JP6779151B2 - Measuring method - Google Patents

Description

The present invention relates to a measuring method, and relates to a measuring method capable of measuring a straight shape or a surface shape of an object to be measured with high accuracy.

In order to accurately measure the surface shape and cross-sectional linear shape of the object to be measured such as a long object, comparative measurement with a standard straightedge may be performed. Alternatively, a method of calculating the linear shape by measuring the inclination of the mirror on the table that contacts the surface to be measured at two points in the scanning direction with an autocollimator based on the linearity of the optical axis is also used. When the reference cannot be used, a method of separating motion error and shape error is adopted by a multipoint method using a multipoint probe. Furthermore, there is also a method of obtaining a linear shape with a spirit level or a Talibel that abuts at two points.

On the other hand, as the object to be measured becomes larger, the standard ruler becomes longer and it becomes difficult to manufacture the ruler. In addition, the reference using the linearity of the optical axis may not be able to maintain sufficient accuracy due to the influence of the fluctuation of light rays in the air. Against this background, the need for measurement using the multipoint method is increasing, but the multipoint method has the problem of parabolic error due to zero-point adjustment error, and the longer the length and the more sequential the number, the more the parabolic error. There is a problem that becomes large.

Patent Document 1 describes, for example, a multipoint method in which the inclination of a stage is measured when the movement start point and the end point in shape measurement are stationary, and is included in the difference in inclination between both ends in a straight shape measured and evaluated by a multipoint probe. A technology that can realize so-called in-situ calibration that can calibrate the zero point of a multipoint probe from the target shape measurement data itself by utilizing the fact that the influence of the parabolic error due to the zero point adjustment error of the probe can be extracted is disclosed. There is.

2016-183887

By the way, according to Patent Document 1, an excellent measuring method capable of accurately measuring the shape of a long object without relying on a reference ruler or the like is realized, and it is detected by an angle measuring unit at a movement start point and an end point. The zero point error is obtained by using the angle difference. However, this method has a problem that it is directly affected by the measurement error caused by the accuracy, resolution and environmental disturbance of the angle measurement unit. Also, when the object to be measured is fixed and the sensor holder is scanned against it, the sensor holder is fixed and the object to be measured is fixed in the same way as the tilt angle of the sensor holder can be detected to obtain the zero point error. The zero point error can also be obtained by scanning the above and detecting the tilt angle due to the scanning of the measured object. However, in the latter case, when scanning the measured object, the zero point error is calculated because the measured object is a rigid body, that is, the measured object and the scanning table on which it is placed do not deform due to its own weight. However, in reality, a slight deformation occurs, so there is a discrepancy between the calculated value and the theoretical value.

In view of such a problem, an object of the present invention is to provide a measuring method capable of measuring the shape of an object to be measured more accurately and efficiently by reducing the influence of measurement error.

In the measurement method according to claim 1, one of the sensor holder and the measurement object is fixed, and while scanning the other, a plurality of sensors attached to the sensor holder are used, and the measurement object is sequentially measured by a multipoint method. In the measuring method for measuring the shape of
Steps to acquire the output of the sensor at N measurement points,
A step of detecting the tilt angle of the other of the sensor holder and the measurement object at an arbitrary measurement point, and
A step of obtaining a zero point error based on the difference between the tilt angle of the first measurement point and the tilt angle of a second measurement point different from the first measurement point, and further changing the measurement point to obtain the zero point error. When,
It has a step of taking the average of the obtained zero points error and obtaining the shape of the measurement object by using the average value and the output of the sensor.
The number of the zero error used for averaging is determined based on the number of measurement points n.

According to the present invention, the number of the zero point errors used for averaging is determined based on the number of measurement points n. Therefore, by obtaining the optimum value of the number of zero point errors by a statistical method, the inclination is obtained. The angle can be measured with an appropriate number, and the shape of the object to be measured can be measured more accurately and efficiently by using the average value of the zero point error and the output of the sensor obtained thereby. ..

The measuring method according to claim 2 is characterized in that, in the invention according to claim 1, the tilt angle of the sensor holder is detected at all measurement points, and thus is optimal from the measured tilt angle. You can choose the one and make a difference.

The measuring method according to claim 3 is characterized in that, in the invention according to claim 1 or 2, the number of the sensors is three, and the shape of the object to be measured is measured by sequentially using a three-point method. ..

According to the present invention, by reducing the influence of measurement error, it is possible to provide a measurement method capable of measuring the shape of an object to be measured more accurately and efficiently.

It is the schematic of the measurement system provided with the measuring apparatus which concerns on this embodiment. It is a figure which looked at the measuring apparatus MD in the Z direction. It is a figure which shows the schematic structure of the angle measuring unit AMU. It is a figure which shows typically the relationship between the optical element OBJ and the probes PB1 to PB3, and shows the case where the difference is 0. It is a figure which shows typically the relationship between the optical element OBJ and the probes PB1 to PB3, and shows the case of difference 1. It is a figure which shows typically the relationship between the optical element OBJ and the probes PB1 to PB3, and shows the case of difference 2. It is a graph which plotted the value when the number of measurement points n = 35 with the evaluation value m as the vertical axis and the difference m as the horizontal axis. It is a graph which plotted the value in the case of the number of measurement points n = 20, 25, 30, 35, 40 with the evaluation value m as the vertical axis and the difference m as the horizontal axis. It is a graph which plotted the measured value with the evaluation value m as the vertical axis and the difference m as the horizontal axis.

Hereinafter, embodiments of the present invention will be described with reference to the drawings. FIG. 1 is a schematic view of a measurement system including the measuring device according to the present embodiment, and shows a state viewed from diagonally below. In FIG. 1, a base plate BP whose lower surface is grounded is provided on a surface plate (not shown). Further, a pair of wall WLs are provided so that the lower ends are in contact with the base plate BP. A top plate CL is joined to the upper end of the wall WL. An optical element OBJ, which is an object to be measured, is attached to the lower surface of the top plate CL as a holding table with the optical surface facing downward. On the base plate BP facing the top plate CL, the measuring device MD is movably arranged with respect to the optical element OBJ. Here, the moving direction of the measuring device MD is the X direction, the gravitational acceleration direction orthogonal to the X direction is the Y direction, and the direction orthogonal to the X direction and the Y direction is the Z direction.

FIG. 2 is a view of the measuring device MD in the Z direction. The sensor holder SH is arranged on the scanning unit SP that can move along the X direction on the base plate BP. In the sensor holder SH, three probes PB1, PB2, and PB3, which are displacement sensors, are arranged along the X direction. The detection sensitivity axis directions of the probes PB1, PB2, and PB3 are in the Y direction, and the detection sensitivity axis spacing thereof is d. The outputs of the three probes PB1, PB2, and PB3 are input to a personal computer (not shown) or the like, and the calculation described later is performed to obtain the shape.

Further, an angle measuring unit AMU for measuring the tilt angle of the sensor holder SH is arranged on the sensor holder SH so as to be integrally tilted. FIG. 3 is a diagram showing a schematic configuration of the angle measuring unit AMU. A support HD holding the case CA is fixed on the sensor holder SH.

A light source LD that emits a collimating luminous flux DL, a beam splitter BS, and a photodetector PD that detects the luminous flux DL are fixed in the case CA. Further, the reference mirror SR is connected to the lower end of the thread SG (it is easier to stabilize if there are two) hanging from the ceiling surface of the case CA. As a result, the reflecting surface of the reference mirror SR is parallel to the gravitational acceleration direction. The light source LD, the reference mirror SR, and the photodetector PD constitute a light emitting / receiving system.

The angle measurement unit AMU is calibrated with the sensor holder SH horizontal. At this time, the luminous flux DL emitted from the light source LD passes through the beam splitter BS and is incident on the reference mirror SR. The luminous flux DL reflected by the reference mirror SR is reflected by the beam splitter BS and is incident on the light receiving surface PDa of the photodetector PD. The incident position at this time is set as the origin and stored in a memory or the like (not shown). When actually measuring the tilt angle of the sensor holder SH, the case CA also tilts together with the sensor holder SH, whereas the reference mirror SR always extends in the direction of gravitational acceleration, so the luminous flux DL incident on the reference mirror SR The angle of incidence of the light flux DL changes, and the position where the reflected luminous flux DL is incident on the light receiving surface PDa of the photodetector PD shifts from the origin. Since this amount of deviation corresponds to the inclination angle of the sensor holder SH, the inclination angle of the sensor holder SH can be known by detecting the amount of deviation. The angle measuring unit AMU is not limited to the above configuration.

Next, a method of measuring the shape of the optical surface of the optical element using the measuring device MD in the present embodiment will be described.

Here, the sequential three-point method used for shape measurement will be described. In the sequential three-point method, since a plurality of probes PB1, PB2, and PB3 are used, there is a zero point error as a measurement error factor generated between the probes. For example, when the position of the central probe PB2 in the Y direction is used as a reference, the other adjacent probes PB1 and PB3 have zero error (deviation in the Y direction) of α _R and α _F , respectively. In this way, the zero point error is the deviation of each zero point between a plurality of probes.

In this case, in order to match the zero points of a plurality of probes, it is usually necessary to hit a reference object (that is, a substantive reference) having some reference straight line and adjust the reading so that it becomes zero. It is theoretically possible. However, in reality, this reference object often does not have an ideal straight line, and when the sequential three-point method is used in shape measurement, it is extremely difficult to align the zero points of the three probes. Therefore, if the probe has a zero error, it will affect the shape measurement as described below.

In FIG. 2, three displacement meters (probes) PB1 to PB3 held by the sensor holder SH are arranged at equal intervals d along the relative movement direction (X direction) between the object to be measured OBJ and the scanning unit SP. When the true surface shape of the object to be measured is g, the surface shape on which the zero point error is superimposed is f, the translational motion error e _{z of} the scanning table, and the rotational motion error e _θ of the scanning table, the central probe PB2 The output is S ₃₀ , the output of the probe PB1 in the front in the relative movement direction is S _3F , the output of the probe PB _{3 in} the rear in the relative movement direction is S _3R, and the zero points of the front and rear probes with respect to the center probe are α _R and α _F As a result, the following equation is obtained when the object to be measured OBJ and the scanning unit SP are relatively moved along the X direction to measure n points.
S ₃₀ (x _i ) = g (x _i ) + _ez (x _i ) (1)
S _3F (x _i ) = g (x _{i + 1} ) + e _z (x _i ) + de _θ (x _i ) + α _F (2)
S _3R (x _i ) = g (x _i-1 ) + e _z (x _i ) -de _θ (x _i ) + α _R (3)
f (x _i ) = g (x _i ) + n (n-1) α / 2 (4)
However, α = α _F + α _R

[When the difference is 0]
FIG. 4 is a diagram schematically showing the relationship between the optical element OBJ and the probes PB1 to PB3. In order to obtain the zero point error, the inclination of the sensor holder SH due to the motion error at the measurement start point and the measurement nth point (for example, the measurement end point) is used. This is called the case where the difference is 0. In the sequential three-point method, the motion error can be separated by arithmetic processing, but if the zero points of each probe are deviated, the amount of each separated motion error is also affected. The following shows the equation of the motion error obtained by the arithmetic processing when the zero point error does not occur (α = 0) and when it does occur (α ≠ 0).

(A) Translational motion error e _z and rotational motion error e _θ when no zero error occurs:
e _z (x _i ) = S ₃₀ (x _i ) -g (x _i )
= S ₃₀ (x _i ) -f (x _i ) (5)
de _θ (x _i ) = S _3F (x _i ) -S ₃₀ (x _i ) -g (x _{i + 1} ) + g (x _i )
= S _3F (x _i ) -S ₃₀ (x _i ) -f (x _{i + 1} ) + f (x _i )
= ΔS _3F (x _i ) −Δf (x _i ) (6)

Further, the rotational motion errors e _theta measurement starting point (x _0), the rotational motion errors at the measurement point n th e _theta difference Δe _{θ (x n)} and (x _n) can be expressed by the following equation.
dΔe _θ (x _n ) = d {e _θ (x _n ) -e _θ (x ₀ )}
= {ΔS _3F (x _n ) -Δf (x _n )}-{ΔS _3F (x ₀ ) -Δf (x ₀ )} (7)

(B) translation error e _z when zero error is generated 'and rotational motion error e _theta':
e _z '(x _i ) = S ₃₀ (x _i ) -g (x _i )
= S ₃₀ (x _i ) -f (x _i ) + n (n-1) α / 2 (8)
de _θ '(x _i ) = S _3F (x _i ) -S ₃₀ (x _i ) -g (x _{i + 1} ) + g (x _i )
= S _3F (x _i ) -S ₃₀ (x _i )-{f (x _{i + 1} )-(n + 1) (n + 1-1) α / 2} + {f (x _i ) -n (n-1) α / 2} -α _F
= ΔS _3F (x _i ) -Δf (x _i ) + nα-α _F (9)

Here, if the zero points of the central probe and the rear probe are considered to be on the same straight line, α _R = 0, so α = α _F. Therefore, equation (9) can be expressed as follows.
de _θ '(x _i ) = ΔS _3F (x _i ) -Δf (x _i ) + nα-α _F
= ΔS _3F (x _i ) −Δf (x _i ) + (n-1) α (10)

Furthermore, rotational motion errors e _theta measurement starting point 'and (x _0), the rotational motion errors at the measurement point n th e _theta' difference Δe _θ '(x _n) and (x _n) is the following formula Can be represented.
dΔe _θ '(x _n ) = d {e _θ '(x _n ) -e _θ '(x ₀ )}
= {ΔS _3F (x _n ) -Δf (x _n )}-{ΔS _3F (x ₀ ) -Δf (x ₀ )} + (n-1) α (11)

That is, when the equations (7) and (11) are compared, the difference is (n-1) α, and the number of measurement points n is known. Therefore, if the zero error α is obtained, the zero error is eliminated. It can be said that the shape of the object to be measured can be obtained. However, dΔe _θ '(x _n ) can be obtained by arithmetic processing from the measured value of the probe, but dΔe _θ (x _n ) that does not include the zero error is an unknown number. In this embodiment, the inclination angle theta ₀ of the sensor holder SH Start of measurement points using the angle measuring unit AMU, Taking the difference by directly measuring the inclination angle theta _n of the sensor holder SH at the measuring point n th , Since it corresponds to {e _θ '(x _n ) -e _θ '(x ₀ )} in Eq. (11), the left side of Eq. (11) can be obtained by further multiplying by the probe interval d. From Eq. 7), dΔe _θ (x _n ) that does not include the zero point error can be obtained. More specifically, the zero error can be obtained from the following equation.
α = d {Δe _θ '(x _n ) −Δe _θ (x _n )} / (n-1) (12)

Using the obtained zero error α, if correction is performed from Eq. (4) so as to subtract n (n-1) α / 2 from the arithmetic processing result f (x _i ) of the sequential three-point method, the true shape g (x _i ) can be obtained.

[In the case of difference 1]
FIG. 5 is a diagram schematically showing the relationship between the optical element OBJ and the probes PB1 to PB3, but the optical element OBJ is divided into two for easy understanding. In this example, the actual measurement length is L, but the actual measurement length is regarded as (Ld) to obtain the zero error. Further, in order to obtain the zero point error, the inclination of the sensor holder SH is measured at the measurement start point, the measurement second point, the measurement (n-1) point, and the measurement nth point. This is called the case of difference 1.

Specifically, as shown in FIG. 5 (a), taken as the inclination angle theta ₀ at the measurement starting point, the difference in inclination between the inclination angle theta _n-1 in the measurement (n-1) th point, As shown in FIG. 5 (b), by taking the difference in inclination between the inclination angle θ ₁ at the second measurement point and the inclination angle θ _n at the nth measurement point, as shown in the equation (12). Therefore, it is possible to calculate the two zero point errors.

[In the case of difference 2]
FIG. 6 is a diagram schematically showing the relationship between the optical element OBJ and the probes PB1 to PB3, but the optical element OBJ is divided into three parts for easy understanding. In this example, the actual measurement length is L, but the actual measurement length is regarded as (L-2d) and the zero point error is obtained. Further, in order to obtain the zero error, the sensor holder SH is used at the measurement start point, the measurement second point, the measurement third point, the measurement (n-2) point, the measurement (n-1) point, and the measurement nth point. Measure the tilt of. This is called the case of difference 2.

Specifically, as shown in FIG. 6, taken as the inclination angle theta ₀ at the measurement starting point, the difference in inclination between the inclination angle theta _n-2 of the measurement (n-2) th point, the measurement second the inclination angle theta ₁ at the point th measurement (n-1) taking the difference between the inclination of the inclined angle theta _n-1 at th point, the inclination angle theta ₂ in the measurement third goal, the measurement point n By taking the difference in inclination from the inclination angle θ _n at the eyes, it is possible to calculate the three zero point errors as shown in the equation (12).

[In the case of difference m]
As is clear from the above, when the actual measurement length is regarded as (L-md) and the zero point error is obtained, m + 1 (however, m <n) zero point errors can be obtained. Therefore, m as the number of differences can be defined as "the number of zero errors that can be obtained-1".

By the way, since the zero point errors in the above measurements can be regarded as the same, if the average value of the zero point errors is used, the effect of the measurement error caused by the accuracy and resolution of the angle measurement unit AMU and the disturbance of the environment can be obtained by the averaging effect. It can be said that it can be reduced and the true shape g (x _i ) can be obtained with higher accuracy. On the other hand, as shown in Eq. (12), the error is included in the numerator, and due to the influence of the denominator (n-1), the error tends to increase as the number of steps for calculating the zero error decreases. There is. Therefore, if m as the number of differences is increased, the error may be reduced accordingly, but even if m is increased indefinitely, it has become clear that the reduction effect is limited due to the variation in error. It was. In the sequential three-point method used in this embodiment, the output from the probe is digitized for arithmetic processing. Therefore, assuming that an error occurs at the minimum digit of ± 1, the variation of the error will be examined below.

Since the error inherent in this digitization occurs randomly, it can be said that "-1", "0", and "1" occur with the same probability. For example, in the case of a difference of 0, there are 3 × 3 = 9 combinations of differential outputs, and the results are classified into 5 categories of “-2”, “-1”, “0”, “1”, and “2”. Will be done. On the other hand, the frequency (ratio) of occurrence is 1: 2: 3: 2: 1 in the above classification order. The standard deviation σ of this variation is 1.504. Hereinafter, the occurrence ratio and the standard deviation are shown according to the type of difference.

[When the difference is 0 (there is one zero error)]
Error = "-1", "0", "1"
Differential output classification = "-2", "-1", "0", "1", "2"
Occurrence ratio = 1: 2: 3: 2: 1
Standard deviation σ ₀ = 1.054

[In the case of difference 1 (use the average value of two zero errors)]
Error = "-4", "-3", "-2", "-1", "0", "1", "2", "3", "4"
Differential output classification = "-2", "-1.5", "-1", "-0.5", "0", "0.5", "1", "1.5", " 2 "
Occurrence ratio = 1: 4: 10: 16: 19: 16: 10: 4: 1
Standard deviation σ ₁ = 0.816

[In the case of difference 2 (use the average value of three zero errors)]
Error = "-6", "-5", "-4", "-3", "-2", "-1", "0", "1", "2", "3", "4" , "5", "6"
Differential output classification = "-2", "-5/3", "-4/3", "-1", "-2/3", "-1/3", "0", "1 /" 3 ”,“ 2/3 ”,“ 1 ”,“ 4/3 ”,“ 5/3 ”,“ 2 ”
Occurrence ratio = 1: 6: 21: 50: 90: 126: 141: 126: 90: 50: 21: 1
Standard deviation σ ₂ = 0.667

Table 1 summarizes the standard deviation σ _m when the difference is 0 to 19.

Since the denominator of the equation (12) is different between the standard deviation σ ₀ when the difference is ₀ and the standard deviation σ _m when the difference is m, the evaluation value m is obtained in consideration of the denominator. Table 2 shows the evaluation value m when the number of measurement points n = 35.

FIG. 7 is a graph in which the evaluation value m is plotted on the vertical axis and the difference m is plotted on the horizontal axis when the number of measurement points is n = 35. As described above, in the equation (12) for obtaining the zero point error, the error is included in the numerator, and as the number of steps for calculating the zero point error decreases due to the influence of the denominator (n-1), FIG. As shown, the error becomes large. However, there is an optimum value of the difference (that is, the number of zero errors used for averaging) with respect to the evaluation value m. Specifically, in the example of FIG. 7, the evaluation value m is the smallest in the case of the difference 11. Therefore, by limiting the number of differences, highly accurate shape measurement can be performed without spending a long time.

FIG. 8 is a graph in which the evaluation values m are plotted on the vertical axis and the difference m is plotted on the horizontal axis when the number of measurement points is n = 20, 25, 30, 35, 40. In any case, it can be seen that the optimum value of the difference exists with respect to the evaluation value m. Further, the optimum value of the difference changes according to the number of measurement points n.

Hereinafter, in the measuring apparatus shown in FIGS. 1 and 2, the present inventors set the probe interval to 30 mm using a glass plate as the measurement object, set the number of measurement points n = 35, and repeatedly measure the shape four times under the same conditions. Was done. The probe was an electric micrometer, and the tilt angle was measured with a spirit level (0.01 mm / m). FIG. 9 shows a graph in which the measured values are plotted with the evaluation value m on the vertical axis and the difference m on the horizontal axis based on the variation in the zero point error obtained in the four measurements.

Comparing the graph of FIG. 9 with the graph of FIG. 7, it was found that the tendency of both graphs was the same, although the number of differences which became the optimum value was different.

The present invention is not limited to the examples described in the specification, and it is clear to those skilled in the art from the examples and ideas described in the present specification that the present invention includes other examples and modifications. Is. The description and examples of the specification are for illustration purposes only, and the scope of the present invention is indicated by the claims described below. For example, in the above-described embodiment, the scanning unit SP is moved, but instead of fixing the sensor holder SH side, the top plate CL side may be moved as the scanning stage. In that case, it is necessary to detect the tilt angle at the measurement point on the moving top plate (or object to be measured) side. As the sensor for detecting the tilt angle, the angle measuring unit AMU shown in FIG. 3 or the like can be used, and the zero point error can be obtained in the same manner as described above. Further, the tilt angle of the sensor holder may be detected together with the output of the probe at each shape measurement point, or the tilt angle of the sensor holder may be detected at the thinned shape measurement points. The sequential multipoint method includes cases other than the sequential three-point method.

AMU angle measurement unit BP base plate BS beam splitter CA case CL top plate DL luminous flux HD support LD light source MD measuring device OBJ optical element PB1-PB3 probe PD photodetector PDa light receiving surface SG thread SH sensor holder SP scanning unit SR reference mirror WL wall

Claims (3)

In a measurement method in which one of a sensor holder and a measurement object is fixed, and the shape of the measurement object is measured by a sequential multipoint method using a plurality of sensors attached to the sensor holder while scanning the other.
The step of acquiring the output of the sensor at n measurement points, and
A step of detecting the tilt angle of the other of the sensor holder and the measurement object at an arbitrary measurement point, and
A step of obtaining a zero point error based on the difference between the tilt angle of the first measurement point and the tilt angle of a second measurement point different from the first measurement point, and further changing the measurement point to obtain the zero point error. When,
It has a step of taking the average of the obtained zero points error and obtaining the shape of the measurement object by using the average value and the output of the sensor.
A measuring method characterized in that the number of zero error used for averaging is determined based on the number of measurement points n. The measurement method according to claim 1, wherein the tilt angle of the sensor holder is detected at all measurement points. The measuring method according to claim 1 or 2, wherein the number of sensors is three, and the shape of the object to be measured is measured by sequentially using a three-point method.