TWI417512B - Linear measurement method and linear measuring device - Google Patents

Description

Linear measuring method and linear measuring device

The present application claims priority based on Japanese Patent Application No. 2008-277597, filed on Oct. 29, 2008. The entire contents of this application are incorporated herein by reference.

The present invention relates to a method of measuring linearity using a 3-point method and a device for measuring linearity.

The measurement of the surface linearity of the object to be measured (Patent Document 1) can be performed by the three-point method. For example, the measurement data of the three displacement meters is described by using the trajectory of the reference point movement of the three displacement meters, that is, the contour of the simulation curve, the surface contour of the measurement object, and the contour of the pitch components of the three displacement meters. The description is solved as a simultaneous equation, which determines the surface contour.

Patent Document 1: Japanese Patent Publication No. 2003-254747

In order to separate the trajectory of the displacement meter based on the data measured by the three-point method, that is, the contour of the simulation curve, the contour of the pitch component generated when the three displacement gauges move, and the surface contour of the measurement object, it is necessary to adjust three precisions with high precision. Zero point of the displacement meter. For example, in order to measure the linearity of the surface having a flatness of several μm , it is necessary to set the offset of the zero point of the three displacement gauges from the target position to several tens of nanometers to several nanometers or less.

Further, the zero point of the non-contact displacement meter such as a laser displacement meter varies depending on the surface properties of the object to be measured, for example, the state of the polishing mark caused by the grinding wheel, the roughness, the material, the reflectance, the transmittance, and the like. Moreover, the change of zero The amount has individual differences. Therefore, it is difficult to perform the zero point adjustment of the displacement meter with high precision in advance.

An object of the present invention is to provide a linear measuring method capable of calculating a surface contour of a measuring object without performing zero adjustment of three displacement meters with high precision.

Another object of the present invention is to provide a linearity measuring apparatus for measuring linearity by the above method.

According to one aspect of the present invention, there is provided a method for measuring a linearity, comprising: displacing three displacement meters arranged in a first direction and a relative position with an object to be measured, and causing a displacement gauge or an object thereof The object that is moved by one of the objects is a moving object, and the other is a fixed object, and the movable object that is one of the objects to be measured is moved in the first direction with respect to the other fixed object, and the measurement is performed from three a step of measuring the distance to the three measured points arranged on the surface of the measuring object along the measuring object line extending in the first direction; calculating the relative position to the living object based on the measurement results of the three displacement meters The trajectory of the fixed reference point is a step of emulating the contour of the curve; the second component of the contour calculated by the above imitating curve is corrected based on the second component of the contour of the imitating curve measured in advance; based on the corrected The step of emulating the contour of the curve and calculating the surface profile of the object to be measured.

According to another aspect of the present invention, a linearity measuring apparatus includes: a table for supporting an object to be measured; and a sensor head including a body that is measured to be aligned in the first direction on a surface of the object to be measured a three displacement meter for measuring the distance of the point; the guiding mechanism movably supporting the movable body of the sensor head and one of the working tables along the first direction with respect to the other fixed object; and the control device stores a second component which is a trajectory fixed to a reference point of the living object, that is, a simulation curve, and the surface along the measurement target line parallel to the first direction is obtained based on measurement data measured by the three displacement meters In the contour, the control device performs the measurement of the distance along the measured point on the surface of the measurement target line by measuring the moving object in the first direction and measuring the distance along the surface of the measurement target line by each of the three displacement meters. The step of calculating the trajectory of the reference point to which the relative position of the living object is fixed, that is, the contour of the emulation curve, based on the measurement results of the three displacement meters a step of correcting the second component of the contour of the calculated contour curve based on the second component of the contour of the stored imitative curve; and calculating a surface profile of the object to be measured based on the contour of the corrected imitative curve The steps.

By measuring the secondary component of the contour of the emulation curve in advance without being affected by the contour variation of the emulation curve, the second component of the emulation curve can be determined even if the zero adjustment of the displacement gauge is not performed. Thereby, it is possible to perform measurement of the surface contour of the measurement object without performing precise zero adjustment.

Fig. 1A shows a perspective perspective view of a linear measuring device according to an embodiment. The movable table 10 is supported by the table guiding mechanism 11 so as to be movable in one direction. An xyz rectangular coordinate system in which the moving direction of the movable table 10 is set to the x-axis and the vertical lower side is set to the z-axis is defined.

The guide rail 18 supports the polishing head 15 above the movable table 10. The polishing head 15 is movable along the guide rail 18 in the y-axis direction. Moreover, the polishing head 15 can also move in the z direction with respect to the guide rail 18. That is, the polishing head 15 can be raised and lowered with respect to the movable table 10. A grinding wheel 16 is attached to the lower end of the polishing head 15. The grinding wheel 16 has a cylindrical outer shape and is attached to the polishing head 15 with its central axis parallel to the y-axis.

The object to be measured (object to be polished) 20 is held on the movable table 10. In a state where the grinding wheel 16 is brought into contact with the surface of the object 20 to be measured, the surface of the object 20 to be measured can be polished by moving the movable table 10 in the x direction while rotating the grinding wheel 16.

The control device 19 controls the movement of the movable table 10 and the polishing head 15.

As shown in FIG. 1B, a sensor head 30 is mounted at the lower end of the polishing head 15. In the sensor head 30, three displacement meters 31i, 31j, and 31k are mounted. The displacement meters 31i, 31j, 31k use, for example, a laser displacement meter. The displacement meters 31i, 31j, 31k can measure the distances from the displacement gauge to the measured points on the surface of the object 20 to be measured, respectively. The three displacement meters 31i, 31j, and 31k are arranged in the y direction. Further, the measured points of the three displacement meters 31i, 31j, and 31k are also arranged in the y direction. Therefore, the height of the surface of the measuring object line parallel to the y direction can be measured. By measuring while moving the polishing head 15 in the y direction, the surface profile of the measurement target line along the surface of the object 20 can be measured. The measurement data is input from the displacement meters 31i, 31j, 31k to the control device 19.

The coordinate system and various functions will be described with reference to Fig. 2 . In Fig. 2, the upper direction is set to the positive direction of the z-axis. Therefore, the upper and lower relationship of the sensor head 30 and the measuring object 20 is opposite to the above-described relationship shown in FIG. 1B. The displacement meters 31i, 31j, and 31k are arranged at equal intervals P in this order in the negative direction of the y-axis. The midpoint of the line segment connecting the zero points of the displacement meters 31i and 31k at both ends is defined as a reference point. The height (zero point error) of the zero point of the displacement meter 31j from the reference point to the center is set to δ.

The surface of the object 20 to be measured and the contour along the line to be measured are set to W(y). The trajectory (imitation curve) of the reference point when moving the sensor head 30 in the y direction is set to h(y). Ideally, the emulation curve h(y) is a straight line, but actually distort from the ideal straight line.

The angle at which the straight line connecting the zero points of the displacement meters 31i and 31k at both ends is inclined from the y-axis is θ(y). Ideally, the tilt angle θ(y) = 0, but actually the pitch is generated as the sensor head 30 moves, whereby the tilt angle θ(y) and the slope of the emulation curve h(y) are independently varied. The difference between the height of the displacement point 31i and the height of the reference point, and the difference between the height of the displacement gauge 31k and the height of the reference point can be expressed as T(y) × P. Here, it is approximated by the pitch component T(y)=sin(θ(y)). When the measured values of the displacement meters 31i, 31j, and 31k are respectively set to i(y), j(y), and k(y), the following expression holds.

[Math 1]

W(y+P)=h(y)+i(y)+T(y)×P (1)

W(y)=h(y)+j(y)+δ...(2)

W(y-P)=h(y)+k(y)-T(y)×P (3)

Since the inclination angle θ(y) is very small, cos(θ(y)) is approximated to 1.

The shape of the object 20 to be measured is, for example, a square having a length of 2 m on one side, and the interval P of the displacement meter is, for example, 100 mm.

When T(y) and h(y) are eliminated from the formulas (1), (2), and (3), the following formula can be obtained.

[Math 3]

W(y+P)-2W(y)+W(y-P)+2δ=i(y)-2j(y)+k(y)...(4)

Here, it is assumed that the surface profile W(y) is expressed by the following three equations (5).

[Math 4]

W(y)=ay ³ +by ² +cy+d ...(5)

When the formula (5) is substituted into the formula (4), the following formula (6) is obtained.

[Math 5]

6aP ² y+2bP ² +2δ=i(y)-2j(y)+k(y)...(6)

The right side of equation (6) is the measurement data, and the interval P of the displacement meter is known. Thus, the unknown a on the left can be calculated from the first component of the variable y on the right. However, even if the zeroth component of y on the right side is obtained, the zero point error δ on the left side is unknown, so the unknown number b cannot be determined. That is, the third component a of the surface profile W(y) can be determined, but the secondary component b cannot be determined. Further, the component of the surface profile W(y) of four or more times may be determined in the same manner as the third component.

In the embodiment, in order to compensate for the secondary component of the undeterminable surface profile W(y), the secondary component of the simulation curve h(y) is measured in advance. The second component of the emulation curve h(y) corresponds to the deflection of the guide rail 18, so that it is considered that there is no large variation in each measurement. Therefore, when the secondary component of the simulation curve h(y) is measured in advance, it is not necessary to re-measure the secondary component of the simulation curve h(y) every time the measurement of the surface profile of the measurement object is performed. Further, it can be considered that the components of the simulation curve h(y) three or more times are unpredictably changed each time the surface profile is measured (when the sensor head 30 moves each time). Therefore, even if the component of the simulation curve h(y) is measured three times or more in advance, the measurement result of the actual measurement object cannot be corrected based on the component measured three times or more in advance.

FIG. 3A is a flowchart showing a method of measuring the secondary component of the emulation curve h(y) in advance as an example. As shown in FIG. 3B, the measurement object 20 is placed on the movable table 10 in step S1. The inclination of the slope along the straight surface is measured by moving the inclinometer 35 along an arbitrary straight line parallel to the y direction on the surface of the measuring object 20. The surface profile W(y) is calculated from the distribution of the inclination. The measurement by the inclinometer is not affected by the skew of the guide rail 18.

In step S2, the measurement data j(y) is obtained by measuring the surface profile of the same line as the straight line measuring the oblique distribution by the inclinometer 35 by using the displacement meter 31j.

In step S3, the secondary component of the emulation curve h(y) is calculated. Hereinafter, the calculation method will be described. The surface profile measured by the displacement meter 31j is the same as the surface profile W(y) obtained from the measurement by the inclinometer. Therefore, the relationship of the equation (2) holds between the surface contour W(y) obtained by the measurement by the tilt meter and the measurement data j(y) measured by the displacement meter 31j. Since the zero point error δ is a constant, the secondary component of the simulation curve h(y) can be calculated from the secondary component of the surface profile W(y) and the secondary component of the measurement data j(y). The calculated secondary component is stored in the control device 19.

The contour of the emulation curve h(y) generally changes each time the polishing head 15 is moved in the y direction, and is not limited to being the same contour each time. However, it can be considered that the secondary component of the emulation curve h(y) determines the low-order component of the approximate shape of the emulation curve and has high reproducibility. That is, it can be considered that there is no major change in each measurement.

A flow chart of the linearity measuring method according to the embodiment is shown in FIG. First, the object 20 to be measured is loaded on the movable table 10. The object 20 to be measured does not need to be the same as the object 20 to be measured by measuring the surface profile with the inclinometer in the step shown in FIG. 3A.

In step SA1, while moving the polishing head 15 and the sensor head 30 in the y direction, the distances i(y), j(y) of the measured points on the surface of the object 20 are measured by the displacement meters 31i, 31j, and 31k. ), k(y). The measured data is input to the control device 19.

In step SA2, a low-pass filter is applied to the measurement data i(y), j(y), and k(y) to remove the noise component. In order to effectively act on the low-pass filter, the measurement data i(y), j(y), k(y) are taken at a very narrow scale with respect to the interval P of the displacement meter. For example, measurement data i(y), j(y), k(y) are obtained with a scale width of 0.05 mm.

In step SA3, the measurement data i(y), j(y), k(y) after the low-pass filter is applied is sampled to generate step data. The sampling period is, for example, one half of the interval P of the displacement meter, that is, 50 mm.

In step SA4, the emulation curve h(y) and the pitch component T(y) are derived using a genetic algorithm based on the step data i(y), j(y), k(y).

A detailed flow chart of step SA4 using the genetic algorithm is shown in FIG. In the genetic algorithm, a group of the emulation curve h(y) and the pitch component T(y) is set to one individual.

A first generation individual group is generated in step SB1. For example, the number of individuals is 200. An example of this is to set the emulation curve h(y) and the pitch component T(y) of one individual to zero. The other 199 individuals' imitate curves h(y) and pitch components T(y) are determined according to random numbers. In addition, in the initial state, the emulation curve h(y) and the pitch component T(y) of all individuals can also be set to zero.

In step SB2, each body is evaluated by an evaluation function, and the fitness of each body is calculated. The evaluation function is set according to the surface profile W(y). The three displacement meters 31i, 31j, and 31k measure the contours of the same measurement target line along the surface of the same measurement object 20, so the three surface contours W ₁ (y) calculated by the equations (1) to (3), respectively. W ₂ (y) and W ₃ (y) should be consistent.

Thus, first obtains a difference W ₁ (y) and W ₂ (y) the amount _{W 1 (y) -W 2 (} y), and W ₂ (y) and W ₃ (y) of the difference between the amount of W ₂ (y )-W ₃ (y). When the surface contour W(y) is expressed by a polynomial, the zero-order component corresponds to the interval between the measurement target 20 and the sensor head 30, and the primary component corresponds to the posture of the measurement target 20. That is, the 0th order component and the 1st order component of the surface profile W(y) are not directly related to the surface profile of the measuring object 20. Therefore, the zero-order component and the primary component are removed from the difference W ₁ (y) - W ₂ (y) and the difference W ₂ (y) - W ₃ (y).

Calculate the standard deviation (standard deviation: also known as standard deviation) of the difference W ₁ (y)-W ₂ (y) and the difference W ₂ (y)-W ₃ (y) of the zero-order component and the first-order component. Or rms difference). The sum of these two standard deviations is set as an evaluation function. The smaller the value of the evaluation function, the higher the fitness. Sort all individuals according to fitness.

In step SB3, the individual who becomes the intersection object is selected. As an example, the more appropriate the individual, the higher the probability of selecting an individual. Based on the selection probability, 10 pairs composed of 2 individuals are selected.

In step SB4, the selected individual crosses at least one of the emulation curve h(y) or the pitch component T(y) to generate a new individual.

The method of intersection will be described with reference to FIG. The emulation curve h(y) and the contour T(y) of the pitch component of the two individuals Ua and Ub selected as the intersecting objects in this generation are shown. A part of the emulation curve h(y) of the individual Ua is replaced (crossed) with the part corresponding to the emulation curve h(y) of the individual Ub, and new individuals Uc and Ud are generated. The contour T(y) of the pitch components of the new individuals Uc and Ud still inherits the contour T(y) of the pitch components of the original individuals Ua and Ub, respectively. In this way, two individuals are newly generated from two individuals. Ten pairs of individuals are selected in step SB3, so 10 pairs, that is, 20 individuals, are newly generated in step SB4.

Alternatively, the contour T(y) of the pitch component may be crossed, or both the contour curve h(y) and the contour T(y) of the pitch component may be crossed.

When the step SB4 ends, in step SB5, the individual who is the subject of the sudden mutation is selected. As an example, except for 10 individuals with high suitability, 80 are selected from the remaining 190 individuals.

In step SB6, a sudden mutation occurs on the selected individual to generate a new individual.

The method of sudden variation will be described with reference to FIG. An individual Ue selected in step SB5 is shown in FIG. A new individual Uf is generated by superimposing a Gaussian curve of arbitrary amplitude and height on the emulation curve h(y) of the individual Ue. Alternatively, the Gaussian curve may be superimposed on the contour T(y) of the pitch component of the individual Ue, or the Gaussian curve may be superimposed on both the emulation curve h(y) and the contour T(y) of the pitch component. Since 80 individuals are selected in step SB5, 80 individuals are newly generated in step SB6.

In step SB7, individuals with low fitness are eliminated. Specifically, 100 individuals with low fitness were replaced with newly generated 100 individuals in this generation of 200 individuals. Thus, a new generation of 200 individuals is determined.

In step SB8, a new generation of 200 individuals is evaluated to determine the fitness. In addition, the fitness has been calculated for the 100 individuals who have not eliminated the previous generation at step SB7, so it is not necessary to recalculate the fitness. Sort a new generation of 200 individuals according to fitness.

In step SB9, it is determined whether or not the generation number reaches the target value, and if the target value is not reached, the process returns to step SB3. When the target value is reached, in step SB10, the emulation curve h(y) of the most suitable individual among the latest generation individuals and the contour T(y) of the pitch component are taken as the optimal solution.

The displacement of the evaluation value is shown in FIG. The horizontal axis represents the number of generations, and the vertical axis represents the value (evaluation value) of the evaluation function of the individual with the highest fitness among the generations. It can be seen that as the generation evolves, the evaluation value decreases (the fitness increases). In the 2000s, the value of the evaluation function dropped to approximately 0.4 μm ² . It can be seen that the standard deviation is 0.63 μm, and sufficient accuracy is obtained. Moreover, in the case of about 500 generations, the evaluation value converges to 90%, and then, based on the slow evolution of the exploration of the optimal solution, it is considered that the parameters of the genetic algorithm are also appropriately set.

Fig. 9A shows the emulation curve h(y) of the most suitable individual and the contour T(y) of the pitch component. The vertical axis represents the values of h(y) and T(y), the unit of h(y) is [μm], and the unit of T(y) is [10 μrad]. The horizontal axis represents the position in the y direction in units of [mm]. Further, the zero-order component and the primary component of the contour curve h(y) and the contour T(y) of the pitch component are not related to the surface profile, and therefore, the zero-order component and the primary component are removed in FIG. 9A.

The measurement data i(y), j(y), k(y) measured by the displacement meters 31i, 31j, 31k are shown in Fig. 9B. The horizontal axis represents the position in the y direction in units of [mm], and the vertical axis represents the value of the measurement data in units [μm]. In addition, the 0th component and the primary component were removed.

FIG. 9C shows the surface contours W ₁ (y), W ₂ (y) obtained by substituting the optimal solution of the simulation curve h(y) and the contour T(y) of the pitch component into the equations (1) to (3). ), W ₃ (y). It can be seen that the three surface profiles calculated from the optimal solution are small compared to the three measurement data shown in FIG. 9B.

Thus, by using the genetic algorithm, it is not necessary to directly solve the simultaneous equations including the three unknown functions, and the simulation curve h(y), the pitch component T(y), and the surface contour W(y) can be found. Good solution.

In the above genetic algorithm, the candidate solution of the genetic algorithm is defined by the emulation curve h(y) and the contour T(y) of the pitch component, and the evaluation function is defined according to the surface contour W(y). Further, the candidate solution may be defined by two contours in the contour curve h(y), the contour T(y) of the pitch component, and the surface contour W(y), or the evaluation function may be defined by the remaining one contour.

In step SA5 of Fig. 4, the correction of the secondary component of the simulation curve h(y) is performed. As shown in the equation (6), the secondary component of the emulation curve h(y) cannot be determined from the simultaneous equations (1) to (3). Therefore, the second component of the optimal solution of the imitation curve h(y) obtained by the genetic algorithm has no meaning. . Therefore, the second-order component is removed from the optimum solution of the simulation curve h(y) obtained by the genetic algorithm, and the simulation curve h(y) containing only three or more components is obtained. On the emulation curve h(y) including only the three or more components, the second component of the emulation curve h(y) calculated in step S2 of Fig. 3A is superposed. Thus, an emulation curve h(y) containing a meaningful secondary component is obtained.

In step SA6, the surface contour W(y) is obtained by substituting the simulation curve h(y) for correcting the secondary component in step SA5 and the measurement data j(y) of the displacement gauge 31j into the equation (2). 2 or more ingredients. Further, since the zero point error δ is a constant, even if the zero point error δ is unknown, it is possible to determine the component of the surface contour W(y) twice or more.

Deviating from the movable table 10 in the x direction, by repeating the steps from steps SA1 to SA6 of Fig. 4, the surface profile of the entire surface of the measuring object 20 can be measured. Even if the moving table 10 is deviated in the x direction, it can be considered that the secondary component of the emulation curve h(y) does not change. Therefore, when it is deviated from the movable table 10 in the x direction, it is not necessary to perform the measurement by the inclinometer shown in Fig. 3A. Moreover, even if the object 20 to be measured is replaced, it is not necessary to perform the measurement by the inclinometer.

Measuring the surface contour by the inclinometer requires a lot of effort and time and is difficult to automate. In the method according to the embodiment, the surface profile of the measuring object 20 can be easily measured by using the measurement of the displacement meter which is easy to automate.

In the above embodiment, the secondary component of the surface profile W(y) can also be determined when the zero point error δ remains. Therefore, there is no need for precise zero adjustment.

In the above embodiment, the displacement measuring instruments 20i, 31j, and 31k are moved relative to the measuring object 20, but the measuring object 20 can be moved relative to the displacement meters 31i, 31j, and 31k. For example, in FIG. 1A, the displacement meters 31i, 31j, and 31k are arranged in the x direction, and the measurement object 20 is moved while moving in the x direction, so that the measurement object parallel to the x direction along the surface of the measurement object 20 can be measured. The contour of the surface of the line. The sensor head 30 shown in Fig. 1B is rotated by 90° about the rotation axis parallel to the z-axis, so that the displacement meters 31i, 31j, 31k can be arranged in the x direction. It is also possible to provide such a rotating mechanism in the sensor head 30.

The two-dimensional surface contour information of the surface of the measuring object 20 can be obtained by overlapping the surface contours of the plurality of measuring object lines parallel to the y direction and the surface contours of the plurality of measuring object lines parallel to the x direction.

The present invention has been described based on the above embodiments, but the present invention is not limited to these. Those skilled in the art will understand, for example, that various modifications, improvements, combinations, and the like can be made.

10. . . Activity workbench

11. . . Workbench guiding mechanism

15. . . Grinding head

16. . . Grinding wheel

18. . . guide

19. . . Control device

20. . . Measuring object

30. . . Sensor head

31i, 31j, 31k. . . Displacement meter

35. . . Inclinometer

Fig. 1 (1A) is a perspective view of a linear measuring device according to an embodiment, and (1B) is a schematic view of a head portion of the sensor.

2 is a view showing a surface contour W(y) of the object to be measured, measurement data i(y), j(y), k(y) of the displacement meter, a simulation curve h(y), and a pitch component T(y). A line graph of the definition.

Fig. 3 (3A) is a flow chart showing a method of measuring the secondary component of the simulation curve in advance, and Fig. 3 (B) is a schematic view showing the appearance of the surface profile by the inclinometer.

4 is a flow chart of a linear measurement method according to an embodiment.

Fig. 5 is a flow chart of a genetic algorithm employed in the linearity measuring method according to the embodiment.

Figure 6 is a diagram for explaining the intersection of genetic algorithms.

Figure 7 is a diagram for explaining the sudden variation by the genetic algorithm.

Fig. 8 is a graph showing a case where the evaluation value is decreased (the fitness becomes higher) as the generation value increases by the genetic algorithm.

Fig. 9 (9A) is a graph showing the best solution of the simulation curve h(y) and the pitch component T(y) obtained by the genetic algorithm, and (9B) is a graph showing the measurement data of the three displacement meters, ( 9C) is a graph showing the surface profile of the best solution obtained by genetic algorithm.

Claims (2)

A method for measuring a linearity, comprising: displacing three displacement meters arranged in a first direction and a relative position with an object to be measured, and measuring the displacement meter or one of the objects to be measured The mover is the live object, and the other is a fixed object, and the movable object of one of the measurement object and the object to be measured is moved in the first direction with respect to the other fixed object, and the three displacement meters are measured. a step of respectively separating the three measured points arranged on the surface of the object to be measured along the measurement target line extending in the first direction; the moving in the first direction is accompanied by an ideal parallel movement The tilt change, that is, the pitch component, and the displacement toward the measurement direction with respect to the ideal linear motion, that is, the emulation curve; based on the result of the above-described movement in the first direction corresponding to the measurement results of the three displacement meters, the calculation is performed. a step of moving the amount of the imitating component corresponding to the imitating curve in the first direction; and calculating the second component of the contour of the imitating curve, 2 in advance of the contour component of the measured curve to emulate the step of correcting; emulate based profile curve is corrected after the step of calculating the surface profile of the measured object. A linear measuring device characterized by comprising: a table supporting a measuring object; and a sensor head including three displacements respectively measuring a distance of a surface of the measuring object arranged at the measured point in the first direction a guiding mechanism that performs measurement while the displacement meter or the object to be measured One of the movers is a movable object, and the other is a fixed object, and the sensor head and the one of the worktables are movable along the first direction with respect to the other fixed object; that is, the movable object; and the control device And storing, in the second-order component of the simulation curve of the displacement in the measurement direction with respect to the movement of the straight line in the first direction, based on the measurement data measured by the three displacement meters, The contour of the surface of the measurement target line in the first direction; the control device is configured to measure the object along the measurement object by moving each of the three movable meters while moving the movable object in the first direction a step of obtaining measurement data by the distance of the measured point on the surface of the line; and calculating a contour of the reference point to which the relative position of the movable object is fixed, that is, the contour of the simulation curve, based on the measurement results of the three displacement meters; The second component of the contour calculated by the above imitating curve, based on the second component of the contour of the stored emulation curve; and The step of correcting the contour of the contour curve to calculate the surface profile of the object to be measured.