JP6666670B2 - 3D shape measurement method using curved surface as reference surface - Google Patents

Description

  The present invention relates to a three-dimensional shape measurement method using a phase shift method and a full space table conversion method.

  The three-dimensional shape measurement for a large object is performed by projecting a grating pattern from a line LED light source through a grating plate, and using a phase shift method and a full spatial table method, similarly to the measurement of a conventional small object. The shape of the object is determined by performing phase analysis on the distortion of the lattice pattern projected on the object (see Patent Document 1).

JP 2008-281491 A

Normally, a planar reference plane is used in the full space tabulation method. When the reference plane is a plane, there is a problem that the reference plane must be moved a long distance from the lower end to the upper end of the large object as shown in FIG. 1 (distance d ₁ in FIG. ₁ ).

  Accordingly, an object of the present invention is to provide a three-dimensional shape measuring method that requires only a short movement of a reference plane in view of the above-described problems of the related art.

The invention according to claim 1 of the present application includes a first step of obtaining three-dimensional coordinates of a reference surface having a curved surface having a two-dimensional lattice pattern on a surface, a second step of obtaining three-dimensional coordinates of the reference surface at an initial position, A third step of reading the phase value of the pixel of interest on the two-dimensional lattice pattern by a phase analysis method, and from the three-dimensional coordinates obtained in the second step and the phase value read in the third step, And a fourth step of creating a reference plane coordinate table having the three-dimensional coordinates as elements.
Here, the “curved surface having a two-dimensional lattice pattern on the surface” may be a curved surface to which a two-dimensional lattice sheet is attached, or may be provided by printing a two-dimensional lattice pattern. If a reference surface was shaped Align object to be measured curved surface, it is possible to measure in movement by a short distance (distance d ₂ in FIG. _2).

Invention has a two-dimensional lattice pattern on the surface, short travel so as to allow measurement in the distance in a given direction the reference plane having a Align was curved to the shape of the object to be measured according to claim 2 A first step of moving the reference plane by the minute amount, a second step of calculating a phase value of the projection grating at a point where the pixel of interest is photographed when the reference plane is moved by the minute amount, and A third step of calculating a phase value of the pixel of interest on the reference plane, wherein the first to third steps are repeatedly performed until the phase value by grid projection exceeds a predetermined value, and And a fifth step of obtaining a relationship between the phase value of the projection grating and the phase value on the reference plane. It is Shon way.

The invention according to claim 3 is the calibration method according to claim 2, wherein the first step of performing grid analysis on the object to be measured and performing phase analysis, and the phase value obtained by the phase analysis with respect to the pixel of interest, 2. A second step of obtaining a moving amount based on the relationship obtained by the following: a third step of obtaining a phase value on the reference plane from the phase value; and a step of obtaining a phase value on the reference plane from the phase value. A fourth step of specifying the three-dimensional position of the pixel of interest using the reference plane coordinate table; and adding the amount of movement to the three-dimensional position specified in the fourth step. And a fifth step of calculating the coordinates of the three-dimensional position of the object.
The invention according to claim 4 is a method for measuring the shape of an object by performing the first to fifth steps of claim 3 for all pixels.

  According to the present invention, it is possible to provide a three-dimensional shape measurement method that requires only a short movement of the reference plane.

It is a figure explaining movement of a reference plane when a plane reference plane is used. It is a figure explaining movement of a reference plane when a curved reference plane is used. It is a figure explaining the reference surface of the curved surface where the two-dimensional lattice was pasted. FIG. 9 is a diagram showing a correspondence relationship between a phase value φx in the x direction and a phase value φy in the y direction. It is a figure explaining a situation of lattice projection. FIG. 9 is a diagram illustrating a relationship between a phase value θ and Δz. FIG. 6 is a diagram illustrating a relationship between a phase value θ and φx. FIG. 7 is a diagram illustrating a relationship between a phase value θ and φy. FIG. 6 is a diagram illustrating a state of grid projection when an object is placed. FIG. 7 is a diagram illustrating a relationship between a phase value θ and Δz when an object is placed. FIG. 9 is a diagram illustrating a relationship between a phase value θ and φx when an object is placed. FIG. 9 is a diagram illustrating a relationship between φy of a phase value θ when an object is placed. It is a figure which shows the correspondence of φx and φy when an object is placed. It is a figure showing a reference plane to which a two-dimensional lattice was pasted. It is a figure showing a situation of an experiment. FIG. 9 is a diagram illustrating a relationship between a phase value θ and Δz. FIG. 9 is a diagram illustrating a relationship between a phase value θ and a phase value φx. FIG. 7 is a diagram illustrating a relationship between a phase value θ and a phase value φy. FIG. 7 is a diagram for explaining Δz obtained from a phase value θ. FIG. 9 is a diagram illustrating a phase value φx obtained from a phase value θ. FIG. 9 is a diagram illustrating a phase value φy obtained from a phase value θ.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
1. Creation of reference plane structure and reference plane coordinate table <Preparation stage 1>
(1) As shown in FIG. 3, a curved surface to which a two-dimensional lattice sheet is attached is set as a reference surface. A grid number is sequentially assigned to each line of the two-dimensional grid in the x and y directions.
(2) The phase values of the two-dimensional grating in the x and y directions are φx and φy. Multiplying the lattice number by 2π gives the phase value. In addition, the space between the grid lines can be finely read as a phase value.
(3) On the reference plane at the initial position, the x, y, and z coordinates of the entire reference plane are obtained in advance by another method (eg, trigonometry using a camera), and the phase value φx of one pixel of interest on the grid sheet is obtained. , Φy are read by the sampling moire method which is one of the phase analysis methods. Based on this, a two-dimensional table (reference plane coordinate table) having (x, y, z) as elements for φx and φy as shown in FIG. 4 is created. In addition to the sampling moiré method, a method such as a Fourier transform method or a weighted phase analysis method can be used.

2. Calibration work <Preparation stage 2>
(1) One pixel (i, j) photographed by a camera indicated by a straight line L in FIG. 5 will be described. Here, it is assumed that the pixel of interest shown as an example is photographing the vicinity of the grid number 29 at the initial position _R0 of the reference plane.
(2) FIG. 5 shows how the grid is projected. The reference plane is gradually translated in the z direction. The movement amount is defined as Δz. The numbers (0, 1, 2, ..., 28, 29, 30) assigned in the x direction indicate the grid numbers in the x direction. The numbers Ri (R ₀ , R ₁ ,..., R _N ) assigned in the z direction are indicated as the position numbers of the reference planes that have been translated.
(3) When the reference plane is moved by Δz, the phase value θ of the projection grating at the point where the pixel of interest is photographed is obtained. Further, the phase values φx and φy of the pixel of interest on the grid sheet are obtained by the sampling moire method.
(4) The above (2) and (3) are performed until the phase value θ by the lattice projection exceeds a predetermined value (for example, 2π).
(5) FIG. 6 is a graph showing the relationship between the phase value θ obtained by the grid projection and the movement amount Δz of the reference plane obtained up to now. FIG. 7 is a graph showing the relationship between the phase value θ and φx, and FIG. 8 is a graph showing the relationship between the phase value θ and φy.
(6) The above (1) to (5) are performed for all pixels of the camera.

3. Measurement of target object (1) With the object placed as shown in FIG. 9, a grid is projected and phase analysis is performed. At this time, in FIG. 9, it is assumed that the lattice number corresponding to the phase value φx at the position indicated by the point S on the object is, for example, 27.9.
(2) For the target pixel, the value of Δz is determined from the obtained phase value θ with reference to the graph of FIG. Assuming that the point S on the object is at a position of, for example, 2.7 mm in the z direction, the phase value θ at that time is 1.58π.
(3) Similarly, φx is determined from the phase value θ with reference to FIG. 11 and φy is determined with reference to FIG. Referring to this correspondence, φx = 27.9 * 2π and φy = 9.7 * 2π at the phase value θ = 1.58π.
(4) Finally, as shown in FIG. 13, (x, y, z) of the target pixel photographed by the camera is specified from φx, φy. The phase values φx = 27.9 * 2π and φy = 9.7 * 2π obtained so far become the phase values φx = 27.9 * 2π and φy = 9.7 * 2π at the initial position of the reference plane, respectively. It corresponds to the x coordinate and the y coordinate.
(5) By adding Δz obtained in (2) to z in the coordinates obtained in (4) above, the coordinates (x, y, z) of one point on the object captured in the target pixel can be obtained. (Z ′ = z + Δz). Note that this addition process can be tabulated by discretizing the value of z.
(6) By performing this for all pixels, it is possible to measure the shape using a reference plane that is not a plane.
(7) In this method, after obtaining the phase distribution of the projection grating, the method refers to a table for obtaining the phase values φx and φy of the pixel of interest on the grid sheet and the reference plane movement amount Δz from the phase value of the projection grating. This is a method of referring to a table for obtaining x, y, and z coordinates from the phase values φx, φy, and further obtaining a coordinate value of the z coordinate by adding a reference plane movement amount Δz. This addition process can also be easily tabulated. That is, three-dimensional coordinates can be obtained at a high speed only by adding a table and performing addition in a short time, or by only referring to a table. Therefore, a three-dimensional shape measuring apparatus that can measure a three-dimensional shape in real time using this method can be constructed.

Next, an embodiment of the present invention will be described.
4. Calibration work <measurement preparation stage>
In this experiment, a flat plate is used, and the camera is installed at an angle α (here, α = 30 °), and the measurement is performed with the curved surface set. When focusing only on one plane element photographed by the camera, the correspondence between the phase value θ by the grid projection that changes with the movement of the reference plane and the phase values φx and φy on the two-dimensional grid and the x, y, and z coordinates. Ask for. The vertical and horizontal pitches of the two-dimensional lattice are defined as px and py, respectively.

  First, a flat plate having a length of 400 mm and a width of 550 mm is used as a reference plane used in this experiment. As shown in FIG. 14, an A4 size two-dimensional lattice sheet is attached to this flat plate (grid pitch x 10 mm in the x direction, 10 mm in the y direction).

The flat plate is fixed, and the projection apparatus on the moving stage is moved in the z direction (a direction approaching the reference plane) to perform calibration according to the present method. FIG. 15 shows the state of the experiment.
(1) The grid is projected at the initial position, the phase value θ at that position is obtained, and then the phase value φx, Find φy. The coordinates at the initial position of the reference plane are: ~ 3. As described in the principle of the above, in order to treat as a known value, in this experiment, it is calculated in advance from the following equations (1) to (3).

The x, y, z coordinates obtained from this equation and the phase values φx, φy of the two-dimensional lattice are coordinates at the initial position of the reference plane.
(2) Next, the projector was moved by Δz (here, set to 20 mm).
(3) This operation is repeated for the N-th sheet (here, photographing is performed five times at intervals of 20 mm from 0 mm to 80 mm) until the phase value θ of the lattice projection exceeds 2π.

  Then, a correspondence relationship between the phase value θ and the movement amount Δz, the phase value φx, and the phase value φy obtained for each of the 0th to Nth reference planes is obtained. In this experiment, attention is paid to only one pixel, and the correspondence can be shown in Table 1.

(4) Data obtained by referring to Table 1 for the correspondence between Δz and the phase values φx and φy with respect to the phase value θ are plotted, and are shown as graphs in FIGS. 16, 17, and 18, respectively. The graph showing the correspondence between the phase value θ and the phase value φx is considered to show such a change due to an error because of a small displacement. The horizontal axis in FIGS. 16, 17, and 18 represents the phase value θ.

5. Coordinate measurement of one point on the object <measurement stage>
4. The calibration was performed by focusing on only one pixel, and the correspondence between Δz and the phase values φx and φy could be obtained from the phase value θ by the grid projection.

  Next, the grid is moved to a position of 50 mm where imaging was not performed earlier, and a grid is projected assuming a reference plane as a target. The phase value θ of one pixel of interest on the target object was 1.06 from the phase projected on the reference plane as if the target object was considered. Table 2 shows values obtained by linearly complementing Δz and phase values φx and φy from the phase value θ. In addition, 4. 19, 20, and 21 show Δz and phase values φx and φy obtained from the phase values with reference to the graphs of FIGS. 16 to 18 obtained by the above calibration.

  Δz thus obtained is added to the z coordinate obtained at the initial position from equation (3), and the z coordinate z ′ on the object is obtained from equation (4).

Further, from the phase value φx obtained from the phase value θ on the object, the x coordinate x ′ on the object can be obtained by using Equation 1 here. Similarly, the y coordinate y ′ on the object can be obtained from the phase value φy and Equation 2 (when this calibration is performed on all pixels, the x and y coordinates are the phase values φx, It is determined from the fact that it corresponds to φy).
z ′ = − 10 * (− 98.941) * sin 30 ° / (2π) + 49.52 = 18.3
x ′ = 10 * (− 98.941) * cos 30 ° / (2π) = − 136.4
y ′ = 10 * (− 33.95) / (2π) = − 54.0
Here, x 'on the x coordinate and y' on the y coordinate are coordinates obtained from a two-dimensional grid, and are obtained from phase value mapping in the case of all pixel measurement. Therefore, in this experiment, only Δz was compared with the actual measurement, and the measurement result was 49.52 mm for a movement of 50 mm, and the error was 0.48 mm.

1 camera 2 projector 3 reference plane

Claims (4)

Has a two-dimensional lattice pattern on the surface, so that it is possible to measure at movement in a short distance, a first step of obtaining a three-dimensional coordinates of the reference plane having a Align was curved to the shape of the object to be measured,
A second step of obtaining three-dimensional coordinates of the reference plane at the initial position;
A third step of reading a phase value of the pixel of interest on the two-dimensional lattice pattern by a phase analysis method;
A fourth step of creating a reference plane coordinate table having the three-dimensional coordinate as an element with respect to the phase value from the three-dimensional coordinate obtained in the second step and the phase value read in the third step;
Method of creating reference plane coordinate table including Has a two-dimensional lattice pattern on the surface, short travel so as to allow measurement in the distance, first to a reference surface having a Align was curved to the shape of the object to be measured is moved little by little in a predetermined direction Steps and
A second step of calculating a phase value of a projection grating at a point where a pixel of interest is photographed when the reference plane is moved by the minute amount;
A third step of obtaining a phase value of the pixel of interest on the reference plane by a phase analysis method;
The first to third steps are repeatedly performed until the phase value by the grid projection exceeds a predetermined value, and the relationship between the phase value by the projection grid and the amount of movement by the small amount is determined. The fourth step to seek;
A fifth step of determining a relationship between the phase value of the projection grating and the phase value on the reference plane;
Calibration method including: A first step of projecting a grid on an object to be measured and performing a phase analysis;
A second step of calculating a movement amount of a target pixel from a phase value obtained by the phase analysis, based on the relationship obtained by the calibration method of claim 2;
A third step of obtaining a phase value on the reference plane from the phase value;
A fourth step of specifying a three-dimensional position of the pixel of interest from the phase value on the reference plane using the reference plane coordinate table of claim 1;
A fifth step of adding the movement amount to the three-dimensional position specified in the fourth step, and obtaining coordinates of the three-dimensional position on the object, which is mapped to the target pixel;
A coordinate calculation method comprising:   A method for measuring the shape of an object by performing the first to fifth steps of claim 3 for all pixels.