JP3536097B2 - Method and apparatus for measuring grating projection shape using frequency modulation grating - Google Patents

Method and apparatus for measuring grating projection shape using frequency modulation grating

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Publication number
JP3536097B2
JP3536097B2 JP2002057776A JP2002057776A JP3536097B2 JP 3536097 B2 JP3536097 B2 JP 3536097B2 JP 2002057776 A JP2002057776 A JP 2002057776A JP 2002057776 A JP2002057776 A JP 2002057776A JP 3536097 B2 JP3536097 B2 JP 3536097B2
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phase
frequency
distribution
θ
grating
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JP2003254732A (en
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吉春 森本
泰之 池田
聡 米山
元治 藤垣
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和歌山大学長
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Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a shape measuring method and apparatus, and more particularly to a method and apparatus for measuring shape from an image of an object on which a grid is projected.

[0002]

2. Description of the Related Art In a conventional shape measuring method, a phase distribution obtained by phase analysis of a lattice has a discontinuous value of 0 to 2π, and in order to obtain a unique value for a position, a resolution is required. It was necessary to drop the grating to project a grating with a large pitch, or to make the phase distribution of the grating continuous (phase connection). By making the phase distribution of the grating continuous, the phase value and the height of the object can be associated one-to-one, and the height of the object can be estimated from the phase value. In the conventional phase connection method, the height cannot be obtained when the object has a sharp step by using only one type of grating. In order to overcome this drawback, there is a method of using a plurality of grids having different pitches, but it has a drawback that the structure of the measuring device becomes complicated and it is not suitable for continuous analysis.

As a method of making the phase distribution of the grating continuous,
Yoshiharu Morimoto, Yasuyuki Seguchi, Toshihiko Azuma, "Strain Analysis by Moire Method Using Fourier Transform," Proceedings of the Japan Society of Mechanical Engineers, 54 (24), 1546-1552, (19).
98), there is a method of referring to the phase values of surrounding pixels. In this method, the phase values of two adjacent pixels are compared, and the point where a sudden change is judged to be a phase change is made continuous, but it is susceptible to noise, and the shape of an object with a sharp step is changed. Has the drawback that it cannot measure.
On the other hand, “Shape measurement using an active liquid crystal light source” by Satoshi Kakuuchi, Kunihiro Nakamoto, Toru Sakamoto and Koichi Iwata is a method that is not easily affected by noise and can perform phase connection accurately even when there is a sharp step. , Proceedings of the Japan Society of Mechanical Engineers, 54 (2
4), pp. 1546-1552 (1995), there is a method of using a plurality of gratings having different pitches. Since this method performs phase connection for each pixel while referencing a plurality of phase distributions having different pitches from each other, it is not affected by surrounding pixels, but a plurality of gratings must be projected. Becomes complicated. The inventors of the present invention, in Japanese Patent Application No. 2000-279457, entitled "Real-time Shape Deformation Measuring Method by Color Rectangular Wave Grating Projection", simultaneously project two types of gratings having different pitches using a color film, and perform color separation after photographing. So I disclosed a method to perform phase connection in real time, but a special camera is required,
It has the drawback that it is difficult to measure dark objects. Further, the inventors of the present invention, in Japanese Patent Application No. 2001-315178 "Shape Measuring Method and Shape Measuring Device Using Monochromatic Rectangular Wave Grating", use a gray grating that combines two kinds of rectangular waves with different pitches in real time. However, there is a drawback that the contrast of the grating is deteriorated in addition to the necessity of photographing at least 12 times.

[0004]

SUMMARY OF THE INVENTION In view of the above,
An object of the present invention is to provide a shape measuring method and device capable of performing phase connection with a device having a simple structure.

[0005]

According to a first aspect of the present invention, in a shape measuring method for obtaining a height distribution of an object, a frequency modulation grating in which frequency and luminance are cyclically changed depending on a position is provided. A step of projecting onto the measurement target object while moving at a speed; a step of continuously photographing the measurement target object onto which the grating is projected; a phase distribution relating to frequency and luminance relating to luminance from the photographed image; A step of obtaining a phase distribution, a step of phase-connecting using the phase distribution regarding the frequency, and a phase distribution regarding luminance, and a step of making the phase-connected phase distribution correspond to the height distribution of the measurement target object. It is characterized by including and.

According to a second aspect of the present invention, in the shape measuring method according to the first aspect, the frequency modulation grating is at coordinates (x, y) in the image of the measurement target object onto which the frequency modulation grating is projected. The luminance I is A, the amplitude of the frequency change, θ 1 (x, y) is the initial phase of the phase change component, and θ 2
(X, y) is the initial phase of the frequency change component, α is the lattice shift
When the moving distance , P 1 is the period of the phase change component, and P 2 is the period of the frequency change component, the following equation (1) is used.

[Equation 2]

According to a third aspect of the present invention, in a shape measuring apparatus for obtaining a height distribution of an object, a grating slide having an image of a frequency modulation grating in which frequency and luminance are cyclically changed depending on a position, and Moving means for moving the lattice slide at a predetermined speed, projection means for projecting the image of the lattice of the lattice slide on the measurement target object, and photographing for continuously capturing the measurement target object on which the grid is projected at constant intervals. Means, means for respectively obtaining a phase distribution regarding frequency and a phase distribution regarding luminance from the captured image, means for performing phase connection using the phase distribution regarding the frequency and the phase distribution regarding luminance, and And a means for associating the phase distribution connected in phase with the height distribution of the object to be measured.

[0008]

According to the first aspect of the present invention, a grid pattern (hereinafter referred to as a frequency modulation grid) in which the pitch periodically changes depending on the position is projected on the object, and the surface shape is non-contact, high speed, and high accuracy. measure. In the frequency modulation grating, two types of components, a brightness change component and a frequency change component, are incorporated in a monochromatic grating. Analyzing the phase distribution of these two components,
By performing phase connection, it is possible to accurately measure the shape of an object having a large step or a discontinuous shape. Also, 1
Since the grids of various types are projected by shifting at regular intervals,
It can be realized with a device having a simple structure.

According to the second aspect of the present invention, the frequency modulated wave grating incorporating the two kinds of components of the luminance change component and the frequency change component can be realized by making the equation (1) hold.

[0010]

DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 1 is a diagram showing a general configuration for executing the shape measuring method according to the present invention. In this example, the shape of the object 10 is measured. A reference grating slide 1 on which a frequency modulation grating is printed is attached to a moving table 2, and the moving table 2 can be finely moved in the x-axis direction by a stepping motor 3 under the control of a controller 6. A projection lens 5 is arranged on the front surface of the reference grid slide 1, and a light source 4 is arranged on the back surface thereof so that the grid is projected onto the measurement object 10. The light source 4 faces the object 10 to be measured, and the projection lens 5 and the surface of the reference grating slide 1 are parallel to each other. CC
The D camera 8 photographs the measurement target object on which the lattice is projected, and supplies the photographed lattice image to the phase calculation computer 7. The phase calculation computer 7 is a controller 6
In accordance with the instruction, the phase difference distribution output image is obtained from the lattice image taken by the CCD camera 8 while moving the reference lattice slide 1, and is supplied to the display device 9. The display device 9 displays the phase difference distribution output image.

The shape measuring method according to the present invention using the above configuration will be described below. 1 pixel (x,
The luminance I of the frequency modulation grating photographed in y) is expressed by the following equation.

[Equation 3] In Expression (1), α represents the moving distance of the lattice. Also,
θ 1 (x, y) is the initial phase of the phase change component, θ 2 (x, y
y) is the initial phase of the frequency change component, and A represents the amplitude of the frequency change. P 1 and P 2 are the periods of the phase change component and the frequency change component, respectively, and in the case of the present embodiment,
P 1 : P 2 = 3: 3n + 1 (n is a natural number) is satisfied. a and b represent a brightness amplitude (contrast) component and a bias component, respectively. The underlined portion shows the frequency change component. The luminance I when the shot nine times by changing each P 2/3 α I 0. . . I 8

[Equation 4] Becomes I obtained when P 1 : P 2 = 3: 22
Images of 0 to I 8 are shown in FIGS. 2 (a) to 2 (i), respectively.
Here, the following expression is established from P 1 : P 2 = 3: 3n + 1.

[Equation 5] Therefore, I 0 to I 8 in the equation (2) can be rewritten as follows.

[Equation 6] Focusing on the luminances I 0 , I 3 , and I 6 , they have the same frequency change component, and each phase change component is 2π /.
You can see that they differ by 3. Therefore, by applying the phase shift method, the initial phase of the grating including the frequency change component can be obtained. If the initial phase including this frequency change component is defined as Θ 0 , Θ 0 is expressed by the following equation.

[Equation 7] However, in Expression (5), arg is an operator for phase calculation, and the definition is shown in the following table. definition of arg (x, y)

[Table 1] The same applies to I 1 , I 4 , I 7, and I 2 , I 5 , I 8 , and Θ 1 and Θ 2 are defined as shown in the following equations.

[Equation 8]

[Equation 9] Images of Θ 0 , Θ 1 , and Θ 2 thus obtained are shown in FIGS. 3a, 3b, and 3c, respectively. Furthermore, equation (5)-
Using (7), the initial phase θ 2 of the frequency change component can be calculated as follows.

[Equation 10] Since the initial phase θ 2 of the frequency change component is obtained from the equation (8), the phase θ 1 of the phase change component can be obtained from the following equation. Finally, by performing phase connection using the two types of initial phases θ 1 and θ 2 obtained by the equations (8) and (9), a phase distribution with high resolution can be obtained for each pixel.
The distributions of the initial phases θ 1 , θ 2 and the initial phase after the continuation are shown in FIGS. 3d, 3e, and 3f, respectively.

A phase connection method using two types of phase distribution will be described. The two types of initial phases θ 1 and θ 2 obtained above are
Both are repeated discontinuous values of 0 to 2π, and it is necessary to make the phase distribution continuous (phase connection) in order to obtain a unique value for the position. A method using a phase distribution of a plurality of pitches is often used as a method of performing phase connection, and in the present invention, phase connection is performed by using two types of initial phases θ 1 and θ 2 having different pitches. Two
Regarding the initial phases θ 1 and θ 2 of the types, the lattice numbers are k 1 and k 2, and the values after phase connection are φ 1 and φ, respectively.
If the value is 2, the initial phase before and after the phase connection is expressed by the following relationship. φ 1 = θ 1 + 2πk 1 φ 2 = θ 2 + 2πk 2 (10) Further, φ1 and φ2 have a relationship shown by the following two expressions. φ 1 -nφ 2 = θ 1 -Mod (nθ 2, 2π) + 2π (k 1 -nk 2) (11)

[Equation 11] Here, Mod (α, 2π) is the remainder obtained by dividing α by 2π.
And Mod (α, 2π) = α-2π [α / 2π]
Define. ([] Indicates Gaussian symbol). Also, P1:
PTwo= 3: 3n + 1, so n = [PTwo/ P1]
It In Fig. 4, the phase distribution φ1, NφTwoAnd θ1, Mod
(NθTwo, 2π). From Fig. 4, θ 1And Mo
d (nθTwo, 2π) changes depending on the position x
Therefore, from the relationships shown in equations (11) and (12), 0 ≦ φ
1<6πPTwo/ P1In the range of, φ1 is calculated by the following formula.
Can be turned on.

[Equation 12]

Real-time processing by dedicated hardware will be described. FIG. 5 is a diagram showing a hardware configuration for performing the shape measuring method according to the present invention at high speed. Reference grid slide 11, moving table 12, stepping motor 1
3, the projection lens 15, the CCD camera 18, the display device 19, and the measurement target object 20 are the reference grid slide 1, the moving table 2, the stepping motor 3, the projection lens 5, the CCD camera 8, the display device 9, and the measurement device in FIG. It is similar to the target object 10. The timing controller 16 changes the moving speed of the reference grid slide to the CCD
Adjusted to move by P 2/3 for each frame rate of the camera 18, in synchronization with the photographing by the CCD camera 18 to emit strobe light source 14. In this way, it is possible to capture an image without blurring due to the movement of the grid.

FIG. 6 shows a frequency modulation grating phase analysis circuit 17
3 is a block diagram showing the configuration of FIG. The lattice image input from the CCD camera 18 is A / D converted by the A / D conversion unit 21, and then the switching unit 22 operates the frame memories I 0 to I 8 according to the frame synchronization signal from the timing controller 16. Are sequentially stored in. By taking every three of these images and passing through the three-dimensional phase calculation table T1, the initial phases Θ 0 , Θ 1 , and Θ 2 including frequency changes can be immediately obtained. Further, by passing these through the three-dimensional phase connection table T 2 , the initial phase θ 1 after continuation can be obtained immediately. Since one of the frame memories I 0 to I 8 is updated every time an image of one frame is input, the phase image output from the table is also updated every frame.
The relationship between the input and output of the three-dimensional phase table T 1 is shown in the following formula.

[Equation 10] Formula (13) is calculated in advance for all combinations of inputs. Further, the three-dimensional phase connection table T 2 receives Θ 0 , Θ 1 , Θ 2 obtained using the table T 2 as an input and outputs the phase distribution φ 1 after the continuation. A method of displaying a phase difference image will be described. In this method, the height distribution of the object is obtained by calculating the difference from the phase distribution on the reference plane. First, the switch S is turned on to store the phase distribution φ 0 on the reference plane in the frame memory 23. Next, the switch S is turned off and the measurement target object 20 is photographed, so that the phase difference distribution image can be output in real time.

The shape measuring method according to the present invention operates correctly.
This is confirmed by the simulation described above.
It is clear from FIGS. 2 and 3 which are graphs showing the image and its distribution.
It's mild. Fig. 2 shows when P1: P2 = 3: 22.
Is an image of the frequency modulation grating projected onto the object of
Are respectively α = 0 and PTwo/ 3, 2PTwo/ 3, PTwo,
4PTwo/ 3, 5PTwo/ 3, 2PTwo, 7PTwo/ 3, 8PTwo
It is an image at / 3. 3a, 3b, 3c
Is the phase distribution Θ containing the frequency change component, respectively. 0, Θ
1, ΘTwoIs. Figures 3d and 3e are derived from these
Two types of phase distribution θ1, ΘTwoIs. Figure 3f
Phase distribution θ1, ΘTwoWith the phase distribution after continuation obtained using
is there. From these images, the 2 contained in the frequency modulation grating
Analyze the phase distributions of various types,
You can see that

FIG. 7 shows a frequency modulation grating projected on an actual object.
This is the result of measuring the shape of the object by casting a shadow. Figure 7a
This is the result of projecting the frequency modulation grating on the plaster image. Figure 7
b, 7c, and 7d are two types of phase distribution θ1,
θTwoAnd the phase distribution φ after continuation 1Is. Figure 7e shows
Phase distribution of the reference plane (flat plate) obtained by the same method
φ1'(After serialization). FIG. 7f shows the image of FIG.
And the phase difference distribution obtained from the image of FIG. 7e. This image
The height distribution of the object without phase wrapping
You can see that

[Brief description of drawings]

FIG. 1 is a diagram showing a general configuration for executing a shape measuring method according to the present invention.

2A to 2I are images of a frequency modulation grating projected on a plane by simulation.

FIG. 3 is a phase distribution of a frequency modulation grating projected on a plane by simulation, a, b, and c are phase distributions of the frequency modulation grating, d is a phase distribution excluding a frequency change component, and e is a frequency. Is the initial phase of the change component,
f is the phase distribution after continuation.

FIG. 4 is a graph showing a phase distribution before and after phase connection.

FIG. 5 is a diagram showing a hardware configuration for performing the shape measuring method according to the present invention at high speed.

6 is a block diagram showing a configuration of a frequency modulation grating phase analysis circuit in FIG.

FIG. 7a is an image obtained by projecting a frequency modulation grating on a plaster image, which is the result of measuring the shape of an object.

FIG. 7b is a diagram showing two types of phase distributions, which are the results of shape measurement of an object.

FIG. 7c is a diagram showing two types of phase distributions, which are results of shape measurement of an object.

FIG. 7d is a diagram showing a phase distribution after continuation, which is a result of shape measurement of an object.

FIG. 7e is a diagram showing a phase distribution after the reference surface is made continuous, which is a result of shape measurement of an object.

FIG. 7f shows the resulting phase difference distribution.

─────────────────────────────────────────────────── ─── Continuation of the front page (56) Reference JP 2003-83730 (JP, A) JP 2000-105109 (JP, A) JP 11-257930 (JP, A) JP 10-122834 ( JP, A) JP 2003-121124 (JP, A) JP 2002-90126 (JP, A) (58) Fields investigated (Int.Cl. 7 , DB name) G01B 11/24 G01B 11/25

Claims (3)

(57) [Claims]
1. A shape measuring method for obtaining a height distribution of an object, the method comprising: projecting onto a measuring object while moving a frequency modulation grating whose frequency and luminance are cyclically changed depending on a position at a predetermined speed. A step of continuously photographing the measurement target object on which the grating is projected, at a constant interval, from the photographed image, a phase distribution regarding frequency,
Steps of respectively obtaining a phase distribution relating to luminance, a phase distribution relating to the frequency, and a phase connection using a phase distribution relating to luminance, and the phase-connected phase distribution corresponding to the height distribution of the measurement target object. A shape measuring method, comprising:
2. The shape measuring method according to claim 1, wherein the frequency I is the frequency I, the brightness I at the coordinates (x, y) in the image of the measurement target object projected by the frequency modulation G, is A. Amplitude of change, θ 1 (x,
y) is the initial phase of the phase change component, θ 2 (x, y) is the initial phase of the frequency change component, α is the moving distance of the lattice , P 1 is the period of the phase change component, and P 2 is the period of the frequency change component. In this case, the shape measuring method is characterized in that the following expression (1) is satisfied. [Equation 1]
3. A shape measuring apparatus for obtaining the height distribution of an object, comprising: a grid slide having an image of a frequency modulation grid in which the frequency and the brightness are cyclically changed depending on the position; and the grid slide is moved at a predetermined speed. Moving means, projection means for projecting the image of the lattice of the lattice slide onto the measurement target object, photographing means for continuously photographing the measurement target object on which the lattice is projected at constant intervals, and from the photographed image , The phase distribution with respect to frequency,
Means for obtaining a phase distribution regarding brightness, a phase connection for using the phase distribution for the frequency, and a phase distribution for brightness, and the phase connection for the phase connection corresponding to the height distribution of the measurement target object A shape meter characterized by comprising:
Measuring device .
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