Phase and/or amplitude aberration correction for imaging

Disclosed is a pulse-echo array imaging system which includes a conventional imaging mode and an aberration-measurement mode. When the system is switched to the aberration mode, several algorithms disclosed in the present invention are used to measure transmission and reception phase- and amplitude-aberration profiles. The measured transmission and reception aberration profiles are then used for aberration corrections for transmission and reception respectively in the conventional imaging mode. Disclosed are phase- and amplitude-aberration correction algorithms using near-field signal redundancy. It applies dynamic near-field correction on common-midpoint signals before the cross-correlation function between them is calculated. Also disclosed are phase- and amplitude-aberration measurement algorithms for measuring and correcting different transmission and reception aberration profiles. Further disclosed are phase- and amplitude-aberration correction algorithms using common-midpoint signals collected with sub-arrays to measure angle-dependent aberration profiles. Also disclosed are methods for implementing the phase- and amplitude-aberration correction algorithms disclosed in the present invention on a two-dimensional array. Further disclosed is a method for the simultaneous collection of common-midpoint signals to reduce the effect of tissue motion on the aberration-measurement accuracy. Other methods and algorithms for improving the measurement accuracy and reducing the measurement time are also disclosed.

FIELD OF THE INVENTION 
This invention relates to coherent imaging systems such as ultrasound 
pulse-echo imaging systems. More particularly, it relates to methods for 
phase and amplitude aberration corrections to improve image quality. It 
can also be used for measurement accuracy improvement in media, such as 
attenuation, velocity, and blood flow velocity. 
BACKGROUND OF THE INVENTION 
The ultrasound pulse-echo technique (echography) is widely used in medical 
imaging. This imaging method currently uses an array of transducer 
elements to transmit a focused beam into the body, and each element then 
becomes a receiver to collect the echoes. The received echoes from each 
element are dynamically focused to form an image. Focusing on transmission 
and reception is performed assuming that the velocity inside the body is 
uniform, and is usually assumed to be 1540 m/s. Unfortunately, the 
velocity inside the body is not constant; it varies from 1470 ms.sup.-1 in 
fat to greater than 1600 ms.sup.-1 in some other tissues, such as 
collagen. This variation will result in increased side lobes and degraded 
lateral resolution. It is one of the major difficulties for improving 
lateral resolution of ultrasound imaging system. Phase aberration caused 
by velocity variation also influence the accuracy of many other 
measurements, such as attenuation and blood flow velocity. Amplitude 
aberrations have also been observed and reported in many works in 
ultrasound medical imaging, especially for imaging some complex tissue 
structures like female breast. Amplitude aberrations also influence the 
quality of images, even though they are not as important as phase 
aberrations. In some cases, both amplitude and phase aberration 
corrections are needed to form a good image. 
Many methods have been developed to correct aberrations. These prior art 
methods are reviewed below. 
One type of prior art method uses the wavefront from a special target, such 
as a dominant point target or a specular reflecting plane, to measure the 
phase-aberration profile. In astronomical imaging, 
direct-wavefront-measurement method is used to measure phase and amplitude 
aberrations caused by the atmosphere (R. K. Tyson, "Principle of adaptive 
optics," Academic Press, ch. 5, 1991). In medical ultrasound imaging, the 
nearest neighbor cross-correlation algorithm (S. W. Flax and M. O'Donnell, 
"Phase-aberration correction using signals from point reflectors and 
diffused scatterers: basic principles," IEEE Trans. Ultrason., 
Ferroelect., Freq. Cont., vol. 35, no. 6, pp. 758-767, November 1988, and 
U.S. Pat. No. 4,989,143 by O'Donnell) and the maximum-sharpness algorithm 
(L. Nock, and G. E. Trahey, "Phase aberration correction in medical 
ultrasound using speckle brightness as a quality factor," J. Acoust. Soc. 
Am., vol. 85, no. 5, pp. 1819-1833, May 1989) can be used when there is a 
dominant point target. 
The nearest-neighbor cross-correlation and maximum sharpness algorithms can 
also uses echoes from randomly distributed scatterers that generate 
speckle in an image to measure the phase-aberrations. In the 
nearest-neighbor cross-correlation method, a focused beam is transmitted 
and the phase-aberration profile is derived from the cross-correlation 
measurements between neighboring elements. An iterative method is used to 
improve the measurement accuracy. The maximum sharpness an iterative 
phase-correction procedure in which the timing of acoustic signals 
transmitted and received from individual elements is adjusted to optimize 
the quality indicator. 
Prior art methods which uses the principle of the nearest-neighbor 
cross-correlation algorithm include U.S. Pat. No. 4,471,785 by Wilson et 
al., U.S. Pat. No. 4,817,614 by Hassler et al., U.S. Pat. No.5,184,623 by 
Mallart, 5,172,343 by O'Donnell, U.S. Pat. No. 5,388,461 by Rigby, U.S. 
Pat. No.5,487,306 and 5,531,117 by Fortes, U.S. Pat. Nos.5,423,318 and 
5,566,675 by Li et al. 
Prior art methods which uses the principle of the maximum sharpness 
algorithm include U.S. Pat. No.4,852,577 by Smith et al., U.S. Pat. No. 
5,331,964 by Trahey et al., and U.S. Pat. No.5,423,318 by Green. 
The Translating Apertures algorithm (W. F. Walker and G. E. Trahey, 
"Speckle coherence and implications for adaptive imaging," J. Acoust. Soc. 
Am., vol. 101, no. 4, pp. 1847-1858, April 1997 and U.S. Pat. No. 
5,673,699 by Trahey et al) is a modification of the nearest neighbor 
cross-correlation algorithm. It uses identical effective apertures to 
collect near-neighbor signals. 
The differences between the near-field signal redundancy algorithm 
described in the present invention, the nearest-neighbor cross-correlation 
algorithm, and the translating apertures algorithm have been discussed in 
Yue Li and Robert Gill, "a comparison of matched signals used in three 
different phase-aberration correction algorithms" 1998 IEEE International 
Ultrasonics Symposium. One of the differences between the nearest-neighbor 
cross-correlation algorithm and the algorithm in present invention is 
that, non-common midpoint signals are included in matched signals 
collected with the nearest-neighbor cross-correlation algorithm, but they 
are not included in the matched signals collected with the algorithm 
described in the present invention. This results in increased similarity 
between matched signals. The translating apertures algorithm is also 
different from the near-field signal redundancy algorithm described in the 
present invention. One of the major differences is that reciprocal signals 
are always included in matched signals collected with the translating 
apertures algorithm, but they are not included in the algorithm described 
in the present invention. It is a disadvantage to include the reciprocal 
signals in matched signals, since reciprocal signals are not sensitive to 
phase aberrations. When phase-aberrations exist they decrease the 
similarity between matched signals and reduce the measurement accuracy. 
A method using the signal-redundancy principle to measure the 
phase-aberration profile has been developed (D. Rachlin, "Direct 
estimation of aberration delays in pulse-echo image systems," J. Acoust. 
Soc. Am. vol. 88, no. 1, pp. 191-198, July 1990 and U.S. Pat. No.5,268,876 
by Rachlin). Since signal redundancy principle is an approximation for 
targets in the near field, common-midpoint signals are not identical for 
targets in the near field. Additional signal processing is required to 
make it work properly for targets in the near field. In the theoretical 
analysis, Rachlin has assumed that targets are small and compact (Col. 3, 
lines 8) located at the focal point so that far field analysis can be 
used, and proposed to use the whole aperture for transmission in the 
algorithm to allow extended target distribution (Col. 6, lines 53), and as 
a result, solving the near-field problem. One disadvantage of transmitting 
from the whole aperture is that the transmitted beam will be distorted by 
phase aberrations and it will influence the measurement accuracy. Another 
disadvantage of transmitting from the whole aperture is that the far-field 
approximation is only valid in a small depth range around the focal point 
(if the focus is not already distorted by phase aberrations), therefore 
only a short signal length can be used for the measurement. The near-field 
signal redundancy algorithm described in the present invention uses a 
different method to solve the near-field problem. A technique of dynamic 
near-field correction applied on common-midpoint signals is proposed to 
make common-midpoint signals become more similar for targets in the near 
field. It allows a long period of signals be used for the measurement to 
increase measurement accuracy. Using small apertures for transmission will 
reduce the influence of aberration on the measurement accuracy. Other 
near-field signal redundancy algorithms described in the present invention 
which are not included in Rachlin's method are: the sub-array technique 
for collecting common-midpoint signals, near-field signal redundancy 
algorithms for measuring phase aberrations when the transmission and 
reception aberration profiles are different, near-field signal redundancy 
algorithms for two-dimensional arrays, near-field signal redundancy 
algorithms for amplitude-aberration corrections etc. 
Common-midpoint signals are also used for aberration measurement in seismic 
imaging (O. Yilmaz, "Seismic data processing," Society of Exploration 
Geophysicists, ch. 3, 1987). It uses echoes from a specular reflecting 
plane which is a special kind of target. The common midpoint signals are 
not redundant when there is a specular reflecting plane in the near field, 
because the position of the reflecting point is different for different 
transmitter or receiver positions. Therefore, the seismic method is not a 
signal-redundancy method and is fundamentally different from the method 
proposed in this invention. 
SUMMARY OF THE INVENTION 
One of the main objects of this invention is to provide a better algorithm 
and apparatus for phase-aberration measurements in pulse-echo imaging 
systems. 
To achieve this object, a near-field signal redundancy algorithm is 
disclosed in this invention. This method comprises collecting 
common-midpoint signals by transmitting from one element at a time and 
receiving at a plural number of elements until all elements have 
transmitted. These common-midpoint signals are dynamically corrected to 
increase the similarity between them for echoes from targets in the near 
field. Corrected common-midpoint signals are then cross-correlated with 
one another and the peak positions and values of these normalized 
cross-correlation functions are measured. The phase-aberration profile is 
derived from a process of weight and adding from the measured peak 
positions of the cross-correlation functions. When necessary, the 
undetermined linear terms are adjusted iteratively to maximize the image 
energy in the region of interest, which will optimize the performance of 
the system. 
Another main object of this invention is to provide algorithms for 
measuring and correcting phase-aberration profiles when the transmission 
and reception phase-aberration profiles are different. 
To achieve this object, two different methods are disclosed. The first 
method can be used if the difference between transmission and reception 
phase-aberration profiles is acceptable for image-formation purposes but 
unacceptable for phase-aberration measurements. In this case, the average 
of the transmission and reception phase-aberration profiles is measured 
and used for phase-aberration corrections. The second method can be used 
if the difference between transmission and reception phase-aberration 
profiles is unacceptable for both image formations and phase-aberration 
measurements. In this case, the transmission and reception 
phase-aberration profiles are measured separately and used for 
transmission and reception phase-aberration corrections respectively. This 
algorithm has taken steps to ensure that the arbitrary linear terms for 
transmitting and reception are identical. This is important; otherwise, 
the transmission and reception beams could be at different directions 
after the phase-aberration correction, which may severely reduce the 
quality of the image. 
A third main object of this invention is to provide algorithms for 
measuring and correcting angle-dependent phase-aberration profiles. 
To achieve this object, a sub-array phase-aberration correction algorithm 
is disclosed in the present invention. This method comprises generating 
common-midpoint signals collected with sub-array steered at a selected 
direction. These common-midpoint signals collected with sub-arrays are 
then used to measure the phase-aberration profile. The measured 
phase-aberration value for each sub-array is then assigned to all elements 
in the sub-array. By changing the steering directions of beams generated 
by sub-arrays, a plural number of phase-aberration profiles are measured, 
and they are used to correct for phase aberrations in the image at 
corresponding directions respectively. Instead of steering at the same 
direction, the beams of sub-arrays can also be formed along an image line. 
A plural number of phase-aberration profiles can be measured, one for each 
(or several) image line, and they are used to correct for phase 
aberrations at corresponding image lines respectively. 
A fourth main object of this invention is to provide algorithms for 
measuring and correcting amplitude aberrations. 
To achieve this object, an amplitude-aberration correction algorithm is 
disclosed in the present invention, which is incorporated into the 
phase-aberration correction algorithm. This method comprises measuring the 
energy of common-midpoint signals in the cross-correlation window and 
taking the logarithm of the ratio of their energies. Then the 
amplitude-aberration profile is derived. This algorithm can also be used 
with the sub-array technique to measure angle-dependent amplitude 
aberration profiles. Algorithms for measuring different (small and large 
difference transmission and reception amplitude-aberration profiles are 
also disclosed in the present invention. 
A fifth main object of this invention is to provide algorithms for 
implementing the phase- and amplitude-aberration measurement algorithms 
disclosed in the present invention on a two-dimensional array. 
To achieve this object, an all-row-plus-two-column algorithm is disclosed 
in the present invention. This algorithm comprises applying the phase- and 
amplitude-aberration measurement algorithms disclosed in the present 
invention for one-dimensional arrays on all rows and two columns, such as 
the two columns at the boundary of the array. The results from the two 
column measurements are used to derive a linear term for each row 
measurement result. These linear terms are incorporated in to the row 
results to obtain the two-dimensional phase- and amplitude-aberration 
profiles. Since the undetermined profile is a curved plane, which is not 
linear, for two-dimensional arrays, one of the four values at the four 
corners of the array is adjusted iteratively to maximize the image energy 
in the region of interest, which will optimize the performance of the 
system. These algorithms have also taken steps to ensure that the 
arbitrary linear terms for transmitting and reception are identical. To 
improve the measurement accuracy, the profiles derived from 
all-row-plus-tow-column and all-column-plus-two-row can be averaged. 
A sixth main object of this invention is to provide a method for reducing 
the influence of tissue movement on the aberration measurement accuracy. 
To achieve this object, signals that occupy different frequency bands can 
be transmitted simultaneously from three or more elements and then, the 
received signals are filtered to obtain individual common-midpoint signals 
that are going to be cross-correlated with one another. In this case, the 
two common-midpoint signals that are used to calculate a cross-correlation 
function are collected simultaneously. Therefore, the tissue-motion effect 
on the measurement accuracy is reduced. 
The foregoing and other objects and algorithms disclosed in the present 
invention will be more readily apparent from the following description and 
appended claims when taken with drawings. It here will be understood that 
the drawings are for purposes of illustration only, the invention not 
being limited to the specific embodiments disclosed therein.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
This invention includes a group of algorithms for phase and/or amplitude 
aberration corrections in imaging. They are based on the near-field signal 
redundancy principle. The problems caused by the fact that targets are in 
the near field have been solved with the application of dynamic near-field 
delay corrections on common-midpoint signals. A block diagram of an 
exemplary ultrasonic imaging system for implementing these algorithms is 
shown in FIG. 1. It contains two operational modes. One is the 
conventional imaging mode and the other is the aberration-measurement 
mode. The system can be switched between these two modes with the mode 
switcher 200. In the conventional imaging mode, the transmit beam former 
400 generates delay values and electrical signals for a selected focusing 
direction .phi. and depth .function. in the tissue 10, and then these 
signals are sent to the transmitter 100, where they are magnified and sent 
to the transducer array 20 through the transmit/receive switch 110, which 
is switched to the transmission position. The transducer array comprises a 
plurality of separately driven transducer elements. The transducer array 
20 may comprise either a one-dimensional array having a plurality of 
linearly disposed transducer elements, or a two-dimensional array in which 
the transducer elements are disposed in a matrix. In either configuration, 
transducer elements in the transducer array 20 convert these electrical 
signals into acoustic waves, which propagate in the tissue 10. These 
acoustic waves travel through various tissue layers of the patient and 
then, they are reflected back from a region of interest. The reflected 
acoustic waves are converted to electrical signals by the transducer 
elements in the transducer array 20. These electrical signals are routed 
to the receiver 120 through the transmit/receive switch 110, which is 
switched to the reception position. The signals are magnified, filtered, 
and converted to digital signals in the receiver 120, and then they are 
sent to the reception beam former 600 to form an imaging beam with dynamic 
focusing along the transmission focusing direction .phi.. By changing the 
value of the transmission focusing direction .phi. through a set of angles 
and repeating the above process, a plurality number of image beams are 
formed. These beams are then sent to the display system 700 for post 
beam-formation processing, compression, scan conversion, and display. 
The focusing on transmission of the system is achieved by delaying the 
transmission signals for each transducer element with a proper amount so 
that the acoustic waves generated by all transducer elements arrive at the 
focal point f at the same time. Similarly, the dynamic focusing on 
reception is achieved by delaying the received signals at each transducer 
element with a proper amount so that echoes from the same depth along the 
focal direction .phi. in all received signals add coherently. The delays 
for focusing are derived with the assumption that the propagation velocity 
of acoustic waves in the body is homogenous. However, as it is known, 
different tissues in the body may have different velocities, and these 
will introduce phase aberrations that cause focusing errors in the imaging 
system. The different attenuation coefficients in different tissue will 
cause amplitude aberrations that may also degrade the performance of the 
imaging system. 
This invention has disclosed a group of phase and/or amplitude aberration 
correction algorithms to improve the image quality. When aberration 
correction is needed, the imaging system in FIG. 1 will be switched to the 
aberration-correction mode with the mode switch 200. In this mode, the 
aberration-measurement transmission system 300 generates electrical 
signals that suitable for the aberration measurement algorithms disclosed 
in this invention. Generally, the aberration-measurement transmission 
system 300 generates only a signal for one selected transducer element at 
a time and sends it to the transmitter 100, where it is magnified. Then, 
this electrical signal is converted to an acoustic wave by the selected 
transmission transducer element in the transducer array 20. The reflected 
acoustic waves from the region of interest generated by the transmitted 
acoustic wave from the selected transducer element are converted to 
electrical signals by the transducer elements in the transducer array 20. 
These received signals are routed to the receiver, which they are 
magnified, filtered, and converted into digital signals. These signals are 
then send to the aberration measurement system 500 for storage and/or 
processing for aberration measurement. Then, the aberration-measurement 
transmission system 300 generates a signal for another selected transducer 
element and sends it to the transmitter 100. The received signals 
generated by transmission from this transducer element are also stored 
and/processed in the aberration measurement system 500. This process will 
be repeated until all transducer elements have transmitted. The selection 
of the transmission transducer element may also be done at the transmitter 
100. It is also not necessary to save and/or process all received signals 
for each transmission in the aberration measurement system 500; depending 
on the aberration correction algorithm, only signals received at a few 
transducer elements are needed for the aberration measurement. The 
collected signals in the aberration measurement system 500 are processed 
according to the selected aberration-correction measurement algorithms to 
derive the aberration profiles. The derived transmission aberration 
profiles are then sent to the transmission beam former 400 for 
transmission aberration corrections, and the derived reception aberration 
profiles are then send to the reception beam former 600 for reception 
aberration corrections. Some algorithms disclosed in this invention 
involve iteratively adjusting the undetermined aberration values for 
transducer elements at the end of the transducer array 20. To implement 
this, the formed beams for the region of interest in the reception beam 
former 600 are send back to the aberration measurement system 500, where 
they are processed according to the selected algorithm for optimizing the 
undetermined aberration values for elements at the end of the transducer 
array 20. 
After the aberration measurement, the system will be switched back to the 
conventional imaging mode with the mode switch 200 to form aberration 
corrected images with improved image qualities. 
Next, the aberration measurement algorithms disclosed in this invention are 
described below in detail. 
I. Phase-Aberration Correction Algorithm Using Near-Field Signal Redundancy 
For One-Dimensional Arrays 
In this phase-aberration algorithm, it is assumed that the transmission and 
reception phase-aberration profiles can be approximated as identical, and 
the aberration profile is not angle dependent. This algorithm includes the 
following steps: 
1. First, a data set y.sub.k,1 (t) is collected by transmitting on all 
elements, one at a time, and receiving at several elements for each 
transmission, where k is the transmitter element index and l is the 
receiver index. This data set is sent to the aberration-measurement system 
500. 
2. Referring to FIGS. 2-4, secondly, the dynamic near-field delay 
correction 510 is applied to common-midpoint signals y.sub.j-1,j+1 (t) 31 
(or y.sub.j+1,j-1 (t) 35) at the correction angle .theta..sub.i 23 to 
obtain signals y'.sub.j-1,j+1,(.theta..sub.i,t) and/or 
y'.sub.j+1,j-1,(.theta..sub.i,t) 
EQU y'.sub.j+1,j-1 (.theta..sub.i,t)=y.sub.j+1,j-1 [t'(.theta..sub.i,t)](1) 
where 
##EQU1## 
j is the center element 21 index, j=2, 3, . . . N-1, N is the total number 
of transducer elements in the transducer array 20, h is the pitch of the 
array, and c.sub.0 is the acoustic wave propagation velocity in the medium 
10. 
3. The normalized cross-correlation functions between y'.sub.j-1,j+1 
(.theta..sub.i,t)(or y'.sub.j+1,j-1 (.theta..sub.i,t)) y.sub.j,j (t) are 
calculated 520 at a selected depth with a selected window length 22. The 
peak positions .DELTA..tau..sub.j-1,j+1 (.theta..sub.i)(or 
.DELTA..tau..sub.j+1,j-1 (.theta..sub.i)), peak values .rho..sub.j-1,j+1 
(.theta..sub.i)(or .rho..sub.j+1,j-1 (.theta..sub.i)), and the signal 
energy values in the window 22 at the peak position of the 
cross-correlation function E.sub.j,j, E.sub.j-1,j+1 (.theta..sub.i) (or 
E.sub.j+1,j-1 (.theta..sub.i)) are derived. 
4. The phase-aberration profiles across the array are derived 530 from 
##EQU2## 
where 
##EQU3## 
The measured aberration profile .tau..sub.j 540 is then sent to the 
transmission beam former 400 and the reception beam former 500 for 
aberration corrections. 
5. Equation (3) is derived by assuming that the phase-aberration values for 
the two elements at the ends of the array 29 are zero. This assumption 
causes a linear-component error between the derived result .tau..sub.j and 
the real phase-aberration value .tau.'.sub.j, 
EQU .tau.'.sub.j =.tau..sub.j +a+b(j-1),j=1, 2, . . . N, (5) 
where a=.tau.'.sub.1 and b=(.tau.'.sub.N -.tau.'.sub.1)/(N-1). If 
.tau.'.sub.1 and .tau.'.sub.N are small, this error is not very important. 
It is approximately a global rotation and shift of the image. For 
situations where .tau.'.sub.1 and .tau.'.sub.N are large, it becomes 
important. An estimation of phase-aberration values at both ends of the 
array from a preliminary image with a priori knowledge. Another way to 
treat this situation is using a trial-and-error iterative method. 
Adjusting their values in the aberration-measurement system 500 and 
measuring the corrected image energy in the region of interest in the 
reception beam former 600, the optimal linear terms are obtained when the 
image energy in the region of interest is maximized. This is the last step 
of this algorithm. 
There are a few methods can be used to enhance the performance of the above 
algorithm, which are described below. 
A. One can average the two signals y.sub.j-1,j+1 (t) 31 and y.sub.j+1,j-1 
(t) 35 first, then apply the dynamic near-field delay correction on the 
averaged signal and cross-correlate it with signal y.sub.j,j (t) 33. This 
can improve the signal-to-noise ratio of the cross-correlation function 
and as a result, improve the measurement accuracy. 
B. One can perform the dynamic near-field correction 510 on signals 
y.sub.j-1,j+1 (t) 31 (or y.sub.j+1,j-1 (t) 35) with several correction 
angle .theta..sub.i 23 and tissue velocities c.sub.0 and then, calculate 
the cross-correlation function 520 between the signal y.sub.j,j (t) 33 and 
each of the corrected signals separately. The peak position of the 
cross-correlation function with the highest cross-correlation coefficient 
will be used for deriving the phase-aberration profile. 
C. Alternatively, one can perform the dynamic near-field correction 510 on 
signals y.sub.j-1,j+1 (t) 31 (or y.sub.j+1,j-1 (t) 35) with several 
correction angles .theta..sub.i 23 and tissue velocities c.sub.0 and then, 
average these signals before cross-correlating with the signal y.sub.j,j 
(t) 33. 
D. Instead of performing the dynamic near-field correction 510 at the same 
angle .theta..sub.i 23 using the center element 26 as the reference as 
shown in FIG. 2, one can perform the dynamic near-field correction at an 
angle toward a region of interest 28 as shown in FIG. 5. This will 
optimize the aberration correction of the image in the region of interest. 
E. The value of cross-correlation coefficient .rho..sub.j can be used to 
eliminate invalid measurement points by letting .tau..sub.j =0 if 
.rho..sub.j &lt;.rho..sub.0, where .rho..sub.0 is a threshold. This will 
improve the measurement accuracy. 
II. Algorithms for Different Transmition and Reception Phase-Aberration 
Profiles with One-Dimensional Arrays 
Phase-aberration profile differences between transmission and reception are 
usually caused by phase differences between electronic systems in each 
channel in an imaging system. Since measurement errors of 
cross-correlation-function peak positions are magnified in the derived 
phase-aberration values at each element, the requirement that channels be 
assumed identical is much stricter for phase-aberration measurement than 
for image formation. Therefore, the system calibration on a commercial 
machine may not be accurate enough. Reciprocal signals are very useful for 
treating the situation of different transmission and reception 
phase-aberration profiles, since reciprocal signals will have a relative 
phase shift if phases for each channel are different and this relative 
phase shift is independent of the phase aberrations caused by the medium. 
Let .phi..sub.j and .theta..sub.j denote the transmission and reception 
phase aberrations of element j respectively, 
A. When the difference between transmission and reception aberration 
profiles is small enough for the purpose of image formation, there is no 
need to measure them separately. In this case, as shown in FIG. 6, the 
dynamic near-field correction 510 should be applied on signals 
y.sub.j-1,j+1 (t) 31 and y.sub.j+1,j-1 (t) 35 and then, they are 
cross-correlated with the signal y.sub.j,j (t) 33. The peak position 
values of .DELTA..tau..sub.j-1,j+1 (.theta..sub.i) and 
.DELTA..tau..sub.j+1,j-1 (.theta..sub.i) should be averaged and then use 
equation (4) to derive the phase-aberration profile in the signal 
processor 530. That is 
##EQU4## 
where .gamma..sub.j =(.phi..sub.j +.theta..sub.j)/2. Since the difference 
between .phi..sub.j and .theta..sub.j is small, .gamma..sub.j can be used 
approximately for both transmission and reception phase-aberration 
corrections. The measured aberration profile .gamma..sub.j 540 is then 
sent to the transmission beam former 400 and the reception beam former 600 
for aberration corrections. 
B. When the difference between transmission and reception aberration 
profiles is large, the two phase-aberration profiles have to be measured 
separately. The average values .gamma..sub.j =(.phi..sub.j 
+.theta..sub.j)/2 are still useful in this case. Another group of 
equations is also needed. The peak position .DELTA..tau..sub.j+1,j of the 
cross-correlation functions between the two reciprocal signals y.sub.j+1,j 
(t) 39 and y.sub.j,j+1 (t) 37, as shown in FIGS. 7 and 8, can be used to 
obtain another group of equations. The peak position 
.DELTA..tau..sub.j+1,j is 
EQU .DELTA..tau..sub.j,j-1 =(.phi..sub.j +.theta..sub.j-1)-(.phi..sub.j-1 
+.theta..sub.j)=.beta..sub.j+1 -.beta..sub.j j=1, 2, . . . N-1,(7) 
where 
EQU .beta..sub.j =.phi..sub.j -.theta..sub.j. (8) 
By assuming 
EQU .beta..sub.1 =0, (9) 
the profile of .beta..sub.j can be derived from 
##EQU5## 
From .gamma..sub.j and .beta..sub.j, the phase-aberration profiles for 
transmission and reception are 
##EQU6## 
The measured transmission aberration profile .phi..sub.j 540 is sent to 
the transmission beam former 400 and the measured reception aberration 
profile .theta..sub.j 540 is sent to the reception beam former 600 for 
aberration corrections. 
III. Small-Element-Array Algorithm Using Near-Field Signal Redundancy 
An important issue that influences the performance of the near-field 
signal-redundancy algorithm is the degree of validity of the "phase screen 
on the transducer surface" model for the effect of aberrators in the 
medium. For small-element arrays, one may have the following problem: each 
element 26 transmits signals into and receives echoes from a wide angular 
range 13, and these echoes 14 may experience different phase-aberration 
values, as shown in FIG. 9; in this case, the peak position of the 
cross-correlation function between common-midpoint signals is not directly 
related to the phase-aberration value at any particular direction. A 
narrower beam, which limits the transmitted signals and received echoes to 
a smaller angular range, may help to make the transmitted and received 
beams experience approximately a single aberration value, and make it 
possible to measure a phase-aberration profile. In this case, the measured 
aberration profiles may be different at different beam angles; therefore, 
several aberration profiles may need to be measured. When using these 
measured profiles to correct the image, one may use each profile for the 
correction of the image in the corresponding direction. 
In this invention, it is disclosed that one can group small elements into 
sub-arrays 42 to collect common-midpoint signals with the required narrow 
directivity pattern 15, and the beam angle of sub-arrays can be steered in 
different directions 15 to measure the phase-aberration values for each 
direction, as shown in FIG. 10. The phase-aberration-correction algorithm 
using near-field signal redundancy for small-element arrays includes the 
following steps. 
1. First, a data set y.sub.k,1 (t) is collected by transmitting on all 
elements, one at a time, and receiving at several elements for each 
transmission, where k is the transmission element index and l is the 
reception element index. The number of receiving elements for each 
transmission depends on the number of elements n in each sub-array. 
2. Second, referring to FIGS. 11--13, the signal y'.sub.s,s (s, 
.theta..sub.i, t) 67, where s is the sub-array index, is formed with 
dynamic sub-array beam former I 512 using all signals transmitted from 
transducer elements, 61, 63, 65, in the center sub-array 42 and received 
at all elements, 62, 64, 66, in the center sub-array 42 at the steering 
angle .theta..sub.I. The signals y'.sub.s-1,s+1 (s, .theta..sub.i, t) 57 
(or y'.sub.s+1,s-1 (s, .theta..sub.i, t)) is formed with dynamic sub-array 
beam former II 511 using all signals transmitted from transducer elements, 
51, 53, 55, in the upper sub-array 41 and received at all elements, 52, 
54, 56, in the lower sub-array 43 at the steering angle .theta..sub.I. 
Assume that each sub-array has n transducer elements, the total number of 
sub-arrays is S, and the total number of transducer elements in the array 
is N=Sn, then 
##EQU7## 
and 
##EQU8## 
where 
##EQU9## 
The steering angle .theta..sub.i 23 is step through the angular range of 
the image and a set of common-midpoint signals is obtained for each 
steering angle. The increment of each step may depend on the beam width. 
1. The third step is to measure the peak position .DELTA..tau..sub.s 
(.theta..sub.i)(s=2,3, . . . S-1) of cross-correlation functions between 
common-midpoint signals y'.sub.s,s (s, .theta..sub.i, t) and 
y'.sub.s-1,s+1 (s, .theta..sub.i, t)(or y'.sub.s+1,s-1 (s, .theta..sub.i, 
t)) in 520. Then the phase-aberration profiles across the array at all 
directions .tau..sub.s (.theta..sub.i) can be derived using (3) 530. The 
derived phase aberration value for each sub-array should be assigned to 
all elements in the sub-array to obtain .tau..sub.j (.theta..sub.i) from 
.tau..sub.s (.theta..sub.i). The measured aberration profile .tau..sub.j 
(.theta..sub.i) 540 is then sent to the transmission beam former 400 and 
the reception beam former 500 for aberration corrections. 
The derived profiles .tau..sub.j (.theta..sub.i) at different steering 
angles .theta..sub.i may have different undetermined linear components. 
For a small aperture array or an image pixel, which is far from the 
transducer, where the angle of an image pixel to all elements in the array 
is about the same, this angle-dependent undetermined linear term generally 
does not influence the focusing. But it may cause image distortion if the 
linear term is very different for different angles. For a large-aperture 
array or an image pixel, which is near the transducer, however, 
phase-aberration values measured at different angles may be used at the 
same image pixel, and therefore, if possible, it is important to estimate 
the linear terms, when they are very different for different angles. 
However, it is usually difficult to estimate these linear terms. 
Therefore, another method is proposed here to solve this problem. It 
measures a phase-aberration profile for each image line 34 instead of each 
angle 27, as shown in FIG. 14. In this case, y'.sub.s,s (s, .theta..sub.i, 
t) 67 and y'.sub.s-1,s+1 (s, .theta..sub.i, t) 57 (or y'.sub.s+1,s-1 (s, 
.theta..sub.i, t)) are still as expressed in (13) and (14), but t'.sub.k1 
(s, .theta..sub.i, t) in (15) becomes 
##EQU10## 
That is, each sub-array forms a beam along each image line 34, and a 
phase-aberration-profile measurement is made from common-midpoint signals 
formed for each image line 34. In this case, the focus quality of each 
pixel is not influenced by the undetermined linear phase-aberration 
profiles. However, the image may still be distorted if the undetermined 
linear terms are very different at different image-line angles 35. 
There are a few methods can be used to enhance the performance of the above 
algorithms, which are described below. 
A. The number of elements in each sub-array should be chosen so that the 
required directivity or beam width, which is determined by the estimated 
changing rate of the phase-aberration value with angles, is achieved. 
However, this is also difficult to estimate. A trial-and-error approach 
may be used by forming common-midpoint signals with several sub-array 
sizes n. 
B. When forming beams using each sub-array for the phase-aberration 
measurement, resolution is not critical. Therefore, one can use 
apodization to concentrate more signal energy around the correction angle 
by reducing energy leakage to side lobes. This is helpful to make echoes 
from the region around the correction angle be dominant in common-midpoint 
signals. 
C. Since the aperture of each sub-array is relatively small, the effective 
aperture concept may be valid for beam patterns. Therefore one may also 
use only part of the available signals (one signal for each midpoint) with 
appropriate weighting to form a beam that has the desired beam pattern. 
This can reduce the computation load of this algorithm. But the 
signal-to-thermal-noise ratio will be lower than that when all the signals 
are used. 
IV. Two-Dimensional Array Algorithm Using Nrear-Field Signal Redundancy 
The principle of phase aberration correction algorithm developed above for 
a one-dimensional array can be applied to two-dimensional arrays 20, as 
shown in FIG. 15. However, this is not straightforward. There are new 
problems and opportunities when they are applied on a two-dimensional 
array and these are discussed below. 
A. The Algorithm for Identical Transmission and Reception Phase Aberration 
Profiles 
First, assuming transmission and reception phase aberration profiles are 
identical, let .phi..sub.m,n where m=1,2, . . . M and n=1,2, . . . N, 
denotes the phase-aberration value for element (m, n), as shown in FIG. 
15. The profile can be derived by applying the algorithm for 
one-dimensional array on rows and columns, then combining these results 
together carefully. The method proposed in the present invention is as 
follows. 
One can first apply the algorithm for one-dimensional array on all rows 70. 
The result of each row is solved by assuming the phase values at both ends 
of each row are zero. The results are 
EQU .phi..sup.r.sub.m,n =.phi..sub.m,n +a.sup.r.sub.m +b.sup.r.sub.m 
(n-1)m=1,2, . . . M n=1,2, . . . N, (17) 
where 
##EQU11## 
.phi..sup.r.sub.m,n is the derived profile, .phi..sub.m,n is the real 
profile, a.sup.r.sub.m and b.sup.r.sub.m are the arbitrary linear terms 
for row measurements. The arbitrary linear terms are generally different 
for different rows. There are 2M undetermined parameters in (17). 
To reduce the unknown parameters, one can apply the one-dimensional 
algorithm again on two columns, such as choosing the first and the last 
columns 71. The results for these two columns are: 
Column 1: 
EQU .phi..sup.c.sub.m,1 =.phi..sub.m,1 +a.sup.c.sub.1 +b.sup.c.sub.1 
(m-1)m=1,2, . . . M, (19) 
where 
##EQU12## 
Column N: 
EQU .phi..sup.c.sub.m,N =.phi..sub.mN +a.sup.c.sub.N +b.sup.c.sub.N (m-1)m=1,2, 
. . . M, (21) 
where 
##EQU13## 
a.sup.c.sub.1, b.sup.c.sub.1, a.sup.c.sub.N and b.sup.c.sub.N are the 
arbitrary linear terms for column measurements. 
From the two column results, a linear term can be derived for each of the 
row measurement results. After adding the linear terms, the resulted 
profile should match the result obtained from columns 1 and N at the first 
and last columns 71. This new profile is: 
EQU .phi..sup.r,c.sub.m,n =.phi..sup.r.sub.m,n +a.sub.m +b.sub.m (n-1)m=1,2, . 
. . M n=1,2, . . . N, (23) 
where: 
##EQU14## 
The number of arbitrary parameters in equation (23) is four: 
a.sup.c.sub.1, b.sup.c.sub.1, a.sup.c.sub.N and b.sup.c.sub.N in (20) and 
(22). If these four values are known, the real aberration profile can be 
obtained. The solution of equation (23) is derived by assuming that the 
phase aberration values at the four elements at the four corners of the 
array 72 are zero. Generally, these four points are not on the same plane, 
which results in an undetermined curved plane difference between the 
measured and real aberration profiles, which, unlike in the 
one-dimensional case, will certainly influence the focusing quality of the 
imaging system. To make the undetermined curved plane into a flat plane, 
which has smaller influence on the focusing quality, an iterative approach 
can be used. One of the four undetermined parameters a, a.sub.N, b.sub.1 
and b.sub.N is adjusted, and the resulted profiles are sent to the 
transmission beam former 400 and the reception beam former 500 for 
aberration corrections. The image energy in the region of interest in the 
reception beam former 600 is measured for each profile. The optimal value 
of the undetermined parameter is obtained when the image energy in the 
region of interest is maximized. 
B. Different Transmission and Reception Phase-Aberration Profiles 
Let .phi..sub.m,n and .theta..sub.m,n denote the transmission and reception 
aberration profiles respectively at element (m, n), where n=1,2, . . . N, 
and m=1,2, . . . M. If the difference between .phi..sub.m,n and 
.theta..sub.m,n is small for image formation purposes, (6) and the method 
for identical transmission and reception algorithm described in the last 
section A can be used. If the difference between .phi..sub.m,n and 
.theta..sub.m,n is large for image formation purposes, they have to be 
measured separately. The one-dimensional algorithm for dealing with this 
problem (7)-(12) can also be applied to all rows 70 plus two columns, such 
as the two columns at the end of the array 71. It can be shown that the 
results from rows are 
EQU .phi..sup.r.sub.m,n =.phi..sub.m,n +a.sup.r.sub..phi.,m +b.sup.r.sub.m 
(n-1)m=1,2, . . . M n=1,2, . . . N, (25) 
EQU .theta..sup.r.sub.m,n =.theta..sub.m,n +a.sup.r.sub..theta.,m 
+b.sup.r.sub.m (n-1)m=1,2, . . . M n=1,2, . . . N, (26) 
where 
##EQU15## 
There are three undetermined parameters in the results for each row, and 3M 
undetermined parameters in total. 
The results from column 1 are 
EQU .phi..sup.c.sub.m,1 =.phi..sub.m,1 +a.sup.c.sub..phi.,1 +b.sup.c.sub.1 
(m-1)M=1,2, . . . M 
EQU .theta..sup.c.sub.m,1 =.theta..sub.m,1 +a.sup.c.sub..theta.,1 
+b.sup.c.sub.1 (m-1)m=1,2, . . . M, (28) 
where 
##EQU16## 
The results from column N are 
EQU .phi..sup.c.sub.m,N =.phi..sub.m,N +a.sup.c.sub..phi.,N +b.sup.c.sub.N 
(m-1)m=1,2, . . . M (30) 
EQU .theta..sup.c.sub.m,N =.theta..sub.m,N +a.sup.c.sub..theta.,N 
+b.sup.c.sub.N (m-1)m=1,2, . . . M, (31) 
where 
##EQU17## 
a.sup.c.sub..phi.,1, a.sup.c.sub..theta.,1, b.sup.c.sub.1, 
a.sup.c.sub..theta.,N, a.sup.c.sub..theta.,N, and b.sup.c.sub.N are the 
arbitrary linear terms for column measurements. 
The next step is to link the row results and the two column results 
together to reduce the unknown parameters. Here, it is done differently 
from the identical transmission and reception aberration profiles case. 
The slope of added linear terms, derived from the two column results, 
should be the same for both .theta. and .phi., so that the undetermined 
planes for them are the same, which will reduce the influence of the 
undetermined planes on the image quality. To do that, the slope of the 
added linear term to row m is the average of the slopes for .theta. and 
.phi. 
##EQU18## 
and the resulted profiles are 
EQU .phi..sup.r,c.sub.m,n =.phi..sup.r.sub.m,n +.phi..sup.c.sub.m,1 +b'.sub.m 
(n-1)m=1,2, . . . M n=1,2, . . . N (34) 
EQU .theta..sup.r,c.sub.m,n =.theta..sup.r.sub.m,n +.theta..sup.c.sub.m,1 
+b'.sub.m (n-1)m=1,2, . . . M n=1,2, . . . N. (35) 
Because of using (33), the six undetermined parameters a.sup.c.sub..phi.,1, 
a.sup.c.sub..theta.,1, b.sup.c.sub.1, a.sup.c.sub..phi.,N, 
a.sup.c.sub..theta.,N, and b.sup.c.sub.N in (34) and (35) have been 
reduced to four parameters a.sup.c.sub..phi.,1 +a.sup.c.sub..theta.,1, 
b.sup.c.sub.1, a.sup.c.sub..phi.,N +a.sup.c.sub..theta.,N, and 
b.sup.c.sub.N. As is in the case of identical transmission and reception 
profiles, the four undetermined parameters result in an undetermined 
curved plane difference between the measured and the real aberration 
profiles, which is the same for both .phi. and .theta. profiles. To make 
the undetermined curved plane into a flat plane, one of the four 
undetermined parameters is adjusted, and the resulted profiles are sent to 
the transmission beam former 400 and the reception beam former 500 for 
aberration corrections. The image energy in the region of interest in the 
reception beam former 600 is measured for each profile. The optimal value 
of the undetermined parameter is obtained when the image energy in the 
region of interest is maximized. 
C. Increase the Signal to Noise Ratio 
For a two-dimensional array, two independent measurements, which have 
similar accuracy, can be performed. Such as, one measurement is performed 
with all rows plus two columns and another is performed with all columns 
plus two rows, as shown in FIG. 15. These two measurements can be averaged 
to improve the measurement accuracy. 
V. Amplitude-Aberration Correction Algorithms Using Near-Field Signal 
Redundancy 
Amplitude aberrations caused by attenuation inhomogeneity in a medium or 
system errors is another limit on imaging system performance. Even though 
imaging systems are less sensitive to amplitude aberrations than they are 
to phase aberrations, when amplitude aberrations are severe, they must be 
corrected to obtain a good quality image. 
The method herein proposed uses the near-field signal redundancy principle, 
which is also used in the phase-aberration correction algorithm discussed 
hereinbefore. In a homogeneous medium, when the distance between three 
neighboring elements is small compared with the target distance, common 
midpoint signals are approximately redundant for targets in the near-field 
after the dynamic near-field correction, and this should be true in terms 
of both phase and amplitude. When the medium is inhomogeneous in terms of 
attenuation, the amplitude of common-midpoint signals will become 
different and it provides a method for measuring and correcting amplitude 
aberrations. 
Since signal redundancy principle for amplitude is much less affected by 
the fact that targets are in the near field compared with that for phase, 
and the measurement accuracy requirement is also lower, common-midpoint 
signals may not need dynamic near-field corrections for 
amplitude-aberration measurement. This will reduce the computation load 
for amplitude-aberration measurements. But, when both amplitude and phase 
aberrations exist, the amplitude-aberration and the phase-aberration 
measurements can be performed together after common-midpoint signals are 
dynamically corrected. 
In the phase-aberration correction algorithm described hereinbefore, there 
is a step for calculating normalized cross-correlation functions and 
measuring their peak positions (step 3 in section I). The signal energies 
used to normalize the cross-correlation functions at its peak position 
E.sub.j,j, E.sub.j-1,j+1 (.theta..sub.i) (or E.sub.j+1,j-1 
(.theta..sub.i)), as shown in FIGS. 4, 6, and 8, can be used directly for 
amplitude-aberration measurements. These energies are calculated with the 
common-midpoint signals, which are dynamically corrected with a high 
sampling rate, and phase shifted to compensate for phase aberrations. 
The energy of the received signal y.sub.j,j (t) 26 in the cross-correlation 
window from time t.sub.1 to t.sub.2 22 is 
##EQU19## 
where z(t) are the normalized signal of y.sub.j,j (t) with unit amplitude, 
which is approximately the same for common-midpoint signals, A.sub.j,R and 
A.sub.j,T are transmission and reception amplitude sensitivities. When the 
amplitude-screen model is valid, A.sub.j,R and A.sub.j,T include both 
system and medium amplitude aberrations. For the signals y'.sub.j-1,j+1 
(t) 31 and y'.sub.j+1,j-1 (t) 35 
##EQU20## 
The following discusses algorithms for measuring amplitude-aberration 
profiles. 
A. Algorithm for Identical Transmission and Reception Amplitude-Aberration 
Profiles 
In this case, from (37) and (38), E.sub.j+1,j-1 =E.sub.j-1,j+1, and the 
measurements of the two values can be average to reduce the influence of 
noise. The logarithm of the square-root of the energy ratio h.sub.j 
##EQU21## 
can be used for the measurement. Let 
EQU .alpha..sub.j =log.sub.10 A.sub.j (40) 
then (39) becomes 
EQU 2.alpha..sub.j -.alpha..sub.j-1 -.alpha..sub.j+1 =h.sub.j j=2,3, . . . 
N-1.(41) 
The profile of .alpha..sub.j can be derive from (41) by assuming 
EQU .alpha..sub.1 =.alpha..sub.N =0, (42) 
which is equivalent to assuming 
EQU A.sub.1 =A.sub.N =1. (43) 
The derived profile is 
EQU .alpha..sub.j =.alpha.'.sub.j +a+b(j-1), (44) 
where .alpha.'.sub.j is the real profile, and 
##EQU22## 
From (40), (44) and (45), the relationship between the measured amplitude 
profile A.sub.j and the real profile A'.sub.j is 
##EQU23## 
Therefore, the measured amplitude value A.sub.j is the real profile 
A'.sub.j normalized by A'.sub.1 and weighted by a factor which depends on 
the element number N. The influence of the weighting factor is equivalent 
to an apodization window. The values of A.sub.1 and A.sub.N may be 
adjusted to reduce its effect. The measured aberration profile A.sub.j 540 
is then sent to the transmission beam former 400 and the reception beam 
former 500 for aberration corrections, as shown in FIG. 4. 
B. Algorithm for Different Transmission and Reception Amplitude Aberration 
Profiles 
When the amplitude-aberration profiles are different for transmissions and 
receptions, E.sub.j-1,j+1 will not equal to E.sub.j+1,j-1. Let 
##EQU24## 
and 
EQU .alpha..sub.j =log.sub.10 (A.sub.j,R A.sub.j,T). (48) 
Then (41)-(45) are still valid, and (46) becomes 
##EQU25## 
If the difference between the transmission and reception profiles is small 
for image-formation purposes, there is no need to separate them. One can 
use the geometric mean of the transmission and reception 
amplitude-aberration profiles 
##EQU26## 
for both transmission and reception aberration corrections by sending it 
to the transmission beam former 400 and the reception beam former 500, as 
shown in FIG. 6. 
When the difference between the transmission and reception profiles is 
large, them must be measured separately. To separate the transmission and 
reception amplitudes, another group of equations is needed. It can be 
obtained from the two reciprocal signals y.sub.j,j+1 (t) 37 and 
y.sub.j+1,j (t) 39 collected by using two neighboring elements. 
##EQU27## 
Note that y.sub.j,j+1 (t) 37 and y.sub.j+1,j (t) 39 are identical even 
without the dynamic near-field correction. Energy values can also be 
obtained from the process of calculating the normalized cross-correlation 
function when measuring the different transmission and reception 
phase-aberration profiles. Let 
##EQU28## 
then 
EQU .beta..sub.j+i -.beta..sub.j =m.sub.j j=1,2, . . . N-1. (54) 
(54) can be solved by assuming .beta..sub.1 =0, that is A.sub.1,R 
=A.sub.1,T. The result is 
##EQU29## 
The derived .beta..sub.j profile and the real profile .beta.'.sub.j are 
linked by 
EQU .beta..sub.j =.beta.'.sub.j +.alpha..sub.1, (56) 
where 
EQU .alpha..sub.1 =-.beta.'.sub.1. (57) 
From .alpha..sub.j and .beta..sub.j, the transmission and reception 
amplitudes can be derived from 
##EQU30## 
It can be shown that the measured profiles A.sub.j,T and A.sub.j,R are 
related to the real profiles A'.sub.j,T and A'.sub.j,R by 
##EQU31## 
It is shown that the measured amplitude profiles are the real profiles 
normalized by the value at the first element and apodized by a window, 
which is the same for both transmission and reception aberration profiles. 
The measured transmission aberration profile A.sub.j,T 540 is sent to the 
transmission beam former 400 and the measured reception aberration profile 
A.sub.j,R 540 is sent to the reception beam former 600 for aberration 
corrections, as shown in FIG. 8. 
C. Two-Dimensional Array Amplitude-Aberration Measurements 
Amplitude-aberration measurements for a two-dimensional array are similar 
to the phase-aberration measurements described before. One can apply the 
one-dimensional array algorithm to all rows plus two columns, or to all 
columns plus two rows, then link the results together carefully. 
D. Using Less Accurate Redundant Signals 
The amplitude-aberration correction can be incorporated into the 
phase-aberration correction algorithm. In phase-aberration measurements, 
signal energies can be measured with signals used for phase-aberration 
measurements, which are dynamically corrected at high sampling rate. It 
costs very little to use these high accuracy signals for 
amplitude-aberration measurement. 
But generally, amplitude-aberration measurements can be performed using 
much less accurate signals, since signal amplitude redundancy is much less 
sensitive to the fact that targets are in the near field compared with the 
phase redundancy. The measurement-accuracy requirement is also not as high 
as that for phase-aberration measurement. Therefore, the following signals 
may be used for amplitude-aberration measurements if it is needed: 
1) signals without the dynamic near-field correction. 
2) demodulated signals. 
3) signals with low sampling rate. 
VI. Noise Control In Aberration-Measurement Algorithms 
The differences between transmission and reception aberration profiles are 
generally caused by system errors. Since the requirement for them to be 
similar in aberration measurements is stricter than that in the image 
formation process, generally they must be treated as different in 
aberration measurements. The differences between transmission and 
reception aberration profiles caused by the system can be calibrate with a 
tissue mimicking phantom and the calibration results can be used to check 
the quality of the peak-position measurement of cross-correlation 
functions in the phase-aberration profile measurements. For example, the 
peak position .DELTA..tau..sub.j+1,j of the cross-correlation function 
between reciprocal signal y.sub.j+1,j (t) 39 and y.sub.j,j+1 (t) 37 is 
shown in equation (7); it can be measured quite accurately by averaging 
many transmissions and/or many speckle-generating regions in the 
tissue-mimicking phantom to reduce the noise effect. The profile of 
.DELTA..tau..sub.j+2,j+1 -.DELTA..tau..sub.j+1,j is 
EQU .DELTA..tau..sub.j+2,j+1 -.DELTA..tau..sub.j+1,j =(.phi..sub.j+2 
-.theta..sub.j+2)-(.phi..sub.j -.theta..sub.j)j=1,2, . . . N-2.(62) 
This profile can be used for monitoring the quality of common-midpoint 
signals in the measurements. In the phase-aberration measurements, the 
profile of signal y.sub.j,j (t) is cross correlated with signal 
y.sub.j-1,j+1 (t) and y.sub.j+1,j-1 (t) separately, and the peak positions 
of cross correlation functions are measured, which gives the following 
values: 
EQU .DELTA..tau..sub.j-1,j+1 =(.phi..sub.j +.theta..sub.j)-(.phi..sub.j-1 
+.theta..sub.j+1) (63) 
EQU .DELTA..tau..sub.j+1,j-1 =(.phi..sub.j +.theta..sub.j)-(.phi..sub.j+1 
+.theta..sub.j-1) (64) 
The profile of .DELTA..tau..sub.j-1,j+1 -.DELTA..tau..sub.j+1,j-1, where 
EQU .DELTA..tau..sub.j-1,j+1 -.DELTA..tau..sub.j+1,j-1 =(.phi..sub.j+1 
-.theta..sub.j+1)-(.phi..sub.j-1 -.theta..sub.j-1)j=2,3, . . . N-1(65) 
should be similar to the calibrated profile in (62). If the difference is 
large, it indicates that the noise is strong, therefore the measurement 
should be discarded. The above algorithm is implemented in the digital 
processor 530 in FIG. 8. 
VII. Reducing the Effects of Tissue Motions 
When the tissue is moving during the aberration measurement, the accuracy 
of the measurement may be reduced. If the movement does not influence the 
aberration profile, this effect can be removed by the following method. 
As shown in FIG. 16, common-midpoint signals, 31, 33, 35, which are going 
to be cross-correlated with one another, can be collected simultaneously 
by transmitting signals 1, 3, and 5, which occupy different frequency 
bands as shown in FIG. 17, from transducer elements 25, 26, 24 
respectively and then, separating them with filtering. 
VIII. Signal Collections With Simultaneous Transmission 
The above method may also be used for reducing the time needed to collect 
all the necessary signals for aberration measurement. The direct method 
for collecting common-midpoint signals is by transmitting at one element 
at a time and receiving at several elements, repeating this until all 
elements have transmitted. However, if a high frame rate is required, this 
method may be too slow. A simultaneous transmission method is disclosed 
below in this invention, with which the time requirement for data 
collection will be reduced. Several methods for reducing the adverse 
effects of the simultaneous transmission method are also disclosed. 
Even though, long pulses will reduce the similarity between common-midpoint 
signals, aberration measurements can use signals with much narrower 
bandwidth compared with that for imaging. Therefore, several signals with 
approximately non-overlapping bandwidths within the transducer bandwidth 
can be transmitted simultaneously to collect common-midpoint signals, as 
shown in FIGS. 16 and 17. Generally, several transmissions are still 
needed to collect all the necessary common-midpoint signals for the 
measurement. The bandwidths of these signals are generally overlapped 
somewhat. To reduce the overlapping problem, the elements used to transmit 
these signals should be arranged in a way so that the two common-midpoint 
signals, which are going to be cross-correlated with one another, are 
collected with non-overlapping signals, or from different groups of 
simultaneous transmissions. This can be done by simultaneously transmit 
from elements located at a large distance from one other. 
While the present invention has been described with reference to a few 
specific embodiments, particularly relating to ultrasound imaging systems, 
many modifications and changes will occur to those skilled in the art. It 
is, therefore, to be understood that the appended claims are intended to 
cover all such modifications and changes as fall within the true spirit of 
the invention. It should also be apparent that the method and apparatus of 
this invention would be equally applicable to other pulse-echo imaging 
modalities, such as radar and sonar imaging systems.