JP2003254784A - Method and device for calibrating displacement - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To reduce uncertainty in calibration below the wavelength cycle of a displacement calibrating system by correcting an error in a position detection signal and reducing an error in position, thereby reducing the calibration time and improving the accuracy in reference position. <P>SOLUTION: Two-phase sine wave-like displacement detection signals ϕA<SB>n</SB>, ϕB<SB>n</SB>(n=1, 2, 3,...) having different phases, and a position detection signal X<SB>n</SB>(n=1, 2, 3,...) of an object for correction 8 are subjected to sampling at the same time for displacement calibration. For each sampled displacement detection signal ϕA<SB>n</SB>and ϕB<SB>n</SB>, based on position detection signals ϕA<SB>n-k1</SB>-ϕA<SB>n+k2</SB>and ϕB<SB>n-k1</SB>-ϕB<SB>n+k2</SB>in a range more than 1 wavelength including ϕA<SB>n</SB>and ϕB<SB>n</SB>, errors in amplitude, offset and phase of the position detection signals ϕA<SB>n</SB>and ϕB<SB>n</SB>are corrected to obtain: ϕA<SB>n</SB>'=A<SB>n</SB>'cos(θ<SB>n</SB>+ΔθA<SB>n</SB>')+VA<SB>n</SB>'; and ϕBn'=B<SB>n</SB>'sin(θ<SB>n</SB>+ΔθB<SB>n</SB>')+VB<SB>n</SB>' (A<SB>n</SB>'=B<SB>n</SB>', ΔθA<SB>n</SB>'=ΔθB<SB>n</SB>', VA<SB>n</SB>'=VB<SB>n</SB>'). A reference position detection signal Pn' in which an error in wavelength cycle and a displacement detection detection signal for 1/2 cycle is reduced is used to calibrate the displacement detection signal Xn as an object for calibration. <P>COPYRIGHT: (C)2003,JPO

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a displacement calibration method and apparatus, and more particularly, to reducing the error of a position detection signal suitable for use in a position displacement detector calibration system using a laser interferometer. The present invention relates to a displacement calibration method and device capable of achieving both high-speed scanning motion and high accuracy of reference position.

[0002]

2. Description of the Related Art A position displacement detector calibration system using a laser interferometer is known. For example, as shown in FIG. 1, an optical axis (laser optical axis) 22 of a laser interferometer (referred to as a laser interferometer) 20 is arranged inside a drive guide mechanism section 12 of a slider 10 which moves horizontally. The position of the measurement reference surface 14 provided on the end surface of the slider 10 is measured by the laser interferometer 20.

For calibration, the calibration target 8 is placed on the measurement reference plane 14, and the two-phase sine wave φAn output from the laser interferometer 20 while moving the measurement reference plane 14 at the slider end face,
This is performed by simultaneously sampling φBn and the output Xn of the calibration target 8 in the data processing unit 30, and calibrating the output Xn of the calibration target 8 based on the output of the laser interferometer 20. In the figure, 24 is a laser light source, 26 is a counter section, and 28 is a drive control section.

Thus, as the position detection signal, a two-phase sine wave φA having a wavelength λ as shown in the following equations (1) and (2)
In the displacement calibration system that outputs n and φBn, position P
n is represented by the wavelength λ and the displacement ΔPn below the wavelength as in the equation (3).

[0005] φAn = An cos (θn + ΔθAn) + VAn (1) φBn = Bn sin (θn + ΔθBn) + VBn (2) n = 1, 2, 3, ... (Sampling number) Pn = mλ + ΔPn (ΔPn <λ) (3) m = 0, ± 1, ± 2, ± 3, ...

Therefore, the sampled φAn and φBn
The angle θ is calculated by the following equations (4), (5) and (6) using the value of
The position Pn of the displacement calibration system can be detected at a position equal to or shorter than the wavelength by calculating n and further obtaining ΔPn by the equation (7).

[0007]

[Equation 1]

Regarding the expressions (1) and (2), the angle θn (0 to 3)
FIG. 2 shows the standard deviation of the angle calculation error in the case where 100 ° is measured 100 times under the condition that white noise with an amplitude of 1% is applied to φAn and φBn in 1 ° increments. From FIG. 2, in calculating the angle θn, the angle calculation error is reduced by using the formula (5) for the range of the formula (8) and the formula (6) for the range of the formula (9). It turns out that it is possible. It is also possible to calculate the angle θn by the expression (4), but in that case, the angle calculation error becomes large at the angle θn shown in the expression (10).

[0009]     L × 180 ° −45 ° ≦ θn ≦ L × 180 ° + 45 ° (L = 0,1,2,3, ...)… (8)     L × 180 ° + 45 ° ≦ θn ≦ L × 180 ° + 135 ° (L = 0,1,2,3, ...)… (9)     θn = L × 180 ° + 90 ° (L = 0,1,2,3, ...) (10)

Now, consider a case where the displacement calibration system operates at positions Pan = 0 to λ, as shown in FIG. FIG. 3 shows the displacement P during constant velocity motion normalized by the wavelength λ.

When there is no amplitude / offset / phase error in the two-phase sine wave, equations (1) and (2) are as follows (11) and (1
It can be expressed as in equation 2).

[0012] φAn = An cos (θn) (11) φBn = Bn sin (θn) (12)

The output waveforms of φAn and φBn are shown in FIG.
FIG. 5 shows a Lissajous waveform showing the relative relationship between and φBn. The radius Rn of the Lissajous waveform can be calculated by the following equation (13).

[0014]

[Equation 2]

The relationship between the angle θn and the radius Rn is normalized by the amplitude R and is shown in FIG. When there are no amplitude / offset / phase errors as shown in equations (11) and (12), the Lissajous waveform has a center (0, 0) and a radius R as shown in FIG.
Is a perfect circle.

As shown in the following equation (14), the actual position Pan
The position error En represented by the difference between the detected position Pn and the detected position Pn is 0 when the two-phase sine wave has no position / offset / phase error, as shown in FIG.

[0017] En = Pan-Pn (14)

[0018]

However, in an actual system, errors of amplitude, offset, and phase occur in the two-phase sine wave due to the influence of detection noise, temperature drift, and the like.

In equations (11) and (12), when there is a 5% error in the amplitude of φAn (An = 1.05R, Bn =
Think about R). Figure 8 shows the output waveforms of φAn and φBn.
The Lissajous waveform is shown in FIG. System position Pan
Is the same as in FIG.

FIG. 10 shows the relationship between the angle θn and the radius Rn when the amplitude error is 5%. 180 ° due to the effect of amplitude error
It can be seen that there is a 5% radius variation in the cycle (= 1/2 wavelength cycle).

ΦA including the actual position Pan and the amplitude error
FIG. 11 shows the position error En with respect to the detected position Pn calculated from n and φBn. It can be seen that a position error of 1/2 wavelength period occurs due to the influence of the amplitude error.

Similarly, FIG. 12 shows the position error when the offset error is 5%, and FIG. 13 shows the position error when the phase error is 5 °. It can be seen from FIGS. 12 and 13 that a position error of one wavelength period occurs when there is an offset error and a half wavelength period occurs when there is a phase error.

As described above, since the accuracy of a general division circuit for real-time high-speed scanning motion control using the detection signal of the high-accuracy laser interferometer includes various errors, a reference of accuracy sufficient for high-accuracy calibration is required. There was a problem that the position could not be obtained.

However, the wavelength λ here means a length corresponding to one cycle of the sine wave signal from the interferometer. The relationship with the laser wavelength λ0 of the laser interferometer depends on the optical design of the interferometer.

In a single-pass Michelson interferometer,
λ = λ0 / 2, and in a double-pass Michelson interferometer, λ = λ0 / 4.

The present invention has been made to solve the above-mentioned problems of the prior art. The error of the position detection signal at the time of calibration is corrected to obtain a high-precision reference position, and high-precision calibration of the position detection signal of the subject is performed. Therefore, it is an object to achieve both the shortening of the calibration time and the high accuracy of the reference position.

[0027]

According to the present invention, a two-phase sinusoidal signal φAn = An cos (θn + ΔθAn) + VAn φBn = Bn sin (θn + ΔθBn) + VBn (n = 1, 2, 3, 3) having different phases in a position detection signal. …) And the position detection signal X to be calibrated
In the displacement calibration method for sampling n (n = 1, 2, 3, ...) Simultaneously, for each sampled position detection signal φAn, φBn, a position detection signal φAn-k1 in the range of one wavelength or more including φAn, φBn. ~ ΦAn + k2, φBn-k1
From φBn + k2, position detection signals φAn ′ = An′cos (θn + ΔθAn ′) + VAn ′ φBn ′ = Bn′sin (θn + ΔθBn ′) + VBn ′ are obtained by correcting the amplitude / offset / phase errors in the position detection signals φAn and φBn. (An '= Bn', ΔθAn '= ΔθBn', VAn '= VBn
′) Is obtained, and the position detection signal Xn to be calibrated is calibrated by using the reference position detection signal Pn ′ in which the error of the position detection signal of the wavelength cycle and its 1/2 cycle is reduced, and It has been resolved.

According to the present invention, a two-phase sinusoidal signal φAn = An cos (θn + ΔθAn) + VAn φBn = Bn sin (θn + ΔθBn) + VBn (n = 1,2,3, ...) Position detection signal X for calibration
In a displacement calibrating device that simultaneously samples n (n = 1, 2, 3, ...) For each sampled position detection signal φAn, φBn, a position detection signal φAn-k1 in the range of one wavelength or more including φAn, φBn. ~ ΦAn + k2, φBn-k1
From φBn + k2, position detection signals φAn ′ = An′cos (θn + ΔθAn ′) + VAn ′ φBn ′ = Bn′sin (θn + ΔθBn ′) + VBn ′ are obtained by correcting the amplitude / offset / phase errors in the position detection signals φAn and φBn. (An '= Bn', ΔθAn '= ΔθBn', VAn '= VBn
′) And a reference position detection signal Pn ′ in which the error of the position detection signal of the wavelength cycle and its half cycle is reduced.
And a means for calibrating the position detection signal Xn to be calibrated by using the above.

Further, when the amplitude / offset / phase errors of the position detection signals φAn and φBn are calculated, 1 is added to the position detection signal for which the error is calculated in accordance with the spatial distribution of the amplitude / offset / phase errors. Weighting is performed for each wavelength period to reduce the estimation uncertainty of the amplitude / offset / phase error.

The present invention also provides a computer program for implementing the above displacement calibration method.

The present invention also provides a computer program for realizing the above-mentioned displacement calibrating device.

Further, the present invention provides a computer-readable recording medium in which the above computer program is recorded.

[0033]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of the present invention will be described in detail below with reference to the drawings.

In this embodiment, the present invention is applied to a position displacement detector calibration system using a laser interferometer 20 as shown in FIG.

In the present embodiment, the two-phase sine waves φAn, φBn output from the laser interferometer 20 and the output X of the calibration target 8 are output.
n is simultaneously sampled by the data processing unit 30, the displacement Pn ′ of the calibration system is calculated by correcting the amplitude / phase / offset error of the two-phase sine waves φAn, φBn, and Pn ′ is used as a reference for the calibration target 8. Calibrate the output Xn.

FIG. 14 shows an example in which the displacement sensor is calibrated by the displacement calibration system. FIG. 14 shows the difference between the output Xn of the displacement sensor and the displacement Pn of the calibration system.
Fluctuations occur in the / 2 wavelength cycle. The difference includes the displacement sensor error and the calibration system position error En.

FIG. 15 shows Lissajous waveforms of the two-phase sine waves φAn and φBn used for position detection, which are sampled at the same time as the output Xn of the displacement sensor in the displacement calibration system. FIG. 16 shows the result of calculating the angle and radius of the Lissajous waveform by the above equations (5) or (6) and (13).
FIG. 17 shows the result of the spatial frequency analysis performed on the radius variation with respect to the angle of 5. The numerical value on the X-axis represents the frequency in one rotation (0 to 360 °) of the Lissajous waveform, and the fluctuations in the 180 ° cycle and the 360 ° cycle are large. From this, the variation of the error of the 1/2 wavelength period in FIG.
It can be said that this is a position error due to an error in the amplitude / offset / phase of the two-phase sine wave.

Therefore, for each sampled two-phase sine wave data, the amplitude / offset / phase error was corrected from the data for one wavelength (one Lissajous rotation) containing the data.

Specifically, as shown in FIG. 18, one wavelength of data φAn-k1 to φAn + k2, φBn-k1 including certain sampling data φAn, φBn (n = 1, 2, 3, ...)
˜φBn + k2 (k1 and k2 are arbitrary), calculate the angle and radius of the Lissajous waveform, and keep An and ΔθAn of Equations (1) and (2) to minimize the radius variation (variation range). VA
Amplitude / offset / phase errors are corrected by correcting the values of n, Bn, ΔθBn, and VBn.

More specifically, for example, the Lissajous radius R
Evaluation function that represents the dispersion of

[Outer 1] The amplitude / phase / offset error that minimizes is estimated and corrected by the bisection method. Here, the initial value of the bisection method can be set to a value larger than the maximum error of the amplitude / phase / offset.

In the embodiment, the two-phase sine wave output from the laser interferometer is ± 10% or less as a result of waveform adjustment by the electric circuit of the conventional laser interferometer. Initial value of offset dichotomy is ± 10
Set to%. The calculation by the bisection method was repeated until the error value converged to 0.0002% or less.

The corrected Lissajous waveform, the radius with respect to the angle, and the spatial frequency analysis (FFT) result of the radius are shown in FIGS. 19, 20 and 21, respectively.

FIG. 21 shows the two-phase sine waves φAn and φBn when the calibration system is moving at a constant speed.
Pn 'is calculated from the equations (5) or (6) and (7),
This is a spatial FFT. Here, the spatial frequency of 1 Hz corresponds to the variation of the λ cycle, and the spatial frequency of 2 Hz corresponds to the variation of the λ / 2 cycle.

By correcting the amplitude / offset / phase error, the radius fluctuation of the 180 ° cycle is reduced to 1/10.
It can be seen that it is reduced to.

The displacement of the calibration system is estimated from the corrected two-phase sine wave, and the result of recalibrating the displacement sensor based on the estimated value is shown in FIG. By correcting the amplitude / offset / phase error of the two-phase sine wave, it can be seen that the fluctuation of the 1/2 wavelength period seen before the correction is reduced.

By reducing the position error in the position detection in this way, it is possible to reduce the uncertainty of calibration within the wavelength period of the displacement calibration system.

Therefore, after the detection signal of the laser interferometer is acquired at the same time as the object output signal, a large number of intervals of more than ½ wavelength before and after the detection signal are acquired for each of the detection signals according to the present invention. By using the data, the error of the detection signal is corrected to obtain a high-precision reference position, and high-precision calibration of the position detection signal of the subject is realized, reducing both the calibration time and the precision of the reference position. can do.

The application of the present invention is not limited to the laser interferometer, and it is obvious that the present invention can be applied to a general displacement calibration system using a two-phase sine wave as a position detection signal.

[0049]

[Embodiment] When the amplitude / offset / phase error gradually changes at each position in the calibration area, for example, as shown in FIG.
3. As shown in FIG. 24, when the phase A offset changes from 0.1 to 0 over 10 wavelength cycles, the position error without correction is 3.0% (P−
P).

In the comparative example in which the offset error is corrected by the data of the entire 10 wavelength cycles, the position error is shown in FIG.
As shown in FIG. 3, it was reduced to 2.3% (PP).

On the other hand, as a result of correcting the error with the data of one cycle of the wavelength according to the present invention, the position error is shown in FIG.
As shown in (1), it was reduced to 0.11% (PP).

As described above, by correcting the error with the data of one cycle of the wavelength, the position error can be corrected with an error of about 1 / n as compared with the case of correcting the error with the data of the entire area.

[0053]

According to the present invention, by reducing the position error in position detection, it is possible to reduce the uncertainty of calibration within the wavelength period of the displacement calibration system. Therefore,
It is possible to achieve both the reduction of the calibration time and the high accuracy of the reference position.

[Brief description of drawings]

FIG. 1 is a cross-sectional view including a partial block diagram showing an example of a position displacement detector calibration system using a laser interferometer, which is an example of an application target of the present invention.

FIG. 2 is a diagram showing an angular error when 1% white noise is applied to the amplitude.

FIG. 3 is a diagram showing a displacement during constant velocity motion normalized by a wavelength λ, for explaining a conventional problem.

FIG. 4 is a diagram showing an output waveform of a two-phase sine wave when there is no amplitude / offset / phase error in the two-phase sine wave.

FIG. 5 is a diagram showing a Lissajous waveform.

FIG. 6 is a diagram similarly showing a relationship between an angle and a radius (normalized by amplitude).

FIG. 7 is a diagram showing a positional error (normalized by wavelength) during one wavelength cycle.

FIG. 8 is a diagram showing an output waveform of a two-phase sine wave when the two-phase sine wave has an error of 5% in amplitude.

FIG. 9 is a diagram similarly showing a Lissajous waveform.

FIG. 10 is a diagram showing a radius error similarly.

FIG. 11 is a diagram similarly showing a position error.

FIG. 12 is a diagram showing a position error when the offset error is 5%.

FIG. 13 is a diagram showing a position error when the phase error is 5 °.

FIG. 14 is a diagram showing a displacement sensor calibration result before correction according to the present invention.

FIG. 15 is a diagram similarly showing a Lissajous waveform.

FIG. 16 is a diagram showing a radius error similarly.

FIG. 17 is a diagram showing a result of spatial frequency analysis of radius similarly.

FIG. 18 shows an amplitude of a two-phase sine wave according to an embodiment of the present invention.
Flowchart showing offset / phase correction procedure

FIG. 19 is a diagram showing a Lissajous waveform after correction according to the embodiment.

FIG. 20 is a diagram showing a radius error similarly.

FIG. 21 is a diagram showing a result of spatial frequency analysis of radius similarly.

FIG. 22 is a diagram showing a displacement sensor calibration result.

FIG. 23 is a diagram showing an output waveform of a two-phase sine wave in the example of the present invention.

FIG. 24 is a diagram showing an A-phase offset voltage.

FIG. 25 is a diagram showing a position error of a conventional example without correction.

FIG. 26 is a diagram showing a position error in a comparative example corrected with data of 10 cycles of wavelength.

FIG. 27 is a diagram showing a position error in the embodiment of the present invention, which is corrected with data for each wavelength cycle.

[Explanation of symbols]

8 ... Target of calibration 10 ... Slider 12 ... Drive guide mechanism 14 ... Measurement reference plane 20 ... Laser (interference) length measuring instrument 22 ... Laser optical axis 24 ... Laser light source 28 ... Drive control unit 30 ... Data processing unit

Claims (7)

[Claims] 1. A two-phase sine wave signal φAn = An cos (θn + ΔθAn) + VAn φBn = Bn sin (θn + ΔθBn) + VBn (n = 1,2,3, ...) And a position to be calibrated. Detection signal X
In the displacement calibration method for sampling n (n = 1, 2, 3, ...) Simultaneously, for each sampled position detection signal φAn, φBn, a position detection signal φAn-k1 in the range of one wavelength or more including φAn, φBn ~ ΦAn + k2, φBn-k1 to φBn + k2, the position detection signal φAn '= An'cos (θn + ΔθAn') + VAn 'φBn' = Bn is obtained by correcting the amplitude / offset / phase error in the position detection signals φAn, φBn. ′ Sin (θn + ΔθBn ′) + VBn ′ (An ′ = Bn ′, ΔθAn ′ = ΔθBn ′, VAn ′ = VBn
′) Is obtained, and the position detection signal Xn to be calibrated is calibrated by using the reference position detection signal Pn ′ in which the error of the position detection signal of the wavelength cycle and its 1/2 cycle is reduced, Method. 2. When the amplitude / offset / phase error of the position detection signals φAn, φBn is calculated, 1 is added to the position detection signal for which the error is calculated in accordance with the spatial distribution of the amplitude / offset / phase error. The displacement calibration method according to claim 1, wherein the estimation uncertainty of the amplitude / offset / phase error is reduced by weighting each wavelength period. 3. A two-phase sinusoidal signal φAn = An cos (θn + ΔθAn) + VAn φBn = Bn sin (θn + ΔθBn) + VBn (n = 1,2,3, ...) And a position to be calibrated as a position detection signal. Detection signal X
In a displacement calibrating device that simultaneously samples n (n = 1, 2, 3, ...) For each sampled position detection signal φAn, φBn, a position detection signal φAn-k1 in the range of one wavelength or more including φAn, φBn. ~ ΦAn + k2, φBn-k1
From φBn + k2, position detection signals φAn ′ = An′cos (θn + ΔθAn ′) + VAn ′ φBn ′ = Bn′sin (θn + ΔθBn ′) + VBn ′ are obtained by correcting the amplitude / offset / phase errors in the position detection signals φAn and φBn. (An '= Bn', ΔθAn '= ΔθBn', VAn '= VBn
′), And a means for calibrating the position detection signal Xn to be calibrated by using the reference position detection signal Pn ′ in which the error of the position detection signal of the wavelength cycle and its half cycle is reduced. Displacement calibration device characterized in that 4. When the amplitude / offset / phase error of the position detection signals φAn, φBn is calculated, 1 is set for the position detection signal for which the error is calculated in accordance with the spatial distribution of the amplitude / offset / phase error. The displacement calibration device according to claim 3, wherein the estimation uncertainty of the amplitude / offset / phase error is reduced by performing weighting for each wavelength period. 5. A computer program for carrying out the displacement calibration method according to claim 1. 6. A computer program for realizing the displacement calibrating device according to claim 3 or 4. 7. A computer-readable recording medium in which the computer program according to claim 5 or 6 is recorded.