Ultrasonic flowmeter

A flowmeter employing an array of ultrasonic wave transducer elements, the flowmeter being arranged in such a way that reception signals of plural reception beams aligned in parallel with one another are formed from detection signals of reflection ultrasonic waves from the transducer elements; the Fourier transformation is performed with respect to a direction of alignment of the reception beams; a moving target indication processing is then performed among a plurality of reception signals derived from the repetitive transmissions; the result of the Fourier transformation is treated as two-dimensional signals of time series corresponding to the transmission of the ultrasonic wave, and with respect to a plurality of straight lines coinciding at respective angles with the origin of a coordinate, signal values on each of the straight lines are treated as a one-dimension sequence of numbers to perform the Fourier transformation; and an axial velocity component and a lateral (transverse) velocity component of a moving object are obtained on the basis of the resulting signal distribution.

BACKGROUND OF THE INVENTION 
The present invention relates to a pulsed ultrasonic flowmeter, i.e., a 
Doppler flowmeter, used in the fields of clinical medicine, underwater 
measurement, and the like, and more particularly to a flowmeter which is 
effective for the measurement of the blood flow in the heart. 
Generally, the method of measuring the velocity of an object based on the 
Doppler shift of the reflected sound wave detects the component of 
velocity in the sound wave beam direction. In contrast, the method 
described in publication: Japanese Journal of Medical Ultrasonics, 40-A-56 
(May 1982), pp. 395-396, calculates vectorial components of velocity from 
measured values based on a plurality of probes by utilization of the 
intersecting angle of beam. 
However, the above-mentioned conventional technique bases the calculation 
on the measured velocities, providing only a mean value of velocity in the 
case of measurement of velocity in distribution, and it is not possible to 
calculate the spatial distribution of the flow direction. 
A method of measuring the velocity at right angle with the ultrasonic beam 
was unveiled in an article entitled "Transverse Doppler Summary" by V. L. 
Newhouse. This method detects a reflected wave from the measurement 
position with a transducer having a wide aperture which covers the 
measurement position in a relatively wide angle, and evaluates the flow 
rate in the transverse direction from the frequency spectrum of the 
detected signal. However, this method can not distinguish the heading of 
flow in the transverse direction, i.e., the polarity of velocity. 
Moreover, expansion of spectrum can be caused also by existence of 
particles staying from main flow, and the accuracy of flow rate is not 
sufficient for the medical use. 
SUMMARY OF THE INVENTION 
Accordingly, an object of the present invention is to provide an ultrasonic 
flowmeter of simple construction which is capable of measuring the 
distribution of the flow rate. 
Another object of the present invention is to provide an ultrasonic 
flowmeter which reveals the accurate magnitude and direction of flow, 
i.e., the heading of flow. 
The present invention is designed in such a way as to process the signals 
from an array of transducer elements, thereby revealing the velocity 
distribution in all directions. 
More specifically, the present invention resides characteristically in an 
ultrasonic flowmeter which comprises an ultrasonic transducer including an 
array of elements, means for driving repeatedly part of the transducer 
elements at a prescribed interval thereby to transmit an ultrasonic wave 
to a target, a parallel reception beam forming device which modifies the 
phases of the signals from the transducer elements to produce inparallel 
reception signals derived from reception beams with different 
directivities, a sampling device which samples the parallel reception 
signals and stores the resulting signals, means for performing moving 
target indication through the differential processing among signals from 
the sampling device having a prescribed duration since transmission, a 
first one-dimension Fourier transform device which performs the Fourier 
transformation with respect to a direction of alignment of reception beams 
for the output of the moving target indication means, and second Fourier 
transform means for performing the Fourier transformation with respect to 
a repetitive transmission direction for the successive outputs of the 
first Fourier transform device, and operates to evaluate the lateral 
velocity and axial velocity of a moving object in the target on the basis 
of the two-dimensional distribution of the outputs of the second Fourier 
transform means. 
Further, the present invention resides characteristically in an ultrasonic 
flowmeter which comprises an ultrasonic transducer including an array of 
transducer elements, means of driving repeatedly part of the transducer 
elements of the ultrasonic transducer at a prescribed interval thereby to 
transmit an ultrasonic wave to a target, a parallel reception beam forming 
device which modifies the phases of the signals from the transducer 
elements of the ultrasonic transducer to produce in parallel reception 
signals drived from reception beams with different directivities, a 
sampling device which samples the parallel reception signals and stores 
therein the resulting signals, moving target indication filter means for 
performing moving target indication through the differential processing 
among signals from the sampling device having a prescribed duration since 
transmission, a first one-dimension Fourier transform device which 
performs the Fourier transformation with respect to a direction of 
alignment of reception beams, a second one-dimension Fourier transform 
device which performs the Fourier transformation in such a way as to treat 
outputs from the first one-dimension Fourier transform device as 
two-dimensional signals of time series corresponding to transmission of 
the ultrasonic wave and to treat, with respect to a plurality of straight 
lines coinciding at respective angles with the origin of a coordinate, 
values of signals on each of the straight lines as a one-dimension 
sequence of numbers thereby to perform the Fourier transformation, a 
coordinate transform device which transforms outputs from the second 
one-dimension Fourier transform device into a lateral velocity and an 
axial velocity of a moving object, whereby the lateral velocity and axial 
velocity of the moving object in the target are evaluated. 
Other features of the present invention will become apparent from the 
following detailed description.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
FIG. 1 is a block diagram showing the arrangement of transducer elements of 
the present invention, where the reference symbol P designates a moving 
object, the reference symbol Q designates an array of transducer elements, 
the reference symbols q.sub.1 through q.sub.N designate the transducer 
elements, and the reference symbol B designates a parallel beam forming 
device for a plurality of reception beams. 
Among the array of transducer elements Q in FIG. 1, all or part of the 
elements transmit ultrasonic waves which focus on the point P at a time 
interval of t.sub.k (k=0, 1, . . . , k). The distance from the array Q to 
the focal point P is L. The ultrasonic waves are reflected on the point P, 
and are received by the elements q.sub.n (n=1, 2, . . . , N) of array Q 
which produces signals a.sub.kn (t). 
The signals a.sub.kn (t) are applied to a parallel beam forming section B. 
FIG. 2 is a view showing a beam pattern of individual reception signals of 
the reception beam parallel forming device B shown in FIG. 1. 
The section B produces simultaneously reception signals b.sub.km (t) (where 
m=1 to M) on the basis of the reception signals a.sub.kn (t) for the 
respective reception ultrasonic beams indicated by B.sub.1, B.sub.2, . . . 
, B.sub.m, . . . , B.sub.M in FIG. 2 having a beam spacing of .epsilon.. 
It is also possible to confine the significant range to .theta.. FIG. 3A 
and FIG. 3B are respectively graphical representations showing the case 
where a reflective object is at rest and the case where it is moving. 
In the description of this specification, by the suffix k, it means each 
time when the ultrasonic wave is repeatedly produced from all or part of 
the array of transducer elements Q at a prescribed interval and the suffix 
k relates to the time base. By the suffix m, it means each of outputs from 
the parallel beam forming device B on the basis of each of the reception 
ultrasonic wave beams B.sub.1, B.sub.2 . . . Bm . . . B.sub.M shown in 
FIG. 2, and the suffix m relates to the direction of arrangement of the 
transducer elements. In the following description, for brevity, the signal 
data line relating to k will be described in the form of the direction of 
the time base, or the k direction. With the signal data line as well 
relating to m, for brevity, it will be described in the form of the 
direction of arrangement of the transducer elements, or the m direction. 
In the case where a reflective object at point P is quiescent, the signal 
b.sub.km (t) appears as a reflection signal produced at the output of 
channel m.sub.p formed in the direction of P as shown in FIG. 3A, and the 
position of output channel is not varied by the number of repetitions of 
transmission. The time length since the transmission to the emergence of 
the reflection signal is the propagation time of the ultrasonic wave, and 
it is 2L/C where C is the velocity of sound. The ultrasonic wave is 
transmitted through the time positions represented by the striping k=0, 
k=1, . . . and the reflected wave emerges in the time position of 2L/C. 
FIG. 4 is a view showing the state in which the reflective object moves in 
parallel to the position of Q. FIG. 5 and FIG. 6 are respectively views 
showing the signal processings for the movement of FIG. 4. 
If the reflective object moves to positions A, B and C at transmission 
times t.sub.0, t.sub.1 and t.sub.3, respectively, as shown in FIG. 4 in 
the direction parallel to Q, the reception signal b.sub.km (t) varies in 
channel of emergence of reflection signals as indicated by m.sub.A, 
m.sub.B and m.sub.C in FIG. 3B. By measuring the amplitude and phase of 
b.sub.km (t) at time points t.sub.e (t.sub.e =2L/C) of emergence of 
reception signals and evaluating them as complex values C.sub.km, these 
values are plotted with respect to the beam positions m as shown in FIG. 
5. That is, in FIG. 5, the complex value corresponding to the reception 
signal is moved successively from the right-hand side position m.sub.A 
towards the left-hand side through the central position m.sub.q. In this 
connection, C.sub.km can be regarded as the function of m, i.e., the 
relationship of C.sub.km =C.sub.k (m) is established. Then, it is assumed 
that the amounts of movement of the lateral direction is .DELTA.m for each 
transmission, the channel is m and the number of transmissions is k. Then, 
if the complex value C.sub.0 (m) when k=0 is used, FIG. 5 reveals the 
following relation. 
EQU C.sub.km =C.sub.0 (m+k.DELTA.m) (1) 
For the amplitude b.sub.km and phase .phi..sub.km of the reception signal 
b.sub.km (te) at time t.sub.e, the C.sub.km is expressed based on FIG. 3B 
as: 
C.sub.km =b.sub.km .multidot.e.sup.j.phi..sbsp.km =b.sub.km 
.multidot.e.sup.j.phi. (2) 
and the movement of the case of FIG. 4 results in the same phase for all 
positions. 
Components indicated by the dashed arrows in FIG. 5 are reflection signals 
from a quiescent object and they do not move. Accordingly, by conducting 
the differential process between adjacent signals in the same channel at 
each repetitive transmission, e.g., between C.sub.1m and C.sub.2m, between 
C.sub.2m and C.sub.3m, and so on, the moving target indication is 
achieved. Namely, the differential process produces an output d.sub.km 
(d.sub.km =C.sub.km -C.sub.(k+l)m) as shown in FIG. 6, and the signals 
created by the quiescent object are removed. 
FIG. 7 and FIG. 8 are respectively views showing a direction of movement 
and a reflection waveform in the case where the reflective object is moved 
diagonally with respect to Q. 
Although a complete transverse movement of a target is assumed in FIG. 4 
for simplicity, it is accompanied by the movement in the depth direction 
in most practical cases as shown in FIG. 7, and the target moves to 
position B' at time point t.sub.1 and to position C' at t.sub.2 for 
example. In such a case, the signal has its phase at time point t.sub.e 
varying with the immediate distance to the reflective object as shown in 
FIG. 8. That is, at the position indicated by the dashed line of k=0, the 
signal has its phase leading by 1/4 of the wavelength, in the position 
indicated by the dashed line of k=1, it has its phase leading by 5/8 of 
the wavelength, and in the position indicated by the dashed line of k=2, 
the phase is leading by 1/2 of the wavelength. The amount of variation 
.phi..sub.d is evaluated in terms of the axial velocity component Vr as: 
##EQU1## 
where .lambda. is the wavelength, t.sub.0 is the transmission interval 
(t.sub.0 =t.sub.k+1 -t.sub.k), and .DELTA.x is the distance of movement in 
the depth direction. Accordingly, when the C.sub.km is expanded to general 
movements represented by C.sub.km, it is given as: 
EQU C.sub.km =C.sub.km .multidot.e.sup.jk.theta..sbsp.d (4) 
and, in this case, the differential process output d.sub.km is as follows. 
##EQU2## 
where 
EQU d.sub..theta..DELTA. (m)=C.sub.0 (m)-C.sub.0 
(m+.DELTA.m)e.sup.j.theta..sbsp.d 
EQU C.sub.0 (m)=C.sub.0m 
The positions of emergence of the d.sub.km in direction m are the same as 
shown in FIG. 6. The amount of movement .DELTA.m in direction m in FIG. 6 
is in correspondence to the target velocity V.phi. in the transverse 
direction as follows. 
##EQU3## 
By conducting the Fourier transformation for the d.sub.km in direction m, 
which is the direction of alignment of reception beams, the result D.sub.k 
(.sigma.) is given as follows. 
##EQU4## 
where D.sub..theta..DELTA. (.sigma.) represents the Fourier transformation 
of d.sub..theta..DELTA. (m) as follows. 
##EQU5## 
Another Fourier transformation for the D.sub.k (.sigma.) on k, i.e., the 
direction of repetitive transmission yields D(.sigma.,.rho.) as follows. 
##EQU6## 
FIG. 9, FIG. 10 and FIG. 11 are respectively a view showing complex values 
and differential processing result, a view showing a power spectrum, and a 
graphical representation showing a cumulative term E of the differential 
processing result subjected to the Fourier transformation. 
The D.sub..theta..DELTA. (.sigma.) is the result of Fourier transformation 
for the d.sub..theta..DELTA. (m) which varies from C.sub.0m and C.sub.1m 
shown by (a) in FIG. 9 to that shown by (b) in FIG. 9. That is, since 
C.sub.0m has its amplitude of 1 in the channel m and C.sub.1m has its 
amplitude of exp(j.theta.d) at the position where the amounts of movement 
.DELTA.m is added to the channel m, the differential processing output 
thereof d.sub..theta. .DELTA.(m)(C.sub.0m -C.sub.1m) has its amplitude 
which is obtained by subtracting the negative value of 
(-exp(j.theta..sub.d)) at the position (m+.DELTA.m) from the positive 
value of 1 at the position m. This Fourier transformation results as 
follows. 
EQU D.sub..theta..DELTA. 
(.sigma.)=1-e.sup.j(.sigma..DELTA.m+.theta..sbsp.d.sup.) (10) 
It has a power spectrum of .vertline.D.sub..theta..DELTA. 
(.sigma.).vertline..sup.2 as follows. 
EQU .vertline.D.sub..theta..DELTA. (.sigma.).vertline..sup.2 
=2{1-cos(.sigma..DELTA.m+.theta..sub.d)} (11) 
and it is as shown in FIG. 10. The power spectrum has, as shown in that 
figure, a peak value at position (.pi.-.theta..sub.d)/.DELTA.m, and this 
position moves in accordance with the transverse velocity .DELTA.m and 
axial velocity .theta..sub.d. The power spectrum has a null point at the 
position which meets .sigma..sub.0 .DELTA.m+.theta..sub.d =0, where 
.sigma..sub.0 =-.theta..sub.d /.DELTA.m. 
Next, the terms of cummulative summation E(.sigma.,.rho.) of the 
D(.sigma.,.rho.) will be examined. 
##EQU7## 
The above is generally the sum of irregular phase components, and is small 
in value. 
The above expression (12) is generally the slum of irregular phase 
components to be small in value. This can be explained using the polar 
coordinates as follows. That is, since the velocity of movement of the 
reflective object has a constant value in each measurement point, the 
components of the velocity, i.e., .DELTA.m and .theta.d are constant so 
that k=1, k=2 . . . form vectors which rotate at equal interval angles. 
Accordingly, the sum of k=1, k=2 . . . becomes zero. 
EQU .theta..sub.d +.sigma..DELTA.m-.rho.=0 (13) 
In the above special case, it represents the sum of inphase components, and 
E(.sigma.,.rho.) has a large value. Therefore, when it is plotted on the 
.sigma.-.rho. plane, it presents a large output only on a specific line as 
shown in FIG. 11. The gradient of the line relates to the transverse 
velocity .DELTA.m(V.phi.), and the intersection with the .rho. axis 
corresponds to the axial velocity .theta..sub.d (V.sub.r). 
FIG. 12 is a plan view of D(.sigma.,.rho.) which is obtained by subjecting 
the output of the differential processing to the Fourier transformation 
two times. FIG. 13 is a plan view relating to the transverse velocity and 
the axial velocity of the reflective object. From the above explanation, 
the D(.sigma.,.rho.) which is given as a product of the 
D.sub..theta..DELTA. (.sigma.) and E(.sigma.,.rho.) is as shown in FIG. 
12, and by using the .DELTA.m and .theta..sub.d measured on the diagram, 
the transverse velocity V.sub..phi. and axial velocity V.sub.r of the 
reflective object are measured independently to present its vectorial 
velocity. 
EQU .sigma..sub.0 =-.theta..sub.d /.DELTA.m (14) 
EQU .theta..sub.d +.sigma..sub.0 .DELTA.m-.rho..sub.0 =0 (15) 
With the relation pertinent to the null point of the D.sub..theta..DELTA. 
(.sigma.) given by equation (14) and the relation pertinent to the maximum 
value of the E(.sigma.,.rho.) given by equation (15) being satisfied 
simultaneously, the .rho..sub.0 becomes zero, and the null point of the 
D.sub..theta..DELTA. (.sigma.) at the position where the E(.sigma.,.rho.) 
exists is as follows. 
EQU .sigma.=-.theta..sub.d /.DELTA.m 
EQU .rho.=0 
Accordingly, the null point always exists on the intersection of the line 
of .theta..sub.d +.sigma..DELTA.m-.rho.=0 and the axis of .rho.=0, as 
shown in FIG. 12. 
The D.sub..theta..DELTA. (.sigma.), which is also a function of the 
.theta..sub.d and .DELTA.m, is determined uniquely from the values of 
.theta..sub.d and .DELTA.m. On this account, in the vicinity of the line 
given by the equation (16), on which the E(.sigma.,.rho.) exists, the 
convolution of the D(.sigma.,.rho.) and the known function 
D.sub..theta..DELTA. (.sigma.) is conducted to perform the optimizing 
filtering process thereby to obtain the detection output which provides 
the maximum signal-to-noise ratio as a function of the .theta..sub.d and 
.DELTA.m corresponding to the target velocity. 
EQU .theta..sub.d +.sigma..DELTA.m-.rho.=0 (16) 
Then, the optimizing filtering processing is conducted using the matched 
filter. In the case where an integration is performed along each straight 
line extending on the plane in FIG. 12, the curve of the power spectrum as 
shown in FIG. 10 rides on the straight line, and therefore, in the portion 
of the spectra curve where the power is low, an integration is conducted 
with its weight being lowered in order to reduce the noise. 
Integration is conducted on the line for the sake of simplicity as follows. 
##EQU8## 
where 
EQU .rho.=.theta..sub.d +.DELTA.m 
The result gives a peak value at the position corresponding to the target 
velocity as shown in FIG. 13. The values of .theta..sub.de and 
.DELTA..sub.me which provide this position are the measured values 
representing the lateral and axial velocities. 
Since this method is based entirely on the linear process, when the target 
velocity is distributed, the R(.theta..sub.d, .DELTA.) is distributed by 
itself in correspondence to the distribution of the flow rate. 
The resolution of the present method, particularly the directional 
resolution is higher when the .epsilon. is smaller and .theta. is larger. 
Namely, when a larger number of reception signals are used, the better 
velocity resolution is obtained. On this account, it is desirable to make 
the exposure range of the ultrasonic wave wider and each reception beam 
formed on B narrower. An effective manner to meet these conditions is to 
make the transducer aperture smaller than the total aperture used for the 
reception. 
It is effective for the axial resolution of the present method to make the 
interval of repetition of the transmission of the ultrasonic wave larger 
thereby to increase the number of repetition of transmissions. 
The preferred embodiments of the present invention will hereinafter be 
described in detail with reference to FIG. 14 through FIG. 19. 
Indicated by Q in FIG. 14 is a transducer made up of N pieces of arrayed 
elements. Part T of the elements are driven by a drive source DR so that a 
pulsed ultrasonic wave is transmitted repeatedly at a transmission 
interval of t.sub.R to a wide space (in the angle .theta. shown in FIG. 2 
or more). 
In the arrangement of the embodiment of FIG. 14, the 64 transducer elements 
are arrayed with a pitch of 0.25 mm. Out of them, the two elements are 
driven. Then, the ultrasonic wave with a frequency of 3.5 MHz is 
transmitted repeatedly 20 times at a transmission interval of 1 msec to a 
wide space having an angle of 36 degrees larger than .theta.=30 degrees of 
the attention region so that a beam selector BL receives reception signals 
b.sub.km (k=1, 2 to 20; m=1, 2 to 30) within the range of the angle 
.theta.=30 degrees. Then, the suffix k indicates the number of 
transmission of interest based on the count of repetitive transmissions. 
A reflection signal from a target derived from the transmitted ultrasonic 
wave is received by the transducer Q, and resulting signals of N in number 
are processed by a parallel reception beam forming device B, which 
produces reception signals in correspondence to ultrasonic beams. The 
parallel reception beam forming device may be formed of a parallel 
integration of well-known beam forming devices which delay signals of 
transducer elements individually and sum the signals thereby to produce 
reception signals for the reception beams having directivities in desired 
directions. The beams have a directional difference by an angle of 
.epsilon. between adjacent ones as shown in FIG. 2. 
In the present embodiment, the beams have a virtually equal focal depth in 
order to accomplish high accuracy flow rate measurement for a specific 
depth. The beam selector BL selects reception signals b.sub.km (t) (where 
m=1 to M) of M in number, which represent reception beams of M in number 
within the range of the angle .theta. as shown in FIG. 2, from among the 
reception signals. The suffix k indicates the reception signal number 
based on the count of repetitive transmissions. The variable t indicates 
the time length expended since transmission. 
The signals are sampled by a sampling device SPL and stored. The SPL output 
C.sub.km for each transmission and reception is assumed to be a function 
of time, and reflection signals from fixed objects are suppressed by means 
of a moving target indication filter MTI which performs a differential 
process on k among a plurality of data having the same value of t. The MTI 
output d.sub.km is treated as a function of m, and it is rendered Fourier 
transformation by a one-dimension Fourier transform device F.sub.m. The 
output D.sub.k (.sigma.) of the F.sub.m is rendered Fourier transformation 
as a function of k by a similar one-dimension Fourier transform device 
F.sub.k in a travel velocity analyzing device u to obtain 
D(.sigma.,.rho.). The D(.sigma.,.rho.) presents the intensity distribution 
as shown in FIG. 12 on the .sigma.-.rho. plane, as has been explained in 
connection with the formulas (9) to (13), and reveals the axial velocity 
component .theta..sub.d of a moving object from the .rho.-cut of the line 
appearing on the distribution and the transverse velocity component 
.DELTA.m from the gradient of the line. Although the output 
D(.sigma.,.rho.) of the Fourier transform device F.sub.k may be displayed 
on a two-dimensional plane, the present embodiment further proceeds to the 
calculation of a two-dimensional correlative function R(.theta..sub.d, 
.DELTA.) between the D(.sigma.,.rho.) and D.sub..theta..DELTA. (.sigma.) 
given to all velocity components by means of a two-dimension correlation 
device COR. Indicated by GEN is a function generator which generates 
D.sub..theta..DELTA. (.sigma.) in correspondence to values of 
.theta..sub.d and .DELTA.m. The position (.theta. .sub.de,.DELTA..sub.me) 
of the peak value of the R(.theta..sub.d,.DELTA.m) represents the lateral 
velocity V.sub..phi., and axial velocity V.sub.r of the moving target, as 
has been explained in connection with FIG. 13. The display unit DISP 
displays the R(.theta..sub.d,.DELTA.m) on the two-dimension plane or reads 
out the measured value of the position (.theta..sub.de, .DELTA..sub.me) of 
the peak value of the R(.theta..sub.d, .DELTA.m). These are the basic 
arrangement of the embodiment shown in FIG. 14. 
FIG. 15 is a block diagram showing a modification of the embodiment of FIG. 
14. The beam forming process by the parallel reception beam forming device 
B in FIG. 14 is known to be a Fourier transformation respecting to the 
space. Accordingly, it is possible to replace the B in FIG. 14 with a 
one-dimension Fourier transform device F.sub..theta.. In this case, the 
Fourier transformation process is generally conducted for sampled values, 
and a sampling device SPL which samples the reception signals and stores 
the signals is placed in front of the one-dimension Fourier transform 
device F.sub..theta. as shown in FIG. 15. That is, the arrangement of 
FIG. 15 is designed in such a way that reception signals a.sub.nk (t) of 
transducer elements of N in number are sampled by the sampling device, and 
are rendered the Fourier transformation with F.sub..theta. in direction n 
and conducted through the beam selector BL, thereby producing outputs 
which are equivalent to the outputs C.sub.km of the sampling device SPL in 
FIG. 14. In FIG. 15, the arrangement of the velocity analyzing device U in 
the rear of the one-dimension Fourier transform device F.sub.m and 
one-dimension Fourier transform device F.sub.k is identical to that of 
FIG. 14. 
FIG. 16 is a block diagram showing still another modification of FIG. 15. 
The MTI process of FIG. 15 has no difference before and after the process 
by the F.sub.m. Accordingly, even with the one-dimension Fourier transform 
device F.sub.m being connected to the front stage of the moving target 
indication filter MTI as shown in FIG. 16, the same operation as of the 
case of FIG. 15 takes place. It will be appreciated from this figure that 
the section marked by "*" in FIG. 16 is Fourier transformation for twice 
and it has basically identical to no operation, but merely confines the 
area of attention to the range of the angle .theta. using the BL. FIG. 17 
is a block diagram showing yet another modification of FIG. 16. From the 
above description, the embodiment of FIG. 17 is simply arranged in such a 
way as to include only the array of transducer elements Q, the sampling 
device SPL, the moving target indication filter MTI and the travel 
velocity analyzing device U by removing the sections marked by "*" in FIG. 
16. In this case, the function of the beam selector BL can be removed by 
carrying out another method. That is, partial element group T' among the 
transducer elements are activated to transmit the ultrasonic wave to the 
region .theta. and the reflection signals from this region are received, 
as shown in FIG. 17, whereby the beam selector BL can be eliminated. 
In the arrangement of the embodiment of FIG. 17, the 32 transducer elements 
are arrayed with a pitch of 0.25 mm. Out of them, only two elements are 
driven. Then, the ultrasonic wave with a frequency of 3.5 MHz is 
transmitted repeatedly 10 times at a transmission interval of 1 msec to 
the wide space of the attention region .theta.=30 degrees so that the 
reception signals a.sub.kn (k=1, 2 to 10; n=1, 2 to 32) from the range of 
the angle .theta.=30 degrees are obtained. Then, the suffix k indicates 
the number of transmission of interest based on the count of repetitive 
transmissions. 
The arrangement of FIG. 17 is designed in such a way that the reception 
signals a.sub.k1, . . . , a.sub.kN from the transducer elements sampled by 
the sampling device SPL are introduced to the moving target indication 
filter MTI, and the outputs of the MTI are directly introduced to the 
one-dimension Fourier transform device F.sub.k in the block U. Although 
the measurement result by this arrangement also becomes the same as that 
of FIG. 12, in the present embodiment, the reception elements are disposed 
on the axis of ordinate. 
FIG. 18 is a block diagram showing the arrangement of another modification 
of FIG. 17. The arrangement is, as shown in FIG. 18, may also be designed 
in such a way that the reception signals a.sub.k1, . . . a.sub.kN from the 
transducer elements are divided into groups through partial apertures, 
with these groups being connected to respective beam forming phasing 
devices R.sub.1, . . . , R.sub.M for implementing the beam forming 
operation, and outputs r.sub.R1,. . . , r.sub.RM indicative of a plurality 
of beams in the range of the region .theta. are sampled with the sampling 
device SPL in the same manner as in the case of FIG. 17 before conducting 
the successive processing. 
In the arrangement of the embodiment of FIG. 18, the 64 transducer elements 
are arrayed with a pitch of 0.25 mm. In this connection, the array of 
transducer elements are divided into 16 groups. Then, the ultrasonic wave 
with a frequency of 3.5 MHz is transmitted repeatedly 10 times at a 
transmission interval of 1 msec so that the reception signals b.sub.km 
(k=1, 2 to 10; m=1, 2 to 16 ) are obtained in the space of the attention 
region .theta.=30 degrees. The suffix k indicates the number of 
transmission of interest based on the count of repetitive transmissions. 
Also in the embodiments of FIGS. 16 through 18, the arrangement of the 
velocity analyzing device U which calculates the lateral velocity 
V.sub.100 and distant velocity V.sub.r is completely identical to the 
embodiment of FIG. 14. The order of disposition of the arrangement can be 
changed arbitrarily. Moreover, instead of using the two-dimension 
correlator COR, the distribution of D(.sigma.,.rho.) may be displayed 
intact. Further, the SPL is arranged using a usual sample-holding circuit, 
A/D converter and the like, or a possible alternative arrangement is a 
sampling device of the type of phase comparison which performs 
multiplication with a reference signal and low band filtering, and an 
improved s/n is expected in this case. 
FIG. 19 is a view showing the flow of a blood flow in a live body. 
According to the embodiments shown in FIG. 14 through FIG. 18, since 
two-direction components of the velocity are obtained, for example, the 
direction, the flow rate and the distribution of directions of a blood 
flow in a live body are evaluated. Consequently, it also becomes possible 
to display a measurement point in the two-dimension tomograph plane and 
the flow rate, the direction and the distribution at the measurement 
point, as shown in FIG. 19. 
In FIG. 19, with respect to the depth direction of the live body, there is 
shown the direction of the blood flow, the direction of the ultrasonic 
wave beam, and the measurement point. 
The method of integrating D(.sigma.,.rho.) (shown in FIG. 12) obtained by 
subjecting the output of the differential processing to the Fourier 
transformation twice to produce the display in which the measurement 
result of large scale is outputted at the position corresponding to the 
velocity of the reflective object as shown in FIG. 13 is not limited to 
the correlation processing by the two-dimension correlator COR shown in 
FIG. 14. 
FIG. 20 is a block diagram showing the arrangement of the embodiment of the 
travel velocity analyzing device U, according to the present invention, 
employing another method. FIG. 21A, FIG. 21B and FIG. 21C are respectively 
views showing an output F.sub.1 of a two-dimension Fourier transformer of 
FIG. 20, an output F.sub.2 of a directional Fourier transformer of FIG. 
20, and an example of coordinate transformation. The travel velocity 
analyzing device U is made up of a one-dimension Fourier transformer 
F.sub.k, a two-dimension Fourier transformer 2DFT, a directional Fourier 
transformer PFT, a coordinate transformer PRC and an image display DISP. 
The one-dimension Fourier transformer F.sub.k subjects the outputs of the 
moving target indication filter MTI, which have been, for example, 
obtained from the arrangement of FIG. 17 or FIG. 18, to the Fourier 
transformation with respect to the direction of the time base (the k 
direction) thereby to obtain D(m,.rho.) which shows the result of the 
two-dimension Fourier transformation and is defined by treating the axis 
of ordinate in FIG. 12 as m. When the D(m,.rho.) is then subjected to the 
two-dimension Fourier transformation by the two-dimension Fourier 
transformer 2DFT with respect to the direction of the time frequency axis 
(the .rho. direction) and the direction of arrangement of the transducer 
elements (the m direction), it is transformed to the output distribution 
of straight line which coincides with the origin diagonally as shown in 
F.sub.1 of FIG. 21A. this result will be readily understood by considering 
the relationship between a projected image in an X ray CT and a 
two-dimension Fourier transformation image. 
The characteristic curve F.sub.1 of FIG. 21A extends in a direction 
perpendicular to the D(.sigma.,.rho.) shown in FIG. 12, and the amplitude 
of the straight line-like region is uniform but only the phase is changed. 
The phase rotation velocity is proportional to a distance .gamma. between 
the origin in FIG. 12 and the D(.sigma.,.rho.). In FIG. 21A, there is 
shown the real number part Re[F.sub.1 ] of F.sub.1 on the straight line 
coinciding with the origin. The characteristic curve F.sub.1 of FIG. 21A 
is transformed to the characteristic curve F.sub.2 shown in FIG. 21B by 
the directional Fourier transformer PFT shown in FIG. 20. That is, the 
directional Fourier transformer PFT carries out the Fourier transformation 
by treating the values on the straight line, which coincides at an angle 
of .theta. with the origin O in FIG. 21A, as a one-dimension sequence of 
numbers, and carries out such a processing with respect to each angle. 
Thus, since the Fourier transformation is carried out with respect to each 
of the inclined directions, there is obtained the display of contour which 
corresponds in direction to the direction of F.sub.1 of FIG. 21A, and is 
distributed around the position apart from the origin O by a distance of r 
with making an angle .theta. with the Y axis, and has a large signal 
intensity. The distance r in FIG. 21B is a distance which is proportional 
to .gamma. in a direction of the angle corresponding to .DELTA.m. We can 
deduce the following relationships from FIG. 12 and FIG. 21A. 
##EQU9## 
By means of the coordinate transformer PRC using the above relationships, 
it is possible to obtain the characteristic curve in the form of 
(.theta.d,.DELTA.m) which is obtained by subjecting the characteristic 
curve in the form of (r,.theta.) of FIG. 21B to the coordinate 
transformation as shown in FIG. 21C, in the same manner as in the case of 
FIG. 23. Incidentally, the constant value A is determined by the 
arrangement factors of the system such as a frequency of the used 
ultrasonic wave, and an interval of arrangement of the transducer 
elements. 
FIG. 22 is a view useful in explaining the arrangement equivalent to the 
Fourier transformation in FIG. 20. FIG. 23 is a block diagram showing the 
arrangement of the best target velocity analyzing device according to the 
present invention. The arrangements of the one-dimension Fourier 
transformer Fk and the two-dimension Fourier transformer 2DFT, shown in 
FIG. 20, become equal to that of one-dimension Fourier transformer Fm, as 
shown in FIG. 22. That is, since the two-dimension Fourier transformation 
is the combination of the k direction (the direction of time base) and the 
m direction (the direction of arrangement of the transducer elements), the 
processing by the one-dimension Fourier transformer Fk and the 
two-dimension Fourier transformer 2DFT becomes equivalent to the Fourier 
transformation of one time with respect to the direction by the 
one-dimension Fourier transformer Fm. As a result, the arrangement of the 
travel velocity analyzing device U shown in FIG. 20 can be simplified as 
shown in FIG. 23. That is, the travel velocity analyzing device U of FIG. 
23 is made up of the one-dimension Fourier transformer Fm, the directional 
Fourier Transformer PFT, the coordinate transformer PRC and the image 
display DISP. After the output distribution of the straight line F.sub.1 
as shown in FIG. 21A has been obtained by the one-dimension Fourier 
transformer Fm, the transformation output F.sub.2 as shown in FIG. 21B is 
obtained by the directional Fourier transformer PFT to be transformed to 
the coordinate of (.theta.d,.DELTA.m) as shown in FIG. 21C by the 
coordinate transformer PRC, so that the resulting data can be outputted to 
the image display DISP. 
In the target velocity analyzing device of the present invention, the 
vectorial movement velocity of the blood flow is measured in such a way 
that the ultrasonic waves are transmitted from the transducer elements 
every time t.sub.k (k=0, 2, . . . , K), the reception signals 
corresponding to the specific depth is subjected to the Fourier 
transformation with respect to the direction of arrangement of the 
transducer elements (the m direction) by the one-dimension Fourier 
transformer Fm, a plurality of frequency spectra as that result are 
produced in a time series manner corresponding to the transmission times 
t.sub.k (k=0, 2, . . . , K) of the ultrasonic waves to consider the 
frequency spectra of the time and the result becomes a two-dimension 
signals, those two-dimension signals are disposed on the (k,.sigma.) 
coordinate, the values on each of the plural straight lines coinciding at 
respective angles with the origin of the (k,.sigma.) coordinate are 
subjected to the Fourier transformation by the directional Fourier 
transformer PFT with being treated as the one-dimension sequence of 
numbers, and the resulting data are transformed to the 
(.theta..sub.d,.DELTA.m) coordinate shown in FIG. 21 by the coordinate 
transformer PRC. 
FIG. 24 is a block diagram showing the arrangement of the travel velocity 
analyzing device in which the moving target indication filter MTI is 
disposed in the rear stage of the one-dimension Fourier transformer Fm. As 
has been described hereinabove, the processing of the moving target 
indication filter MTI utilizes that there is no difference before and 
after the processing by the one-dimension Fourier transformer Fm. However, 
when the moving target indication filter MTI is disposed in the rear stage 
of the one-dimension Fourier transformer Fm, the signal can be obtained 
with the higher S/N ratio being provided. FIG. 25 and FIG. 26 are 
respectively block diagrams showing the arrangements of embodiments of the 
ultrasonic flowmeter employing the travel velocity analyzing device shown 
in FIG. 24. In each of the embodiments shown in FIG. 25 and FIG. 26, the 
conditions of transmission and reception of the ultrasonic wave (the 
attention region, the frequency, the transmission interval, the number of 
repetition of the transmissions, and the like), and the arrangement of the 
sampling device SPL are the same as those of the embodiments of FIG. 17 
and FIG. 18. 
In the embodiments as well shown in FIG. 25 and FIG. 26, it will be readily 
understood that the blood flow in the live body can be displayed. 
As set forth in detail hereinabove, according to the present invention, it 
is possible to construct the ultrasonic flowmeter having a very simple 
construction, and since all of the processings are performed in the linear 
processing manner, when the velocity of the reflective object is 
distributed, the distribution can be measured, and even when the 
transverse velocity has the flow of positive direction and that of 
negative direction, both the flows can be measured. Of course, even in the 
case where there are a plurality of reflective objects, and they have 
different flow directions and velocity distributions, it is possible to 
measure the direction of flow and the velocity distribution every 
reflective object. Thus, the velocity of the reflective object can be 
measured as the vector quantity having its direction and magnitude 
irrespective of the direction of movement of the reflective object. 
According to the present invention, in addition to the blood flow, any 
thing can be measured as long as it reflects the ultrasonic wave. 
Moreover, the present invention also is applicable to the navigation and 
the like. 
Thus, flow rate and the direction of the flow in a two-dimensional plane, 
i.e., two-dimensional vector of flow can be accurately detected. Moreover, 
three-dimensional vector of flow can also be detected by employing a 
two-dimensional transducer array and two-dimensional Fourier transformers.