JP2008281491A - Shape measurement method and shape measuring device using a number of reference planes - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a shape measurement method and a shape measuring device capable of precisely measuring a shape in a lattice in which luminance distribution is not in a cosine wave and a lattice having an unequal interval by utilizing a number of reference planes for the projection of the lattice. <P>SOLUTION: The shape measuring device comprises: a reference flat plate 11 including the reference plane 12; a stage 13 for moving the reference flat plate 11 in the direction of a normal line; a projector 14 for projecting a lattice pattern at each position of translation; a camera 15 for obtaining a first photographed image obtained by photographing the lattice formed on the reference plane 12 at each position, a second photographed image obtained by photographing the projection lattice of the reference plane 12 at each position, and a third photographed image obtained by photographing the lattice projected on a sample object 17; and an analyzer 16 for analyzing the lattice of the first photographed image and the projection lattice of the second photographed image for each pixel, forming a table for allowing space coordinates comprising the amount of travel of the reference plane 11 and the two-dimensional coordinates of the lattice to correspond to a phase θ in the projection lattice, and obtaining the space coordinates of the sample object 17, based on the table and the third photographed image. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a shape measurement method using a large number of reference surfaces and a shape measurement apparatus using a large number of reference surfaces, which can perform shape measurement of a sample object such as an object or a human body with high accuracy without contact.

  As a conventional technique of the non-contact type three-dimensional shape measuring method, there are, for example, a conventional technique 1 and a conventional technique 2 described below.

  Prior art 1 (see Patent Document 1) is intended to perform highly accurate shape measurement without being influenced by lens aberration of a camera or projector in a shape measurement device using a camera, and a lattice pattern is drawn. Rather than calculating the lens center coordinates of the camera or projector from the image of the reference plate, the optical path through which the line of sight for each pixel of the camera passes from the two-dimensional grid fixed to the reference plane, and the optical path of the light projected from the projector Is a shape measuring method and a shape measuring device used in the method for calculating spatial coordinates as intersections of the optical paths.

  Prior art 2 (see Patent Document 2) is a vibrating object that obtains measurement results in real time for shape measurement and analysis of minute deformation using laser interference fringes that have been analyzed over time. The purpose is to make it possible to observe dynamic changes of moving objects on the spot, with a CCD camera while continuously shifting the phase of the lattice pattern for one period in 4/30 seconds. In this method, one image is taken every 1/30 seconds, a total of four images are taken, and the position distribution is obtained from these images.

Japanese Patent No. 2913021 Japanese Patent No. 3265476

  In the non-contact type three-dimensional shape measuring method of the prior art 1, since it is necessary to project both the x-direction grid and the y-direction grid separately from the projector, it takes time to project the grid, and the coordinates Since the calculation is complicated, the coordinate calculation takes a long time.

In the phase shift method used in the non-contact type three-dimensional shape measurement method of the prior art 2, the phase value is obtained on the assumption that the photographed grating has a cosine wave-like luminance distribution. However, in an actual grid image, the brightness distribution of the grid projected by the projector often deviates from the cosine wave, and in the case of grid projection by a liquid crystal projector, the input value of the liquid crystal and the displayed density (transmittance). ) Is nonlinear, the luminance distribution deviates from the cosine wave. It is actually difficult to create an accurate cosine wave-like luminance distribution even when using a film with a grid burned. It is also difficult to create a cosine wave lattice on the glass substrate. There is also a method of projecting a pattern close to a cosine wave lattice by creating a rectangular wave lattice on the glass substrate and projecting it with the focus shifted, but it does not become a cosine wave shape with high accuracy, and the projector The luminance distribution also changes depending on the distance from.
The non-contact type three-dimensional shape measurement method of the prior art 2 is a lattice projection method in which measurement is performed by projecting a cosine wave-like lattice onto a sample object to be measured. In this method, the height of the sample object is calculated. When the pitch distribution of the projected grating has to be changed to the cosine wave distribution at equal intervals in the vertical or horizontal direction, the projected grid luminance distribution deviates from the ideal distribution due to defocusing etc. Since the grid is not evenly spaced and the cosine wave distribution does not change, and the measurement error increases, the calculation formula must be complicated to match the projected grid, and the coordinate calculation is complicated. Coordinate calculation takes a lot of time.
FIG. 22A is a diagram illustrating the luminance distribution of a cosine wave lattice and a distorted lattice in the non-contact type three-dimensional shape measurement method of the prior art 2, and FIG. 22B is a diagram illustrating each of the luminance distributions of FIG. It is a figure which illustrates distribution of the phase value obtained by the phase shift method from luminance distribution. 22 (a) and 22 (b), in the case of a cosine wave-like grating, the horizontal axis phase and the calculated vertical axis phase have substantially the same value, but have a luminance distribution shifted from the cosine wave. In the case of a grating, it can be seen that an error occurs in the calculated phase distribution.

  The present invention uses a large number of reference planes when a reference flat plate including a reference plane is translated by a minute amount in the direction of the ray in projection of a pattern that can be digitized by forming a two-dimensional pattern or dividing a space. Therefore, even if the luminance distribution of the pattern to be projected is not cosine-like, even if the pitch of the pattern to be projected is unequal, the shape measurement method and shape using a large number of reference planes can be measured with high accuracy. It aims at providing a measuring device.

  In order to achieve the above object, the shape measuring method using a large number of reference surfaces of the present invention translates a reference plate including a reference surface on which a two-dimensional pattern is formed by a minute amount in the normal direction of the reference plate. A first step, a second step of obtaining a first photographed image by photographing a two-dimensional pattern formed on the reference surface at each position of the parallel movement, and the reference surface at each position of the parallel movement. A third step of capturing a pattern that can be digitized by dividing the space projected onto the second captured image, and dividing the two-dimensional pattern of the first captured image and the space of the second captured image. By analyzing the pattern that can be digitized for each pixel, the position of the pattern that can be digitized by dividing the space and the space coordinates composed of the movement amount of the reference plate and the two-dimensional coordinates of the two-dimensional pattern. A fourth step of forming a table in which one-to-one correspondence is established, a fifth step of obtaining a third photographed image by photographing a pattern projected onto a sample object and dividing the space into a numerical value, And a sixth step of obtaining a spatial coordinate of the sample object based on the table and the third photographed image.

  As a preferred example of the shape measuring method using a large number of reference planes of the present invention, when the table elements are created for each reference plane and the spatial coordinates for the phase between the reference planes are obtained, the phase Calculating spatial coordinates interpolated by a predetermined mathematical formula using table elements having values close to, and setting the table elements more finely than the reference plane spacing, and for each of the finely set elements, the phase Preliminarily calculated as spatial coordinates interpolated by a predetermined formula using an element of a table having a value close to the phase, and creating a table with the calculation result as the value of each element, The pattern that can be digitized by dividing the space may be an equidistant lattice, and the pattern that can be digitized by dividing the space may be an unequally spaced lattice including a radial lattice.

  In order to achieve the above object, a shape measuring apparatus using a large number of reference surfaces according to the present invention includes a reference flat plate including a reference surface on which a two-dimensional pattern is formed, and the reference flat plate in a direction normal to the reference flat plate. A stage that translates by an amount, a projection device that projects a pattern that can be digitized by dividing a space on the reference plane at each position of the translation, and a projection that is formed on the reference plane at each position of the translation A first photographed image obtained by photographing a two-dimensional pattern to be obtained, and a second photographed image obtained by photographing a pattern that can be digitized by dividing the space, projected onto the reference plane, and projected onto a sample object. An imaging device that obtains a third photographed image by photographing a pattern that can be digitized by dividing the two-dimensional pattern of the first photographed image and the space of the second photographed image. By analyzing each pattern for each pixel, a pair of spatial coordinates composed of the movement amount of the reference plate and the two-dimensional coordinates of the two-dimensional pattern and the phase of the pattern that can be digitized by dividing the space are paired. And an analysis device that forms a table associated with 1 and obtains spatial coordinates of the sample object based on the table and the third photographed image.

As a preferred example of the shape measuring apparatus using a large number of reference planes according to the present invention, the analysis apparatus creates the table elements for each reference plane and obtains spatial coordinates for the phase between the reference planes. Calculating spatial coordinates interpolated by a predetermined mathematical expression using table elements having values close to the phase, and the analysis apparatus sets the table elements more finely than the interval between reference planes. For each of the finely set elements, the spatial coordinates for the phase are calculated in advance as spatial coordinates interpolated by a predetermined mathematical expression using the elements of the table having values close to the phase, and the calculation result is calculated as the value of each element. The projection device is configured to divide the projected space into a digitized pattern, and the projection device is configured to project the space to be projected. The pattern that can be divided and digitized is a pattern of unequal intervals including a radial grid, the projection device is a projection device that projects the pattern that can be digitized by dividing the space and defocused, The projection device is a liquid crystal projector or a DMD projector, and the projection device is a projection device capable of performing a phase shift by a predetermined shift amount when projecting a pattern that can be digitized by dividing the space, The imaging apparatus may be an imaging apparatus that can capture the second captured image in synchronization with the phase shift.
[The invention's effect]

  According to the shape measuring method using a large number of reference surfaces of the present invention, when the above-mentioned first to sixth steps are performed, the reference flat plate including the reference surface is translated by a minute amount in the normal direction. Since many reference planes are used for the formation of two-dimensional patterns and the projection of patterns that can be digitized by dividing the space, the pitch of the projected pattern is not evenly spaced even if the luminance distribution of the projected pattern is not cosine-like Even so, it is possible to provide a shape measuring method using a large number of reference planes that can accurately measure the shape.

  According to the shape measuring apparatus using a large number of reference surfaces of the present invention, a reference flat plate including a reference surface on which a two-dimensional pattern is formed, and the reference flat plate are translated by a minute amount in the normal direction of the reference flat plate. A stage, a projection device that projects a pattern that can be digitized by dividing a space on the reference plane at each position of the parallel movement, and a two-dimensional pattern formed on the reference plane at each position of the parallel movement A first photographed image obtained by photographing the image and a second photographed image obtained by photographing the pattern that can be digitized by dividing the space and projected on the reference plane, and the numerical value obtained by dividing the space projected on the sample object. An imaging device that captures a pattern that can be converted into a third captured image, and a solution of the pattern that can be digitized by dividing the two-dimensional pattern of the first captured image and the space of the second captured image For each pixel, one-to-one correspondence between the spatial coordinates composed of the movement amount of the reference plate and the two-dimensional coordinates of the two-dimensional pattern and the phase of the pattern that can be digitized by dividing the space. And the analysis device for obtaining the spatial coordinates of the sample object based on the table and the third photographed image, the luminance distribution of the pattern to be projected is not cosine wave-like In addition, it is possible to provide a shape measuring method using a large number of reference planes that can accurately measure the shape even when the pitch of the pattern to be projected is unequal.

Hereinafter, the best mode for carrying out the present invention will be described in detail with reference to the drawings.
First, the “calibration method using a large number of reference surfaces” used in the shape measuring method of the present invention will be described.
The conventional method of the calibration method in the three-dimensional shape measurement by the grid projection method is to obtain each element of the matrix for associating the world coordinate system with the camera coordinate system and the projector coordinate system. Since a pinhole model without lens distortion is used, an error due to lens aberration is actually included, and high-precision shape measurement cannot be expected. Moreover, coordinate calculation is also complicated and requires a lot of measurement time.
The inventors of the present application, as one of the shape measurement methods based on the lattice projection method, perform various calibrations for each pixel of the image sensor, thereby causing various distortions such as distortion due to lens aberration and measurement errors in geometric parameters of the optical system. We have proposed a shape measurement method that improves the measurement accuracy by eliminating the above error factors, and applied this concept to shape measurement by grid projection and micro deformation / strain measurement by phase shift digital holography. A method of performing calibration for each pixel has begun to be used in recent image measurement, and is also applied to deformation measurement by a digital image correlation method.
In the “calibration method using a large number of reference planes in lattice projection shape measurement” used in the shape measurement method of the present invention, the reference plate is moved in parallel in the z direction of the spatial coordinates (normal direction of the reference plate) by a minute amount. Then, the phase distribution of the projection grating on the reference plane is obtained at each position, and then a table in which the phase and the z coordinate are associated one by one for each pixel of the captured image of the camera is created. At that time, by using a special liquid crystal panel capable of displaying a lattice on the reference plane, the x-coordinate and y-coordinate of the spatial coordinate are tabulated in a one-to-one correspondence with the phase as well as the z-coordinate. By this calibration method, accurate shape measurement without the influence of the distortion of the lens and the influence of the phase error due to the luminance unevenness of the projection grating can be easily realized. In addition, since it takes almost no time for calculating spatial coordinates, real-time shape measurement can be realized.

[Principle of calibration method using multiple reference planes]
In the present invention, the concept of calibration in shape measurement is greatly changed from the conventional method, and in the present invention, the correspondence between the phase of the projected grating and the three-dimensional coordinates is obtained for each pixel of the camera (imaging device). Call. If calibration can be performed, three-dimensional coordinates can be obtained immediately by obtaining the phase of the grating projected onto the sample object.
FIG. 1 is a diagram showing the principle of a calibration method using a large number of reference surfaces in the present invention. A reference plane installed perpendicular to the z-axis is translated little by little in the z-axis direction. The camera (photographing device) and the projector (projection device) are fixed above the reference plane. From the projector, a grid that is a two-dimensional pattern is projected onto the reference plane. At this time, the projected grids need not be evenly spaced. The phase of the projected grating can be easily calculated by the phase shift method. It is assumed that one pixel of the camera is shooting a point on the straight line L shown in FIG. The pixel is, the reference plane _{R 0, R 1, R 2} , ··, according to R _N, respectively point _{P 0, P 1, P 2} , ··, it will shoot P _N. The phases θ ₀ , θ ₁ , θ ₂ ,..., Θ _{N at} each point can be obtained by the phase shift method.

FIG. 2 is a diagram showing the relationship between the photographing line L of one pixel and the x, y, z coordinates on the reference plane in the present invention. For the points P ₀ , P ₁ , P ₂ ,..., P _N on each reference plane captured by one pixel of the camera, the x and y coordinates are obtained from the two-dimensional pattern formed on the reference plane. To obtain the z coordinate from the position of the reference plane. As the two-dimensional pattern formed on the reference surface, a pattern that can obtain the x coordinate and the y coordinate from the pattern is necessary.
When a two-dimensional lattice is used as a two-dimensional pattern, the phase values in the x and y directions of the two-dimensional lattice are obtained, and further, phase connection is performed, so that the x coordinate and y coordinate at each point can be determined. Obtainable. For details of “phase connection”, refer to Japanese Patent No. 3281918.

One method for obtaining phase values in the x and y directions from a two-dimensional lattice pattern is the Fourier transform lattice method. Also, by using a liquid crystal panel with a light diffusing plate attached to the surface as a reference surface, the lattice pattern can be displayed on the reference surface, and the phase distribution method is used to obtain the phase distribution from the image obtained by capturing the lattice pattern There is also. In addition to the phase shift method, the method for obtaining the phase of the grating is the Fourier transform fringe pattern analysis method (“Takeda, M. and Mutoh, K., Fourier transform profilometry for the automatic measurement of 3-D object shapes, Applied Optics , Vol. 22, No. 24, 3977-3982 (1983)).
In this way, for each position of each reference plane, three-dimensional coordinates (x, y, z coordinates) with respect to the phase θ of the projection grating are obtained for each pixel. The phase θ of the projection grating can be obtained only at the position of the reference plane, but the three-dimensional coordinates for all phases can be obtained with high accuracy by reducing the interval between the reference planes as necessary and interpolating between them. Can do.

[Reference plate using liquid crystal display]
The calibration method described above requires a two-dimensional pattern formed on the reference surface. Although a method of forming a two-dimensional pattern on the reference surface by drawing a two-dimensional lattice pattern on a flat plate is effective, there is a problem that an error increases in the surroundings when the Fourier transform lattice method is used. Furthermore, there is a disadvantage that the accuracy of the phase of the projection grating varies depending on the position in the reference plane when the grid projection is performed by drawing a shading pattern on the reference plane. Therefore, in the present invention, by using a liquid crystal display, a reference plate that can accurately obtain the phase values in the x direction and the y direction and can obtain the phase of the projection grating with high accuracy is used. This reference flat plate can obtain the x coordinate and y coordinate of each pixel with high accuracy by performing phase analysis by the phase shift method. Further, the phase accuracy of the projection grating does not vary with respect to the projection grating depending on the position in the reference plane.
For details on “phase analysis”, see “Motoharu Fujigaki, Phase Analysis Technology in Optical Whole-Field Measurement, System / Control / Information, Vol.48, No. 12, 495-503 (2004)”. thing.

FIGS. 3A and 3B are diagrams showing the configuration of the shape measuring apparatus of the present invention using a reference plate using a liquid crystal display and a stage to which the reference plate is attached. A light diffusing plate 2 is attached to the surface of the liquid crystal display 1, and an image displayed on the liquid crystal panel 1a is projected onto the light diffusing plate 2 from the back by illumination light 4 from the backlight light source 3. Yes. The liquid crystal display 1 is mounted on a moving stage 5 that moves in the z direction so that the display surface is perpendicular to the z axis. The position of the moving stage 5 is controlled in the z direction by a moving stage control signal from a computer (analyzer) 6.
FIG. 3B shows a state in which a grid (also called a projection grid) is projected from the projector (projection device) 7. When photographing the grid projected from the projector 7, the illumination light 4 from the backlight source 3 is blocked by displaying a black pattern as a reference plane display image on the liquid crystal panel 1 a. A grid image is projected as a projection image from the projector 7 and photographed by a camera (photographing device) 8. The projection grating projected from the projector 7 is projected onto the surface of the light diffusion plate 2. Therefore, the surface of the light diffusing plate 2 becomes a reference plane. The position of the reference surface 2 by using a moving stage _{5 z 0, z 1, z} 2, move ... and z _N, by performing a phase analysis of the projected grid at each location, is captured by the camera 8 phase theta ₀ for each position for each pixel of the image, theta _1, theta _2, can be obtained ..., a theta _N.

4 (a) and 4 (b) are diagrams for explaining how the lattice image is displayed on the reference plane of the reference flat plate of the shape measuring apparatus of the present invention. By inputting a black pattern as a projection image to the projector 7, the light from the projector 7 is prevented from reaching the reference plane 2. In the liquid crystal panel 1a, as a display image on the reference plane 2, a lattice image in the x direction is displayed in the case of FIG. 4A, and a lattice image in the y direction is displayed in the case of FIG. The lattice image displayed on the liquid crystal panel 1a is projected from the back onto the light diffusion plate 2 attached to the liquid crystal panel by the illumination light emitted from the backlight light source 3. The projected image is transmitted through the light diffusing plate 2 while being scattered inside, and is displayed on the surface of the light diffusing plate 2, that is, the reference plane. Therefore, the grid image displayed on the reference plane 2 by the camera 8 can be taken.
The position of the reference surface 2 by using a moving stage _{5 z 0, z 1, z} 2, ··, navigate to z _N, performs a phase analysis of the x and y directions of the grating at each location, to the phase Then, phase connection is performed, and further, conversion from the phase connected to the x coordinate or y coordinate is performed, so that the x coordinate x ₀ , x ₁ for each position of each pixel of the image captured by the camera 8 is obtained. , x _2, ..., x _N and y-coordinate _{y 0,} y _1, y _2, can be obtained ..., the y _N.

The above procedure is organized as follows.
1 Move the reference plane to a predetermined position.
1-1 Change the reference surface display image to a black pattern.
1-2 Project a grid image from the projector.
2. Shoot multiple images while shifting the phase, and obtain the phase for each pixel using the phase shift method.
2-1 Make the projected image on the projector a black pattern.
2-2 Display the reference plane display image on the LCD panel as a grid in the x direction.
2-3 Shoot multiple images while shifting the phase, and obtain the phase for each pixel using the phase shift method.
3 Make a phase connection.
4 Convert the phase and x coordinate.
4-1 Display the reference plane display image on the liquid crystal panel as a grid in the y direction.
4-2 Shoot multiple images while shifting the phase, and obtain the phase for each pixel using the phase shift method.
5 Perform phase connection.
6 Perform phase and y coordinate conversion.
7 Move the reference plane by a small amount and repeat step 1 and subsequent steps.

[Method of obtaining spatial coordinates of sample object]
By the above-described calibration method, the phases θ ₀ , θ ₁ , θ ₂ ,..., Θ _N and the x coordinates x ₀ , x ₁ , x ₂ , ..., x _N , y coordinates y ₀ , y ₁ , y ₂ , · ·, y _N and z-coordinate _{z 0, z 1, z 2} , ··, the relationship between the z _N is obtained respectively for each pixel. Their relationship is as shown in FIGS.
6 is a diagram showing an installed state of the sample object 9 between the reference plane R ₀ and the reference surface R _N in the shape measuring apparatus of the present invention. In this state, since the same lattice as that at the time of calibration is projected onto the sample object 9, in the case of a pixel photographing on the straight line L, the point P on the object is photographed and projected onto the point P. The phase [theta] _{P of the} grating is obtained as the phase of the pixel.
First, as shown in FIG. 6, the phase theta x-coordinate x _P corresponding to _P includes a phase theta _i and theta _{i + 1} before and after having between the phase theta _P, x coordinate x _i and x _i the corresponding _{Using +1} , it can be obtained by equation (1). Similarly, the y coordinate can be obtained by the equation (2) using the y coordinates y _i and y _{i + 1} , and the z coordinate can be obtained by using the z coordinates z _i and z _{i + 1.} It can be obtained in (3). Here, θ = θ _P. When θ _{i + 1} qi + 1 <θ _i (for example, when i = 3 in FIGS. 5A to 5C), 2π is added to θ _{i + 1} to obtain the equation (1), Formula (2), and Formula (3) are used.

In addition, by using equations (1), (2), and (3), tables of x, y, and z coordinates corresponding to equally spaced phases θ can be created in advance. By doing so, it is possible to immediately obtain the spatial coordinates (x coordinate, y coordinate, z coordinate) of the point from the phase obtained by photographing the sample object.
In each of FIGS. 5A, 5B, and 5C, with respect to the phase in the section indicated by K, among the front and rear phases θ _N and θ _{N + 1} having the phase therebetween, θ _{N + 1} does not exist. Therefore, the relationship between the phase and the space coordinates is obtained using Formula (1), Formula (2), and Formula (3) with i = N−1. That is, the calculation is performed using the phase and coordinate values on the previous reference plane. In this way, spatial coordinates can be obtained for all phases from 0 to 2π.

[Principle of calibration method using multiple reference planes when projection grating phase connection is possible]
When the phase connection can be made to the projection grating, the installation range of the reference plane can be widened. When phase connection is not performed, the installation range of the reference plane is limited to a range where the phase does not change by 2π or more, but when phase connection is possible, it can be expanded to the range where phase connection is possible. The shape of an object with large irregularities can be measured.
FIG. 7 is a diagram showing the relationship between the position of the reference plane and the phase φ connected in phase when phase connection is performed in the shape measuring apparatus of the present invention. Similar to the calibration method described above, for each position of each reference plane, three-dimensional coordinates (x, y, z coordinates) with respect to the phase φ connected in phase to the projection grating are obtained for each pixel.

[Method for obtaining the coordinates of the sample object when the phase connection of the projection grating is possible]
By the above-described calibration method, the phases θ ₀ , θ ₁ , θ ₂ ,..., Θ _N and the x coordinates x ₀ , x ₁ , x ₂ , ..., x _N , y coordinates y ₀ , y ₁ , y ₂ , · ·, y _N and z-coordinate _{z 0, z 1, z 2} , ··, the relationship between the z _N is obtained respectively for each pixel. Their relationship is as shown in FIGS.
Figure 9 is a view showing an installed state of the sample object 9 between the reference plane R ₀ and the reference surface R _N in the shape measuring apparatus of the present invention. In this state, since the same lattice as that at the time of calibration is projected onto the sample object 9, in the case of a pixel photographing on the straight line L, the point P on the object is photographed and projected onto the point P. The phase [theta] _{P of the} grating is obtained as the phase of the pixel.
First, as shown in FIG. 9, the phase theta x-coordinate x _P corresponding to _P includes a phase theta _i and theta _{i + 1} before and after having between the phase theta _P, x coordinate x _i and x _i the corresponding _{Using +1} , it can be obtained by equation (4). Similarly, the y coordinate can be obtained by the equation (5) using the y coordinates y _i and y _{i + 1} , and the z coordinate can be obtained by using the z coordinates z _i and z _{i + 1.} It can be obtained by (6). Here, φ = φ _P.

Further, by using the equations (4), (5), and (6), tables of x coordinate, y coordinate, and z coordinate corresponding to the equally-spaced phase φ can be created in advance. By doing so, it is possible to immediately obtain the spatial coordinates (x coordinate, y coordinate, z coordinate) of the point from the phase obtained by photographing the sample object.
In each of FIGS. 8A, 8B, and 8C, there is no phase before or after the phase in the section indicated by K. Therefore, the relationship between the phase and the spatial coordinates is obtained by using Equation (4), Equation (5), and Equation (6) with i = 0 or i = N−1. That was calculated using the values of the phase and coordinates in 0-th and 1-th reference plane for the phi ₀ is less than phi, with respect to the phi ₀ is greater than phi (N-1) -th and N-th Calculation is performed using the phase and coordinate values on the reference plane. In this way, spatial coordinates can be obtained for all phases from 0 to 2π.

The advantages of the “calibration method using a large number of reference surfaces” used in the shape measuring method of the present invention are listed below.
(1) A coordinate value can be obtained with high accuracy without being affected by distortion caused by distortion of the lens.
(1a) When configured to shoot with a plurality of cameras from different directions, the obtained coordinate data can be easily combined.
(1b) All-around measurement can be realized easily.
(1c) In the case where a single camera is used to shoot using a grid projected from a plurality of projectors from different directions, the composition can be easily performed, so that the shadowed portion can be reduced.
(2) Measurement is possible even when the pitch of the grating is unequal.
(2a) Shape measurement can be performed by projecting while rotating a radial grid or spiral grid.
(2b) Shape measurement using a grating that is not equally spaced (hereinafter, referred to as non-uniformly spaced grating) such as laser interference fringes becomes possible.
(2c) The shape can be measured with high accuracy using a projection method using a lens system (such as a fisheye lens) that distorts the projected image.
(3) Measurement is possible even if the luminance distribution of the grating is not cosine-like.
(3a) Shape measurement can be performed with high accuracy even when a rectangular wave grating is defocused and projected as a grating having a luminance distribution close to a cosine wave.
(3b) Shape measurement can be performed with high accuracy even when grid projection is performed using a liquid crystal panel that has a nonlinear relationship between the input value and the display density.

[First Embodiment]
FIG. 10 is a diagram showing a configuration of a shape measuring apparatus used for carrying out the shape measuring method according to the first embodiment of the present invention. The shape measuring device of this embodiment is configured as a real-time shape measuring device, and includes a reference flat plate 11, a reference surface 12, a stage 13, a projection device 14, a photographing device 15, and an analysis device (for example, a personal computer, (Hereinafter referred to as PC) 16.

In the present embodiment, a liquid crystal display is used as the reference flat plate 11. On the surface of the liquid crystal display 11, a light diffusing plate serving as a reference surface 12 is attached. The liquid crystal display 11 is installed on the stage 13.
The reference surface (light diffusing plate) 12 is mounted on a plane parallel to the x and y planes of FIG. 10 so as to be perpendicular to the normal direction (z direction of FIG. 10) of the reference plate. On the reference surface (light diffusing plate) 12, as described later, a predetermined two-dimensional pattern (using an equidistant grid in the present embodiment) is formed, and a pattern (which can be digitized by dividing the space) In this embodiment, an equally spaced grid is used).
In this embodiment, a liquid crystal display is used as the reference flat plate 11, and a predetermined two-dimensional pattern (in this embodiment, an equidistant grid is used on the reference plane (light diffusing plate) 12 when an image used for calibration is taken. However, it is also possible to use a flat plate in which a predetermined two-dimensional pattern (an equidistant lattice) is fixedly drawn on the reference plane (light diffusing plate) 12 as the reference flat plate 11. .
In the present embodiment, phase analysis is performed using a lattice pattern using an equally spaced grid as a “pattern that can be digitized by dividing a space”, but as “a pattern that can be digitized by dividing a space”. It is also possible to use a “shading pattern” (see Japanese Patent Application No. 2003-328230) or to use a “spatial coding method” using a “spatial code”. In that case, the “value obtained by dividing the space into a numerical value” is the phase when using a grid, the luminance ratio for a gray pattern, and the encoded value for the spatial coding method. .

The stage 13 translates the reference flat plate 11 by a minute amount in the normal direction (z direction in FIG. 10) of the reference flat plate. In this embodiment, a linear motion stage is used.
As the projection device (projector) 14, a liquid crystal projector is used in this embodiment, but a DMD projector may be used instead. The liquid crystal projector 14 includes a liquid crystal panel, a light source, and a lens, and displays on the liquid crystal panel of the liquid crystal projector at each position (R ₀ , R ₁ ,..., R _N ) of the stage 13 in the z-direction translation. The projected pattern (for example, a grid-like light and shade pattern) is projected onto the reference plane 12, and the liquid crystal projector is provided with a liquid crystal as a "pattern that can be quantified by dividing the space" on the sample object 17 placed in a predetermined positional relationship. A pattern (for example, a grid-like shading pattern) displayed on the liquid crystal panel of the projector is projected. Note that the projector 14 focuses on the “pattern that can be digitized by dividing the space” even if the projector can perform phase shift by a predetermined shift amount when projecting the “pattern that can be digitized by dividing the space”. It may be a projection device that projects by shifting.

  In the present embodiment, a camera (for example, a CCD camera) is used as the photographing device 15. The imaging device 15 is installed in front of the reference surface 12 as shown in FIG. 10, and images a two-dimensional pattern formed on the reference surface 12 at each position of the stage 13 in the z-direction translation. A first photographic image signal corresponding to the first photographic image and a second photographic image signal corresponding to the second photographic image projected on the reference plane 12 and obtained by photographing a pattern that can be digitized by dividing the space are input to the PC 16. At the same time, a third photographed image signal corresponding to a third photographed image obtained by photographing the pattern that can be digitized by dividing the space projected onto the sample object 17 is input to the PC 16. Note that when obtaining a second photographed image by capturing a pattern that can be digitized by dividing the space while performing phase shift, the camera 15 captures the second photographed image in synchronization with the phase shift. And Further, when the sample object 17 is photographed, the reference plane 12 is moved backward so as to move away from the camera 15.

  As the analysis device 16, a personal computer (hereinafter referred to as a PC) is used in the present embodiment. The PC 16 inputs a projection image signal (for example, a projection grid image signal) to the projector 14 for image projection, inputs a stage control signal to the stage 13 for controlling the position of the stage 13 in the z direction, and a predetermined two-dimensional pattern. A display image signal (equal interval grid image signal) generated for displaying (equal interval grid is used in the present embodiment) is input to the liquid crystal display 11, and a captured image signal (first captured image signal, no. 2 shot image signals and 3rd shot image signals).

  FIG. 11 is a functional block diagram showing the configuration of the analysis device 16 of the shape measuring apparatus according to the first embodiment. The analysis device 16 includes a calibration processing unit 21, a continuous photographing unit 22, a real time analysis unit 23, and a precision analysis unit 24.

  The calibration processing unit 21 performs calibration work. A display image to be displayed on the reference surface 12 using the liquid crystal display 11 as a reference plate, a projection image (for example, a lattice image) projected from the projector 14, or a stage control signal to the stage 13 is generated. These are output at a predetermined timing, and an image of the reference plane 12 is taken by the camera 15. The phase analysis is performed for each pixel from the captured image captured by the camera 15 to obtain the phase θ of the projection grating, and the x coordinate and the y coordinate are respectively obtained from the phase of the grating displayed on the reference plane 12. Regarding the z coordinate, since the position (the amount of movement of the reference flat plate 11) where the reference plane 12 moves corresponds to the z coordinate, the value is used. From these, a table (phase-coordinate table) in which a phase and a spatial coordinate are associated with each other one by one by calculating the x coordinate, the y coordinate, and the z coordinate when the phase is divided at equal intervals by interpolation. The created phase-coordinate table is stored in a storage device (for example, a hard disk).

  In the continuous photographing unit 22, in order to measure the shape of the sample object 17 in real time, all photographed images photographed by the camera 15 using DMA transfer are recorded in a ring memory. At this time, a pattern image (for example, a lattice image) that can be digitized by dividing the space in accordance with the timing of shooting is input to the projector 14 as a projection image while phase-shifting. The time-series captured images stored in the ring memory are also stored in a storage device (for example, a hard disk) for precise analysis after the measurement is completed.

The real-time analysis unit 23 extracts the latest four consecutive frames I ₀ , I ₁ , I ₂ , and I ₃ from the ring memory of the continuous shooting unit 22 and stores them in the buffer memory. From each image, I ₂ -I ₀ and I ₃ -I ₁ are obtained for each pixel, and the phase θ is obtained from each result using the phase analysis table. From the obtained phase θ, the x-coordinate or y-coordinate and the z-coordinate are obtained using the phase-coordinate table created by the calibration processing unit 21, display image processing is performed, and the distribution of the z-coordinate is displayed on the monitor. Alternatively, a stereoscopic image (3D image) is displayed on the monitor using the x coordinate, the y coordinate, and the z coordinate. When this series of processes ends, the process returns to the beginning of the process of the real-time analysis unit 23 again, and the process of the same content is repeated again.

The precision analysis unit 24 extracts four frames of images I ₀ , I ₁ , I ₂ , and I ₃ that are sequentially sequential with respect to the time-series captured images stored in the continuous imaging unit 22 and stores them in the buffer memory. From each image, I ₂ -I ₀ and I ₃ -I ₁ are obtained for each pixel, and the phase θ is obtained from each result using the phase analysis table. From the obtained phase θ, the x-coordinate, the y-coordinate, and the z-coordinate are obtained using the phase-coordinate table created by the calibration processing unit 21, and stored as a shape measurement result in a storage device (for example, a hard disk). . Unlike the real-time analysis unit 23, the precision analysis unit 24 obtains time-series shape measurement results for all frames.

[Calibration and shape measurement results]
First, the reference plane is moved to 100 positions at intervals of 0.2 mm in the range from z = 0 mm to 19.8 mm, and the correspondence between the phase of the projection grating and the spatial coordinates at each position is changed for each pixel. Asked. The phase-coordinate indicating the correspondence between the phase of the projection grating and the x, y, z coordinates for each phase 2π / 100, based on the correspondence between the phase of the projection grating obtained in this way and the spatial coordinates. A table was created for each pixel.
Next, a sample object whose central portion was raised to have a trapezoidal cross section was prepared as the sample object 17, and the real-time shape measurement of the sample object 17 was performed as described above. Then, the spatial coordinates (x, y, z) of the sample object 17 were obtained based on the captured image of the sample object 17 and the phase-coordinate table.

FIG. 12 is a drawing-substituting photograph showing a lattice projected onto the sample object 17 in the real-time shape measurement of the first embodiment. FIG. 13 is a drawing-substituting photograph showing the phase distribution of the grating projected onto the sample object 17 in the real-time shape measurement of the first embodiment. FIG. 14 is a drawing-substituting photograph showing the distribution of z coordinates of the measurement result of the real-time shape measurement of the sample object 17 of the first embodiment. FIG. 15 is a diagram showing a cross-sectional shape of the central portion of the sample object 17 obtained by the real-time shape measurement of the first embodiment.
From the above measurement results, the difference between the average z coordinate distribution of the central portion (upper part of the trapezoid) of the sample object 17 and the average z coordinate distribution of the peripheral part (left and right lower parts of the trapezoid) of the sample object 17 is obtained. The average error of the z coordinate measurement was calculated by comparing the coordinate distribution average difference value with the actual height, resulting in 0.015 mm. In addition, the standard deviation of the z coordinate distribution at the center of the sample object 17 was determined to be 0.086 mm. From this result, it was confirmed that the shape measurement could be performed with sufficiently good accuracy by the shape measurement method of the first embodiment of the present invention.

[Second Embodiment]
As a shape measuring device used for carrying out the shape measuring method of the second embodiment of the present invention, a shape measuring device having the same configuration as that of the first embodiment is used. The shape measuring apparatus of the present embodiment uses a radial grid that is a non-uniformly spaced grid in this embodiment as a “pattern that can be digitized by dividing a space” projected from the projector 14 onto the reference plane 12 or the sample object 17. The shape measuring device is configured to measure the shape of the sample object 17.

FIG. 16 is a drawing-substituting photograph showing a radial grating used for shape measurement of the second embodiment. This radial grating is constructed by drawing a large number of rectangular gratings with a pitch of 3 ° on a disk, and projection was performed using only a part of the radial grating shown in the shape measurement diagram 16 of the present embodiment. The disk on which the radial grating was drawn was attached to a radial grating rotary projection device (not shown), and the phase shift was performed by driving the stepping motor.
The radial grating was blurred and projected on the measurement surface, and measurement was performed with a grating that was not a perfect cosine wave. As the sample object 17, a step (height 10.00 mm) at the center of the sample object was measured using a “sample object whose center was raised in a trapezoidal cross section” having the same shape as the first embodiment. As the reference plane, in the range from z = 0 mm to 19 mm, the measurement was performed at 20 positions at intervals of 1 mm, and the measurement was performed on a total of 20 reference planes. For the phase shift, a phase shift method using four images obtained by shooting at a position where the phase was changed by π / 2 was used. Note that the projection of the grating was performed using the same radial grating grid, and the shape of the sample object was measured.

[Shape measurement result]
FIG. 17 is a drawing-substituting photograph showing a radial grating projected onto the sample object 17 in the shape measurement of the second embodiment. FIG. 18 is a drawing-substituting photograph showing the phase distribution of the radial grating projected onto the sample object 17 obtained by the phase shift method in the shape measurement of the second embodiment. FIG. 19 is a drawing-substituting photograph showing the distribution of the z coordinate of the measurement result of the shape measurement of the sample object 17 of the second embodiment. FIGS. 20A to 20C are graphs showing the luminance distribution, phase distribution, and height distribution of the grating, which are shown by extracting one line from the shape measurement results of FIGS. As can be seen from FIGS. 20A to 20C, it was confirmed that the measurement can be performed even if the projected grating is not a perfect cosine wave. In particular, in the case of the line C in FIG. 20C, it can be seen that the luminance distribution of the lattice can be measured with the height distribution despite the trapezoidal shape.

  FIG. 21 is a graph showing the height of one central line obtained from the measurement result of the shape measurement of the sample object 17 of the second embodiment. In FIG. 21, the “distance between the point and the straight line” between the upper point group of the central part of the sample object 17 (the upper part of the trapezoid) and the approximate straight line of the peripheral part of the sample object 17 (the left and right lower parts) is obtained. The accuracy with respect to the z coordinate was calculated. As a result, while the step of the sample object was 10 mm, in the shape measurement of this embodiment, the error from the average was 0.2 mm, and the standard deviation was 0.13 mm. From this result, it was confirmed that shape measurement could be performed with sufficiently good accuracy by the shape measurement method of the second embodiment of the present invention.

  The shape measuring method using a large number of reference surfaces and the shape measuring apparatus using a large number of reference surfaces according to the present invention include object shape measurement (for example, shape inspection in the manufacturing industry) and human body shape measurement (medical welfare field, clothing). Field).

It is a figure which shows the principle of the calibration method using many reference planes in this invention. It is a figure which shows the relationship between the imaging | photography line L of 1 pixel in this invention, and the x, y, z coordinate on a reference plane. (A), (b) is a figure which shows the structure of the shape measuring apparatus of this invention using the stage to which the reference | standard flat plate using a liquid crystal display and a reference | standard flat plate are attached, respectively. (A), (b) is a figure for demonstrating a mode that a grid image is displayed on the reference plane of the reference | standard plate of the shape measuring apparatus of this invention, respectively. (A) to (c) are obtained by a calibration method using a large number of reference planes used in the shape measurement method of the present invention, and the phase θ and spatial coordinates (x, y, z) when no phase connection is performed. It is a graph which shows the relationship with each coordinate. It is a figure which shows the state which installed the sample object between the reference plane and the other reference plane in the shape measuring apparatus of this invention. It is a figure which shows the relationship between the position of the reference plane in the case of performing phase connection in the shape measuring apparatus of this invention, and phase (phi) connected in phase. (A) to (c) are obtained by a calibration method using a large number of reference surfaces used in the shape measuring method of the present invention, and the phase θ and phase coordinates (x, y, z) in the case of phase connection are obtained. It is a graph which shows the relationship with each coordinate. It is a figure which shows the state which installed the sample object between the reference plane and the other reference plane in the shape measuring apparatus of this invention. It is a figure which shows the structure of the shape measuring apparatus used for implementation of the shape measuring method of 1st Embodiment of this invention. It is a functional block diagram which shows the structure of the analyzer of the shape measuring device of 1st Embodiment. It is a drawing substitute photograph which shows the grating | lattice projected on the sample object in the real-time shape measurement of 1st Embodiment. It is a drawing substitute photograph which shows the phase distribution of the grating | lattice projected on the sample object in the real-time shape measurement of 1st Embodiment. It is a drawing substitute photograph which shows distribution of the z coordinate of the measurement result of the real-time shape measurement of the sample object of 1st Embodiment. It is a figure which shows the cross-sectional shape of the center part of the sample object obtained by the real-time shape measurement of 1st Embodiment. It is a drawing substitute photograph which shows the radial grating | lattice used for the shape measurement of 2nd Embodiment. It is a drawing substitute photograph which shows the radial grating | lattice projected on the sample object in the shape measurement of 2nd Embodiment. It is a drawing substitute photograph which shows the phase distribution of the radial grating projected on the sample object obtained by the phase shift method in the shape measurement of 2nd Embodiment. It is a drawing substitute photograph which shows distribution of the z coordinate of the measurement result of the shape measurement of the sample object of 2nd Embodiment. (A)-(c) is a graph which shows the luminance distribution, phase distribution, and height distribution of the grating | lattice which each extracted and showed from the shape measurement result of FIGS. 17-19. It is a graph which shows the height in the center 1 line obtained from the measurement result of the shape measurement of the sample object of a 2nd embodiment. (A) is a figure which illustrates the luminance distribution of a cosine-wave-like grating | lattice and the distorted grating | lattice in the non-contact-type three-dimensional shape measuring method of a prior art, (b) is a phase shift method from each luminance distribution of (a). It is a figure which illustrates distribution of the obtained phase value.

Explanation of symbols

1 Liquid crystal display (reference plate)
1a Liquid crystal panel 2 Light diffusion plate (reference plane)
3 Backlight light source 4 Illumination light 5 Moving stage 6 Computer (analyzer)
7 Projector (Projector)
8 Camera (photographing device)
9 Sample object 11 Reference plate (liquid crystal display)
12 Reference surface (light diffusion plate)
13 stages (linear motion stage)
14 Projector (Projector; Liquid crystal projector)
15 Imager (Camera; CCD camera)
16 Analysis device (personal computer; PC)
17 Sample object 21 Calibration processing unit 22 Continuous imaging unit 23 Real-time analysis unit 24 Precision analysis unit

Claims (13)

A first step of translating a reference plate including a reference surface on which a two-dimensional pattern is formed by a minute amount in the normal direction of the reference plate;
A second step of obtaining a first photographed image by photographing a two-dimensional pattern respectively formed on the reference plane at each position of the parallel movement;
A third step of obtaining a second photographed image by photographing a pattern projected on the reference plane, which can be quantified by dividing the space, at each position of the parallel movement;
By analyzing the two-dimensional pattern of the first photographed image and the pattern that can be digitized by dividing the space of the second photographed image for each pixel, the amount of movement of the reference plate and the two-dimensional pattern A fourth step of forming a table in which one-to-one correspondence between spatial coordinates composed of two-dimensional coordinates and pattern phases that can be digitized by dividing the space;
A fifth step of obtaining a third photographed image by photographing a pattern projected onto the sample object and which can be digitized by dividing the space;
A shape measuring method using a number of reference planes, wherein a sixth step of obtaining a spatial coordinate of the sample object based on the table and the third photographed image is performed.   When the elements of the table are created for each reference plane and the spatial coordinates for the phase between the reference planes are obtained, the spatial coordinates interpolated by a predetermined formula using the elements of the table having values close to the phase The shape measuring method using a large number of reference planes according to claim 1, wherein:   A space in which the elements of the table are set more finely than the interval between the reference planes, and for each of the finely set elements, the spatial coordinates for the phase are interpolated by a predetermined formula using the table elements having values close to the phase. 2. A shape measuring method using a plurality of reference surfaces according to claim 1, wherein a table is prepared in advance as coordinates, and a table in which the calculation result is a value of each element is created.   The shape measuring method using a large number of reference surfaces according to claim 1, wherein the pattern that can be digitized by dividing the space is an equidistant grid.   The shape measuring method using a number of reference planes according to any one of claims 1 to 3, wherein the pattern that can be digitized by dividing the space is a non-uniformly spaced grid including a radial grid. A reference plate including a reference surface on which a two-dimensional pattern is formed;
A stage that translates the reference flat plate by a minute amount in the normal direction of the reference flat plate;
A projection device for projecting a pattern that can be digitized by dividing a space into the reference plane at each position of the parallel movement;
A first photographic image obtained by photographing a two-dimensional pattern formed on the reference plane at each position of the parallel movement, and a second photographic image obtained by photographing a pattern projected onto the reference plane and divided into a space. An image capturing apparatus that obtains a third captured image by capturing an image and capturing a pattern that is projected onto the sample object and that can be digitized by dividing the space;
By analyzing the two-dimensional pattern of the first photographed image and the pattern that can be digitized by dividing the space of the second photographed image for each pixel, the amount of movement of the reference plate and the two-dimensional pattern A table is formed in which one-to-one correspondence is made between a spatial coordinate composed of two-dimensional coordinates and a phase of a pattern that can be digitized by dividing the space, and the sample is based on the table and the third photographed image. A shape measuring device using a large number of reference planes, comprising: an analyzing device for obtaining spatial coordinates of an object.   The analysis device creates an element of the table for each reference plane, and when obtaining a spatial coordinate with respect to a phase between the reference planes, a predetermined mathematical formula is used using an element of the table having a value close to the phase. The shape measurement apparatus using a large number of reference planes according to claim 6, wherein spatial coordinates interpolated by the calculation are calculated.   The analysis device sets the elements of the table more finely than the interval between the reference planes, and for each of the finely set elements, the spatial coordinates for the phase are determined using a table element having a value close to the phase. 7. A shape measuring apparatus using a large number of reference planes according to claim 6, wherein a space coordinate interpolated by a mathematical formula is calculated in advance, and a table in which the calculation result is a value of each element is created.   The shape using a large number of reference planes according to claim 6, wherein the projection device has a pattern that can be digitized by dividing the projected space, and is a pattern of equal intervals. Measuring device.   9. The plurality of criteria according to claim 6, wherein in the projection device, the pattern that can be digitized by dividing the space to be projected is an unevenly spaced pattern including a radial grid. Shape measuring device using a surface.   9. The projection apparatus according to claim 6, wherein the projection apparatus is a projection apparatus that projects a pattern that can be digitized by dividing the space by defocusing the pattern. Shape measuring device.   9. The shape measuring apparatus using multiple reference planes according to claim 6, wherein the projection apparatus is a liquid crystal projector or a DMD projector.   The projection device is a projection device capable of performing a phase shift by a predetermined shift amount when projecting a pattern that can be digitized by dividing the space, and the imaging device synchronizes with the phase shift. The shape measuring device using a large number of reference planes according to any one of claims 6 to 8, wherein the shape measuring device is a photographing device capable of photographing an image.