

50. A high-performance machine comprising a tool for working at a surface of a material, a support which supports said material, and a measuring arrangement mounted so as to extend substantially across said surface and serving to measure the distance between said tool and a referencing region of said measuring arrangement.

51. A machine according to claim 50, wherein said measuring arrangement comprises a metrology frame which includes said referencing region.

52. A machine according to claim 51, wherein said referencing region is in the form of a mirror and said machine further comprises a laser interferometer system mounted on the high-performance tool.

53. A machine according to claim 52, wherein said mirror is a low-mass straight-edge mirror and the laser interferometer system is a small independent laser interferometer mounted on a carriage unit which carries the tool.

54. A machine according to claim 52 or 53, wherein said laser interferometer is mounted on the upper end of an invar support beam, at the lower end of which there is an air-bearing linear variable differential transducer (LVDT) contact probe.

55. A machine according to any one of claims 50 to 54, wherein said measuring arrangement is structurally unloaded.

56. A machine according to any one of claims 50 to 55, the machine being substantially symmetrical in two substantially vertical planes substantially perpendicular to and intersecting each other.

57. A machine according to any one of claims 50 to 56, wherein said machine is a numerically controlled machine having two substantially linear axes and a rotational axis, a tool surface having a predetermined shape, and a data processing system for generating geometric information in relation to said tool surface.

58. A machine according to claim 57, the arrangement being such that said tool is restricted to movement with respect to said material in said two substantially linear axes.

59. A machine according to claim 57 or 58, wherein said tool is substantially linearly movable across said apparatus, and further comprises a forming device located in the substantially linear path of said tool for forming a desired cross-sectional profile on said tool surface, a conditioning device having a conditioning surface for conditioning the formed tool surface, and an inspecting device for determining a cross-sectional profile of said conditioning surface.

60. Apparatus comprising a tool for working at a surface of a material, a symmetrical metrology device, and a support upon which said metrology device is mounted, said metrology device being structurally unloaded and including a single referencing device for providing positional information of said tool with respect to said surface.

61. Apparatus according to claim 60, wherein said symmetrical metrology device is a fully symmetrical metrology frame.

62. Apparatus according to claim 60 or 61, and further comprising a laser interferometer system mounted on said tool which has only two axes of tool movement.

63. Apparatus according to claim 62, wherein said two axes of tool movement are substantially linear axes transverse to each other.

64. Apparatus according to any one of claims 60 to 63, wherein said metrology device is outside of the working volume.

65. Apparatus according to any one of claims 60 to 64, said apparatus being substantially symmetrical in two substantially vertical planes substantially perpendicular to and intersecting each other.

66. Apparatus according to any one of claims 63 to 65, wherein said tool is a numerically controlled tool having said two substantially linear axes, a tool surface having a pre-determined shape, and a data processing system for generating geometric information in relation to said tool surface.

67. Apparatus according to claim 66, wherein said tool surface is an abrasive surface of a grinding tool.

68. Apparatus according to claim 66 or 67, wherein said data processing system uses Non-Uniform Rational B-Splines (NURBS) to monitor wear of said tool surface.

69. Apparatus according to claim 67 or 68, wherein said tool is substantially linearly movable across said apparatus, and further comprises a forming device located in the substantially linear path of said tool for forming a desired cross-sectional profile on said abrasive surface, a conditioning device having a conditioning surface for conditioning the formed abrasive surface, and an inspecting device for determining a cross-sectional profile of said conditioning surface.

70. Apparatus comprising a tool for working at material, said apparatus being substantially symmetrical in two substantially vertical planes substantially perpendicular to and intersecting each other.

71. Apparatus according to claim 70, wherein said apparatus is substantially box-shaped.

72. Apparatus according to claim 70 or 71, wherein said tool is for forming an aspherical surface on said material, and further comprising a support for supporting said material for rotation about an axis, the arrangement being such that said tool is restricted to movement with respect to said material in two substantially linear axes transverse to each other.

73. Apparatus according to claim 72, and further comprising a measuring arrangement mounted so as to extend substantially across said surface and serving to measure the distance between said tool and a referencing region of said measuring arrangement.

74. Apparatus according to claim 73, wherein said measuring arrangement is a symmetrical metrology device, said metrology device being structurally unloaded and including said referencing region for providing positional information of said tool with respect to said surface.

75. Apparatus according to any one of claims 72 to 74, wherein said tool is a numerically controlled tool having said two substantially linear axes, a tool surface having a pre-determined shape, and a data processing system for generating geometric information in relation to said tool surface.

76. Apparatus according to claim 75 wherein said tool is linearly movable across said apparatus, and further comprises a forming device located in the substantially linear path of said tool for forming a desired cross-sectional profile on said tool surface, a conditioning device having a conditioning surface for conditioning the formed tool surface, and an inspecting device for determining a cross-sectional profile of said conditioning surface.

77. A numerically controlled machine comprising a tool and having two substantially linear axes and a rotational axis, a tool surface having a predetermined shape, and a data processing system for generating geometric information in relation to said tool surface.

78. A machine according to claim 77, wherein said tool surface is an abrasive surface of a grinding tool.

79. A machine according to claim 77 or 78, wherein said data processing system uses Non-Uniform Rational B-Splines (NURBS) to monitor wear of said tool surface.

80. A machine according to any one of claims 77 to 79, wherein said tool is for forming an aspherical surface on a material, and further comprises a support for supporting said material for rotation about an axis, the arrangement being such that said tool is restricted to movement with respect to said material in said two substantially linear axes which are transverse to each other.

81. A machine according to claim 80, and further comprising a measuring arrangement mounted so as to extend substantially across the surface of said material and serving to measure the distance between said tool and a referencing region of said measuring arrangement.

82. A machine according to any one of claims 77 to 81, wherein said numerically controlled machine is a high-performance numerically controlled machine.

83. A machine according to claim 81 or 82, wherein said measuring arrangement comprises a symmetrical metrology device, and a support upon which said metrology device is mounted, said metrology device being structurally unloaded and including said referencing region for providing positional information of said tool with respect to the surface of said material.

84. A machine according to any one of claims 77 to 83, wherein said machine is substantially symmetrical in two substantially vertical planes substantially perpendicular to and intersecting each other.

85. A machine according to any one of claims 77 to 84, said tool being substantially linearly movable across said apparatus, and further comprising a forming device located in the substantially linear path of said tool for forming a desired cross-sectional profile on said tool surface, a conditioning device having a conditioning surface for conditioning the tool surface, and an inspecting device for determining a cross-sectional profile of said conditioning surface.

86. A method comprising providing a pre-determined shape to a surface of a tool, operating the tool surface against a material surface, and generating using a data processing system geometric information in relation to the tool surface.

87. A method according to claim 86, wherein said data processing system uses Non-Uniform Rational B-Splines (NURBS) for monitoring wear of said tool surface.

88. A method according to claim 86 or 87, and further comprising forming an asphercial surface on said material surface, said aspherical spherical surface formed by rotating the material about an axis of rotation, moving said tool with respect to said surface, and restricting the movement of said tool to movement in two substantially linear axes transverse to each other.

89. A method according to any one of claims 86 to 88, and further comprising forming with a forming device a desired cross-sectional profile of the tool surface, the tool being arranged to move in a substantially linear path, said forming occurring in said substantially linear path, conditioning the tool surface by a conditioning surface of a conditioning device, and determining with an inspection device the cross-sectional profile of said conditioning surface.

90. Apparatus comprising a tool having a material-contacting surface, said tool being substantially linearly movable across said apparatus, a forming device located in the substantially linear path of said tool for forming a desired cross-sectional profile on said material-contacting surface, a conditioning device having a conditioning surface for conditioning the formed material-contacting surface, and an inspecting device for determining a cross-sectional profile of said conditioning surface.

91. Apparatus according to claim 90, wherein said forming device is a forming wheel, the conditioning device is a dressing stick and the inspecting device is a surface-contacting probe which contacts the conditioning surface of the dressing stick.

92. Apparatus according to claim 90 or 91, wherein said material-contacting surface is an abrasive surface of a grinding tool having a cup wheel which has a symmetrical toric cross-sectional profile when formed.

93. Apparatus according to any one of claims 90 to 92, wherein said determining of the cross-sectional profile of the conditioning surface in one direction can be electronically transposed to give measurements in a direction substantially perpendicular to that in which the determination is taken.

94. Apparatus according to claim 92 or 93, wherein said grinding tool is for forming an aspherical surface on a material, and further comprises a support for supporting said material for rotation about an axis, the arrangement being such that said grinding tool is restricted to movement with respect to said material in two substantially linear axes transverse to each other.

95. Apparatus according to claim 94, and further comprising a measuring arrangement mounted so as to extend substantially across said material and serving to measure the distance between said grinding tool and a referencing region of said measuring arrangement.

96. Apparatus according to any one of claims 92 to 95, wherein said grinding tool is a high-performance grinding tool.

97. Apparatus according to claim 95 or 96, wherein said measuring arrangement comprises a symmetrical metrology device, and a support upon which said metrology device is mounted, said metrology device being structurally unloaded and including said referencing region for providing positional information of said grinding tool with respect to the material surface.

98. Apparatus according to any one of claims 90 to 97, wherein said apparatus is substantially symmetrical in two substantially vertical planes substantially perpendicular to and intersecting each other.

99. Apparatus according to any one of claims 90 to 98, wherein said tool is a numerically controlled tool, said material-contacting surface having a predetermined shape, and a data processing system for generating geometric information in relation to said material-contacting surface.

100. Apparatus according to claim 99, wherein said data processing system uses Non-Uniform Rational B-Splines (NURBS) to monitor wear of said material-contacting surface.

101. A method comprising forming with a forming device a desired cross-sectional profile of a material-contacting surface of a tool arranged to move in a substantially linear path, said forming occurring in said substantially linear path, conditioning said material-contacting surface by a conditioning surface of a conditioning device, and determining with an inspection device the cross-sectional profile of said conditioning surface.

102. Apparatus according to claim 101, wherein said tool is a grinding tool having a cup wheel which has a symmetrical toric cross-sectional profile when formed, said method further comprising electronically transposing the determination of the cross-sectional profile of the conditioning surface taken in one direction to give measurements in a direction substantially perpendicular to that in which the determination is taken.

103. A method according to claim 101 or 102, and further comprising forming an asphercial surface on a material, including rotating said material about an axis of rotation, moving said tool with respect to said surface, and restricting the movement of said tool to movement in two substantially linear axes transverse to each other.

104. A method according to any one of claims 101 to 103, and further comprising providing a pre-determined shape to said material-contacting surface, operating said material-contacting surface against the material surface, and generating using a data processing system geometric information in relation to the tool surface.

105. A method according to claim 104, wherein said data processing system uses Non-Uniform Rational B-Splines (NURBS) for monitoring wear of said material-contacting surface.