JP2003222505A - Displacement measuring method and displacement measuring device using the same - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To solve the problem that an error of at least ±0.5 pixel is generated because measurement resolution can not be reduced below one pixel. <P>SOLUTION: An error function of a reference image is determined, and high resolution is imparted to the error function by interpolation operation. An error function between the reference image and a measuring image is determined, and an error function between the error function and the error function of the reference image to which high resolution is imparted is operated, and the shift quantity between the reference image and the measuring image is determined from the error function, and displacement is calculated from the shift quantity. Hereby, high resolution and high accuracy can be realized. <P>COPYRIGHT: (C)2003,JPO

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a displacement measuring method and apparatus for optically measuring vibration, displacement and velocity, and more particularly to a displacement measuring method capable of achieving high resolution and a displacement measuring apparatus using the same. is there.

[0002]

2. Description of the Related Art In the specification of Japanese Patent Application No. 2000-055857, the applicant proposed an invention of a displacement measuring device capable of optically measuring minute movements and vibrations of various devices with high precision. The outline of the present invention will be described below.

FIG. 5 is a block diagram of a displacement measuring device. Figure 5
At, the measurement object 3 is irradiated with illumination such as infrared light from the illumination system 4. The reflected light from the measuring object 3 is collected by the image forming optical system 5 and forms an image on the image sensor unit 6.

The image sensor unit 6 uses a CCD linear image sensor in which a large number of pixels (image elements) are arranged one-dimensionally. A clock signal is input to the image sensor unit 6 from the clock generation unit 7, and the output signals of the pixels are sequentially read. This output signal is converted into a digital signal by the A / D converter 8 and output to the signal processing unit 9.

The reference image storage unit 12 stores the output signal of the image sensor unit 6 in the reference state, that is, image data. Similarly, the measurement image storage unit 13 stores the image data of the measurement state.

The signal processing unit 9 compares the image data stored in the reference image storage unit 12 and the image data stored in the measurement image storage unit 13 to calculate the displacement and displays it on the display 11. Further, the displacement data is converted into an analog signal by the D / A converter 10 and output to the outside.

Next, the procedure for obtaining the displacement will be described with reference to FIG. The image sensor unit 6 is a CCD linear image sensor, and N pixels are arranged one-dimensionally.

The upper part of FIG. 6 is the image data of the reference image stored in the reference image storage unit 12, and the lower part is the image data of the measurement image stored in the measurement image storage unit 13. In each figure, the vertical axis represents the output value of each pixel and the horizontal axis represents the position of each pixel. For example, the output value at the position m is the output of the (m + 1) th pixel.

In the upper diagram of FIG. 6, the range from the position m to the position (m + M-1) is the reference image range. This range is composed of data of M pixels. The signal processing unit 9 searches the image data of the lower measurement waveform for a pattern similar to the image pattern in the reference image range.

FIG. 6 shows that an image pattern similar to the reference image range is detected at a position shifted by x pixels from the reference image on the measurement waveform. The displacement amount X can be calculated from the image displacement amount x by the following equation (1). X = A · x (1) A is a proportional constant determined by the optical magnification of the optical system.

When the previous displacement amount is X ', the current displacement amount is X, and the sampling period is T, the velocity V can be calculated by the following equation (2). V = (X-X ') / T ... (2)

A pattern matching operation such as the shortest distance method or the cross correlation method is used as a means for retrieving the reference image from the measured images. The shortest distance method is a method in which the error function R (τ) is calculated by the following equation (3) and the value of τ that minimizes this R (τ) is used as the deviation amount.

[Equation 1]

Note that m is the position of the starting point of the reference image range, and M
Is the number of pixels in the reference image range, and S ₀ (i) and S (i) are output values of the i-th pixel of the reference image and the measurement image, respectively. There is also a method of calculating the sum of squares instead of the absolute value.

In the cross-correlation method, the cross-correlation function C (τ) is calculated by the following equation (4), and the value of τ at which this C (τ) becomes the largest is taken as the deviation amount.

[Equation 2] m is the position of the starting point of the reference image range, and M is the number of pixels in the reference image range.

[0015]

However, such a displacement measuring device has the following problems.

As can be seen from the equation (3) or the equation (4), the resolution of this displacement measuring device is limited by the resolution of the pixels of the image sensor section 6. For example, if a CCD image sensor having 1024 pixels is used as the image sensor unit 6, it is 1/1024 of the field of view.
Is the resolution. Therefore, there is a problem that an error of at least ± 0.5 pixel occurs in the calculation in pixel units.

Therefore, the problem to be solved by the present invention is
An object of the present invention is to provide a displacement measuring method and a displacement measuring apparatus using the same, which can improve the resolution and the measuring accuracy.

[0018]

In order to solve such a problem, the invention according to claim 1 of the present invention obtains an error function between a measurement image of a measurement object and a reference image, and the error function is obtained. A displacement measuring method for calculating a displacement amount between the measurement image and the reference image from the above, and calculating a displacement amount from the displacement amount, wherein a first error function is obtained from image data of the reference image, And a second error function is obtained from the image data of the reference image, and at least one error function of the first and second error functions is increased in resolution by interpolation calculation, and a third error function is obtained from these error functions. Is calculated, the shift amount between the reference image and the measurement image is calculated from the third error function, and the displacement of the measurement object is calculated from the shift amount. The resolution can be improved.

According to a second aspect of the present invention, in the first aspect of the invention, the error function is obtained by the shortest distance method. The error function can be easily obtained.

According to a third aspect of the present invention, in the second aspect of the present invention, the operation of the shortest distance method is performed by adding the absolute value of the difference between the image data or the error function. . It can be calculated easily.

According to a fourth aspect of the present invention, in the second aspect of the present invention, the calculation of the shortest distance method is performed by adding the square of the difference between the image data or the error function. . It can be calculated easily.

According to a fifth aspect of the invention, in the first aspect of the invention, the error function is obtained by a cross-correlation function. A general-purpose means can be used.

According to a sixth aspect of the invention, in the inventions of the first to fifth aspects, the resolution of the error function is increased by linear interpolation. It can be calculated easily.

According to the seventh aspect of the present invention, the reference image storage unit 12 in which the reference image is stored, the measurement image storage unit 13 in which the measurement image of the measurement object 3 is stored, and the reference image storage unit 12 and the measurement are performed. A signal processing unit 9 that performs arithmetic processing using the image data stored in the image storage unit 13. The signal processing unit 9 uses the first error function based on the image data stored in the reference image storage unit 12. And a second error function is obtained from the image data stored in the reference image storage unit 12 and the measurement image storage unit 13, and at least one of these first and second error functions is increased in resolution by interpolation calculation. , A third error function is calculated from these error functions, and the deviation amount between the reference image and the measurement image is obtained from the third error function,
The displacement of the measuring object 3 is calculated from this displacement amount. The resolution can be increased.

According to an eighth aspect of the present invention, in the seventh aspect of the invention, the signal processing section 9 obtains the error function based on the shortest distance method. It can be calculated easily.

According to a ninth aspect of the invention, in the eighth aspect of the invention, the shortest distance method calculation is performed by adding the absolute values of the differences between the image data or the error function. It can be calculated easily.

According to a tenth aspect of the present invention, in the eighth aspect of the invention, the shortest distance method is calculated by adding the square of the difference between the image data or the error function. It can be calculated easily.

The invention described in claim 11 is the invention described in claim 7, wherein the error function is obtained based on a cross-correlation function. A general-purpose means can be used.

According to a twelfth aspect of the present invention, in the invention according to the seventh to eleventh aspects, the resolution of the error function is increased by linear interpolation. It can be calculated easily.

[0030]

BEST MODE FOR CARRYING OUT THE INVENTION The present invention will be described in detail below with reference to the drawings. FIG. 1 is a flow chart showing an embodiment of the displacement measuring method according to the present invention. Note that the hardware configuration is the same as that in FIG.

In FIG. 1, the reference image is first stored in the reference image storage unit 12, and the reference image range is set. next,
A matching operation is performed between the reference images to obtain the error function R ₀ . This error function R ₀ is a function that has a value in pixel units. In this embodiment, since the error function matching calculation is also performed when the displacement is measured, the error function R ₀ of the reference image is obtained in advance.

The error function R ₀ is calculated by using the pattern matching calculation such as the shortest distance method or the cross correlation method described above. Equation (5) shows the error function R ₀ using the shortest distance method.

[Equation 3] Here, S ₀ (i) is the output value of the i-th pixel of the reference image, M is the number of pixels in the reference image range of the reference image, and m is the starting point of the same reference image range.

Next, the obtained error function R ₀ is subjected to interpolation calculation to obtain a high resolution error function R ₀ ′. This interpolation calculation may be simple linear interpolation, or may be interpolation using a higher-order curve. An example of the error function R ₀ ′ subjected to the linear interpolation is shown in (6) below.

[Equation 4]

Here, d is the number of interpolation divisions, and τ ₀ is the maximum integer not exceeding τ ′, that is, τ ₀ ≤τ '≤τ ₀ +
An integer that satisfies 1, k is a division ratio (0, 1, ... D), and is an integer that satisfies k = d · (τ′−τ ₀ ). For example, if d = 10, 0.1
The error function R ₀ ′ can be calculated in 0.1 pixel units by calculating R ₀ ′ with τ ′ of the step.

Next, the measurement image is stored in the measurement image storage unit 13, a matching operation is performed between this measurement image and the reference image range portion of the reference image to obtain an error function R, and the deviation amount between them is calculated. Ask. The error function R can be obtained by the following equation (7) according to the shortest distance method.

[Equation 5]

Here, S (i) and S ₀ (i) are the measured image and the output value of the i-th pixel of the reference image, M is the number of pixels in the reference image range, and m is the start position thereof. Τ that minimizes the error function R is the shift amount x, and the positions are similar to each other. This shift amount x has a resolution in pixel units.

Then, the matching function is performed by comparing the error function R ₀ 'in the reference image obtained by the equation (6) with the error function R of the measurement image obtained by the equation (7). This matching operation is performed by calculating an error function RR (τ ′) representing the similarity of the error function by the following expression (8), for example. The value of τ ′ at which this value becomes the minimum is the point at which the error functions are similar, and becomes the shift amount x ′.

This displacement amount x'has a resolution of less than a pixel unit. For example, when the 10-division operation is performed by the equation (7), a resolution of 0.1 pixel unit can be obtained.

[Equation 6] Here, R (i) and R ₀ ′ (i) are the error function of the measurement image and the error function of the reference image with high resolution, h
Is the width from the center of the range in which the error functions are compared. The number of pixels in the comparison range is (2h + 1). Note that j
The range of is not necessarily symmetric with respect to the center like (x ± h).

It is sufficient that the calculation range of τ'is within the range of the deviation amount x ± 0.5 per pixel. For example, when the interpolation calculation of 10 divisions is performed by the equation (6), τ ′ can be obtained as a shift amount of 0.1 pixel unit.

Next, the displacement amount X is calculated from the optical magnification A by the following equation (9). X = A · x ′ + X ₀ (9) Note that X ₀ is the position of the reference image. Then, the previous displacement amount X, the previous sampling period T, and the current displacement amount X
Then, the speed V is obtained by the following (10). V = (X-X last time) / T ... (10)

Then, the previous displacement amount X is updated with the displacement amount X of this time, the calculation result is displayed on the display unit 11, and the D / A converter 10 converts it into an analog signal and outputs it to the outside. After that, it is checked whether or not the measurement is completed. If the measurement is completed, the measurement is ended. If not, a new measurement image is stored in the measurement image storage unit 13 and the same operation is repeated.

Next, the operation of the flowchart of FIG. 1 will be specifically described with reference to FIG. FIG. 2A is a reference image, where the horizontal axis is the pixel position and the vertical axis is the output value of each pixel.
Reference numeral 1 denotes the reference image range, and the thick line portion is the reference image.

FIG. 9B shows the error function R ₀ of the reference image (A) obtained by the above equation (5). The horizontal axis is the amount of deviation τ,
The vertical axis is the value of the error function R ₀ , and the diagonal line is the error function R 0.
Represents ₀ . This error function has a resolution on a pixel-by-pixel basis as indicated by a black circle.

FIG. 6C shows an error function R ₀ ′ having a higher resolution, which is obtained by interpolating the error function R ₀ by the equation (6). As can be seen from the figure, this error function R ₀ '
Has a smaller resolution than a pixel. For example, if the number of divisions is 10, it has a resolution of 0.1 pixel.

FIG. 3D shows a measurement image, and 2 is a portion similar to the reference range of the reference image. (E) is the above (7)
It is the error function R (τ) of the measurement image obtained by the equation.
This error function R (τ) also has a resolution in pixel units as in (B), and the shift amount is x.

FIG. 6F shows an error function RR of the error functions R ₀ '(τ) and R (τ) obtained by the equation (8).
(Τ '). 10 between x-0.5 and x + 0.5
And the shift amount becomes x + 0.3, and the shift amount can be obtained with 10 times accuracy.

Thus, the error function R of the reference image
Error function R with high resolution by performing interpolation calculation on ₀ (τ)
₀ ′ (τ) is calculated, the error function R ₀ ′ (τ) and the error function RR (τ ′) of the error function R (τ) of the measurement image are calculated, and the shift amount is calculated.

If there is no change in the shape of the image depending on the location, the error function should have the same shape everywhere, but in reality, it shows different shapes as shown in FIGS. 2B and 2E. Therefore, by calculating the error function of these error functions, it is possible to actually obtain the near amount less than the pixel unit.

FIG. 3 shows another embodiment of the present invention. Figure 3
(A) is a reference image, and 1 is its reference range, which is the same as (A) in FIG. Similarly, FIG. 3B shows the error function R ₀ (τ) of the reference image, which is the same as FIG. 2B.

FIG. 3 (C) is a measurement image, 2 is a portion similar to the reference image range of the reference image, and is the same as FIG. 2 (D). Similarly, FIG. 3D shows the error function R of the measurement image.
(Τ), which is the same as that in FIG.

FIG. 3E shows the error function R (τ) of the measurement image.
Is interpolated in the same manner as the equation (6), and has a resolution of 1 pixel or less. FIG. 3 (F) shows the error function R ₀ (τ) of the reference image of (B) and the error function R ′ (τ) of the high-resolution measurement image of (E) by the same method as the above equation (8). It is the calculated error function RR (τ ′). Also in this case, the shift amount τ ′ can be obtained with a resolution of one pixel or less, as in FIG.

That is, in the embodiment shown in FIG. 2, while the error function R ₀ (τ) of the reference image is interpolated to increase the resolution,
In the embodiment of FIG. 3, the error function R (τ) of the measurement image is interpolated to increase the resolution. Even in this case, the same effect can be obtained.

FIG. 4 shows the configuration of the signal processing section. The same elements as those in FIG. 5 will be assigned the same reference numerals and explanations thereof will be omitted. In FIG. 4, 90 is a signal processing unit,
1, 902 and 904, an interpolation calculation unit 903, a displacement amount calculation unit 905, and a displacement amount calculation unit 906.

The error calculation unit 901 inputs the reference image data stored in the reference image storage unit 12, and calculates the error function R ₀ (τ) based on the equation (5). Interpolation calculation unit 90
3 raises the resolution of the error function R ₀ (τ) calculated by the error function calculation unit 901 based on the equation (6).

The error function calculation unit 902 is the reference image storage unit 1.
The reference image stored in 2 and the data of the measurement image stored in the measurement image storage unit 13 are input, and the error function R (τ) is calculated based on the equation (7). The error function calculation unit 904 inputs the error functions R ₀ ′ (τ) and R (τ), and from these error functions, the error function RR is calculated by the equation (8).
Calculate (τ ').

The deviation amount calculation unit 905 calculates the error function RR.
The shift amount between the reference image and the measurement image is calculated from (τ ′).
The displacement amount calculation unit 906 calculates the displacement amount of the measurement object from the equation (9) using the displacement amount calculated by the displacement amount calculation unit 905.

Although the error function is obtained by the shortest distance method in these embodiments, it may be obtained by another method such as a cross-correlation function. Also, the shortest distance method may be a method of obtaining the sum of squares instead of the method of obtaining the absolute value as in the equations (5) and (7).

Further, although the case of the absolute measurement has been described in these embodiments, it is also possible to use it for the incremental measurement in which the reference image is updated and integrated. further,
It can be used for velocity measurement as well as displacement measurement.

[0059]

As is apparent from the above description,
According to the present invention, the following effects can be expected. According to the invention of claim 1, an error function between the measurement image of the measurement object and the reference image is obtained, a deviation amount between the measurement image and the reference image is calculated from the error function, and a displacement amount is calculated from the deviation amount. A displacement measuring method for calculating, wherein a first error function is obtained from image data of the reference image, and a second error function is obtained from image data of the measurement image and the reference image. At least one error function of the error functions is increased by interpolation calculation to obtain a third error function from these error functions, and the deviation amount between the reference image and the measurement image is calculated from the third error function. The calculation is performed, and the displacement of the measurement target is calculated from the displacement amount.

Conventionally, since the resolution was only one pixel, an error of at least ± 0.5 pixel occurred. For example, 10
± 0.05% when using a sensor with 24 pixels
Was limited in resolution and accuracy.

On the other hand, according to the present invention, since resolution of 0.1 pixel unit can be achieved, there is an effect that the resolution and accuracy of displacement measurement can be improved by one digit. If the number of divisions of the interpolation calculation is increased, the resolution and accuracy can be further improved.

When displacement measurement was actually performed using the present invention, it was possible to measure with an error of about ± 0.3 pixel in the instantaneous value for each sampling. Furthermore, the displacement calculation result is 1
By averaging about 000 times, the error could be reduced to about ± 0.1 pixel.

In addition, since the present invention can be entirely processed by software and does not require addition or modification of hardware, there is an effect that the resolution and accuracy can be easily improved.

According to the invention of claim 2, in the invention of claim 1, the error function is obtained by the shortest distance method. There is an effect that the error function can be obtained by a simple calculation.

According to the invention of claim 3, in the invention of claim 2, the operation of the shortest distance method is performed by adding the absolute value of the difference between the image data or the error function. Since the calculation can be performed only by addition and subtraction, there is an effect that the calculation can be performed at high speed.

According to the invention described in claim 4, in the invention described in claim 2, the operation of the shortest distance method is performed by adding the square of the difference between the image data or the error function. Since the sum of products can be obtained, there is an effect that it can be easily calculated.

According to the invention of claim 5, in the invention of claim 1, the error function is obtained by a cross-correlation function. There is an effect that a general-purpose means can be used.

According to the invention of claim 6, in the invention of claims 1 to 5, the resolution of the error function is increased by linear interpolation. This has the effects of simplifying the calculation and increasing the resolution by increasing the number of divisions.

According to the seventh aspect of the present invention, the reference image storage unit 12 in which the reference image is stored, the measurement image storage unit 13 in which the measurement image of the measurement object 3 is stored, and the reference image storage unit 12 are stored. And a signal processing unit 9 that performs an arithmetic process using the image data stored in the measurement image storage unit 13. The signal processing unit 9 uses the image data stored in the reference image storage unit 12 as a first An error function is obtained, a second error function is obtained from the image data stored in the reference image storage unit 12 and the measurement image storage unit 13, and at least one of the first and second error functions is interpolated to obtain a high error function. The resolution is increased, and the third error function is calculated from these error functions,
The deviation amount between the reference image and the measurement image is obtained from the third error function, and the displacement of the measuring object 3 is calculated from the deviation amount.

Conventionally, since the resolution was only one pixel, an error of at least ± 0.5 pixel occurred. For example, 10
± 0.05% when using a sensor with 24 pixels
Was limited in resolution and accuracy.

On the other hand, in the present invention, a resolution of 0.1 pixel unit can be achieved, so that there is an effect that the resolution and accuracy of displacement measurement can be improved by one digit. If the number of divisions of the interpolation calculation is increased, the resolution and accuracy can be further improved.

When displacement measurement was actually performed using the present invention, it was possible to measure with an error of about ± 0.3 pixel in the instantaneous value for each sampling. Furthermore, the displacement calculation result is 1
By averaging about 000 times, the error could be reduced to about ± 0.1 pixel.

Further, the present invention can be entirely processed by software and does not require addition or modification of hardware, so that the resolution and accuracy can be easily improved.

According to the invention described in claim 8, in the invention described in claim 7, the signal processing section 9 obtains the error function based on the shortest distance method. There is an effect that the error function can be obtained by a simple calculation.

According to a ninth aspect of the invention, in the eighth aspect of the invention, the calculation by the shortest distance method is performed by adding the absolute value of the difference between the image data or the error function. Since it can be calculated only by addition and subtraction,
There is an effect that it can be calculated at high speed.

According to the invention of claim 10, claim 8 is provided.
In the described invention, the shortest distance method is calculated by adding the square of the difference between the image data or the error function. Since the sum of products can be obtained, there is an effect that it can be easily calculated.

According to the invention of claim 11, claim 7 is provided.
In the described invention, the error function is obtained based on the cross-correlation function. There is an effect that a general-purpose means can be used.

According to the invention of claim 12, claim 7 is provided.
In the invention according to claim 11, the resolution of the error function is increased by linear interpolation. This has the effects of simplifying the calculation and increasing the resolution by increasing the number of divisions.

[Brief description of drawings]

FIG. 1 is a flowchart showing an embodiment of the present invention.

FIG. 2 is a characteristic diagram for explaining the operation of the embodiment of the present invention.

FIG. 3 is a characteristic diagram for explaining the operation of the embodiment of the present invention.

FIG. 4 is a configuration diagram of a signal processing unit.

FIG. 5 is a configuration diagram of a displacement measuring device.

FIG. 6 is a characteristic diagram for explaining the operation of a conventional displacement measuring device.

[Explanation of symbols]

1 standard image 12 Reference image storage unit 13 Measurement image storage 2 Similar parts to the reference image in the measurement image 3 Object to be measured 6 Image sensor section 9,90 Signal processing unit 901, 902, 904 Error function calculator 903 Interpolation calculation unit 905 Deviation amount calculator 906 Displacement amount calculation unit

Claims (12)

[Claims] 1. Displacement measurement for obtaining an error function between a measurement image of a measuring object and a reference image, calculating a deviation amount between the measurement image and the reference image from the error function, and calculating a displacement amount from the deviation amount. In the method, a first error function is obtained from the image data of the reference image, a second error function is obtained from the image data of the measurement image and the reference image, and at least one of the first and second error functions is obtained. The resolution of the error function is increased by interpolation calculation, and the third function is obtained from these error functions.
Is calculated, the shift amount between the reference image and the measurement image is calculated from the third error function, and the displacement of the measurement object is calculated from the shift amount. Displacement measurement method. 2. The displacement measuring method according to claim 1, wherein the error function is obtained by a shortest distance method. 3. The displacement measuring method according to claim 2, wherein the calculation by the shortest distance method is performed by adding the absolute values of the differences between the image data or the error function. 4. The displacement measuring method according to claim 2, wherein the calculation by the shortest distance method is performed by adding the square of the difference between the image data or the error function. 5. The displacement measuring method according to claim 1, wherein the error function is obtained by a cross-correlation function. 6. The displacement measuring method according to claim 1, wherein the resolution of the error function is increased by linear interpolation. 7. A reference image storage unit for storing a reference image,
A measurement image storage unit that stores a measurement image of the measurement object;
It has a signal processing unit that performs arithmetic processing using the image data stored in the reference image storage unit and the measurement image storage unit,
The signal processing unit obtains a first error function from the image data stored in the reference image storage unit, and a second error function from the image data stored in the reference image storage unit and the measurement image storage unit. Is calculated, and at least one of the first and second error functions is increased in resolution by interpolation calculation, and a third error function is calculated from these error functions,
A displacement measuring apparatus, wherein a displacement amount between the reference image and the measurement image is obtained from the third error function, and the displacement of the measurement object is calculated from the displacement amount. 8. The displacement measuring device according to claim 7, wherein the signal processing unit obtains the error function based on a shortest distance method. 9. The displacement measuring device according to claim 8, wherein the calculation by the shortest distance method is performed by adding the absolute values of the differences between the image data or the error function. 10. The displacement measuring device according to claim 8, wherein the shortest distance method is calculated by adding the square of the difference between the image data or the error function. 11. The displacement measuring device according to claim 7, wherein the error function is obtained based on a cross-correlation function. 12. The displacement measuring device according to claim 7, wherein the resolution of the error function is increased by linear interpolation.