JPH0426683B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to shape measurement of objects whose shape is relatively close to flat, such as measurement of flatness of steel plates.

[Conventional technology]

The method of finding the shape using the moiré method is as follows:
Contour line observation device (for example, Special Publication No. 1983-34947)
It has been known. This method is called moiré topography, and is based on the light source and the imaging point of the observation system (for example, the pupil).
are placed at equal vertical distances from the lattice plane, and a group of contour lines appears on the surface of the object, thereby allowing the shape of the surface of the object to be observed quickly and accurately. However, this method does not know the relative heights of contour lines, so-called unevenness, and is difficult to automate.

Therefore, if the slope is larger than the maximum slope of the shape of the object to be measured,
It is easy to think of a shape measuring method in which the height of the stripes is uniquely specified without making a determination of concavities and convexities by installing the object to be measured at an angle with respect to the grid.

[Problem that the invention seeks to solve]

However, if the object to be measured is a heavy object such as a steel plate, it is not easy to tilt it whether it is stationary or during transportation, and the entire optical system including the grating must be tilted.

However, it is difficult to accurately tilt a large grid, and it is also not easy to adjust the tilt angle to match the shape.

An object of the present invention is to measure the shape of the surface of an object using moiré fringes without adjusting the inclination of the grating and the object to be measured, and without determining the unevenness.

[Means for solving problems]

The present invention has been made to advantageously solve the above-mentioned problems. When determining the shape of the surface of a plate-like object from the moiré fringes that occur when the shadow is projected onto the object surface and observed through the original grid, the perpendicular distance h ₁ between the light source and the lattice plane, the imaging point and the lattice plane The vertical distance h ₂ of is deliberately set as h ₁ ≠ h ₂ so that the light section group is inclined with respect to the plate-like object, and the pitch P of the grating, the horizontal distance l between the light source and the imaging point, and the distance between the grating plane and the transport roll are Based on the value Z ₀ , which is obtained by subtracting the thickness of the plate-like object from the interval, the maximum point of the light intensity of any moire fringe on the measurement surface is set as the reference point P ₀ , and the reference point of the maximum light intensity of any moire fringe is This is an inclined moiré shape measurement method characterized by determining the height _YN from a point using the following formula.

Y _N =ΔZ・(x _N /W−N) However, ΔZ=P/<lh ₂ /(Z ₀ +h ₂ ) ² +x(h ₂ −h ₁ )(h ₁ h ₂
−Z ₀ ² ) / [(Z ₀ + h ₁ ) ² (Z ₀ + h ₂ ) ² ]> Here, x is the horizontal distance of the moire fringe position with the light source at the apex, and W is the vertical distance of Z ₀ from the lattice plane downward. It is the interval of moiré fringes that occur on a flat plate placed at a distance, and is W = [h ₁ h ₂ + (h ₁ + h ₂ ) Z ₀ + Z ₀ ² ]・P/[(h ₂ − h ₁
) Z ₀ ] x _N is the horizontal distance from the reference point P ₀ to the maximum light amount point of the moiré fringe whose height is to be determined, and N is the relative order from the reference point.

[Effect]

The measuring method of the present invention will be explained with reference to FIG.

The symbols shown in Figure 1 have the following meanings:

h ₁ : Vertical distance between the light source 11 and the grating plane 13.

h ₂ : Image forming point of observation system (pupil shown) 12 and grating plane 1
3, l: distance between the light source 11 and the imaging point 12 of the observation system, P: pitch of the grating 13, N: called fringe order, the order of the light cutting plane group 14 from the grating plane 13.

Now, as an example of one light path, from the light source 11, it passes through the gap A point on the grating 13, hits the object to be measured at point C, is reflected, passes through the gap B point in the grating 13, and becomes the imaging point of the observation system. Think about the route back to 12th. Let the distance between point A and point B be NP. As is clear from Figure 1,
The fringe order of the moire fringes at point C is N. In the case of FIG. 1, N=3.

x indicates the horizontal distance of point C from the light source 11 as the origin, and Z indicates the depth of point C. Also, in preparation for deriving the basic formula, let the horizontal distance between points A and C be ξ. ΔZ is the change in fringe depth when the fringe order N changes by 1, Z ₀ is the distance from the grating 13 to the reference plane 15,
W indicates the interval between moire fringes appearing on the reference plane, and θ indicates the inclination angle of the light section group 14 with respect to the reference plane 15. In moire topography, h ₁ = h ₂ , but the feature of the present invention is that h ₁ ≠ h ₂ .

From FIG. 1, the following basic equation is obtained from the triangle similarity condition.

(h ₁ +Z):x=Z:ξ ( _h2 +Z):(1-x)=Z:(NP-ξ)...(1) Eliminating ξ from both equations, N=lZ/[P( Z+h ₂ )](h ₂ −h ₁ )xZ/[P(Z+
h ₁ ) (Z + h ₂ )]...(2). To find the change ΔZ in the fringe depth Z when the fringe order N changes by 1, by differentiating N with respect to Z, we get dN/dZ=lh ₂ /[P(Z+h ₂ ) ² ]+(h ₂ −h ₁ ) (h ₁ h ₂
−Z ² )x/[P(Z+h ₁ ) ² (Z+h ₂ ) ² ]...(3) Since ΔZ is the change dZ in Z when the change in N dN=1, ΔZ=P/< lh ₂ / [(Z + h ₂ ) ² ] + (h ₂ − h ₁ ) (h ₁ h
₂ −Z ² ) x/[(Z+h ₁ ) ² (Z+h ₂ ) ² ]>...(4).

Further, the stripe interval W with respect to the reference plane 15 is determined as follows.

Transforming equation (2), x = [h ₁ h ₂ NP + (h ₁ NP + h ₂ NP - h ₁ l) Z + (NP - l) Z
² ]/[(h ₂ − h ₁ )Z]…(5). The stripe spacing W at Z=Z ₀ is WΔ = xN=N+1 Z=Z ₀ −xN=N Z=Z ₀ = [h ₁ h ₂ + (h ₁ + h ₂ ) Z ₀ + Z ₀ ² ] ・P/[ (h ₂ −h ₁ )Z ₀ ] …(6) becomes an exactly constant value.

Furthermore, the inclination angle θ of the optical section group 14 with respect to the reference plane 15 is determined as follows.

Differentiating equation (5) with respect to Z gives dx/dZ=[(NP−1l)Z ² −h ₁ h ₂ NP] / [(h ₂ −h ₁ )Z ₂ ] …(7), and the inclination angle θ is as follows: θ=tan ⁻¹ <(h ₂ −h ₁ )Z ₀ ² /[(NP-l)Z ₀ ² −h ₁ h ₂ NP]> …(8). Here, N is a variable of Z and x, and formula (2)
More sought after.

From the above preparations, we will specifically describe how to obtain the shape. FIG. 2 shows the intersection of the measurement object surface 16 and the optical section group 14. In FIG. 2, the intersection of the optical section group 14 and the measurement object surface 16 is shown from the left.
Let P ₀ , P ₁ , .... The shape is determined using one of these intersection points as a reference point.

Here, as a measurement condition, it is assumed that the maximum inclination of the shape of the object to be measured is smaller than the inclination of the optical section group 14. Under this condition, the fringe order N of the moiré fringes appearing on the surface 16 of the object to be measured increases monotonically. In other words, the relative fringe order of the Nth intersection from P ₀ is N,
can be uniquely determined.

To obtain the shape from the fringe order N, proceed as follows. For example, the height y ₁ of point P ₁ can be found as follows. First, the relative fringe order of _one point Q can be found by the following formula.

Q Fringe order of _one point=x ₁ /W (9) Here, W is given by the above-mentioned equation (6).

Therefore, the height y ₁ of point P ₁ can be found as follows: y ₁ =ΔZ (fringe order of point Q ₁ − fringe order of point P ₁ ) = ΔZ (x ₁ /W−1) (10). Similarly, the height of any point P _N can be found using the following formula.

y _N =ΔZ(x _N /W−N) (11) Here, ΔZ is given by the above-mentioned equation (4) and is a function of x.

The shapes of points other than the intersections between the optical section group 14 and the surface of the object to be measured can be determined, for example, by interpolation calculation using a spline function.

Here, the key point of the present invention is to set the vertical distance h ₁ between the light source and the grating plane and the vertical distance h ₂ between the imaging point 12 and the grating plane to satisfy h ₁ ≠ h ₂ , but if the vertical distances are different, The amount to be applied varies depending on the shape of the object to be measured. An example of the geometric dimensions for a flat material such as a steel plate is shown below.

Pitch of grating plane 13 P = 1.5 mm Vertical distance between light source 11 and grating plane 13 h ₁ = 3800 mm Vertical distance between image forming point 12 and grating plane 13 h ₂ = 4200 mm Horizontal distance between light source 11 and image forming point 12 l = 3000 mm Assuming that the distance Z ₀ between the grating plane 13 and the reference plane 15 is 500 mm, first, from equation (6), the stripe interval W on the reference plane 15 is 151.6 mm.
Also, the change in fringe depth ΔZ 1 when the fringe order N changes by ₁ , and the inclination angle θ between the reference plane 15 and the group of optical cutting planes.
is a function of the horizontal distance x from the light source 11,
From equations (4) and (8), at the point x = 0, ΔZ = 2.63 mm, θ = 00.99°; at the point x = 3000 mm, ΔZ = 2.43 mm, θ = 0.92°.

In other words, at the point x=0, the shape is ΔZ=2.43mm
As the height increases, the moiré fringes move almost to the right in Figure 1.
Moved 152mm and the shape is 2.63mm at the point x = 3000mm
As the height increases, the moiré fringes also move 152 mm to the right.

Since the inclination of the optical section group is approximately 0.9°, the maximum shape inclination that can be used to determine unevenness is 16 mm/1000 mm (≒tan 0.9°), but this range is sufficient for general steel plates.

If the shape of the object to be measured is poor, by increasing the step between the light source 11 and the imaging point 12, θ becomes larger and unevenness can be determined, but W becomes smaller and moiré occurs due to changes in shape. The distance the stripes move becomes smaller, and the sensitivity of shape measurement becomes worse.

〔Example〕

A third example in which the present invention is applied to a steel plate flatness meter is shown below.
This will be explained using figures.

13 in Figure 3 is 5m in the board width direction and 2m in the longitudinal direction.
It is a large lattice with a lattice pitch of 1.5 mm and a lattice wire diameter of 0.5 mm, and is installed parallel to the steel sheet conveying roll 21. The distance from the surface of the transport roll 21 is set to 550 mm to prevent collisions during transport.

17 is a laser light source (YAG laser, wavelength 532 mm, output 4.5 W) that is the light source for forming moire fringes.
The laser beam passes through a beam expander 18, is changed direction by a reflection mirror 19, passes through a concave lens 20, passes through a grating 13, and hits a steel plate 22.
form moire fringes on the surface. 23 is an ITV camera that detects the formed moire fringes through the grating 13. 24 is a monitor television;
This is for visually observing moiré fringes detected by the ITV 23. 25 is an image processing device which takes in the output of ITV 23 and calculates the above-mentioned calculation formula.
Using (4), (6), and (11), find the change ΔZ in the fringe depth Z when the fringe order N changes by 1, the fringe interval W with respect to the reference plane, and the height y _N of an arbitrary point P _N. , find the flatness of the steel plate. 26 is an output display device,
Contour line, P/H (P: wave pitch, H: wave height)
etc. will be displayed.

In the case of this example, the vertical distance h ₁ between the concave lens 20 and the grating 13 was set to 4150 mm, and the vertical distance h ₂ between the ITV 23 (imaging point) and the grating 13 was set to 3750 mm.
Also, the distance I between the concave lens 20 and the ITV 23 is 3100 mm.
The resolution of the fringes was adjusted to ΔZ = 2.5 mm, and the inclination of the optical section group θ = 0.103°.

An actual thick steel plate was measured using a flatness meter with such an equipment configuration.

Steel plate dimensions: Width max 4500mm x length max 25000mm Material: All steel types Steel plate surface temperature: 250℃ or less Steel plate conveyance speed: 0.1m/sec, 1m/sec Flatness measurement value: Wave height 0-15mm Transfer steel plates of the same thickness to a flat surface Flatness was measured manually using a scale. A static accuracy of ε=±0.5mm was obtained from comparison with many actual measurements.

On the other hand, also in the running measurement, that is, when the steel plate was measured while running on the conveying roller, high accuracy of the running measurement accuracy ε=±1.0 mm was obtained.

〔Effect of the invention〕

The advantages of tilting the optical section group toward the measurement object are as follows.

No need to judge unevenness.

The resolution is improved because the curved shape of the moiré fringes is determined. In the above example, ΔZ=2.5 mm, but a measurement accuracy of ε=±0.5 mm was obtained.

Image processing is easy because moiré fringes with a fixed pattern always appear.

The above effect can be obtained by tilting the entire optical system including the grating using the principle of moire topography, but in the present invention, since the grating is placed parallel to the object to be measured, the following effect can be obtained.

Easy to adjust the parallelism of the grid.

By installing multiple cameras at different positions and heights, moiré fringes with different inclination angles θ and resolutions ΔZ can be obtained simultaneously.

[Brief explanation of drawings]

FIG. 1 is a drawing for explaining the measuring method of the present invention, and shows a cross section of a moiré measuring grating. FIG. 2 is a perspective view showing the intersection of the light section group and the object to be measured in the measurement mode shown in FIG. 1. Third
The figure is a perspective view showing an example of an apparatus configuration when the present invention is applied to a plate flatness meter. 11: light source, 12: observation system, 13: grating, 1
4: Optical section group, 15: Reference plane, 16: Measured object surface, 17: Laser light source, 18: Beam expander, 19: Reflecting mirror, 20: Concave lens, 2
1: Conveyance roll, 22: Steel plate, 23: ITV, 2
4: Monitor, 25: Image processing device, 26: Output display.

Claims (1)

[Claims] 1. Projecting the shadow of a plane grating onto the surface of the object to be measured using light emitted from a point-like or slit-like light source, and obtaining this shadow at an observation point through the original grating, When determining the shape of the surface of a plate-like object using moiré fringes caused by the shadow of a plane grating, we purposely set the vertical distance h ₁ between the light source and the grating plane and the vertical distance h ₂ between the imaging point and the grating plane.
The group of optical cutting planes is inclined with respect to the plate-shaped object with h ₁ ≠ h ₂ , and the plate of the plate-shaped object is Based on the value Z ₀ , minus the thickness,
The reference point is the maximum point of the light intensity of any moiré fringe on the measurement surface.
A tilted moiré shape measurement method characterized by setting P ₀ and determining the height Y _N of the maximum light intensity point of any moiré fringe from the reference point using the following formula: Y _N =ΔZ・(x _N / W−N) However, ΔZ=P/<lh ₂ /(Z ₀ +h ₂ ) ² +x(h ₂ −h ₁ )(h ₁ h ₂
−Z ₀ ² ) / [(Z ₀ + h ₁ ) ² (Z ₀ + h ₂ ) ² ]> Here, x is the horizontal distance of the moire fringe position with the light source at the apex, and W is the vertical distance of Z ₀ from the lattice plane downward. It is the interval of moiré fringes that occur on a flat plate placed at a distance, and is W = [h ₁ h ₂ + (h ₁ + h ₂ ) Z ₀ + Z ₀ ² ]・P/[(h ₂ − h ₁
) Z ₀ ] x _N is the horizontal distance from the reference point P ₀ to the maximum light amount point of the moiré fringes whose height is to be determined, and N is the relative order from the reference point.