Encoder scale error compensation employing comparison among multiple detectors

1. An encoder, comprising:

a scale operative to produce a spatially periodic pattern; and

a multi-section detector configured to detect multiple periods of the spatially periodic pattern, the detector comprising spatially separated first and second sections, the detector sections generating respective sets of detector output signals; and

a signal processor operative in response to the detector output signals to:

(i) derive first and second measured phase values for the first and second detector sections respectively, the measured phase values being indicative of an uncorrected estimate of the position of the scale with respect to the detector;

(ii) calculate a position error value based on the difference between the first and second measured phase values;

(iii) calculate a compensation value from the position error value; and

(iv) combine the compensation value with at least one of the first and second measured phase values to produce a corrected estimate of the position of the scale with respect to the detector.

2. An encoder according to claim 1 , wherein the signal processor is operative to perform steps (ii)–(iv) on the fly during normal operation of the encoder.

3. An encoder according to claim 2 , wherein the signal processor is further operative:

in step (ii), calculate a position error value by calculating the difference between the first and second measured phase values;

in step (iii), to calculate a compensation value by multiplying the position error value by 2π/S, where S is a step size equal to the phase interval between adjacent correction points of the scale; and

in step (iv), to produce the corrected estimate of the scale position at a given correction point (1) when the scale position is moving away from a home position, by incrementing an immediately preceding estimate of the scale position by a value equal to the sum of one least significant bit plus the compensation value, and (2) when the scale position is moving towards the home position, by decrementing the immediately preceding estimate of the scale position by a value equal to the sum of one least significant bit plus the compensation value.

4. An encoder according to claim 3 , wherein the signal processor is further operative:

in step (ii), to calculate the position error value by subtracting Δ from the calculated difference between the first and second measured phase values, wherein Δ represents a nominal phase separation modulo 2π between the first and second sections of the detector.

5. An encoder according to claim 1 , wherein the signal processor is further operative:

to perform steps (i)–(iii) during a calibration operation preceding normal operation of the encoder, the calibration operation producing a table of compensation values reflecting respective position error values for respective correction points of the scale; and

in step (iv), to retrieve, at each correction point during normal operation of the encoder, a corresponding compensation value from the table.

6. An encoder according to claim 5 , wherein the signal processor is further operative:

in step (ii), to calculate the position error value by calculating the difference between the first and second measured phase values;

in step (iii), to calculate the compensation value by multiplying the position error value by 2π/S, where S is a step size equal to the phase interval between adjacent correction points of the scale; and

in step (iv), to produce the corrected estimate of the scale position at a given correction point (1) when the scale position is moving away from a home position, by incrementing an immediately preceding estimate of the scale position by a value equal to the sum of one least significant bit plus the compensation value, and (2) when the scale position is moving towards the home position, by decrementing the immediately preceding estimate of the scale position by a value equal to the sum of one least significant bit plus the compensation value.

7. An encoder according to claim 5 , wherein the signal processor is further operative:

in step (ii), to calculate the position error value by calculating the difference between the first and second measured phase values;

in step (iii), to calculate the compensation value by multiplying the position error value by (2π/S)/T, where S is a step size equal to the phase interval between adjacent correction points of the scale, and T is the number of least significant bits of encoder resolution between adjacent correction points; and

in step (iv), to produce the corrected estimate of the scale position at a given least significant bit (LSB) (1) when the scale position is moving away from a home position, by incrementing an immediately preceding estimate of the scale position by a value equal to the sum of one least significant bit plus the compensation value, and (2) when the scale position is moving towards the home position, by decrementing the immediately preceding estimate of the scale position by a value equal to the sum of one least significant bit plus the compensation value.

8. An encoder according to claim 5 , wherein the signal processor is further operative:

in step (ii), to calculate the position error value by calculating the difference between the first and second measured phase values;

in step (iii), to calculate the compensation value as the sum of (the position error value and 2π) divided by 2π; and

in step (iv), to produce the corrected estimate of the scale position at each least significant bit (LSB) (1) when the scale position is moving away from a home position, by incrementing an immediately preceding estimate of the scale position by a value equal to the product of one least significant bit and the compensation value, and (2) when the scale position is moving towards the home position, by decrementing the immediately preceding estimate of the scale position by a value equal to the product of one least significant bit and the compensation value.

9. An encoder according to claim 1 , wherein the signal processor is further operative to perform steps (i)–(iii) during a calibration operation preceding normal operation of the encoder, and to calculate the compensation value in step (iii) for a given correction point as a cumulative error value by summing the position error values from all correction points between a home position and the given correction point.

10. An encoder according to claim 9 , wherein the signal processor is further operative (1) during the calibration operation, to produce a table of corrected estimates of the scale position as a function of measured positions of the scale position, and (2) during normal operation, at each of a set of measured scale positions, to retrieve the corresponding corrected estimate of the scale position from the table.

11. An encoder according to claim 9 , wherein the signal processor is further operative (1) during the calibration operation, to produce data representing a function Z which is a curve-fit approximation of corrected estimates of the scale position as a function of measured positions of the scale position, and (2) during normal operation, at each of a set of measured scale positions, to multiply the measured scale position by a corresponding value of Z.

12. An encoder according to claim 1 , wherein the signal processor is further operative:

during a calibration operation preceding normal encoder operation, to produce data representing a function Z which is a curve-fit approximation position error values as a function of measured positions of the scale position; and

during normal operation, at each of a set of measured scale positions:

to produce a re-created position error value by multiplying the measured scale position by a corresponding value of Z;

in step (iii), to calculate the compensation value by multiplying the re-created position error value by 2π/S, where S is a step size equal to the phase interval between adjacent correction points of the scale; and

in step (iv), to produce the corrected estimate of the scale position at a given correction point (1) when the scale position is moving away from a home position, by incrementing an immediately preceding estimate of the scale position by a value equal to the sum of one least significant bit plus the compensation value, and (2) when the scale position is moving towards the home position, by decrementing the immediately preceding estimate of the scale position by a value equal to the sum of one least significant bit plus the compensation value.

13. An encoder according to claim 1 , wherein the signal processor is further operative:

during a calibration operation preceding normal encoder operation, to produce data representing a function Z which is a curve-fit approximation position error values as a function of measured positions of the scale position; and

during normal operation at each of a set of measured scale positions:

to produce a re-created position error value by multiplying the measured scale position by a corresponding value of Z;

in step (iii), to calculate the compensation value by multiplying the re-created position error value by the sum of (the position error value and 2π) divided by 2π; and

in step (iv), to produce the corrected estimate of the scale position at each least significant bit (LSB) (1) when the scale position is moving away from a home position, by incrementing an immediately preceding estimate of the scale position by a value equal to the product of one least significant bit and the compensation value, and (2) when the scale position is moving towards the home position, by decrementing the immediately preceding estimate of the scale position by a value equal to the product of one least significant bit and the compensation value.

14. An encoder according to claim 1 , wherein the first and second detector sections partially overlap.

15. An encoder according to claim 14 , wherein the overlapping portions of the first and second detector sections are interleaved with each other.

16. An encoder according to claim 1 , wherein the spatially periodic pattern is a spatially periodic optical interference pattern, and wherein the encoder is an optical encoder including an optical source operative to direct optical energy at the scale to produce the spatially periodic optical interference pattern.

17. An encoder according to claim 1 , wherein the spatially periodic pattern is a spatially periodic magnetic field pattern, and wherein the encoder is a magnetic encoder in which the scale comprises an array of magnetic elements collectively operative to produce the spatially periodic magnetic field pattern.

18. An encoder according to claim 1 , wherein each of the detector sections is a polyphase detector operative to detect respective intra-period phase components of the spatially periodic pattern, and wherein the signal processor is operative, when deriving each of the first and second measured phase values for the respective detector section, to perform a trigonometric calculation based on the respective intra-period phase components.

19. An encoder according to claim 18 , wherein the number of intra-period phase components detected by each of the detector sections is four.

20. An encoder according to claim 18 , wherein the detector sections are nominally separated by one or more whole periods of the spatially periodic pattern.

21. A method of compensating for spatially varying position errors in a scale of an encoder, the scale being operative to produce a spatially periodic pattern, the method comprising:

(i) providing a multi-section detector configured to detect multiple periods of the spatially periodic pattern, the detector comprising first and second spatially separated sections, the first and second sections generating respective sets of output signals;

(ii) deriving first and second measured phase values for the first and second detector sections respectively, the measured phase values being indicative of an uncorrected estimate of the position of the scale with respect to the detector;

(iii) calculating a position error value based on the difference between the first and second measured phase values;

(iv) calculating a compensation value from the position error value; and

(v) combining the compensation value with at least one of the first and second measured phase values to produce a corrected estimate of the position of the scale with respect to the detector.

22. A method according to claim 21 , wherein steps (iii)–(v) are performed on the fly during normal operation of the encoder.

23. A method according to claim 22 , wherein:

calculating a position error value in step (iii) comprises calculating the difference between the first and second measured phase values;

calculating a compensation value in step (iv) comprises multiplying the position error value by 2π/S, where S is a step size equal to the phase interval between adjacent correction points of the scale; and

in step (v), the corrected estimate of the scale position at a given correction point is produced (1) when the scale position is moving away from a home position, by incrementing an immediately preceding estimate of the scale position by a value equal to the sum of one least significant bit plus the compensation value, and (2) when the scale position is moving towards the home position, by decrementing the immediately preceding estimate of the scale position by a value equal to the sum of one least significant bit plus the compensation value.

24. A method according to claim 23 , wherein calculating a position error value in step (iii) comprises subtracting Δ from the calculated difference between the first and second measured phase values, wherein Δ represents a nominal phase separation modulo 2π between the first and second sections of the detector.

25. A method according to claim 21 , wherein:

steps (ii)–(iv) are performed during a calibration operation preceding normal operation of the encoder, the calibration operation producing a table of compensation values reflecting respective position error values for respective correction points of the scale; and

step (v) includes retrieving, at each correction point during normal operation of the encoder, a corresponding compensation value from the table.

26. A method according to claim 25 , wherein:

calculating a position error value in step (iii) comprises calculating the difference between the first and second measured phase values;

calculating a compensation value in step (iv) comprises multiplying the position error value by 2π/S, where S is a step size equal to the phase interval between adjacent correction points of the scale; and

in step (v), the corrected estimate of the scale position at a given correction point is produced (1) when the scale position is moving away from a home position, by incrementing an immediately preceding estimate of the scale position by a value equal to the sum of one least significant bit plus the compensation value, and (2) when the scale position is moving towards the home position, by decrementing the immediately preceding estimate of the scale position by a value equal to the sum of one least significant bit plus the compensation value.

27. A method according to claim 25 , wherein:

calculating a position error value in step (iii) comprises calculating the difference between the first and second measured phase values;

calculating a compensation value in step (iv) comprises multiplying the position error value by (2π/S)/T, where S is a step size equal to the phase interval between adjacent correction points of the scale, and T is the number of least significant bits of encoder resolution between adjacent correction points; and

in step (v), the corrected estimate of the scale position at each least significant bit (LSB) is produced (1) when the scale position is moving away from a home position, by incrementing an immediately preceding estimate of the scale position by a value equal to the sum of one least significant bit plus the compensation value, and (2) when the scale position is moving towards the home position, by decrementing the immediately preceding estimate of the scale position by a value equal to the sum of one least significant bit plus the compensation value.

28. A method according to claim 25 , wherein:

calculating a position error value in step (iii) comprises calculating the difference between the first and second measured phase values;

the compensation value calculated in step (iv) is equal to the sum of (the position error value and 2π) divided by 2π; and

in step (v), the corrected estimate of the scale position at each least significant bit (LSB) is produced (1) when the scale position is moving away from a home position, by incrementing an immediately preceding estimate of the scale position by a value equal to the product of one least significant bit and the compensation value, and (2) when the scale position is moving towards the home position, by decrementing the immediately preceding estimate of the scale position by a value equal to the product of one least significant bit and the compensation value.

29. A method according to claim 21 , wherein steps (ii)–(iv) are performed during a calibration operation preceding normal operation of the encoder, and the compensation value calculated in step (iv) for a given correction point is a cumulative error value calculated by summing the position error values from all correction points between a home position and the given correction point.

30. A method according to claim 29 , wherein the calibration operation produces a table of corrected estimates of the scale position as a function of measured positions of the scale position, and further comprising, during normal operation at each of a set of measured scale positions, retrieving the corresponding corrected estimate of the scale position from the table.

31. A method according to claim 29 , wherein the calibration operation produces data representing a function Z which is a curve-fit approximation of corrected estimates of the scale position as a function of measured positions of the scale position, and further comprising, during normal operation at each of a set of measured scale positions, multiplying the measured scale position by a corresponding value of Z.

32. A method according to claim 21 , further comprising performing a calibration operation preceding normal encoder operation to produce data representing a function Z which is a curve-fit approximation position error values as a function of measured positions of the scale position, and further comprising, during normal operation at each of a set of measured scale positions:

producing a re-created position error value by multiplying the measured scale position by a corresponding value of Z;

in step (iv), calculating the compensation value by multiplying the re-created position error value by 2π/S, where S is a step size equal to the phase interval between adjacent correction points of the scale; and

in step (v), producing the corrected estimate of the scale position at a given correction point (1) when the scale position is moving away from a home position, by incrementing an immediately preceding estimate of the scale position by a value equal to the sum of one least significant bit plus the compensation value, and (2) when the scale position is moving towards the home position, by decrementing the immediately preceding estimate of the scale position by a value equal to the sum of one least significant bit plus the compensation value.

33. A method according to claim 21 , further comprising performing a calibration operation preceding normal encoder operation to produce data representing a function Z which is a curve-fit approximation position error values as a function of measured positions of the scale position, and further comprising, during normal operation at each of a set of measured scale positions:

producing a re-created position error value by multiplying the measured scale position by a corresponding value of Z;

in step (iv), calculating the compensation value by multiplying the re-created position error value by the sum of (the position error value and 2π) divided by 2π; and

in step (v), producing the corrected estimate of the scale position at each least significant bit (LSB) (1) when the scale position is moving away from a home position, by incrementing an immediately preceding estimate of the scale position by a value equal to the product of one least significant bit and the compensation value, and (2) when the scale position is moving towards the home position, by decrementing the immediately preceding estimate of the scale position by a value equal to the product of one least significant bit and the compensation value.

34. A method according to claim 21 , wherein each of the detector sections is a polyphase detector operative to detect respective intra-period phase components of the spatially periodic pattern, and wherein deriving each of the first and second measured phase values for the respective detector section includes performing a trigonometric calculation based on the respective intra-period phase components.

35. A method according to claim 34 , wherein the number of intra-period phase components detected by each of the detector sections is four.

36. A method according to claim 34 , wherein the detector sections are nominally separated by one or more whole periods of the spatially periodic pattern.