JP2657977B2 - High-precision motion measurement method of object using spatial frequency - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION (1) Description of the technical field to which the invention pertains The present invention relates to all kinds of objects (general macro objects / materials indoors, on the ground / at sea, in the air / space, and micro objects such as those handled by a microscope). This is related to the measurement of the motion (velocity and rotational speed) of an object by electromagnetic waves centered on the light region.

(2) Description of the Related Art Conventionally, as a method of measuring the speed of an object, a method using the “Doppler effect” is generally used.
That is, when an electromagnetic wave is transmitted or reflected from a moving object, a frequency displacement proportional to the speed (correctly, a component in the line of sight of the speed) occurs, and the speed is obtained from the frequency displacement of the received electromagnetic wave. Is the way. The method using the Doppler effect has been put to practical use as a Doppler radar which is the most effective means especially in a frequency band in the electromagnetic region. Recently, an optical Doppler radar using a coherent laser beam has been researched and developed because it is effective for a minute object such as a particle.

The Doppler radar of such an already completed technology is not perfect for measuring velocity, but only the component of the finger direction (the method of connecting the object and the observer) is determined by the physical principle. Has one imperfection determined from

In addition, the Doppler radar is a so-called active remote sensing system, which has a limit on the distance due to the transmission power.In general, the size of the device is large, and it is effective when targeting aircraft, ships, and the like. It is not suitable for simple measurement or as a measuring device for micro objects.
In addition, there is a drawback that it cannot be used for an object that is not allowed to be irradiated with electromagnetic waves. There is also a method of obtaining a speed by analyzing (correlating) an image such as a photograph. However, it is difficult to perform analysis in real time and cannot measure high-speed motion. It is not used as an effective method.

On the other hand, unlike the method using the Doppler effect, there is a method using a spatial frequency as a method for measuring the velocity in a direction perpendicular to the line of sight. Conventionally, a rectangular wave grating has been used as a means for generating a spatial frequency. However, as will be apparent from the description of the principle described later, the maximum efficiency has not been obtained.

(3) Object of the Invention The object of the present invention is to measure the motion of an object by a new means, and it is possible to determine the component perpendicular to the finger line direction of the velocity that cannot be obtained by the technique using the Doppler effect with higher accuracy than the conventional method It is what makes it possible to ask for.

Focusing on the time change of the detected light intensity when one spatial frequency (periodic pattern) is used, it has been clarified that "the time frequency is proportional to the product of the spatial frequency of the periodic pattern used and the speed of the object." In addition to the principle, "amplitude corresponds to one spatial frequency component (of the periodic pattern used) of the Fourier transform of the spatial intensity distribution of the object"
Based on the discovery of a new fundamental fact, the feature of the present invention is to use a new idea that using a sine wave periodic pattern can obtain a larger amplitude than using a conventional square wave periodic pattern. is there.

(4) Description of the Principle of the Invention FIG. 1 is a description of the physical principle of the present invention, wherein 1 is a spatial distribution of an object, and 2 is a periodic pattern created in space. For simplicity, we will consider one dimension. The spatial distribution of the object in the x direction is F (x), and the periodic pattern is ｛a ₀ + Re [a exp (i
2πux)]｝. Here, a ₀ is the average level, a is the amplitude, and Re is the real part. u is the spatial frequency and is defined as the reciprocal of the wavelength λ of the pattern (or the spatial period of the pattern).

The coordinate system fixed to the object is x, and the coordinate system fixed to the periodic pattern (and thus fixed to the observer) is x '. Assuming now that the object is moving at a velocity v in the x direction with respect to the periodic pattern, x = x′−vt (2) In order to simplify the calculation, formulas will be treated as complex numbers below. The intensity I of the detected electromagnetic wave is the product of the spatial distribution of the object and the periodic pattern (details will be described in the section of the operation of the invention), but when the object is moving, I changes with time, If the time-varying component is I (t), it can be expressed as follows in a coordinate system x ′ fixed to the observer (however, a DC component that does not vary with time will be described later).

I (t) = aF (x′−vt) exp (i2πux ′) dx ′ (3) By substituting equation (2) into equation (3), I (t) = aF (x) exp） i2πu (x + vt )｝ Dx (4) is obtained. By transforming equation (4), I (t) = a [F (x) exp (i2πux) dx] exp (i2πuv
t) = aG (u) exp (i2πft) (5) where G (u) = F (x) exp (i2πux) dx (6) f = uv (7) G (u) is exactly the value of F (x) Note that it is a Fourier transform.

Looking at equation (5), the detection intensity I (t) is expressed as “the amplitude is F
In the product of the u component of the Fourier transform of (x) and a constant a (where a and 1 correspond to the Fourier component), the temporal frequency f is the product of the spatial frequency u and the velocity v of the object. It can be seen that it fluctuates with time. Now, the time frequency f 'when the wave of wavelength λ advances at the speed v is Is represented by (1), (7) and (8), f = f '(9) (9) In the equation (9), the time frequency of the fluctuation of I (t) is such that the periodic pattern of FIG. It shows that it is completely equal to the time frequency sometimes observed.

As an example, consider F (x) in the extreme case. F
When a small object such that (x) is close to a point, F (x) can be represented by a delta function, and F (x) = δ (x) (10), but the Fourier transform of the delta function is 1 Therefore, the expression (6) is given by G (u) = δ (x) exp (i2πux) dx = 1 (11) Conversely, when F (x) is completely uniform, F (x) is represented by a constant. If the uniform distribution is F (x) = b (12), the Fourier transform of a constant value is a delta function Equation (6) gives G (u) = bexp (i2πux) dx = bδ (u) = 0 (∵u ≠ 0) (13) By substituting equation (11) into equation (5), I (t) = exp (i2πft) (14) On the other hand, substituting equation (13) into equation (5), I (t) = 0 (15) (14) Equations (15) and (15) indicate that the amplitude is a for a point-like object.
This indicates that an AC signal having a frequency f is detected (equal to the amplitude of the periodic pattern), whereas an AC signal is not detected for a uniform object (the speed is indefinite).

For a general object, u of the Fourier transform of F (x)
Although the component G (u) is smaller than 1 (therefore, the amplitude is smaller than a), unless the spatial frequency u uses an extremely large periodic pattern, G (u) except for a special case.
Since (u) does not become 0, an AC signal of frequency f is always observed, and the speed v becomes Is obtained as

Since the length of the periodic pattern cannot be made infinite but becomes finite (p), F (x) is defined in the p region. Therefore, when an object larger than the area p of the periodic pattern is moving, F (x) changes with time, so G (u) in the equation (5) also changes. That is, the amplitude of the observed AC signal changes with time. However, the frequency does not change as long as the speed does not change, and the frequency can be measured accurately, so that the speed can be determined with high accuracy from equation (16).

Until now, we have assumed a sine wave function as a periodic pattern. However, it is not always necessary to use a sine wave. But it turns out to be good. That is, it is sufficient that the component of the spatial frequency u is included (as a main component). The general periodic pattern includes the nth harmonic component instead of a exp (i2πux) It is represented by (17) Equation (4) and substituting into (5), the AC component of the detected light intensity as a result of I (t) is, a _n ex
p Each component I _n (t) appears respect of (iπnux), The _{I n (t) = F (} x) a n exp (i2πnux + i2πnuvt) dx = a n G (nu) exp (i2πnft) (19). Here, G (nu) is nu of the Fourier transform of F (x).
Component. Equations (18) and (19) indicate that the detected light intensity is superimposed with the fundamental component (n = 1) of the time frequency f and its higher harmonic component. This means that when a periodic pattern such as a rectangular wave is used, the light intensity is dispersed into harmonic components, and the efficiency is lower than in the case of a sine wave periodic pattern in which only the fundamental wave component appears. The velocity can be obtained based on the fundamental frequency f. The condition a ₁ ≫a ₂ , a ₃ ,... ( ₁ ) that the fundamental wave component of the spatial frequency u is included as a main component in the periodic pattern as described above. If (20) is satisfied, then | I ₁ (t) | ≫ | I ₂ (t) |, | I ₃ (t) |,... From equation (19), and the frequency spectrum is also a fundamental wave of time frequency f. Becomes sufficiently larger than the other harmonic components, so that it becomes easier to obtain.

In other words, in the rectangular wave period pattern used in the conventional spatial frequency form velocity measurement, the light intensity is dispersed into harmonic components, but a sine wave period pattern in which only the fundamental wave component appears in the detected light intensity signal is used. In such a case, a high S / N ratio can be obtained by increasing the light detection efficiency.
Can be obtained with high accuracy. This gives f / u
Is obtained with higher accuracy when the sine wave periodic pattern is used than when the rectangular wave periodic pattern is used.

Now, assuming that the intensity of the DC signal component remaining until now is I ₀ , I ₀ is obtained by substituting a ₀ into equation (4) instead of a exp (i2πux), and I ₀ = a ₀ F (x) dx (21). Since the signal intensity I is the sum of the DC component and the AC component, I = I ₀ + I (t) (22) However, the DC component I ₀ is so appears regardless motion of the object, not useful for the measurement of speed.

(5) Description of Configuration and Operation of the Invention FIGS. 2 and 3 show an embodiment of the present invention using active means and passive means, respectively. In FIG. 2, 1 is a transmitting antenna (optical system such as a lens and a telescope in the case of light), 2 is a periodic pattern mask, and 3 is a transmitting (irradiating) electromagnetic wave. In FIG. 3, 1 is a receiving (receiving) electromagnetic wave, 2 is a receiving antenna (in the case of light, a lens, an optical system such as a telescope), 3 is a transmission periodic grating,
4 is a detector.

In the case of implementation by active means, a mask 2 having a fixed periodic pattern is placed in front of the antenna 1 (or the antenna may be an array type) as shown in FIG. Is spatially modulated and emitted with a periodic pattern. Then, an equivalent periodic pattern is generated in the object space. In particular, in the case of light, the divergence angle of the three electromagnetic wave beams can be freely changed, and in the case of a short distance, the same pattern as the mask can be easily formed in the object space using a laser beam. . However, it should be noted that, at a distance equivalent to infinity, the pattern becomes a Fraunhofer diffraction pattern (which becomes a Fourier transform of the mask pattern), and the pattern changes considerably. In any case, a periodic pattern having one spatial frequency (referred to as u) can be formed in the object space. If the reflected light of the electromagnetic wave having a spatial pattern from the moving object is detected, an AC signal having a time frequency f appears. Therefore, the speed is obtained from f (measured by a spectrum analyzer or the like) according to the principle described above. In this case, the reflectance distribution may be used as the spatial distribution F (x) of the object, and the electromagnetic wave intensity pattern may be used as the periodic pattern. Second
Instead of using a periodic pattern mask as shown in the figure, a periodic pattern can also be created by interference of two coherent beams.

In the case of implementation by passive means, an electromagnetic wave radiated from an object, that is, reflection of sunlight or radiation emitted by the object itself is used. First, as shown in FIG. Light is collected at 2. A periodic pattern is detected in 4 through a transmission periodic grating 3 placed on a focal plane (correctly, an image forming plane; the focal point changes depending on the distance to the object). Since it is physically equivalent to making the object, the motion of the object can be measured in the same manner according to the principle described above.
However, the distribution of the radiation intensity may be used as the spatial distribution F (x) of the object, and the transmittance pattern of the grating may be used as the periodic pattern. A sine-wave grating is optimal as the transmission periodic grating, but a rectangular-wave slit grating is the optimal alternative. Instead of using the transmission synchronization grating, it is equivalent that the detector itself has the same array type as the periodic pattern.

When there is no radiation from the object, the active means described in the above, or alternatively, a uniform (spatially and temporally uniform) artificial light is used, and the means in the above may be used. it can.

Assuming that the distance to the object is R, the spatial frequency u is R
Is defined as the number per unit distance (eg, cycle / cm) when R is finite, and defined per unit viewing angle (eg, cycle / rad) when R is equivalent to infinity. In each case, u in the actual object space can be easily calculated geometrically. The speed determined as v = f / u is determined in units of, for example, cm / sec and rad / sec according to each case.

Since the movement of the object and the movement of the observer are equivalent, the movement of the observer can be measured by using a stationary object. When they are moving with each other, the relative speed is obtained.

As mentioned above (explanation of principle), when the object is uniform,
No AC signal appears. Therefore, the time frequency f does not appear as a spectrum. To take advantage of this, multiple u
Or the like, the shape of the target object can also be estimated. The magnitude can be estimated from the duration of the signal. These are particularly effective for ultra-high-speed objects and substances that cannot be imaged.

In general, the larger the value of u, the higher the speed measurement accuracy, but the smaller the signal strength (the smaller G (u)). Therefore, an appropriate u should be selected according to each case.

Using one periodic pattern, the axis method (defined in the direction that follows the pattern and perpendicular to the optical axis or line of sight)
Can be obtained. This velocity component has been treated as velocity v in one dimension. this
v ₁ and redefined, if the angle of the axial movement direction and the periodic pattern of the object in three-dimensional space and theta, velocity v of the object is _{v = v 1 / cosθ (23} ). In contrast to the Doppler radar, the smaller θ is, the higher the accuracy is obtained (observing the motion of the object from the lateral direction).

(6) Description of Effect As described above, the use of the electromagnetic wave measurement system according to the present invention enables highly accurate measurement of the movement of the target object in the direction perpendicular to the line of sight. Both active and passive means can be implemented. Furthermore, while the velocity measurement using the Doppler effect measures the component in the direction of the line of sight, the present method measures a component perpendicular to the direction of the line of sight, so that it can play a complementary role.

The present invention is applicable to a wide range of applications, such as measurement of the motion of macro objects and materials in laboratories and factories (both translation and rotation are possible), measurement of the motion of micro materials in rooms, ground / sea, air / space It can be used to measure the movement of objects and substances. In particular, the passive means according to the present invention has a great effect on the measurement of the motion of a special object in which the radar as the conventional active means cannot be used or the active electromagnetic wave irradiation is not allowed. The motion measurement can be performed by observing an object from the outside, or conversely, by mounting the present system on a moving object and observing a stationary object (for example, the ground surface). Another feature is that the shape can be estimated in addition to the motion measurement.

The present invention can be applied to a wide electromagnetic wave region centered on a light region.

[Brief description of the drawings]

FIG. 1 is an explanatory view of the principle of the present invention, and FIGS. 2 and 3 are conceptual diagrams of an embodiment of the present invention using active and passive means. FIG. 1 shows the spatial distribution of an object 1... 2... A periodic pattern (formed in an object space or an image space corresponding to an active means and a passive means, respectively). In FIG. 2, reference numeral 1 denotes a transmitting antenna (in the case of light, an optical system such as a lens or a telescope); 2... A periodic pattern mask; 3. As shown in FIG. 3, 1... Incident electromagnetic wave, 2... Receiving antenna (in the case of light, a lens, an optical system such as a telescope), 3.
The transmission periodic grating, 4... Are electromagnetic wave detectors (electron tubes or semiconductors).

Claims (2)

(57) [Claims] An electromagnetic wave beam having an in-beam intensity having a sine wave periodic pattern is radiated into a measurement target space to create a sine wave periodic pattern in the measurement target space, and reflected electromagnetic waves from the measurement target in the measurement target space. To detect
A high-precision object motion measurement method using a spatial frequency, wherein a motion of a measurement object is measured from a frequency of a time change of the intensity of the reflected electromagnetic wave. 2. A sine wave transmission periodic grid is arranged near a focal plane of an electromagnetic wave detection system that detects an electromagnetic wave passing through a measurement target space, so that a sine wave periodic pattern passing through the transmission periodic grid can be obtained. Detects electromagnetic waves from an object passing through the object space, and measures the motion of the object to be measured from the frequency of the time change of the electromagnetic wave intensity of the electromagnetic waves. Exercise measurement method.