METROLOGICAL STYLUS ASSEMBLY

Abstract: A metrological instrument usable for scanning a small area (for example 0.5 mm x 0.5 mm) of the surface of a workpiece to detect roughness features has a stylus assembly in which a short (10 mm) lightweight (5 mg) stylus arm (9) is loaded with a hairspring (17) which provides most of the static stylus force (100 mg force). This construction provides a high acceleration for the stylus tip (13), allowing the stylus to track features of an amplitude over 0.1 mu m with data points 1 mu m apart and a stylus traverse speed of at least 5 mm s<-1>. The stylus assembly (7) is supported and driven by a two dimensional traverse unit (5) having two one dimensional stages. Each stage has a balanced compound rectilinear spring mounting using flexure springs arranged to resist gravity through their resistance to bending within the plane of the spring.

Description: METR0L0GICAL STYLUS ASSEMBLY The present invention relates to a metrological instrument of the type which drives a stylus over a surface so as to detect very small surface features at a scale where the features are generally considered to contribute to the texture (roughness) of the surface, e.g. surface features having a wavelength of the order of 1 millimetre down to a wavelength of the order of 1 micrometre. The invention also relates to a stylus assembly for use in such apparatus, and a drive unit for driving the stylus of such apparatus. In the present invention, the detected roughness-scale data may be used, e.g. to provide values for roughness parameters or to provide an image, map or profile of the surface shape showing these very small surface features . In a typical metrological instrument for detecting surface roughness, such as the Form Talysurf series available from Rank Taylor Hobson Limited of Leicester, United Kingdom, a stylus is arranged to pivot about an axis generally parallel to the surface to be measured (which is usually horizontal), and the pivot is mounted on a datum bar which is movable generally parallel to the surface to be measured and transverse to the pivot axis, so as to move the stylus over the surface. The datum bar is mounted on a precision reference datum with slide bearings. In use, the stylus will normally be held spaced from the surface while the datum bar is extended to the start point for a measurement traverse. Then the system as a whole is moved towards the surface or the stylus is released, so that the tip of the stylus rests gently on the surface, and then the datum bar is slowly retracted, dragging the stylus over the surface. The movement of the stylus tip relative to the datum bar is detected using a transducer while the stylus tip is moving over the surface, and the transducer output values are logged in association with signals indicating the instantaneous position of the stylus tip along its line of travel over the surface to be measured, so as to provide data from which a measure or a mapping of the roughness of the surface can be calculated. Typically, such instruments are arranged to sample the transducer output at up to about 500 Hz, depending on the speed at which the datum bar is moving the stylus tip over the surface, to obtain a measurement of the height of the stylus tip approximately once per micrometre of movement over the surface. The stylus tip may move over the surface at about 500 μm per second, although the speed may be less if it is desired to have data points closer together on the surface. In practice, the transducer output may be sampled at a frequency above 500 Hz, and two or more successive samples combined to obtain a single data value, with data values being provided at a frequency below 500 Hz. The stylus will typically weigh a small number (e.g. 1 to 5) grams, although the force which the stylus tip applies to the surface will be much less than this because most of the weight is relieved by a counter balance or a counter spring. The stylus will typically apply a force of 100 mg-force, or less, to the surface. Such machines can provide a highly accurate measurement of the roughness of a surface as measured on a straight line traversed by the stylus tip over the surface. They are suitable for measuring the surfaces of small workpieces, such as optical lenses and machines bearings, which are mounted on workpiece holders positioned under the stylus of the apparatus. The workpiece holder may include a stage to rotate or translate the workpiece, so that measurements can be taken along a plurality of lines on the surface or in a plurality of directions across it. With some metrological instruments, it is possible to use a "three-dimensional" mode in which a series of measurement traverses are made across a worxpiece surface and the workpiece is moved sideways slightly between successive traverses, so as to build up data about the surface texture over a designated area. The output is three-dimensional distributed in two directions (the x and y directions) . The apparatus can obtain data for a relatively large area. The maximum distance through which the datum bar can traverse the stylus tip over the surface is typically about 10 cm, and the workpiece holder may be able to move the workpiece sideways by several cm. However, an excessive amount of data is obtained if a large area is scanned. If an area 1 cm 2 is scanned with data points at 1 μm in the x and y directions, data is taken at IO 8 points on the surface. In practice, useful information about the roughness of a surface or a sample of its small-feature profile can be obtained from a much smaller area. The size of area required depends on the size of the features it is desired to detect, but for most engineering surfaces the area can be for example a square 0.5 mm long on each side. A square this size implies 250000 data points spaced 1 μm apart. A considerable time is taken to scan even a square as small as 0.5 mm, in view of the slow speed of the tip of the stylus over the surface being measured. Even if the speed is increased to 0.5 mm per second, each line across the square will take one second to scan, and for a 1 μm spacing between data points there will need to be five hundred scans across the square, so that it will take almost ten minutes to complete the scanning operation. The use of such a system to detect surface texture over an area is also limited because it can only be used with workpieces which can be placed on the workpiece holder, which limits the maximum size of the workpiece. The time taken to scan an area would be reduced if the stylus could be driven over the surface faster. However, this cannot be done with existing systems. The immediate limit on the speed at which the stylus can move over the surface in existing systems is the tendency of the stylus to fail to track the height of the surface accurately at faster traverse speeds. If the surface was absolutely smooth, the stylus would always apply a force to it equal to the static stylus force (i.e. the force which the stylus applies to the surface if it is not moving). If the stylus moves over a surface the height of which varies sinusoidally, the stylus will apply force equal to the static force while it is on the straight sections of the sinusoidal slope. However, dynamic effects mean that the stylus force is increased as it passes through a trough, and is reduced as the stylus passes over a crest. These dynamic effects increase as the traverse speed of the stylus increases, until a point is reached at which the stylus force at the bottom of the trough is twice the static force and the stylus force at the top of a crest is zero. A stylus force of zero implies that the stylus will no longer track the surface but can separate from it. Accordingly, after this point has been reached, any further increase in the speed at which the stylus moves over the sinusoidal surface will cause the stylus to separate from the surface, typically in the region of the crests. In practice, the roughness or the microscopic shape features of surfaces are not sinusoidal. However, the surface profile can be considered as being made up of sinusoidal components having spatial frequencies up to the highest spatial frequency which the system can measure, which depends on parameters such as the radius of the stylus tip and the separation between the data points (in accordance with Nyquist sampling theories). In practice, it is normally the highest measurable spatial frequency component which is hardest to track. This analysis is used in "A Revised Philosophy of Surface Measuring Systems", D J Whitehouse, Proceedings of the Institution of Mechanical Engineers, Volume 202, No. C3, Pages 169 to 185 (1988). The dynamic performance of stylus systems has also been considered in "The Dynamic Response of Stylus", Shigeyasu Ajioka, Bulletin of the Japanese Society of Precision Engineering, Volume 1, No. 4, Pages 228 to 233 (1963). However, the analyses provided in the prior art appear to be largely academic, and have not provided practical guidelines for increasing the speed at which a stylus can traverse over a surface for roughness measurement in the manner proposed in the present invention. It appears that there are many possible ways in which the mathematics of the stylus behaviour can be analyzed, and various different parameters can be selected for review in trying to optimise the system. The prior art analyses appear to have concentrated on maximising the frequency of vertical oscillation which the stylus can track accurately or on limiting dynamic aspects of stylus force, and this has led to proposals for providing particular damping and resonating properties in the stylus. By focusing on the static force applied by the stylus and the inertia of the stylus the present inventor has been able to establish that a conventional pivoted stylus arrangement, in which the stylus has substantially uniform density along its length and the stylus force is derived from the weight of the stylus, cannot provide a stylus with the ability to track the roughness of a surface at high traverse speeds. Similarly, in a stylus which moves linearly towards and away from the surface, a system which obtains the stylus pressure from the weight of the stylus cannot provide a stylus which can track the roughness of a surface at high traverse speeds . The present invention provides rules for the construction of a stylus, in order to obtain tracking at high traverse speeds, which are related to the ability of the static stylus force to accelerate the stylus tip. According to an aspect of the present invention, there is provided a stylus assembly for a metrological instrument for detecting surface features, in which a stylus has a tip for contacting the surface and is mounted to rotate about a pivot, and the stylus is biassed to press the tip against the surface with a force (the static force) when the tip is not rotating about the pivot axis, such that the value defined by the magnitude of the static force multiplied by the square of the length of the stylus between the pivot axis and the tip divided by the moment of inertia of the stylus is greater than 1.5 g, where g is the acceleration due to gravity. Preferably, this value is at least 5 g, more preferably at least 10 g, and most preferably at least 20 g. On a simplified analysis of the behaviour of a pivoting stylus, ignoring factors such as damping and resonance, this value provides a measure of the rate of acceleration of the tip under the static stylus force. It will be referred to hereinafter as the theoretical acceleration of the stylus tip. It is an inherent property of the stylus assembly, which can be selected by appropriate construction of the assembly, and as will be explained below, the rate at which the tip can accelerate under the static force is directly related to the rate at which the tip can be traversed over the surface without losing contact. The value of 1.5 g for the expression given above is the theoretical acceleration for a horizontally extending stylus of uniform distribution of mass along its length, pivoted precisely at its end away from the stylus tip (i.e. having no counter balance), and using the whole of its weight to provide the stylus force. Consequently, a stylus of uniform cross-section which obtains the stylus force solely from its weight cannot meet the condition set out above. The theoretical acceleration of the stylus tip can be increased above 1.5 g to some extent by providing a stylus with a non-uniform distribution of weight along its length, with the weight being concentrated close to the pivot axis. If all of the stylus weight was concentrated close to the pivot axis, and the rest of the length of the stylus had no weight at all, the theoretical acceleration of the stylus tip would approach infinity. However, any real stylus must be made from material having some mass, and it is not practical to raise the theoretical acceleration of the stylus tip above 3 or 4 g purely by non-uniform distribution of mass . In order to raise the theoretical acceleration of the stylus tip substantially above 1.5 g, it is necessary to provide a biassing means, such as a spring, so that at least a part of the stylus force, preferably more than half of it, is provided by the biassing means and not by the weight of the stylus. Other types of biassing means are possible, such as electromagnetic biassing means, but such means tend to increase the moment of inertia of the stylus . It is known in "balanced stylus" arrangements to provide the stylus force by a biassing means, such as a spring, other than the weight of the stylus, but these are arrangements in which a counter balance extends beyond the pivot axis in the direction away from the stylus tip, to counteract the effect of the stylus weight. This is done, for example, to enable the stylus to operate with the tip pressing against the surface from any angle, rather than just from above. In such systems, the counter weight increases the overall mass and moment of inertia of the stylus, so that the theoretical acceleration of the stylus tip will normally be very low unless the static stylus force is unacceptably high. In order to prevent the stylus from damaging the surface which it is moving over, the static force of the stylus tip on the surface normally needs to be limited. Since reducing the static stylus force reduces the theoretical acceleration of the stylus tip, limiting the static stylus force implies a corresponding limit to the ratio of the moment of inertia to the square of the distance from the pivot to the stylus tip (this ratio can be regarded as the effective mass of the stylus) if the theoretical acceleration is not to be reduced. Preferably, the static stylus force is less than 1 gram- force and the effective mass of the stylus (i.e. the moment of inertia divided by the square of the distance from the pivot to the stylus tip) is less than 2/3 of a gram. More preferably, the static stylus force is less than 0.5 gram-force, more preferably still it is less than 0.2 gram-force, and most preferably it is less than 0.1 gram-force. Table 1 below gives values for the effective mass of the stylus depending on the static stylus force and the theoretical acceleration of the stylus tip. TABLE 1 Values for the Moment of Inertia/(pivot-to-tip length^ 2 , in grams F = Static Stylus Force, in grams-force a = Theoretical Tip Acceleration, in g (acceleration due to gravity) F = 1 F = 0 5 F = 0. 2 F = 0.1 a = 1.5 0.66 0.33 0.133 0.066 a 5 0.2 0.1 0.04 0.02 a = 10 0.1 0.05 0.02 0.01 a = 20 0.05 0.025 0.01 0.005 It can be seen that if a high theoretical acceleration of the stylus tip is desired for a low static stylus force, the effective mass of the stylus must be kept very low. In practice, this normally means that the stylus must be kept short. For a constant mass, the moment of inertia depends on the square of the length of the stylus. However, increasing the length of the stylus tends to increase its mass as well, and for a uniform density stylus the moment of inertia varies in proportion with the cube of its length. Since the denominator in the expression for the effective mass varies with the square of the length of the stylus, the expression as a whole is reduced by reducing the length. For a = 20g and F = 0.1 gram-force, the effective mass of the stylus must be no more than 5 milligrams. This can be provided with a stylus approximately 1 cm long and constructed in a similar manner to a known high fidelity record player stylus. In another aspect of the present invention, the theoretical acceleration of the stylus tip is defined as three times the static stylus force divided by the mass of the stylus, ignoring any mass closer to the pivot axis than one-tenth of the pivot-to-tip length of the stylus . The same preferred values apply as for the previous definition. This definition is based on the formula for the moment of inertia of a stylus of uniform distribution of mass along its length. In practice, it is often easier to measure the mass of the stylus than to measure its moment of inertia, and in most cases the distribution of mass will not cause the moment of inertia to be greatly different from the moment of inertia for a uniform distribution of mass. According to another aspect of the present invention there is provided a stylus assembly for a metrological instrument, comprising • a stylus with a tip to be traversed over a surface to detect a surface characteristic thereof, the stylus having a total mass, excluding in the case of a pivoting stylus any mass within one-tenth of the pivot-to-tip length of the stylus from the pivot axis, of not more than 25 mg. More preferably, the mass is not more than 20 mg, still more preferably it is not more than 10 mg, and most preferably it is not more than 5mg. The range of preferred static stylus forces is as given above. In the case of a pivoting stylus, the limit on the value for the mass is preferably met even if only mass within one-twentieth of the length from the pivot axis is excluded. In the case of a pivoting stylus, the pivot-to-tip length of the stylus is preferably no more than 2 cm, more preferably no more than 1 cm. In all aspects of the present invention which involve a pivoting stylus, it is preferred that the stylus does not extend away from the stylus tip substantially beyond the pivot axis. In practice, a small extent beyond the pivot axis is normally unavoidable, for example because the stylus includes a pivot pin which extends beyond the axis in all directions by the length of its radius . In another aspect the present invention provides a stylus assembly for a metrological instrument for detecting the roughness of a surface or fine details of its shape, comprising a stylus mounted to move substantially linearly to press a tip of the stylus against the surface the roughness or shape of which is to be detected, and biassing means to bias the stylus tip against the surface with a force in the absence of movement of the tip in the direction towards or away from the surface (the static stylus force), such that the static stylus force divided by the mass of the stylus is greater than 1.5 g, where g is the acceleration due to gravity. In this arrangement, of a translationally moving stylus rather than a pivotally moving stylus, the static stylus force divided by the mass of the stylus provides the theoretical acceleration of the stylus tip. The same preferred values for static stylus force and theoretical acceleration of the stylus tip apply in this case as in the case of a pivotally moving stylus, and the values given in Table 1 above apply in this case also except that the values in the body of the Table are for the actual mass of the stylus in place of the effective mass defined for a pivoting stylus. This means that the mass constraint on the construction of a linearly moving stylus is more severe than on the construction of a pivoting stylus, since the effective mass of a pivotally moving stylus will normally be less than its actual mass. When ε stylus is traversed over a surface, the speed of movement of the stylus over the surface together with the desired spacing between data points on the surface defines the frequency with which data values must be obtained for the data points. For example, if the stylus is to travel over the surface at 5 mm per second, and it is desired to have data points 1 μm apart, data values for the data points must be obtained at a frequency of 5 kHz. Preferably, the stylus should be constructed so that it has no mechanical resonances below the desired data sampling frequency. In order to ensure that the resonant frequencies of the stylus arm are as high as possible, the arm should be stiff, light and short. These requirements are compatible with the requirement for a high theoretical acceleration of the stylus tip, since a short light stylus will tend to have a low effective mass . Additionally, it is preferable to try to minimise resonances between the stylus tip and the point on the stylus the position of which is tracked by the transducer which provides the data output, so that the data output from the transducer accurately reflects movement of the stylus tip. For this reason, in a pivoting stylus it is preferable for the transducer to be arranged to track the position of the tip end of the stylus, and commonly used arrangements in which the transducer follows movement of a different part of the stylus, frequently a part extending beyond the pivot axis away from the tip, should preferably be avoided. Further aspects of the present invention relate to the mechanism for driving the stylus across the surface to be measured. In one aspect, the present invention provides a metrological instrument for detecting the roughness or small-feature profile of a surface, having a stylus mounted for movement of the stylus tip towards and away from a surface to be measured and a drive assembly for driving the stylus over the surface with its tip in contact with the surface in a first direction generally parallel to the surface and transverse to the direction of movement of the stylus tip and a second direction generally parallel to the surface, transverse to the first direction and transverse to the direction of movement of the stylus tip. Such a metrological instrument, in which the stylus tip can be driven over the surface in two dimensions, provides a more convenient means for measuring areas than an arrangement in which the drive assembly drives the stylus in one dimension only and the workpiece must be moved by a workpiece support. This aspect of the present invention opens up the prospect of measuring the roughness or profile of small areas of the surface of a workpiece which cannot easily be mounted on a precision movable workpiece support of the type used with typical prior art instruments for measuring surface roughness . In another aspect of the present invention there is provided a support assembly for supporting a stylus of a metrological instrument for detecting a surface characteristic, comprising a first member which supports a second member from one or more generally planar flexure springs for movement of the second member relative to the first member in a first substantially horizontal direction, the flexure spring being arranged in a vertical plane extending in a second horizontal direction substantially transverse to the first horizontal direction and being fast with the first member along a first substantially vertical line and being fast with the second member along a second substantially vertical line spaced from the first line in the second horizontal direction, so that flexure of the spring permits movement of the second member relative to the first member in the first horizontal direction and the stiffness of the flexure spring against bending within its plane resists gravity and supports the second member from the first member. An additional flexure spring may be provided between the first and second members, spaced from the first flexure spring in the first horizontal direction, so as to provide a parallelogram type linkage between the first and second members in which the second member cannot rotate relative to the first member. One or more additional flexure springs may be provided vertically spaced from the first flexure spring. The mounting arrangement may be a compound spring assembly in which the second member supports a third member through one or more further similar flexure springs, and the mounting assembly may be arranged or the third member may be constrained so that the third member moves in a straight line relative to the first member. In prior art instruments such as the Form Talysurf series discussed above, the stylus is carried on a datum bar which slides over precisely located slide bearings on a precision datum mount, which define the datum line of movement. The datum bar is pressed firmly against the slide bearings, and the arrangement is relatively stiff, requiring substantial force to move the datum bar over the slide bearings. Accordingly, the motor for driving the datum bar must be powerful enough to overcome the stiffness of the bearings, and the arrangement is not suitable for moving the stylus at a high speed while making a surface measurement, for example owing to vibration from the motor. If the stylus is arranged to be carried on a support through one or more mounting assemblies according to the present aspect of the invention, the datum line or datum plane of movement of the stylus can be defined by the position of the mount and the very high resistance of a flexure spring against bending within its plane, so that stiff sliding bearings can be avoided. If a stylus is mounted in this way, movement of the stylus relative to the mount is accommodated by flexure of one or more flexure springs, and by choosing the strength of the springs appropriately the mounting can be arranged so that the stylus can be moved rapidly and smoothly with relatively little effort. According to another aspect of the present invention a stylus for a metrological instrument for detecting a surface characteristic is mounted on a mounting member through a symmetric balanced compound spring mounting, in which flexure springs extend in opposing directions from the mounting member to respective intermediate members, and further flexure springs extend from the intermediate members to a second member in opposing directions which are substantially parallel to the directions in which the flexure springs extend between the mounting member and the intermediate members, the second member supporting the stylus and being aligned with the mounting member in a direction transverse to the plane of the flexure springs, the flexure springs tending to constrain the second member to move in a straight line towards and away from the mounting member. Preferably the said opposing directions and the direction in which the second member is aligned with the mounting member are substantially horizontal directions, and the second member is supported against the effect of gravity by the resistance of the flexure springs against bending within their planes . The present inventor has found that this mounting allows relatively fast smooth movement between the second member supporting the stylus and the mounting member, with good linearity of movement at least over distances of about 1 mm. An example of a suitable spring mounting is the flexure type double compound rectilinear spring mounting shown in Figure 4.9 of "Foundations of Ultra-Precision Mechanism Design", S T Smith and D G Chetwynd, Published 1992 by Gordon and Breach Science Publishers SA (ISBN 2- 88124-840-3). Spring mountings are also discussed in Paper V "Parallel and Rectilinear Spring Movements" in "Instruments and Experiences" by R V Jones, published 1988 by John Wiley & Sons Limited (ISBN 0 471 91763 X). In another aspect of the present invention there is provided a mounting assembly for a stylus of a metrological instrument for detecting a surface characteristic, in which the stylus is mounted, for movement in the plane of the surface to be measured, by flexure of a flexure spring, the said movement in the plane of the surface is detected by a sensor means, and the stylus is moved by an actuator controlled through a feedback loop in accordance with the output of the sensor means to ensure that the stylus adopts the desired position. Preferably, a signal representing the desired position of the stylus is input to the feedback loop to be combined with the output from the sensor means, enabling the stylus to be moved by varying the desired position signal while maintaining feedback control of the actuator from the sensor means. The feedback control allows the position of the stylus to be controlled accurately regardless of uncertainty or variability in the characteristics of the actuator and the flexure spring, and can also stabilise the stylus position against the effects of resonant oscillations of the mounting assembly. An electromagnetic actuator is preferred, but other kinds of actuator are possible. An embodiment of the present invention, given by way of non-limiting example, will now be described with reference to the drawings, in which: Figure 1 is a schematic view of a generalised stylus system for use in developing a theoretical analysis; Figure 2 is a sectional side view of a metrological instrument embodying the present invention; Figure 3 is a top view of the instrument of Figure 2; Figure 4 is a side view of the stylus assembly of the instrument to Figure 2; Figure 5 is a view from beneath of the stylus assembly of the instrument of Figure 2; Figure 6 is an enlarged view of the detector for detecting the position of the tip of the stylus of the stylus assembly of Figures 4 and 5; Figure 7 is a feedback control circuit for a light emitting diode for use with the detector of Figure 6; Figure 8 is the output circuit for a stylus position detecting photodiode of the detector of Figure 6; Figure 9 is a plan view of one traverse stage of the traverse unit of the instrument of Figure 2; Figure 10 is a view of a flexure spring strip for the traverse stage of Figure 9; Figure 11 is a view of the path of the stylus tip of the instrument of Figure 2 over the surface of a workpiece; Figure 12 shows the change in the x position of the stylus tip with time; Figure 13 shows the change in the y position of the stylus tip with time; Figure 14 is a feedback control circuit for the x direction traverse stage of the traverse unit of the instrument of Figure 2; Figure 15 is a feedback control circuit for the y direction stage of the traverse unit of the instrument of Figure 2; Figure 16 is an overview of the data acquisition and control system for the instrument of Figure 2; Figure 17 shows the circuit for generating the y direction scan drive signal input to the circuit of Figure 15 from the x direction scan drive signal input to the circuit of Figure 14; Figure 18 shows an example of an output image of the surface shape which can be obtained with an embodiment of the invention; Figure 19 shows a stylus arm and tip suitable for metrology use; Figure 20 is an enlarged view of an alternative detector arrangment, particularly for detecting the position of the x and y traverse unit stages; Figure 21 shows an alternative traverse unit instructions with mechanical damping; Figure 22 is a simplified partial sectional side view of the stylus assembly showing a stylus cover; Figure 23 is a bottom view of the stylus cover; Figure 24 is a triangle wave generator circuit; and Figure 25 shows an alternative circuit for generating the y direction scan drive signal. Figure 1 shows schematically the features of a generalised pivoting stylus system (ignoring factors such as damping, resonance etc). The stylus pivots about a pivot point P. The stylus tip is a distance lj from the pivot point P, and has a mass m 1 . A counter balance with a mass m 2 is a distance 1 2 away from the pivot P in the direction away from the stylus tip. It is assumed that the remainder of the stylus has no mass . The stylus tip rests against the surface with a force made up of the net torque of the masses m x and m 2 about the pivot point P and the effect of any externally applied bias force F b applied between the pivot point P and the stylus tip at a distance l b away from the pivot point P. As the stylus moves over a surface, roughness of the surface will cause the stylus tip to move up and down in the z direction, and changes in the speed of movement in the z direction will be resisted by the inertia of the system, which will add a dynamic or inertial component to the force of the stylus tip on the surface. The force of the stylus tip on the surface is equal to and is opposed by a reaction R. Assuming that the stylus extends horizontally, the equation of motion for small displacements of the stylus in terms of the net torque on the stylus tip can be written as I- - =g (m 1 l 1 -m 2 l 2 ) +F b l b -Rl 1 ( 1 ) where g is the acceleration due to gravity and I is the moment of inertia of the stylus and is given by As explained above, the highest spatial frequency component of the roughness or profile features which can be measured by the system depends on parameters such as the curvature of the stylus tip and the physical spacing of the data points, in accordance with the Nyquist criteria. This maximum detectable spatial frequency can be represented as a sinusoidal variation in height of the surface, having an amplitude A and a spatial period d. As the stylus moves over the surface with a velocity v, the vertical position of the stylus z can be expressed as follows z-A sinω t (3) where ω is given by ω=^ (4) d Differentiating both sides of equation (3) twice with respect to time (t) gives f= -J-ω 2 sinω t ( 5 ) and then substituting in equation (3 ) gives z= -ω 2 z ( 6 ) If equation (6) is substituted in equation (1), which is re-arranged to obtain an expression for R, one gets R >== ^ 3- {m l -m 2 l 2 ) + Vi, Iω 2 z 1 7 2 (?) The critical condition, for the stylus to track the surface accurately, is that the stylus should not lose contact with the surface when passing over the feature mentioned above having amplitude A and spatial period d. The stylus will lose contact with the surface when the force it applies to the surface, and the reaction R of the surface, falls to zero. It can be seen from equation (4) that the traverse speed v of the stylus over the surface is directly related to ω, and accordingly in order to maximise the traverse speed at which the stylus leaves the surface, the values in equation (7) should be adjusted to maximise the value of ω at which R becomes zero. As the traverse speed is increased, the stylus will initially begin to lift off the surface at the crests of the waveform, i.e. when sinωt = -1, and z = -A. If R in equation (7) is set to zero and z is set to -A, the equation can be re-arranged as follows Aω 2 (8) Ignoring the last term in equation 8 (i.e. assuming that the external bias force F b = 0) , it can be seen that ω is maximised if m 2 l 2 is minimised. That is to say, the stylus should so far as possible have no counter weight portion extending beyond pivot point P in the direction away from the stylus tip. A balanced system in which m 2 l 2 equals m l l should be avoided. If m 2 l 2 is zero (i.e. there is no counter weight portion of the stylus at all), the remaining mass and length terms cancel with the moment of inertia I, and in the absence of an external bias force F b , Aω 2 = g. If m 2 l 2 = 0, equation (8) can be rewritten as Aω 2 _ rr+ Fb 1_b (g ) l x m The value of Aω 2 can be increased above g by providing an external bias force F b . However, this will tend undesirably to increase the static force of the stylus on the surface to be measured. The static stylus force F s for a stylus with no counter weight is given by F b lt 1^ Comparing equations (9) and (10), it can be seen that the static stylus force F s can be reduced while the value of ω 2 is increased if the mass l is reduced. The static stylus force F s can then be returned to its previous value by increasing the bias force F b , which further increases the value of ω 2 . In practical terms, this means that the designer should seek the minimum stylus mass, so that the weight of the stylus provides a relatively small part of the total static stylus force, and an external bias force can be applied so as to increase the ability of the stylus to follow surface features at high traverse speeds without excessively increasing the static stylus force. A metrological instrument embodying the present invention is illustrated in sectional side view in Figure 2. It comprises a main housing 1 which may rest on the surface of a workpiece 3 and supports a traverse unit 5. The traverse unit 5 in turn supports a stylus assembly 7, which includes a stylus having a tip which rests against the surface of the workpiece 3. (The stylus is considered to be the part which moves to accommodate movement of the stylus tip as the height of the surface varies. ) For a small workpiece, the main housing 1 can be placed on a support plate, which supports the workpiece at the location of the stylus tip. In this way the instrument can be used with workpieces which are too small to support it. The traverse unit 5 is arranged to move the stylus assembly 7 in two dimensions parallel to the plane of the surface of the workpiece 3 by a selectable distance of up to approximately 0.5 mm in each dimension. In this way, the instrument uses movement of the stylus tip to obtain information about the roughness of the surface of the workpiece 3 over a square area up to about 0.5 mm along each side. Figure 3 is a top view of the metrological instrument of Figure 2, showing an upper (y direction) stage of the traverse unit 5 in broken lines . Figure 2 is a section taken along, the line II-II in Figure 3. The stylus assembly 7 is shown in section in Figure 2. Figure 4 is a side view of the stylus assembly and Figure 5 is a view of the stylus assembly from below. The stylus assembly 7 comprises a stylus made up of a stylus arm 9 and a pivot pin 11. One end of the stylus arm 9 is joined to the pivot pin 11, and the other end carries a stylus tip 13 which extends downwardly from the stylus arm 9 to contact the surface of the workpiece. An optical shutter fin 15 extends upwardly from the tip end of the stylus arm 9, and forms part of an optical transducer for detecting movement of the stylus tip 13 about the axis of the pivot pin 11, in a manner which will be described below. In a working prototype of the embodiment, the stylus arm 9 was provided by a Sonotone VI00 HiFi record player stylus, and a stylus tip 13 was provided by the diamond HiFi stylus tip. The length of the stylus arm in this case was about 1 cm, and it had a mass of about 4 mg. This may be compared with a pivoting stylus for a Form Talysurf instrument, in which the stylus arm is typically at least 10 cm from the pivot axis to the tip and weighs one or a small number of grams. For a precision metrological instrument, the stylus tip 13 should have a curvature in accordance with accepted metrology standards (which normally require a radius of curvature in the range of 1 to 5 μm) , and therefore the HiFi record playing tip of the Sonotone V100 stylus (which has a radius of curvature of about 10 μm) may not be suitable. However, the construction of the stylus arm 9 from the Sonotone VI00 HiFi stylus was found to be satisfactory. This is a lightweight hollow aluminium or aluminium alloy tube. A stainless steel tube could also be used. Although stainless steel is denser than aluminium it is stiffer, and accordingly a thinner grade of material could be used. The pivot pin 11 is a conventional pivot pin, similar to the one used in the Form Talysurf series of instruments. The mass of the pivot pin 11 has very little effect on the performance of the stylus, because its mass is concentrated about the pivot axis. The ends of the pivot pin 11 are tapered and are held in a conventional three-ball cup bearing. The optical shutter fin is a thin sheet of aluminium alloy, which has been blackened, e.g. by being anodised. It has negligible weight. Because of the low mass of the stylus arm 9, its weight provides very little static stylus force at the stylus tip 13 on the surface of the workpiece 3. A hairspring 17, preferably provided by a thin beryllium copper strip, is attached to the pivot pin 11 and is adjusted so that the static force at the stylus tip 13 is approximately 100 mg force. The hairspring 17 is arranged in a spiral coil as shown in Figure 2, so that the slight rotation of the pivot pin 11 as the stylus tip 13 moves up and down does not significantly change the degree to which the hairspring 17 is stressed and therefore the static stylus force remains reasonably constant, for example varying by less than 5% for a vertical movement of the stylus tip 13 over 0.1 mm. The stylus is carried by a stylus mount 19, which is an aluminium alloy yoke having a horizontal crosspiece 21 and side members 23, 25 extending forwardly from the crosspiece 21 and downwardly below the level of the crosspiece 21. As can be seen in Figure 2, the end of the hairspring 17 remote from the pivot pin 11 is attached to a pin 26 extending between the side members 23, 25 of the stylus mount 19. The stylus is mounted for rotation on the side members 23, 25 of the stylus mount 19. More particularly, the three-ball cup bearings are fixed in the ends of short pieces of threaded rod 27, and these are screwed into tapped holes in the side members 23, 25 of the stylus mount 19, so as to capture the tapered ends of the pivot pin 11 and thereby support the stylus. Screws 29 pass through holes in the crosspiece 21 of the stylus mount 19, to attach the stylus assembly 7 to the traverse unit 5. An aluminium alloy plate 31 connects aluminium alloy blocks 33, 35 which carry the static part of the stylus transducer. The assembly of the plate 31 and the blocks 33, 35 is cemented across the open front of the stylus mount 19, with the plate 31 passing above the stylus arm 9. One of the aluminium blocks 33 carries a light emitting diode 37, which shines light towards the optical shutter fin 15. The other aluminium block 35 carries a detector panel 39, which carries two rectangular photodiodes 41, 43. The photodiodes 41, 43 are arranged one above the other, and the LED 37 and detector panel 39 are positioned relative to the position of the optical shutter fin 15 when the stylus tip 13 is resting on the surface of the workpiece 3, so that the top edge of the optical shutter fin 15 is in line between the LED 37 and the lower photodiode 43. Figure 6 is an enlarged view of the detector panel 39 showing the shadow 45 cast by the optical shutter fin 15 under illumination from the LED 37. As the stylus tip 13 moves up and down, the proportion of the lower photodiode 43 covered by the shadow 45 will vary, and therefore the signal output from the photodiode 43 will vary correspondingly. The top edge of the optical shutter fin 15 is angled so that the edge of the shadow 45 crosses the edges of the lower photodiode 43 substantially at right angles, in order to improve the linearity of the relationship between the height of the stylus tip 13 and the output signal from the photodiode 43. However, in order to obtain a reliable stylus tip position signal the output of the lower photodiode 43 is calibrated by measuring the signal as the stylus tip 13 is moved through a precisely known series of positions. Each photodiode 41, 43 is about 2 mm long and 1 mm high, and it is has been found by calibration that the output of the lower photodiode 43 varies substantially linearly with vertical movement of the stylus tip 13 over a range of movement of about 0.2 mm, and with calibration a usable transducer range of about 0.4 mm displacement of the stylus tip 13 can be obtained. The upper photodiode 41 remains exposed to light from the LED 37 for all positions of the stylus tip 13 within in the intended measurement range of movement, and accordingly provides a reference signal. In theory, the output from the upper photodiode 41 as a gain control and the output from the lower photodiode 43 as a signal could be input to a variable gain amplifier to obtain a signal dependent on the ratio between them, in order to eliminate the effect of .variation in the output strength of the LED 37. However, in practice it is preferred to control the energising current applied to the LED 37 through a feedback circuit using the output of the upper photodiode 41 so as to maintain the signal from the upper photodiode 41 at a constant level. Figure 7 shows the feedback control circuit connecting the upper photodiode 41 used for light intensity monitoring and the LED 37. The output of the photodiode 41 is amplified in an amplifying circuit 47, and is input to a comparison circuit 49 which also receives a reference signal level from a reference signal generator 51. The comparison circuit 49 acts as a differential amplifier, and outputs a control signal to a drive transistor 53 for the LED 37. The control signal represents the difference between the amplified photodiode signal received from the amplifier circuit 47 and the reference signal level received from the reference signal generator 51. The comparison circuit 49 and the drive transistor 53 act as a high gain negative feedback control, so that the current for the LED 37 passing through the drive transistor 53 is controlled to maintain the amplified photodiode signal at a constant level as set by the reference signal generator 51. Figure 8 shows the output circuit for the lower photodiode 43, which is used to sense the position of the stylus tip 13. The output signal from the photodiode 43 is amplified in an amplifier circuit 55 constructed in the same manner as the amplifier circuit 47 for the intensity monitoring photodiode 41. The amplified signal from the amplifier circuit 55 is output as the stylus tip position signal. The prototype stylus assembly mentioned above, using the Sonotone VI00 HiFi stylus for the stylus arm 9 and the stylus tip 13, was tested for mechanical resonance and no detectable mechanical resonance was found at frequencies below 5 kHz . This is in contrast to a conventional stylus assembly using a stylus approximately 10 cm long with a mass of 1 g, which had several resonant peaks below 5 kHz. The tracking ability of the prototype stylus assembly was tested by resting the tip on a vibrating platform with independently monitored vibration movements, and also by repeatedly measuring the profile of an edge of a copper strip at various traverse speeds, and it appears that in the prototype stylus assembly the stylus tip 13 will begin to lose contact with surface features having an amplitude of 0.35 μm and a period of 1 μm at a traverse speed of 5 mm per second. Since precision machined surfaces do not normally have surface roughness features with an amplitude greater than 0.1 μm, this suggests that the stylus assembly can be used reliably for traverse speeds up to and beyond 5 mm per second with 1 μm spacing between data points . The traverse unit 5 comprises two stages . The lower, x direction stage moves the stylus assembly 7 over the surface of the workpiece 3 in an x direction, which is the horizontal direction within the plane of the paper in Figure 2 and is the direction identified by the arrow x in Figure 3. The upper, y direction stage moves the x direction stage, and with it the stylus assembly 7, over the surface of the workpiece 3 in a y direction which is transverse to the x direction and is into and out of the plane of the paper in Figure 2 and is the direction marked with arrow y in Figure 3. The movement of the stylus tip 13 towards and away from the surface of the workpiece 3 is regarded as the z direction. Both stages have the same basic construction, and the basic construction of one stage is shown in plan in Figure 9. In the stage construction of Figure 9, blocks D and E are rigidly connected together, and block A is mounted with a symmetric compound flexure spring mounting using blocks B and C as intermediate blocks, so as to be freely movable substantially in a straight line relative to blocks D and E. Blocks D and E support freely movable intermediate blocks B and C through planar flexure springs F. These provide a parallelogram type linkage, so that intermediate blocks B and C are freely movable within the plane of the paper in Figure 9 along curving paths which are generally aligned with the direction between blocks D and E but which are closer to blocks D and E at each end of the path than in the middle of the path. The resistance of the flexure springs F to bending within their planes supports the blocks B and C against gravity, which would tend to move them out of the plane of the paper. The intermediate blocks B and C in turn support the movable block A through planar flexure springs G, to provide a parallelogram type linkage between the movable block A and each of the intermediate blocks B and C. The stiffness of the flexure springs G against bending within their planes supports the block A against the influence of gravity. The symmetric nature of the two parallelogram linkages for the movable block A, one linkage to intermediate block B and one linkage to intermediate block C, together with the symmetry between the parallelogram linkage supporting intermediate block B through flexure springs F and the parallelogram linkage supporting intermediate block C through flexure springs F, means that the central block A tends to move in a straight line in the direction between blocks D and E. The use of the intermediate blocks B and C compensates for the arcuate movement of the flexure springs F and G. The accuracy of the straight line movement of the central block A depends on the accuracy of the lengths, thickness and width of the flexure springs F, G. Preferably, these are all the same. For good straight line movement it is important that at least all of the flexure springs sharing a common plane, i.e. those represented by a shared straight line shown in Figure 9, have the same flexing characteristics. This is most easily achieved if all of the springs sharing a common plane are made from the same strip of material, and Figure 10 is a view, in the direction from block E to block D, of a flexure spring strip which extends from block B to block C, providing two of the flexure springs of Figure 9. If one end of a spring bends within the plane of the paper in Figure 10, about an axis normal to the plane of the paper, this is referred to as bending of a spring within its plane. If an end of a spring bends relative to the other end about an axis in the plane of the paper in Figure 10, the spring flexes if the axis is parallel to a short side of the strip shown in Figure 10 and the spring twists if the axis is parallel to a long side of the paper. As can be seen from Figure 10, each flexure spring strip has a rectangular hole at the part which extends between blocks, so that each flexure spring shown in Figure 9 is made of two vertically spaced spring portions . For a given strength of the spring against flexing, the strength against twisting is increased if the spring is in such vertically spaced portions . The dimensions of the strip are shown on Figure 10. The spring strip of Figure 10 was made from half hard beryllium copper approximately 0.004 inches (approx 0.1 mm) thick. Turning to Figure 2, the stylus assembly 7 fits within a recess in the underside of a mounting plate 57, and is held by the screws 29 passing through the stylus mount 19. The mounting plate 57 functions as block A in the x direction traverse stage. The mounting plate 57 is supported for movement in the x direction relative to end pieces 59, 61 which function as the blocks D and E for the x direction traverse stage. These end pieces 59, 61 are rigidly attached to a joining plate 63, which extends above the x direction traverse stage and below the y direction traverse stage. The joining plate 63 holds the end pieces 59, 61 rigid with each other, and is also fast with a centre piece 65 which forms block A of the y direction traverse stage. Suspended blocks 67, 69 form blocks B and C for the y direction traverse stage. As can be seen in Figure 3, mounting blocks 71, 73 fast with the main housing 1 form blocks D and E for the y direction traverse stage. This flexure spring traverse stage construction allows each stage to move the stylus assembly 7 in a respective straight line direction with a low force, while the strong resistance of the flexure springs to bending in the z direction defines an x-y datum plane for the stylus assembly 7. Where possible, holes are formed in the movable parts of the traverse unit, to reduce its weight. In the present embodiments, holes are formed in the central block A and the intermediate blocks B and C in both stages. The pattern of holes in the y stage centre piece 65 is shown in Figure 3. In order to move the stylus assembly 7, each stage of the traverse unit 5 has a magnetic actuator arranged between block D and block A, i.e. between end piece 59 and the mounting plate 57 in the x direction stage and between mounting block 71 and the centre piece 65 in the y direction stage. The magnetic actuator for the x direction stage is shown in Figures 2 and 9. A strong permanent magnet 75 is constructed of two neodymium iron boron discs, one 10 mm in diameter and 5 mm thick and the other 5 mm in diameter and 3 mm thick, arranged coaxialiy, is mounted on block D (the end piece 59). A coil 77 of about 500 turns of 0.13 mm diameter enamel coated copper wire wound on a bobbin is mounted on block A (mounting plate 57) through spacers 79 which help to isolate block A (mounting plate 57) and its associated flexure spring G from heat generated in the coil 77. The coil (including bobbin) is 5 mm thick, has an outer diameter of 14 mm and an inner diameter of 8 mm. The smaller disc of the magnet 75 extends partially into the central hole of the coil 77. By varying the magnitude and direction of current through the coil 77, the coil 77 can be attracted towards or repelled away from the magnet 75 with a controlled force, causing the block A (mounting plate 57) to move until the force provided flexure of the flexure springs F, G balances the force between the coil 77 and the magnet 75. This provides an effective actuator for driving the stage, and is substantially free from vibration. The magnet 75 and the coil 77 are mounted along the centre line of the traverse stage, so that the force applied to the block A (mounting plate 57) is along the line of intended movement and does not apply any twisting force to block A (mounting plate 57). In the prototype of this embodiment, the coil 77 had a resistance of about 28 ohms, and the actuator provided about 280 grams-force per amp of current in the coil. An oscillating drive signal provided an actuator force of 18 grams-force rms, causing oscillating movement of about 125 μm in amplitude, for a power dissipation of about 120 mW. A sensor arrangement is provided between blocks A and E (the mounting plate 57 and the end piece 61), for measuring the position of block A (mounting plate 57). Its construction and operation is very similar to the transducer arrangement for the stylus arm 9 provided by the optical shutter fin 15, the LED 37 and the detector panel 39 bearing photodiodes 41, 43. Block A (mounting plate 57) carries a rectangular fin 81 which extends between first and second sensor blocks mounted on block E (end piece 61). The first sensor block 83 carries an LED, which shines towards a detector panel on the second sensor block 85. The detector panel carries two photodiodes and is arranged in the same manner as the detector panel 39 of the stylus transducer. The two photodiodes are spaced from each other in the direction of movement of block A (mounting plate 57), so that the shadow of the edge of the sensor fin 81 intersects one of the photodiodes, which provides the x position signal output. The shadow of the sensor fin 81 does not reach the other photodiode, which provides a feedback control signal for controlling the drive current for the LED. The second photodiode and the LED are connected by a feedback control circuit as shown in Figure 7 and as already discussed with reference to the stylus transducer. As is shown in broken lines in Figure 3, the y direction stage has a similar actuator and sensor arrangement. The sensor for the y direction stage is provided by a fin 87 mounted on mounting block 73 and sensor blocks 89, 91, respectively carrying an LED and a detector panel, mounted on the centre piece 65. The actuator for the y direction stage comprises a magnet 93, identical to the magnet 75 for the x direction stage, mounted on the centre piece 65 and a coil 95, identical with the x direction coil 77, mounted on mounting block 71. It can be seen that the actuator and the sensor arrangement for the y direction stage have been turned round as compared with the way in which they are mounted for the x direction stage. This means that the part which carries the magnet 75 for the x direction stage (the end piece 59) and the part which carries the magnet 93 for the y direction stage (the centre piece 65) are rigidly connected to each other. This avoids any movement between parts of the traverse unit caused by any interaction of magnetic fields between the two permanent magnets 75 , 93 . In use, the traverse unit is arranged to drive the stylus tip 13 backwards and forwards across the surface of the workpiece 3 in a bi-directional raster scan as shown in Figure 11. The prototype stylus assembly 7 described above was found to operate reliably when driven over the surface either forwards or backwards in the x direction, and the use of a bi-directional scan reduces the time taken to scan an area of the surface of the workpiece 3. Accordingly, the x position of the stylus tip varies with time in a triangular wave pattern as shown in Figure 12, whereas the y position of the stylus tip increases in a staircase pattern as shown in Figure 13. The staircase pattern for the y position increments at each peak and each trough of the triangular waveform of the x position. In practice, the corners of the scan pattern of Figure 11 and the waveforms of Figures 12 and 13 are rounded rather than sharp. This avoids giving the stylus assembly a sudden jolt when reversing the direction of the x-scan. In each stage of the traverse unit 5, the output from the position sensor is used to control the current applied to the coil 77, 95 through a feedback control circuit, εo as to hold the stylus assembly 7 precisely at a desired location regardless of the precise strength of the flexure springs and the interaction between the coils and the magnets. The position of the stylus assembly 7 is changed by feeding appropriate drive signals into the respective feedback circuits. This feedback control also stabilises the traverse unit stages against oscillating at their inherent resonant frequencies, which tend to be below 5 kHz, and may be as low as 30 Hz. Figure 14 shows the feedback control circuit for the coil 77 of the drive actuator for the x direction traverse stage, and Figure 15 shows the feedback control circuit for the coil 95 of the drive actuator for the y direction traverse stage. As can be seen, the circuits are almost identical. In each circuit, the input signal from the position sensing photodiode 97, which indicates the position of the respective traverse stage, is amplified in an amplifier circuit 99, and the amplified position signal is provided to a monitor output for other circuitry, as a signal indicating the current position of the respective stage. The position signal is also provided to a summing node 101. An offset signal generating circuit 103 generates a constant DC offset signal which is also provided to the summing node 101. A drive input circuit 105 receives a drive input signal for moving the respective stage, and after filtering the drive input signal passes it to the summing node 101. The feedback control circuit acts to control the current through the actuator coil 77, 95 so as to keep the signal at the summing node 101 at a constant value. Accordingly, if the drive input signal does not change, the circuit will act to keep the position signal from the photodiode 97 at a constant value, and therefore will act to hold the respective traverse stage at a constant position. If the drive input signal changes, the feedback control circuit will change the current through the coil 77, 95 so as to move the respective traverse stage until the position signal from the photodiode 97, amplified by the amplifier circuit 99, has changed by an equal and opposite amount so as to keep the signal level at the summing node 101 constant. Since changing the current through the coil 77, 95 and changing the signal obtained from the photodiode 97 imply changing the position of the respective traverse stage, it can be seen that varying the input drive signal causes the feedback control circuit to move the respective traverse stage. The value of the offset signal provided from the offset signal generating circuit 103 represents a shift in the position of the respective traverse stage for any particular level of the input drive signal, as compared with the position which the traverse stage would adopt if there was no offset signal. The magnitude of the offset signal is selected, relative to the range of input drive signals, so that the range of input drive signals corresponds to a range of positions of the traverse unit which falls in the middle of the total range of positions through which the coil 77, 95 can drive the respective traverse stage. The signal from the summing node 101 is amplified in an amplifier circuit 107 and passed through a phase shift network 109 before being input to a drive amplifier 111 for the coil 77, 95. The details of the construction of the phase shift network 109 are chosen in accordance with the mechanical resonances of the traverse stage. The illustrated phase shift network has corner frequencies at around 130 Hz and 1.4 kHz. At low frequencies of oscillation in the traverse unit, changes in the current through the actuator coil 77, 95 will result in corresponding changes, substantially in-phase, in the position of the respective stage and the output from the position sensing photodiode 97. However, resonance in the spring mounting arrangement means that at higher frequencies of oscillation, the position of the traverse stage can have a substantial phase difference from the drive current through the coil 77, 95. The phase shift network 109 provides an appropriate phase advance so that when the open loop gain through the mechanical circuit of the traverse stage and the feedback electrical circuit of Figure 14 or Figure 15 approaches unity, the phase is kept less than 0° but greater than -180° by a suitable phase margin (preferably at least a margin of 30°) . This ensures that the feedback circuit is stable and does not cause the position of the traverse stage to oscillate when the input drive signal is constant. The coils 77, 95 carry relatively large currents, and it is preferred to make their ground connections to the power supply independently of the rest of the circuitry, through low resistance wiring, to prevent the coil currents from undesirably affecting the level of the ground plane for the circuitry. In Figures 14 and 15, the amplifier circuit 107 is also designed so that it does not connect the signal to ground, to avoid any effect of the amplified x and y drive signals on the ground plane for the circuitry. In use, the metrological instrument is operated under the control of a computerised processing system, such as a personal computer or an intelligent terminal, which both logs the data provided by the instrument and also interacts with the control circuits for the traverse unit 5. The overall data acquisition and control system is shown in Figure 16. The x position "monitor output" signal from the amplifier circuit 99 of Figure 14, the y position "monitor output" signal from the amplifier 99 in Figure 15 and the z position signal (i.e. the stylus tip position signal) output from the amplifier circuit 55 of Figure 8 are input to a three channel analogue-to- digital converter 113. Each signal is sampled at a frequency (e.g. 5 kHz) determined by the speed at which the traverse unit 5 drives the stylus tip 13 across the surface, and by the desired spacing between data points. The digital values are input to the controlling personal computer 115. The analogue-to-digital converter 113 can be implemented as an A/D card (e.g. a Keithley DAS 1402) installed in the personal computer 115. While the stylus tip 13 is being scanned across the surface of the workpiece 3, a fast DMA (direct memory access) transfer mode of output from the A-to-D converter 113 to the personal computer 115 is used to accumulate data in the personal computer 115. As mentioned above, the control circuits of Figures 14 and 15 and the traverse unit 5 do not reverse the x direction of movement of the stylus assembly 7 and increment its y position instantaneously, and accordingly the path of the stylus tip 13 over the surface of the workpiece 3 is curved at the end of each x direction scan line rather than being rectangular as shown in Figure 11. Accordingly, it may be preferred for high precision scanning to discard data for data points near each end of the x scan, although the actual position of the stylus tip 13 for each data point is provided through the x and y position signals sampled by the analogue-to-digital converter 113. In some computer configurations there may not be sufficient memory space allocated by the software for DMA transfers to contain all of the data provided if a 0.5 mm square is sampled with a grid of data points spaced by 1 μm. In such a case, the personal computer 115 can be arranged to perform a routine in which it instructs the control circuits to stop the y direction scan (and optionally also the x direction scan) every few x direction scan lines, and the data accumulated from the A-to-D converter 113 is dumped to another memory store, for example a magnetic disc. The y scan is then restarted. The timing at which the acquisition of data from the analogue-to-digital converter 113 and the y scan are restarted is chosen with reference to the x direction scan timing, to ensure that no y direction positions are omitted and no data points are omitted in the acquisition of data. The personal computer 115 receives signals from the control circuits and provides control signals to them, to enable the synchronisation to be carried out, as is described in more detail below. After the operation of scanning an area of the surface of the workpiece 3 has been completed, the x, y and z direction data accumulated by the personal computer 115 from the A-to-D converter 113 can be processed by any suitable three dimensional data analysis package, such as the Rank Taylor Hobson Digisurf 3D software system. The results of the analysis may be printed using a graphics plotter either as a two dimensional plan view or as a perspective view of the surface shape. Additionally, the values of standard surface texture and roughness parameters may be calculated and output on a printer or a display to provide a report on the quality of the surface of the portion of the workpiece 3 which has been scanned. Any or all of the data may also be stored for future reference, and data from scans of different areas may be used, for example, for comparison purposes or to build up an overall profile of the surface of a workpiece from analysis of sampled areas taken at various positions . A perspective view of the scanned area of the surface, printed using a graphics plotter, is particularly useful to provide a human recipient with an easily comprehensible overall view of the shape of the surface which has been measured. In order to generate the triangle waveform pattern of movement of the stylus tip 13 in the x direction, as shown in Figure 12, a triangular waveform signal is provided to the drive signal input for the x stage control circuit of Figure 14. This signal can be generated by the personal computer 115, or a suitable triangular wave generator circuit can be provided. The drive signal for the y direction stage, input to the drive input circuit 105 of the y direction control circuit of Figure 15, is generated from the x direction signal by the circuit shown in Figure 17, which ensures that the y direction movements are synchronised with the reversals of the x direction scan. In the circuit of Figure 17, the triangular wave x drive signal is input to a first differentiator circuit 117. This differentiates the triangle waveform and therefore outputs a substantially constant high level signal during x scans in one direction and a substantially low level signal during x scans in the reverse direction, and switches rapidly between these two levels when the x scan reverses direction. The output from the first differentiator circuit 117 is input to a second differentiator circuit 119 which is also a rectifying circuit. Simple differentiation of the output of the first differentiator circuit 117 would produce alternating positive-going spikes and negative-going spikes, with a spike being provided each time the x scan reverses direction. However, the arrangement by which the signal is provided to both inputs of the operational amplifier in the second differentiator circuit 119 through respective diodes means that the second differentiator circuit 119 provides all the spikes as positive-going spikes. A pulse generator circuit 121 generates a brief pulse in response to each spike output from the second differentiator circuit 119. The inverting input to the comparator in the pulse generator circuit 121 is connected to receive a signal set to be a few volts above ground, so that the pulse generator circuit 121 responds to the large amplitude spikes output by the second differentiator circuit 119 each time the x scan changes direction, but the pulse generator 121 does not respond to any low amplitude noise at its input. Accordingly, the pulse generator circuit 121 outputs a train of pulses, with one pulse being provided each time the x scan reverses direction. The pulses output by the pulse generator 121 are provided to the personal computer 115, to enable it to monitor the x direction scanning and to enable it to provide control signals synchronised with the x direction scanning. The pulses from the pulse generator 121 are also input to a counter 123. The digital count value output by the counter 123 represents the desired y scan position. At the beginning of an operation to scan an area of the surface of the workpiece 3, the counter 123 is cleared so that its output count value is zero, and the count value is incremented in response to each pulse received from the pulse generator circuit 121. The personal computer controls the y scan through two control signals applied to the counter 123. The first control signal sets the "clear" input to the counter so as either to hold the counter output continuously at zero or to permit other counter outputs to be generated. The second control signal enables or disables the counting operation, but does not clear the count value. The personal computer 115 uses the first control signal to ensure that the counter is cleared before each operation for scanning an area of the surface of the workpiece 3. When it is desired to halt the scanning operation temporarily to enable data received in the personal computer 115 to be dumped to disc, the personal computer 115 uses the second control signal to disable the counter 123 between pulses output by the pulse generator 121. When the current x direction scan is completed, the pulse generator 121 will provide a pulse output but the counter 123 will not increment and therefore the y position of the stylus tip 113 does not change. The personal computer 115 responds to this pulse by stopping the direct memory access process for acquiring data from the analogue-to-digital converter 113, and begins the process for dumping data to disc. When the process for dumping data to disc is completed, the personal computer 115 enables the counter 123 between pulses from the pulse generator 121. When the current x direction scan is completed, the pulse generator 121 will provide a pulse and the counter 123 will be incremented, to provide a new y position. The personal computer 115 will respond to this pulse by restarting the direct memory access process for acquiring data from the analogue-to-digital converter 113. By ensuring that the counter 123 is switched between disabled and enabled at instants between pulses from the pulse generator 121, and stopping and starting the data acquisition process in response to the next successive pulse from the pulse generator 121, the personal computer 115 is able to ensure that there is no uncertainty about the y position count value after the interruption of data acquisition, and it is also able to ensure that it does not acquire data twice for the same y position. In an alternative arrangement, the personal computer 115 re-starts the data acquisition process before the counter 123 is incremented. For example, it may respond to a pulse from the pulse generator 121 by re-starting the data acquisition process and immediately thereafter may re-enable the counter 123. At the time of halting the scan, the data acquisition process may be halted simultaneously with the disabling of the counter 123, part way through an x-scan. In such an arrangement, data is duplicated for some positions of the stylus tip 13, but the duplicated data can be discarded or averaged in subsequent processing. If desired, the personal computer 115 can be programmed to keep track of whether it has received an odd number of pulses or an even number of pulses from the pulse generator 121 while the counter 123 is disabled, so that it can wait to enable the counter 123 until the x scan is progressing in the same direction as it was progressing in when the counter 123 was disabled. The digital count value output by the counter 123 is converted into the- y direction drive signal by a digital-to-analogue converter 125, and the resulting analogue signal is provided as the input drive signal to the control circuit of Figure 15. Returning to Figures 2 and 3, the main housing 1 of the metrological instrument comprises a substantially rigid side wall 127, to which the mounting blocks 71, 73 of the traverse unit 5 are connected. The metrological instrument rests on the workpiece 3 through three feet 129 attached to the side wall 127. Some or all of the feet 129 can be adjustable to allow the instrument to be levelled. The housing 1 is closed by a top plate 131. Below the top plate 131 but above the traverse unit 5, the side wall 127 supports a circuit board 133. A flexible cable 135 carries the electrical connections for the instrument, and these connections are made to the circuit board 133. The circuit board 133 in turn is connected through highly flexible copper wires to the coils, light emitting diodes and photodiodes of the traverse unit 5 and the stylus assembly 7. In the prototype of the instrument referred to above, the whole of the control circuitry of Figures 7, 8, 14, 15 and 17 was provided outside the instrument. However, it is preferred that the amplifier circuits 47, 55, 99 in Figures 7, 8, 14 and 15 for each of the photodiodes is provided on the circuit board 133. This means that the photodiode output signals are amplified, and therefore are stronger signals, before they enter the flexible cable 135 which connects the circuit board 133 to the external circuitry. This enables the flexible cable 135 to be longer than if the signals were not amplified, and therefore allows operation of the system with the instrument of Figures 2 and 3 at a greater distance from the remainder of the circuitry, which is more convenient. The traverse unit 5 is constructed so that a hole in the mounting plate 57 of the x stage and a hole in the centre piece 65 of the y stage are positioned over the stylus tip 13. Holes over the stylus tip 13 are also provided in the joining plate 63, the circuit board 133 and the top plate 131. These holes are all aligned, so that an operator can look down through them from above the instrument and see the stylus tip 13. This assists the operator to ensure that the stylus tip 13 is correctly positioned at the desired location on the workpiece 3. This is particularly useful for positioning the stylus tip 13 on small workpieces which do not extend sideways beyond the walls 127 of the housing 1. After the operator has checked the position of the stylus tip 13, these holes are covered by a cover piece 137 mounted on the top plate 131 before the measurement operation takes place. The holes are covered to prevent ambient light passing down them to the photodiodes 41, 43 of the stylus transducer during operation, as this might interfere with the correct reading of the height of the stylus tip 13. Preferably a magnifying lens is fitted in the hole in the top plate 131 and a light (switched off in operation of the instrument) is provided near the stylus tip 13, to assist the operator to see the stylus tip 13 and the workpiece 3. Figure 18 is a photograph of a display formed on a screen of the PC 115, showing a perspective view of the surface of part of an integrated circuit EPROM chip. This was generated using the continuous axonometric output option in the Digisurf software referred to above, on the basis of data obtained using the prototype of the illustrated embodiment. Figure 18 provides an image of approximately a 200 μm x 200 μm square of the surface, and is generated from about 200 single line profiles. The surface features shown in the image have heights in the range of about 0.2 μm to 1 μm, and widths in the range of about 2 μm to 15 μm. The scanning operation to generate the data used to create Figure 18 took about 20 seconds (with the tip moving at about 2.5 mm per second) . The illustrated embodiment has been provided by way of example, and it will be apparent to those skilled in the art that it can be modified in many ways. Many of its features are logically separable from each other and those skilled in the art will readily be able to see that modifications can be made which take some but not all of the, optional features of the embodiment. For example, the stylus tip transducer can be altered, e.g. by providing a corner-cube or similar reflector and shining a laser beam at it to obtain an interferometric measurement of the stylus tip position. However, care should be taken not to increase the mass of the stylus unduly. A further discussion of stylus dynamics will now be provided, which will assist those skilled in the art in appreciating which factors are important in designing a stylus assembly suitable for use at high traverse speeds. Equation (4) above can be rearranged to give an expression for the velocity of the stylus v, as follows v= ωd (11) 2π As the stylus traverse speed v is increased, the stylus first begins to lose contact with the workpiece surface at the crests of surface features. At these points, sinωt equals -1, and z is at its maximum. From equation (5) it can be seen that the maximum value of z equals Aω 2 , and this provides an expression for ω as follows where max(z) is the maximum value of z. Substituting equation (12) into equation (11) gives an expression for the maximum possible traverse speed v as follows vs _d_ t maxTzT ( 13 ) 2π In equation (13), d and A are features of the surface being examined. The only parameter in equation (13) which is under the control of the stylus designer is the maximum z direction acceleration max(z). The maximum possible acceleration which can be obtained for a stylus tip is the acceleration of the stylus tip if it is unsupported. This acceleration, which is an inherent property of the stylus assembly, will be referred to as For a pivoting stylus, the acceleration a of the stylus tip is the product of the pivot-to-tip length of the stylus 1 and the angular acceleration of the stylus tip about the pivot ώ. It should be noted that in the following discussion, ω refers to the angular velocity of the stylus about its pivot, and has a different meaning from its meaning in the preceding discussion. The static stylus force F at the stylus tip will create a torque T which is the product of the static stylus force F and the pivot-to-tip length of the stylus 1. If the tip of the stylus is allowed to fall unsupported, its angular acceleration ώ under the effect of the torque T depends on the moment of inertia I of the stylus in accordance with the following relationship ώ = -j (14) For small movements of the stylus tip, equation (14) can be rewritten in linear terms as follows FI (15) 1 I which can be rewritten to give an expression for the linear acceleration a as follows a-- FI (16) I In the analysis of equations (1) to (10) it was assumed that the mass of the stylus was concentrated at the stylus tip and in any counterweight. If there is no counter weight and all of the mass of the stylus is concentrated at the tip, the acceleration of the stylus tip due to gravity in the absence of any externally applied bias force is equal to g (acceleration of a free mass due to gravity) . In practice, a stylus will almost inevitably have a uniform distribution of mass along its length, except for counter weights which have sometimes been applied in the prior art, and except for the mass of the pivot pin which can be ignored since the mass is so closely concentrated about the pivot axis that its effect on the moment of inertia and the torque of the stylus are negligible. If a stylus of uniform mass distribution is pivoted at one end and is provided with a tip at the other, and there is no external bias force so that the static stylus force is provided entirely by the weight of the stylus, its properties are as given in equations (17) to (20). PERFORMANCE OF UNIFORM STYLUS I= ml 2 (17) (19) 2 I a=1 . 5g (20) T= mgl (18) Accordingly, it can be seen that with a conventional stylus of uniform cross-section, the maximum possible tip acceleration in the absence of a bias force to increase the static stylus force is 1.5 g. This shows clearly that a stylus which is able to track a surface at a high traverse speed cannot be provided by a conventional stylus of uniform cross-section having a static stylus force no greater than the maximum force which can be applied by the weight of the stylus even if any counter balance portion is removed. The acceleration of the stylus tip can be increased by a non-uniform weight distribution. For example, if a theoretical stylus could be constructed which had no mass at all, and an accelerating weight of mass m was provided 1/20 of the distance from the pivot towards the tip, its properties would be as given in equations (21) to (24) . PERFORMANCE OF MASSLESS STYLUS WITH WEIGHT AT (1/20 1 τ- l 2 (21) 4 ! m 00 T= —mql (22) 20 - ώ =20 9 (23) 1 a=20 9 (24) Although this shows that, in theory, a non-uniform distribution of mass can provide a high acceleration for the stylus tip, in practice the improvement which can be provided by a non-uniform distribution of mass is limited because a stylus arm with zero mass cannot be produced. For example, a stylus arm having a uniform distribution of mass along its length, and total mass m, may be loaded with an accelerating weight of mass 20 m positioned 1/20 of the distance from the pivot to the stylus tip. The properties of this stylus are as given in equations (25) to (28). PERFORMANCE OF UNIFORM STYLUS LOADED WITH MASS 20m at (1/20 1 I= ml 2 - ■ml 23 ml- ' (25) 3 20 60 T=-mgl+mgl = 1-mgl (26) ώ = ° (27) 23 1 a=3.9g (28) It can be seen that even this extreme loading of a conventional uniform stylus arm has increased its acceleration by a factor of only 2.6, whereas the torque (and therefore the static stylus force) has tripled. It can be seen that in practice any acceleration of the stylus tip above about 4 g will require an external bias force to be applied. Returning to equation (16) it can be seen that one rule for the stylus designer is to provide the stylus with a very light construction, provided that the necessary strength and stiffness can be maintained. This will reduce the mass of the stylus and therefore reduce its moment of inertia. It might be thought from equation (16) that the performance of the stylus would be improved by increasing its pivot-to-tip length 1. However, it is almost inevitable that the mass of the stylus will increase proportionally as its length increases, and therefore the moment of inertia I tends to increase with l 3 . Therefore the acceleration a of the stylus is normally improved by shortening the stylus. By way of comparison with the three theoretical stylus constructions discussed above, in which the static stylus force was provided only by the weight of the stylus, an approximate analysis can be performed for the stylus assembly 7 of the illustrated embodiment. In this approximate analysis, the mass of the pivot pin 11 is ignored because it is concentrated above the pivot axis, and it is assumed that the stylus arm 9 has a total mass of 5 mg uniformly distributed (this is greater than the actual mass of the Sonotone V100 stylus), and it is assumed that the pivot-to-tip length is 10 mm. In this stylus assembly, the hairspring 17 biasses the stylus arm 9 to provide a static stylus force at the stylus tip 13 equivalent to 100 mg force. The approximate characteristics of the stylus assembly, calculated on this basis, are given in equations (29) to (32). It should be noted that the units for equations (30) and (31) are not the standard units for torque and angular acceleration, because they take into account the fact that g (acceleration due to gravity) is not a pure number but contains within it the units of acceleration (ms" 2 ).- APPROXIMATE THEORETICAL PERFORMANCE OF ILLUSTRATED STYLUS ASSEMBLY I = -ml 2 = -^x5xl0 ~3 χ(10 ~2 ) 2 gm 2 (29) = -^xlO -7 gm 2 T =F1 =100xl0 ~3 xgxltJ- 2 gm (30) =10 "3 χ gm = 6x10 3 x g rad m ~ = 60g These calculations predict that the stylus tip 13 has a maximum possible acceleration of 60 g. This roughly corresponds with the observed performance of the prototype stylus assembly. This performance can be compared with the acceleration of 3.9 g in equation (28) for a uniform mass stylus loaded with an accelerating weight, and the acceleration of 1.5 g from equation (20) for a uniform stylus with no means for increasing its acceleration. For a stylus arm with uniform mass distribution along its length, the maximum acceleration of the tip is three times the static stylus force divided by the mass. Accordingly, it is preferred that the mass of the stylus arm (ignoring any mass concentrated within about 1/20 of the length of the stylus from the pivot axis) is at most 20 mg (providing fifteen times the acceleration due to gravity for a stylus force of 100 mg force), and more preferably is at most 10 mg. From the above analysis, those skilled in the art will be able to predict the approximate maximum tip acceleration for substantially any proposed stylus design, and they will also see how stylus design features may be selected so as to increase the stylus tip acceleration and therefore improve the high traverse speed performance of the stylus, particularly with reference to equation (16) above. Some modifications to the embodiment described above may be useful in making the apparatus more convenient to use or manufacture, and work on preparing a design for production has shown that the following points may advantageously be considered. The flexure springs F,G may be made of a slightly thinner material, of approximately 0.075 mm thick. This assists in increasing the maximum length of traverse through which the stylus assembly 7 can be driven. It is now proposed that the length of traverse during scanning measurements can be up to 1 mm in both the x and y directions. Figure 19 illustrates a metrological instrument stylus which it is proposed should be used in place of the Sonotone V100 Hi-Fi stylus used in the prototype. In the stylus of Figure 19 the stylus arm 9 is a thin walled aluminium tube, weighing approximately 5 milligrams. It has a flattened end portion on which the stylus tip 13 is mounted. The stylus tip 13 has a conical diamond point with a 5 μm radius in accordance with normal metrology standards. The flattened end part of the stylus arm 9 on which the stylus tip 13 is mounted makes an angle of about 15° with the axis of the main part of the stylus arm 9. The stylus arm is about 10 mm long. The optical shutter fin 15 is a thin aluminium sheet weighing about 4 milligrams, and is about 6.5 mm long. In order to increase the range of movement of the traverse mechanism, the orientation and position of the photodiode detector panel 39 relative to the x and y stage sensor fins 81, 87 is altered from the arrangement shown in Figure 6. In the arrangement shown in Figure 6, which is retained for the optical shutter fin 15 of the stylus, the shadow 45 of the fin moves over the lower (signal) photodiode 43 in the direction towards and away from the upper (reference) photodiode 41, so that the range of possible movements of the shadow 45 which can be measured is approximately equal to the height of the lower photodiode 43. In the alternative arrangement, shown in Figure 20, the detector panel 39 is arranged so that the shadow 45 of the x stage sensor fin 81 or the y stage sensor fin 87 moves over the lower photodiode 43 in the direction along the length of the photodiode. The top of the shadow 45 is arranged to lie between the two photodiodes 41, 43. Accordingly the maximum traverse length which can be measured is now approximately the same as the length of the lower photodiode 43. With this arrangement, it is easy to provide a sensor having a range of at least 1.5 mm. The traverse unit drive circuits of Figures 14 and 15, in combination with the respective x and y stages of the traverse unit, provide closed feedback loops, and there is a possibility that the system may resonate. Normally, feedback resonances can be avoided by careful construction of the electronic circuitry but it may be more convenient to provide mechanical damping in the traverse unit to avoid resonance so that the design of the electronics is less critical. Figure 21 shows a modification to the traverse unit of Figure 2, in which movement of the suspended blocks 67, 69 in the y stage is damped relative to the joining plate 63. As shown in Figure 21 the joining plate 63 extends below each suspended block 67, 69 and damping is provided by a jelly-like silicone damping material 139 between the suspended blocks 67, 69 and the joining plate 63. The silicone damping material 139 is not highly fluid, and does not tend to flow away, but it may creep slowly under the influence of gravity. Accordingly, the parts of the joining plate 63 underneath the suspended blocks 67, 69 are formed with troughs, as shown in section in Figure 21 in order to retain the silicone damping material 139 in the correct position. When the metrological instrument is lifted off the surface being measured, the surface no longer restrains downward movement of the stylus tip 13 under the influence of the hair spring 17, and accordingly the hair spring 17 tends to rotate the stylus arm 9 so that the end of the arm bearing the stylus tip 13 protrudes from the bottom of the instrument to a substantial extent. In order to limit the extent of this movement, and reduce the risk of damage to the stylus assembly 7 by accidental impact to the stylus tip 13 when the instrument is not in use, the stylus assembly 17 can be fitted with a stylus cover 141 as shown in Figures 22 and 23. Figure 22 is a sectional view a part of the stylus assembly 7. The stylus cover 141 is a thin metal sheet fitted to close the underside of the stylus assembly. A hole or notch 143 is formed in the stylus cover 141 at the location of the stylus tip 13, so that the stylus tip can protrude through the stylus cover 141 and contact the surface being measured. When the instrument is removed from the surface being measured, the hair spring 17 rotates the stylus arm 9 so that the stylus tip 13 protrudes further out through the hole or notch 143, until the stylus arm 9 contacts the stylus cover 141 as shown in Figure 22. This restrains further movement of the stylus arm 9. In this way, partial protection is given to the stylus when the instrument is not in use. Figure 23 shows the stylus cover 141 seen from below, with the stylus tip 13 in the hole or notch 143. The stylus arm 9 is not shown in Figure 23 in order to improve clarity. It is proposed that the circuit board 133 shown in Figure 2 should carry the whole of the feedback control circuit of Figure 7 and the amplifier circuit 55 of Figure 8 for the optical detectors for each of the stylus position, the x direction traverse stage and the y direction traverse stage. Additionally, the amplifier circuits 99 from Figures 14 and 15 are provided on the circuit board 133. The remainder of the circuits are provided in a separate unit (not illustrated), which acts as an interface between the instrument and the personal computer 115. This ensures that the signals from the photodiodes are output before they enter the flexible cable 135, while providing only a small proportion of the total circuitry inside the main housing 1 and thereby allowing the size of the main housing 1 to be kept to a minimum. In order to provide greater control over the operation of the traverse unit 5, and provide greater flexibility of the operation of the instrument, it is proposed that a controllable triangle wave generator, for example as shown in Figure 24, should be used to generate the triangular wave x direction drive signal input for the circuit of Figure 15, and the circuit of Figure 17 should be replaced with an arrangement as shown in Figure 25. In Figure 24, a constant value reference voltage, generated by any convenient reference voltage generator circuit, is input to a variable gain amplifier 145. The gain of the variable gain amplifier 145 is controllable by a gain input signal . The output of the variable gain amplifier 145 is provided in parallel to an inverting buffer 147 and a non-inverting buffer 149. A switch 151 selects the output from one of the buffers 147, 149 as the input to an integrator 153. The integrator 143 integrates the voltage input to it, and therefore outputs a steadily changing voltage. The output of the integrator 153 is provided to a comparator 155 which compares it with a threshold value input to the comparator 155. All the circuits are constructed using operational amplifiers, with power supplies of plus or minus 15 volts or 12 volts together with 0 volts. When the input to the comparator 155 varies from 0 volts either positively or negatively by an amount set by the threshold input signal, the comparator 155 controls the switch 151 to change position, thereby changing which of the buffers 147, 149 provides the input to the integrator 153. Accordingly, the output value of the integrator 153 begins to change in the opposite direction. In this way, the output of the integrator 153 is a triangular wave. Each time the comparator 155 detects that the threshold value has been reached, and operates the switch 151, it also outputs a pulse signal. Accordingly, a pulse is output by the comparator 155 at each time the triangle wave changes direction. The pulses output by the comparator 155 replace the pulses output by the pulse generator circuit 121 in Figure 17. In the triangle wave generator circuit of Figure 24, the value of the threshold signal input to the comparator 155 determines the amplitude of the triangular wave signal input to the x direction drive circuit of Figure 14, and therefore the value of the threshold signal determines the traverse length of the traverse unit 7 in the x direction. Additionally, the gain signal input to the variable gain amplifier 145 controls the magnitude of the positive and negative voltages integrated by the integrator 153, and therefore this controls the rate at which the integrator output changes. Accordingly, the gain control input in Figure 24 controls the speed of movement of the stylus assembly 7 in the x direction. When there is no power to the metrological instrument, the traverse unit 5 will tend to adopt a position holding the stylus assembly 7 in the middle of its range of movement in the x and y directions . Because the control circuits are based on operational amplifiers using positive and negative power supplies, this central position corresponds to zero volts input to the x and y feedback control circuits of Figures 14 and 15. In Figure 25 the operation of the x and y stages of the traverse unit 5 is controlled by control logic 157. As shown in Figure 25, the triangle wave signal from the circuit of Figure 24 is not input to the circuit of Figure 14 directly, but is input via a switch 159 which is controlled by the control logic 157. In a similar manner, the y direction drive input signal to the circuit of Figure 15 passes through a switch 161 controlled by the control logic 157. Additionally, at the drive amplifiers 111 at the circuits of Figures 14 and 15 a relay switch is provided which is open when no power is supplied, so as to prevent the drive signals from being applied to the coils 77, 95. These switches close automatically, providing the drive signals to the coils 77, 95, a few seconds after power is supplied. This delay ensures that the outputs from the various circuit components and the control operation of the circuit of Figure 7 has stabilised before the x and y stage drive coils 77, 95 receive drive currents. When the power supply to the metrological instrument is turned on, the control logic 157 holds the switches 159, 161 so as to connect zero volts to the x and y stage feedback control circuits of Figures 14 and 15 in place of the drive signals. When the relay switches close, the input signals to the x and y drive circuits of Figures 14 and 15 are at zero volts through the switches 159, 161 and accordingly the traverse unit 5 is already approximately at the position defined by the drive input signals. This means that when the power supply is turned on, the traverse unit 5 is not moved sharply from its rest position by the initial outputs from the feedback control circuits of Figures 14 and 15. In Figure 25, the counter 123 is a bi-directional counter operating under the control of control logic 157, and receiving the pulses from the comparator 155 of Figure 24 as the clock input. After power is supplied, the control logic 157 automatically resets the counter 123, so that its count is zero, and the counter 123 remains at zero until the personal computer 115 instructs the control logic 157 otherwise. The digital to analog converter 125 converts a digital value of zero to an analog signal of zero volts. Accordingly, the control logic 157 can then move the switch 161 so that the y stage feedback control circuit of Figure 15 receives the drive signal from the digital to analog converter 125 under the control of the counter 123, without causing any sudden movement of the traverse unit 5. The operator can select the size of the area to be scanned and the scan speed through the personal computer 115. When these details have been selected and the system is ready to begin a scan, the personal computer 115 issues a "start-up" command to the control logic 157, which will specify the y direction position at which scanning is to start. The range of the y direction scan is chosen to be centred on the zero position for the counter 123, and the start position is chosen to be a positive count number for the counter 123. The control logic 157 generates the gain and threshold input control signals for the triangle wave generator circuit 24. When it receives the "start-up" command from the personal computer, the control logic 157 holds switch 159 to connect the input of the x direction feedback control circuit to ground and isolate it from the triangle wave signal from the circuit of Figure 24. The control logic 157 then sets a high level for the gain signal and a low value for the threshold signal in Figure 24, so that the pulses from the comparator 155 are generated at a high rate. The counter 123 is controlled to count upwards, and accordingly it counts rapidly until it reaches the value corresponding to the start position selected by the personal computer 115. At this point, the control logic 157 stops the counter 123. This operation has the effect of moving the stylus tip 13 rapidly in the y direction to the correct position for the start of the scan. In order to start the scanning operation, the personal computer 115 sends a "scan" command to the control logic 157, and informs the control logic 157 of the required scan speed and x direction traverse range. The control logic 157 sets the gain value for the triangle wave generator of Figure 24 in accordance with the scan speed and sets the threshold value in accordance with the x direction traverse range, and then operates the x direction switch 159 to connect the triangle wave signal to the drive input of the x stage feedback control circuit of Figure 14. The switch 159 is switched as the value of the triangular wave signal passes through zero volts, so that moving the switch 159 does not cause a sudden change in the x position which would give the stylus assembly 7 a jolt in the x direction. At the same time, the control logic 157 enables the counter 123 and sets it to count down, so as to begin the y direction movement of the scan. In this embodiment, the data acquisition and processing software in the personal computer 115 is sufficiently fast to keep up with the x position, y position and stylus height (z position) data, and the scanning proceeds continuously without being stopped to allow data transfer. It is now proposed to use a Data Translation DT 2812A data acquisition card, set to sample all three channels at 20 kHz. This allows data to be averaged before processing and still provide data at a suitable frequency (e.g. 5 kHz), in order to reduce the effects of electronic noise. The data acquisition card (which includes the 3-channel analog to digital converter 113 of Figure 16) outputs data to a DMA buffer from which it is read by the personal computer 115. The personal computer 115 processes the data as it is received, and because it is able to keep up with the rate at which data is provided from the data acquisition card, the DMA buffer does not overflow. Since the data input and processed by the personal computer 115 includes the y position of the stylus tip 13, the personal computer 115 is able to monitor the progress of the scan, and when the desired end point is reached it sends a signal to the control logic 157 to stop the scan. The control logic 157 then moves the x direction switch 159 to disconnect the x direction feedback control circuit of Figure 14 from the triangle wave signal, again moving the switch as the triangle wave passes through zero volts . With the x direction control circuit isolated from the triangle wave, the control logic 157 once again sets the gain input to the triangle wave generator at a high value and sets a threshold input at a low value so as to provide rapid pulses to the counter 123, and instructs the counter to count down until it reaches zero. In this way, the traverse unit is driven to return the stylus tip 13 to the rest position. As a safety feature, the control logic 157 also monitors the count value of the counter 123, and if this value approaches the minimum possible count value the control logic 157 automatically stops the scan even in the absence of a signal from the personal computer 115. This ensures that if anything goes wrong with the operation in the personal computer 115 so that it fails to stop the scan, the scan is stopped automatically. The scan is stopped before the counter 123 rolls over from its minimum count to its maximum count, since this would cause a sudden change in the output from the digital to analog converter 125, causing the traverse unit 5 to drive the stylus tip 13 rapidly from one end of its y direction range to the other. When the range of the y direction scan does not exceed 0.5 mm, each step of the stylus tip 13 in the y direction is 1 μm. The gain of the D/A converter 125 is arranged to create this movement in the y stage of the traverse unit for each change in the output value of the counter 123. For y direction scans having a range of greater than 0.5 mm, the steps are arranged to be 2 μm. In this case, the control logic 157 controls the counter 123 as if the size of the y direction scan was half of the actual size, and it provides a signal to the D/A converter 125 to double the gain in the output stage of the converter, so that each count value of the counter 125 is converted to twice the voltage provided for the same count value in scans of less than 0.5 mm. The maximum value from the y scan monitor output signal of Figure 15 appears at the end of the scan, and therefore the greater the range of the scan the greater is the maximum value of this signal. This signal is amplified in a preamplifier 163 before being passed to the A/D converter 113 of the data acquisition card. In order to prevent the input of the A/D converter from saturating at large y direction displacements, the control logic 157 outputs a control signal to halve the gain of the preamplifier 163 for scans having a y direction range greater than 0.5 mm. In a similar manner, the x scan monitor output signal of Figure 14 is amplified in a preamplifier 165 before being passed to the A/D converter 113 of the data acquisition card. The control logic 157 outputs a control signal to halve the gain of the preamplifier 165 for scans having an x direction range greater than 0.5 mm. The changes in the x and y displacements represented by the signals are automatically compensated for in the subsequent processing of the data.

Claims: CLAIMS 1. A stylus assembly for a metrological instrument for measuring a surface characteristic by moving a tip of a stylus over the surface, the stylus assembly comprising a stylus arm movable about a pivot axis and carrying the stylus tip, or comprising a stylus movable substantially linearly towards and away from the surface and carrying the stylus tip, arranged to press the stylus tip against the surface to be measured with a predetermined force in the absence of movement of the stylus tip, such that the theoretical acceleration of the stylus tip, or the approximated theoretical acceleration of the stylus tip, is greater than 1.5 g, where g is the acceleration due to gravity of a free mass, and: the theoretical acceleration of the stylus tip in the case of a pivotable stylus arm is the value defined by the magnitude of the predetermined force, multiplied by the square of the length of the stylus arm from the pivot axis to the stylus tip, divided by the moment of inertia of the stylus arm; the theoretical acceleration of the stylus tip in the case of a substantially linearly movable stylus is the value defined by the predetermined force divided by the mass of the stylus; and the approximated theoretical acceleration of the stylus tip (which applies only in the case of a pivotable stylus arm) is the value defined by three times the magnitude of the predetermined force, divided by the mass of the stylus arm (ignoring any mass less than one-tenth of the way from the pivot axis to the tip) . 2. A stylus assembly according to claim 1 in which the said theoretical acceleration or approximated theoretical acceleration is at least 5 g. 3. A stylus assembly according to claim 1 in which the said theoretical acceleration or approximated theoretical acceleration is at least 10 g. 4. A stylus assembly according to claim 1 in which the said theoretical acceleration or approximated theoretical acceleration is at least 20 g. 5. A stylus assembly according to any one of claims 1 to 4 comprising a pivotable stylus arm, and in which the length of the stylus arm from the pivot axis to the stylus tip is not more than 2 cm. 6. A stylus assembly according to any one of claims 1 to 4 comprising a pivotable stylus arm and in which the length of the stylus arm from the pivot axis to the stylus tip is not more than 1 cm. 7. A stylus assembly for a metrological instrument for measuring a surface characteristic by moving a tip of a stylus over the surface, the stylus assembly comprising a stylus arm mounted for rotation about a pivot axis and carrying the stylus tip, the mass of the stylus arm (ignoring any mass less than one-tenth of the way from the pivot axis to the tip) being not more than 25 milligrams. 8. A stylus assembly according to claim 7 in which the length of the stylus arm from the pivot axis to the stylus tip is not more than 2 cm. 9. A stylus assembly according to claim 7 in which the length of the stylus arm from the pivot axis to the stylus tip is not more than 1 cm. 10. A stylus assembly for a metrological instrument for measuring a surface characteristic by moving a tip of a stylus over the surface, the stylus assembly comprising a stylus mounted for substantially linear movement towards and away from the surface and carrying the stylus tip, the mass of the stylus being not more than 25 milligrams. 11. A stylus assembly according to any one of claims 1 to 6 comprising a pivotable stylus arm and in which the mass of the stylus arm (ignoring any mass less than one-tenth of the way from the pivot axis to the tip) is not more than 25 milligrams . 12. A stylus assembly according to any one of claims 1 to 4 comprising a substantially linearly movable stylus and in which the mass of the stylus is not more than 25 milligrams. 13. A stylus assembly according to any one of claims 7 to 12 in which the said mass is not more than 20 milligrams. 14. A stylus assembly according to any one of claims 7 to 12 in which the said mass is not more than 10 milligrams. 15. A stylus assembly according to any one of claims 7 to 12 in which the said mass is not more than 5 milligrams. 16. A stylus assembly according to any one of the preceding claims comprising biassing means to provide a contribution to the force with which the stylus tip presses against the surface to be measured in addition to any contribution from the weight of the stylus. 17. A stylus assembly according to claim 16 in which the biassing means comprises spring means for biassing the stylus tip towards the surface. 18. A stylus assembly according to any one of the preceding claims in which the force with which the stylus tip presses against the surface to be measured, in the absence of any movement of the stylus tip, is no more than 1 gram-force. 19. A stylus assembly according to claim 18 in which the said force is no more than 500 milligrams- force. 20. A stylus assembly according to claim 18 in which the said force is no more than 200 milligrams- force. 21. A stylus assembly according to claim 18 in which the said force is no more than 100 milligrams- force. 22. A metrological instrument for detecting the roughness or texture or small-scale shape of a surface by moving a stylus over the surface, the instrument comprising: a stylus; movement means for moving the stylus in a first direction over the surface and for moving the stylus in a second direction over the surface transverse to the first; and transducer means associated with the stylus to provide an output in response to changes in the level of the surface with respect to the plane defined by the first and second directions, whereby the movement means is able to move the stylus over an area of the surface thereby to detect changes in the level of the surface in the area. 23. An instrument according to claim 22 in which the first and second directions are horizontal and the transducer provides an output in response to changes in the height of the surface. 24. An instrument according to claim 22 or claim 23 in which the movement means comprises a mounting member and a carriage member for carrying the stylus, the mounting member and the carriage member being connected via flexure springs for relative movement by flexing the springs . 25. A metrological instrument for detecting a surface characteristic by moving a stylus over a surface, the instrument comprising a stylus and movement means for moving the stylus over the surface, the movement means comprising a first member, first flexure springs extending away from the first member in opposing directions to respective intermediate members, and second flexure springs extending in opposing directions from the respective intermediate members to a second member, whereby the second member is movable substantially in a straight line towards and away from the first member by flexing of the flexure springs. 26. An instrument according to claim 25 in which the said opposing directions and the direction of the straight line of movement by the second member are all substan ially horizontal. 27. A metrological instrument for detecting a surface characteristic by moving a stylus over a surface, the instrument comprising: a stylus; movement means for moving the stylus substantially horizontally over the surface; and transducer means associated with the stylus to provide an output in response to changes in the height of the surface, the movement means comprising a first member and a second member movable horizontally with respect to the first member and supporting the stylus, the first member being connected to the second member and supporting the second member through a substantially planar flexure spring arranged in a vertical plane and extending substantially horizontally between the first and second members, whereby flexure of the spring permits horizontal movement of the second member and the resistance of the spring to bending within its plane supports the second member against gravity. 28. An instrument according to claim 27 in which the movement means further comprises a third member which carries the stylus, the stylus and the third member being supported by the second member via a second substantially planar flexure spring arranged in vertical plane substantially parallel with the plane of the first- mentioned flexure spring and extending substantially horizontally between the second and third members, whereby flexure of the second flexure spring permits horizontal movement of the third member relative to the second member and resistance of the second flexure spring to bending within its plane supports the third member against gravity. 29. An instrument according to claim 28 in which the movement means further comprises a fourth member connected to the first and third members via respective further flexure springs arranged in respective vertical planes and extending substantially horizontally between the members. 30. An instrument according to claim 29 in which the second member is arranged on one side of the line between the first and third members and the fourth member is arranged opposite the second member on the other side of the line. 31. An instrument according to any one of claims 25 to 30 in which each said flexure spring is accompanied by a further flexure spring spaced horizontally therefrom and extending between the same members. 32. An instrument according to any one of claims 25 to 31 in which each said flexure spring is provided by a plurality of vertically spaced spring portions. 33. An instrument according to any one of claims 25 to 32 in which the movement means comprises drive means for driving the stylus over the surface by varying a magnetic force between parts of the movement means . 34. A metrological instrument for detecting a surface characteristic by moving a stylus over a surface, the instrument comprising a stylus and movement means for moving the stylus over the surface, the movement means comprising a mounting member and a movable carriage member which carries the stylus, the members being connected via one or more flexure springs for relative movement between the members by flexing of the flexure springs, and the movement means further comprising drive means for driving the carriage member relative to the mounting member, sensor means for detecting the position of the carriage member, and feedback control means for controlling the drive means in response to an output from the sensor means. 35. An instrument according to claim 34 in which the drive means drives the carriage member by applying a variable magnetic force between parts of the movement means .

Inventors: MORRISON EUAN, MORRISON, EUAN
Applicants: MORRISON EUAN, RANK TAYLOR HOBSON LTD, MORRISON, EUAN, RANK TAYLOR HOBSON LIMITED
Application year: 1995
Main classification: G01B7
IPC codes: G01B5, G01B7, G01B21