WO2000006973A1

WO2000006973A1 - Angle encoder

Info

Publication number: WO2000006973A1
Application number: PCT/AU1999/000590
Authority: WO
Inventors: Karl Yarnos Eisenhauer; John Baxter
Original assignee: Bishop Innovation Pty. Limited
Priority date: 1998-07-24
Filing date: 1999-07-21
Publication date: 2000-02-10
Also published as: CA2338637A1; AUPP482598A0; JP2002521684A; KR100571346B1; EP1108198A4; KR20010074741A; BR9912682A; MXPA01000833A; EP1108198A1; CN1175249C; CN1311852A

Abstract

An angular position sensor comprising a body (1) rotatable about an axis of rotation (8) fixed with respect to a surrounding housing (5). The body having a grating element (2) comprising a surface of revolution about the axis of rotation. The surface comprising a pseudo-random distribution of regions of high (21) and low (22) EMR reflectivity arranged in the form of endless succession of individual binary bar codes. The sensor having an EMR source (10) and an array of EMR sensitive detectors (9) fixed with respect to the housing. The source irradiating the surface and the array receiving incident reflected EMR. A pattern produced by incident EMR on the array resulting from the alternate regions of low and high reflectivity on the surface. The pattern processed by a processor (11) to derive the absolute angular position of the regions with respect to the housing, providing a measure of the absolute angular position of the rotatable body with respect to the housing.

Description

ANGLE ENCODER

Field of Invention

This invention relates to angular position sensors, particularly the sensing of the absolute rotational angle of a rotatable body without requiring counting from a reference mark.

Background

Conventionally, angular position sensors have been used for sensing the rotational angle of a rotatable body. These conventionally consists of a detector unit and a graduated scale of material with contrasting bars formed of alternatively transparent and opaque or reflecting bars, the displacement of which is detected by the detector unit, comprising photoemitting, photodetecting and optical means.

The scale is illuminated by the photoemitting means, being a source of electro-magnetic radiation (EMR), typically UV, visible or IR light, that generates patterns on one or more arrays of photodetectors sensitive to the EMR. Such arrays include CCD devices, VLSI vision chips, one and two dimensional photodetector arrays and lateral effect photodiodes (commonly referred to as PSD's or position sensitive devices). The output of the one or more arrays is processed to produce a measure of the angular position of the rotatable body. The scale can be arranged axially or radially about the axis of rotation of the body, and is of such a nature that allows a continuous output of the arrays regardless of the angular position of the body, as the limited array dimensions may not allow the complete circumference or radial face to be viewed by the arrays at any instant in time.

Such sensors commonly provide a signal based on the incremental angular position of the scale, and absolute angular position is determined by counting from a known reference position. The accuracy of incremental sensors is often substantially improved by the use of well known techniques such as quadrature interpolation. Such quadrature methods require a non-varying bar angular spacing. Alternatively, the sensor may provide a signal based on absolute position by the use of bar codes applied to the scale. These bar codes generally do not have constant angular bar spacing as each set of bar codes are unique for each angular position to be sensed, and such absolute position sensors generally do not provide the position measurement accuracy provided by incremental sensors as they cannot use quadrature interpolation techniques.

However, if an absolute position sensor is required having high accuracy, two scales are required. The first measures coarse absolute position by interrogation of a bar code, and the second provides a fine relative position by quadrature interpolation of a regular bar pattern.

The prior art which provides a high accuracy absolute position measurement and which is most closely related to that of the present invention is described in US Patent 5,235,181 (Durana et. al.) This describes a sensor composed of 2 scales, a pseudorandom bar code scale for coarse absolute position and a regularly spaced scale for fine position.

The position sensor described in US Patent 5,235,181 has several inherent drawbacks. The use of two scales necessitates the use of multiple photodetector arrays which is of increased cost compared to a single array. Also, the scales and the arrays need to be positioned relative to each other very accurately which also increases cost and limits the maximum accuracy of the sensor. In addition, inevitable changes in mechanical deflection and assembly clearances in service cause uncertainty of the relative position of the two arrays which further limits the maximum accuracy possible.

The essence of the present invention resides in the provision of both coarse resolution absolute position detection and fine resolution incremental position sensing with a single scale which provides all the necessary information. Preferably this is achieved by the use of a bar code which has a constant bar pitch and a varying bar width or, alternatively, special forms of bar codes with varying bar pitch. Thus, the bar code provides the binary information necessary for absolute position sensing and also provides a regular bar pattern enabling fine resolution interpolation of position. In addition, the sensor preferably relies on reflective principles, where the photoemitting means and photodetecting means are located on the same side of the rotating body, and the scale comprises regions of high and low reflectivity.

There are several advantages of such a design compared to that described in US Patent 5,235,181. Firstly, as only a single scale is used only one photodetector array is necessary, reducing cost. Secondly, as both scales are combined, inaccuracy due to relative scale misalignment is eliminated providing better measurement accuracy. Thirdly, the combination of the two scales makes the sensor less sensitive to mechanical distortion, tolerances or bearing clearances, as the variation in the relative position of two scales and arrays described in the prior art is eliminated. Fourthly, the use of a reflective scale allows simpler and more compact construction as it allows the photoemitting and photodetecting means to be packaged in the same assembly with further savings in space and cost in the sensor. Fifthly, another advantage with the use of reflective scales compared to transmissive scales is that the EMR is reflected from the surface of the scale and is not affected by edge scattering as is the case with apertures, or other problems from internal reflection, diffraction or degradation over time as is the case with transparent materials where the EMR has to travel through the medium in the transmissive regions. Such effects would otherwise limit the maximum resolution of the sensor.Finally, the combined scale is less complex than two separate scales hence can be produced quicker and at lower cost, especially if applied by direct writing techniques such as laser marking.

Summary of Invention

The present invention consists in an angular position sensor comprising at least one body at least partially surrounded by a housing, the body rotatable about an axis of rotation fixed with respect to the housing, the body having a grating element attached thereto or integral therewith, the grating element comprising a surface of revolution about the axis of rotation, the surface comprising a pseudo-random distribution of regions of high and low EMR reflectivity arranged in the form of an endless succession of individual binary bar codes, the sensor also comprising at least one EMR source and at least one array of EMR sensitive detectors, the source irradiating the surface and the array receiving incident EMR reflected from the surface, the source and the array fixed with respect to the housing, a pattern thereby produced by incident EMR on the array resulting from the alternating regions of low and high reflectivity on the surface of the grating element, the pattern on the array processed by a processor to derive the absolute angular position of the regions with respect to the housing, and hence provide a measure of the absolute angular position of the rotatable body with respect to the housing.

In one embodiment the at least one body comprises two rotatable bodies each of which has a respective grating element, the two bodies connected by a member of predetermined torsional stiffness, and at the at least one array of EMR sensitive detectors receiving the incident EMR reflected from the surfaces of the grating elements, the pattern or patterns processed to derive the absolute angular position of the regions on the surfaces of the grating elements with respect to the housing, and the difference between the angular positions further processed to derive the relative angular displacement of the grating elements, and hence provide a measure of the torque transmitted by the member. The at least one array of EMR sensitive detectors may be two arrays of EMR sensitive detectors, each of which is associated with a respective grating element. The at least one EMR source may be two EMR sources, each of which is associated with a respective grating element.

It is preferred that the surface of revolution may at least be partially cylindrical or partially conical.

It is preferred that either the regions of high EMR reflectivity or the regions of low EMR reflectivity comprise bars having a constant centreline pitch and varying thickness. It is preferred that the varying thickness bars comprise bars of at least two discrete thicknesses. It is preferred that the bars have only two thicknesses ie. wide bars and narrow bars.

Alternatively, it is preferred that either the regions of high EMR reflectivity or the regions of low EMR reflectivity comprise bars with varying centreline pitch and the pitches are an integer multiple of a fundamental pitch. It is preferred that the bars of varying centreline pitch are of constant thickness. Alternatively the bars may be of varying thickness. It is preferred that the varying thickness bars comprise bars of at least two discrete thicknesses. It is preferred that the bars have only two thicknesses ie. wide bars and narrow bars.

In some embodiments the surface of revolution has a plurality of castellations protruding radially therefrom. It is preferred that the regions of high reflectivity correspond to areas of maximum protrusion of the castellations, and the regions of low reflectivity are angularly aligned with the areas of lesser protrusion between the castellations. It is further preferred that the areas of maximum protrusion are smoothly machined, moulded or sintered, or surface treated with paint or material deposition to impart high reflectivity, and the discontinuous gap areas or areas of lesser protrusion are machined, moulded or sintered, or surface treated with paint or material deposition to impart low reflectivity.

It is preferred that the regions of high reflectivity are metallised, shiny or light coloured, and the regions of low reflectivity are substantially transparent, matt, roughened or dark coloured, thus forming a reflective scale.

The at least one array of EMR detectors is positioned radially inside or outside of the surface.

It is preferred that the at least one array of EMR detectors comprises a one dimensional or a two dimensional array, a CCD, a VLSI vision chip or a lateral effect photodiode.

It is preferred that the pattern is also processed by the processor to derive the angular velocity of the rotatable body with respect to the housing. Brief Description of the Drawings

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

Fig. 1 a is a diagrammatic sectional view of an angular position sensor according to a first embodiment of the present invention showing the rotatable body consisting of regions of high and low reflectivity provided by radially protruding castellations, and a radially disposed photodetector array,

Fig. 1 b is a larger scale view of a portion of the grating element shown in Fig. 1a,

Fig. 2a is a diagrammatic sectional view of an angular position sensor similar to that shown in Fig. 1 a employing axially protruding castellations and an axially disposed photodetector array,

Fig. 2b is a larger scale view of a portion of the grating element shown in Fig. 2a,

Fig. 3a is a diagrammatic sectional view of an angular position sensor according to a second embodiment of the present invention showing a rotatable body consisting of a cylindrical scale surface with regions of high and low reflectivity and a radially disposed photodetector array,

Fig. 3b is a larger scale view of a portion of the grating element shown in Fig. 3a,

Fig. 4a is a diagrammatic sectional view of an angular position sensor similar to that shown in Fig. 3a employing a disc shaped scale surface with an axially disposed photodetector array,

Fig. 4b is a larger scale view of a portion of the grating element shown in Fig. 4a,

Fig. 5 is a diagram illustrating the pattern incident on the photodetector array and a technique employed providing both coarse resolution absolute angle measurement and fine resolution interpolated incremental measurement, and

Fig. 6 is a diagrammatic sectional view of an angular position sensor according to a third embodiment of the present invention where the sensor comprises two rotatable bodies connected by a torsional member, and the sensor providing for measurement of the torque transmitted by the torsional member.

Mode of Carrying Out Invention

Figs. 1a & 1b show an angular position sensor according to a first embodiment of the present invention. Rotatable body 1 comprises grating element 2 with a discontinuous outer cylindrical surface 14 composed of alternating regions of high and low EMR reflectivity, arranged in the form of a succession of individual binary bar codes. Grating element 2 comprises radially protruding castellations 3 interposed between radially extending cavities 4. The regions of high reflectivity on cylindrical surface 14 correspond to areas of maximum radius 12 of castellations 3 with respect to axis of rotation 8 of rotatable body 1 , and may be smoothly machined, moulded or sintered, or surface treated with paint or material deposition to impart the required high reflectivity. The regions of low reflectivity on cylindrical surface 14 correspond to discontinuous gap areas 13, and are substantially non-reflective due to the presence of cavities 4, comprising areas of minimum radius 15 which are disposed at lesser radius than aforementioned areas 12, and are ideally machined, moulded or sintered, or surface treated with paint or material deposition to impart low reflectivity. Rotatable body 1 is enclosed in housing 5 and supported in bearings 6 and 7, and is able to rotate about axis of rotation 8. EMR source 10 and EMR sensitive photodetector array 9 are fixed in housing 5 and arranged such that EMR source 10 illuminates discontinuous surface 14, which reflects EMR to the substantially radially disposed array 9. Thus a pattern is produced on array 9, which is processed by processor 11 to provide a measure of the absolute angular position of rotatable body 1 with respect to housing 5. It should be noted that the words "reflection", "reflected" and "reflectivity" in this specification are relate to specular and/or diffused reflection.

Figs. 2a & 2b show an alternative angular position sensor according to the first embodiment of the present invention. Rotatable body 1 comprises grating element 2 with a discontinuous radially oriented flat disc surface 14 composed of alternating regions of high and low EMR reflection, arranged in the form of a succession of individual binary bar codes. Grating element 2 comprises axially protruding castellations 3 interposed between axially extending cavities 4. The regions of high reflectivity correspond to areas of maximum axial protrusion 12 of castellations 3 with respect to axis of rotation 8 of rotatable body 1 , and may be smoothly machined, moulded or sintered, or surface treated with paint or material deposition to impart the required high reflectivity. The regions of low reflectivity correspond to discontinuous gap areas 13, and are substantially non-reflective due to the presence of cavities 4. Rotatable body 1 is enclosed in housing 5 and supported in bearings 6 and 7, and is able to rotate about axis of rotation 8. EMR source 10 and EMR sensitive photodetector array 9 are fixed in housing 5 and arranged such that EMR source 10 illuminates discontinuous surface 14, which re-radiates EMR to the substantially axially disposed array 9. Thus a pattern is produced on array 9, which is processed by processor 11 to provide a measure of the absolute angular position of rotatable body 1 with respect to housing 5.

Figs. 3a & 3b show an angular position sensor according to a second embodiment of the present invention. Grating element 2 of rotatable body 1 comprises a continuous cylindrical surface in the form of graduated scale 20 composed of alternating regions of high and low EMR reflectivity, arranged in the form of a succession of individual binary bar codes. A metallised coating, or other shiny or light coloured material or surface treatment, provides substantially axially aligned regions of high reflectivity 21. A substantially transparent, roughened or dark coloured material or surface treatment provides the interspaced regions of low reflectivity 22. Rotatable body 1 is enclosed in housing 5 and supported in bearings 6 and 7, and is able to rotate about axis of rotation 8. EMR source 10 and EMR sensitive photodetector array 9 are fixed in housing 5 and arranged such that EMR source 10 illuminates the regions of high and low reflectivity 21 and 22 which re-radiates EMR to the substantially radially disposed array 9. Thus a pattern is produced on array 9, which is processed by processor 11 to provide a measure of the absolute angular position of rotatable body 1 with respect to housing 5. Figs. 4a & 4b show an alternative angular position sensor according to a second embodiment of the present invention. Grating element 2 of rotatable body 1 comprises a continuous radially oriented flat disc surface in the form of graduated scale 20 composed of alternating regions of high and low EMR reflectivity, arranged in the form of a succession of individual binary bar codes. A metallised coating, or other shiny or light coloured material or surface treatment, provides substantially radially aligned regions of high reflectivity 21. A substantially transparent, roughened or dark coloured material or surface treatment provides the interspaced regions of low reflectivity 22. Rotatable body

1 is enclosed in housing 5 and supported in bearings 6 and 7, and is able to rotate about axis of rotation 8. EMR source 10 and EMR sensitive photodetector array 9 are fixed in housing 5 and arranged such that EMR source 10 illuminates the regions of high and low reflectivity 21 and 22 which re-radiates EMR to the substantially axially disposed array 9.

Thus a pattern is produced on array 9, which is processed by processor 11 to provide a measure of the absolute angular position of rotatable body 1 with respect to housing 5.

In the case of both first or second embodiments, it will be appreciated that processor 11 can readily be programmed or hardwired to calculate the rate of change of absolute angular position of rotatable body 1 as a function of time, and therefore also provide a measure of absolute angular velocity of rotatable body 1 with respect to housing 5.

Fig. 5 shows an example of a pattern produced by incident EMR on array 9 according to the first or second embodiment of the present invention (also according to a third embodiment described below). The individual bits 30a-e represent dark areas of the pattern on array 9 caused by reduced levels of reflection from the regions of low reflectivity 13 (first embodiment) or 22 (second embodiment). Array 9 is a one- dimensional "linear" array, for example a Texas Instruments TSL1410 Black & White Linear Array chip with 128 pixels and an active window length of approximately 8 mm. This array is adapted to provide both an absolute angular position measurement and a fine resolution incremental angular position measurement. The absolute angular position measurement is performed by the reading of at least one complete word formed by a predetermined number of successive bits, in this case word 31 comprising five bits, so as to permit the identification of the word of the pseudo-random sequence representing the absolute angular position measurement. The disposition and use of such pseudorandom sequences are generally well known in the art of image analysis, and are described in US Patent 5,576,535 in reference to the measuring absolute linear displacement. Another example of one combination of such sequences is described as an Ouroborean ring in "Game, Set and Math" by Ian Stewart, Penguin Books, 1989.

The disposition of the regions of high and low EMR reflectivity employed in this embodiment of the present invention differs, however, since the pattern produced on array 9 comprises a sequence of bits of a constant centreline pitch "a" (ie. the spacing distance between the centreline of adjacent bars) with varying width "p" and "q". Fig. 5 shows five bit word 31 , with binary number "1 " represented by bits 30a and 30d having width "p" and binary number "0" represented by bits 30b, 30c and 30e having width "q". The complete word 31 is thus 10010 (ie. 18 in base 10), which is processed by processor 11 to provide a unique absolute angular position of rotatable body 1. Importantly, the disposition of regions of high and low EMR reflectivity, which results in a pattern on array 9 with constant pitch, allows the same pattern, and hence array, to be used for the measurement of fine resolution incremental angular position. One such interpolation technique is also shown in Fig. 5. The EMR intensity pattern on array 9 is denoted by P(x) where x is the horizontal scale representing angular displacement and P is a function of x.

If the EMR intensity pattern is sinusoidal, then:

P(x) = sin[2n(x-d)/a]

Where a = pitch of the pattern, and d = displacement of the pattern

The pattern P(x) is sampled by the individual pixels of array 9. Let Pj denote the i-th sample. Thus the "pattern vector" of n samples can be denoted as P = [Pi, P₂, P₃,...P_n].

Two weighting functions are now defined, being the sine and cosine weighting vectors: K_IJ = sin(2ni/a) for i = 1....n

K₂i = cos(2ni/a) for i = 1....n

Hence phase angle α is given by:

α=arctan [(ΣPiKu) / (ΣPjKa)] for i = 1....n

The resulting phase angle α is a measure of the incremental displacement of the pattern relative to the sine and cosine weighting vectors and provides a fine resolution angular position measurement that is, on a statistical basis, many times finer than the width of one bit of the pattern. The coarse resolution absolute angular position measurement and fine resolution incremental angular position measurement is combined to provide an absolute angular position detector with fine resolution requiring only one detector array and with low susceptibility to mechanical deflection and misalignment.

The use of other styles of bar codes with constant pitch can be similarly processed according to this "convolution algorithm", for example where the binary bit information is coded as a difference in length of the bar rather than width. Also, the binary bit information can be encoded as a difference in the level of attenuation of the re-irradiated EMR such as by the use of a greyscale code. Moreover, although this embodiment demonstrates the convolution algorithm based on a bar code with constant bar pitch and variable bar width, it should be appreciated that the algorithm will also function equally successfully for a variable bar pitch situation, providing that that the bar pitching selected is an integer multiple of a "fundamental pitch". For example, referring to the terminology used in Fig. 5, the centreline pitching separating bits 30a-e may be arranged as respectively "a", "3a", "2a", and "a" (with a fundamental pitch of "a") rather than the constant pitch of "a" as shown in Fig. 5. Indeed any integer multiple of "a" may be used for the centreline pitch between successive bits. In the situation where such a varying pitch format of bar code is selected, the bar code encryption can be achieved via the varying pitch spacing rather than via bar width (as shown by the bit pattern in Fig. 5), thus it is feasible in this situation to use a constant bar width and still achieve satisfactory bar code encryption for coarse resolution absolute angular position measurement. It should also be noted that the succession of bar codes could have reverse reflectivity compared to the embodiments described, that is high reflectivity regions imposed over a low reflectivity background.

Also in the present specification "high reflectivity" and "low reflectivity" is broadly defined in reference to the particular EMR source selected. For example, if a red light EMR source was used, the regions of high and low reflectivity of the surfaces of the reflective gratings may consist of regions which are painted (or otherwise coloured by some means) with a red and blue surface coating respectively.

Fig. 6 shows an angular position sensor according to a third embodiment of the present invention. The angular position sensor comprises two rotatable bodies 1a & 1 b which are connected by torsion bar 23 of predetermined torsional stiffness. Grating elements 2a & 2b are respectively attached to or integral with rotatable bodies 1a & 1 b and arrays 9a & 9b respectively receive incident EMR re-radiated from surfaces 20a & 20b. In certain other embodiments (not shown) arrays 9a & 9b may be combined as a single array. This single array will therefore necessarily be a 2D array, and will receive EMR reflected from both surfaces 20a & 20b. Similarly, in certain other embodiments (not shown), EMR sources 10a & 10b may be combined as a single EMR source.

Surfaces 20a & 20b are shown as similar to surface 20 in Figs. 3a & 3b, that is these surfaces are cylindrical and each comprise a graduated scale composed of alternating regions of high and low EMR reflectivity, and arranged in the form of an endless succession of individual binary bar codes. It will be recognised that other types of "surfaces of revolution" could alternatively be employed in place of these continuous cylindrical surfaces 20a & 20b, for example continuous flat disk surfaces (similar to surface 20 in Figs. 4a & 4b), discontinuous cylindrical surfaces (similar to surface 14 in Figs. 1a & 1 b), or discontinuous flat disk surfaces (similar to surface 14 in Figs. 2a & 2b). A "surface of revolution" of a body in this specification is defined as a surface which is equally disposed about the axis of rotation about which the body rotates. The patterns on arrays 9a & 9b, or the pattern on the earlier mentioned single array (not shown), are processed in processor 11 to derive the absolute angular position of the regions of high and low reflectivity (or transmissibility in other embodiments) on surfaces 20a & 20b of each grating element 2a & 2b respectively with respect to housing 5. The difference between these absolute angular positions is further processed by processor 11 to derive the relative angular displacement of grating elements 2a & 2b, and hence provide a measure of the torque transmitted by torsion bar 23.

Thus this third embodiment of the angular position sensor not only provides a measure of the absolute angular position of each of the two rotatable bodies 1a & 1 b (and potentially their angular velocity as described earlier) with respect to housing 5, but also provides a measure of the torque applied between rotatable bodies 1a & 1 b (which is reacted by torsion bar 23).

It will be appreciated by those skilled in the art that numerous variations and modifications may be made to the invention without departing from the spirit and scope of the invention.

Claims

CLAIMS:

1. An angular position sensor comprising at least one body at least partially surrounded by a housing, the body rotatable about an axis of rotation fixed with respect to the housing, the body having a grating element attached thereto or integral therewith, the grating element comprising a surface of revolution about the axis of rotation, the surface comprising a pseudo-random distribution of regions of high and low EMR reflectivity arranged in the form of an endless succession of individual binary bar codes, the sensor also comprising at least one EMR source and at least one array of EMR sensitive detectors, the source irradiating the surface and the array receiving incident EMR reflected from the surface, the source and the array fixed with respect to the housing, a pattern thereby produced by incident EMR on the array resulting from the alternating regions of low and high reflectivity on the surface of the grating element, the pattern on the array processed by a processor to derive the absolute angular position of the regions with respect to the housing, and hence provide a measure of the absolute angular position of the rotatable body with respect to the housing.

2. An angular position sensor as claimed in claim 1 , wherein the at least one body comprises two rotatable bodies each of which has a respective grating element, the two bodies connected by a member of predetermined torsional stiffness, and at the at least one array of EMR sensitive detectors receiving the incident EMR reflected from the surfaces of the grating elements, the pattern or patterns processed to derive the absolute angular position of the regions on the surfaces of the grating elements with respect to the housing, and the difference between the angular positions further processed to derive the relative angular displacement of the grating elements, and hence provide a measure of the torque transmitted by the member.

3. An angular position sensor as claimed in claim 2, wherein the at least one array of EMR sensitive detectors is two arrays of EMR sensitive detectors, each of which is associated with a respective grating element.

4. An angular position sensor as claimed in claim 2, wherein the at least one EMR source is two EMR sources, each of which is associated with a respective grating element.

5. An angular position sensor as claimed in claim 1 , wherein the surface of revolution is at least partially cylindrical.

6. An angular position sensor as claimed in claim 1 , wherein the surface of revolution is at least partially conical.

7. An angular position sensor as claimed in claim 1 , wherein either the regions of high EMR reflectivity or the regions of low EMR reflectivity comprise bars having a constant centreline pitch and varying thickness.

8. An angular position sensor as claimed in claim 7, wherein the varying thickness bars comprise bars of at least two discrete thicknesses.

9. An angular position sensor as claimed in claim 8, wherein the bars have only two thicknesses.

10. An angular position sensor as claimed in claim 1 , wherein either the regions of high EMR reflectivity or the regions of low EMR reflectivity comprise bars with varying centreline pitch and the pitches are an integer multiple of a fundamental pitch.

11. An angular position sensor as claimed in claim 10, wherein the bars of varying centreline pitch are of constant thickness.

12. An angular position sensor as claimed in claim 10, wherein the bars are of varying thickness.

13. An angular position sensor as claimed in claim 12, wherein the varying thickness bars comprise bars of at least two discrete thicknesses.

14. An angular position sensor as claimed in claim 13, wherein the bars have only two thicknesses.

15. An angular position sensor as claimed in claim 1 , wherein the surface of revolution has a plurality of castellations protruding radially therefrom.

16. An angular position sensor as claimed in claim 15, wherein the regions of high reflectivity correspond to areas of maximum protrusion of the castellations, and the regions of low reflectivity are angularly aligned with the areas of lesser protrusion between the castellations.

17. An angular position sensor as claimed in claim 16, wherein the areas of maximum protrusion are smoothly machined, moulded or sintered, or surface treated with paint or material deposition to impart high reflectivity, and the discontinuous gap areas or areas of lesser protrusion are machined, moulded or sintered, or surface treated with paint or material deposition to impart low reflectivity.

18. An angular position sensor as claimed in claim 1 , wherein the regions of high reflectivity are metallised, shiny or light coloured, and the regions of low reflectivity are substantially transparent, matt, roughened or dark coloured, thus forming a reflective scale.

19. An angular position sensor as claimed in claim 1 , wherein the at least one array of EMR detectors is positioned radially inside or outside of the surface.

20. An angular position sensor as claimed in claim 1 , wherein the at least one array of EMR detectors comprises a one dimensional or a two dimensional array, a CCD, a VLSI vision chip or a lateral effect photodiode.

1. An angular position sensor as claimed in claim 1 , wherein the pattern is also processed by the processor to derive the angular velocity of the rotatable body with respect to the housing.