JP2005257562A - Method and device for calibrating displacement - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To improve calibration accuracy of a displacement calibration technology using two-phase sine waves as position detection signals by reducing errors of an interpolation position in a wavelength of the two-phase sine wave. <P>SOLUTION: By using a position detection means which obtains two-phase sine wave-like signals having different phases: ϕA<SB>n</SB>=A<SB>n</SB>cos(θ<SB>n</SB>+Δθ<SB>An</SB>)+V<SB>An</SB>, ϕB<SB>n</SB>=B<SB>n</SB>sin(θ<SB>n</SB>+Δθ<SB>Bn</SB>)+V<SB>Bn</SB>(wherein n=1, 2, 3, etc.) to detect the position of a measuring surface, actions such that the measuring surface is stopped at an arbitrary calibration position P<SB>x</SB>and an output signal of an object to be calibrated Y<SB>x</SB>is calibrated are repeated, while the calibration position P<SB>x</SB>is moved. When the calibration position P<SB>x</SB>is moved, the number α of the wavelength λ of the position detection signal is counted, and when it stops, values of ϕA<SB>n</SB>and ϕB<SB>n</SB>within the range of more than 1 wavelength of the two-phase sine wave-like signal including each calibration position P<SB>x</SB>are obtained. Errors of amplitude/offset/phase of the obtained ϕA<SB>n</SB>and ϕB<SB>n</SB>are estimated and corrected. From the corrected position detection signals, a position Δp<SB>x</SB>' within the wavelength interval is obtained. Each calibration position Px' is calculated from an equation P<SB>x</SB>'=αλ+Δp<SB>x</SB>', and then the output signal of the object to be calibrated Y<SB>x</SB>is calibrated with reference to P<SB>x</SB>'. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to a displacement calibration method and apparatus, and more particularly to a displacement calibration method and apparatus suitable for use in calibrating position displacement using a laser interferometer for position detection.

  FIG. 1 shows an example of a displacement calibration apparatus using a two-phase sine wave as a position detection signal. The calibration apparatus includes a position detection unit 10 including a laser interferometer, a slider 12 through which a laser can pass, and a driving roller (moving unit) 14 that moves the slider 12 in the left-right direction. This is because the displacement meter 16 to be calibrated is arranged on the measurement surface 12A of the slider end surface, and the position of the measurement surface when the slider 12 is moved and the output data of the displacement meter 16 are simultaneously acquired, thereby performing data processing. This is a device for calibrating the displacement meter 16 by the unit 18.

Here, the position of the measurement surface 12A is detected by the position detection means 10 as a displacement of the measurement surface 12A with respect to the position reference surface 10A, and the position detection signal has a wavelength as shown in equations (1) and (2). Two-phase sine waves φA _n and φB _{n of} λ are output. From these two-phase sine waves φA _n and φB _n , the position P _n is expressed by the wavelength λ and the displacement Δp _n less than the wavelength (within the wavelength interval) as shown in the equation (3).

However, the wavelength λ here is a length corresponding to one cycle of the sine wave signal from the interferometer included in the position detecting means 10, and the relationship with the laser wavelength λ ₀ of the laser interferometer is the optical property of the interferometer. It depends on the design, for example, in the Michelson interferometer single pass, λ = λ _0/2, in the Michelson interferometer of double pass, and λ = λ _0/4.

φA _n = A _n cos (θ _n + Δθ _An ) + V _An (1)
φB _n = B _n sin (θ _n + Δθ _Bn ) + V _Bn (2)
n = 1, 2, 3 (sampling number)
P _n = αλ + Δp _n (Δp _n <λ) (3)
α = 0, 1, 2, 3, ...

Therefore, for example, using the signal values of the two-phase sine waves φA _n and φB _n obtained by sampling in increments of 1 °, the angle θ _n is calculated by the equation (4), and Δp _n is further calculated by the equation (5). By inserting, the position P _n of the measurement surface 12A in the displacement calibration device can be detected in the range of the wavelength or less.

θ _n = tan ⁻¹ (φB _n / φA _n ) (4)
θ _n = sin ⁻¹ (φB _n / √ (φA _n ² + φB _n ² ) (4a)
θ _n = cos ⁻¹ (φA _n / √ (φA _n ² + φB _n ² ) (4b)
Δp _n = θ _n / 2π · λ (5)

However, when the two-phase sine waves φA _n and φB _n include an error in at least one of the amplitude, the offset, and the phase, the Lissajous waveform whose radius is given by √ (φA _n ² + φB _n ² ) deviates from a perfect circle. As a result, an error (interpolation error) occurs between the actual position and the position detected by interpolation, increasing the uncertainty of calibration. This will be described below with a specific example.

FIG. 2 shows waveforms of the two-phase sine waves φA _n and φB _n with respect to the position of the calibration device. In this figure, the position on the horizontal axis is the wavelength λ, and the two-phase sine wave on the vertical axis is normalized by the amplitude value. FIG. 3 shows an interpolation error when the two-phase sine waves φA _n and φB _n have an amplitude error of 5%. The position on the horizontal axis is shown normalized by the wavelength λ. The interpolation error on the vertical axis is the difference between the actual position and the position calculated by the equations (3) to (5), and indicates the ratio of the interpolation error to the wavelength λ.

Thus, when there is an amplitude error in the two-phase sine waves φA _n and φB _n , an interpolation error of λ / 2 period occurs. Similarly, an interpolation error of λ period occurs when there is an offset error, and a λ / 2 period occurs when there is a phase error.

With respect to the interpolation error that occurs when such two-phase sine waves φA _n and φB _n include amplitude, offset, and phase errors, the two-phase sine waves obtained by moving the calibration device at a constant speed within the calibration range. Interpolation error is obtained by simultaneously acquiring signal data of sine waves φA _n and φB _n and output data to be calibrated, and correcting errors in amplitude, offset, and phase of two-phase sine waves φA _n and φB _n. A technique for reducing is proposed in Patent Document 1.

Here, by stopping the measurement surface 12A of the device at any calibration position (target position) P _x, after calibrating the output Y _x to be calibrated, stop the device moves to a different calibration positions P _{x + 1} Let us consider a calibration method in which the operation of calibrating the output Y _{x + 1} to be calibrated is repeatedly performed.

FIG. 4 shows an example of calibration of the displacement meter when the calibration range is stopped at each calibration position divided by 10 and the calibration and movement are repeated. The calibration procedure in this case, as shown in FIG. 5, there performs positioning the calibration position P _x, the position P _x to be calibrated displacement gauge 16 outputs data Y _x of the measurement surface 12A of the calibration device at the same time After the acquisition, the operation of moving to the next calibration position P _{x + 1} is performed at each calibration position P _x (x = 1, 2,..., M + 1: m is the number of divisions of the calibration range), and the calibration position P _x The output data Y _x to be calibrated is calibrated with reference to.

In such a calibration method that repeats stationary and calibration, if there are three or more calibration positions P _x during the wavelength λ, the two-phase sine waves φA _n and φB _n are obtained by the correction method proposed in Patent Document 1. It is possible to estimate and correct the error of amplitude, offset, and phase from the value of, and to reduce the interpolation error.

JP 2003-254784 A

  However, when the calibration position between the wavelengths λ is less than three points, it is difficult to reduce the interpolation error because the estimated values of the amplitude, offset, and phase errors of the two-phase sine wave do not converge. .

Therefore, as a calibration method in the case where the calibration position P _x between the wavelengths λ is less than three points, the two-phase sine waves φA _n and φB _n are also used in the movement between the calibration positions in addition to the calibration positions. It is conceivable to acquire data. However, in this case, the correction method can be applied, but this calibration method has the following problems.

In order to correct the interpolation error at each calibration position P _x , signal data of the two-phase sine waves φA _n and φB _n are acquired over the entire calibration range, so that a memory capacity for storing the data is required.

  In order to estimate the amplitude, offset, and phase errors of the two-phase sine wave, at least three points of data per one wavelength period are required as described above. However, it is said that about 60 points of data per period of wavelength are required to sufficiently converge the error estimation value (Etsukazu Ozeki and others, Journal of Precision Engineering, Vol. 69, No. 9 (2003) p1296). In addition, the upper limit Vc of the moving speed is subject to the restriction expressed by the equation (6) from the number of data acquired per one wavelength period.

Vc = (λ / N) × (1 / Ts) (6)
N: number of data per wavelength period Ts: sampling period

  The present invention has been made to solve the above-described conventional problems, and relates to a displacement calibration technique using a two-phase sine wave as a position detection signal. When the calibration position is moved and the calibration operation is repeated, the two-phase sine wave is used. It is an object of the present invention to realize highly accurate calibration by reducing an error at an interpolation position within the wavelength of.

The present invention is a two-phase sinusoidal signal having different phases φA _n = A _n cos (θ _n + Δθ _An ) + V _An
φB _n = B _n sin (θ _n + Δθ _Bn ) + V _Bn
(N = 1, 2, 3 ...)
Using the position detecting means for detecting the position of the measuring surface by acquiring as a position detection signal, stops the measurement surface at any calibration position P _x, an operation of calibrating the output Y _x to be calibrated, the calibration position In the displacement calibration method in which P _x is moved repeatedly, the number α of the wavelengths λ of the position detection signal is counted when the measurement surface is moved, and each calibration position P _x is measured when the measurement surface is stationary. The values of φA _n and φB _n are acquired within a range of one wavelength or more in a two-phase sinusoidal signal including the signal, and the amplitude, offset, and phase errors in the acquired position detection signals φA _n and φB _n are estimated, corrected, and corrected. Position detection signal φA _n '= A _n ' cos (θ _n + Δθ _An ') + V _An '
φB _n ′ = B _n ′ sin (θ _n + Δθ _Bn ′) + V _Bn ′
(A _n '= B _n ', Δθ _An '= Δθ _Bn ', V _An '= V _Bn ')
From 'by determining, by reducing the error position in the wavelength interval, position Delta] p _x number α and the wavelength interval of the wavelength' position Delta] p _x within the wavelength interval each calibration position from the _{P x '= αλ + Δp x} ' And the above-described problem is solved by calibrating the output signal Y _x to be calibrated using each calibration position P _x ′ as a reference.

The present invention also using the displacement calibration method, when measuring the dimensions of the measurement object, the reference position P ₀ and dimension measuring position P ₁ for measuring the dimensions, each position P _0, P ₁ The values of the position detection signals φA _n and φB _n are acquired in the range of one wavelength or more including each, and the amplitude / offset / phase errors in the position detection signals φA _n and φB _n are estimated and corrected, and the corrected position detection signal φA _n '= A _n ' cos (θ _n + Δθ _An ') + V _An '
φB _n ′ = B _n ′ sin (θ _n + Δθ _Bn ′) + V _Bn ′
(A _n '= B _n ', Δθ _An '= Δθ _Bn ', V _An '= V _Bn ')
Thus, positions P ₀ ′ and P ₁ ′ with reduced position errors within the wavelength interval are obtained, and the dimension of the measurement object is measured from the difference between the positions P ₀ ′ and P ₁ ′.

The present invention also provides a two-phase sinusoidal signal having different phases φA _n = A _n cos (θ _n + Δθ _An ) + V _An
φB _n = B _n sin (θ _n + Δθ _Bn ) + V _Bn
(N = 1, 2, 3 ...)
In order to repeatedly perform the operation of calibrating the output Y _x to be calibrated by stopping the measurement surface at an arbitrary calibration position P _x and the position detection means for detecting the position of the measurement surface by acquiring the signal as a position detection signal. The moving means for moving the measurement surface, the counting means for counting the number α of the wavelengths λ of the position detection signal when the measurement surface is moved, and each calibration position P _x when the measurement surface is stationary. Two-phase sinusoidal signal Obtains φA _n and φB _n values in the range of 1 wavelength or more, estimates and corrects amplitude, offset, and phase errors in the obtained position detection signals φA _n and φB _n , and corrects position detection Signal φA _n '= A _n ' cos (θ _n + Δθ _An ') + V _An '
φB _n ′ = B _n ′ sin (θ _n + Δθ _Bn ′) + V _Bn ′
(A _n '= B _n ', Δθ _An '= Δθ _Bn ', V _An '= V _Bn ')
From 'by determining, by reducing the error position in the wavelength interval, position Delta] p _x number α and the wavelength interval of the wavelength' position Delta] p _x within the wavelength interval each calibration position from the _{P x '= αλ + Δp x} ' And a data processing means for calibrating the output signal Y _x to be calibrated on the basis of each calibration position P _x ′. Is a solution.

  The present invention also provides a computer-readable program for implementing the displacement calibration method or the dimension measurement method.

  The present invention also provides a computer-readable program for realizing the displacement calibration apparatus.

  The present invention further provides a recording medium on which the computer-readable program is recorded.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

  The displacement calibration apparatus of the present embodiment has substantially the same configuration as that shown in FIG. 1, and various functions to be described in detail below other than the hardware configuration are the data processing unit 18 comprising a computer. In the program.

  FIG. 6 shows the features of the calibration method according to the present embodiment, and FIG. 7 shows the movement procedure during calibration.

That is, moves the slider 12, to stop the measurement surface 12A at an arbitrary calibration position P _x, an operation of calibrating the output Y _x of displacement gauge 16 is calibrated, by moving the calibration position P _x in calibration method repeatedly performed, positioning the calibration position P ₁ of the first (x = 1), when acquiring the output data Y ₁ to be calibrated at the P _1, as first operation a, including calibration position P ₁ The slider 12 is moved at a velocity V _c or less at least in the wavelength λ range (360 ° or more), and data of the two-phase sine waves φA _{n (1)} and φB _{n (1)} are sampled and acquired. Here, the acquisition of the data of the two-phase sine waves φA _{n (1)} and φB _{n (1)} is performed before the acquisition of the output data Y _{1 to be} calibrated, but it may be performed later.

Next, as operation B, after acquiring data at the calibration position P _1, it moves to the _second calibration position P ₂ while counting the number of wavelengths α by a counting means (not shown). At the time of movement, data such as the position of the measurement surface 12A of the calibration device, the two-phase sine wave signal, and the output of the displacement meter 16 are not acquired, and the movement is performed quickly.

The operations of A and B are repeated for all calibration positions, and the amplitude is calculated from the data of the two-phase sine waves φA _{n (x)} and φB _{n (x) in} the wavelength λ range including the acquired calibration positions P _x. -Offset and phase errors are corrected and the corrected position detection signal φA _n '= A _n ' cos (θ _n + Δθ _An ') + V _An '
φB _n ′ = B _n ′ sin (θ _n + Δθ _Bn ′) + V _Bn ′
(A _n '= B _n ', Δθ _An '= Δθ _Bn ', V _An '= V _Bn ')
Get.

Then, the position error in the wavelength interval is reduced by obtaining the position Δp _x ′ in the wavelength interval by the above equation (5).

Next, each calibration position P is calculated from the number α of wavelengths counted at the time of movement and the position Δp _x ′ within the wavelength interval obtained from the two-phase sine wave corrected for amplitude, offset, and phase errors by the above equation (3). _x ′ = αλ + Δp _x ′ is calculated, and the output data Y _x to be calibrated is calibrated with reference to each calibration position P _x ′.

Next, a method for measuring the size of an object (measurement target) using the displacement calibration apparatus of this embodiment that uses two-phase sine waves φA _n and φB _n as position detection signals will be described.

As shown in FIG. 8, abutted against the measuring surface 12A of the calibration device to the dimensions metric 20 measures the reference position P ₀ of the dimension measurement. At that time, data of the two-phase sine waves φA _n and φB _n are acquired at least between the wavelength λ from P ₀ (360 ° or more), and the amplitude / offset / phase errors of the two-phase sine waves are obtained in the same manner as in the calibration. Is corrected, the position P ₀ ′ of the dimension measurement reference in which the interpolation error is corrected is calculated.

Next, as shown in FIG. 9, the measurement target T is disposed so as to abut against the dimension reference 20, and the measurement surface 12 </ b> A of the calibration device is abutted against the contact point between the measurement target T and the dimension reference 20. To measure the dimension measurement position P ₁ . At this time, the data of the two-phase sine waves φA _n and φB _n between P ₁ and at least the wavelength λ are acquired, and similarly the position P ₁ ′ where the interpolation error is corrected is calculated.

The dimension of the measuring object T is obtained from the difference between the two positions P ₀ ′ and P ₁ ′ calculated as described above. With this dimension measurement method, the accuracy of dimension measurement can be improved by reducing the interpolation error at the calibration position.

  According to the displacement calibration apparatus of the present embodiment described in detail above, at each calibration position, data of two-phase sine waves of one wavelength or more including each calibration position is acquired, and the amplitude / offset / phase errors are corrected. Thus, it is possible to reduce the interpolation error at each calibration position, reduce the calibration uncertainty, and improve the accuracy.

  Further, since it is not necessary to acquire two-phase sine wave data when moving between the calibration positions, the moving speed can be moved at the maximum speed of the apparatus regardless of the value of Vc. Therefore, the calibration throughput can be increased as compared with the conventional method.

  Also, since the two-phase sine wave data to be acquired is data for one wavelength including each calibration position, the memory capacity required for data acquisition is reduced compared to acquiring data in the entire calibration range by the conventional method. be able to.

  Further, according to the dimension measuring method using the displacement calibration device, when measuring the dimension of the object, the data of the two-phase sinusoidal wave for at least one wavelength including the respective positions at the dimension measuring reference position and the dimension measuring position. By correcting the error of amplitude, offset, and phase, the interpolation error at the dimension measurement reference position and the dimension measurement position can be reduced, the uncertainty of dimension measurement can be reduced, and the accuracy can be improved.

  As described above, according to the present invention, with respect to the displacement calibration technique using a two-phase sine wave as a position detection signal, the accuracy of calibration is improved by reducing the error at the interpolation position within the wavelength of the two-phase sine wave. It becomes possible to improve the accuracy of dimension measurement.

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

Schematic diagram showing the outline of the displacement calibration device Diagram showing output waveform of two-phase sine wave Diagram showing interpolation error Diagram showing examples of displacement meter calibration results Diagram showing movement pattern during conventional calibration The flowchart which shows the calibration procedure of embodiment Diagram showing movement pattern during calibration of embodiment Schematic diagram showing dimension measurement procedure 1 Schematic diagram showing dimension measurement procedure 2

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 ... Position detection means 10A ... Position reference surface 12 ... Slider 12A ... Measurement surface 14 ... Drive roller 16 ... Displacement meter 18 ... Data processing part

Claims (6)

Two-phase sinusoidal signals with different phases φA _n = A _n cos (θ _n + Δθ _An ) + V _An
φB _n = B _n sin (θ _n + Δθ _Bn ) + V _Bn
(N = 1, 2, 3 ...)
Using the position detecting means for detecting the position of the measuring surface by acquiring as a position detection signal, stops the measurement surface at any calibration position P _x, an operation of calibrating the output Y _x to be calibrated, the calibration position in displacement calibration method is repeated by moving the P _x,
When moving the measurement surface, the number α of wavelengths λ of the position detection signal is counted,
When the measurement surface is stationary, the values of φA _n and φB _n are acquired in the range of one wavelength or more of the two-phase sinusoidal signal including each calibration position P _x ,
Estimate and correct amplitude, offset, and phase errors in the obtained position detection signals φA _n and φB _n ,
Corrected position detection signal φA _n '= A _n ' cos (θ _n + Δθ _An ') + V _An '
φB _n ′ = B _n ′ sin (θ _n + Δθ _Bn ′) + V _Bn ′
(A _n '= B _n ', Δθ _An '= Δθ _Bn ', V _An '= V _Bn ')
From this, the position error within the wavelength interval is reduced by obtaining the position Δp _x ′ within the wavelength interval,
Each calibration position P _x '= αλ + Δp _x ' is obtained from the number α of wavelengths and the position Δp _x 'within the wavelength interval, and the output signal Y _x to be calibrated is calibrated using each calibration position P _x ' as a reference. Displacement calibration method characterized. When measuring the dimension of the measuring object using the displacement calibration method according to claim 1,
At the reference position P ₀ and the dimension measurement position P _{1 for} measuring the dimensions, the values of the position detection signals φA _n and φB _n are respectively acquired in a range of one wavelength or more including the positions P ₀ and P ₁ .
Estimate and correct amplitude, offset, and phase errors in position detection signals φA _n and φB _n ,
Corrected position detection signal φA _n '= A _n ' cos (θ _n + Δθ _An ') + V _An '
φB _n ′ = B _n ′ sin (θ _n + Δθ _Bn ′) + V _Bn ′
(A _n '= B _n ', Δθ _An '= Δθ _Bn ', V _An '= V _Bn ')
, A position measurement method in which a position P ₀ ′, P ₁ ′ with reduced position error within the wavelength interval is obtained, and the dimension of the measurement object is measured from the difference between the positions P ₀ ′, P ₁ ′. Two-phase sinusoidal signals with different phases φA _n = A _n cos (θ _n + Δθ _An ) + V _An
φB _n = B _n sin (θ _n + Δθ _Bn ) + V _Bn
(N = 1, 2, 3 ...)
A position detection means for detecting the position of the measurement surface by obtaining a position detection signal,
Moving means for stopping the measurement surface at an arbitrary calibration position P _x and moving the measurement surface to repeatedly perform the operation of calibrating the output Y _x to be calibrated;
When moving the measurement surface, the counting means for counting the number α of wavelengths λ of the position detection signal,
When the measurement surface is stationary, the values of φA _n and φB _n are acquired in the range of one wavelength or more of the two-phase sinusoidal signal including each calibration position P _x ,
Estimate and correct amplitude, offset, and phase errors in the obtained position detection signals φA _n and φB _n ,
Corrected position detection signal φA _n '= A _n ' cos (θ _n + Δθ _An ') + V _An '
φB _n ′ = B _n ′ sin (θ _n + Δθ _Bn ′) + V _Bn ′
(A _n '= B _n ', Δθ _An '= Δθ _Bn ', V _An '= V _Bn ')
From this, the position error within the wavelength interval is reduced by obtaining the position Δp _x ′ within the wavelength interval,
'Seeking, each calibration position _{P x' = αλ + Δp x} ' each calibration position P _x from the' position Delta] p _x number α and the wavelength interval of the wavelength as a reference, the data processing of calibrating the output signal Y _x to be calibrated And a displacement calibration apparatus.   A computer-readable program for executing the displacement calibration method according to claim 1 or the dimension measurement method according to claim 2.   A computer-readable program for realizing the displacement calibration apparatus according to claim 3.   A recording medium on which the computer-readable program according to claim 4 is recorded.

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