## Abstrict A flow meter, in which pulsed continuous ultrasonic wave is transmitted
towards an object at predetermined intervals T to obtain a phase
vector from a reception signal of wave reflected by the object and
which calculates a Doppler frequency from the average value of phase
differences between phase vectors at the sampling interval T to
obtain a signal indicating the speed of the object, comprising a
phase difference calculator by the auto-correlation method, by which
a plurality of phase difference vectors indicating phase differences
between phase vectors are added, the argument of the sum vector
thus obtained representing the average phase difference, or a phase
difference calculator by the 2-axial-component method, by which
a phase difference is divided into 2 axial components, a cosine
value and a sine value, and the average phase difference is obtained
by using the average value for each of the components, and a phase
difference calculator by the phase difference averaging calculator,
by which a plurality of phase differences are added, as they are,
to obtain the average thereof, in order to obtain a phase difference
average value having small errors by switching them.
## Claims We claim:
1. An ultrasonic pulse Doppler flow meter comprising:
transmitter-receiver means for transmitting ultrasonic pulsed continuous
wave towards an object with a predetermined interval and receiving
wave reflected by said object to obtain a reception signal;
phase detecting means for generating a phase vector indicating
the phase of said reception signal, each time said reception signal
is obtained;
first average phase difference calculating means for obtaining
the phase difference .DELTA..theta. between the phase vector at
current time point and the phase vector at the time preceding by
one time period, each time said phase vector is obtained, decomposing
it into a cosine component and a sine component, and calculating
the angle represented by the average of a plurality of cosine components
and the average of a plurality of sine components as a first average
phase difference;
second average phase difference calculating means for adding said
phase difference .DELTA..theta. a plurality of times to obtain the
average thereof as a second average phase difference; and
selecting means for selecting one of said first and said second
average phase difference, depending on the magnitude of the speed
of said object, as a signal indicating the speed of said object.
2. An ultrasonic pulse Doppler flow meter according to claim 1
wherein said selecting means selects the output of said second average
phase difference calculating means when the absolute value of the
output of said first average phase difference calculating means
is smaller than a predetermined angle and the output of said first
average phase difference calculating means when said absolute value
is greater than said predetermined angle.
3. An ultrasonic pulse Doppler flow meter according to claim 2
wherein said predetermined angle is in a region comprised between
.pi./3 and .pi./2.
4. An ultrasonic pulse Doppler flow meter according to claim 1
further comprising means for obtaining successively the speed indicated
by said phase difference .DELTA..theta. to calculate the variation
of the speed and means for obtaining the intensity of said reflection
signal, said selecting means using said variation of the speed and
said intensity of the reflection signal in addition to the output
of said first phase difference detecting means as parameters for
the selection of the phase difference.
5. An ultrasonic pulse Doppler flow meter according to claim 4
wherein when said variation of the speed exceeds a predetermined
value and said intensity of the reflection signal is smaller than
a predetermined value, the speed is judged to be impossible to measure
or zero.
6. An ultrasonic pulse Doppler flow meter according to claim 1
wherein said selecting means select one of said first and said average
phase difference when an average power of said phase vector is larger
than a threshold value, and select `zero` when said average power
is not larger than said threshold value.
7. An ultrasonic pulse Doppler flow meter comprising:
transmitter-receiver means for transmitting ultrasonic pulsed continuous
wave towards an object with a predetermined interval and receiving
wave reflected by said object to obtain a reception signal;
phase detecting means for generating a phase vector indicating
the phase of said reception signal, each time said reception signal
is obtained;
first average phase difference calculating means for obtaining
the phase difference .DELTA..theta. between the phase vector at
current time point and the phase vector at the time preceding by
one time period, each time said phase vector is obtained, decomposing
it into a cosine component and a sine component, and calculating
the angle represented by the average of a plurality of cosine components
and the average of a plurality of sine components as a first average
phase difference;
second average phase difference calculating means for adding arguments
of said phase difference vector to obtain the average thereof as
a second average phase difference; and
selecting means for selecting one of said first and said second
average phase difference, depending on the magnitude of the speed
of said object, as a signal indicating the speed of said object.
8. An ultrasonic pulse Doppler flow meter according to claim 7
wherein said selecting means selects the output of said second average
phase difference calculating means when the absolute value of the
output of said first average phase difference calculating means
is smaller than a predetermined angle and the output of said first
average phase difference calculating means when said absolute value
is greater than said predetermined angle.
9. An ultrasonic pulse Doppler flow meter according to claim 8
wherein said predetermined angle is in a region comprised between
.pi./3 and .pi./2.
10. An ultrasonic pulse Doppler flow meter according to claim 7
further comprising means for obtaining successively the speed indicated
by said phase difference .DELTA..theta. to calculate the variation
of the speed and means for obtaining the intensity of said reflection
signal, said selecting means using said variation of the speed and
said intensity of the reflection signal in addition to the output
of said first phase difference detecting means as parameters for
the selection of the phase difference.
11. An ultrasonic pulse Doppler flow meter according to claim 10
wherein when said variation of the speed exceeds a predetermined
value and said intensity of the reflection signal is smaller than
a predetermined value, the speed is judged to be impossible to measure
or zero.
12. An ultrasonic pulse Doppler flow meter according to claim 7
wherein said selecting means select one of said first and said average
phase difference when an average power of said phase vector is larger
than a threshold value, and select `zero` when said average power
is not larger than said threshold value.
13. An ultrasonic pulse Doppler flow meter comprising:
transmitter-receiver means for transmitting ultrasonic pulsed continuous
wave towards an object with a predetermined interval and receiving
wave reflected by said object to obtain a reception signal;
phase detecting means for generating a phase vector indicating
the phase of said reception signal each time said reception signal
is obtained;
first average phase difference calculating means for obtaining
the phase difference .DELTA..theta. between the phase vector at
current time point and the phase vector at the time preceding by
one time period, each time said phase vector is obtained, decomposing
it into a cosine component and a sine component, and calculating
the angle represented by the average of a plurality of cosine components
and the average of a plurality of sine components as a first average
phase difference;
second average phase difference calculating means for adding said
phase difference .DELTA..theta. a plurality of times to obtain the
average thereof as a second average phase difference; and
correcting means for correcting said second average phase difference,
using said first average phase difference, so that the addition
and averaging in said second average phase difference calculating
means is substantially effected by using the angle of said first
average phase difference as the reference axis for the angle,
wherein the average phase difference corrected by said correcting
means is adopted as the signal indicating the speed of said object.
14. An ultrasonic pulse Doppler flow meter according to claim 13
wherein the correction by means of said correcting means is effected,
when the absolute value of said first average phase difference exceeds
a predetermined threshold value.
15. An ultrasonic pulse Doppler flow meter comprising:
transmitter-receiver means for transmitting ultrasonic pulsed continuous
wave towards an object with a predetermined interval and receiving
wave reflected by said object to obtain a reception signal;
phase detecting means for generating a phase vector indicating
the phase of said reception signal, each time said reception signal
is obtained;
first average phase difference calculating means for obtaining
the phase difference .DELTA..theta. between the phase vector at
current time point and the phase vector at the time preceding by
one time period, each time said phase vector is obtained, decomposing
it into a cosine component and a sine component, and calculating
the angle represented by the average of a plurality of cosine components
and the average of a plurality of sine components as a first average
phase difference;
second average phase difference calculating means for adding arguments
of said phase difference vector to obtain the average thereof as
a second average phase difference; and
correcting means for correcting said second average phase difference,
using said first average phase difference, so that the addition
and averaging in said second average phase difference calculating
means is substantially effected by using the angle of said first
average phase difference as the reference axis for the angle,
wherein the average phase difference corrected by said correcting
means is adopted as the signal indicating the speed of said object.
16. An ultrasonic pulse Doppler flow meter according to claim 15
wherein the correction by means of said correcting means is effected,
when the absolute value of said first average phase difference exceeds
a predetermined threshold value.
17. An ultrasonic pulse Doppler flow meter comprising:
transmitter-receiver means for transmitting ultrasonic pulsed continuous
wave towards an object at predetermined intervals T and receiving
wave reflected by said object to obtain a reception signal;
phase detecting means for detecting the phase of said reception
signal and generating phase vectors sampled at said intervals T;
first auto-correlating means for obtaining a first phase difference
vector by correlating phase vectors having said interval T therebetween
among said phase vectors sampled at said intervals T to calculate
the argument thereof;
second auto-correlating means for obtaining a second phase difference
vector by correlating phase vectors having an interval nT (n being
an integer not smaller than 2) therebetween among said phase vectors
sampled at said intervals T to calculate the argument thereof; and
selecting means for selecting the argument of said first phase
difference vector for a high speed region and the argument of said
second phase difference vector for a low speed region to obtain
a signal indicating the speed of said object.
18. An ultrasonic pulse Doppler flow meter according to claim 17
wherein said selecting means selects the argument of said second
phase difference vector when the absolute value of the argument
of said first phase difference vector is smaller than a threshold
value, which is equal to or slightly smaller than .pi./n, and the
argument of said first phase difference vector when the absolute
value of the argument of said first phase difference vector is greater
than said threshold value.
19. An ultrasonic pulse Doppler flow meter comprising:
transmitter-receiver means for transmitting ultrasonic pulsed continuous
wave towards an object at predetermined intervals T and receiving
wave reflected by said object to obtain a reception signal;
phase detecting means for detecting the phase of said reception
signal and generating phase vectors sampled at said intervals T;
first auto-correlating means for obtaining a first phase difference
vector by correlating phase vectors having said interval T therebetween
among said phase vectors sampled at said intervals T to calculate
the argument thereof;
second auto-correlating means for obtaining a second phase difference
vector by correlating phase vectors having an interval nT (n being
an integer not smaller than 2) therebetween among said phase vectors
sampled at said intervals T to calculate the argument thereof; and
correcting means for judging in which region the argument of said
first phase difference vector is among angular regions devided by
.+-..theta..sub.L1 and .+-..theta..sub.L2 wherein .theta..sub.L1
is .pi./n and .theta..sub.L2 is an angle at which spectral characteristics
of said first auto-correlation means is a little higher than that
of said second auto-correlation means, and effecting corrections
on the argument of said second phase difference vector, depending
on the judgement result to obtain a signal indicating the speed
of said object.
## Description BACKGROUND OF THE INVENTION
This invention relates to a pulse Doppler measuring apparatus and
in particular to an apparatus for measuring the velocity of an object
by using ultrasonic wave, e.g. a pulse Doppler measuring apparatus
capable of measuring it with a high signal to noise ratio, in the
case where the blood flow speed in a living body is measured in
real time.
Heretofore various sorts of apparatuses are known for measuring
the flow speed of an object by using the Doppler effect of acoustic
wave. In particular, in an apparatus using the pulse Doppler method
(cf. e.g. D. W. Baker; Pulsed Ultrasonic Doppler Blood Flow Sensing;
IEEE Trans: Sonics and Ultrasonics; vol. SU-17 No. 3 July 1970
pp. 170-185), it is known that it is possible to identify a measured
part by transmitting a pulsed continuous wave and setting a time
gate corresponding to the distance to the measured part on the received
signal.
As prior art ultrasonic Doppler blood flow measuring apparatuses,
as disclosed in e.g. JP-A-No. 58-188433 JP-A-No. 60-119929 and
JP-A-No. 61-25527 there are known apparatuses for measuring blood
flow by transmitting ultrasonic wave towards blood vessel and measuring
the Doppler shift frequency of the ultrasonic wave reflected by
the blood in the blood vessel to obtain vcos.theta., where .theta.
represents the angle between the direction of the blood flow and
the transmission direction of the ultrasonic wave and v indicates
the blood flow speed.
Further techniques, by which distribution of the blood flow speed
in a certain cross-section in a living body is measured and displayed
in color on a tomographic image, called color flow mapping, are
disclosed in C. KASAI et al; Real-Time Two-Dimmensional Blood Flow
Imaging Using an Autocorrelation Technique; IEEE Trans. Sonics and
Ultrasonics, vol. SU32 No. 3 May 1985 pp. 458-464. For effecting
this color flow mapping, in order to achieve a desired image frame
rate, the blood flow speed at each of pixels is obtained by averaging
measured values of the Doppler shift of a relatively small number
of measurements. In the example described above, the auto-correlation
method is used, by which a difference vector is obtained, each repeated
measurement, by means of a auto-correlator between a vector indicated
by a Doppler signal detected currently and a vector indicated by
a Doppler signal detected the last time and the average speed is
calculated by using the argument of a vector representing the sum
of a plurality of difference vectors.
On the other hand, in U.S. patent application Ser. No. 101444
filed Sept. 28 1987 copending with this application, is disclosed
a method, called 2-axial-component method, by which measurements
being repeated, a phase difference .DELTA..theta. of the Doppler
signal is obtained for every measurement, which difference is decomposed
into a cosine component and a sine component; a plurality of values
obtained for each of the components are added and averaged; and
the phase difference indicated by the averaged cosine and sine components
thus obtained is transformed into the velocity.
Furthermore, in 1978 Ultrasonic Symposium Proceedings, pp. 348-352
is disclosed a method, by which a phase difference of the Doppler
signal is obtained for every measurement and an averaged phase difference
is calculated by adding directly a plurality of values of the phase
difference, which averaged phase difference is transformed into
the velocity. Hereinbelow this is called phase difference averaging
method.
SUMMARY OF THE INVENTION
According to the phase difference averaging method described above,
if the phase difference corresponding to the true blood flow speed
is close to .pi. or -.pi., the phase difference detected by each
measurement can exceed .pi. or -.pi. because of variations in the
detected phase difference due to noise, which gives rise to a phenomenon
that the total sum is at the neighborhood of zero due to aliasing
of the value at .pi. and -.pi.. Consequently it has a drawback that
the measurement domain at a high speed region is restricted. On
the other hand, as results of study of the applicants of this application
it was found that the effect to improve the precision by averaging
a plurality of measured values by the auto-correlation method or
the 2-axial-component method is inferior to that obtained by the
phase difference averaging method and further that very great errors
in the averaging calculation are produced in a low speed region,
where variation in the phase of the Doppler detection signal due
to noise is great.
An object of this invention is to provide a pulse Doppler flow
meter having a satisfactorily wide measurement domain also in the
high speed region and small measurement errors due to noise in the
low speed region.
In order to achieve the above object, according to this invention,
there are disposed 2 kinds of means for calculating the average
phase difference having characteristics basically different from
each other. The first of them calculates a first average phase difference
corresponding to the Doppler shift by the auto-correlation method
or the 2-axial-component method and the second calculates a second
average phase difference corresponding to the Doppler shift obtained
by the phase difference averaging method. The above object can be
achieved by selecting either one of the first and the second average
phase difference, depending on the speed region.
Further the above object can be achieved not only by the selection,
as described above, but also by obtaining correction values from
the output of the first average phase difference calculating means
and effecting corrections on the second average phase difference
so that the addition and averaging of angles obtained from the second
average phase difference is an operation producing no errors in
the high speed region.
Still further the above object can be achieved also by constructing
the first and the second average phase difference detecting means
by two average phase difference detecting means by the auto-correlation
method using two different time parameters and selecting one of
the output thereof.
The other objects of this invention will be obvious from the following
detailed explanation.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a block diagram showing the whole construction of embodiments
of this invention;
FIGS. 2 6 7 9 11 12 and 14 are block diagrams showing different
embodiments;
Fi. 3 is a graph indicating in- and output characteristics obtained
by two kinds of the average phase difference calculating methods;
FIG. 4 is a PAD flowchart indicating the judging method in FIG.
2;
FIG. 5 is a graph indicating in- and output characteristics in
the embodiment indicated in FIG. 2;
FIGS. 8A and 8B are PAD flow charts indicating the judging method
in FIG. 7;
FIGS. 10A and 10B are conceptional schemes indicating the operating
method in FIG. 9;
FIG. 13 is a graph indicating characteristics of the MTI filter
in FIG. 12; and
FIG. 15 is a block diagram illustrating another example of the
MTI (moving target indicator) filter in FIG. 12.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
Hereinbelow the principle and the preferred embodiments of this
invention will be described in detail, referring to the drawings.
At first the outline of the construction and the principle of the
operation of this invention will be explained.
FIG. 1 is a block diagram of the pulse Doppler device, which is
an embodiment of this invention.
The pulse Doppler measuring apparatus according to this invention
consists of a transmitting circuit 2 a receiving circuit 3 an
A/D converter 4 a phase comparator 5 an MTI filter (fixed substance
removing filter) 6 a Doppler average phase difference calculating
circuit 7 a divider 8 a controller 9 and a display device 10.
The transmitting circuit 2 gives a transducer 1 a pulsed continuous
wave at predetermined periods T. In this way the transducer 1 emits
an ultrasonic pulsed continuous wave at the predetermined periods
T towards a reflecting body 11. Reflected acoustic wave thus produced
returns again to the transducer 1 and reflection signals therefrom
are detected one after another by the receiving circuit 3. In the
phase comparator 4 the detected received signals are mixed with
two kinds of reference signals .alpha.=A cos .omega.t and .alpha.'=A
sin .omega..sub.o t and in this way Doppler signal V.sub.R and V.sub.I
having phase information of the reflection signals, respectively,
are obtained. The A/D converter 5 samples the signals V.sub.R and
V.sub.I of the wave reflected by the reflecting body 11 located
at a specified depth, converts them into digital signals, at the
periods T. The signals thus digitized can be expressed by V.sub.Rn
and V.sub.In represented by the following equation by using n (n=1
2 3 . . . ) indicating the number of repetition of the transmitted
wave; ##EQU1##
The MTI filter 6 forms a first order difference of the output of
the A/D converter 5 stated above to remove the unvariable reflected
wave signal coming from fixed substance. For the sake of the simplicity,
writing Eq. (1) in one equation as follows:
the output of the MTI filter is expressed by
Hereinbelow V.sub.n is called phase vector. The average phase difference
calculating circuit 7 has a structure peculiar to this invention
and forms the averaged Doppler argument obtained from a plurality
of values of the phase vector V.sub.n stated above.
FIG. 2 illustrates an example of the average phase difference calculating
circuit 7. A memory 711 has a function to convert data of the 2-axial-component
of a vector into an argument. That is, in the memory 711 values
of the argument corresponding to a 2-dimensional address, in which
values of the x and y components of the vector, are arranged, are
stored. The MTI filter gives the address input terminal thereof
the imaginary and the real part of the phase vector V.sub.n and
the value of .theta..sub.n =tan.sup.-1 (V.sub.Rn /V.sub.In) is read
out from the memory 712. In the phase difference detector 712 the
difference between the argument .theta..sub.n-1 preceding by one
step and the argument .theta..sub.n read out at this time is formed
to obtain the phase difference .DELTA..theta..sub.n =.theta..sub.n
-.theta..sub.n-1. A memory 713 has a function to convert the angle
to the cosine thereof and a memory 714 has a function to convert
the angle to the sine thereof. That is, when the phase difference
.DELTA..theta..sub.n is given as the address input, the value of
sin .DELTA..theta..sub.n is read out from the memory 713 and the
value of cos .DELTA..theta..sub.n from the memory 714. Adders 715
and 716 add outputs of the memories 713 and 714 respectively, for
a predetermined number of times. Typically they add the cosine and
the sine for n times, going back from the current values cos .DELTA..theta..sub.n
and sin .DELTA..theta..sub.n, respectively. That is, the output
R of the adder 715 and the output I of the adder 716 are given by:
##EQU2##
The memory 717 has a function together with the memory 712 to convert
the data of the 2-axial component of the vector into the argument.
When the values of R and I are given as the address input, the phase
difference expressed by: ##EQU3## is obtained from the memory 717.
The part described above is a part for obtaining the average phase
difference by the 2-axial-component method.
On the other hand, an adder 718 adds outputs .DELTA..theta..sub.i
of the phase difference detector for a predetermined number of times.
Typically, it adds them for N times, going back from the current
value .DELTA..theta..sub.n. The output .DELTA..theta..sub.S of the
adder 718 can be transformed into the average of .DELTA..theta..sub.i
expressed by the following equation by modifying the meaning of
the bit. ##EQU4## This part is a part for obtaining the average
phase difference by the phase difference averaging method.
One of the two average phase differences .DELTA..theta..sub.T and
.DELTA..theta..sub.S thus obtained is selected by a multiplexer
719. Since the selected average phase difference .DELTA..theta.
indicates a Doppler phase shift during the period of time of the
wave transmission interval T, it is converted by the divider 8 in
FIG. 1 into a Doppler frequency by using the following equation:
##EQU5##
The switching over of .DELTA..theta..sub.T and .DELTA..theta..sub.S
by the multiplexer 719 stated above is executed by an instruction
from the controller 9. The algorithm for the switching over in this
embodiment will be explained below, referring to FIGS. 3 4 and
5. FIG. 3 shows characteristics of the average phase differences
obtained by the 2-axial-component method and the phase difference
averaging method, in which the abscissa represents the input phase
difference corresponding to the real blood flow speed and the ordinate
the output phase difference really calculated, and results obtained
by simulation is shown. At this time, as a model of the output signal
of the phase comparator (block 4 in FIG. 1), which is the Doppler
signal,
is used. However, it is supposed here that phase noises W'.sub.n
and W".sub.n are white noises and normal random numbers according
to the normal distribution N (0 1) are used.
W".sub.n is generated with an initial value of the random
number different from that for W'.sub.n and therefore they have
no correlation. As factors of the generation of this noises, each
variation in the reflected signal due to microscopic variations
in the blood flow, acoustic noise produced by non-uniformity in
the structure at the propagation process of the acoustic wave, electric
noise in amplifiers used for signal amplification in the measuring
apparatus, etc. are taken into account. Further W'.sub.n represents
noise in the real part and W".sub.n noise in the imaginary
part. .omega..sub.d indicates the Doppler frequency.
The curve indicated by (a) in FIG. 3 indicates characteristics
of the phase difference obtained by the 2-axial-component method,
i.e. .DELTA..theta..sub.T stated above. The phase difference between
Doppler signals is obtained through the MTI filter and the gain
is small for the low speed region because of the characteristics
of the MTI filter. That is, in a region where the absolute value
of the phase difference is close to O, the amplitude A.sub.n of
the true Doppler signal is small and the relative amplitude B.sub.n
of the noise component is great. Accordingly, phase difference .DELTA..theta..sub.n
which are actually obtained through sequential measurements, tend
to distribute over the range of .+-..pi./2 arround a true average
phase difference .DELTA..theta. in this low speed region. Though
the average angle of two angles ##EQU6## and ##EQU7## is .DELTA..theta.,
the output .DELTA..theta..sub.T of the 2-axial component method
when those two angles are given have an error of .pi. or -.pi. from
.DELTA..theta., since the method uses vector summation for averaging.
That is why errors becomes greater by the 2-axial component method,
as the true phase difference approaches more closely to zero. Further,
another averaging method called "autocorrelation method"
have a simillar output characteristics to the curve (a) in FIG.
3 since the method also uses vector summation for averaging.
On the other hand, the curve indicated by (b) in FIG. 3 indicates
the phase difference obtained by the phase difference averaging
method, i.e. characteristics of .DELTA..theta..sub.S stated above.
In the low speed region, even if phase differences of the noise
are widely distributed around the phase difference of the true Doppler
signal, since noise components are approximately cancelled by averaging
the angle itself, errors are small. On the other hand, if the phase
difference corresponding to the true blood flow speed is close to
.pi. or -.pi., it happens that each detected phase difference exceeds
.pi. or -.pi. because of variations of the detected phase difference
due to the noises. Due to aliasing of the value at .pi. and -.pi.,
a phenomenon takes place that the operation result of the addition
and the averaging of the angle becomes close to zero. Consequently
by the phase difference averaging method remarkable errors take
place in the high speed region.
According to the examination of the simulation result and the cause
of the errors described above, in this embodiment, the algorithm
as indicated in FIG. 4 is adopted and one of .DELTA..theta..sub.T
and .DELTA..theta..sub.S in FIG. 2 is selected. That is;
(1) a difference between .vertline..DELTA..theta..sub.T .vertline.
obtained from the memory 717 and .vertline..DELTA..theta..sub.S
.vertline. obtained from the adder 718 is formed and if the value
of .vertline..DELTA..theta..sub.T .vertline.-.vertline..DELTA..theta..sub.S
.vertline. doesn't exceed a threshold value .alpha., the multiplexer
719 is connect on the T side so that the output .DELTA..theta..sub.T
obtained by the 2-axial-component method is selected;
(2) if the value of .vertline..DELTA..theta..sub.T .vertline.-.vertline..DELTA..theta..sub.S
.vertline. exceeds .alpha., the maximum of the absolute values of
N phase differences used for the averaging operation max {.vertline..DELTA..theta..sub.n-N+1
.vertline., .vertline..DELTA..theta..sub.n-N+2 .vertline., . . .
.vertline..DELTA..theta..sub.n .vertline.} is compared with a threshold
value .beta.; and if the maximum value doesn't exceed .beta., the
multiplexer 719 is connected on the S side so that the output .DELTA..theta..sub.S
obtained by the phase difference averaging method is selected;
(3) if .vertline..DELTA..theta.hd T.vertline.-.vertline..DELTA..theta..sub.S
.vertline.>.alpha. and the maximum value stated above exceeds
.beta., it is examined whether all the N phase difference signals
have a same sign, and if they have a same sign, i.e. .DELTA..theta..sub.i
.multidot..DELTA..theta..sub.i-1 >0 is valid for all i=n-N+2
. . . , n, the multiplexer 719 is connected on the S side so that
.DELTA..theta..sub.S is selected; and
(4) if .vertline..DELTA..theta..sub.T .vertline.-.vertline..DELTA..theta..sub.A
.vertline.>.alpha., the maximum value stated above exceeds .beta.,
and the N phase difference signals have different signs, i.e. there
is at least one case where .DELTA..theta..sub.i .multidot..DELTA..theta..sub.i-1
>0 is not valid, the multiplexer 719 is connected on the T side
so that .DELTA..theta..sub.T is selected.
When one of the average phase difference .DELTA..theta..sub.T obtained
by the 2-axial-component method and the average phase difference
.DELTA..theta..sub.S obtained by the phase difference averaging
method is selected according to the algorithm described above, variations
in the output phase difference with respect to the input phase difference
corresponding to the true blood flow speed can be represented by
the full line in FIG. 5. Also in the region where the input phase
difference is comprised between 0 to -.pi., the characteristics
are completely symmetric to those indicated in FIG. 5. Therefore
the speed detection can be effected with small errors over all the
speed detection region from -.pi. to .pi.. Further, in the case
of (1) stated above, since .DELTA..theta..sub.S .apprxeq..DELTA..theta..sub.T,
.DELTA..theta..sub.T may be selected.
As described previously, since the auto-correlation method has
error characteristics completely similar to those of the 2-axial-component
method, it is possible to switch over the output phase difference
.DELTA..theta..sub.A by the auto-correlation method and the output
phase difference .DELTA..theta..sub.S by the phase difference averaging
method by applying the algorithm indicated in FIG. 4 as it is.
FIG. 6 shows an example of the average phase difference calculating
circuit 7 indicated in FIG. 1 which executes such a switching.
In FIG. 6 the auto-correlator 701 calculates a complex product
of the phase vector V.sub.n at the current time point given through
the MTI filter 6 indicated in FIG. 1 by V.sub.n-1 *, which is the
conjugate complex vector of the phase vector V.sub.n-1 at the time
preceding by 1 period. The result Y.sub.n thus obtained is a vector
having an argument indicating the phase difference between V.sub.n
and V.sub.n-1 which is expressed by: ##EQU8## A complex adder 702
adds Y.sub.n =R.sub.n +jI.sub.n, which is outputs of the phase difference
detector 701 an arbitrary number of times. Typically, going back
from Y.sub.n which is the current time point, N vectors are added.
The obtained sum vector is represented by: ##EQU9##
A memory 703 is one, in which arguments are stored, using 2-axial
components as addresses, similarly to the memory 717 described,
referring to FIG. 2. When the values of R and I described above
are given to the memory 702 a corresponding argument .DELTA..theta..sub.T
=tan.sup.-1 (I/R) is read out. The value of this .DELTA..theta..sub.T
is the average phase difference by the auto-correlation method.
On the other hand the real part R.sub.n and the imaginary part I.sub.n
of the output Y.sub.n of the auto-correlator 701 described above
are given to a memory 704 in which arguments are stored similarly,
using 2-axial components as addresses and in this way the argument
.DELTA..theta..sub.n =tan.sup.-1 (I.sub.n /R.sub.n) of the phase
difference vector is read out from the memory 704. An adder 705
adds .DELTA..theta..sub.n a predetermined number of times. Since
.DELTA..theta..sub.i is added typically N times, going back from
the current value .DELTA..theta..sub.n, the output thereof is expressed
by: ##EQU10##
This .DELTA..theta..sub.S is the average phase difference by the
phase difference averaging method. A multiplexer 706 selects one
of .DELTA..theta..sub.A and .DELTA..theta..sub.S by the same algorithm
as that used for .DELTA..theta..sub.T and .DELTA..theta..sub.S in
FIG. 2 as indicated between parentheses in FIG. 4. In this way
it is possible to obtain an average phase difference having small
errors, as indicated by the full line in FIG. 5 completely identically
to the example indicated in FIG. 2.
FIG. 7 illustrates still another example of the average phase difference
calculating circuit 7. The items represented by 701 702 and 703
are identical to those indicated in FIG. 6 and thus the average
phase difference .DELTA..theta..sub.A by the auto-correlation method
can be obtained. The items represented by 704 and 705 are similarly
a memory, in which arguments corresponding to the 2-axial components
are stored, and an adder, respectively, similarly to FIG. 6. However,
in this embodiment, since the memory 704 is read out not by the
output of the auto-correlator 701 but by the output of the MTI filter
6 the difference between the phase .theta..sub.n of the Doppler
signal at current time and the phase .theta..sub.n-1 of the Doppler
signal at the time preceding by one period is formed by an angle
detector 720 to obtain .DELTA..theta..sub.n and then these differences
are added and averaged by an adder 705. .DELTA..theta..sub.S obtained
in this way is the average phase difference by the phase difference
averaging method. On the other hand, the output of the auto-correlator
701 is given to a memory, in which arguments corresponding to 2-axial
components are stored, and in this way the phase difference .DELTA..theta..sub.n
is obtained. A variance operator executes a following operation,
using values of N phase differences .DELTA..theta..sub.i (i=n-N+1
. . . , n) and the average phase difference .DELTA..theta..sub.A
by the auto-correlation method obtained from the memory 703 to calculate
the variation .sigma..sub.S of .DELTA..theta..sub.i ; ##EQU11##
Further, a power operator 723 calculates the average power of the
phase vector signal, which has passed through the MTI filter 6 by
using the following equation; ##EQU12## A selector 724 selects either
one of .DELTA..theta..sub.T and .DELTA..theta..sub.S according to
the algorithm indicated in FIG. 8A, using the variance .sigma..sub.S
and the value of the average power P.sub.S stated above, or determines
not to output any phase difference signal because of mixing of noise.
That is,
(1) if the variance .sigma..sub.S is smaller than the threshold
value .sigma..sub.C, it compares the absolute value .vertline..DELTA..theta..sub.A
.vertline. of the average phase difference by the auto-correlation
method with a predetermined angle .theta..sub..alpha. and if .vertline..DELTA..theta..sub.A
.vertline.<.theta..sub..alpha., it selects the average phase
difference .DELTA..theta..sub.S by the phase difference averaging
method;
(2) if .sigma..sub.S <.sigma..sub.C and .vertline..DELTA..theta..sub.A
.vertline..gtoreq..theta..sub..alpha., it selects the average phase
difference .DELTA..theta..sub.A by the auto-correlation method;
(3) if .sigma..sub.S .gtoreq..sigma..sub.C, it compares the average
power P.sub.S with a threshold value P.sub.n and if P.sub.S >P.sub.n,
it selects similarly the average phase difference .DELTA..theta..sub.A
by the auto-correlation method; and
(4) if .sigma..sub.S .gtoreq..sigma..sub.C and P.sub.S .gtoreq.P.sub.n,
phase difference output is zero.
66.degree. or 86.degree. is used for the value of .sigma..sub.C.
In the case where the MTI filter is of first order, .sigma..sub.C
of about 76.degree. is suitable. This value varies, depending on
the order of the MTI filter 6. The angles in the region comprised
between .pi./3 and .pi./2 (60.degree. and 90.degree.) are suitable
for .theta..sub..alpha.. P.sub.n is a threshold value determined
after measuring the power of electric noise of the device, etc.
In this embodiment indicated in FIGS. 7 and 8 the measurement incapable
region for the low speed region is similar to that of the embodiment
indicated in FIGS. 2 and 6 and blood flow measurement having errors
smaller than those by the prior art techniques is possible. In addition,
when the value of the blood flow speed fluctuates, it is possible
to judge whether fluctuations are produced by noise or a turbulent
flow is really produced. Further the selection algorithm may be
used for switching the 2-axial-component method and the phase difference
averaging method.
FIG. 8B shows another algorithm used for selection in the selector
724 in FIG. 7. In this algorithm, the variance .sigma..sub.S is
not use for selection. If the average power P.sub.S is larger than
the threshold value P.sub.n, .vertline..DELTA..theta..sub.A .vertline.
is compared to the threshold .theta..sub..alpha.. Then, if .vertline..DELTA..theta..vertline.<.theta..sub..alpha.,
.DELTA..theta..sub.S is selected as the output .DELTA..theta.. If
.vertline..DELTA..theta..vertline..gtoreq..theta..sub..alpha., .DELTA..theta..sub.A
is selected. If the power P.sub.S is not larger than P.sub.n, `zero`
is selected as the output.
FIG. 9 shows still another embodiment of the average phase difference
detecting circuit 7. The blocks indicated by the reference numerals
711 to 718 are the same items as those indicated in FIG. 2. Consequently
the average phase difference .DELTA..theta..sub.T by the 2-axial
component method is obtained from the memory 717 and on the other
hand the average phase difference .DELTA..theta..sub.S by the phase
difference average method is obtained. However, in this embodiment
the value of .DELTA..theta..sub.T is used only for obtaining correction
values to correct errors by the phase difference averaging method
for a high speed region. When the adding and averaging operation
in the adder 718 is effected at the neighborhood of .+-..pi., an
angle correcting circuit 730 corrects the values, as if the adding
operation were effected substantially at the neighborhood of angle
zero, so as to remove the errors due to aliasing in the adder 718.
At first, the angle correcting circuit 730 judges whether the value
of .DELTA..theta..sub.T is in a region ##EQU13## or not. If it is
in this region, since the output .DELTA..theta..sub.S of the adder
718 has no great errors, no correction is effected, but .DELTA..theta..sub.S
is outputted, as it is, as the average phase difference .DELTA..theta..
If ##EQU14## the angle correcting circuit 730 effects correction
represented by the following equation, and after having effected
the operation to add and average the angle in a right-handed new
polar coordinate system, using the direction of .DELTA..theta..sub.T
as the reference axis, effects substantially an operation to return
the angles to those in the initial coordinate system; ##EQU15##
where S.sub.g and M in Eq. (14) has the following values; (1) if
.DELTA..theta..sub.T >.pi./4 S.sub.g =-1 and M represents the
number of phase differences .DELTA..theta..sub.i among N, which
satisfy .DELTA..theta..sub.i <.DELTA..theta..sub.T -.pi.; and
(2) if .DELTA..theta..sub.T <-.pi./4 S.sub.g =+1 and M represents
the number of phase differences .DELTA..theta..sub.i among N, which
satisfy .DELTA..theta..sub.i >.DELTA..theta..sub.T +.pi..
The correcting operation by Eq. (12) stated above can be explained,
referring to FIGS. 10A and 10B. FIG. 10A indicates an operation,
when .DELTA..theta..sub.T >.pi./4. For the sake of simplicity
it is supposed that the number of phase differences added in the
adder 718 is 8 from .DELTA..theta..sub.1 to .DELTA..theta..sub.8.
Since .DELTA..theta..sub.1 to .DELTA..theta..sub.8 are dispersed
around .DELTA..theta..sub.T, if the operation to add and average
the angle is effected in the new polar coordinate system, which
is right-handed with respect to the direction of .DELTA..theta..sub.T
(indicated by chain-dotted lines in the figure), no errors due to
aliasing are produced. The phase differences in this new polar coordinate
system being denoted by .DELTA..theta.'.sub.i (i=1 . . . 8), since
the arithmetic average thereof is represented by ##EQU16## the true
average phase difference .DELTA..theta. returned to the original
coordinate system is given by; ##EQU17## .DELTA..theta..sub.i can
be expressed by using the following equations: ##EQU18##
The number of .DELTA..theta..sub.i satisfying .DELTA..theta..sub.i
<.DELTA..theta..sub.T -.pi. being denoted by M, substituting
.DELTA..theta..sub.i ' in Eq. (15) by Eq. (16), the following equation
is obtained: ##EQU19##
On the other hand, FIG. 10B indicates the case where .DELTA..theta..sub.T
<-.pi./4. Similarly to the case indicated in FIG. 10A, the number
of .DELTA..theta.'.sub.i satisfying .DELTA..theta..sub.i >.DELTA..theta..sub.T
+.pi. being denoted by M, the true average phase difference .DELTA..theta.
can be obtained by the following equation; ##EQU20## Consequently,
putting together Eqs. (17) and (18), denoting the number of phase
differences generally by N, it can be understood that the true phase
difference average value can be obtained by using Eq. (14).
FIG. 11 shows still another example of the average phase difference
detecting circuit 7. In this example, similarly to the example indicated
in FIG. 9 the true average phase difference .DELTA..theta. is obtained
by correcting the errors produced at the adding and the averaging
by the phase difference averaging method in the high speed region.
However the correction values are calculated by using the auto-correlation
method. Reference numerals 701 702 703 704 and 705 represent
the same items as those indicated in FIG. 3. The angle correcting
circuit 730 is the same as that indicated in FIG. 9 and effects
the correction operation explained, referring to FIGS. 10A and 10B.
However, for calculating the correction values not .DELTA..theta..sub.T
but .DELTA..theta..sub.A read out from the memory 703 is used.
By using the average phase difference calculating circuit indicated
in FIG. 9 or 11 since errors in the high speed region by the phase
difference averaging method are corrected, a blood flow speed measurement
having small errors can be effected in a wide speed region. Further,
by the auto-correlation method or the 2-axial-component method,
when the number of phase difference detection values used for the
average phase difference calculation is N, the improvement in the
signal to noise ratio is .sqroot.N times, whereas by the phase difference
averaging method it is N/.sqroot.2 times. Consequently blood flow
measurement of lower noise is possible.
FIG. 12 shows still another embodiment of this invention and indicates
the parts replacing those indicated by the reference numerals 4
5 6 7 and 8 in FIG. 1. The phase comparator 4 and the A/D converter
5 are identical to those indicated in FIG. 1. An MTI filter 6-1
obtains a phase vector V.sub.n expressed by ##EQU21## in which the
signals from the fixed substance is removed, by using the difference
between the Doppler signal V'.sub.n obtained at current time point
and the Doppler signal obtained at the time preceding by one time
period, i.e. preceding the Doppler signal V'.sub.n by a transmission
interval T. Reference numerals 701-1 702-1 and 703-1 indicate items
identical to those indicated by 701 702 and 703 in FIG. 6 respectively,
and in this way the average phase difference .DELTA..theta..sub.A
by the auto-correlation method can be obtained.
On the other hand an MTI filter 6-2 calculates a phase vector V.sub.n
expressed by;
by using the difference between the Doppler signal V'.sub.n obtained
at current time point and the Doppler signal V'.sub.n-1 obtained
at the time preceding by two time periods, i.e. preceding the Doppler
signal V'.sub.n by 2T.
An auto-correlation 701-2 calculates a complex product X.sub.n
of a phase vector U.sub.n at current time point by the conjugate
complex vector U.sub.n-2 * of the phase vector U.sub.n-2 preceding
it by two periods among the phase vectors obtained one after another
with a period T. X.sub.n is indicated as follows.
An adder 702-2 adds N-1 vectors X.sub.n, going back from current
time point to obtain a sum vector. The result of the calculation
can be expressed by: ##EQU22##
When the real part R' and the imaginary part I' of this sum vector
is given to an angle detecting memory 703-2 as addresses, the argument
.DELTA..theta..sub.A of this sum vector expressed by the following
equation is read out; ##EQU23##
.DELTA..theta..sub.A obtained by the ATAN memory 703-1 stated above
is a phase difference obtained by the correlation with the interval
T of the phase vectors sampled successively with the interval T
and corresponds to the Doppler phase shift during the time parameter
T. Further .DELTA..theta..sub.A ' obtained by the angle detecting
memory 703-2 is a phase difference obtained by the correlation with
the interval 2T of the phase vectors stated above and corresponds
to the Doppler phase shift during the time parameter 2T. Consequently
Doppler frequences .omega..sub.d and .omega..sub.d ' are obtained
by the following operations by dividers 8-1 and 8-2 respectively;
##EQU24##
Now, when the frequency characteristics of the MTI filters 6-1
and 6-2 are compared with each other, it can be seen that the transfer
gain of the MTI filter 602 is greater than that of the MTI filter
6-1 in the low speed region, as indicated in FIG. 13. Further, since
the phase difference indicated by the argument of the output X.sub.n
of the auto-correlator 701-2 is twice as great as that of the output
Y.sub.n of the auto-correlator 701-1 for a same blood flow speed,
.omega..sub.d ' is measured with a higher precision than .omega..sub.d.
However the measurement limit is .+-..pi./T for .omega..sub.d and
.+-..pi./2T for .omega..sub.d '. Therefore a discriminator compares
the absolute value .vertline..DELTA..theta..sub.A .vertline. of
.DELTA..theta..sub.A with a threshold value .theta..sub.k and if
.vertline..DELTA..theta..sub.A .vertline.<.theta..sub.k, it selects
.omega..sub.d '. On the other hand, if .vertline..DELTA..theta..sub.A
.vertline..gtoreq..theta..sub.k, it selects .omega..sub.d to output
it to a display as a measured value for the blood flow velocity.
It is desirable that the value of .theta..sub.k is equal to or slightly
smaller than .pi./2.
FIG. 14 shows still another embodiment. The construction of the
parts indicated by 6-1 6-2 701-1 701-2 702-1 702-2 703-1 and
703-2 are completely identical to the corresponding parts in FIG.
12. That is, the average value .DELTA..theta..sub.A of the phase
difference corresponding to the time parameter T is obtained from
the angle detector 703-1 and the average value .DELTA..theta.'.sub.A
of the phase difference corresponding to the time parameter 2T is
obtained from the angle detector 703-2. The output .DELTA..theta..sub.A
is used not for obtaining the Doppler frequency, but for correcting
ambiguity corrections of the value of .DELTA..theta.'.sub.A in the
high speed region. That is, a quadrant discriminator 14 judges,
in which quadrant the value of .DELTA..theta..sub.A is, .vertline..DELTA..theta..sub.A
.vertline..ltoreq..theta..sub.L1 .theta..sub.L2 >.DELTA..theta..sub.A
>.theta..sub.L1 -.theta..sub.L2 <.DELTA..theta..sub.A <-.theta..sub.L1
; or .vertline..DELTA..theta..sub.A .vertline..gtoreq..theta..sub.L2.
Where, .theta..sub.L1 equal .pi./2 and .theta..sub.L2 is a threshold
angle at which the spectral characteristics of MTI filter 6-1 is
a little higher than that of MTI filter 6-2. Typically, .theta..sub.L2
is about 3.pi./4 at which the spectral characteristics of MTI filter
6-1 is 3 dB higher than that of MTI filter 6-2. An angle corrector
15 uses the judgement result of the quadrant discriminator 14 to
correct the value of .DELTA..theta.'.sub.A as follows: ##EQU25##
A divider 802 uses the average phase difference .DELTA..theta.".sub.A
corrected, depending on the value of .DELTA..theta..sub.A as described
above, to obtain the Doppler frequency .omega..sub.d, using the
following equation: ##EQU26##
As described above, in FIG. 12 or 14 errors by the auto-correlation
method in the low speed region are reduced by combining the average
phase difference detection by the auto-correlation method using
the time parameter T with the average phase difference detection
using the time parameter 2T. Generally the time parameters not T
and 2T but T and nT (n being an integer not smaller than 2) may
be combined. At this time, by the method indicated in FIG. 12 the
threshold value .theta..sub.k used for the discrimination may be
equal to or slightly smaller than .pi./n. On the other hand, by
the method indicated in FIG. 14 the threshold angle .theta..sub.L1
in Eq. (26) becomes .pi./n and the threshold angle .theta..sub.L2
becomes about 3.pi./2n. It is possible further to reduce errors
to a lower speed region by combining more than 2 time parameters
such as T, 2T and 4T, etc. Further, the MTI filters 6-1 and 6-2
in FIGS. 12 and 14 may be constructed, unified in one MTI filter
6-3 as indicated in FIG. 15. That is, delaying elements 65 and
66 each of which has a delay time T, are connected in cascade and
the Doppler signal V.sub.n ' is inputted through the input thereof.
A subtracting element 67 forms the difference between the value
on the input side and that on the output side of the delaying element
65 to obtain the phase vector V.sub.n expressed by Eq. (19). On
the other hand another subtracting element 68 forms the difference
between the value on the input side of the delaying element 65 and
the value on the output side of the delaying element 66 to obtain
the phase vector U.sub.n expressed by Eq. (20). |