JP2015033473A - Convergent ultrasonic wave forming method by frequency modulation - Google Patents

Abstract

PROBLEM TO BE SOLVED: To realize setting of a focus at a close-range arbitrary position and realize ultrasonic wave measurement with higher azimuth resolution with a simple device configuration without using any acoustic lens at all in order to solve the problems of an enlarged device scale due to necessity of an acoustic lens for improving the close-range azimuth resolution and a difficulty in changing a focal distance.SOLUTION: An irradiation direction and a focal distance of a concave convergent wavefront to be formed are electronically controlled by using an FM signal to drive one-dimensionally-arrayed oscillators and then controlling a shape of the FM signal.

Description

  The present invention relates to an ultrasonic wave transmission system with high spatial resolution.

  Various configurations for visualizing spatial three-dimensional information using ultrasound are known. Among them, as an example of the most effective method, a signal having a constant frequency is applied to a polarization inversion type array transmitter (see Patent Document 1) whose polarization axis is inverted, and the irradiation direction is changed by changing the signal frequency. By doing so, there is a configuration in which information of the three-dimensional space is collected by sweeping and irradiating the three-dimensional space with an ultrasonic signal and receiving a reflection signal from the object (see Patent Document 2).

However, if the number of array elements is increased and the total length of the array is increased to narrow the main beam width, the near field distance (D ² / λ, D: aperture, λ: wavelength) increases rapidly, and the near field sound In the field, since the resolution is about the aperture, the azimuth resolution is lowered.

  For this reason, a cylindrical acoustic lens is usually used to improve the azimuth resolution near the observation target distance.

JP 47-26160 A Japanese Patent Publication No. 51-44773 Japanese Patent Laid-Open No. 5-281212

  In the conventional configuration, since an acoustic lens is used to improve the resolution that decreases in the near field, the apparatus becomes large-scale and has a problem that it is difficult to change the focal length.

  Therefore, in the present invention, the transducers of the array transmitter are driven in common by the FM signal, so that the transmitted acoustic beam can be converged electronically, and the focal length that is the distance to the convergence point can also be changed electronically. And

  The present invention has the advantage of improving the resolution at any location in the near field without using an acoustic lens.

  In the ultrasonic apparatus, the best mode is realized by adopting a configuration in which the polarization inversion type array transmitter is driven in common by the FM signal.

  The simplest configuration method of a transmitter for transmitting ultrasonic waves having different frequencies for each direction is shown in FIG. 1 by alternately inverting the polarization axis 2 of the piezoelectric element 1 as shown in FIG. In addition, the polarization inversion type array transmitter has a common electrode composed of the ground electrode 3 and the hot electrode 4 formed on both sides thereof.

  When a burst wave drive signal 5 is applied between the electrodes 3 and 4, the direction θ differs depending on the signal frequency (θ is the normal direction of the ultrasonic wave emitting surface, that is, the transducer array surface, and the ultrasonic wave emitting direction. The ultrasonic beam 6 can be emitted at an angle of

  Here, when the burst wave drive signal 5 is applied between the electrodes 3 and 4, a wavefront shown in the arc of FIG. 2a) b) is formed.

  Here, since the polarization axes are alternately inverted, the phases of adjacent wavefronts at the same time are inverted (indicating that the phase is 180 degrees different between the solid line and the broken line).

  Thus, since the phase of the wave front is reversed, the radiated sound wave is canceled in the normal direction, and the ultrasonic beam is emitted only in the direction 6 inclined with respect to the normal direction of the ultrasonic wave emission surface. It becomes.

  In FIG. 2, when the frequency is high, the wavelength is short, so as shown in FIG. 2a), in the direction near the front, while when the frequency is low, the wavelength is long, so as shown in FIG. 2b) A wavefront is formed in a more inclined direction.

  This radiation angle θ is given by Equation 1 as the vibrator pitch d, drive frequency f, and wavelength λ thereof.

(Equation 1)
θ = sin ⁻¹ (λ / (2d))

  Further, the long-distance sound field directivity characteristic R (θ) at this time is given by Equation 2.

(Equation 2)
R (θ) = sin (0.5n (φ−γ)) / sin (0.5 (φ−γ))
φ = π, γ = 2πdsin (θ) / λ

In this configuration, the ultrasonic beam is scanned using these relationships, and the ultrasonic beam can be sector-scanned by frequency sweeping with one signal line.

The outline of electron convergence by driving this polarization inversion type array transmitter with the FM signal will be described below.

When the polarization inversion type array transmitter is driven by a sine wave having a constant frequency, the plane wave shown in FIG.

Here, when the polarization inversion type array transmitter is driven by a signal whose wavelength (or frequency) changes with time, as shown in FIG. 3b), the wavefront formed is curved and a concave wavefront can be transmitted. It becomes.

  The relationship between the focus forming operation and the drive waveform of the concave wavefront formed in this way is analyzed with reference to FIG.

The distance D _n from the n-th element to the point P is _expressed by Equation 3 _where ε is the interval between the array elements, the direction from the first element is θ, and the point where the distance is R is P.

(Equation 3)
D _n = [(Rcosθ) ² + {Rsinθ + (n-1) ε} ² ] ^1/2
= [R ² + {(n-1) ε} ² + 2R (n-1) εsinθ] ^1/2
= R [1 + {(n-1) ε / R} ² +2 (n-1) εsinθ / R] ^1/2

  Hereinafter, the relationship between the drive signal wavelength, the irradiation direction θ, and the focal length R will be described using mathematical formulas.

Here, the m-th half-wavelength value of the drive waveform whose wavelength changes with time, which is applied to the domain-inverted array resonator, is λ ^h _m .

If this half-wavelength value λ ^h _m satisfies the relationship of Equation 4, the sound waves from each element are all in phase on the circumference L _{R of} radius R centered on point P.

(Equation 4)
_N-1
D _n -Σ λ ^h _m = R ・ ・ ・ ・ (Constant)
^{m = N-n + 1}

Accordingly, the concave wavefront formed on the circumference L _R propagates through the medium and converges to the point P.

  Here, N is the total number of array elements.

From this relationship, the half-wavelength value λ ^h _m is given as Equation 5.

(Equation 5)
_N-1
Σλ ^h _m = D _n -R ・ ・ ・ ・ (n: 1, ---, N)
^{m = N-n + 1}

  Here, Equation 6 is obtained by setting n to n + 1.

(Equation 6)
_N-1
Σλ ^h _m = D _{n + 1} -R ・ ・ ・ ・ (n: 0, ---, N-1)
^{m = Nn}

By calculating the difference between the two, the half-wavelength value λ ^h _m is given by Equation 7.

(Equation 7)
λ ^h _Nn = D _{n + 1} -D _n・ ・ ・ ・ (n: 1, ---, N-1)

  Here, Expression 8 is obtained by expressing as k = N−n.

(Equation 8)
λ ^h _k = D _{N-k + 1} -D _Nk
= R [1 + {(Nk) ε / R} ² +2 (Nk) εsinθ / R] ^1/2
-R [1 + {(Nk-1) ε / R} ² +2 (Nk-1) εsinθ / R] ^1/2・ ・ ・ ・ (k: 1, ---, N-1)

Here, a specific example of λ ^h _k will be described in the case of convergence at a long distance with a relatively long focal length.

Here, _assuming that the focal length is relatively long, focusing on only the first term of the macrolin expansion, D _n is given by Equation 9.

(Equation 9)
D _n ≒ R + {(n-1) ε} ² / (2R) + (n-1) εsinθ

  Therefore, for n + 1, Equation 10 is obtained.

(Equation 10)
D _{n + 1} ≒ R + (nε) ² / (2R) + nεsinθ

From the difference between the two, the half-wavelength value λ ^h _m is given by Equation 11.

(Equation 11)
λ ^h _Nn = D _{n + 1} -D _n ≒ (2n-1) ε ² / (2R) + εsinθ ・ ・ ・ (n: 1, ---, N-1)

Here, when Nn is expressed as k, the half-wavelength value λ ^h _m is expressed by Equation 12 from Nn = k.

(Equation 12)
λ ^h _k = D _{N-k + 1} -D _Nk ≒ {2 (Nk) -1} ε ² / (2R) + εsinθ
= (N-1 / 2) ε ² / R + εsinθ-kε ² / R ・ ・ ・ ・ ・ ・ (k: 1, ---, N-1)

From this relationship, in the case of convergence at a relatively long distance, the half-wavelength value λ ^h _k of the drive signal has a waveform that is sequentially shortened by a certain amount (ε ² / R) according to the value of k.

In the case of convergence to a relatively long distance, the half-wave value λ ^h of the drive signal for converging to a point of distance R in the θ direction
_m is given by Equation 12, and has a waveform that is sequentially shortened by a certain amount (ε ² / R) according to k.

As described above, the waveform in which the half wavelength value λ ^h _k of the drive signal is sequentially shortened by a certain amount (ε ² / R) according to the value of _k is a characteristic of a linear FM wave whose frequency increases linearly. Therefore, a configuration in which the drive signal is a linear FM wave is assumed.

  Hereinafter, the relationship between the shape of the linear FM wave, the irradiation angle θ of the formed beam, and the focal length R will be analyzed.

An initial angular frequency ω ₀ , a phase angle ψ (t), an angular frequency ω (t), and a linear FM wave y (t) having a frequency increase rate 2α is expressed by Equation 13.

(Equation 13)
y (t) = sinψ (t)
dψ (t) / dt = ω (t) = 2πf (t)
ω (t) = ω ₀ + 2αt

From this relationship, the phase angle ψ (t) is expressed by Equation 14.

(Equation 14)
_t
ψ (t) = ∫ω (t) dt = ω ₀ t + αt ^2
0

Here, at time t ^h _n as a half wavelength to the n-th phase angle [psi (t) from becoming a n?, The time t ^h _n as a half-wavelength is related several 14 number 15.

(Equation 15)
ω ₀ t ^h _n + αt ^h _n ² = nπ

By obtaining the root of the quadratic equation, the time t ^h _{n at} which the half wavelength is reached is obtained as in Expression 16.

(Equation 16)
t ^h _n = {(ω ₀ ² + 4αnπ) ^1/2 -ω ₀ } / (2α) = {ω ₀ (1 + 4αnπ / ω ₀ ² ) ^1/2 -ω ₀ } / (2α)

By expanding this relationship to Macrolin's expansion, the time t ^h _{n at} which the half wavelength is reached is given by Equation 17.

(Equation 17)
t ^h _n = [ω ₀ {1 + 2αnπ / ω ₀ ² -2 (αnπ / ω ₀ ² ) ² + ---}-ω ₀ ] / (2α)
= {2αnπ / ω ₀ -2 (αnπ) ² / ω ₀ ³ + ---} / (2α)
= nπ / ω ₀ -α (nπ) ² / ω ₀ ³ + ---

Here, _assuming that α is relatively small and omitting the higher-order term of α, the time t ^h _{n at} which the half wavelength is reached is _expressed by Equation 18.

(Equation 18)
t ^h _n ≒ nπ / ω ₀ -α (nπ) ² / ω ₀ ³

  When this relationship is expressed with respect to n + 1, Equation 19 is obtained.

(Equation 19)
t ^h _{n + 1} ≒ (n + 1) π / ω ₀ -α (n + 1) ² π ² / ω ₀ ³

Due to the difference between Equation 18 and Equation 19, the half period τ ^h _n of the linear FM wave y (t) becomes Equation 20.

(Equation 20)
τ ^h _n = t ^h _{n + 1} -t ^h _n = π / ω ₀ -α (n + 1) ² π ² / ω ₀ ³ + αn ² π ² / ω ₀ ³
= π / ω ₀ -2αnπ ² / ω ₀ ³ -απ ² / ω ₀ ³
= (π / ω ₀ ) (1-απ / ω ₀ ² ) -2αnπ ² / ω ₀ ³

Therefore. The half wavelength λ _L ^h _n of the linear FM wave y (t) is given by Equation 21 with the sound speed as c.

(Equation 21)
λ _L ^h _n = cτ ^h _n = (cπ / ω ₀ ) (1-απ / ω ₀ ² ) -2cαnπ ² / ω ₀ ³

On the other hand, the half wavelength value λ ^h of the drive signal for convergence to the point of the distance R in the θ direction
_m is Equation 12, and when this is shown again, Equation 22 is obtained.

(Equation 22)
λ ^h _k = (N-1 / 2) ε ² / R + εsinθ-kε ² / R

  By comparing these equations 21 and 22, equation 23 is obtained as the first relationship.

(Equation 23)
2cαπ ² / ω ₀ ³ = ε ² / R

  Similarly, Expression 24 is obtained as the second relationship.

(Equation 24)
(cπ / ω ₀ ) (1-απ / ω ₀ ² ) = (N-1 / 2) ε ² / R + εsinθ
cπ / ω ₀ -cαπ ² / ω ₀ ³ = (N-1 / 2) ε ² / R + εsinθ

  From these equations 23 and 4, when α is deleted, equation 25 is obtained.

(Equation 25)
cπ / ω ₀ -ε ² / (2R)) = (N-1 / 2) ε ² / R + εsinθ
cπ / (εω ₀ ) -ε / (2R)) = (N-1 / 2) ε / R + sinθ
cπ / (εω ₀ ) = ε / (2R)) + (N-1 / 2) ε / R + sinθ
cπ / (εω ₀ ) = Nε / R + sinθ
cπ / ω ₀ = Nε ² / R + εsinθ
ω ₀ = cπ / (Nε ² / R + εsinθ) ・ ・ ・ ・ ・ ・ ・ ・ [rad / s]

Equation 25 defines the relationship between the initial angular frequency ω ₀ of the linear FM wave, the irradiation direction θ, and the focal length R.

  In Equation 25, c: sound velocity, N: total number of array elements, and ε: array element spacing are known.

When this relationship is expressed with respect to the initial frequency f ₀ of the linear FM wave, Expression 26 is obtained from f ₀ = ω ₀ / (2π).

(Equation 26)
f ₀ = ω ₀ / (2π) = c / {Nε ² / (2R) + (ε / 2) sinθ} ・ ・ ・ [s ^-1 ]

Further, when expressed with respect to the initial wavelength λ ₀ of the linear FM wave, Equation 27 is obtained from λ ₀ = c / f ₀ .

(Equation 27)
λ ₀ = c / f ₀ = Nε ² / (2R) + (ε / 2) sinθ ・ ・ ・ [m]

  On the other hand, the frequency increase rate α is given by Equation 23, which is again shown by Equation 28.

(Equation 28)
α = ω ₀ ³ ε ² / (2cRπ ² ) ・ ・ ・ ・ [rad / s ² ]

Thus, Equations 25 and 28 represent the known variables (c, N, ε), the target irradiation direction θ and focal length R, and the linear FM wave initial angular frequency ω ₀ and frequency increase rate α. Give relationships explicitly.

Therefore, it is possible to determine the initial angular frequency ω ₀ and the frequency increase rate (half) α of the linear FM wave that realize the desired irradiation direction θ and focal length R.

Further, since the irradiation direction θ and the focal length R can be freely selected, the focal length R and the irradiation direction θ can be freely changed by changing the linear FM wave condition ω ₀ (or f ₀ ) and α. It becomes possible to change to.

  In order to realize the spatial resolution of the entire aperture, it is necessary that the signals from all the elements contribute. From the operation principle of FIG. 4, the wave number (half of the number of elements is half) as shown in FIG. In FIG. 5, a long drive signal 7 having 5 cycles) is required, and the length of the ultrasonic signal transmitted in the wavefront forming direction 8 becomes long.

  In the example shown in FIG. 5, the ultrasonic signal length transmitted in the wavefront forming direction becomes 2T with respect to the time length T of the drive signal, and the distance resolution is lowered.

For this reason, since the resolution in the distance direction is lowered, the partial aperture transmission method according to Patent Document 3 is used.

In the configuration example of the partial aperture transmission system shown in FIG. 6, the transmitter is divided (FIG. 6 is divided into 3) to have partial apertures 9, 10, and 11, and the time difference T ′ (= n _s T _0/2 ). By transmitting with the short drive signals 12, 13, and 14 having the above, a short ultrasonic signal is transmitted in the direction of the ultrasonic beam 15, and high distance resolution is realized. Here, the number of elements in the partial aperture is n _s , and the signal period is T ₀ .

According to this configuration example, since a short ultrasonic signal (time length = 2T ′) is transmitted, high distance resolution is realized.

  A partial aperture FM wave drive concave surface converging configuration using an FM wave as a drive signal in the partial aperture transmission system will be described with reference to FIG.

Also in the partial aperture FM wave driven concave convergence configuration example shown in FIG. 7, the transmitter / receiver is divided (FIG. 7 is divided into 3) to have partial apertures 9, 10, and 11 (the number of elements in the partial aperture: n), and the partial aperture Wave transmission is performed by partial FM drive signals 16, 17, and 18 (time length≈T ″) having a wave number (n / 2) that is half the number of inner elements.

By using such an FM drive signal, the ultrasonic beam 19 converges on the concave surface, and the azimuth resolution at a short distance is improved.

  In addition, according to this configuration example, since a short ultrasonic signal (time length≈2T ″) is transmitted, a high distance resolution can be realized at the same time.

  According to the present invention, it is possible to set a focal point at an arbitrary position at a short distance without using any acoustic lens, and it is possible to perform ultrasonic measurement with high azimuth resolution with a simple apparatus configuration.

It is explanatory drawing which showed the structure of the polarization inversion type | mold arrangement | sequence transmitter in this invention apparatus. It is explanatory drawing which showed the principle which sends out the ultrasonic wave from which a frequency differs for every azimuth | direction. It is principle explanatory drawing which forms a concave-converged wave front by the waveform from which a frequency changes. It is explanatory drawing which shows the positional relationship of a transmitter and a focus. It is explanatory drawing which showed the reason that ultrasonic signal length becomes long. It is explanatory drawing which showed the well-known example structure which divides | segments a transducer. It is explanatory drawing which forms a concave-converged wave front with the waveform and partial aperture which a frequency changes.

DESCRIPTION OF SYMBOLS 1 Piezoelectric element 2 Polarization axis 3 Ground electrode 4 Hot electrode 5 Drive signal 6 Ultrasonic beam 7 Long drive signal 8 Wavefront formation direction 9, 10, 11 Partial aperture 12, 13, 14 Short drive signal 15 Ultrasonic beam 16, 17, 18 FM drive signal 19 Ultrasonic beam

If this half-wavelength value λ ^h _m satisfies the relationship of Equation 4, the sound waves from each element are all in phase on the circumference L _{R of} radius R centered on point P. A specific example of a drive waveform that satisfies this relationship is illustrated in Equation 4 as s (t).

(Equation 4)
_N-1
D _n -Σ λ ^h _m = R ・ ・ ・ ・ (Constant)
^{m = N-n + 1}
s (t) = sin [k ₀ {X _T -((R-ct) ² -Y _T ² ) ^1/2) }]
c: speed of sound
k ₀ = π / ε
X _T = Rsinθ + (N-1) ε
Y _T = Rcosθ
0 <t <(RY _T ) / c

(Equation 4)
_N-1
D _n -Σ λ ^h _m = R ・ ・ ・ ・ (Constant)
^{m = N-n + 1}
s (t) = sin [k ₀ {X _T -((R ₀ -ct) ² -Y _T ² ) ^1/2) }]
k ₀ = π / ε
X _T = Rsinθ + (N-1) ε
Y _T = Rcosθ
R ₀ = (X _T ² + Y _T ² ) ^1/2
0 <t <(R ₀ -R ) / c

Claims (4)

In a configuration in which an ultrasonic signal is transmitted by applying a drive signal to an array element having a common electrode, and the ultrasonic irradiation direction is changed by changing the frequency of the drive signal for each transmission, the drive signal An ultrasonic wave transmission device configured to change the period of adjacent waveforms constituting the. An ultrasonic wave transmitting device, wherein the array element having the common electrode according to claim 1 is a polarization inversion type array transmitter. An ultrasonic transducer according to claim 1, wherein the array element having the common electrode according to the first aspect is realized by a plurality of partial apertures. The ultrasonic transmission characterized in that the drive signal described in the first item is a linear FM wave, the initial frequency of the FM wave corresponds to the irradiation direction, and the frequency increase rate corresponds to the focal length. apparatus.

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