JP2913021B2 - Shape measuring method and device - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a non-contact and non-destructive shape measuring method and apparatus using a television camera and a projector and having no influence on lens aberration. The field to which the invention belongs is a measuring device and a shape measuring device, and a product name that can be applied particularly is a non-contact shape measuring device.

[0002]

2. Description of the Related Art Conventional non-contact three-dimensional shape measurement methods include:
A grid projection method of projecting a grid on an object and analyzing an image obtained by projecting the grid from different angles to obtain a three-dimensional shape is often used. In order to perform accurate measurement, it is important to accurately determine a lattice phase value from a lattice image and to accurately determine parameters used when calculating three-dimensional coordinates from the lattice phase value.

As a method of analyzing a lattice image, a phase shift method,
Phase analysis methods such as a Fourier transform grid method, a Gabor transform grid method, and a Fourier transform phase shift method have been developed. In the phase analysis method, a grid number can be obtained as a real value in every pixel, so that a precise grid analysis can be performed. In particular, the Fourier transform phase shift method is an effective method in which a phase value can be obtained with extremely high accuracy because there is almost no influence of noise.

[0004]

Conventionally, optical system parameters such as the center position of a lens between a camera and a projector and the direction of an optical axis have been used as parameters used for calculating the three-dimensional coordinates. The shape of the measurement object is calculated using the position coordinates.

[0005] As a method for accurately obtaining optical system parameters, there is a method in which a reference plane on which a two-dimensional grid is drawn is moved in parallel and images taken at respective positions are used. In this method, since the amount of information is much larger than that of a conventional method using a cube, the optical system parameters can be obtained with high accuracy.

However, since the optical system parameters are determined on the assumption that there is no lens aberration, the effect actually appears as an error. If the measurement accuracy is not so high as in the conventional case, the effect can be ignored. However, if the phase value of the projection grating can be obtained with high accuracy and the measurement accuracy is improved, the influence of the lens aberration becomes relatively large and cannot be ignored.

[0007] The problem is that the measurement results are affected by the aberrations of the lenses of the television camera and the projector, so that the measurement results are distorted.

Accordingly, the present invention has developed a method for performing high-accuracy shape measurement without any influence of lens aberration, by directly using an image drawn on a reference plate for coordinate calculation without obtaining optical system parameters.

[0009]

The present invention provides: (1) a step of setting a reference plate on which a two-dimensional grid is drawn on a one-axis table so as to be able to translate in a direction perpendicular to the reference plate; (3) installing a television camera at a position on the near side where the two-dimensional grid can be projected onto the reference plate; and (3) installing a grating projection device at a position near the side where the two-dimensional grating can be projected onto the reference plate. 4) calculating a phase value distribution from an image obtained by photographing a two-dimensional grid drawn on the reference plate at a plurality of positions before and after the movement of the reference plate, and recording the result in a computer memory; (5) photographing a two-dimensional lattice projected from a lattice projection device onto a reference plate at the plurality of positions, converting the photographed image into phase value data, and recording it in a memory of a computer; Position and position of plate before movement The two-dimensional grid projected from the grid projection device on the sample object, which is the measurement target placed between the rear position, is photographed by a television camera, and for each pixel, the in-screen coordinates of the pixel and the projection grid Calculating spatial coordinates of a point on a measurement target imaged on the pixel from data recorded in a phase value and phase value distribution calculation memory and a phase value data memory converted from a captured image. This is a shape measuring method characterized by comprising a combination.

The present invention further provides: (1) means for setting a reference plate on which a two-dimensional grid is drawn on a one-axis table so that the reference plate can be translated in a direction perpendicular to the reference plate; (3) means for installing the grid projection device at a front position where the grid can be projected at two positions, ie, before and after movement of the reference plate; (4) means for calculating a phase value distribution from an image obtained by photographing a two-dimensional grid drawn on the reference plate at a plurality of positions before and after the movement, and recording the result in a memory of a computer; 5) means for converting an image obtained by photographing a two-dimensional grid projected from a grid projection device onto a reference plate at a plurality of positions of the pre-movement position and the post-movement position from a lattice projection device into phase value data and recording the same in a memory of a computer; (6) Before moving the flat plate A two-dimensional grid from the grid projector and projected onto the sample object was placed between the post-move location position,
The projected two-dimensional lattice is photographed by a television camera, and for each pixel, the coordinates of the pixel in the screen, the phase value of the projection lattice and the phase value distribution calculation memory, and the phase value data memory converted from the photographed image are recorded. And a means for calculating spatial coordinates of a point on a measurement target imaged on the pixel from the obtained data.

[0011]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The shape measuring method of the present invention will be described in more detail with reference to the drawings. FIG. 1 shows an arrangement of a reference plate 1, a television camera 5, a grid projection device 6, and a computer 10. In FIG. 1, a reference plate 1 is mounted on a one-axis table 3 provided on a base 4 so as to be able to move back and forth in one axis direction perpendicular to the reference plate 1, and is fixed on the base 4. A television camera 5 and a grid projection device 6 are provided on the near side of the base 4, and the television camera 5 and the grid projection device 6 are connected to a computer 10. Reference numeral 1 'indicates the position of the reference plate which has been translated in front of the reference plate 1. In the grating projection device 6, 7 denotes a two-dimensional grating slide, 8 denotes a two-axis micro stage, and 9 denotes a color filter.

The surface of one side of the reference flat plate 1
A two-dimensional lattice 2 is drawn. The reference plate 1 is attached to a one-axis table 3 attached to a base 4 so that it can be translated in a direction normal to the surface of the reference plate 1. The moving distance of the reference plate 1 is measured using a moving distance meter 12 attached to the one-axis table 3. The reference plate before the movement is 1 and the reference plate after the movement is 1 '. The television camera 5 is installed at a position where the two-dimensional grid 2 can be displayed on the entire screen. An image signal of the two-dimensional lattice 2 captured by the television camera 5 is converted into an A / D signal in the computer 10 shown in FIG.
The data is converted into image data by the converter 10a, the phase value is calculated by the CPU 10b, and the phase distribution obtained as a result of the calculation is stored in the memory 10c. The two-dimensional grating slide 7 attached to the two-axis microstage 8 is a grating projection device 6
Mounted on The image of the two-dimensional grating slide 7 is projected on the reference plate 1 by the grating projection device 6. In the two-dimensional grid slide 7, the vertical grid and the horizontal grid are made of different colors, and only the vertical grid or the horizontal grid is individually projected by the color filter 9. A signal for minutely changing the position of the projected grating is transmitted from the computer 10 to the two-axis microstage 8. The projected grid pattern is photographed by the television camera 5 and stored in the memory 10c as a phase distribution as in the case of the reference plate 1. The image of the two-dimensional lattice 2 and the image of the projected lattice pattern as described above are stored in the memory 10c as a phase distribution together with before and after the movement of the reference plate 1 back and forth. (Refer to Fig. 11
Shown)

FIG. 3 shows a case where the shape of the sample object 11 is measured. FIG. 4 is a side view of the arrangement of FIG. The sample object 11 is set so as to be located between the positions of the reference plate 1 before movement and the reference plate 1 'after movement. While the positions of the television camera 5 and the grid projection device 6 are not changed, a grid pattern is projected from the grid projection device 6 onto the sample object 11 and the television camera 5 captures an image. The captured grid image is stored in the memory 10c as a phase distribution in the same manner as the grid image projected on the reference plate 1.

FIG. 6 shows a procedure of shape measurement using the measurement method of the present invention. The procedure is roughly divided into two. Step 1
The second is the measurement of the optical system parameters using the reference object, and the second is the shape measurement by photographing the sample object 11. Firstly, it is only necessary to perform the operation once after the television camera 5 and the grid projection device 6 are installed. The second can be repeated. First, the procedure for measuring the optical system parameters is as follows.

(1) An image of the reference plate 1 is photographed, the photographed two-dimensional lattice image is A / D-converted through an A / D converter 10a, and is taken into a CPU 10b. (2) The CPU 10b obtains a phase distribution by using a Fourier transform grid method (described later) and stores it in the memory 10c. (3) The grating projection device 6 projects the gratings in the vertical and horizontal directions while slightly changing the phase by one cycle, and continuously captures a plurality of images. (4) A phase distribution is obtained from these images by using a Fourier transform phase shift method (described later) and stored in the memory 10c. (5) The position of the reference plate 1 is translated in the z direction to the position of the reference plate 1 '. (6) to (9) The same procedure as (1) to (4) is performed on the reference flat plate 1 'to obtain a phase distribution, which is recorded in the memory 10c.

Next, the procedure for photographing the second sample object will be described. (10) The sample object 11 is set so as to be between the positions of the reference plate 1 before movement and the reference plate 1 'after movement. (11) The same procedure as (3) is performed on the sample object 11. (12) A phase distribution is obtained from the plurality of images obtained in (11). (13) Using the phase distribution of the image obtained by photographing the reference object obtained in the first procedure, spatial coordinates are calculated from the phase distribution obtained in (12).

FIG. 7 shows the flow of data processing. FIG. 8 shows how the optical system parameters are measured. FIG. 9 shows the sample object 11
3 shows a state of shape measurement. In the measurement of the optical system parameters in FIG. 7, the result of calculating the phase value from the image of the reference plate 1 before and after the movement is stored in the memory as the phase value data.
Recorded at 10c. In the shape measurement shown in FIG.
The phase values are calculated by calculating the phase values from the images of the grids in the x and y directions projected on 11. For each pixel, the spatial coordinates of the point on the object to be measured that is mapped to the pixel are calculated from the in-screen coordinates, the phase value of the projection grating, and the phase value data recorded in the memory 10c in the measurement of the optical system parameters.

Now, focusing on the point S on the sample object 11, the details of how to obtain the spatial coordinates will be described. In FIG. 7, the phase value of the same coordinate (point A ′) as the coordinate at which the point S is depressed is changed to the phase distribution of the reference grating before movement.

[Outside 1] (Dotted arrow in FIG. 7). Phase distribution of a grid obtained by projecting a point (point B ′) having the phase value of the projection grid at point S onto reference flat plate 1

[Outside 2] , And the phase value of the same coordinate (point B ″) as that of the point is obtained from the phase distribution of the reference grating before the movement.

[Outside 3] (Solid arrows in FIG. 7). Since the two-dimensional grating drawn on the reference plate 1 has the same pitch, it can be easily converted to spatial coordinates by multiplying the phase value by a constant. Accordingly, the spatial coordinates of the points A and B in FIGS. 8 and 9 can be obtained from the phase values of the points A 'and B ". Because it can be accurately read by the moving distance system attached to the one-axis table,
Similarly, the spatial coordinates of the points C and D in FIGS. 8 and 9 can be easily obtained. Point S is a straight line A
It can be obtained as the intersection of C and the straight line BD. However, in principle, these two straight lines have an intersection because they pass through the same point. However, the two straight lines do not necessarily have an intersection due to a measurement error or a numerical calculation error. As described above, the point closest to the straight line BD on the straight line AC is the point S ₁
And then, the point closest to the straight line AC on a straight line BD as a point S _2, seeking the point S as the midpoint of the point S ₁ and the point S _2. By performing the above method for each pixel, the spatial coordinates of all points on the surface of the sample object 11 captured in the image can be obtained.

FIGS. 11 (A), (B), (C), (D),
(E) illustrates a method of converting a lattice image into a phase distribution. In FIG. 11, FIG. 11 (A) is a grid image, and FIG. 11 (B) shows the change in brightness. When the change in brightness is regarded as a wave, a phase from -π to π can be defined for each wave according to the degree of progress of the wave. This is shown in FIG. 11 (C). In FIG. 11C, the phase is from -π to
Although the repetition is performed up to π, the phase change can be continuously connected by adding 2π each time the wave advances by one. FIG. 11 (D) shows the result of this, and FIG. 11 (E) shows the result as an image.

The description of the Fourier transform grid method is as shown in FIG. In FIG. 12, FIG. 12A is a two-dimensional lattice image. When the two-dimensional Fourier transform is performed on FIG.
The Fourier spectrum shown in FIG. 12 (B) appears. FIG.
(B) shows the amount of the spatial frequency component of the original lattice image by brightness for each frequency. Nine bright spots appear near the center.
The part shown in (C) represents the frequency component of the horizontal grid, and the part shown in FIG. 12 (D) represents the frequency component of the vertical grid. When the inverse Fourier transform is performed on FIG. 12C, a grid only in the horizontal direction as shown in FIG. 12E is obtained. FIG. 12E has values of the real part and the imaginary part, and the inverse tangent of the ratio between the real part and the imaginary part represents the phase value. FIG.
FIG. 12G shows the values of the phase at each point obtained from FIG. In the vertical direction, a phase distribution as shown in FIG.

[Experimental Example] 1. Three-dimensional shape measurement by grid projection; FIG. 13 shows the principle of the grid projection method. It is assumed that one line of sight can be determined for coordinates in an image captured by the camera, and a grid projection plane in space can be determined from the grid number of the projection grid. As shown in FIG. 13A, when a one-dimensional lattice is projected on an object by a projector and photographed by a camera from different directions, an image of a lattice distorted according to the shape of the object is obtained.
Focusing on a point P 'in the image where the point P on the object is captured, a straight line L is determined from the coordinates in the screen. The grid projection plane γ is determined from the number of the grid projected on the point P ′, and the three-dimensional coordinates of the point P on the object can be calculated as their intersection. By obtaining the lattice number as a phase value as a real value, accurate shape measurement can be performed.
As shown in FIG. 13B, when projecting a two-dimensional grid, grid projection planes γ _x and γ _y are obtained from the phase values of the projection grid in the x and y directions at point P ′ in the image. . The three-dimensional coordinates of the point P on the object can be calculated as the intersection of the intersection line Lp and the straight line L.

2. Regarding the Fourier transform phase shift; When the phase of the projection grating is shifted, the luminance distribution of the grating can be expressed by the following equation. f (x, y) = a (x, y) cos ｛φ (x, y) + α｝ + b (x, y) (1) Here, the point (x, y) is a point in the photographed image. , F
(X, y), a (x, y), b (x, y) represent the luminance value, luminance amplitude, and background luminance at each point, respectively, φ represents the grid phase value, and α represents the phase shift amount. α from 0 to 2π
Images are continuously captured while shifting slightly up to, and the images are superimposed in the depth direction to obtain a three-dimensional image. FIG. 14A is a schematic diagram of a luminance distribution in one line in the x direction. Focusing on a certain point, with respect to a change of α in one cycle, the brightness at that point changes by exactly one cycle while having the same brightness change as that of the projection grating, and its initial phase is the phase of the projection grating at α = 0 Matches. Equation (1)
Is Fourier transformed to obtain a spectrum as shown in equation (2).

(Equation 1) Here, δ is a delta function, ω is a frequency, and ω ₀ is a fundamental frequency. As shown in FIG. 14B, the component of frequency 1 represents the first-order component of the luminance change obtained by the phase shift, and components unnecessary for obtaining the phase value such as noise are mostly other than 1. Obtained as frequency. Therefore, if only the spectrum of frequency 1 is extracted by filtering and the arc tangent of the ratio of the imaginary part to the real part is calculated, the phase value at that pixel can be obtained with extremely high accuracy.

3. Regarding the influence of lens aberration; In the conventional method using the optical system parameters, it is assumed that the focal point of the lens is one point. In this case, light passing through the lens can be considered as a straight line passing through the lens center point. However, in an actual lens, the focal point is not exactly one point due to spherical aberration, distortion, and the like. Therefore,
When shape measurement calculation is performed using optical system parameters that are assumed to be a straight line passing through the lens center point, light passing through the lens causes a measurement error due to the effect. FIG. 15 (A)
Fig. 3 shows a schematic diagram of the distortion. FIG. 15 (B) is an image obtained by photographing a lattice having no distortion, and FIG. 15 (C) shows a distribution of a shift amount between an ideal lattice and an actual lattice, which is inversely obtained from optical system parameters. . The shift amount was calculated by a phase analysis using a Fourier transform. In this case, the amount of deviation due to aberration increases as the distance from the center increases as compared with FIG. 15C, and the maximum value is 0.6 mm. Assuming that the angle between the optical axis of the camera and the projector is 30 degrees, the effect of this shift results in an error of about 1.0 mm in the coordinate value in the z direction.

4. Regarding shape measurement method without using optical system parameters; First, a plane reference object on which a two-dimensional grid of equal pitch is drawn as shown in FIG. 16 is translated (plane α and plane β). At each position, (1) the grid drawn on the reference object,
(2) x-direction grid projected by projector, (3) y
Take an image of the directional grid. By performing a two-dimensional Fourier transform on (1), the vertical and horizontal components of the grid drawn on the reference object are separated, and the phase value in each direction is accurately obtained. The x-direction grating (2) and the y-direction grating (3) are photographed while changing the phase of the grating by one period, and the phase value is accurately obtained by using the Fourier transform phase shift method. In FIG. 16, points A and C are points that are mapped to the same pixel in the image. The spatial coordinates of points A and C can be obtained by multiplying the phase values obtained from (1) by a constant. The spatial coordinates on the plane α and the plane β can be similarly obtained for any pixel. Next, as shown in FIG. 17, the sample object is placed between the plane α and the plane β, and the grids in the x direction and the y direction are projected to obtain respective phase values. Focusing on the point P on the object, the coordinates in the screen of the point B and the point D on the planes α and β having the same phase value as the phase value of the projection grid at the point P are x
It is obtained from the phase values of the directional grating (2) and the y-directional grating (3). The spatial coordinates can be obtained from the coordinates in the screen by the above-described method. That is, from the in-screen coordinate values where the point P is captured and the phase value of the projection grid, the points A to D shown in FIG.
Can be obtained, and the spatial coordinates of the point P can be calculated as the intersection of the straight line AC and the straight line BD. In this method, since the image of the reference object is directly used for calculating the spatial coordinates, three-dimensional shape measurement that is not affected by lens aberration can be performed.

5. Regarding the measurement of the shape of a flat plate;-To confirm the effect of the method of the present invention, z = z by both the conventional method using the optical system parameters and the method of the present invention.
The shape of a flat plate set at a position of 20 mm was measured. The measurement result is shown in FIG. 18 as a cross-sectional shape in the x direction at a position 10% from the upper end of the measurement area. It can be seen that the error is large at the end of the measurement area in the conventional method, whereas the error distribution is uniform in the method of the present invention. The measurement accuracy is
The maximum value of the error is 0.42 for each of the conventional method and the method of the present invention.
mm and 0.28 mm, the average of the absolute value of the error is 0.092 mm and 0.064
mm, and it was confirmed that highly accurate shape measurement can be performed by the method of the present invention.

[0026]

According to the present invention, since the center coordinates of the lens are not used for calculating the spatial coordinates as in the prior art, it is possible to measure the shape without being affected by the aberration of the lens and without distortion. Since the lens aberration is large, the shape measurement using a microscope, an endoscope, or the like, which is unsuitable for the shape measurement in the conventional method, can be accurately performed.

[Brief description of the drawings]

FIG. 1 is a layout diagram showing a relationship between a television camera, a grid projection device, and a two-dimensional grid for explaining a shape measurement principle of the present invention.

FIG. 2 is a side view of FIG. 1;

FIG. 3 is a layout diagram showing a relative position between a television camera, a grid projection device, and a sample object for explaining a shape measurement principle of the present invention.

FIG. 4 is a side view of FIG. 3;

FIG. 5 is a circuit diagram showing a relationship between a television camera and a computer in the shape measuring method of the present invention.

FIG. 6 is an explanatory diagram showing a measurement procedure in the shape measurement method of the present invention.

FIG. 7 is a view showing a halftone image in which a sequential step of measurement of an optical system parameter and shape measurement in the shape measurement method of the present invention is displayed on a display.

FIG. 8 is an explanatory diagram of a measurement principle for obtaining spatial coordinates of points A and B by the shape measurement method of the present invention.

FIG. 9 is an explanatory diagram of a measurement principle showing a relationship between points A and B on the sample object and points C and D after moving the reference plate by the shape measurement method of the present invention.

FIG. 10 is an explanatory diagram showing how to obtain spatial coordinates in the shape measurement method of the present invention.

FIG. 11A is a diagram showing a halftone lattice image displayed on a display. FIG. 11B is a diagram showing the relationship between the brightness and the position of the same lattice image. FIG. 11C is a diagram showing a relationship of calculating a phase from the same phase distribution and a position. FIG. 11D is a diagram showing a state where the phase distribution and the position are connected in phase. FIG. 11E is a diagram showing a halftone grayscale image displaying the same phase distribution on a display.

FIG. 12 is a diagram showing a halftone image displaying on a display a method of obtaining a phase distribution by dividing a grid in each direction using a Fourier transform grid method, and FIG. 12B is an image showing a Fourier spectrum. FIG. 12C is an image showing a first harmonic in the x-direction. FIG. 12D is an image showing a first harmonic in the y-direction. FIG. 12 (F) is an image showing a complex grating in the y direction. FIG. 12 (G) is an image showing a phase distribution in the x direction. FIG. 12 (H) is an image showing a phase distribution in the y direction. .

FIG. 13 is an explanatory diagram of a measurement principle showing a measurement method by grid projection according to the present invention. FIG. 13A is a diagram showing a projection method of the one-dimensional lattice, and FIG. 13B is a diagram showing a projection method of the two-dimensional lattice.

FIG. 14 is a diagram for explaining a Fourier transform phase shift method used in the present invention. FIG. 14 (A) is a diagram showing a change in luminance on the same line, and FIG. It is a figure which shows the Fourier spectrum in the same 1 point.

FIG. 15 is a diagram showing a halftone image displayed on a display for explaining the effect of lens aberration in the present invention, and FIG. 15 (a) is an image showing a schematic diagram of the distortion. ) Is an image showing the lattice image. FIG. 15C is an image showing the distribution of the shift amount due to the lens aberration.

FIG. 16 is a diagram illustrating a shooting state of a reference object according to the present invention.

FIG. 17 is a diagram for explaining a method of calculating coordinates according to the present invention.

FIG. 18 is a diagram comparing plate shape measurement results between the method of the present invention and the conventional method.

[Explanation of symbols]

 REFERENCE SIGNS LIST 1 reference plate 1 'reference plate after movement 2 2D grating 3 1 axis table 4 base 5 TV camera 6 grating projection device 7 2D grating slide 8 2 axis micro stage 9 color filter 10 computer 10a A / D converter 10b CPU Phase value of 10c memory 11 sample object

Continuing from the front page There is an application for the application of Article 30 (1) of the Patent Act. Presentation (58) Field surveyed (Int.Cl. ⁶ , DB name) G01B 11/00-11/30

Claims (2)

(57) [Claims] (1) installing a reference plate on which a two-dimensional grid is drawn on a one-axis table so as to be able to translate in a direction perpendicular to the reference plate; and (2) mounting a television camera on the reference plate. (3) installing the grid projection device at a near side position where the two-dimensional grid can be projected onto the reference flat plate, and (4) before moving the reference flat plate. A step of calculating a phase value distribution from an image of the two-dimensional grid drawn on the reference plate at the plurality of positions after the movement and recording the result in a memory of a computer; Photographing a two-dimensional lattice projected from the lattice projection device onto the reference plate, converting the photographed image into phase value data and recording it in the memory of the computer; (6) the position before and after the movement of the reference plate Measurement between the position The two-dimensional grid projected from the grid projection device onto the sample object, which is an object, is photographed by a television camera. And a step of calculating spatial coordinates of a point on a measurement target imaged on the pixel from data recorded in a phase value data memory converted from an image and a pixel. Method. 2. A means for setting a reference plate on which a two-dimensional grid is drawn on a one-axis table so as to be able to translate in a direction perpendicular to the reference plate. (3) means for installing the grid projection device at a front position where the grid can be projected at two positions of the reference plate before and after movement, and (4) Means for calculating a phase value distribution from an image obtained by photographing a two-dimensional grid drawn on a reference plate at a plurality of positions before and after the movement, and recording the result in a memory of a computer; Means for converting an image obtained by photographing a two-dimensional grid projected from the grid projection device onto the reference plate at a plurality of positions before and after the movement from the grid projection device into phase value data and recording the same in a memory of a computer; Position before and after movement of the flat plate Projecting a two-dimensional grating from the grating projection device onto a sample object which is placed between,
The projected two-dimensional lattice is photographed by a television camera, and for each pixel, the coordinates of the pixel in the screen, the phase value of the projection lattice and the phase value distribution calculation memory, and the phase value data memory converted from the photographed image are recorded. And a means for calculating spatial coordinates of a point on a measurement object captured by the pixel from the obtained data.