Image processing system and method for estimating acoustic property of a movable sound source

An image processing system for estimating acoustic properties emitted from a movable sound source on a point in the sound field thereof comprises photoelectric sensors 11 and 12 for measuring a velocity and a moving direction of the sound source; a microphone array 13 for detecting an acoustic energy from the sound source on a detection surface at plural points having an interval smaller than one half of the wave length of the acoustic property, the microphone array 13 moved in a direction perpendicular to the detection surface; a multiplexer 14 for multiplexing signals inputted from the photoelectric sensors 11 and 12 and the microphone array 13 through a single output line, wherein the signals represent a value of the acoustic energy, a velocity and a moving direction of the sound source, and a velocity and a moving direction of the microphone array 13, respectively; and a personal computer 15 for setting relative coordinate systems comprising a hologram coordinate system and a detective coordinate system, in which the hologram coordinate system is moved in the velocity and the direction same with those of the sound source, and the relative coordinate system is moved in the velocity and the direction same with those of the microphone array 13, and in which in order to estimate a value of the acoustic property on a point in the sound field, the personal computer 15 carries out Fourier transform of data relating to the microphone array 13 in the detective coordinate system by a time factor.

TECHNICAL FIELD 
This invention relates to an image processing system for estimating 
acoustic property of a sound source using a hologram in a surface to show 
a position and radiation properties of the sound source, more 
particularly, to the image processing system to be able to detect and 
disclose a position and radiation properties of a static or movable sound 
source by only a few microphones. This invention also relates to an image 
processing method for estimating acoustic property of a sound source by 
the image processing system. 
BACKGROUND ART 
Holography that obtains an information concerning to a sound source from a 
hologram of sound pressure emitted from the sound source and measured on a 
reference surface in the sound field of the sound source. It has been 
broadly uesed in civilian and munition industries. Informations to be 
obtained from the hologram may comprise a farfield directivity 
information, a nearfield vector intensity information, a surface velocity 
information, a total sound power information and so forth. 
More particularly, the holography may be applied in an apparatus for 
finding out the enemy's soldiers in the munition industry. In a civilian 
industry, for example, it is applied to detect a sound source and then to 
eliminate the sound source or to build a soundproofing wall. Nowadays, 
growing demand to life environmental protection results in increasing a 
need for appropriately coping with any bothersome noise. 
Studies of holography which are remarkably related to this invention are as 
follows: "Nearfield acoustic holography (NAH)-1. Theory of generalized 
holography and the development of NAH by J. D. Maynard, E. G. Williams and 
Y. Lee, disclosed in Journal of the Acoustical Society of America, Vol. 
74, No. 4, pp1395-1413; "Nearfield acoustic holography (NAH)-2". 
Holographic reconstruction algorithms and computer implementation" by W. 
A. Veronesi and J. D. Maynard, disclosed in Journal of the Acoustical 
Society of America, Vol. 81, No. 5, pp1307-1322; U.S. Pat. No. 4,415,996 
entitled "Nonwavelength-limited holographic sound field reconstruction" by 
J. D. Maynard and E. G. Williams; "Method of Spatial Transformation of 
Sound Fields--a unique technique for scan-based near-field acoustic 
holography without restrictions on coherence" by J. Hald, disclosed in 
Technical Review No 1, 1989, B&K publication; and "Broadband acoustic 
holography reconstruction from acoustic intensity measurement" by Loyau, 
J. C. Pascal and P. Gaillard, disclosed in Journal of the Acoustical 
Society of America, Vol. 84, No. 5, pp1744-1750. 
In holography, a hologram is obtained on a reference surface that is so 
called "a hologram surface" and then the hologram is analized to estimate 
an acoustic property on any point in the environmental space. The hologram 
surface may be a plane or a cylindrical surface. In shape of the hologram 
surface, it is discriminated into a planar acoustic holography, a 
cylindrical acoustic holography and spherical acoustic holography. 
In the planar acoustic holography, it is needed theoretically to measure 
sound pressure on an infite number of points in order to obtain a hologram 
showing distribution of the sound pressure on an infinitely great plane. 
In practice, however, a hologram is obtained by measuring sound pressure 
on a limited number of points considering time and cost taken in 
measurement. 
Accuracy of the hologram is affected by density of measuring points, i.e., 
distance between adjacent measuring points. Accuracy of the hologram is 
inversely proportionated to the distance. Low accuracy of the hologram 
results in deteriorating accuracy of an estimated sound pressure in the 
sound field. Therefore, it is needed to provide technics for obtaining a 
highly accurate hologram while decreasing time and cost taken in 
measurement. 
In U.S. Pat. No. 4,415,996 by W. A. Veronesi and J. D. Maynard, based on 
the thesis of "Nearfield acoustic holography (NAH)-2. Holographic 
reconstruction algorithms and computer implementation" disclosed in 
Journal of the Acoustical Society of America, Vol. 81, No. 5, pp1307-1322, 
"Nonwavelength-limited holographic sound field reconstruction" is 
described, in which a hologram is obtained by a microphone array 
comprising microphones on matrix positions of 16 rows by 16 lines. In this 
method, very highly cost has to be taken, because of the number of 
microphones up to 256. 
In the thesises of "Method of Spatial Transformation of Sound Fields--a 
unique technique for scan-based near-field acoustic holography without 
restrictions on coherence" by J. Hald, disclosed in Technical Review No 1, 
1989, B&K publication, and "Broadband acoustic holography reconstruction 
from acoustic intensity measurement" by Loyau, J. C. Pascal and P. 
Gaillard, disclosed in Journal of the Acoustical Society of America, Vol. 
84, No. 5, pp1744-1750, there are described methods for measuring sound 
pressure in turn on plural points by a set of microphones fewer than the 
number of measurement positions. One of problems in these methods is that 
in order to measure sound pressure on each measurement position, a 
microphone has to be stayed on the position for a given time. 
Aforementioned measuring methods have a basic limitation that accurate 
measurement of sound pressure is able to only the time when a microphone 
is stayed on a measurement position since there is no consideration about 
any relative motion between the microphone and the sound source. That is, 
it is not able to measure for a movable sound source. In measurement for a 
static sound source, scanning method in which sound pressure is measured 
during movement of the microphone. 
SUMMARY OF INVENTION 
Therefore, one of objectives of this invention is that provides technics 
for measuring sound pressure with a microphone moved on a hologram surface 
so that very accurate hologram can be obtained for a shot time using fewer 
microphones with no relation to movability of a sound source. 
According to the invention for achieving the objectives, there is provided 
an image processing system for estimating acoustic properties emitted from 
a movable sound source on a point in the sound field thereof, the sound 
source radiating an acoustic energy into the enviromental space, in which 
a value of an acoustic property is estimated by a hologram of the acoustic 
property in a hologram surface keeping pace with the sound source. The 
image processing system comprises means for measuring a velocity and a 
moving direction of the sound source. The image processing system also 
comprises means for detecting an acoustic energy from the sound source on 
a detection surface at plural points having an interval smaller than one 
half of the wave length .lambda. of the acoustic property. The detecting 
means is moved in a direction perpendicular to the detection surface. The 
image processing system comprises means for multiplexing signals inputted 
from the measuring means and the detecting means through a single output 
line. The signals represent a value of the acoustic energy, a velocity and 
a moving direction of the sound source, and a velocity and a moving 
direction of the detecting means, respectively. Moreover, the image 
processing system comprises an operator for setting relative coordinate 
systems comprising a hologram coordinate system and a detective coordinate 
system. The hologram coordinate system is moved in the velocity and the 
direction same with those of the sound source, and the relative coordinate 
system is moved in the velocity and the direction same with those of the 
detecting means. In order to estimate a value of the acoustic property on 
a point in the sound field, the operator carries out Fourier transform of 
data relating to the detecting means in the detective coordinate system by 
a time factor using Equation 7 as follows: 
##EQU1## 
in which F.sub.T represents a Fourier transform function, p.sub.hol 
represents a value of an acoustic property including a time factor in the 
detective coordinate system, u represents a relative velocity of the 
detective coordinate system to the hologram coordinate system, z.sub.H 
represents a Z-axis coordinate of the hologram surface in the hologram 
coordinate system, t represents a time, P.sub.hol represents a value of 
acoustic property including a frequency factor by a number of waves 
measured in the hologram coordinate system, P.sub.hol.sup.* represents a 
conjugate complex number of P.sub.hol, f represents a frequency factor, 
and f.sub.i represents an individual frequency factor for each hologram. 
In the image processing system for estimating sound pressure emitted from a 
movable sound source on a point in the sound field thereof, the measuring 
means may comprise at least two photoelectric sensors. The detecting means 
may comprise a microphone array for detecting a sound pressure from the 
sound source and for generating an electric signal corresponding to the 
sound pressure. The multiplexing means may comprise mulitiplexer for 
outputting plural signals through only a single line, in which the 
outputted signals include signals relating to a velocity and a moving 
direction of the microphone array and the sound source and an electric 
signal emitted from the microphone array. Furthermore, the operator may 
comprise a personal computer for estimating a value of the sound pressure 
on a point in the sound field using a value of the sound pressure detected 
by the microphone array. Preferably, the microphone array has sixteen 
microphones disposed in an interval along with a line perpendicular to the 
moving direction of the microphone array. In operation, the personal 
computer setes relative coordinate systems comprising a hologram 
coordinate system and a detective coordinate system, in which the hologram 
coordinate system is moved in the velocity and the direction same with 
those of the sound source, and the relative coordinate system is moved in 
the velocity and the direction same with those of the microphone array. 
The personal computer also carries out Fourier transform of data relating 
to the microphone array in the detective coordinate system by a time 
factor using Equation 7 as abovementioned. 
According to the invention, there is also provided an image processing 
method for estimating acoustic properties emitted from a movable sound 
source on a point in the sound field thereof, the sound source radiating 
an acoustic energy into the enviromental space, in which a value of an 
acoustic property is estimated by a hologram of the acoustic property in a 
hologram surface keeping pace with the sound source. The image processing 
method comprise steps for inputting initial data to an operator, in which 
the initial data comprises data of initial positions of the sound source 
and a detecting means; for setting relative coordinate systems comprising 
a hologram coordinate system having the orign disposed on the initial 
position of the sound source and a detective coordinate system; and for 
estimating a value of the acoustic property on a point in the sound field 
by carrying out Fourier transform of data relating to the detecting means 
in the detective coordinate system by a time factor using Equation 7 as 
abovementioned. 
In the image processing method for estimating sound pressure emitted from a 
movable sound source on a point in the sound field thereof, the detecting 
means may comprise a microphone array. In this method, the initial data 
inputted in the inputting step may comprise data of the initial position 
of the sound source detected by photoelectric sensors and data of an 
initial position of the microphone array. The setting step and the 
estimating step may be carried out by a personal computer.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
Hereinafter, an embodiment of an image processing system used for a movable 
sound source according to an embodiment of this invention will be 
specifically described referring to the drawings. 
The image processing system 10 showed FIG. 1 can be used in image 
processing to estimate sound pressure emitted from a movable sound source 
on a point in the sound field thereof. A value of the sound pressure is 
estimated by a hologram of the sound pressure in a hologram surface 22 
keeping pace with the sound source. 
The image processing system 10 according to this embodiment comprises at 
least two photoelectric sensors 11 and 12 as means for measuring speed and 
direction of the sound source. The image processing system 10 also 
comprises a microphone array 13 for receiving sound pressure from the 
sound source and for generating an electric signal corresponding to the 
sound pressure. A mulitiplexer 14 is provided to output plural signals 
through only a single line. The signals include signals relating to a 
velocity and a moving direction of the microphone array 13, signals 
relating to a velocity and a moving direction of the sound source, and an 
electric signal emitted from the microphone array 13. A personal computer 
15 is used as a operator for estimating a value of the sound pressure on a 
point in the sound field using a value of the sound pressure received by 
the microphone array. 
In this embodiment, the microphone array 13 has sixteen microphones 13A 
disposed in an interval "d" along with a line perpendicular to the moving 
direction of the microphone array 13. 
As showed in FIG. 2, the personal computer 15 is controlled to set relative 
coordinate systems comprising a hologram coordinate system C.sub.hol and a 
detective coordinate system C.sub.mic, in which the hologram coordinate 
system C.sub.hol is moved in the velocity and the direction same with 
those of the sound source, and the relative coordinate system C.sub.mic is 
moved in the velocity and the direction same with those of the microphone 
array 13. The personal computer 15 also carries out Fourier transform of 
data relating to the microphone array 13 in the detective coordinate 
system C.sub.mic by a time factor using Equation 7 as follows. 
##EQU2## 
in which F.sub.T represents a Fourier transform function, p.sub.hol 
represents a value of an sound pressure including a time factor in the 
detective coordinate system C.sub.mic, u represents a relative velocity of 
the detective coordinate system C.sub.mic to the hologram coordinate 
system C.sub.hol, z.sub.H represents a Z-axis coordinate of the hologram 
surface 22 in the hologram coordinate system C.sub.hol, t represents a 
time, P.sub.hol represents a value of sound pressure including a frequency 
factor by a number of waves measured in the hologram coordinate system 
C.sub.hol, P.sub.hol.sup.* represents a conjugate complex number of 
P.sub.hol, f represents a frequency factor, and f.sub.i represents an 
individual frequency factor for each hologram. 
Examples of hologram of acoustic intencity, e.g., sound pressure estimated 
by the personal computer 15 are showed in FIGS. 3 and 4. FIGS. 3 and 4 
show sound pressure and acoustic intencity estimated at a side of the car. 
The hologram can be displayed by a displayer, e.g., a monitor or a printer 
connected to the personal computer 15. In this embodiment, a 32 channel 
signal analyzer. 
Now, it will be described how an estimated sound pressure p.sub.hol in the 
hologram coordinate system C.sub.hol is Fourier-transformed from a 
measured sound pressure p.sub.mic in the detective coordinate system 
C.sub.mic. In the relative coordinate systems and the absolute coordinate 
system set by the personal computer 15, sound pressure can be represented 
as follows. 
(A) Sound pressure in the absolute coordinate system; 
p(x, y, z; t) 
(B) Sound pressure in the detective coordinate system; 
p.sub.mic (x.sub.m, y.sub.m, z.sub.m ; t) 
(C) Sound pressure in the hologram coordinate system; 
p.sub.hol (x.sub.h, y.sub.h, z.sub.h ; t) 
In assumption of that at the time of t=0, all of the coordinate systems 
have a same position and attitude with each other, and that between the 
coordinate systems, only a relative motion along X-axis direction is 
existed, and Y-coordinates and Z-coordinates in all of the coordinate 
systems correspond with each other. That is, there are relations of 
y=y.sub.m =y.sub.h and z=z.sub.m =z.sub.h. Sound pressure measured by the 
microphone array 13 disposed at the position of x.sub.m =0 in the hologram 
surface (z=z.sub.H) can be represented by Equation 1. 
Equation 1 
EQU p.sub.mic (0, y, z.sub.H ; t)=p.sub.hol (ut, y, z.sub.H ; t) 
in which u means a relative speed of the detective coordinate system 
C.sub.mic to the hologram coordinate system C.sub.hol. 
A coordinate of the sound pressure measured by the microphone array 13 is 
transformed to a coordinate in the hologram coordinate system C.sub.hol 
and in turn the transformed coordinate is used to estimate sound pressure 
in the sound field. 
A hologram that means a map of distribution with frequency in a space can 
be obtained by Fourier-transforming a sound pressure signal in each 
measurement point with time. Therefore, Equation 2 and Equation 3 can be 
obtained. 
##EQU3## 
For a sound pressure affected by the relative motion, a distance factor x 
includes a component of a time factor t. Therefore, a sound pressure for 
the hologram can not be directly calculated by Fourier transform with time 
using Equation 2 or Equation 3. For such a case, Equation 4 can be used. 
##EQU4## 
in which the right term 
##EQU5## 
means a spectrum of wave number which is obtained by Fourier transform of 
the hologram in three dimensions. 
The spectrum of wave number has a relation with the hologram that meets 
Equation 5 and Equation 6. 
##EQU6## 
In Fourier transform of the measured sound pressure signal, the spectrum of 
wave number for each frequency f.sub.h forms a zone around the associated 
frequency f.sub.h. Therefore, a hologram for a frequency can be obtained 
by separating a spectrum of wave number for the associated frequency and 
then carrying out inverse Fourier transform of the spectrum. 
For separating the spectrum exactly, spectrums for adjacent frequencies 
shall not be overlapped on each other. That is, the zone of the spectrum 
has to be narrower than an interval of adjacent frequencies. Therefore, it 
is noticed that acoustic signals emitted from the sound source shall not 
comprise any zoned frequency, but only independent component frequencies. 
A sound pressure signal measured in the sound field in which pure sound 
components by the number of / are emitted from the sound source can be 
Fourier transformed with Equation 7. 
##EQU7## 
in which F.sub.T represents a Fourier transform function, p.sub.hol 
represents a value of an sound pressure including a time factor in the 
detective coordinate system, u represents a relative velocity of the 
detective coordinate system to the hologram coordinate system, z.sub.H 
represents a Z-axis coordinate of the hologram surface in the hologram 
coordinate system, t represents a time, P.sub.hol represents a value of 
sound pressure including a frequency factor by a number of waves measured 
in the hologram coordinate system, P.sub.hol.sup.* represents a conjugate 
complex number of P.sub.hol, f represents a frequency factor, and f.sub.i 
represents an individual frequency factor for each hologram. 
As showed in FIG. 5, a method for obtaining a hologram P.sub.hol (ut, y, 
z.sub.H ; f.sub.0) comprises STEP 1 for measuring a sound pressure signal 
p.sub.mic (0, y, z.sub.H ; t)=p.sub.hol (ut, y, z.sub.H ; t) for each 
frequency and for Fourier transforming the signal, STEP 2 for filtering 
the transformed signal, STEP 3 for demodulating the filtered signal, and 
STEP 4 for inverse Fourier transforming the demodulated signal. Relation 
between the frequency and the wave number meets Equation 8. 
##EQU8## 
Using Equation 8, a condition for interval between adjacent frequencies 
against a given size of the zone of tne spectrum can be obtained. 
Under the planar acoustic holography, interval between adjacent measurement 
points shall be smaller than on half of the wave length .lambda.. In this 
embodiment, the interval was set to be quarter of the wave length 
.lambda.. Firstly, the relative velocity u of the detective coordinate 
system to the hologram coordinate system was set to meet Equation 9 in 
which M means Mach number u/c. 
Equation 9 
EQU M&lt;0.5 
Interval between adjacent frequencies is calculated with Equation 10. 
##EQU9## 
From Equation 10, f.sub.i+1 is always larger than f.sub.i apparently. Since 
in general practice, the relative speed u is very smaller than the speed 
of sound c, the condition with Equation 10 can be easily met. 
Referring to FIGS. 6, 7 and 8a to 8d, there is exemplified a test using the 
image processing system according to this embodiment and the method as 
above mentioned, in which estimation of sound pressure of a sound source 
by a computer under the condition of the relative speed u=3.4 m/sec 
(M=0.01) is simulated. In the test, a value of sound pressure is 
calculated by sound pressure signals measured at measuring points on a 
hologram surface 22 at the distance of 0.3 m from a sound source plane 
including four in-frequency sound sources combined from a single-polarity 
sound source and a double-polarity sound source. FIG. 6 shows a graph for 
illustrating intensity of sound pressure with time and FIG. 7 shows a 
spectrum transformed from a signal of sound pressure in estimation by the 
image processing system showed in FIG. 1. Furthermore, FIG. 8a shows 
spectrum of wave number around the frequency of 340 Hz, FIG. 8b shows 
spectrum of wave number around the frequency of 390 Hz, FIG. 8c shows 
spectrum of wave number around the frequency of 680 Hz and FIG. 8d shows 
spectrum of wave number around the frequency of 440 Hz. As showed in FIGS. 
8a to 8d, each spectrum of wave number with frequency is represented to be 
a narrowed zone. Moreover, a inherent hologram of sound source will be 
seen from a consideration of the spectrums. 
Now, there is exemplified a method for obtaining a hologram for a moving 
sound source using the image processing system according to this 
embodiment. 
A speaker that is mounted on a front window of a car on moving in the speed 
of 8.024 m/sec (28.9 Km/sec) and emits a monotone sound of 700 Hz was used 
as a moving sound source. The microphone array 13 was arranged in a plane 
spaced from a side of the car by the distance of 62 cm. After obtaining a 
hologram from sound pressure signals measured by the microphone array 13, 
a value of sound pressure in the sound field was calculated using the 
measured sound pressure signals. A linear microphone array used for the 
microphone array 13 of the measuring means 10 had sixteen microphones 
comprising a first lowest microphone disposed at the height of 5 cm and 
other fifteen microphones spaced from each next microphone by the height 
of 10 cm. The photoelectric sensors 11 and 12 were disposed respectively 
at the right and the left of the microphone array 13 and spaced from the 
microphone array 13 by the distance of 3 m in the direction of X-axis. For 
the multiplexer 14, a 32-channel signal analyzer was used. In FIGS. 3 and 
4, the acoustic property measured by the system and the method for image 
processing, that is, sound pressure and acoustic intensity are showed 
respectively. As seen from FIGS. 3 and 4, the hologram obtained by the 
image processing system according to this embodiment includes useful 
information relating to acoustic properties, i.e., sound pressure or 
acoustic intensity. 
The aforementioned embodiment was described only for exemplifying not for 
limiting this invention. To a person skilled in this technical field, it 
may be apparent that any alteration, modification or change from the above 
preferred embodiment can be carried out without departing from the 
inventive idea. Although the method for obtaining a planar hologram in the 
above embodiment, this invention is not limited to the case of the planar 
hologram. Using a cylindrical microphone array on moving linearly in 
relation to the sound source, a cylindrical hologram may be obtained. 
Therefore, this invention has to be fully protected within the attached 
claims that aim to include any change, alteration or modification without 
departing from the inventive idea.