Medical Ultrasonic array transducer beam tolerance analysis and variant Processing

Medical Ultrasonic array transducer beam tolerance analysis and variant Processing

Wang Bo Wanming Xi Wang supin Chen Zhongmin

SummaryThe beam characteristics of medical ultrasonic array transducer with amplitude error, phase error and array element failure are studied by using the directed function, this paper proposes and uses amplitude-weighted variant tracing processing, phase variant processing, and aperture variant processing to improve the beam direction of the array transducer. the calculation results show that the phase error and the Gaussian distribution amplitude error cause the increase of the Side Lobe, the increase of the gate flap, and the variation of the beam characteristics. Their influence on the sound field characteristics is determined by the error size and distribution. both amplitude-weighted trace modification and aperture trace modification can effectively suppress the side lobe and change the direction. A constant aperture emission and a variable aperture receiving ultrasonic array system have an optimal receiving aperture, at this time, the maximum side lobe is exceeded. this conclusion has important application value for medical ultrasound and industrial ultrasound.
Keywords: Line array, ing function, tolerance analysis, variant Processing
Classification of Chinese books and materials: R197.39

Tolerance Analysis and Apodization processing of medical
Utrasound array transducer wave Beams

Wang Bo, Wan Mingxi, Wang supin, Chen Zhongmin
(XI 'a Jiaotong University, Xi 'a 710049, China)

Abstract : The directivity function is used for determining the beamforming wave properties of ultrasound array for medical use. it is affected by efficacy loss of elements, Amplications and Phase Error Distribution of array elements. A method is developed by combining amplitude weighting, phase and aperture Apodization for improving beam patterns. the computed results show that (1) phase error and Gauss distribution ampl;error give rise to larger sidelobes, more grating lobes and deteriorating beam quality whose effect to sound field properties was determined by Error Distribution. (2) amplitude weighting and phase Apodization processing can restrain sidelobes and improve the directieffeceffectively. (3) In an ultrasound Array System with fixed transmitting aperture and changeable inform ing aperture, there exists a best practice ing aperture, at which sidelobes are the lowest. this conclusion is important to the medical and industrial application of ultrasonic.
Keywords : Linear Array; directivity function; tolerance analysis; Apodization Processing

Ultrasonic instruments have the advantages of safety and no trauma, so they have been widely used in clinical disease diagnosis. b-ultrasound and Doppler flow imager are currently the most widely used ultrasonic diagnostic instruments, which can provide two-dimensional distribution of human physiological information and perform real-time dynamic observation. Therefore, they are very popular in clinical diagnosis. however, the quality of ultrasound images is significantly different from that of other imaging methods (such as CT), which affects the reliability of diagnosis and limits its application scope.
The most important factor affecting image resolution is the directionality of the ultrasonic beam. at present, there is still a lack of systematic research on the beam characteristics of various medical ultrasonic array transducer, there is no clear theoretical basis for circuit and improvement, there is a certain degree of blindness, therefore, it is difficult to greatly improve the image quality. therefore, it has theoretical and practical value to calculate the Direction Distribution of the ultrasonic array transducer. some overseas researchers have studied the effects of Amplitude Errors and phase errors on phased-out arrays. [1, 2], however, so far, no special research results have been found on the effects of amplitude-weighted trace modification, phase trace modification, and aperture trace Modification on the beam characteristics of ultrasonic arrays.
Based on the most widely used line arrays in the current ultrasonic array transducer, This paper derives the function of beam direction in different situations, then, the characteristics of their ultrasonic array beam are calculated and discussed ~ 5].

1 key theoretical formula

1.1 non-deflection and deflection direction Functions
The line array consists of n elements, with the spacing of the elements being D1. Each element is a rectangular piston plane. The length of the element is l, the width is D2, and the ultrasonic length is λ, therefore, a line array can be seen as a combination of a rectangular piston surface and a point source line array. by the product of the composite array, the directed function of the non-deflection line array can be obtained.

(1)

The linear array transducer is on the XY plane, and the coordinate origin is on the center of the transducer;αObserve the angle between the sound line and the array element width (I .e., the X axis;θObserve the angle between the sound line and the central axis (I .e. the Z axis.
The phase control technology is used to enable various arrays of the linear array to be stimulated by delayed pulses of different levels. The main beam of the synthesized acoustic wave is continuously deflected on the scanning surface, assuming that the deflection angle of the main beam isθ0. When the targeted surface is retrievedXzPlane,α= 0 (for convenience, the following discussions specify that the beam scan is on the xz Z plane). At this time, the direction function of the deflection line arrayDS(θ) Is

(2)

Influence of 1.2 amplitude error and Phase Error
Because the design of the actual acoustic system and circuit system cannot fully meet the theoretical requirements, there may be some errors in the acoustic amplitude emitted by each array element of the transducer, at the same time, the inaccuracy of the delayed Network Controlling the beam deflection may also lead to phase errors, and one or several elements may fail. these errors will affect the beam characteristics of the ultrasonic array transducer, which will be discussed in three cases below.
1.2.1 amplitude error it is assumed that the normalized amplitude error of the I array element of the array transducer isDelta IIn this caseIThe normalized range of elements is 1 +Delta IPhase, derived the direction function of the deflection line array is

(3)

(3) The phase error is not taken into account, and the mean of the amplitude of the array element is assumedMaThe standard variance can be used.σAnd standard second-order center distanceσ′XTo indicate the size and distribution of the amplitude error:
Standard variance

(4)

Standard second-order center distance

(5)

(6)

The larger the amplitude error,σLarger.σ′XIt is used to represent the distribution of positive Amplitude errors from the center to the edge. When the central array element amplitude is large and the peripheral array element amplitude is small,σ′X<1. The amplitude distribution of the array element is convex, that is, Gaussian distribution. When the peripheral array element range is large and the central array element range is small,σ′X> 1. The amplitude distribution of the array element is concave. When the amplitude error is randomly distributed,σ′X≈ 1. At this time, the amplitude of the array element fluctuates around the average amplitude.
1.2.2 Phase Error assuming Phase Error of array element II, The amplitude error is 0, and the direction function of the derived deflection line array is

(7)

The standard variance of the phase error is

(8)

1.2.3 both amplitude and phase errorsDelta I, Phase ErrorIIn this case, the direction function of the deflection line array can be deduced

(9)

1.3 amplitude-weighted variant processing directed Functions
In order to improve the image resolution, the side-lobe of the array transducer beam must be reduced. in the process of transmitting and receiving, you can set different gains (I .e., amplitude weighting) for different element channels to perform amplitude variation. in general, the weight coefficient from the central element to the peripheral element is gradually reduced during design, that is, the amplitude is convex, which can highlight the main valve and suppress the side lobe, and the beam direction is better.
SetthIArray Element weight isWiDerived, the directed function of the deflection line array is

(10)

In amplitude-weighted variant processing, Gaussian function, cosine function, and Hanning function can be used as the weight coefficient function. In this paper, Gaussian function and cosine function are used.

(11)

Formula:K> 0, which is the control factor,KYou can control the downgrading slope of the weight coefficient,KThe larger the weight coefficient, the more obvious the weighting effect. The cosine weight function is

(12)

FormulaK1 is a natural number,K2 <π, Both are control factors,K1,K2. The larger the weight,K1> 1 hour,WiIs a cosine function.

1.4 phase variant processing direction function
In the process of transmitting and receiving, setting a time delay for different elements enables the beam to focus, thus reducing the beam width and improving the beam characteristics.

(13)

Formula:ZFIs the focal length. The direction function of the deflection line array processed by phase variation is

(14)

1.5 pore size variant Processing
In medical ultrasound imaging, dynamic focusing and variable aperture technology can be used to achieve good near-field and far-field beam characteristics by fan scanning of Phased Array and line array. In this paper, we only discuss aperture variation. the so-called variable aperture or aperture variation means to use allNArray elements, while only the centerMArray elements. through the superposition and offset between the two sides, the two sides can be reduced, while the main lobe is basically unaffected. in the previous discussion of the line array's directionality function, since all elements are used for transmitting and receiving, that is, constant aperture transmission and receiving, we only calculate the directionality of the emission beam. total line array direction functionD(θ) Is equal to the emission direction function.DT(θ) And receive direction FunctionsDr(θ), That is

D(θ) =DT(θ)Dr(θ) (15)

In the aperture variation processing, the emission is a constant aperture, and the dynamic aperture is used for receiving. The total direction function of the phased array is derived from the (15) formula.

(16)

For linear array systems,θ0 = 0, the emission element isN1. The receiving element isM1. The total direction function of the system is

(17)

2. Calculation

ComputingProgramIt is written in the Turbo Pascal language and can be run on a PC. the calculation is completed by two programs. program 1 calculates the direction of the offline array with errors and amplitude-weighted traces, and the maximum side lobe under various receiving aperture. After calculation, the program subroutine is called to output the result graph on the display. the directed function of the line array is

(18)

To facilitate computation, convert the form above into a trigonometric function

(19)

Formula:D1 (θ() Is the direction function of the rectangular piston plane;AIThe range of array I;Phi IArray ElementIIn the program, after modification as needed, the direction of the offline array can be calculated in various situations.
In program 2, in order to reduce the calculation amount and find the peak value of the Side Lobe, the direction sharpness angle is calculated first, and then from this point, the maximum value is the maximum side lobe.

3 calculation results and discussion

The following is the result of the line array's directed function in different situations. The ultrasonic frequency is calculated. F = 3.5 MHz, sound speed C = 1540 m/s, line array parameters N = 64,D 1 = 0.25, D 2 = 0.2, L = 8mm.
3.1 amplitude error and Phase Error
When the amplitude error is Gaussian, σ ′ X > 1. The array element range is concave, and the surrounding array element range is large while the center element range is small. the calculation results show that when there is a amplitude error, the beam side lobe of the line array increases significantly, the opening angle of the half power point remains unchanged, the direction sharpness angle decreases slightly, and the beam direction is deteriorated. therefore, when designing the gain of each element in the transmitting and receiving channels, we should avoid this situation as much as possible. when the amplitude error is distributed in the opposite direction, that is, the amplitude of the array element is convex, which is actually the amplitude-weighted variant processing. We will discuss it in section 3.2. when the amplitude error is distributed randomly, the ripple diagram is basically the same as that without error. In the actual system, this type of amplitude error is the most common.
Array Element failure is a special form of amplitude error. At this time, the amplitude of one or more arrays is 0. because the number of elements decreases, the width of the main wave bundle increases, and the array element failure also leads to the increase of the sides, the degradation of the beam characteristics becomes more serious. the center element failure has a great influence on the direction. The influence of the amplitude error on the line array's direction is determined by the size and distribution of the error.
Similarly, the effect of phase errors on the direction is closely related to the distribution and size of the entire aperture. The standard variance of Phase Errors σ P Larger, the longer the beam feature of the line array. the effect of phase errors on the direction varies greatly with the distribution. In severe cases, the main lobe degrades, the position changes, and the amplitude of the Side Lobe increases significantly, the direction deteriorated significantly. it can be seen that the phase error is an important factor in the variation of the beam characteristics. When designing a delayed network, pay special attention to avoid high-frequency hop errors.
When the linear array has both amplitude and phase errors, its direction is affected by these two factors. The beam side lobe is further increased, and the direction degradation is more serious.
3.2 amplitude-weighted variant Processing
In the amplitude-weighted variant processing, the amplitude distribution of the array element is taken from the large portion in the middle and the small portion on both sides. when the coefficient K of formula (11) is 2.0, the maximum side lobe is reduced by about 20 dB through Gaussian weighted processing, and the opening angle of the half power point remains unchanged, but the sharpness angle of the direction increases, the beam characteristics of the array transducer have been significantly improved. the weight function when the amplitude is cosine-weighted. the computation results show that cosine weighting can also suppress the Side-lobe. The maximum side-lobe is reduced by about 8 dB, and the width of the main side is basically unchanged. changing formula (11) and (12) K Or K 1, K The value of 2 can change the weight characteristics of the weight function. because the decrease of the side lobe is always accompanied by the increase of the beam width, the selection of the weight coefficient must take into account the requirements of the two aspects, and minimize the Side Lobe when the beam width meets the requirements. in addition, the overall system sensitivity must be considered in actual design. the optimal selection of Weight Coefficient in amplitude-weighted variant processing of various medical ultrasonic arrays, including line arrays, remains to be further studied.
Obviously, amplitude-weighted variant processing can improve the beam characteristics of line arrays under Gaussian distribution. However, it has a complex effect on the direction of line arrays with phase errors, which is closely related to its distribution.
3.3 aperture trace Modification
In a phased array fan sweep, when the number of transmitting elements N is 64, the relationship curve between the system's maximum side lobe and the number of receiving elements is an approximate cosine function (half wave ). the calculation shows that when the receiving array element is 46, the main lobe is sharp, the side lobe is low, the beam features are good, and the receiving aperture is the best. of course, the optimal aperture can also be determined by the peak value of the first side lobe or the average value of all side lobe peaks. The program only needs to make slight modifications to achieve this, and the sharpness angles of all kinds of receiving aperture are the same, the half-power point opening angle decreases as the number of elements increases.
During online array scanning, the number of transmitting elements is 12, and the remaining parameters are the same as those of the phased array. The relationship between the maximum number of sides in the system and the number of elements in the receiving array does not change much. When the number of elements in the receiving array is 9, the features are similar to those of phased array, but the beam width is large.
In order to obtain good near-field and far-field beam characteristics, the receiving aperture in the phased array and line array generally increases with the depth. The near-field side lobe is higher than the far-field side, and the beam width is also large, far-field beam is superior to near-field.
The author has read a lot of relevant materials during his writing on the study of sound field characteristics of ultrasonic array transducer ~ 9] available for readers.

4 Conclusion

(1) The impact of amplitude error on the line array's directionality is determined by the size and distribution of the error. The amplitude error can be determined by the standard variance.σAnd standard second-order center distanceσ′XTo completely characterize,σThe larger the value, the greater the impact on the direction.σ′X> 1, the amplitude error is in Gaussian distribution, the peripheral element amplitude is large, and the central element amplitude is small, it increases the Side-lobe of the line array beam, and the direction is deteriorated.σ′XWhen ≈ 1, the amplitude error is randomly distributed, with little impact on the direction.σ′X<1, the amplitude error is in a concave distribution, and the amplitude of the array element decreases from center to two weeks, which can suppress the side lobe and improve the beam characteristics.
(2) The phase error increases the side lobe, the gate flap increases, and the beam direction deteriorates. standard variance of the Phase Errorσ PThe greater the effect, the more obvious it is. The distribution of phase errors varies greatly with the impact on the direction.
(3) amplitude-weighted variant processing can reduce the side lobe and improve the beam direction, but also increase the width of the beam. Therefore, the selection of the weight coefficient must comprehensively consider the Side Lobe characteristics and the width of the beam, and is in Gaussian distribution.
(4) the aperture variation processing can reduce the side lobe without changing the sharpness angle of the beam direction, thus improving the beam characteristics.D1 = 0.25,D2 = 0.2,L= 8mm,F= 3.5 MHz,C= 1540 Mb/s, the optimal receiving aperture of the 64-Element Phased Array is, and the optimal receiving aperture of the 12-element array is 9.

Fund Project: funded by the National Natural Science Foundation of China (69771005 ).

Description: Wang Bo, male, born in July 1947, Associate Professor, Department of Biomedical Engineering and instruments, School of electronic and information engineering.

Authors: Xi'an Jiaotong University, 710049, Xi'an

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