The present invention relates to a position sensor. It is applicable directly to linear measurement, and can be applied to angular measurement by performing a quasi linear measurement of distance round the circumference of a circle. Some features of it are also applicable to pure angular measuremen . SUMMARY OF THE PRIOR ART

In our earlier European patents EP 0100243A and EP 0184286 we disclosed position sensors in which binary and bar pattern tracks on a scale act on a detector having sensitive elements in a two-dimensional array. Each sensitive element detects the overlap between itself and an indicium of the track (for a bar pattern, each bar of the pattern, whether light or dark, forms an indicium). The signals detected by the sensitive elements of the detector are processed to yield precise data regarding the position of the tracks, and hence the scale, relative to the detector. The scale is preferably the optical image of the pattern of markings on one body, with the detector being mounted on another body, so that the relative positions of the two bodies may be

determined.

Position sensors using the detection of patterned tracks on a scale were known prior to the above European patents, and generally involved reading binary tracks of the scale at a single radial (or linear) position, and determining the position as a binary number represented by the reading across the tracks. With this arrangement, it was possible to determine the position of the scale relative to the detector to a resolution equal to the smallest pitch of the indicia forming the scale. EP 0100243A introduced the idea of interpolation of position to fractions of a pitch of the indicia, by providing one or more tracks having a pitch less or greater than, but not equal to, the pitch of the sensitive elements of the detector. This difference in pitch creates a periodic variation (known in optics as moire fringes) in the overlap of the indicia and the sensitive elements. This results in signals from the sensitive elements which can be regarded as a moire waveform when considered over a track (circular or straight) of sensitive elements. Measurement of the changes in overlap of indicia and sensitive elements over at least part of the two-dimensional array of the detector enabled the changes in outputs from the sensitive elements of the detector to be analysed, i.e. the moire waveform to be analysed, and this analysis

provided interpolation as was discussed in EP 0100243A. In EP 0100243A the coarse position value (i.e. the measurement to give the position to an accuracy corresponding to the pitch of the indicia) was carried out by computer correlation of the signal from the sensitive elements with a stored binary number equivalent to the scale pattern, with the effect that there was measurement at a large number of positions (effectively at all the sensitive elements in a pattern corresponding to the scale pattern). It was realized that if a correlation operation was carried out on all the elements of the detector acted on by the scale pattern, then it was possible to generate a unique value at one position of the scale that was much greater than any of the other values at other positions. Then, if a part of the scale was obscured, that unique value would be reduced, as compared with the values at other positions, but nevertheless would still be sufficiently greater than those other values to be detected easily. To facilitate this correlation operation, EP 0184286A proposed the modification of direct measurement of overlap of scale indicia and detector elements followed by a computer correlation, to provide in association with each detector element a multiplication coefficient (referred to as weighting values in EP 0184286A) so that the correlation operation could be carried out in

analogue form at the detector. The use of a pseudo-random scale, in conjunction with the appropriate multiplication coefficients, enabled the unique value to differ by typically an order of magnitude from the value at any other position. The result then did not depend critically on any one of the detector element signals, since it represented a correlation of them all, and so was free from error due to a defect at the location of one or more elements.

Once the coarse position was determined in this way, the interpolation system of EPO 184286 A could be used. However, EP 0184286A also discussed a way of processing the mathematical operations to determine that interpolation. It was appreciated that the inter¬ polation could be achieved by generating and examining a correlation function, i.e. performing a correlation operation between all the detector element signals acted on by the "interpolation" tracks of the scale, and the corresponding multiplication coefficients. That correlation was then repeated in a series of possible relationships of signals to multiplication coefficients, with the value of the correlation being expressed as a function of the position of the signal pattern. Thus, the generation of the correlation function involves the summation of the overlaps of the sensitive elements and the "interpolation" indicia (as signals modified by a

corresponding multiplication coefficient) and then the repetition of this summation for many possible relative relationships of the pattern of signals with the pattern of multiplication coefficients.

Furthermore, if the pattern of multiplication coefficients represents a sine or a cosine waveform, that generation of a correlation function for many different positions is equivalent to Fourier analysis of the spatial waveform of the sensor signals, i.e. the moire waveform. The frequency of that waveform corresponds to that of the fundamental of the Fourier analysis, with distortions of the scale pattern appearing as harmonics. By concentrating the analysis on the fundamental frequency of the waveform, the effect of some distortions may be eliminated.

EP 0184286A also went on to discuss even more accurate interpolation, by analyzing the crossing points of waveforms thus produced. However, that analysis is not relevant to the present invention and will therefore ■ not be discussed further now. SUMMARY OF THE INVENTION

The use of a pseudo-random scale, and the signal from the sensitive elements correlated with a stored binary number equivalent to the scale pattern (as described in EP 0100243A), or with an appropriate set of multiplication coefficients (as described in EP

0184286A), is an extremely efficient arrangement for locating the coarse position of the scale, always provided that the psuedo-random scale remains wholly or substantially on the detector. This condition is satisfied if the scale and detector are of circular form, as in an angular position sensor, or if they are of linear form but the range of movement is small compared with the length of the pseudo-random scale and detector. However, if the range of movement is large compared with the extent of the scale which is imaged on the detector an alternative technique is required. This could, for example, simply repeat the pseudo-random number string contiguously over the length of the scale, and identify each particular repeat by means of a supplementary code, which could be a set of adjacent binary scales. This approach is illustrated in simple form in EP 0100243A; in the case of a long scale it would still be inconvenient, since it would involve a large number of supplementary tracks alongside the principal scale. Each of these would require to be sensed, with provision made to ensure that dirt particles or other contamination on the scale did not introduce errors, and thereby degrade the very high integrity of the pseudo-random scale correlation.

In a practical encoder design, the question of integrity becomes of considerable importance. Unlike the

theoretical concept of perfect clear and opaque divisions being imaged geometrically accurately on a set of sensing elements have uniform sensitivity and accurate linear response, in a practical encoder the scale may be dirty, with some divisions or groups of divisions completely obscured, the illumination is likely to be non-uniform, an imperfect image will be produced as a result of aberrations in the optical system, the sensitivity, linearity, and zero signal (dark current) of the sensing elements will vary: some may even be totally inoperative, and there will be various forms of electrical "noise" on the signal.

Proposals have been made to divide a long scale into blocks, as in EP 0012799 and EP 0039921, with each block being given a binary identification number, and a marker feature to enable the identification number to be located. The problem with any scheme of this type is that if a part of the detail is lost, perhaps as a result of obscuration or a faulty sensor element, the marker is not found or even a single digit of the identification is misread, a totally inaccurate answer is likely to result. Techniques have also been described, for example in EP 0012799, in which the phase of a moire waveform is determined by examining the position where the alternating output of successive pixels changes phase, or the 50% level of the moire waveform, or the intersection

of the odd and even element signal envelopes. Again, if the feature which is being searched for is obscured, a wong answer is likely to result; in the case of an interpolation, it may not be as serious as an incorrect reading of the coarse position, but there is little point in an interpolation which is unreliable under practical conditions.

Relative to both the above examples, correlation techniques provide means of processing which afford a very high degree of immunity to corruptions of the signals, and can prove valuable when high integrity of reading is required. An extreme example if their use is provided by the feasibility, described in the following pages, of extracting a moire waveform from a pseudo¬ random number pattern.

An effective solution to the problem of high integrity coarse position sensing in long scales is offered by the present invention. It is proposed that the coarse scale should have two different individual patterns, e.g. two different pseudo-random binary numbers, which alternate along the length of the scale, and one of which patterns varies along the scale by a predetermined rule.

Normally, the predetermined rule of variation of the varying pattern (or patterns) comprises a shift in the indicia of that varying pattern, which shift leaves

unchanged the cyclic order of the indicia of the varying pattern (or patterns).

For example at the start of the scale the two numbers can be adjacent, but at each repetition along the scale an additional single digit spacing is introduced at the start of the varying pattern, so that each time the patterns are recognized, the number of digits separating their constant parts indicates which repetition it is, and hence the precise position on the scale. However, merely changing the spacing between the two patterns has the disadvantage that it leaves portions of the scale effectively blank, and therefore is not making the best use of the portion of the scale which is sensed, because the degree of redundant information is reduced. An alternative arrangement is to vary one pattern cyclically, e.g. by varying the starting digit of one of two pseudo-random numbers, regarding it as a string repeating cyclically, so that a given location in the number string changes its position relative to the other number by one digit at each repetition.

In this way, a pair of 256 digit pseudo-random numbers can be repeated 256 times with the starting digit of one of them changing each time, so that the total useful scale length is 256 repetitions of the pair, or 256 x (256 + 256) divisions, i.e. 21^ divisions. The practical significance of this technique is that the

accuracy of the scale reading will be unimpaired even if, due to dirt or damage, a group of the order of 100 consecutive divisions is completely obscured; in conventional scales, by comparison, the obscuration of a single division can result in an error.

. Having established the position of the scale to the nearest division, interpolation to a fraction of a division may be achieved by a variety of methods, one of which is the addition alongside the pseudo-random number scale of a regular bar pattern scale, which can be used in conjunction with the detector to generate moire fringes. Techniques based on this approach are discussed in EP 0100243A and EP 0184286A. However, moire fringes can also be generated by interaction between the pseudo-random number scale with a detector having a pitch of its sensitive elements differing from that of the indicia, e.g. the pseudo-random number digits. In this case the regular moire fringe which would be produced by a simple bar pattern is interrupted by the locations in the pseudo-random number where consecutive repetitions of a digit occur. Notwithstanding these interruptions, with typical pseudo-random numbers there will be sufficient alternating edge transitions for a measurable moire fringe to be generated, and for its phase to be extracted, so that the precise position of the scale can thereby be determined.

One way for the phase of an impure moire waveform to be extracted is by performing a Fourier analysis on the signal, to extract only the fundamental frequency of the waveform, and to reject the harmonics which represent distortions of it. This can be achieved, for example, by computer processing of the digitized signal, or by an analogue processing technique as described in EP 0184286A. However, the presence of interruptions due to consecutive repetitions of the same digit, as already mentioned, tends to distort the phase of the moire waveform, giving rise typically to a cyclic error in measurement of the scale position having a period corresponding to half the pitch of the moire waveform.

To overcome this problem the present invention proposes that the detector has a pair of tracks of sensitive elements, the pitch of the sensitive elements of each being the same, and differing from the pitch of the indicia of the scale as required to generate the moire waveform. The two detector tracks are displaced longitudinally by a half an indicium pitch, with the result that the moire waveforms generated by the two sensors are nominally 90° out of phase. The result of this phase displacement is that the cyclic errors having a period corresponding to half the pitch of the moire waveform will be of the same amplitude, but of opposite phase.

By then extracting the fundamental frequency components of the two moire waveforms, and summing them, the cyclic error can substantially be eliminated. BRIEF DESCRIPTION OF THE DRAWINGS

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

Fig. 1 represents a portion of a scale consisting of a pair of alternating pseudo-random number strings, with the spacing between them varying along the length of the scale;

Fig. 2 represents a portion of an alternative scale arrangement consisting of a pair of pseudo-random number strings, with a cyclic change in one of them at each successive repetition along the scale, together with an arrangement of detector and correlation processor to determine the position of the sensor along the scale;

Fig. 3 illustrates the principle of operation of a type of correlation processor suitable for processing the data from the sensor shown in Fig. 2;

Fig. 4 represents an alternative form of correlation processor suitable for processing the data from the sensor shown in Fig. 2;

Fig. 5 depicts the processed signal from a detector reading near the start of a scale of the type illustrated in Figs. 1 or 2.

Fig. 6 represents the processed signal from a detector reading at a position remote from the start of a scale of the type illustrated in Fig. 1 or 2;

Fig. 7 illustrates the principle of generating a moire waveform by the interaction of the image of a bar pattern scale with a detector having discrete sensitive elements at a spacing which differs from that of the bar pattern;

Fig. 8 represents the signals on the sensitive elements of a sensor of the type shown in Fig. 7, but with many more elements, when illuminated with a bar pattern image as in Fig. 7;

Fig. 9 illustrates a moire type waveform generated from a scale consisting of pseudo-random number strings imaged on a detector in which the pitch of the sensitive elements differs slightly from the pitch of the indicia of the scale;

Fig. 10 represents the fundamental frequency component of the moire waveform of Fig. 9;

Fig. 11 illustrates a scale suitable for more accurate measurements than those previously discussed, which consists of a bar pattern track separate from the pseudo-random number track, 'so that the phase of the moire interpolation waveforms is not perturbed by the consecutive repeated digits in the pseudo-random number strings;

Fig. 12 shows a technique of generating from the same scale two moire waveforms having a phase difference of 90° between them;

Figs. 13 and 14 illustrate moire waveforms having a phase difference of 90° generated from a scale consisting of pseudo-random number strings as for Fig. 9;

Figs. 15 and 16 represent the tap weights in correlation processors of the type illustrated in Fig. 3, suitable for processing the waveforms of Figs. ' 13 and 14;

Figs. 17 and 18 illustrate respectively the fundamental frequency components derived from the waveforms of Figs. 13 and 14;

Fig. 19 represents the combination of the two waveforms of Figs. 17 and 18 into a single waveform in which the phase errors are substantially less than in the two original waveforms;

Fig. 20 demonstrates the reduction of cyclic errors which can be achieved by a two phase moire system of the type illustrated in Figs. 12 to.19;

Fig. 21 represents a two phase electrical output resulting from the motion of a detector having two tracks of sensitive elements in which signal processing is carried out on the instantaneous photoelectric signal pattern;

Fig. 22 represents a three phase electrical output resulting from the motion of a detector similar to that

of Fig. 21 but having three tracks of sensitive elements and associated signal processing;

Figs. 23 to 25 illustrate further arrangements of tracks of the scale and detector;

Fig. 26 illustrates a possible mechanical configuration for a linear position measuring device based on the principles of the present invention; and Fig. 27 represents the application to a weighing device of a measuring system based on the principles of the present invention. DETAILED DESCRIPTION

Turning now to Fig. 1, this represents a portion of a scale 2, consisting of a sequence of successive sections (hereinafter referred to as "blocks"), each containing sixteen divisions. Within each of the blocks 4 there are two five-place strings, illustrated as A1-A5 and B1-B5, which in the simplest embodiment could be two five-digit binary numbers. The positions of the individual 'A' and 'B' strings can be recognized very reliably by correlation with matching reference strings. In the first block, Block 0, the 'A' and 'B' strings are adjacent, in Block 1 there is a single additional division, at the start of the 'B' string and in each successive block to the right an additional division spacing is introduced at the start of the "B" scale. Using this technique it is possible to identify any one

of seven blocks 4 by the spacing between constant parts of the 'A' and 'B' strings, and the position within the block in relation to the 'A' string, so that a position can be determined to a precision of one division along a scale of 112 divisions. It will be appreciated that the example used for illustration is a somewhat trivial one, with strings only five digits long, whereas in a practical application they would probably be at least an order of magnitude longer.

The type of scale illustrated in Fig. 1 suffers from the disadvantage that a substantial proportion of the divisions are blank, i.e. they contain no information; if the design were using binary number strings, the blanks would simply be all ones or all zeros. One of the practical benefits of a binary number string is that it embodies a high degree of redundancy, and can accordingly be recognized reliably notwithstanding a high degree of corruption or obscuration: a property which lends itself to the design of instruments capable of operating reliably under extremely adverse circumstances. This benefit is reduced as the string length is reduced. Additionally, the number of blocks in the example shown is limited to the number of blanks in each block, so that there is an element of tradeoff between scale length and reliability.

An alternative arrangement which overcomes these

disadvantages is illustrated in Fig. 2. In this example the scale 6 is, as in the previous example, divided into blocks 8 of sixteen divisions. Within each block 8 there are two eight-place strings, represented by A1-A8 and B1-B8, but in contrast with the scale 2 of Fig. 1, there are no blank spaces. In Block 0 the two strings run respectively from Al to A8, and from Bl to B8. In each block the 'A' string remains the same, but the sequence of the 'B' string is varied cyclically, so that in Block 1 the string starts with B2, in Block 2 the string starts with B3, and so on. Thus the scale can contain up to eight separately identifiable blocks of sixteen divisions, making a total of 128 divisions. In a practical application both the 'A' and 'B' strings could be 8-digit binary numbers.

It will be appreciated that in a sense the scale 2 of Fig. 1 can be regarded as being formed with a B string of eleven digits, six of which are blanks, which varies cyclically along the scale. Further, although the examples given show blocks of constant size, there is no fundamental reason why the blocks should not vary in size, so long as the pattern of variation is unambiguously defined, or can be stored as a "lookup table" in the processor; this will, of course, make the calculation of position somewhat more complicated.

In operation, a portion of the scale is sensed by a

detector 10, which may in practice be a linear array of photosensitive elements on which the scale is imaged. The nominal position of the detector 10 is taken to be where indicated by the arrow 12, although a length of the scale 6 from A7 in Block 1 to A6 in Block 3 is imaged on the sensor 10. Determination of the position of the detector in relation to the scale 6 is achieved by taking the signals 14 from the detector 10 and successively shifting them in the direction of the arrow 16, checking after each shift the• matching with the a and b portions of the reference 18. The reference 18 consists of a string al-a8, which will match A1-A8 of the scale 6, and two sequences of the string bl-b8, which will match B1-B8 of the scale 6. It will be evident from the oblique lines 20 that six shifts of the signals 14 are required before A1-A8 are brought into coincidence with al-a8 of the reference, and an additional two shifts are required before the string B3-B2 coincides with b3-b2 of the reference. The position of the detector 10 is thereby determined to be immediately to the right of the sixth division in Block 2.

Again, the example taken is a trivial one, and serves merely to illustrate the principle. In a practical application the A and B strings may be 256 digits long, with a resultant scale length of 256 x

512 (= 131,072) divisions; the correlation processing technique would enable reliable position measurements to be made even if (say) a hundred consecutive scale divisions were completely obscured. Further, although the example showed two pseudo-random number strings in each block, with one being fixed and the other varying, there is no reason why there should not be three or more, with one fixed and all the others varying since increasing the number of pseudo-random number strings will increase substantially the number of blocks which can be identified. Obviously, since it is usually convenient (although not essential) for blocks to occupy a number of digits which can be expressed as 2 ⁿ if there are an odd number of pseudo-random number strings they cannot all be of the same length, or there will have to be one or more blank spaces in the block; it would even be possible to combine variable spacing, as shown in Fig. 1, with cyclic variation of the pseudo-random number string, as illustrated in Fig. 2. The design of a scale according to the present invention represents a tradeoff between integrity under adverse conditions, which demands long pseudo-random number strings, and sensor length, which will typically require to cover approximately two blocks if the correlation processing is to be straightforward. Thus, for example, as already

mentioned, a pair of 256 digit strings will serve to identify 131,072 divisions, and require a sensor of about 1024 pixels, whereas three 42 digit strings in blocks 128 digits long will identify 42 ² x 128 (= 225,792) divisions, and require a sensor of only 256 pixels. Certainly the degree of discrimination in the correlation achieved by the 256 digit strings (which may be regarded as the mathematical signal to noise ratio) will be greater by a factor of some 2.5 than that of the 42 digit strings, but it will be evident that under favourable conditions the three 42 digit strings could offer a more economical system.

In constructing a scale of the type described, the essential requirement is for each block to be uniquely identified, and there can be regarded as complete freedom of choice in this respect. However, it will obviously be advantageous if the identification can readily be decoded as a block number, which in this type of scale will almost invariably be binary. To achieve this, it will be desirable for one of the varying pseudo-random number strings to be taken completely through its intended range of cyclic variation before it reverts to its starting sequence, and the cyclic variation of the next string is varied by one step. In other words, as a sequence of cyclic variation of one string is completed, there is a "carry" to the next

string. To take the example of two 256 digit strings, the block length of 512 digits represents 29 divisions, and there are 28 possible variations of the "B" string, so that if the variation of the "B" string is represented as BBBBBBBB, and the position in the block is represented as XXXXXXXXX, the identification of any position within the entire scale can be written by concatenation of the two binary numbers as

BBBBBBBBXXXXXXXXX. Taking the other example of the 42 digit strings, it will obviously be preferable to use no more than 32 (2*-*) variations of one of them, even if all

42 variations of the other variable string are used. A position within the scale can then be expressed as

BBBBBBCCCCCXXXXXXX, albeit with the limitation that the

BBBBBB portion can only reach 101010 (42 expressed in binary), and the total number of divisions in the scale

42 x 32 x 128 (= 172,032).

One way of achieving the correlation processing of the detector signals 14 of Fig. 2 is by a tapped CCD shift register of the type illustrated in Fig. 3. A CCD shift register 24 has along its length alternate transport electrodes 26 and charge sensing electrodes 28, 30 (only a few of the electrodes have been numbered, and the drive connexions to the transport electrodes have been omitted, to avoid confusing the diagram). Each charge sensing electrode is divided into two

portions, one of which is connected to the positive input of a differential amplifier 32, and the other is connected to the negative input. If the division is near the end of the electrode connected to the negative input of the differential amplifier, the net multiplication or "tap weight" of the electrode is positive, as in the examples at 28; if the division is near the other end, as at 30, the net tap weight is negative. The arrangement is well known in the field of signal processing, where it is referred to as a "transversal filter". In operation, signals are injected at 34 and are propagated as charge packets to the right through the register 24 by the combined operation of the transport electrodes 26 and the sensing electrodes 28. When the signal charges are under the sensing electrodes 28, the output 36 of the differential amplifier represents the summation of the products of the signal charges and the respective tap weights of the sensing electrodes. With a binary signal input at 34, the output 36 is uniquely high only when the signal sequence corresponds to the sequence of tap weights. Thus the example shown in Fig. 3, which has a sequence of tap weights, reading from left to right, of 1,1,-1,-1,1,-1,1,1,-1,1,-1,1,1,1,-1,1, will yield a uniquely high output when it contains the binary signal 1100101101011101. Note that in this example the binary

signal would have been injected at 34 in the reverse order to that quoted, and also that for convenience of illustration both this shift register and the one illustrated in Fig. 4 have only 16 stages, whereas to perform the function required in Fig. 2 would require 24 stages, and a practical application might require 768 stages. This type of correlation processor may be designed entirely separate from the sensor, or it may be wholly or partly integrated with a solid state detector array.

Although the transversal filter shown in Fig. 3 represents a convenient way of carrying out the correlation operation, and one which lends itself to integration with the detector, a similar result can be achieved by conventional logic circuits as illustrated in Fig. 4. The signal 38 from the detector (not shown) is fed into a thresholding circuit 40, which gives a logic "1" output when the signal 38 is above the threshold level, and a logic "0" when the signal is below the threshold level; the threshold level is set to approximately half the maximum signal input level. The output signals from the thresholding circuit 40 are fed into a shift register 42, through which they are moved successively by drive pulses applied at 44. The logical signal sequence appears at the outputs 1 to 16 of the shift register 42 in a similar way to the signal

charges propagating through the CCD shift register 24 of Fig. 3. Stages which require to correspond to the negative tap weights of Fig. 3 have inverting amplifiers, as at 46, coupled to their outputs, and the summation of the products of the logic signals and the (arithmetic) signs of the outputs are achieved by the resistors as at 48. The resultant output at 50 corresponds closely with the output which would be obtained at 36 in Fig. 3.

To illustrate the operation of a practical design of scale of the general type illustrated in Fig. 2, a computer model was constructed of a scale consisting of two pseudo-random number strings each 256 digits long, with the second string being varied cyclically by one digit in the manner shown in Fig. 2. The processor was of the type shown in Fig. 3, and was 768 digits long, consisting of one repetition of the first number string, followed by two repetitions of the second, with logical zeros in the number strings represented by tap weights of -1 in the processor. The output from the processor near the beginning of the scale is illustrated in Fig. 5. It will be seen that a correlation peak 52 was obtained from the 'A ¹ output after 20 signal shifts, and that a peak 54 was obtained simultaneously from the 'B' output. The second 'B' peak 56 is 256 shifts after the first, and can be disregarded. The results indicate that the sensor

position was at +20 divisions in Block 0, i.e. at 20 divisions from the beginning of the scale. An example of a processor output obtained farther along the scale is shown in Fig. 6: the 'A' peak 58 is obtained after 180 signal shifts, and the subsequent 'B' peak 60 after a further 218 shifts. The earlier 'B' peak 62 is 256 shifts before the peak 60, and can be disregarded: only the first 'B' peak following the 'A' peak is relevant. The results show that the sensor was at +180 divisions in Block 218, i.e. that the sensor was at 180 + (218 x 512) = 111,796 divisions from the start of the scale.

The technique thus far described is capable of extremely reliable position sensing on long scales, to the nearest scale division. However, there will frequently be requirements for position sensing to a fraction of a scale division, in preference to the adoption of very small scale divisions, or when accurate measurements are required over very long scales. In these cases it will be advantageous to be able to perform an interpolation between scale divisions. One way in which this can be achieved is by generating moire fringes using an indicia bar pattern image on a detector having sensitive elements at a pitch different from the indicia bars in the image; techniques of this type were disclosed in our earlier European applications

EP 0100243A and EP 0184286A. The principle is illustrated in Fig. 7, which shows a portion of a bar pattern scale 64 imaged on a detector 66, such that sixteen sensitive elements on the detector correspond to eighteen bars of the scale. Note that in this case a "bar" is one element, or indicium, of the scale, whether dark or light.

An idealized moire output from a sensor under these conditions is shown in Fig. 8; in this example the sensor has 256 elements, with 260 bars imaged on it. The signals on the sensitive elements, or "pixels", of the detector, which appear at the sensor output, show two complete cycles of light and dark, with the odd numbered pixels showing the inverse of the even numbered pixels. In practice the moire signal would tend to have the troughs and crests rounded by aberrations in the optics and the sensor, and would exhibit some unevenness due to variations in sensitivity between one pixel and the next, and due to residual signals on the pixels, but these factors do not significantly affect the operation of a system of this type, and for clarity are not illustrated.

However, moire fringes do not have to be restricted to plain bar patterns: and it does not appear previously to have been realized that provided that there is an appropriate mismatch in pitch, they can also be generated

by the interaction of a binary pseudo-random bar pattern with the elements of a detector track. Fig. 9 represents the output signal generated by a portion of the scale which gave rise to Figs. 5 and 6, with 260 digit pitches imaged on a 256 element sensor. The similarity between Figs. 9 and 8 will be evident. The difference in phase of the two moire patterns is due to the fact that for Fig. 9 the sensor was positioned with the end pixel at a fraction of a bar spacing along the bar pattern, and the signals at Max. and zero in Fig. 9 are due to the bars in the pattern which are more than a single bar width, representing repeated digits.

To derive useful information from the signals shown in Fig. 9 the positions of the crossovers require to be established, and one way of doing this is for the fundamental frequency component of the moire element to be extracted. This can be achieved using a signal processor of the type illustrated in Fig. 3, in which the tap weights of successive elements are of ±sine or +cosine form. Mathematically, convolution of the signal with sine or cosine tap weights represents a Fourier analysis, to extract both in phase and amplitude the frequency component corresponding to the particular tap weight profile being used. EP 0184286A referred to this technique in connexion with position interpolation using moire fringes derived from bar patterns. Applying

it to the signal of Fig. 9 yields a moire fundamental component of the form illustrated in Fig. 10: visibly related to the moire element of Fig. 9, but also evidently not accurately in phase with it. This phase error is due to perturbation of the pure moire waveform by the repeated digits in the scale pattern which give rise to the zero and Max. level outputs. Clearly any attempt at extraction of a moire phase from the signal of Fig. 9 will be of limited application if the errors are as substantial as they are in Fig. 10.

One solution to this problem lies in using alongside the pseudo-random string scale a simple bar pattern to generate the moire, as illustrated in Fig. 11; the pseudo-random scale would be imaged on the coarse position detector track, and the bar pattern scale on a second detector track to generate the moire waveform for the interpolation function. The scale of Fig. 11 represents a practical solution, and where the highest accuracy of interpolation is required it may be the best one. In other cases it represents an unnecessary cost if means can be devised for extracting a moire phase of sufficient accuracy from the basic pseudo-random scale pattern, by adopting a technique which is less affected by the repeated digits in the pseudo-random scale. One way in which this can be done is illustrated in Fig. 12, which represents on an enlarged scale, the generation of

a two phase moire from a pair of detector tracks and a bar pattern image. Although the present application is to a pseudo-random scale pattern, a bar pattern has been shown in Fig. 12 to facilitate understanding. The scale pattern 68 is imaged on to detector tracks 70 and 72, which have a relative longitudinal displacement corresponding to half the width of a bar in the scale pattern 68.

A similar effect may be achieved if the scale/detector relationship is reversed so that there are two tracks of indicia imaged on aligned detector tracks, with the indicia of one track of indicia being displaced relative to the indicia of the other track of indicia. In each case the displacement is preferably, but not necessarily, half the pitch of the indicia or the elements of the detector track.

Typical moire waveforms from a pseudo-random scale and a pair of 256 element sensors displaced by half a bar width are given in Figs. 13 and 14, where the 90° phase difference will immediately be apparent. The moire signals of Figs. 13 and 14 may be processed by tapped shift register processors having respectively cosine and sine wave tap weight profiles, as illustrated in Figs. 15 and 16, to yield fundamental frequency components, Figs. 17 and 18, which in the absence of phase errors would be in phase. In practice, the two

processed moire outputs are found to have substantially equal and opposite phase errors, and if they are combined, for example by using a common tapping amplifier for the two tapped shift registers, the resultant fundamental frequency component, shown in Fig. 19, has a greatly reduced error.

It will be understood that although the signal processing has been described principally with reference to the use of tapped shift registers, similar results can be obtained by digitizing the sensor signals and carrying out the processing using appropriate software in a digital signal processor (DSP). This method, although likely to be slower, has the advantage of avoiding the high development cost of dedicated sensors or processors.

The magnitude of error reduction which can be achieved by the two phase moire system is demonstrated in Fig. 20, which shows at 74 and 76 the actual errors of the two separate moire phases over a movement corresponding to one complete cycle of moire, compared with the error of the resultant combined moire fundamental frequency waveform at 78. It will be seen that the technique reduces the peak error by an order of magnitude, and in this example enables an interpolation accuracy of better than 1/64 of a bar pitch to be achieved, compared with 1/6 of a bar pitch using a single phase moire.

If a pseudo-random number string is to be used in conjunction with a detector having sensitive elements of appropriate pitch to generate a moire waveform, it will be found that one important property which the psuedo- random number should possess is that it should as far as possible have a consistent phase. The concept of the phase of a pseudo-random string has been developed for the present invention and needs to be explained.

Consider the following diagram: Digit 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Pattl 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 Patt2 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0

It is self-evident that the two bar patterns are of opposite phase, because each has a "1" where the other has a "0" and vice versa. Then, the phase of the first can be defined by saying that the 1 to 0 transitions are all odd to even digits, and the 0 to 1 transitions are all even to odd digits. Then, these tests can be applied to the pseudo-randon number strings PSRN 1 and PSRN2. Digit 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 PSRNl 1 1 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 PSRN2 1 1 1 0 0 1 1 0 1 1 1 0 0 1 1 0 1 Looking first at PSRNl, it can be seen that it has 1 to 0 transitions at digits 3-4, 7-8, 10-11, and 15-16; three of these are odd to even and the others even to odd, so that the PSRN does not have a consistent phase. By

contrast, PSRN2 has 1-0 transitions at digits 3-4, 7-8, 11-12 and 15-16; all are odd to even, so that the phase can be regarded as consistent. Closer examination will show that the 0 to 1 transitions in both strings are of variable phase, arising from the even runs of repeated digits, but that the difference between the two is that in PSRN2 every even run is paired with an even run of the opposite digit in order to correct the phase.

One way to achieve consistency of phase within a PSRN would be to use only odd number runs of the same digit; unfortunately, this detracts considerably from the "randomness" of the PSRN, and reduces the correlation peak relative to the spurious peaks. It is preferable to permit even number runs, and to follow each by another even number run to correct the phase, as has been done in PSRN2 in the example above. In orderto maintain the balance between odd and even runs, after each pair of even runs the next even run produced by the PSRN generator is suppressed. In this context, therefore, the term "consistent phase" istaken to mean that a predominance of 0 to 1 transitions occur at even to odd number digits, and predominance of 1 to 0 transitions occur at odd to even number digits (or vice versa), rather than implying that all transitions have to obey those rules.

Although it is apparently possible to generate moire

fringes from a pseudo-random number string of variable phase, when an attempt is made to extract the fundamental frequency component, the amplitude is found to be about 1% of the amplitude which would be obtained from a bar pattern. This results in a poor signal to noise ratio, and in phase errors in the moire waveform. By contrast, pseudo-random number strings in which the even number runs are paired, as explained above, in order to maintain a consistent phase, yield fundamental frequency components having amplitudes of about 20% of that produced by a bar pattern, with adequate signal to noise ratio, and minimal phase error. Consequently, for linear encoder applications in which the moire will be derived from pseudo-random mnumber strings, it is necessary to employ pseudo-randon numbers or consistent phase.

For the purposes of the present invention, the figure of merit of a pseudo-random number is its "signal to noise ratio" the ratio of the correlation peak to the highest spurious peak of the corrrelation outputs in all other positions, both relative to the datum determined by the design of the correlation processor: typically either the average value or the zero level. SNR figures of about 8.0 are obtainable for numbers of the length of interest, indicating that the correlation peak is about eight times the height of the next highest spurious peak. Bearing in mind that under conditions of partial

obscuration all the signals decrease, there should be no difficulty in detecting the correlation peak, even under the most unfavourable conditions which are likely to be encountered.

Thus, the scale will be based on blocks each consisting of two or more pseudo-random number strings, one of which will remain constant, while the other(s) will change cyclically from block to block thereby enabling each individual block to be identified. However, to achieve satisfactory performance from the moire interpolation, all the pseudo-random numbers in the scale should normally be of the same phase. This in turn means that the cyclic shift in numbers from block to block must be two digits each time, with the result that the number of blocks which can be identified by a given string is halved.

In some cases it may be more convenient to generate a scale whose blocks consist of four pseudo-random number strings instead of three, arranged ADBCADBC, in place of the three strings arranged ACBCACBC. In this case, in any block both the C and D strings will have the same cyclic shift, and the operation of the system will be the same, but with a processor block taking the place of two of the C processor blocks and with appropriate adjustment of the processor block spacings.

In the angular position sensors described in EP

0100243A and EP 0184286A it was necessary to use two moire scales, in which the moire fringes moved in opposite directions as the scale moved, and to take the phase difference between the two moire waveforms, in order to obtain an interpolation to 2n parts. Although this consideration does not arise in linear measurement, since a sensor having 2n pixels can cover a number of scale indicia which is greater or less than 2 ⁿ , there may be circumstances in which greater accuracy can be achieved by taking the phase difference between two sets of moire waveforms, and this technique can also be adopted within the scope of the present invention. Similarly, the pitch difference between the sensitive elements of the detector and the scale indicia which are required to generate the moire waveform has to be achieved by appropriate choice of pixel pitch and .->" ^* :■tical magnification. Unlike complete circular scales, in which changes of magnification have no effect on the generation of the moire waveforms, provided that the bar patterns remain covering the sensitive elements, with linear scales the magnification becomes critical, and if a high degree of interpolation is required the magnification must be controlled within close limits. This consideration may dictate the use of an optical system which is inherently substantially constant in its magnification, which will typically be

1:1, and appropriate choice of the size of the sensitive elements. Thus the detector is likely to embody sensitive elements of different sizes for the pseudo-random number correlation and for the moire generation. Under some circumstances it will be found that a single track of sensitive elements on the detector can be used for both purposes, although correlation with a pseudo-random number is not likely to prove satisfactory if the number of sensitive elements on which n scale indicia are imaged is outside the range n + 1.

The effects which have been described relate to techniques in which a stationary image of a scale is cast on a detector, or an effectively stationary image is produced by the use of strobed illumination in conjunction with a moving scale. Signal processing is then carried out by electrically shifting the resultant signal pattern through the processor, which may be separate from the detector, or integrated with it as described in EP 0184286A. Alternatively, however, a detector may be used in which the signal level on each sensitive element, is directly proportional to the level of the incident illumination at any instant; this may be achieved by arranging for each sensitive element to have a resistive load through which the photo-current passes, instead of charging a capacitor which loses its charge or

is discharged during, or directly after, readout. If on a detector of this type the pixels have charge sensing taps as described in relation to Fig. 15 or 16, signal processing will take place as the detector is moved relative to the scale, and an analogue electrical output, or outputs, can be generated which can be processed by conventional means to yield information on the detector position. The resultant instrumental performance would in terms of the pseudo-random scale correspond closely with that of the reference mark on an incremental position sensor, while the moire outputs would be comparable with those of an electromagnetic instrument.

By way of example, Fig. 21 represents the processed signal outputs from a detector array having two adjacent tracks of 256 sensitive elements, while a bar pattern image having 260 bars to 256 sensitive elements on the is moved through a distance of two indicia, or bar pitches. One track of sensitive elements has tappings corresponding to two cycles of ±cosine and yields the curve 80, while the other has tappings corresponding to two cycles of ±sine and yields the curve 82. A similar effect could of course be obtained by having the same tapping profile on both tracks of sensitive elements, and displacing one of them through half an indicium pitch relative to the other.

Alternatively, four tracks of sensitive elements could be used to constitute a pair of two phase moire systems, in order to derive accurately phased signals from a pseudo-random scale, or a bar pattern corrupted by dirt.

In a similar manner, three detector tracks, or three detectors, may be used, either spaced longitudinally by two thirds of an indicium pitch, or having ±sine or +cosine tappings mutually displaced electrically by 120°, to yield, as shown in Fig. 22, a complete cycle of three phase output over a sensor displacement of two indicia. When reference is made to more than one detector track, these do not necessarily have to be physically separate components; in practice, it will usually be found more economical for them to be formed "monolithically" on a single piece of silicon. Further, it will be evident that a comparable form of construction may be applied to angular measuring devices, similar to those described in EP 0 184 286 A, to give polyphase electrical outputs as the scale is rotated relative to the detector.

To illustrate the factors which have to be taken into account in the desing of an instrument according to the present invention, consider a scale having 12.8um divisions (25.6μm cycle) which can be subdivided using the moire technique described, to O.lum. The question which then arises is the block length which is to be used

for defining the coarse position on the scale, and the structure of the block which together determine the total length of the scale which can be identified unambiguosuly. The requirement for block length is that it should desirably be 2 ⁿ divisions, and that it should be long enough to contain two, three, or more pseudo¬ random numbers which will afford a sufficient number of permutations to count the required number of blocks. For the present purpose a 256 digit block length has been sleected, containing three pseudo-random numbers having respectively 86, 84 and 86 indicia. Bearing in mind that each cyclic shift must be of 2 digits in order to maintain phase and that only the most significant pseudo¬ random numbers can conveniently have a maximum count which is not 2 ⁿ - 1, this combination will provide 43 x 32 blocks of 256 divisions, amounting to 352,256 divisions, or approximately 4.5m in length. This is considered adequate.

Given a block of 256 divisions, the next consideration is the number of divisions which have to be sensed in order to derive the coarse positional information. Taking into account the redundancy properties of pseudo-random numbers, it might be suggested that all of the pseudo-randon numbers and half of a third might well suffice; a total of perhaps 214 divisions. However, this is throwing away much of the

redundancy which enables the system to produce accurate readings from a contaminated scale, and would be better avoided. To sense a full 256 divisions provides all the information but, as shown in Fig. 23 requires a double length processor in order to produce the correct output no matter what the relative positions of the scale and the detector.

One problem of a double length processor is that the electrical performance is liable to be inferior to a single length version, since half the sensitive elements will at any time have no signal on them. The alternative is to make the photosensitive region two blocks long, and use only a single length processor as illustrated in Fig. 24.

Electrically this may offer superior performance, although the optical image required will be twice as long, and will inevitably increase the size of the optical system. The choice between double length image and double length processor will ultimately depend on the ^' particular requirements needed. The single block length image may be regarded as the preferred choice provided that the required processor performance can be achieved. In both cases the moire photoregisters and processors will occupy a similar length to the primary processors illustrated; probably 254 scale divisions in the case of a single block length processor, and 508 scale divisions

in the case of a single double length processor, and 508 scale divisions in the case of a double block length processor. Since both occupy the same area of silicon, and the moire processor fits into the same space, there is little to choose between them on grounds of cost.

However, in a practical situation the B string, for example, will be subject to a cyclical variation between successive appearances on the scale, and the C string will have a cyclic variation each time the B string returns to its starting order and has a "carry". The consequence is that two separate fragments of the B string will only correlate simultaneously in separate B processor sections isf thespacing between them is adjusted for the cyclic shift. While in the case of the B processor this solution is satisfactory, the C processor presents more of aproblem, since the C string only changes periodically, for example, once every thirty-two blocks; no arrangement of the processor can be correct for both the varied and the unvaried conditions.

Undoubtedly it is possible to operate with a 256 division image; the problem is really to incorporate the essential decoding logic in the processor hardware. To achieve this is likely to necessitate duplicating the second section of the processor with and without the adjustment for cyclic shift, and using additional logic circuits to determine, from the position of the B string

which output should be used. An alternative approach is to use a scale built up from 256 division blocks, using a reference string A which never changes, a string B which shifts cyclically by two digits every 32 blocks; to ensure that it can always be processed unbroken, the C string appears twice in each block.

The scale, sensor, and processing are then arranged as illustrated in Fig. 25, where the scale calibration is regarded as increasing from left to right. C _n represents the C PSRN shifted cyclically through n digits, B52 represents the B PSRN shifted cyclically through 62 digits, and Bg represents the B PSRN having completed a full cycle of 32 2-digit shifts and returned to its original sequence. When the B PSRN reaches this point, the C PSRN is incremented.

The block marked "image" represents the portion of the scale which is imaged on the sensor, and therefore available for processing. It will be shifted to the right through the four processors a, b, c and c', the number of shifts between the 'A' correlation peak and the 'B' and 'C correlation peaks establishing the state of cyclic shift of each of the B and C PSRN strings, and hence the position of the 256 digit block in which they are situated.

The difficulty which arises is illustrated in the figure, where the image straddles two blocks of the

scale. To the left of the A PSRN in the image is the block identified by C _n Bg ₂ while to the right of the A PSRN is the block C _n+ 2Bo. There will always be a cyclic shift between the two B PSRNs, which is accommodated by reducing the spacing between the two b processor pairs by two digits, so that in this example B52 and BQ reach their correlation peak simultaneously. The same cannot be done with the c ¹ and c processor pairs, however, because the C PSRNs are usually identical: it is only when the B PSRN reaches B _Q that there is a difference in the C PSRNs. The c' and c processor pairs are regarded as separate processors; usually their correlation peaks will occur simultaneously, so that an output from either can define the C count, but when the B _Q condition is detected, the C count is regarded as the output from c' plus 2 digits, or the output from c. In this way, maximum integrity of reading can be maintained.

Fig. 26 represents a typical configuration in which a linear measuring system of the type described may be used. An elongated member 84 of uniform cross-section provides guiding surfaces for a carriage 86 to slide along it, and also carries a scale 88. Both the member 84 and the carriage 86 may in practice be parts of a machine tool, or they may be parts of a linear encoder, which is designed to measure the linear displacement of objects inextensibly coupled to the

carriage 86, for example by a rod or metal tape. On a suitable surface along its length the member 84 also carries a scale 88, which may be of any of the types described in the present document, but typically will be of the general form described in connexion with Fig. 2. The lengths of the two pseudo-random number strings will depend on the length of the scale 88, and the accuracy with which position measurements are required to be made. For example, as already explained in relation to Fig. 2, if the pseudo-random number strings are 256 digits long, the maximum scale length is 131,072 divisions. If the moire is derived from the pseudo-random pattern, and a two phase moire sensing system is used, having the performance illustrated in Fig. 20, a measurement accuracy of 1/64 of a division could be obtained. This would result in a scale covering 64 x 131,072 = 8,388,608 measurable units, and depending on the size of the basic scale division, or indicium, this could for example represent a measuring accuracy of 0.5um over a length of 4m, or an accuracy of 0.2um over a length of 1.6m. Higher accuracies could of course be obtained by using a separate bar pattern to generate the moire. Mounted on the carriage 86 is a circuit board 90, carrying the detector 92 on which a portion of the scale 88 is imaged by the lens 94. The scale 88 may be illuminated by conventional means (not

shown) in transmissive or reflective mode.

In practice it will usually be found desirable to use an optical system of unity magnification, in order to afford the best control of the relationship between the sensitive elements of the detector and scale indicia, and alternative designs of optics will be well known to those skilled in the art. This consideration is likely to dictate a size of the scale indicia in the range 10-20um, to suit the most effective sizes of the sensitive elements of the detector, so that for scale lengths over approximately 2.5m, it may be more appropriate to use pseudo-random number strings of 512 digits each, permitting a total scale length of 524,288 indicia, or alternatively to use three or more pseudo-random number strings.

In contrast to Fig. 26, in which total scale length could be an important consideration, Fig. 27 represents a longitudinal section through a possible design of a load cell, a weighing device for which the principal requirement is likely to be accuracy of measurement of small displacements. The unit consists of a tube 96, which may be of circular cross-section, and made typically from high grade steel. The tube 96 is supported near each end by supports 98 of triangular prismatic shape, and loads are applied at the centre of the span by another triangular prismatic member 100. In

practice, to prevent inaccuracy due to the tube rolling, the supports 98 and the member 100 could conveniently bear on flat surfaces formed on the tube wall, but for simplicity these are not shown in the illustration. The end of the tube 96 is closed at 102, and carries a threaded stud 104 supporting a reflecting imaging system 106. The threaded stud 104 can be adjusted by screwing it in and out of the end 102, in order to adjust the precise length of the optical system to set the sensitivity of the load cell, and can then be locked by the nut 108. The other end of the tube 96 is closed by a plug 110, which carries a circuit board 112 on which are mounted, side by side, a scale 114 and a detector 116. The scale is illuminated by conventional means either in transmissive or reflective mode (not shown), or using modern semiconductor technology could be made self-luminous. Connexion to the circuits within the tube 96 is made by a multi-way connector 118 mounted in the plug 110.

In operation, when a load is applied at 100 the tube 96 bends, causing the ends 102 and 110 to move out of parallel. Due to the reflective nature of the optical system, the displacement of the image of the scale 114 on the detector 116 is equal to twice the mechanical length of the system multiplied by the angle (in radians) through which the ends 102 and 110 move out of

parallel. This feature means that the arrangement constitutes a measuring instrument with a very long "pointer", so that the accuracy of measurement attainable is extremely high. It also means that the tube 96, on whose flexure the operation of the instrument depends, can be operated well within its elastic range, so that non-linearity errors are reduced to a minimum. Due to the limited range of movement to be measured, the coarse scale is unlikely to require a large number of blocks. The design shown is very basic, and may be varied freely without departing from the general principle; possible changes might be to use a rectangular tube or a more complex imaging system than the simple refracting and reflecting surfaces illustrated.

In the general design of instruments accordingto the present invention, GaAlAs solid state emitters may conveniently be used as illumination sources, principally because they are very effficient sources of IR, and also because the narrow spectral range substantially eliminates chromatic effects in the optics. Alternative sources of illumination may of course be used, including

light emitting diodes, solid state lasers, and with appropriate sensor design, incandescent lamps. An exposure time which is a small fraction of a milisecond is often desirable, in order to yield a sufficiently rapid update rate, and also to maintain reading accuracy at useful speeds of movement. It is normally assumed that an encoder of this type will maintain full reading accuracy up to a rate of movement at which the scale moves half a division during the illumination time; typically this would imply a rate of 30mm/s with a 200μs illumination period, or 60mm/s with a lOOμs illumination period.

Position sensor encoder accuracy is affected by several parameters, primarily, tap weight accuracy; signal to noise ratio at processor output; optical magnification; number of moire cycles in the image length and the combined contrast transfer function of the sensor and optics. As will be seen below, three of these parameters prove to be relatively unimportant at normal practical levels, while two of them are rather more significant. Using a computer simulation with values for the various parameters which would be readily achievable in practice, a typical performance for an encoder deriving both coarse postion and dual moire interpolation from a single pseudo-random scale over a series of 100 different positions is accuracy ±O.Olμm, and standard

deviation +0.04μm.

Consider first the tap weight accuracy applying a normal distribution to randomly generated moire tap weight errors, increased from a standard deviation of 0.01 (1% of maximum), to 0.1 (10% of maximum), the encoder accuracy was reduced from a standard deviation of 0.04um to a standard deviation of 0.05μm. The latter figures are somewhat academic, since no manufacturer is likely to have any problem producing moire taps to 1% accuracy, but it does serve to indicate the lack of sensitivity to tap weight errors.

Now consider the number of moire cycles in the image. No significant differences were found with either one, two or four moire cycles in the 512 pixel image. Two moire cycles in the image might well be considered preferable in practice, since a simple moire pixel shift count would yield interpolation to O.lum.

Next, consider the processor signal to noise ratio in the moire processing, there are effectively three signal to noise ratios which should be considered: the signal to noise ratio of the signal on an individual pixel, the tap weight accuracy, and the signal to noise ratio of the tapping amplifier. The signal to noise ratio of the signal on an individual pixel is represented by the square root of the number of electrons on the pixel; in the case of the moire pixels which would be

typical for the linear encoder the pixel signal to noise ratio would be of the order of 2000, which if processed by an ideal processor would result in a signal to noise ratio of 2000 x 512 = 45,255. Clearly this noise source is negligible in comparison with others.

The tap weight accuracy has already been investigated, and the remaining noise source to be considered is that generated by the moire tapping amplifier, which might reasonably be expected to lie in the range 2500 to 5000. Variations in signal to noise ratio of the tapping amplifier have no significant effect until it is reduced to about 100, when the standard deviation is increased to 0.06μm. It may be concluded that practical values of tapping amplifier signal to noise ratio will have no effect on accuracy. For the purpose of other calculations, a conservative figure of 2500 has been assumed.

Next, in any moire interpolation system, magnification is bound to be critical; the difference between one moire cycle in 512 pixels and two moire cycles in the same image is after all, only 510/508 or approximately 1.004. At small magnification errors, in the example considered the principal effect is a fixed error in the apparent position of the first pixel of the sensor amounting to 0.33μm per 0.0001 departure in the magnification from 1.0000. In effect, this is only an

expression ofthe fact that the moire interpolation determines the mean position with reference tothe centre ofthe image, whereasthe reading is normally expressed with reference to pixel 1. A magnification of 1.0004 increases the standard deviation by 50% to 0.06μm. At greater departures that this from 1.0000 magnification the primary processor logic is liable to take wrong decisions so that an error of one scale division can occur.

It is evident that close control of magnification will be essential if the system is to work correctly. Although by using telecentric optics variations in magnification can be virtually eliminated, the problem will be to ensure that the optics are truly telecentric, and this may increase their cost. The solution is likely to be to avoid conventional imaging optics,**nd "shadow" the sacle on to a sensor mounted as close to it as possible, probably using a collimated light beam.

It is believed that a satisfactory contrast transfer may be achieved provided that the sensor can be brought within about 0.2mm of the scale. To do this will require a variation from the normal sensor packaging, in which the seonsor surface is typically about 1mm from the outer surface of the window, and a fibre optic faceplate may be the answer. The cost will be far less than that of the fibre optical faceplates currently uused on CCD area

arrays for coupling to intensifiers, and may well be less than that of conventional imaging optics; it is likely also to lead to a more compact assembly.

The combined contrast transfer function of the optics and the sensor affects the accuracy through its effect on the signal to noise ratio, by changing the signal amplitude. As has already been seen, the moire signal to noise ratio is relatively non-critical, and no practical value of contrast transfer function is likely to have any signficant effect on accuracy.

The effect of variations in contrast transfer function on the primary processor is similar, inthat it changes the ratio between the amplitude of the correlation peak ofthe pseudorrandom number and the various spurious peaks from which it has to be distinguished - in effect, the signal to noise ratio of the correlation. Again, at normal values of contrast transfer function this presents no problem, and with appropriate processing logic no errors are likely.