GB2499662A

GB2499662A - Surface measurement apparatus and method

Info

Publication number: GB2499662A
Application number: GB1203343.7A
Authority: GB
Inventors: Daniel Mansfield
Original assignee: Taylor Hobson Ltd
Current assignee: Taylor Hobson Ltd
Priority date: 2012-02-27
Filing date: 2012-02-27
Publication date: 2013-08-28
Anticipated expiration: 2032-02-27
Also published as: GB201203343D0; GB2499662B

Abstract

In a metrological apparatus a stylus (11) is deflected as a stylus tip of the stylus follows surface variations along a measurement path on a surface of a workpiece and a transducer (39) provides measurement data in a measurement coordinate system. A data processor is configured to: determine a relationship between the measurement data in the measurement coordinate system and nominal surface data representing the expected surface characteristic of the workpiece in a workpiece coordinate system; simulate a measurement data set for the nominal surface using the nominal surface data and the determined relationship, the simulation providing a simulated measurement data set having a simulated range of simulated measurement values; if the simulated range does not meet a given criterion the processor adjusts a selected measurement data value for a selected measurement point and repeats the simulation to determine an adjusted measurement data value for which the simulated range meets the given criterion. Subsequently, the processor determines measurement start conditions required for a measurement procedure to provide the adjusted measurement data value for the selected measurement point.

Description

1

SURFACE MEASUREMENT APPARATUS AND METHOD

This invention relates to a surface measurement apparatus and method for facilitating measurement of one or more surface characteristics, in particular surface form.

5

Surface form or profile measurements may be made by effecting relative movement between a pivotally mounted stylus arm and a workpiece along a traverse path (measurement path) and detecting, using a transducer, the deflection of the stylus arm as a tip of a stylus carried by the stylus arm follows variation in the form of the surface 10 transverse to the traverse path. Accurate measurement requires care in the setting up of the apparatus which can be time consuming.

Measurement of surfaces having significant form, such as aspheric lenses as may be used in optical storage devices such as digital versatile discs (DVD) recorders and 15 players, and moulds for such lenses, present particular challenges because the steepness of the local slope of the surface being measured may result in a higher than desired contact angle between stylus tip and the surface being measured increasing the likelihood of the stylus tip slipping or dragging on the surface which could render the measurement inaccurate and may also damage the stylus. Also the height (depth) to 20 width aspect ratio of the form of the component may make access to the surface difficult, increasing the likelihood of collisions between the stylus arm and the workpiece surface which may, again, detrimentally affect the measurement and damage the stylus.

25 In order to address the above problems, Taylor Hobson Ltd of Leicester England have produced metro logical apparatus sold under the trade name "Talysurf PGI Blu" which enables precision 3-D for measurement of shallow and steep-sided aspheric lenses and moulds and offers 100 nm for measurement capability.

30 This apparatus addresses problems discussed above by enabling the orientation of a traverse unit carrying the stylus to be adjusted so that the stylus arm and the measurement path direction are inclined to the plane of a support surface, such as a

2

turntable, on which the workpiece to be measured is mounted. Allowing the angle of the stylus arm to be adjusted reduces the possibility of the contact angle exceeding a desired limit and also should facilitate access to the surface to be measured. Setting up of the instrument at the start of a measurement procedure may, however, be more 5 difficult for the operator because of the inclination of the traverse unit and the measurement path direction.

Embodiments of the present invention facilitate setting up of a metrological instrument for a measurement procedure allowing more rapid and accurate measurements of the 10 surface characteristic to be made.

In one aspect, the present invention provides a metrological apparatus for measuring a surface characteristic of a workpiece, the apparatus comprising:

a mover to carry out a measurement procedure by effecting relative movement in a 15 measurement direction between a workpiece and a stylus such that the stylus is deflected as a stylus tip of the stylus follows surface variations along a measurement path on a surface of the workpiece;

a transducer to provide a measurement data set in a measurement coordinate system representing the deflection of the stylus at measurement points along the measurement 20 path, the transducer having a measurement range; and a data processor configured to:

receive nominal surface data representing the expected surface characteristic of the workpiece in a workpiece coordinate system;

determine a relationship between the measurement data in the measurement coordinate 25 system and the nominal surface data in the workpiece coordinate system;

simulate a measurement data set for the nominal surface using the nominal surface data and the determined relationship, the simulation providing a simulated measurement data set having a simulated range of simulated measurement values;

determine whether the simulated range meets a given criterion;

30 if the simulated range does not meet the given criterion, adjust a selected measurement data value for a selected measurement point and repeat the simulation to determine an

3

adjusted measurement data value for which the simulated range meets the given criterion; and determine measurement start conditions required for a measurement procedure to provide the adjusted measurement data value for the selected measurement point.

5

The selected measurement point may be a first measurement point of a measurement procedure.

The given criterion may be a point at which a difference between a maximum and 10 minimum simulated measurement value is less than a threshold value.

The given criterion may be a point at which a difference between the magnitude of the maximum simulated measurement value and the magnitude of the minimum simulated measurement value is less than a threshold value.

15

The adjusted measurement data value may be a measurement data value based on the selected measurement data value and a difference between maximum and minimum simulated measurement values.

20 The adjusted measurement data value may be a measurement data value based on a difference between the selected measurement data value and an average or mean of maximum and minimum simulated measurement values.

The adjusted measurement data value may be G'o = Go - (Gmax-Gmin)/2 where Go is the 25 selected measurement data value, and Gmax and Gmin are the maximum and minimum simulated measurement values.

The stylus may be movable by a traverse unit to move the stylus in the measurement direction.

30

The measurement direction may be at an angle P to an axis, x, of the workpiece coordinate system.

4

A pivotal mounting may be provided for the stylus such that an arm of the stylus pivots about a pivot axis as the stylus tip follows surface variations.

5 The surface characteristic may be a surface form of a surface of the workpiece.

In an embodiment, a pivotal mounting is provided for the stylus such that an arm of the stylus pivots about a pivot axis through an angle a as the stylus tip follows surface variations, the measurement coordinate system is given by G, X, where G is related to 10 the angle a and X is the measurement direction, and wherein the workpiece coordinate system is x, z, where x is a direction along a workpiece support surface of the apparatus, z is a normal to the workpiece and X is at an angle P to x.

In an embodiment, the relationship may given by:

15

Lcos(j8 + a0)+ Xcos/3 -Lcosa = xs Lsm(p + a0)+ Xsin /3 + AZcol - L sin a =zs where a is the degree of deflection of the stylus arm and a = a0 + /3 - (GIL) where G is the measurement data or transducer output;

20 X is the traverse or measurement direction which extends at the angle P to the x axis; AZcoi is the distance in the z direction when the stylus tip is at a measurement point on the surface being measured from the corresponding z position at which G=0;

ao is a pivot offset angle;

L is the distance between the centre of the stylus tip and the pivot axis which on 25 inversion:

v v _av _Jt(sin(a-^)-sina0)-xJsin^ + zJcos^

c ^ flat LS^col x =

cos/3

L(cosa - cos(j3 +a0))+

cos P

5

The measurement data set may be simulated by simulating the nominal surface form and rotating the simulated nominal surface form to the measurement direction. A gauge calibration relationship relating a measurement data value and a measurement direction position to a distance zg in z may be used to determine a data set in G and X 5 and if the measurement range G does not meet the given criterion, the selected measurement data value for the selected measurement point adjusted until the range meets the given criterion.

In an embodiment, the measurement data set may be simulated by:

10 simulating the nominal surface form and rotating the simulated nominal surface form by -(3 so that, referring to the nominal profile as z(x) + zflat :

f V \

vzg j

^cos(~p) -sin(-p)Vxs ^

sin(-p) cos(-p) J[zs (xs)- (Zc - Zflat)

15 determining gauge calibration relationships zG = atG + a2G2 + a3G3

xg = x"'"plzg p 2zg l^3zg deriving from the gauge relationships:

G = Yizg + Y2zg + Y3zg X = XG — (Pizg + P2zg + (^3zg )

setting G to a selected measurement data value, such as zero,

determining a starting value for Zc - Zflat to be determined at S14 in accordance with: z(sin(a - fi)-sin a0)-sin /3 + zs cos/3

Z -Z „ = AZ , =

c flat col

X =

cosjS

l(cosa -cos (/3+a0))+xs cosjS

25 then determining a (G, X) data set in accordance with:

6

xr. cos(— p) - sin(- p) x vzg j

»¥ xs ^

sin(-p) cos(-p) J1 zs (xs)- (Zc - Zflat)

G = YiZg + y2zG +y3z3G X = xg — (ptzg + P2zg + (^3zg )

and, if the measurement range does not meet the given criterion, adjusting a selected measurement data value for a selected measurement point and repeating the determination of Zc - Zflat and the (G, X) data set to determine an adjusted measurement data value for which the range meets the given criterion.

In another aspect, the present invention provides a data processor for a metrological apparatus for measuring a surface characteristic of a workpiece, the apparatus 10 comprising:

a mover to carry out a measurement procedure by effecting relative movement in a measurement direction between a workpiece and a stylus such that the stylus is deflected as a stylus tip of the stylus follows surface variations along a measurement path on a surface of the workpiece; and 15 a transducer to provide a measurement data set in a measurement coordinate system representing the deflection of the stylus at measurement points along the measurement path, the transducer having a measurement range, the data processor being configured to:

receive nominal surface data representing the expected surface characteristic of the 20 workpiece in a workpiece coordinate system;

determine a relationship between the measurement data in the measurement coordinate system and the nominal surface data in the workpiece coordinate system;

simulate a measurement data set for the nominal surface using the nominal surface data and the determined relationship, the simulation providing a simulated measurement 25 data set having a simulated range of simulated measurement values;

determine whether the simulated range meets a given criterion;

if the simulated range does not meet the given criterion, adjust a selected measurement data value for a selected measurement point and repeat the simulation to determine an adjusted measurement data value for which the simulated range meets the given 30 criterion; and

7

determine measurement start conditions required for a measurement procedure to provide the adjusted measurement data value for the selected measurement point.

In another aspect, the present invention provides a method for facilitating measurement 5 of a surface characteristic of a workpiece using an apparatus comprising:

a mover to carry out a measurement procedure by effecting relative movement in a measurement direction between a workpiece and a stylus such that the stylus is deflected as a stylus tip of the stylus follows surface variations along a measurement path on a surface of the workpiece; and 10 a transducer to provide a measurement data set in a measurement coordinate system representing the deflection of the stylus at measurement points along the measurement path, the transducer having a measurement range,

the method comprising:

determining a relationship between the measurement data in the measurement 15 coordinate system and nominal surface data representing the expected surface characteristic of the workpiece in a workpiece coordinate system;

simulating a measurement data set for the nominal surface using the nominal surface data and the determined relationship, the simulation providing a simulated measurement data set having a simulated range of simulated measurement values; 20 determining whether the simulated range meets a given criterion;

if the simulated range does not meet the given criterion, adjusting a selected measurement data value for a selected measurement point and repeating the simulation to determine an adjusted measurement data value for which the simulated range meets the given criterion; and

25 determining measurement start conditions required for a measurement procedure to provide the adjusted measurement data value for the selected measurement point.

In an embodiment, a stylus is deflected as a stylus tip of the stylus follows surface variations along a measurement path on a surface of a workpiece and a transducer 30 provides measurement data in a measurement coordinate system. A data processor is configured to: determine a relationship between the measurement data in the measurement coordinate system and nominal surface data representing the expected

8

surface characteristic of the workpiece in a workpiece coordinate system; simulate a measurement data set for the nominal surface using the nominal surface data and the determined relationship, the simulation providing a simulated measurement data set having a simulated range of simulated measurement values; if the simulated range does 5 not meet a given criterion, adjust a selected measurement data value for a selected measurement point and repeat the simulation to determine an adjusted measurement data value for which the simulated range meets the given criterion; and determine measurement start conditions required for a measurement procedure to provide the adjusted measurement data value for the selected measurement point.

10

Embodiments of the present invention will now be described, by way of example, with reference to the accompanying drawings, in which:

Figure 1 shows a very schematic representation of a metrological instrument of 15 apparatus embodying the present invention looking in a direction, y, perpendicular to a measurement direction;

Figure 2 shows a functional block diagram of data processing and control apparatus of apparatus embodying the present invention;

Figure 3 shows a functional block diagram of setup functionality provided by 20 programming of the control apparatus shown in figure 2 for enabling a balanced gauge measurement;

Figure 4 shows a flow chart illustrating processes for enabling a balanced gauge measurement;

Figures 5 to 8 show diagrams for explaining the setup functionality shown in 25 Figures 3 and 4; and

Figures 9 and 10 show a diagram and flow chart for explaining another method for enabling a balanced gauge measurement.

With reference to the drawings in general, it will be appreciated that the Figures are not 30 to scale and that for example relative dimensions may have been altered in the interest of clarity in the drawings. Also any functional block diagrams are intended simply to show the functionality that exists within the device and should not be taken to imply

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that each block shown in the functional block diagram is necessarily a discrete or separate entity. The functionality provided by a block may be discrete or may be dispersed throughout the device or throughout a part of the device. In addition, the functionality may incorporate, where appropriate, hard-wired elements, software 5 elements or firmware elements or any combination of these.

Referring now to the drawings, an example metrological apparatus will be described which comprises a metrological instrument and a control apparatus.

10 Figure 1 shows a very diagrammatic representation of the metrological instrument 2 of the metrological apparatus 1.

The metrological apparatus 2 has a base 5 that is designed to be supported by a workbench 6. The base 5 carries a column 7 that defines a vertical or z axis reference 15 datum. A column carriage 8 is mounted to the column 7 so as to be movable in the z direction with respect to the column 7. The movement of the column carriage 8 is effected by a motorised drive arrangement (not shown), such as for example a. leadscrew, pulley or other suitable drive arrangement. The base 5 also carries turntable 16 to support a workpiece 14. The turntable 16 has a centring and levelling 20 mechanism (not shown) such as that shown in Figures 2 and 3 of GB2,189,604A, the whole contents of which are hereby incorporated by reference.

The column carriage 8 carries a traverse unit 9, which is arranged at an angle P (the transverse angle) to the x-axis (which in the example is represented by the plane of the 25 turntable surface and is generally the horizontal). The transverse unit 9 is movable relative to the column carriage 8 by means of a motorised drive arrangement (not shown) along a straight reference datum (not shown) provided by the traverse unit 9. The direction of this straight reference datum is determined by the orientation of the transverse unit so that the traverse unit 9 is movable in an X direction which extends at 30 the angle P to the x-axis.

The traverse unit 9 carries a measurement probe (or gauge unit) 10 which consists of a

10

pivotally mounted stylus arm (shown very diagrammatically in Figure 1 in dotted lines within the traverse unit 9) carrying at its free end a stylus arm 11 having a stylus tip 12 which in operation comes into contact with the surface of the workpiece or component under test during a measurement operation so that, as the traverse unit 9 is moved in 5 the measurement direction, the stylus arm 11 pivots to enable the stylus tip 12 to follow surface variations along a measurement path on the surface. Deflection of the stylus arm is detected by a measurement transducer (or displacement provider) 39 shown in dotted lines in Figure 1. The measurement probe 10 may be mounted to the traverse unit 9 by a y-position adjuster (not shown) so as to be movable in the y-10 direction with respect to the traverse unit 9. The movement of the measurement probe 10 in the y-direction may be effected by a manual or motorised leadscrew, pulley or other drive arrangement (not shown).

In an example, the traverse unit 9 may be mounted to the column carriage 8 by means 15 of a pivot pin to enable the angle P of the traverse unit 9 with respect to the x-axis to be adjusted. In this particular example, the angle P of the traverse unit 9 is manually adjustable and the traverse unit 9 is held in place at the manually adjusted angle by means of an air brake (not visible in the Figure). As another possibility, the adjustment of the angle P may be automated. As another possbility, the angle P may for some 20 applications be fixed.

Figure 2 shows a block diagram illustrating functional components of the metrological instrument 2 and the control apparatus 3 of the metrological instrument 1.

25 Referring now to Figure 2, the control apparatus 3 is generally a personal computer and has a processing unit 13 coupled via a bus 13a to associated data and program instruction/software storage 14 in the form generally of RAM 15, ROM 16, a mass storage device 17 such as a hard disc drive and at least one removable medium drive 18 for receiving a removable medium (RM) 19, such as a CD-ROM, solid state 30 memory card, DVD, or floppy disc. As another possibility, the removable medium drive may itself be removable, for example it may be an external hard disc drive.

11

The control apparatus is also coupled via the same or a different bus to input/output devices 20 comprising in this example a display 21, a keyboard 22, a pointing device 23 such as a mouse, a printer 24 and, optionally, a communications device 25 such as 5 at least one of a MODEM and a network card for enabling the control apparatus 3 to communicate signals S via a wired or wireless connection with other control apparatus or computers via a network such as the Internet, an intranet, a WAN or a LAN.

The processing unit 13 is programmed by program instructions and data provided by 10 being at least one of: downloaded as a signal S via the communications device 25; pre-stored in any one or more of ROM 16, RAM 15 and mass storage device 17; read from a removable storage medium 19 received by the removable medium drive 18; and input by the user using the keyboard 22.

15 The metrological instrument 2 has a data acquisition and processing unit (DAPU) 30 that communicates with the processing unit 13 of the control apparatus 3 via an appropriate link, for example a serial link, 30a to enable data regarding a measurement operation to be communicated to the control apparatus 3.

20 The control components of the metrological apparatus 2 comprise a column drive controller 31 for driving the carriage 8 up and down the column in the z direction, a measurement direction position controller 32 for driving the measurement probe or gauge unit along the reference datum provided by the traverse unit 9 in the measurement direction X at an angle P to the x-axis and an interferometric z 25 displacement provider 35 for providing a measure of the z displacement of the stylus tip 12 as the stylus arm 11 follows the surface being measured during movement of the traverse unit 9 along a measurement path in a direction at an angle P to the x-axis.

If rotation of the turntable is automated, then the metrological apparatus will also 30 comprise a y (where y represents the angle of rotation of the turntable 16 about its spindle axis) position controller 38 for controlling rotation of the turntable 16. Similarly, if the attitude of the traverse unit 9 is adjustable and this adjustment is

12

automated, then a P position controller 36 will be provided for changing the attitude P of the traverse unit 9. y and P position providers 39, 37 (which may for example be shaft encoders, for example optical shaft encoders, or a linear grating type position provider) are provides to supply signals respectively indicating the angles y and P to 5 the DAPU 30. Generally the interferometric z displacement provider 35 will be provided within the traverse unit 9.

The measurement direction position controller 32 is associated with a position provider 34 that may be, for example, a shaft encoder associated with a motor providing the 10 position controller 32 or may be a linear grating type of transducer. The column drive 31 may also be associated with a column z position provider 33 (shown in phantom lines in Figure 4a), for example a shaft encoder associated with a motor providing the column drive 31, or the column z position may be determined in an open loop manner directly from the column motor drive signal. As show in Figure 2, the column drive 31 15 and position controller 32 (and other controllers if present) are coupled to the control apparatus 3 (via a link 13b and appropriate interfaces, not shown) for control by instructions from the control apparatus 3. At least some of these instructions may be supplied by the user.

20 The measurement probe or gauge unit is in this example the measurement probe used in the instruments supplied by Taylor Hobson as the Form Talysurf PGI series and is described in detail in US-A-5,517,307 (the whole contents of which are hereby incorporated by reference) to which reference should be made for further information. In particular the measurement probe or gauge unit may be based on Taylor Hobson's 25 Form Talysurf PGI 1240 metrological instrument, described in the brochure produced by Taylor Hobson entitled "Form Talysurf PGI 1240, Aspherics Measurement system". This Form Talysurf PGI series of metrological instruments is particularly suited to measuring the surface form of surfaces having significant form because, as described in US-A-5,517,307, the interferometric z displacement provider 35 uses a curved 30 diffraction grating that has a radius of curvature which is coincident with the axis about which the stylus arm pivots to provide more accurate z displacement measurements over a longer range.

13

The processing unit is programmed by program instructions to enable carrying out of measurements further details of examples of such programming may be found in W02010/943906, the whole contents of which are hereby incorporated by reference.

5

In the following (see Figures 5 to 8):

O is the origin, that is the location at which x=0, z=0

®a is the nominal base diameter of the workpiece or component whose surface form is to be measured, for example an aspheric lens mould 100 as shown in solid lines in 10 Figure 5 or an aspheric lens mounted on the attached to a base, the lens being illustrated by the dot-dash line 101 in Figure 5;

a is the stylus deflection angle between the line passing through the pivot axis A and the centre of the stylus tip 12 and the x axis and represents the degree of deflection of the stylus arm;

15 G is the gauge reading which as will be explained below is related to the stylus deflection angle a;

P is the angle of the traverse unit to the x axis;

X is the traverse or measurement direction which extends at the angle P to the x axis; Xi is the distance the traverse unit has moved in the traverse or measurement direction 20 X from a zero position Xo;

z(x) is the distance in the z direction of a point on the surface being measured from a top surface of the flat part (the body of the mould or the base upon which the aspheric lens is mounted);

Ax is the distance in the x direction of the centre of the stylus tip 12 from x=0 where 25 x=0 corresponds to the turntable spindle axis on which the component to be measured will be centred and aligned, for example as discussed in W02100/043906, so that a rotational axis of the component (the optical axis in the case of an aspheric lens) is coincident with and aligned to the spindle axis;

AZC or AZcoi is the distance in the z direction when the stylus tip is at a measurement 30 point on the surface being measured from the corresponding z position at which G=0 (see Figure 5);

14

Azflat is the distance in the z direction from z=0 to the top surface of any flat part, part 100 in Figure 5;

Lo is the length of the stylus arm 11;

A is the location of the pivot axis of the stylus arm;

5 ao is the pivot offset angle which as shown in Figure 7 is an angle between a line parallel to the x axis passing through the pivot axis A and a line passing through the pivot axis A and the centre of the stylus tip 12 with the stylus arm parallel to the traverse axis and is determined, as illustrated in Figure 7, by the offset P of the pivot axis A from the stylus arm, the length of the stylus arm L and the length S of the stylus 10 shank 11a from the stylus arm to the centre of the stylus tip 12;

L is the distance between the centre of the stylus tip 12 and the pivot axis A, which distance is determined by the length of the stylus arm L, the pivot offset P and the length S of the stylus shank 11a from the stylus arm to the centre of the stylus tip 12.

15 Figure 3 shows a functional block diagram illustrating functionality provided by programming of the processor unit to facilitate efficient use of the measurement range of the gauge, such that a measurement of a given surface form (component) exhibits opposite polarity extreme excursions of the same magnitude, that is the measurement is a "balanced gauge" measurement. Figure 4 shows a flow chart illustrating processes 20 carried out by in order to facilitate a "balanced gauge" measurement whilst Figures 5 to 8 are diagrammatic representations of assistance in explaining these processes.

As shown in Figure 3, the gauge balancing functionality includes a data receiver 40 (which may be provided by the input/output devices shown in Figure 2) to receive data 25 and store the data in a data store 41 which may be provided by, for example, any one or more of the RAM 15, ROM16 and/or mass storage 17 shown in Figure 2. As will be explained below, data stored in the data store 41 includes: initial gauge data Go; traverse angle P; a nominal form of the surface of the workpiece to be measured, that is the form that the surface was designed or intended to be and the height Azflat which as 30 set out above is the distance in the z direction from z=0 to the top surface of the flat part; stylus characteristics data including, for example, the length L of the stylus arm 11, a pivot offset angle ao, the length S of a stylus shank projecting from the stylus arm

15

11 and carrying at its free end the stylus tip 12. The data store 41 also provides storage for storing start data determined by the functionality to be described below.

The functionality shown in Figure 3 includes a stylus tip location determiner 42 for 5 determining a relationship between a stylus tip location (xs, zs) in a component coordinate system x, z (where xs, zs represents the location of a centre of a sphere defined by a contact surface of the stylus tip) and a stylus tip location in a measurement coordinate system (G, X) where G represents the gauge data and Xi represents the position along the traverse direction X, a surface data set simulator 45 10 for simulating the form of the surface to be measured using the nominal form data in the data store 41 and a start data determiner 47 for determining z and x start positions for the gauge data to facilitate a balanced gauge measurement for the surface form under consideration starting from a given xs, zs stylus tip measurement start location.

15 The processes now to be described with reference to Figure 4 in order to facilitate a balanced gauge measurement may be carried out using the functionality described with reference to Figure 3 or any other appropriate functionality.

In order to explain the processes shown in Figure 4, reference should also be made to 20 Figures 5 to 8 which illustrate aspects of the geometry of the metrological instrument.

Referring to Figures 5 to 8, the vector from origin O to pivot location A in Figure 6 is given by:

25

1)

where i and k are the unit vectors in the x and z directions.

30

(In the example illustrated in Figure 5 the traverse unit has been driven in the negative X direction from Xo and so Xi has a negative value.)

16

The vector b from origin O to the stylus tip centre in Figure 6 is given by:

A~l(i cosa + ksma)=iAx + k(AZflat +z(Ax})= iAxs+kzs 2)

5 The gauge reading G and its relationship with the stylus deflection angle a are given by:

G = l(a0+f3-a) =^>a =a0 + f3-(G/l) 3)

10 Extracting the orthogonal components (x,z) from equations 1 and 2 allows a pair of relationships to be defined that relate the stylus tip centre values (xs,zs) in terms of the stylus and instrument parameters as follows:

Lcos(/3+a0)+Xcos/3 -Lcosa = xs L sin(j0 + a0)+ Xsin /3 + AZcol - L sin a =

15

Data representing the nominal form of the component to be measured may be input by the operator but may be pre-stored. Again, the data store may store data representing various different nominal surface forms for selection by the user.

20

Figures 7 and 8 in particular show the geometry and dimensions of the stylus. This data is either pre-stored or input by the operator. Where a number of different styli are available, the operator may select the stylus characteristics data form a number of pre-stored sets of stylus characteristics data. As another possibility, the stylus itself may 25 carry the data in a local non-volatile memory or may carry identification data identifying the stylus so that the control apparatus can select the correct set of stylus data from its data store. In this example, the stylus data includes the length Lo is of the stylus arm 11, the pivot offset angle ao which as shown in Figure 7 is an angle between a line parallel to the x axis passing through the pivot axis A and a line passing through 30 the pivot axis A and the centre of the stylus tip 12 with the stylus arm parallel to the traverse axis and is determined, as illustrated in Figure 7, by the offset P of the pivot

17

axis A from the stylus arm, the length of the stylus arm L and the length S of the stylus shank 11a from the stylus arm to the centre of the stylus tip 12, and the length S of the stylus shank 11a from the stylus arm to the centre of the stylus tip 12.

5 The traverse angle P will generally be input by the operator but could be determined by detecting the degree of rotation using an appropriate transducer. The measurement step X; may be pre-defined but could be operator-selectable.

The stylus characteristics data also includes the geometry and dimensions of the stylus 10 tip. In this example, the stylus tip is in the form of a sphere of given radius r. The centre of that sphere will not coincide with the point on the stylus tip that contacts the surface being measured. If the nominal form of the component to be measured is dz represented as z(x) then it has a gradient of— = tan f . For a stylus tip of radius r dx

15

traversing this surface, the tip centre is then defined by zs = z + rcosvF

5)

x„ = x -rsm where the point of contact between the stylus tip and the surface is (x, z). These stylus tip centre values (xs, zs) are used throughout the following.

20

In order to determine a (and so G), Zc and X, the equations 4) above may be inverted to yield:

v v _ L(sin(a-p)-sina0)-xs sinP + zs cosP

— Zflat = -

cosp ^

_ L(cosa-cos(p + a0))+xs

A =

cosP

25

At S1 in Figure 4, equation 6) is used to determine the relationship between the stylus tip location (xs, zs) in the component coordinate system (x, z) and in the measurement system (G,X). The stylus and instrument parameters a0 , P and L may be pre-stored f

18

they are fixed for the instrument but will generally be input by the operator via the data receiver during the set up procedure prior to starting a measurement operation for a particular surface form. As another possibility, the data storm may store various different stylus and instrument parameters and the operator may select the parameters 5 appropriate for the stylus and traverse angle he has selected

An initial gauge reading for a measurement start position is determined at S2 and a simulated surface data set is determined at S3. Now considering simulating the measurement of (xs, zs), if the gauge signal at the beginning of the measurement 10 simulation (G„) is set at, say, zero at S2, then since a = ao + (3 - (G / L) generally, this inverted equation may be solved for X and Zc-Zflat. The original main equation pair 4) may also be usefully inverted to yield (G, X) in terms of (xs, zs):

X+ =

-B + A/B2 -4C

15

where

B = 2(Lcosa0 +(ZC -z)sin|3-xs cos|3)

C = (x2 -2Lxcos(p + aJ+2L(Zc -zs)sin(p + a0) + (Zc -zs)2)

and

^Lsin(|3 + ao)+Xsin|3 + (Zc -zs)^

7)

a = tan~

L cos(p + a 0) + X cos |3 + x

8)

s J

The simulation selects the most appropriate one of the two solutions for X. In t his example, for the data pair adjacent to the first (xs,zs) data pair, the correct solution for 20 X is chosen to be the one that is closest to the original X value. This enables the determination of V and hence G for the simulated surface form data set. The process of comparing the two possible solutions for the jth value of X with the known (j-l)th value enables the entire data set to be analysed to determine a set of values for G for the simulated surface form data set.

The maximum and minimum values of G, Gmax and Gmin, in the determined set of values for G are then identified at S4 and, if at S5 the difference between the

19

magnitudes |Gmax| and |Gmin| is not below a determined threshold (which may be preset or defined by the operator), G0 is updated at S6 to be:

G' = G -(G -G . )/2 9)

o o V max nun / '

5 and S3 and S4 repeated.

When the difference between |Gmax| and |Gmin| is determined at S5 to be below the threshold, this iterative process is halted, at which point the starting values for both X and G will have been determined. Once these are known then Zc-Zflat can be determined 10 and the values of z and X required for the measurement start position to achieve a balanced gauge measurement stored so that, once the operator has completed the initial centring and levelling procedures and inputs a command to the control apparatus to start a measurement, then the control apparatus can drive the carriage 8 and the traverse unit 9 to the z and X positions to achieve a balanced gauge measurement. This 15 should facilitate more accurate measurement and also should speed up the measurement process because the operator does not have to try to determine the best z and X starting positions by trial and error something which would be a time-consuming procedure because generally there may be more than one combination of z and X that results in a given stylus angle a. The described process is particularly advantageous 20 where the traverse unit extends at an angle to the x axis because, in those circumstances, the relationship between the gauge signal G and z and X is not intuitive or straightforward and so it is even more difficult for the operator to try to determine, by trial and error, a starting value for G to achieve a balanced gauge measurement.

25 Another way of facilitating a balanced gauge measurement using calibration coefficients of the gauge will now be described with the aid of Figure 9 which shows a diagram of a geometrical representation of part of the stylus and traverse geometry and Figure 10 which shows a flow chart illustrating the process.

30 At S10 in Figure 10, the nominal surface form or profile is simulated and at Sll this nominal surface form or profile is rotated to lie in the frame of reference of the stylus

20

by rotation by -(3 (-traverse angle) about the location (0, Zc) so as to lie in the frame of reference of the stylus. So, for brevity referring to the nominal profile as z(x) + zflat :

\ZG J

IV

cos(- p) - sin(- p)

vsin(-p) cos(-p) J1 zs (xs)- (Zc - Zflat)

10)

The gauge (transducer 39 in Figure 1) has gauge calibration relationships given by:

zr = a,G + a9G2 + a,G3

g 1 2 3 n)

xg = ^"l"plzg p 2zg l^3zg

The relationship for zg may be inverted by a least-mean squares approach and the relationship for xG may be simply re-expressed to give, at S12:

G = YiZg + Y2ZQ + Y3ZQ

X = Xq - (ptzG + p2zG + p3zG )

These relationships may be pre-stored from an earlier gauge calibration so that data representing G and X on the basis of the gauge calibrations is provided with the measurement apparatus or may be calculated when the gauge is calibrated by an operator.

The subsequent procedure is similar to that shown in Figure 4 in that the gauge signal is set to zero at S13 in Figure 10 for the start of the (xs,zs) data. This, as discussed above, defines V and so enables a starting value for Zc -Zflat to be determined at S14

in accordance with equation 6. The corresponding (G, X) data set is then determined at S15 in accordance with equations 10 and 12.

Assuming that the threshold criterion at S16 is not met, then a new starting value for G (G0) is determined at S17 as before in accordance with equation 9 and at S14 the equivalent V is determined from equation 3 and an updated value for Zc.-Zflat generated in accordance with equation 6 from which an updated (G, X) data set is determined at S15. S14 to S17 are repeated until the difference between the magnitudes

21

|Gmax | and |Gmin | is below a threshold at which point the starting values for both X and

G to provide a balanced gauge measurement have been determined. Once these are known then Zc-Zflat can be determined and the values of z and X required for the measurement start position to achieve a balanced gauge measurement stored so that, 5 once the operator has completed the initial centring and levelling procedures and inputs a command to the control apparatus to start a measurement, then the control apparatus can drive the carriage 8 and the traverse unit 9 to the z and X positions to achieve a balanced gauge measurement. As before, this should facilitate more accurate measurement and also should speed up the measurement process because the operator 10 does not have to try to determine the best z and X starting positions by trial and error something which would be a time-consuming procedure because there may be more than one combination of z and X that results in a given stylus angle a. The described process is particularly advantageous where the traverse unit extends at an angle to the x axis because, in those circumstances, the relationship between the gauge signal G and z 15 and X is not intuitive or straightforward and so it is even more difficult for the operator to try to determine, by trial and error, at a starting value for G to achieve a balanced gauge measurement.

Subsequent measurements may be carried out in known manner, for example as 20 discussed in WO 2010/043906, the whole contents of which are hereby incorporated by reference.

Modifications and Variations

A person skilled in the art will appreciate that a number of different methods of 25 centring and levelling could be employed with the above-described techniques. For example, as one possibility, mechanical centring is used. It may be possible to use software centring and/or levelling, for example as described in US-A-5926781, the whole contents of which are hereby incorporated by reference, which may enable omission of at least some of the centring and levelling mechanisms discussed herein.

30

Other forms of centring and levelling mechanism may be used. For example, it may be possible to use wedge assemblies of the type described in the Applicant's International

22

Application Publication No. W02007/091087, the whole contents of which are hereby incorporated by reference. Other levelling mechanism that do not use wedge assemblies may be used, for example, as discussed in US-A-4731934, the whole contents of which are hereby incorporated by reference.

5

In the above example, the stylus tip is in the form of a sphere of given radius r but it could have another form, for example a frusto-conical form with a part-spherical contact surface.

10 It will be appreciated that the traverse angle P could be zero. Also, the stylus need not necessarily be a contact stylus but could be any form of stylus that follows the frame of a surface, although this may require modification of the definition of the stylus tip centre.

15 Also, other gauge units or transducer units than the ones described above may be used, for example it may be possible to use an LVDT gauge or a different form of optical interferometric gauge.

A person skilled in the art will appreciate that the methods and apparatus described 20 herein need not be limited in their application to instruments for the measurement of aspheric, concave or convex surfaces, and may equally be applied to instruments for the measurement of other surfaces.

As one possibility, there is provided a computer program, computer program product, 25 or computer readable medium, comprising computer program instructions to cause a programmable computer to carry out any one or more of the methods described herein.

Various features described above may have advantages with or without other features described above.

30

The above embodiments are to be understood as illustrative examples of the invention. Further embodiments of the invention are envisaged. It is to be understood that any

23

feature described in relation to any one embodiment may be used alone, or in combination with other features described, and may also be used in combination with one or more features of any other of the embodiments, or any combination of any other of the embodiments. Furthermore, equivalents and modifications not described above 5 may also be employed without departing from the scope of the invention, which is defined in the accompanying claims.

24

Claims

1. A metrological apparatus for measuring a surface characteristic of a workpiece, the apparatus comprising:

a mover to carry out a measurement procedure by effecting relative movement in a 5 measurement direction between a workpiece and a stylus such that the stylus is deflected as a stylus tip of the stylus follows surface variations along a measurement path on a surface of the workpiece;

a transducer to provide a measurement data set in a measurement coordinate system representing the deflection of the stylus at measurement points along the measurement 10 path, the transducer having a measurement range; and a data processor configured to:

determine a relationship between the measurement data in the measurement coordinate 15 system and the nominal surface data in the workpiece coordinate system;

determine whether the simulated range meets a given criterion;

20 if the simulated range does not meet the given criterion, adjust a selected measurement data value for a selected measurement point and repeat the simulation to determine an adjusted measurement data value for which the simulated range meets the given criterion; and determine measurement start conditions required for a measurement procedure to 25 provide the adjusted measurement data value for the selected measurement point.

2. A metrological apparatus according to claim 1, wherein the data processor is configured to use as the selected measurement point a first measurement point of a measurement procedure.

30

25

3. A metrological apparatus according to claim 1 or 2, wherein the data processor is configured to use as the given criterion the point at which a difference between a maximum and minimum simulated measurement value is less than a threshold value.

5 4. A metrological apparatus according to claim 1 or 2, wherein the data processor is configured to use as the given criterion the point at which a difference between the magnitude of the maximum simulated measurement value and the magnitude of the minimum simulated measurement value is less than a threshold value.

10 5. A metrological apparatus according to any of the preceding claims, wherein the data processor is configured to use as the adjusted measurement data value a measurement data value based on the selected measurement data value and a difference between maximum and minimum simulated measurement values.

15 6. A metrological apparatus according to any of claims 1 to 4, wherein the data processor is configured to use as the adjusted measurement data value a measurement data value based on a difference between the selected measurement data value and an average or mean of maximum and minimum simulated measurement values.

20 7. A metrological apparatus according to any of claims 1 to 4, wherein the data processor is configured to use as the adjusted measurement data value G'o = Go -(Gmax-Gmin)/2 where Go is the selected measurement data value, and Gmax and Gmin are the maximum and minimum simulated measurement values.

25 8. A metrological apparatus according to any of the preceding claims, comprising a traverse unit to move the stylus in the measurement direction.

30

9. A metrological apparatus according to any of the preceding claims, wherein the measurement direction is at an angle P to an axis, x, of the workpiece coordinate system.

26

10. A metrological apparatus according to any of the preceding claims, providing a pivotal mounting for the stylus such that an arm of the stylus pivots about a pivot axis as the stylus tip follows surface variations.

5 11. A metrological apparatus according to any of the preceding claims, wherein the surface characteristic is a surface form of a surface of the workpiece.

12. A metrological apparatus according to any of the claims 1 to 7, wherein a pivotal mounting is provided for the stylus such that an arm of the stylus pivots about a

10 pivot axis through an angle a as the stylus tip follows surface variations, the measurement coordinate system is given by G, X, where G is related to the angle a and X is the measurement direction, and wherein the workpiece coordinate system is x, z, where x is a direction along a workpiece support surface of the apparatus, z is a normal to the workpiece and X is at an angle P to x.

15

13. A metrological apparatus according to Claim 12, comprising a traverse unit to move the stylus in the measurement direction.

14. A metrological apparatus according to Claim 13, wherein the traverse unit is 20 movable in the z direction.

15. A metrological apparatus according to Clam 13, wherein the measurement start conditions are a position along the measurement direction X and a position along the z direction.

25

16. A metrological apparatus according to Claim 12, 13, 14 or 15, wherein the relationship is given by:

Lcos(j0 + a0)+ Xcos/3 - Lcosa =

Lsin(j8 + a0)+ Xsin /3 + AZcol - L sin a =zs

30 where

27

10

a is the degree of deflection of the stylus arm and a = a0 + /3 - (GIL) where G is the measurement data or transducer output;

X is the traverse or measurement direction which extends at the angle P to the x axis; AZcoi is the distance in the z direction when the stylus tip is at a measurement point on the surface being measured from the corresponding z position at which G=0;

ao is a pivot offset angle;

L is the distance between the centre of the stylus tip and the pivot axis which on inversion:

v v _av _Jt(sin(a-^)-sina0)-xJsin^ + zJcos^

c ^ flat LS^col x =

cos/3

L(cosa -cos(j0 +a0))+

cos P

17. A metrological apparatus according to any of claims 12 to 15, wherein the data processor is configured to determine the relationship between the measurement data in the measurement coordinate system and the nominal surface data in the workpiece coordinate system and to simulate the measurement data set by simulating the nominal 15 surface form and rotating the simulated nominal surface form to the measurement direction.

18. A metrological apparatus according to claim 17, wherein the data processor is configured to use a gauge calibration relationship relating a measurement data value

20 and a measurement direction position to a distance zG in z to determine a data set in G and X and if the measurement range G does not meet the given criterion, to adjust the selected measurement data value for the selected measurement point until the range meets the given criterion.

25 19. A metrological apparatus according to Claim 12, 13, 14 or 15, wherein the data processor is configured to determine the relationship between the measurement data in the measurement coordinate system and the nominal surface data in the workpiece coordinate system and to simulate the measurement data set by:

28

simulating the nominal surface form and rotating the simulated nominal surface form by -(3 so that, referring to the nominal profile as z(x) + zflat :

f V \

Vzg j

^cos(~p) -sin(-p)Vxs ^

sin(-p) cos(-p) J [zs (xs) - (Zc - Zflat)

determining gauge calibration relationships zG = atG + a2G2 + a3G3

xg = x"'"plzg p 2zg l^3zg deriving from the gauge relationships:

G = YiZg + Y2zg + y3zG X = XG — (Pizq + P2zg + (^3zg )

setting G to a selected measurement data value, such as zero,

determining a starting value for Zc - Zflat to be determined at S14 in accordance with: z(sin(a - /?)-sin a0)-sin /3 + zs cos/3

Z -Z„=AZ , =

c flat col

X =

L(cosa - cos(/3 +a0 ))+ cos /3

cos/3

then determining a (G, X) data set in accordance with:

iVv ^

xr. cos(— p) - sin(- p)^i x„

Vzg j sin(-p) cos(-p) Jlvzs (xs)- (Zc - Zflat)

G = YiZg + Y2zg + Y3zg X = XG — (Pizg + P2zg + P3zg )

29

20. A data processor for a metrological apparatus for measuring a surface characteristic of a workpiece, the apparatus comprising:

a mover to carry out a measurement procedure by effecting relative movement in a measurement direction between a workpiece and a stylus such that the stylus is 5 deflected as a stylus tip of the stylus follows surface variations along a measurement path on a surface of the workpiece; and a transducer to provide a measurement data set in a measurement coordinate system representing the deflection of the stylus at measurement points along the measurement path, the transducer having a measurement range, the data processor being configured 10 to:

15 simulate a measurement data set for the nominal surface using the nominal surface data and the determined relationship, the simulation providing a simulated measurement data set having a simulated range of simulated measurement values;

determine whether the simulated range meets a given criterion;

if the simulated range does not meet the given criterion, adjust a selected measurement 20 data value for a selected measurement point and repeat the simulation to determine an adjusted measurement data value for which the simulated range meets the given criterion; and determine measurement start conditions required for a measurement procedure to provide the adjusted measurement data value for the selected measurement point.

25

21. A data processor according to claim 20, wherein the data processor is configured to use as the selected measurement point a first measurement point of a measurement procedure.

30 22. A data processor according to claim 20 or 21, wherein the data processor is configured to use as the given criterion the point at which a difference between a maximum and minimum simulated measurement value is less than a threshold value.

30

23. A data processor according to claim 20 or 21, wherein the data processor is configured to use as the given criterion the point at which a difference between the magnitude of the maximum simulated measurement value and the magnitude of the

5 minimum simulated measurement value is less than a threshold value.

24. A data processor according to any of Claims 20 to 23, wherein the data processor is configured to use as the adjusted measurement data value a measurement data value based on the selected measurement data value and a difference between

10 maximum and minimum simulated measurement values.

25. A data processor according to any of claims 20 to 23, wherein the data processor is configured to use as the adjusted measurement data value a measurement data value based on a difference between the selected measurement data value and an

15 average or mean of maximum and minimum simulated measurement values.

26. A data processor according to any of Claims 20 to 23, wherein the data processor is configured to use as the adjusted measurement data value G'o = Go -(Gmax-Gmin)/2 where Go is the selected measurement data value, and Gmax and Gmin are the

20 maximum and minimum simulated measurement values.

27. A data processor according to any of Claims 20 to 26ms, wherein the measurement direction is at an angle P to an axis, x, of the workpiece coordinate system.

25

28. A data processor according to any of Claims 20 to 27, wherein the surface characteristic is a surface form of a surface of the workpiece.

29. A data processor according to any of Claims 20 to 26, wherein a pivotal 30 mounting is provided for the stylus such that an arm of the stylus pivots about a pivot axis through an angle a as the stylus tip follows surface variations, the measurement coordinate system is given by G, X, where G is related to the angle a and X is the

31

measurement direction, and wherein the workpiece coordinate system is x, z, where x is a direction along a workpiece support surface of the apparatus, z is a normal to the workpiece and X is at an angle P to x.

5 30. A data processor according to Claim 29, wherein the measurement start conditions are a position along the measurement direction X and a position along a z direction in which a traverse unit carrying the stylus is movable.

31. A data processor according to Claim 29 or 30, wherein the relationship is given 10 by:

Lcos(/3 + a0)+ Xcos/3 - Lcosa = xs Lsin(/3 + a0)+ Xsin /3 + AZcol - L sin a = zs where a is the degree of deflection of the stylus arm and a = a0 + /3 - (GIL) where G is the 15 measurement data or transducer output;

ao is a pivot offset angle;

20 L is the distance between the centre of the stylus tip and the pivot axis which on inversion:

v v _av _Jt(sin(a-^)-sina0)-xJsin^ + zJcos^

c ^ flat LS^col x =

cos/3

z(cosa — cos(/3 +a0 ))+x5 cos/3

32. A data processor according to any of claims 29 to 31, wherein the data 25 processor is configured to determine the relationship between the measurement data in the measurement coordinate system and the nominal surface data in the workpiece coordinate system and to simulate the measurement data set by simulating the nominal

32

surface form and rotating the simulated nominal surface form to the measurement direction.

33. A data processor according to claim 32, wherein the data processor is 5 configured to use a gauge calibration relationship relating a measurement data value and a measurement direction position to a distance zq in z to determine a data set in G and X and if the measurement range G does not meet the given criterion, to adjust the selected measurement data value for the selected measurement point until the range meets the given criterion.

10

34. A data processor according to Claim 29 or 30, wherein the data processor is configured to determine the relationship between the measurement data in the measurement coordinate system and the nominal surface data in the workpiece coordinate system and to simulate the measurement data set by:

15 simulating the nominal surface form and rotating the simulated nominal surface form by -(3 so that, referring to the nominal profile as z(x) + zflat :

\ZG J

cos(-p) -sin(-p)Vxs sin(- p) cos(-p) J1 zs (xs) - (Zc - Zflat)

20 determining gauge calibration relationships zG = atG + a2G2 + a3G3

xg = x"'"plzg p 2zg l^3zg deriving from the gauge relationships:

G = YiZg + Y2zg + y3zG X = XG — (Pizq + P2zg + P3zg )

setting G to a selected measurement data value, such as zero,

determining a starting value for Zc - Zflat to be determined at S14 in accordance with:

33

Z -Z „ = AZ , =

c flat col

Z.(sin(a - (3)-sin a0)-sin /3 + zs cos/3

X =

L(cosa — cos(j0 +a0 ))+ cos/3

cos/3

then determining a (G, X) data set in accordance with:

iVv ^

xr. cos(— p) - sin(- p)^i x„

\ZG J

sin(-p) cos(-p) J1 zs (xs)- (Zc - Zflat)

G = YiZg +Y2Zq +y3z3G X = xg - (ptzg + (32zg p3zg )

35. A method for facilitating measurement of a surface characteristic of a workpiece using an apparatus comprising:

a mover to carry out a measurement procedure by effecting relative movement in a measurement direction between a workpiece and a stylus such that the stylus is deflected as a stylus tip of the stylus follows surface variations along a measurement path on a surface of the workpiece; and a transducer to provide a measurement data set in a measurement coordinate system representing the deflection of the stylus at measurement points along the measurement path, the transducer having a measurement range,

the method comprising:

determining a relationship between the measurement data in the measurement coordinate system and nominal surface data representing the expected surface characteristic of the workpiece in a workpiece coordinate system;

simulating a measurement data set for the nominal surface using the nominal surface data and the determined relationship, the simulation providing a simulated measurement data set having a simulated range of simulated measurement values; determining whether the simulated range meets a given criterion;

34

if the simulated range does not meet the given criterion, adjusting a selected measurement data value for a selected measurement point and repeating the simulation to determine an adjusted measurement data value for which the simulated range meets the given criterion; and 5 determining measurement start conditions required for a measurement procedure to provide the adjusted measurement data value for the selected measurement point.

36. A method according to claim 35, wherein the selected measurement point is a first measurement point of a measurement procedure.

10

37. A method according to claim 35 or 36, wherein the given criterion is a point at which a difference between a maximum and minimum simulated measurement value is less than a threshold value.

15 38. A method according to claim 35 or 36, wherein the data processor is configured to use as the given criterion the point at which a difference between the magnitude of the maximum simulated measurement value and the magnitude of the minimum simulated measurement value is less than a threshold value.

20 39. A method according to any of claims 35 to 38, wherein the adjusted measurement data value is a measurement data value based on the selected measurement data value and a difference between maximum and minimum simulated measurement values.

25 40. A metrological apparatus according to any of claims 35 to 38, wherein the adjusted measurement data value is a measurement data value based on a difference between the selected measurement data value and an average or mean of maximum and minimum simulated measurement values.

30 41. A method according to any of claims 35 to 38, wherein the adjusted measurement data value is G'o = Go -(Gmax-Gmin)/2 where Go is the selected

35

measurement data value, and Gmax and Gmin are the maximum and minimum simulated measurement values.

42. A method according to any of claims 35 to 41, wherein the apparatus comprises 5 a traverse unit to move the stylus in the measurement direction.

43. A method according to any of claims 35 to 42, wherein the measurement direction is at an angle P to an axis, x, of the workpiece coordinate system.

10 44. A method according to any of claims 35 to 43, wherein the apparatus provides a pivotal mounting for the stylus such that an arm of the stylus pivots about a pivot axis as the stylus tip follows surface variations.

45. A method according to any of claims 35 to 44, wherein the surface 15 characteristic is a surface form of a surface of the workpiece.

46. A method according to any of claims 35 to 41, wherein a pivotal mounting is provided for the stylus such that an arm of the stylus pivots about a pivot axis through an angle a as the stylus tip follows surface variations, the measurement coordinate

20 system is given by G, X, where G is related to the angle a and X is the measurement direction, and wherein the workpiece coordinate system is x, z, where x is a direction along a workpiece support surface of the apparatus, z is a normal to the workpiece and X is at an angle P to x.

25 47. A method according to Claim 46, wherein the apparatus has a traverse unit to move the stylus in the measurement direction.

48. A method according to Claim 47, wherein the traverse unit is movable in the z direction.

30

49. A method according to Clam 47, wherein the measurement start conditions are a position along the measurement direction X and a position along the z direction.

36

50. A method according to any of claims 46 to 49, wherein the relationship is given by:

Lcos(/3+a0)+Xcos/3 -Lcosa = xs Lsm(/3 + a0)+ Xsin /3 + tsZcol - L sin a = zs where a is the degree of deflection of the stylus arm and a = a0 + /3 - (GIL) where G is the measurement data or transducer output;

X is the traverse or measurement direction which extends at the angle P to the x axis; 10 AZcoi is the distance in the z direction when the stylus tip is at a measurement point on the surface being measured from the corresponding z position at which G=0;

ao is a pivot offset angle;

v v _av _L(sm(a-/3)-sma0)-xssm/3 + zscos/3

c ^ flat ^col 0

15 C0S^

_ L(cosa — cos(j0 +a0))+

JC —

cos/3

51. A method according to any of claims 46 to 49, comprising determining the relationship between the measurement data in the measurement coordinate system and the nominal surface data in the workpiece coordinate system and simulating the

20 measurement data set by simulating the nominal surface form and rotating the simulated nominal surface form to the measurement direction.

52. A method according to claim 51, comprising using a gauge calibration relationship relating a measurement data value and a measurement direction position to

25 a distance zg in z to determine a data set in G and X and if the measurement range G does not meet the given criterion, adjusting the selected measurement data value for the selected measurement point until the range meets the given criterion.

37

53. A method according to any of claims 46 to 49, comprising determining the relationship between the measurement data in the measurement coordinate system and the nominal surface data in the workpiece coordinate system and simulating the measurement data set by:

simulating the nominal surface form and rotating the simulated nominal surface form by -P so that, referring to the nominal profile as z(x) + zflat :

xr. cos(— p) - sin(- p) x vzg j

|Vv ^

sin(-p) cos(-p) J1 zs (xs)- (Zc - Zflat)

7

determining gauge calibration relationships zG = atG + a2G2 + a3G3

xg = ^"l"Plzg P 2zg l^3zg deriving from the gauge relationships:

G = YiZg + Y2zg + y3zG X = XG — (Pizq + P2zg + P3zg )

setting G to a selected measurement data value, such as zero,

determining a starting value for Zc - Zflat to be determined at S14 in accordance with: Z(sin(a - /?)-sin a0)-xs sin f3 + zs cosf3

Z -Z„ = AZ , =

c flat col x =

L(cosa - cos(/3 +a0 ))+ cos /3

cos/3

then determining a (G, X) data set in accordance with:

iVv ^

xr. cos(— p) - sin(- p)^i x„

\ZG J

sin(-p) cos(-p) Jlvzs (xs)- (Zc - Zflat)

G = YiZg + Y2zg + Y3zg X = XG — (Pizg + P2zg + P3zg )

38

54. A metrological apparatus substantially as hereinbefore described with reference to and//or as illustrated in the accompanying drawings.

55. A data processor substantially as hereinbefore described with reference to 5 and//or as illustrated in the accompanying drawings.

56. A method substantially as hereinbefore described with reference to and//or as illustrated in Figure 4 or 10 of the accompanying drawings.

10 57. A computer program product comprising program instructions to program a processor to carry out data processing of a method according to any of claims 35 to 53 and 56 or to program a processor to provide the data processor of any of claims 1 to 34, 54 and 55.