Displacement calculation device and displacement calculation method

Abstract

To provide a displacement calculation device capable of correcting errors that occur in a large period exceeding one period of a displacement detection signal.SOLUTION: A displacement calculation device 30 calculates a displacement from two or more displacement detection signals having different phases. The displacement calculation device 30 includes a detected displacement calculation unit 32 that calculates a detected displacement based on the displacement detection signal, a signal analysis unit 33 that calculates an amplitude error, an error of the vibration center, and a phase error between the displacement detection signal and a reference signal, a periodic displacement error calculation unit 34 that calculates a periodic displacement error and a period thereof based on the errors calculated by the signal analysis unit 33, and a displacement correction unit 35 that corrects the detected displacement calculated by the detected displacement calculation unit 32 based on the displacement error and a period thereof calculated by the periodic displacement error calculation unit 34, and outputs the corrected calibrated displacement.SELECTED DRAWING: Figure 4

Description

[Technical Field]

[0001] The present invention relates to a displacement calculation device and a displacement calculation method for calculating a displacement based on a displacement detection signal output from a displacement detection sensor that constitutes a displacement detection device such as a linear encoder or a rotary encoder. [Background technology]

[0002] Conventionally, linear encoders and rotary encoders have been known as devices for detecting displacement, and known encoder methods for detecting displacement include, for example, optical and magnetic types. In optical encoders, an interference signal whose intensity changes according to the displacement of a diffraction grating scale or the like is received by a light-receiving element of a displacement detection sensor and photoelectrically converted, and the converted sinusoidal electrical signals with periodically changing A and B phases are output from the displacement detection sensor. In magnetic encoders, a magnetic force that changes according to the displacement of a magnetic scale is detected by a magnetic sensor, and a signal related to the detected magnetic force is output from a displacement detection sensor including a magnetic sensor as a sinusoidal electrical signal with periodically changing A and B phases.

[0003] Generally, the B phase of the electrical signal (displacement detection signal) output from these displacement detection sensors is shifted in phase by 1 / 4 cycle, or 90°, from the A phase. When detecting displacement, whether the relative direction of movement between the displacement detection sensor and the scale is positive or negative can be determined by whether the B phase is leading or lagging behind the A phase.

[0004] The displacement detection signals output from these displacement detection sensors are input to a displacement calculation device, where they are generally converted into analog-to-digital (A / D) signals, and interpolated for phase A and phase B of the displacement detection signals, before being output as information relating to the displacement of the scale.

[0005] In this displacement calculation device, for example, the digitally converted A-phase and B-phase displacement detection signals are expanded into a Lissajous waveform on a lookup table, which represents A-phase as the X-axis and B-phase as the Y-axis for each sampling frequency.The radius and angle of the Lissajous waveform are then calculated from the Lissajous waveform on the lookup table.One revolution of the Lissajous waveform corresponds to one period of the A-phase and B-phase displacement detection signals output from the displacement detection sensor, and the displacement per unit time is calculated by determining the change in angle per sampling frequency.

[0006] Incidentally, the Lissajous waveform created on the lookup table may not be a perfect circle but may have a distorted shape depending on the conditions of the displacement detection sensor, scale, etc. If the Lissajous waveform matches an ideal Lissajous waveform (ideal Lissajous waveform), which is a perfect circle, no periodic detection error occurs. However, if the Lissajous waveform is distorted, the signal input from the displacement detection sensor will contain periodic errors.

[0007] This error, called an interpolation error, is relatively stable and occurs every cycle of the displacement detection signal output from the displacement detection sensor. Therefore, by tracing the trajectory of the Lissajous waveform for one cycle, the interpolation error can be corrected for the next cycle, making correction relatively easy. A known method for correcting such an interpolation error is disclosed in Japanese Patent Laid-Open Publication No. 8-122097. Japanese Patent Laid-Open Publication No. 2022-93252 also discloses a method for correcting the radius fluctuation waveform of the Lissajous waveform using a correction value averaged over the most recent cycle. [Prior art documents] [Patent documents]

[0008] [Patent Document 1] Japanese Patent Application Publication No. 8-122097 [Patent Document 2] Japanese Patent Publication No. 2022-93252 Summary of the Invention [Problem to be solved by the invention]

[0009] However, depending on the state of the displacement detection sensor or the scale, the shape of the Lissajous waveform may not be constant, and the shape of the Lissajous waveform may change at a period longer than one period of the displacement detection signal output from the displacement detection sensor -- in other words, errors may occur at a period longer than one period. For example, the shape of the Lissajous waveform may change periodically due to pitching, rolling, or yawing of the movable stage to which the scale is attached, and may also change periodically due to distortion of the scale surface or noise generated during scale recording. In these cases, the shape of the Lissajous waveform changes at a period longer than one period of the displacement detection signal, and at a period that is independent of the period of the displacement detection signal.

[0010] For this reason, the above-mentioned conventional correction method, which corrects the Lissajous waveform (or displacement data) for one period of the displacement detection signal output from the displacement detection sensor, was unable to sufficiently correct errors that fluctuated over periods exceeding one period of the displacement detection signal. In other words, in this case, the difference between the Lissajous waveform based on the displacement detection signal output from the displacement detection sensor and the ideal Lissajous waveform, which is a perfect circle, constantly changes, making it impossible to converge the residual error of the correction.

[0011] The present invention has been made in consideration of the above-mentioned circumstances, and an object of the present invention is to provide a displacement calculation device that can correct errors that fluctuate in a period that exceeds one period of the displacement detection signal and that is independent of the period of the displacement detection signal. [Means for solving the problem]

[0012] In order to solve the above problem, the present invention provides a displacement calculation device including a scale and a displacement detection sensor that detects a relative displacement between the scale and the scale, a detected displacement calculation unit that calculates a displacement based on two or more displacement detection signals (periodic signals) having different phases output from the displacement detection sensor; a signal analysis unit that calculates an amplitude difference, a center position difference, and a phase difference between the displacement detection signal and a reference signal corresponding to the displacement detection signal; a periodic displacement error calculation unit that calculates, based on the difference calculated by the signal analysis unit, (i) a first displacement difference signal that fluctuates with a period equal to or shorter than the period of the displacement detection signal, and (ii) a second displacement difference signal that fluctuates with a period that exceeds the period of the displacement detection signal and that is at least independent of the period of the displacement detection signal; and a displacement correction unit that corrects the displacement calculated by the detected displacement calculation unit based on the first displacement difference signal and the second displacement difference signal calculated by the periodic displacement error calculation unit, and outputs a corrected calibration displacement.

[0013] The present invention also provides a method for detecting a displacement relative to a scale, comprising: a detected displacement calculation step of calculating a detected displacement based on two or more displacement detection signals (periodic signals) having different phases output from a displacement detection sensor that detects a displacement relative to the scale; a signal analysis step of calculating an amplitude difference, a center position difference, and a phase difference between the displacement detection signal and a reference signal corresponding to the displacement detection signal; a periodic displacement error calculation step of calculating, based on the difference calculated in the signal analysis step, (i) a first displacement difference signal that fluctuates with a period equal to or shorter than the period of the displacement detection signal, and (ii) a second displacement difference signal that fluctuates with a period that exceeds the period of the displacement detection signal and that is at least independent of the period of the displacement detection signal; and a displacement correction step of correcting the displacement calculated by the detected displacement calculation step based on the first displacement difference signal and the second displacement difference signal calculated by the periodic displacement error calculation step, and outputting a corrected calibration displacement.

[0014] According to this aspect of the displacement calculation device (displacement calculation method), the detected displacement (detected displacement) is calculated by the detected displacement calculation unit (detected displacement calculation step) based on two or more displacement detection signals (periodic signals) with different phases. Furthermore, the signal analysis unit (signal analysis step) calculates the amplitude difference (amplitude error), center position difference (vibration center error) (offset), and phase difference (phase error) between the displacement detection signal and its corresponding reference signal. These differences (errors) are error components contained in the displacement detection signal.

[0015] Then, in the periodic displacement error calculation unit (periodic displacement error calculation process), a periodically fluctuating displacement difference signal (corresponding to the displacement error and its period) is calculated based on the difference (error) calculated by the signal analysis unit (signal analysis process), and in the displacement correction unit (displacement correction process), the detected displacement calculated by the detected displacement calculation unit (detected displacement calculation process) is corrected based on the calculated displacement difference signal, and a corrected calibrated displacement is output.

[0016] The periodic displacement difference signal (corresponding to the displacement error and its period) calculated in the periodic displacement error calculation unit (periodic displacement error calculation step) includes a first displacement difference signal (corresponding to the first displacement error and its period) that fluctuates with a period equal to or shorter than the period (one period) of the displacement detection signal, and a second displacement difference signal (corresponding to the second displacement error and its period) that fluctuates with a period that exceeds the period of the displacement detection signal and is at least independent of the period of the displacement detection signal. Therefore, when a displacement error having a period equal to or shorter than the period of the displacement detection signal and a displacement error having a period that exceeds the period of the displacement detection signal and is independent of the period of the displacement detection signal occur, the displacement corrector (displacement correcting step) corrects the displacement calculated by the detected displacement calculation unit (detected displacement calculation step) for these errors.

[0017] As described above, the displacement calculation device (displacement calculation method) according to the present invention can correct both displacement errors having a period equal to or shorter than the period of the displacement detection signal and displacement errors having a period exceeding the period of the displacement detection signal and independent of the period of the displacement detection signal. Therefore, it is possible to accurately (precisely) correct the detected displacement calculated based on the displacement detection signal and to cause the correction residual to converge.

[0018] As described above, displacement errors include errors caused by pitching, rolling, and yawing of the movable stage to which the scale is attached, distortion of the scale surface, and errors caused by noise generated during scale recording, and these errors occur with periods that exceed the period of the displacement detection signal and are independent of the period of the displacement detection signal. According to the present invention, such displacement errors can be corrected accurately (with high precision), and the residual error of the correction can be converged.

[0019] The period that exceeds the period of the displacement detection signal and is at least independent of the period of the displacement detection signal includes a period defined as follows: A period that exceeds the period (one period) of the displacement detection signal, excluding periods that are integer multiples of the period of the displacement detection signal.

[0020] The period that exceeds the period of the displacement detection signal and is independent of the period is preferably "a period that exceeds the period of the displacement detection signal but is less than 100 times the period of the displacement detection signal" or "a period that exceeds the period of the displacement detection signal but is less than 1 / 10 of the effective length of the scale." The effective length of the scale refers to the length over which the displacement detection sensor can acquire a displacement detection signal (periodic signal) from the scale, and refers to the length of the scale if the scale is linear, or the length of one circumference if the scale is cylindrical. Since the present invention detects errors that fluctuate (change) periodically and their periods, it is empirically determined that the range of the effective length preferably includes a period that is at least 10 times the period of the displacement detection signal, and errors with periods less than 100 times the period of the displacement detection signal can be detected.

[0021] the periodic displacement error calculation unit (periodic displacement error calculation step) comprises an in-period error calculation unit (in-period error calculation process) that calculates a first displacement difference signal (corresponding to a first displacement error and its period) that fluctuates with a period equal to or shorter than the period of the displacement detection signal, and an out-of-period error calculation unit (out-of-period error calculation process) that calculates a second displacement difference signal (corresponding to a second displacement error and its period) that fluctuates with a period that exceeds the period of the displacement detection signal and is at least independent of the period of the displacement detection signal, The displacement correction unit (displacement correction process) may be configured to correct the detected displacement calculated by the detected displacement calculation unit (detected displacement calculation process) based on a first displacement difference signal calculated by an in-period error calculation unit (in-period error calculation process) of the periodic displacement error calculation unit (periodic displacement error calculation process) and a second displacement difference signal calculated by the out-of-periodic error calculation unit (out-of-periodic error calculation process).

[0022] The displacement calculation device may further include a storage unit that stores data relating to the displacement difference signal (corresponding to the displacement error and its period) calculated by the periodic displacement error calculation unit, and the periodic displacement error calculation unit may be configured to store the calculated displacement error and the data relating to its period in the storage unit.

[0023] The present invention also provides a displacement calculation device that calculates a displacement from a displacement detection signal (periodic signal) that is output from a displacement detection sensor that detects a displacement relative to a scale and that periodically varies in accordance with the displacement, comprising: a signal analysis unit that calculates an amplitude difference (amplitude error), a center position difference (vibration center error), and a phase difference (phase error) between two or more of the displacement detection signals having different phases and a reference signal corresponding to the displacement detection signals; a periodic displacement error calculation unit that calculates, based on the difference (error) calculated by the signal analysis unit, a first displacement difference signal (corresponding to a first displacement error and its period) that fluctuates in a period equal to or shorter than the period (one period) of the displacement detection signal, and a second displacement difference signal (corresponding to a second displacement error and its period) that fluctuates in a period that exceeds the period of the displacement detection signal and is at least independent of the period of the displacement detection signal; a signal correction unit that corrects the displacement detection signal based on a first displacement difference signal that fluctuates with a period equal to or shorter than the period of the displacement detection signal calculated by the periodic displacement error calculation unit, and a second displacement difference signal that fluctuates with a period that exceeds the period of the displacement detection signal and is at least independent of the period of the displacement detection signal; a calibration displacement calculation unit that calculates a calibration displacement based on the displacement detection signal corrected by the signal correction unit, and outputs the calculated calibration displacement.

[0024] The present invention also provides a method for calculating a displacement from a displacement detection signal (periodic signal) that is output from a displacement detection sensor that detects a displacement relative to a scale and that periodically varies in accordance with the displacement, the method comprising: a signal analysis step of calculating an amplitude difference (amplitude error), a center position difference (vibration center error), and a phase difference (phase error) between two or more of the displacement detection signals having different phases and a reference signal corresponding to the displacement detection signals; a periodic displacement error calculation step of calculating, based on the difference (error) calculated by the signal analysis step, a first displacement difference signal (corresponding to a first displacement error and its period) that fluctuates in a period equal to or shorter than the period (one period) of the displacement detection signal, and a second displacement difference signal (corresponding to a second displacement error and its period) that fluctuates in a period that exceeds the period of the displacement detection signal and is at least independent of the period of the displacement detection signal; a signal correction step of correcting the periodic signal based on a first displacement difference signal that fluctuates with a period equal to or shorter than the period of the displacement detection signal calculated in the periodic displacement error calculation step, and a second displacement difference signal that fluctuates with a period that exceeds the period of the displacement detection signal and is at least independent of the period of the displacement detection signal; a calibration displacement calculation step of calculating a calibration displacement based on the displacement detection signal corrected in the signal correction step and outputting the calculated calibration displacement; The present invention relates to a displacement calculation method including the steps of:

[0025] According to this aspect of the displacement calculation device (displacement calculation method), the signal analysis unit (signal analysis step) calculates the amplitude error, vibration center error (offset), and phase error between the displacement detection signal and the corresponding reference signal. Furthermore, the periodic displacement error calculation unit (periodic displacement error calculation step) calculates a periodic displacement difference signal (corresponding to the displacement error and its period) based on the errors calculated by the signal analysis unit (signal analysis step), and the signal correction unit (signal correction step) corrects the displacement detection signal based on the calculated displacement difference signal. Then, the calibrated displacement calculation unit (calibrated displacement calculation step) calculates a calibrated displacement based on the displacement detection signal corrected by the signal correction unit (signal correction step), and outputs the calculated calibrated displacement.

[0026] The periodic displacement error calculated by the periodic displacement error calculation unit (periodic displacement error calculation step) includes a displacement error that fluctuates with a period equal to or less than the period (one period) of the displacement detection signal, and a displacement error that fluctuates with a period that exceeds the period of the displacement detection signal and is at least independent of the period of the displacement detection signal. Therefore, when a displacement error having a period equal to or less than the period of the displacement detection signal and a displacement error having a period that exceeds the period of the displacement detection signal and is independent of the period of the displacement detection signal occur, the signal correction unit (signal correction step) corrects each displacement detection signal for these error amounts. Then, a calibrated displacement is calculated based on the displacement detection signals corrected in this way.

[0027] In this way, according to this aspect of the displacement calculation device (displacement calculation method), it is possible to correct both the displacement error having a period equal to or shorter than one period of the displacement detection signal and the displacement error having a period exceeding one period of the displacement detection signal and independent of the period of the periodic signal. Therefore, it is possible to accurately (precisely) correct the detected displacement calculated based on the periodic signal and to cause the correction residual to converge.

[0028] In each of the above aspects, the periodic displacement error calculation unit (periodic displacement error calculation step) includes an in-period error calculation unit (in-period error calculation process) that calculates a first displacement difference signal (corresponding to a first displacement error and its period) that fluctuates with a period equal to or shorter than the period of the displacement detection signal, and an out-of-period error calculation unit (out-of-period error calculation process) that calculates a second displacement difference signal (corresponding to a second displacement error and its period) that occurs with a period that exceeds the period of the displacement detection signal and is at least independent of the period of the displacement detection signal, The signal correction unit (signal correction step) may be configured to correct the displacement detection signal based on a first displacement difference signal calculated by an in-period error calculation unit (in-period error calculation process) of the periodic displacement error calculation unit (periodic displacement error calculation step) and a second displacement difference signal calculated by the out-of-periodic error calculation unit (out-of-periodic error calculation process).

[0029] The displacement calculation device may further include a storage unit that stores data relating to the displacement difference signal (corresponding to the displacement error and its period) calculated by the periodic displacement error calculation unit, and the periodic displacement error calculation unit may be configured to store the data relating to the calculated displacement difference signal (displacement error and its period) in the storage unit.

[0030] The present invention also provides a displacement calculation device for calculating a displacement from signals corresponding to two or more phases including at least a first phase and a second phase different from the first phase, the device comprising: a displacement calculation unit that calculates a first displacement based on signals corresponding to the first phase and the second phase; a signal analysis unit that detects a period associated with a locus of the center of the Lissajous waveform from signals corresponding to the first phase and the second phase, and analyzes the detected period of the signal; a displacement error calculation unit that calculates a displacement error corresponding to the periodicity associated with the center locus of the Lissajous waveform of the signal for the period based on the analysis by the signal analysis unit; and a displacement correction unit that corrects the displacement calculated by the displacement calculation unit based on the displacement error calculated by the displacement error calculation unit and outputs the corrected corrected displacement (calibrated displacement).

[0031] In this displacement calculation device, the signal analysis unit analyzes a signal of one or more periods, and the displacement error calculation unit calculates both a displacement error having a period equal to or shorter than one period of the signal and a displacement error having a period longer than one period of the signal and independent of the period of the periodic signal.Based on these errors, the displacement correction unit can correct the displacement calculated by the displacement calculation unit.As a result, the detected displacement calculated based on the signal can be corrected accurately (with high precision), and the correction residual can be converged. [Effects of the Invention]

[0032] The displacement calculation device and displacement calculation method according to the present invention can correct both the displacement error that fluctuates in a period equal to or less than one period of the displacement detection signal and the displacement error that fluctuates in a period that exceeds one period of the displacement detection signal and is independent of the period of the displacement detection signal. This makes it possible to correct the displacement calculated based on the displacement detection signal accurately (with high precision) and to cause the correction residual to converge. [Brief explanation of the drawings]

[0033] [Figure 1] 1 is an explanatory diagram showing a schematic configuration of a displacement detection device according to a first embodiment of the present invention. [Figure 2] FIG. 2 is an explanatory diagram showing a schematic configuration of a light receiving section according to the first embodiment. [Figure 3] FIG. 2 is an explanatory diagram showing a schematic configuration of a light receiving section and a differential amplifier according to the first embodiment. [Figure 4] 1 is a block diagram showing a schematic configuration of a displacement calculation device according to a first embodiment. [Figure 5] 4 is an explanatory diagram showing a displacement detection signal A-phase and a displacement detection signal B-phase output from the displacement detection head. FIG. [Figure 6] 5 is an explanatory diagram showing the relationship between a displacement detection signal and a Lissajous waveform. FIG. [Figure 7] FIG. 10 is an explanatory diagram showing the relationship between a Lissajous waveform containing an error and an ideal Lissajous waveform containing no error. [Figure 8] 5 is an explanatory diagram showing an example of a displacement detection signal output from a detection head. FIG. [Figure 9] FIG. 3 is an explanatory diagram for explaining processing in a signal analysis unit and a cyclic error calculation unit according to the first embodiment. [Figure 10] FIG. 10 is a block diagram showing a schematic configuration of a displacement calculation device according to a second embodiment of the present invention. [Figure 11] FIG. 10 is a block diagram showing a schematic configuration of a displacement calculation device according to a third embodiment of the present invention. [Figure 12] FIG. 10 is a block diagram showing a schematic configuration of a displacement calculation device according to a fourth embodiment of the present invention. [Figure 13] FIG. 10 is an explanatory diagram for explaining processing in a signal analysis unit and a periodic error calculation unit according to the fourth embodiment. [Figure 14] FIG. 10 is a block diagram showing a schematic configuration of a displacement calculation device according to a fifth embodiment of the present invention. [Figure 15] FIG. 10 is a block diagram showing a schematic configuration of a displacement calculation device according to a sixth embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0034] Hereinafter, specific embodiments of the present invention will be described with reference to the drawings.

[0035] 1. First embodiment First, a first embodiment will be described. As shown in Fig. 1, a displacement detection device 1 according to the first embodiment is configured to include at least a scale 2, a detection head (displacement detection sensor) 3, and a displacement calculation device 30. The displacement detection device 1 includes an encoder, such as a linear encoder or a rotary encoder. In this example, an optical encoder is used as the encoder system, but this is not limitative and a magnetic encoder may also be used. In this example, the scale 2 and detection head (displacement detection sensor) are separate from the displacement calculation device 30, but the displacement calculation device 30 may also be configured to include the scale 2 and detection head 3.

[0036] The scale 2 is a linear scale on which multiple diffraction gratings are formed, and is fixed to, for example, an immovable structure. The detection head 3 is disposed on a movable body such as a movable stage so as to face the scale 2, and detects displacement relative to the scale 2.

[0037] Specifically, as shown in Fig. 1, the detection head 3 of this example is composed of a light source 4 that emits laser light, which is coherent light, a polarizing beam splitter 5, two mirrors 6 and 7, two mirrors 8 and 9, a light receiving unit 10, and a differential amplifier 21. In Fig. 1, the light source 4 emits laser light obliquely downward at an angle of 45°, and the polarizing beam splitter 5 is located on the optical path of the laser light emitted from the light source 4 and splits the laser light into two laser beams, one of which (first laser beam) is transmitted as is and the other laser beam (second laser beam) passes through an optical path reflected by 90°.

[0038] A mirror 6 is arranged on the optical path of the first laser beam so as to reflect it at an angle of 90°, and similarly, a mirror 7 is arranged on the optical path of the second laser beam so as to reflect it at an angle of 90°, and the first laser beam reflected by mirror 6 and the second laser beam reflected by mirror 7 each enter scale 2. The first laser beam diffracted by scale 2 is then reflected by mirror 8 arranged on its optical path so as to return along the same optical path, and similarly, the second laser beam is reflected by mirror 9 arranged on its optical path so as to return along the same optical path. The first laser beam then enters polarizing beam splitter 5 via mirror 6, while the second laser beam enters polarizing beam splitter 5 via mirror 7, and these first and second laser beams are superimposed again by polarizing beam splitter 5 and enter light receiving unit 10.

[0039] The intensity of the light reflected by the scale 2, i.e., the diffracted light, varies depending on the positional relationship between the diffraction grating provided on the scale 2 and the incident laser light. For example, when the irradiation position of the incident light is aligned with the diffraction grating, the intensity of the diffracted light is highest. As the irradiation position of the incident light moves away from the diffraction grating, the intensity of the diffracted light gradually decreases, and when the irradiation position of the incident light is completely displaced from the diffraction grating, the intensity of the diffracted light is lowest. Then, as the irradiation position of the incident light moves closer to the diffraction grating again, the intensity of the diffracted light gradually increases. Therefore, when the detection head 3 moves relatively along the scale 2, the irradiation position of the incident light and the position of the diffraction grating move relatively, and the intensity of the diffracted light received by the detection head 3 varies sinusoidally, i.e., periodically.

[0040] 2, the light receiving section 10 is composed of a phase plate 11, a half mirror 12, a first light receiving section 13, and a second light receiving section 17. The first light receiving section 13 is composed of a polarizing beam splitter 14, a first light receiving element 15, and a second light receiving element 16, and the second light receiving section 17 is composed of a polarizing beam splitter 18, a third light receiving element 19, and a fourth light receiving element 20.

[0041] The phase plate 11, half mirror 12, and second light receiving unit 17 are arranged in sequence on the straight optical path of the laser light incident on the light receiving unit 10, and after passing through the phase plate 11, the incident laser light is split by the half mirror 12 into two laser lights: laser light that is reflected at 90 degrees (reflected laser light) and laser light that is transmitted and travels straight (transmitted laser light).The reflected laser light is incident on the first light receiving unit 13 provided on the optical path, and the transmitted laser light is incident on the second light receiving unit 17.

[0042] The reflected laser light incident on the first light-receiving unit 13 is further split into two optical paths by the polarizing beam splitter 14; one is reflected 90° and received as an interference signal by the first light-receiving element 15, and the other is transmitted as is and received as an interference signal by the second light-receiving element 16. Similarly, the transmitted laser light incident on the second light-receiving unit 17 is split into two optical paths by the polarizing beam splitter 18; one is reflected 90° and received as an interference signal by the third light-receiving element 19, and the other is transmitted as is and received as an interference signal by the fourth light-receiving element 20. The first light-receiving element 15, the second light-receiving element 16, the third light-receiving element 19, and the fourth light-receiving element 20 then photoelectrically convert the received interference signal and output it as an electrical signal (voltage signal). The electrical signals output from the first light-receiving element 15, the second light-receiving element 16, the third light-receiving element 19, and the fourth light-receiving element 20 are output to a differential amplifier 21. As described above, the intensity of the reflected laser light (interference signal) incident on the first light receiving unit 13 and the intensity of the transmitted laser light (interference signal) incident on the second light receiving unit 17 each fluctuate sinusoidally (periodically) due to the relative movement between the scale 2 and the detection head 3.

[0043] Furthermore, the third light receiving element 19 and the fourth light receiving element 20 are attached with their polarization axes rotated 45° with respect to the first light receiving element 15 and the second light receiving element 16, and therefore the interference signals incident on the first light receiving element 15 and the second light receiving element 16 are shifted in phase by 90° with respect to the interference signals incident on the third light receiving element 19 and the fourth light receiving element 20. Therefore, the displacement detection signals output from the first light receiving element 15 and the second light receiving element 16 are shifted in phase by 90° with respect to the displacement detection signals output from the third light receiving element 19 and the fourth light receiving element 20.

[0044] As shown in FIG. 3, the differential amplifier 21 is composed of a first differential amplifier 22 and a second differential amplifier 23. The first differential amplifier 22 outputs a displacement detection signal (displacement detection signal A-phase) as an A-phase (first phase) which is an amplified electrical signal (voltage signal) based on the electrical signals output from the first light-receiving element 15 and the second light-receiving element 16, and the second differential amplifier 23 outputs a displacement detection signal (displacement detection signal B-phase) as an amplified electrical signal (voltage signal) based on the electrical signals output from the third light-receiving element 19 and the fourth light-receiving element 20.

[0045] The displacement detection signals A and B are signals (periodic signals) that exhibit sine waves that change periodically depending on the intensity of the interference signal, i.e., depending on the relative displacement between the scale 2 and the detection head 3. As can be seen from the above explanation, the displacement detection signal B is out of phase with the displacement detection signal A by 90°, in other words, by ¼ of a period. In general, the displacement detection signal A is treated as a sine signal, and the displacement detection signal B is treated as a cosine signal (see FIG. 5). Using the displacement detection signals A and B, which are out of phase with each other by 90°, it is possible to determine whether the displacement detection signal B leads or lags the displacement detection signal A, thereby determining whether the direction of the relative displacement between the scale 2 and the detection head 3 is positive or negative. The period (one period) of the displacement detection signals A and B corresponds to one division of the scale 2. Incidentally, in the case of the optical type in this example, the period (one period) of the displacement detection signals A and B phases is several hundred nm, and therefore one division of the scale 2 is several hundred nm.

[0046] The displacement detection signals A and B phases output from the detection head 3 in the manner described above are input to the displacement calculation device 30, which calculates the relative displacement (first displacement) between the scale 2 and the detection head 3.

[0047] 4, the displacement calculation device 30 includes various processing units such as an A / D conversion unit 31, a detected displacement calculation unit 32, a signal analysis unit 33, a periodic displacement error calculation unit 34, and a displacement correction unit 35. Each processing unit is synchronized at a high-speed sampling frequency.

[0048] The A / D conversion unit 31 converts the displacement detection signals A and B as analog signals input from the detection head 3 into digital signals, performs interpolation processing, and then transmits the displacement detection signals A and B as digital signals to the detected displacement calculation unit 32 and the signal analysis unit 33.

[0049] The detected displacement calculation unit 32 develops the A-phase and B-phase displacement detection signals into a Lissajous waveform on a lookup table, which represents the A-phase displacement detection signal on the X-axis and the B-phase displacement detection signal on the Y-axis for each sampling frequency, as shown in FIG. 6. Then, from the Lissajous waveform on this lookup table, it calculates the radius R and angle θ of the Lissajous waveform. One revolution of this Lissajous waveform corresponds to one period of the A-phase and B-phase displacement detection signals, and by determining the angle change Δθ [° or rad] per sampling frequency (unit time), it is possible to calculate the displacement [pm or nm] per unit time. In other words, it is possible to calculate the relative displacement between the scale 2 and the detection head 3 for one division of the scale 2.

[0050] For example, in FIG. 6, if the number of samples is n (a natural number) and i=1 to n, then θ i =tan -1 (X i / Y i ) and R i =(X i 2 +Y i 2 ) 1 / 2 Therefore, If the length of one division on scale 2 is L, L=2π×R Here, R is the average radius of one revolution of the Lissajous waveform. Δθ in the sampling interval i [° or rad] is Δθ i =θ i -θ i-1 =tan -1 (X i / Y i )-tan -1 (X i-1 / Y i-1 ) This becomes: Then, the displacement in the sampling interval is Δd i If you specify [pm or nm], Displacement Δd i =(Δθ i / 2π)×R i This becomes:

[0051] In this way, the detected displacement calculation section 32 calculates the relative displacement between the scale 2 and the detection head 3 from the A-phase and B-phase displacement detection signals, for example.

[0052] The signal analysis unit 33 is a processing unit that calculates the amplitude error (amplitude difference), vibration center error (difference in center position), and phase error (phase difference) between the A-phase and B-phase displacement detection signals input from the A / D conversion unit 31 and an ideal error-free reference signal. Specifically, the signal analysis unit 33 calculates, from the difference between a perfectly circular ideal Lissajous waveform drawn by expanding the reference signal on a lookup table and an actual Lissajous waveform (real Lissajous waveform) drawn by expanding the A-phase and B-phase displacement detection signals on the lookup table, the amplitude error of the real Lissajous waveform relative to the ideal Lissajous waveform, an offset (corresponding to the difference between the vibration center of the reference signal and the vibration center of the displacement detection signal) which is the difference between the center of the ideal Lissajous waveform and the center of the real Lissajous waveform, and a phase difference for the A-phase and B-phase as residuals. This error is an error component contained in the A-phase and B-phase displacement detection signals and includes multiple error components that fluctuate at a predetermined period.

[0053] Then, arbitrary distance data (displacement, data corresponding to Δθ) is stored as three residual data for the displacement. The period for acquiring this arbitrary displacement is desirably sufficiently longer than at least the signal period of the A-phase and B-phase displacement detection signals, and can be, for example, 100 periods. On the other hand, the interval for acquiring one data item is desirably sufficiently shorter than the signal period of the A-phase and B-phase displacement detection signals, and is desirably, for example, about 1 / 100 of a period. From the above, for example, 100 × 100 × 3 (= 30,000) points of residual data are acquired, and the acquired residual data is transmitted to the periodic displacement error calculation unit 34.

[0054] The periodic displacement error calculation unit 34 extracts only residual data that has periodicity, in other words, that fluctuates periodically, from the residual data acquired by the signal analysis unit 33, for example by frequency analysis, and converts each extracted residual data with periodicity into angle data to calculate an error (displacement error) for the angle data indicating displacement, as well as its fluctuation period. This periodic displacement error is an error that occurs in response to the relative displacement between the scale 2 and the detection head 3, and includes displacement errors that fluctuate within one period of the A-phase and B-phase displacement detection signals, and displacement errors that fluctuate with periods exceeding one period (including periods independent of the A-phase and B-phase displacement detection signals). The displacement error for each period and its fluctuation period (equivalent to a displacement difference signal) are calculated and transmitted to the displacement correction unit 35.

[0055] For example, when displacement detection signals A and B as shown in Fig. 8 are input to the signal analysis unit 33, the signal analysis unit 33 calculates residual data as shown in Fig. 9(a) and (b), for example. Fig. 9(a) shows residual data calculated for offset, and Fig. 9(b) shows residual data calculated for amplitude. In both cases, the horizontal axis represents the relative displacement between the scale 2 and the detection head 3. Although not specifically shown, residual data related to phase is also calculated by the signal analysis unit 33 in a similar manner.

[0056] Then, as described above, the residual data acquired by the signal analysis unit 33 is processed by the periodic displacement error calculation unit 34, and only the residual data having periodicity is extracted. By converting the extracted residual data having periodicity into angular data, a displacement error (displacement difference signal) is calculated. An example of the displacement error calculated in this way is shown in FIGS. 9(c) and (d). FIG. 9(c) shows the calculated displacement error that varies with a period exceeding one period of the displacement detection signals A-phase and B-phase (including a period independent of the periods of the displacement detection signals A-phase and B-phase), and FIG. 9(d) similarly shows the calculated displacement error that varies with a period exceeding one period of the displacement detection signals A-phase and B-phase having a different period from that in FIG. 9(c) (including a period independent of the periods of the displacement detection signals A-phase and B-phase). In both cases, the horizontal axis represents the relative displacement between the scale 2 and the detection head 3.

[0057] Also, the displacement error can be calculated, for example, from the following relational expressions. That is, an ideal reference signal can be expressed as R·sin(md + θ) and R·cos(md + θ) using the distance d, phase θ, amplitude R, and wave number m. Here, the wave number m can be expressed as m = 2π / L using the period L corresponding to the length of one scale division of the scale 2. Assume that noise represented by r·sin(kd + φ) and r·cos(kd + φ), which has a phase φ, amplitude r, and wave number k, is added as a noise signal that causes a periodically varying displacement error. However, the amplitude of the displacement error is sufficiently smaller than that of the reference signal (r << R), and the wave number is smaller than that of the reference signal (0 < k < m). At this time, the displacement correction amount for correcting the displacement error component due to this noise is approximately given by the following equation. Correction amount = (1 / m)·(r / R)·sin{(m - k)d + (θ - φ)} And, in practice, the correction amount can be calculated using only the data corresponding to the differences such as r / R, (m - k), and (θ - φ).

[0058] The displacement correction unit 35 sequentially receives the displacement per unit time calculated by the detected displacement calculation unit 32, in other words, the relative displacement between the scale 2 and the detection head 3, and also receives the displacement error and its fluctuation period (corresponding to the displacement difference signal) calculated by the periodic displacement error calculation unit 34, corrects the relative displacement between the scale 2 and the detection head 3 calculated by the detected displacement calculation unit 32 based on the displacement error and its fluctuation period calculated by the periodic displacement error calculation unit 34 so that the error is canceled out, and outputs the corrected displacement.

[0059] As described above, according to the linear encoder device 1 of this example, the periodic displacement error calculation unit 34 calculates the displacement error occurring within one period of the displacement detection signals A and B phases and the displacement error occurring in periods exceeding one period (including periods independent of the periods of the displacement detection signals A and B phases), and transmits these to the displacement correction unit 35. The displacement correction unit 35 corrects the relative displacement between the scale 2 and the detection head 3 calculated by the detected displacement calculation unit 32 based on the displacement error in each fluctuation period calculated by the periodic displacement error calculation unit 34 so that the error is canceled out.

[0060] As described above, the linear encoder device 1 of this example can correct both displacement errors having a period within one period of the displacement detection signals A and B phases and displacement errors having a period exceeding one period of the displacement detection signals A and B phases (including periods independent of the periods of the displacement detection signals A and B phases). This makes it possible to accurately (precisely) correct the detected displacement calculated based on the displacement detection signals A and B phases, and also to converge the correction residual.

[0061] As described above, displacement errors include errors caused by pitching, rolling, and yawing of the movable stage to which the scale is attached, distortion of the scale surface, and errors caused by noise generated during scale recording, and these errors fluctuate over a period that exceeds the period (one period) of the displacement detection signals A and B phases, and fluctuate over a period that is independent of the period of the displacement detection signals A and B phases. According to the present invention, such displacement errors can be corrected accurately (with good precision), and the residual error of the correction can be converged.

[0062] The period that exceeds the period of the displacement detection signals A and B phases and is independent of the period of the displacement detection signals A and B phases includes a period defined as follows: A period that exceeds the period of the displacement detection signals A and B phases, but excludes periods that are integer multiples of the displacement detection signals A and B phases.

[0063] Note that the period that exceeds the periods of the A-phase and B-phase displacement detection signals and is independent of those periods is preferably "a period that exceeds the periods of the A-phase and B-phase displacement detection signals but is less than 100 times the period of the A-phase and B-phase displacement detection signals" or "a period that exceeds the periods of the A-phase and B-phase displacement detection signals but is less than 1 / 10 of the effective length of the scale 2." The effective length of the scale 2 refers to the length over which the detection head 3 can acquire the A-phase and B-phase displacement detection signals from the scale 2. When the scale 2 is linearly arranged, as in this example, this is the length. In other embodiments, when the scale 2 is cylindrically arranged, this refers to the length of one circumference of the scale. Since the present invention detects errors that change periodically and their periods, it is empirically preferable that the range of the effective length includes at least 10 periods or more. Errors with periods less than 100 times the signal period can be detected.

[0064] 2. Second embodiment Next, a displacement calculation device according to a second embodiment of the present invention will be described with reference to Fig. 10. As shown in Fig. 10, a displacement calculation device 40 of this example corresponds to the displacement calculation device 30 of the first embodiment, and the configuration of a periodic displacement error calculation unit 41 is different from the configuration of the periodic displacement error calculation unit 34 of the displacement calculation device 30. Therefore, in Fig. 10, the same components as those in the displacement calculation device 30 are denoted by the same reference numerals.

[0065] The periodic displacement error calculation unit 41 is configured to include an in-period error calculation unit 42, a first out-of-period error calculation unit 43, and a second out-of-period error calculation unit 44. The in-period error calculation unit 42 receives from the signal analysis unit 33 the residuals for the amplitude error, offset, and phase difference for each period of the A-phase and B-phase displacement detection signals analyzed by the signal analysis unit 33, converts the received residual data into angle data to calculate the displacement error for each period, calculates the fluctuation period of the displacement error, and transmits the calculated displacement error for each period and its fluctuation period (corresponding to the displacement difference signal) to the displacement correction unit 35.

[0066] Furthermore, the first out-of-period error calculation unit 43 extracts residual data that exceeds one period and has periodicity within the first period (including periods that are independent of the periods of the A-phase and B-phase displacement detection signals) from the residual data acquired by the signal analysis unit 33, for residual data for a predetermined first period that exceeds one period of the A-phase and B-phase displacement detection signals (for example, periods that exceed one period and are up to i periods (where i is an integer greater than 1)), converts the extracted residual data into angle data to calculate a displacement error for the first period, calculates a fluctuation period of the displacement error, and transmits the calculated displacement error for each first period and its fluctuation period (corresponding to a displacement difference signal) to the displacement correction unit 35.

[0067] Furthermore, the second out-of-period error calculation unit 44 extracts residual data that exceeds i periods and has periodicity within the second period (including periods that are independent of the periods of the A-phase and B-phase displacement detection signals) from the residual data acquired by the signal analysis unit 33 for residual data for a period that exceeds i periods of the A-phase and B-phase displacement detection signals and that is a preset second period (for example, a period that exceeds i periods and is up to n periods (where n is an integer greater than i)), converts the extracted residual data into angle data to calculate a displacement error for the second period, calculates a period of fluctuation of the displacement error, and transmits the calculated displacement error for each second period and its fluctuation period (corresponding to a displacement difference signal) to the displacement correction unit 35.

[0068] The displacement correction unit 35 sequentially receives the displacement error for each period and its fluctuation period (corresponding to the displacement difference signal) transmitted from the in-period error calculation unit 42, the first out-of-period error calculation unit 43, and the second out-of-period error calculation unit 44, corrects the relative displacement between the scale 2 and the detection head 3 sequentially received from the detected displacement calculation unit 32 based on the received displacement error for each period and its fluctuation period, and outputs the corrected displacement as a calibrated displacement.

[0069] Specifically, for the displacement error transmitted from the in-period error calculation unit 42, the relative displacement corresponding to the next period in which the error was detected is corrected using the displacement error. Also, for the displacement error transmitted from the first out-of-period error calculation unit 43, the relative displacement corresponding to the next period in which the error was detected (the next period in which the error occurs) is corrected using the displacement error. Similarly, for the displacement error transmitted from the second out-of-period error calculation unit 44, the displacement corresponding to the next period in which the error was detected (the next period in which the error occurs) is corrected using the displacement error.

[0070] According to this aspect, the period in which an error occurs is divided into three ranges: within one period of the A-phase and B-phase displacement detection signals, within a first period exceeding one period, and within a second period exceeding the first period. For each divided period range, the in-period error calculation unit 42, the first out-of-period error calculation unit 43, and the second out-of-period error calculation unit 44 calculate a periodic (periodically fluctuating) displacement error, so that even if displacement errors fluctuating in various periods are combined, it is possible to accurately calculate the displacement error for each period, and ultimately to correct the displacement error with high precision.

[0071] In this embodiment, the out-of-periodic error calculation section is configured to include two calculation sections, the first out-of-periodic error calculation section 43 and the second out-of-periodic error calculation section 44, but the present invention is not limited to this and may include one out-of-periodic error calculation section, or three or more out-of-periodic error calculation sections. Providing more out-of-periodic error calculation sections allows for more precise correction of cyclic errors, but increases the processing load, so it is preferable to set the number of out-of-periodic error calculation sections taking into account the balance between these two.

[0072] 3. Third embodiment Next, a displacement calculation device according to a third embodiment of the present invention will be described with reference to Fig. 11. As shown in Fig. 11, a displacement calculation device 45 of this example corresponds to the displacement calculation device 40 of the second embodiment, and differs from the displacement calculation device 40 in that it has a configuration in which a data storage unit 46 is provided. Therefore, in Fig. 11, the same components as those of the displacement calculation device 40 are denoted by the same reference numerals.

[0073] According to the displacement calculation device 45 of this example, the displacement errors and their fluctuation periods (corresponding to displacement difference signals) calculated by the in-period error calculation section 42, the first out-of-period error calculation section 43, and the second out-of-period error calculation section 44 constituting the periodic displacement error calculation section 41 are stored in the data storage section 46, and the stored data is updated with newly calculated data.

[0074] According to this displacement calculation device 45, the periodic displacement error calculation unit 41 can read out the displacement errors having each error period stored in the data storage unit 46 at a timing delayed by one period for each error period and transmit the readout to the displacement correction unit 35. Therefore, the displacement correction unit 35 can accurately correct the displacements sequentially transmitted from the detected displacement calculation unit 32 in accordance with each period in which an error occurs.

[0075] As described above, the number of out-of-periodic error calculation units is one or more, and is not limited to the configuration in which two out-of-periodic error calculation units are provided as in this example, but may be a configuration in which one out-of-periodic error calculation unit is provided, or a configuration in which three or more out-of-periodic error calculation units are provided.

[0076] 4. Fourth Embodiment Next, a fourth embodiment of the present invention will be described with reference to Fig. 12. As shown in Fig. 12, a displacement calculation device 50 of this example corresponds to the displacement calculation device 30 of the first embodiment, and differs from the configuration of the displacement calculation device 30 in that a signal correction unit 51 and a calibrated displacement calculation unit 52 are provided instead of the detected displacement calculation unit 32 and the displacement correction unit 35 of the displacement calculation device 30. Therefore, in Fig. 12, the same components as those of the displacement calculation device 30 are denoted by the same reference numerals.

[0077] In this displacement calculation device 50, the periodic displacement error and its period calculated by the periodic displacement error calculation unit 34 are transmitted to a signal correction unit 51. The signal correction unit 51 continuously receives the A-phase and B-phase displacement detection signals, and also receives the periodic displacement error and its period from the periodic displacement error calculation unit 34, and performs processing to correct the A-phase and B-phase displacement detection signals based on the received periodic displacement error.

[0078] Specifically, when the displacement error is an error that fluctuates within one period of the A-phase and B-phase displacement detection signals, the signal correction unit 51 synchronizes the A-phase and B-phase displacement detection signals in the period following the period in which the displacement error was detected and corrects the A-phase and B-phase displacement detection signals with the received displacement error. On the other hand, when the displacement error is an error that fluctuates over a period exceeding one period of the A-phase and B-phase displacement detection signals, the signal correction unit 51 corrects the A-phase and B-phase displacement detection signals with the received displacement error in correspondence with the displacement error occurring in the period following the period in which the displacement error was detected.

[0079] As an example, Fig. 13 shows correction signals transmitted from the periodic displacement error calculation unit 34 to the signal correction unit 51. Fig. 13(b) shows the correction signal transmitted from the periodic displacement error calculation unit 34 to the signal correction unit 51, which is a correction signal for the A-phase of the displacement detection signal, and Fig. 13(c) shows the correction signal transmitted from the periodic displacement error calculation unit 34 to the signal correction unit 51, which is a correction signal for the B-phase of the displacement detection signal. Fig. 13(a) also shows a trajectory when the correction signal for the A-phase of the displacement detection signal is taken on the horizontal axis and the correction signal for the B-phase of the displacement detection signal is taken on the vertical axis.

[0080] Then, the calibration displacement calculation unit 52 calculates the displacement per unit time (calibration displacement) based on the displacement detection signal A-phase and the displacement detection signal B-phase corrected by the signal correction unit 51, by the same processing as the detection displacement calculation unit 32. The Lissajous waveform obtained from the displacement detection signal A-phase and the displacement detection signal B-phase corrected by the signal correction unit 51 is a Lissajous waveform that is close to an ideal perfect circle.

[0081] As described above, according to the displacement calculation device 50 of this example, the periodic displacement error calculation unit 34 calculates the displacement errors occurring within one period of the A-phase and B-phase displacement detection signals and the displacement errors occurring in periods exceeding one period (including periods independent of the A-phase and B-phase displacement detection signals), and transmits them to the signal correction unit 51. The signal correction unit 51 corrects the A-phase and B-phase displacement detection signals based on the received errors so as to cancel out the displacement errors, and the calibrated displacement calculation unit 52 calculates the calibrated displacement based on the corrected A-phase and B-phase displacement detection signals.

[0082] As described above, the displacement calculation device 50 of this example can also correct both displacement errors having periods within one period of the A-phase and B-phase displacement detection signals and displacement errors having periods exceeding one period of the A-phase and B-phase displacement detection signals (including periods independent of the A-phase and B-phase displacement detection signals), so that the detected displacement calculated based on the A-phase and B-phase displacement detection signals can be corrected accurately (with high precision), and the residual error of the correction can be converged.

[0083] 5. Fifth Embodiment Next, a displacement calculation device according to a fifth embodiment of the present invention will be described with reference to Fig. 14. As shown in Fig. 14, a displacement calculation device 60 of this example corresponds to the displacement calculation device 40 of the second embodiment described above, and differs from the configuration of the displacement calculation device 40 in that the signal correction unit 51 and the calibrated displacement calculation unit 52 of the displacement calculation device 50 of the fourth embodiment described above are provided instead of the detected displacement calculation unit 32 and the displacement correction unit 35 of this displacement calculation device 40. Therefore, in Fig. 14, the same components as those of the displacement calculation device 40 and the displacement calculation device 50 are denoted by the same reference numerals.

[0084] As described above, in the displacement calculation device 60 of this example, the in-period error calculation unit 42 of the periodic displacement error calculation unit 41 calculates the displacement error and its period for each period based on the residuals for the amplitude error, offset, and phase difference for each period of the A-phase and B-phase displacement detection signals analyzed by the signal analysis unit 33. Furthermore, the first out-of-period error calculation unit 43 calculates the displacement error and its period for a first period based on residual data having periodicity within a predetermined first period that exceeds one period of the A-phase and B-phase displacement detection signals (including a period independent of the A-phase and B-phase displacement detection signals). Furthermore, the second out-of-period error calculation unit 44 calculates the displacement error and its period for a second period based on residual data having periodicity within a predetermined second period that exceeds the first period of the A-phase and B-phase displacement detection signals (including a period independent of the A-phase and B-phase displacement detection signals). Then, each displacement error having periodicity and its period (corresponding to a displacement difference signal) calculated by the in-period error calculation unit 42, the first out-of-period error calculation unit 43, and the second out-of-period error calculation unit 44 are transmitted to the signal correction unit 51.

[0085] The signal corrector 51 corrects the A-phase and B-phase displacement detection signals based on the periodic displacement errors transmitted from the in-period error calculator 42, the first out-of-period error calculator 43, and the second out-of-period error calculator 44. Specifically, for the displacement error transmitted from the in-period error calculator 42, the signal corrector 51 corrects the A-phase and B-phase displacement detection signals corresponding to the period next after the error was detected, based on the displacement error. For the displacement error transmitted from the first out-of-period error calculator 43, the signal corrector 51 corrects the A-phase and B-phase position detection signals corresponding to the period next after the error was detected (the period next after an error occurs), based on the displacement error. Similarly, for the displacement error transmitted from the second out-of-period error calculator 44, the signal corrector 51 corrects the A-phase and B-phase position detection signals corresponding to the period next after the error was detected (the period next after an error occurs), based on the displacement error.

[0086] Then, the calibration displacement calculation unit 52 calculates the displacement per unit time (calibration displacement) based on the displacement detection signals A and B phases corrected by the signal correction unit 51, using the same processing as the detection displacement calculation unit 32.

[0087] As described above, according to the displacement calculation device 60 of the present example, similarly to the displacement calculation device 40 according to the second embodiment, the displacement detection signal is divided into three ranges: within one period of the A-phase and B-phase, within a first period exceeding one period, and within a second period exceeding the first period. For each divided period range, the in-period error calculation section 42, the first out-of-period error calculation section 43, and the second out-of-period error calculation section 44 calculate a displacement error having periodicity (including a period independent of the periods of the A-phase and B-phase displacement detection signal). Therefore, even if displacement errors having various periodicities are combined, it is possible to accurately calculate the displacement error for each period, and ultimately to correct the displacement error with high precision.

[0088] In this embodiment, the out-of-periodic error calculation section is configured to include two calculation sections, the first out-of-periodic error calculation section 43 and the second out-of-periodic error calculation section 44, but the present invention is not limited to this and may include one out-of-periodic error calculation section, or three or more out-of-periodic error calculation sections. Providing more out-of-periodic error calculation sections allows for more precise correction of cyclic errors, but increases the processing load, so it is preferable to set the number of out-of-periodic error calculation sections taking into account the balance between these two.

[0089] 6. Sixth Embodiment Next, a displacement calculation device according to a sixth embodiment of the present invention will be described with reference to Fig. 15. As shown in Fig. 15, a displacement calculation device 65 of this example corresponds to the displacement calculation device 60 of the fifth embodiment, and, like the displacement calculation device 45 of the third embodiment, differs from the displacement calculation device 60 in that it has a data storage unit 66. Therefore, in Fig. 11, the same components as those in the displacement calculation device 60 are denoted by the same reference numerals.

[0090] According to the displacement calculation device 65 of this example, the displacement errors and their fluctuation periods (corresponding to displacement difference signals) calculated by the in-period error calculation section 42, the first out-of-period error calculation section 43, and the second out-of-period error calculation section 44 constituting the periodic displacement error calculation section 41 are stored in the data storage section 66, and the stored data is updated with newly calculated data.

[0091] According to this displacement calculation device 65, the periodic displacement error calculation section 41 can read out the displacement errors having each error period stored in the data storage section 46 at a timing delayed by one period for each error period and transmit the readout to the signal correction section 51, so that the signal correction section 51 can accurately correct the input A-phase and B-phase displacement detection signals in accordance with each period in which the error occurs. Note that, depending on the magnitude of the signal periods of the A-phase and B-phase displacement detection signals and the degree of regularity of the fluctuations of the Lissajous waveform, the capacity of the data storage section 41 may be reduced in some cases compared to the data storage section 46 of the displacement calculation device 45 according to the third embodiment.

[0092] Each of the displacement calculation devices 30, 40, 45, 50, 60, and 65 in the above embodiments can be configured from a computer including a CPU, RAM, ROM, etc., or can be realized by an electronic device equipped with appropriate electronic circuits.

[0093] Although the embodiments of the present invention have been described above, the descriptions of these embodiments are illustrative in all respects and are not limiting. Variations and modifications are possible for those skilled in the art. The scope of the present invention is defined not by the above-described embodiments but by the claims. Furthermore, the scope of the present invention includes modifications from the embodiments within the scope of the claims and their equivalents. [Explanation of symbols]

[0094] 1. Displacement detection device 2. Scale 3 Detector head 5 Polarizing Beam Splitter 6,7 Mirror 8,9 Mirror 10 Light receiving part 11 Phase plate 12 Half mirror 13 1st light receiving section 14 Polarizing beam splitter 15 First light receiving element 16 Second light receiving element 17 2nd light receiving section 18 Polarizing Beam Splitter 19 Third light receiving element 20 Fourth light receiving element 21 Differential Amplifier 22 First differential amplifier 23 Second differential amplifier 30 Displacement calculation device 31 A / D conversion section 32 Detected displacement calculation unit 33 Signal analysis section 34 Periodic displacement error calculation section 35 Displacement correction unit

Claims

1. A displacement calculation device for calculating a displacement, comprising: a scale; and a displacement detection sensor for detecting a relative displacement between the scale and the scale, a detected displacement calculation unit that calculates a displacement based on two or more displacement detection signals having different phases output from the displacement detection sensor; a signal analysis unit that calculates an amplitude difference, a center position difference, and a phase difference between the displacement detection signal and a reference signal corresponding to the displacement detection signal; a periodic displacement error calculation unit that calculates, based on the difference calculated by the signal analysis unit, (i) a first displacement difference signal that fluctuates with a period equal to or shorter than the period of the displacement detection signal, and (ii) a second displacement difference signal that fluctuates with a period that exceeds the period of the displacement detection signal and that is at least independent of the period of the displacement detection signal; a displacement correction unit that corrects the displacement calculated by the detected displacement calculation unit based on the first displacement difference signal and the second displacement difference signal calculated by the periodic displacement error calculation unit, and outputs a corrected calibrated displacement.

2. A displacement calculation device that calculates a displacement from two or more periodic signals with different phases, a detected displacement calculation unit that calculates a detected displacement based on the periodic signal; a signal analysis unit that calculates an amplitude error, an error in vibration center, and a phase error between the periodic signal and a reference signal corresponding thereto; a periodic displacement error calculation unit that calculates, based on the errors calculated by the signal analysis unit, a displacement error having a period equal to or shorter than one period of the periodic signal, and a displacement error having a period longer than one period of the periodic signal and at least independent of the period of the periodic signal, as well as the periods; and a displacement correction unit that corrects the displacement calculated by the detected displacement calculation unit based on a displacement error calculated by the periodic displacement error calculation unit, the displacement error having a period equal to or less than one period of the periodic signal, and the displacement error having a period longer than one period of the periodic signal and at least independent of the period of the periodic signal, and the periods, and outputs a corrected calibrated displacement.

3. 1. A displacement calculation device for calculating a displacement from signals corresponding to two or more phases including at least a first phase and a second phase different from the first phase, a displacement calculation unit that calculates a first displacement based on signals corresponding to the first phase and the second phase; a signal analysis unit that detects a period associated with a locus of the center of a Lissajous waveform from signals corresponding to the first phase and the second phase, and analyzes the detected period of the signal; a displacement error calculation unit that calculates a displacement error corresponding to the periodicity associated with the center locus of the Lissajous waveform of the signal for the period based on the analysis by the signal analysis unit; a displacement correction unit that corrects the displacement calculated by the displacement calculation unit based on the displacement error calculated by the displacement error calculation unit and outputs the corrected displacement.

Images