# Ultrasonic Total Focusing Imaging Method of Multilayer Composite Structures Using the Root-Mean-Square (RMS) Velocity

Authors: Xufei Guo; Yan Han
Journal: Advances in Materials Science and Engineering
 (2021)

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## Abstract

Multilayer composite structures have been widely used in industrial manufacturing, and nondestructive testing of these multilayer structures is to ensure their reliable quality and performance. Currently, ultrasonic total focusing method (TFM) imaging using full-matrix capture (FMC) technology has been proven to sense small defects in a single homogeneous medium and improve the imaging signal-to-noise ratio. However, these algorithms cannot be accurately applied to imaging of multilayer composite structures, due to the acoustic impedance variation and because reflection and refraction occur at the interface between the layers, which makes it very difficult to calculate the ultrasonic propagation path and time. To solve this problem, a root-mean-square (RMS) velocity algorithm for total focusing imaging of multilayer structures is proposed in the article. Based on the theory of RMS velocity for processing of seismic data, the approximated delays can be easily and quickly calculated by a hyperbolic time-distance relationship under circumstances of short lateral distance and horizontal layers. The performance of the proposed algorithm is evaluated by total focusing imaging of a two-layer medium with drilled holes and conducted by the finite element simulation. To further improve imaging efficiency, the partial data in the full-matrix data were used for imaging which is the simplified matrix focusing method (SFM). The results verify that the proposed methods are capable of total focusing imaging of two-layered structures. However, the imaging performance and efficiency of these algorithms are different.


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## Body

## 1. Introduction

Multilayer structures play an important role in the production and manufacturing of industrial products, such as solid rocket motors, aircraft skin, and generator blade, due to their advantages in corrosion protection, wear-resistant and strength enhancement, and so on [1, 2]. In order to ensure the reliable quality and performance of these layered structures, nondestructive testing (NDT) of these structures is essential [3]. Ultrasonic NDT is the well-established method that is widely applied to a broad range of applications, especially the detection of multilayer structure, mainly including the characterization of its material properties, the judgment of interface bonding quality, and the determination of structural consistency.At present, the ultrasonic phased array is a well-known nondestructive testing (NDT) method, and its application has increased dramatically [4–7]. Compared with single-element ultrasonic transducers, ultrasonic arrays have advantages in sensitivity, coverage, etc. [8]. Conventionally, the ultrasonic phased array method is based on the same time delay law by controlling each array element to form a coherent beam and receiving echo signals to image [9]. In order to further improve the imaging resolution, different postprocessing imaging algorithms have been developed, such as dynamic focusing [10], compound imaging [11], and full-matrix imaging [12]. In the time domain, full-matrix capture (FMC) excites each array element in turn, and all array elements (including transmitting array elements) receive echo signals. The total focus method (TFM) realizes imaging by processing the captured full-matrix data [13]. Nevertheless, the total focus method is time-consuming due to the large amount of processing data [12]. To improve imaging efficiency, different total focus algorithms have been proposed [14–19]. Note that both the algorithms based on TFM are only suitable for homogeneous and isotropic materials. Therefore, these algorithms are invalid for multilayer structures as the acoustic impedance varies between different layers.Several methods to ultrasonic imaging of multilayer structures were developed. The ray-tracing method [20, 21] is used for imaging by accurately calculating the sound beam propagation path and time, but the complexity of iterative operation reduces its imaging efficiency. Ultrasonic imaging with virtual sources [22, 23] is introduced to improve the calculating time. However, this approach is susceptible to the detection characteristics and cannot obtain high imaging resolution. Recently, the method in seismic imaging is used for reference, and the phase shift migration (PSM) algorithm [21] based on the plane wave theory was employed to synthetic aperture focusing technique (SAFT) of multilayer structures. To improve calculation efficiency and imaging resolution, several frequency-domain ultrasound imaging algorithms based on PSM are proposed [24–28]. Unfortunately, the programming of this method is both complicated and needed.In this work, we propose an ultrasonic TFM, based on root-mean-square (RMS) velocity, which is derived from processing of seismic data. Using the RMS velocity, the ultrasonic TFM in single medium can be modified for applied on multilayer structures. The remainder of this work is organized as follows. In Section2, the TFM of single medium, traditional multilayer structure TFM, the RMS velocity theory, and the proposed multilayer TFM are presented. Simulation has been conducted in to evaluate imaging performance of multilayer TFM, and the results are presented in Section 3. Finally, the main conclusions of the paper are in Section 4.


## 2. Theory and Methods

### 2.1. TFM in a Single Medium

Consider the typical FMC setup shown in Figure1. Each transducer is excited in turn along a line in the x direction, and all transducers (including transmitting transducer) receive echo signals from a scatterer. Finally, a full-matrix data is obtained. The TFM is defined by(1)Ipxp,zp=∑i=1N∑j=1NAijtijxp,zp,where xp,zp is coordinates of scatterer P, Aij is a amplitude intensity of scatterer P excited by transducer i and received by transducer j,tijxp,zp is the time of flight staring from the transducer i, passing through to the scatterer P and arriving at the transducer j, and Nis the number of transducers. The time of flight is calculated by(2)tijxp,zp=xi−xp2+zp2+xj−xp2+zp2c,where c is ultrasonic velocity in the single medium and xi,0 and xj,0 are the Cartesian coordinates of the transmitting transducer and the receiving transducer, respectively. Assume that t0zp=zp/c is the normal incidence one-way flight time from ith ultrasonic transducer to the scatterer P in the single medium. The time of flight can be modified as(3)tijxp,zp=t02zp+xi−xp2c2+t02zp+xj−xp2c2.Figure 1
Schematic diagram of FMC and TFM.Consider the energy of weight of different transducers to the imaging area, and Equation (1) can be modified by(4)Ipxp,zp=∑i=1N∑j=KMAijtijxp,zp,1<K,M<N.Since the amount of postprocessing data is part of the full-matrix data, theoretically, the calculation time of this simplified matrix focusing method (SFM) will also be reduced. To superimpose and offset the random noise of positive and negative values, it is necessary to normalize the captured full-matrix data [18, 19]. The amplitude is normalized by(5)Ipxp,zp=Ipxp,zpImaxxp,zp×128,Ipxp,zp≥0,Ipxp,zp=−Ipxp,zpIminxp,zp×127,Ipxp,zp<0.


### 2.2. Traditional Multilayer Structure TFM (TML-TFM)

The principle of traditional multilayer structure TFM [29] is shown in Figure2. The height of layer 1 is h. The propagation speed of ultrasonic waves in layer 1 and layer 2 are c1 and c2, respectively. Assuming that the incident point of the ith element at the interface of the double-layer structure is S1, the incident angle and refraction angle are θ1 and θ2, respectively, and P represents any point in the imaging area.Figure 2
The principle of traditional multilayer structure TFM.In Figure2, the following equation can be obtained by(6)xp=htanθ1+zp−htanθ2.According to Snell’s law, the following equation can be obtained by(7)sinθ1sinθ2=c1c2.Then, the flight time of the ultrasonic wave reflected from theith element through point P to the jth element in the double-layer structure can be expressed as(8)tijxp,zp=xi−xit2+zit2+xj−xjr2+zit2c1+xp−xit2+zp−zit2+xp−xjr2+zp−zjr2c2.In the double-layer structure, because the acoustic impedances of the two materials are different, the ultrasonic waves are reflected and refracted at the interface. According to Fermat’s principle, the speed of sound always travels along the path with the shortest flight time. Therefore, the minimum value oftijxp,zp needs to be solved as the time index value of the full-matrix data processing.


### 2.3. Multilayer TFM Based on the RMS Velocity (RML-TFM)

In the case of multilayer structures, the ultrasonic propagation path becomes a bit more complicated. The ultrasonic propagation path is illustrated in Figure3. Because these layers have different sound velocities, reflection and refraction occur at the interfaces. In this case, the precise time of flight and delay between the scatterer and the each transducer cannot be calculated analytically [20]. In seismic signal processing technology, the RMS velocity is often adopted to calculate the migration imaging velocity in the geological layers of the Earth [30–32]. And, some seismic signal processing methods [33] are also suitable for ultrasonic data processing. Therefore, the RMS velocity model derived from seismic data processing can approximately calculate the time delay of ultrasonic propagation in multilayer structures.Figure 3
Wave propagation through multilayer with different sound velocities.In Figure3, it is assumed that the ultrasound array transducer is placed on top of layer 1, and the layers are, respectively, named 1, 2, …, L. The normal incidence one-way flight time from ithultrasonic transducer to the scatterer P in layer number L is calculated by(9)t0zp=∑k=1L−1hkck+ΔzcL,where hk and ck are the thickness and wave velocity of layer k, respectively, and Δz=zp−∑k=1L−1hk is vertical distance from the scatterer P to the interface between the last two layers. The RMS velocity of multilayer structures is defined by(10)crmszp=∑k=1L−1ck2tk+cL2t0zp−∑k=1L−1tkt0zp,where tk=hk/ck is the normal incidence one-way flight time of layer k. Substituting equation (9), Δz=zp−∑k=1L−1hk, and hk=cktk into equation (10), the RMS velocity can be modified as(11)crmszp=∑k=1L−1ckhk+cLΔzt0zp.Based on the law of RMS velocity, it is possible that the time of flight starting from the transduceri, passing through to the scatterer P, and arriving at the transducer j is derived.In multilayer structures, the flight time in a multilayer structure is similar to that in the single medium case:(12)tzp,xp,xi,xj=t02zp+xi−xp2crms2zp+t02zp+xj−xp2crms2zp.The conclusion can be obtained from [30] that expression (equation (12)) for t is equivalent to ignoring the higher-order part of the Taylor series expansion of xp−xi=0 for t. Therefore, this corresponding flight time is an approximate analytical solution. Using the imaging equation that was applied for TFM in a single medium (equation (1)), the modified equation (equation (12)) for t can be adopted for full focusing in multilayer structures. We call this algorithm multilayer TFM (RML-TFM). If the expression (equation (4)) is combined with the expression (equation (12)), this method can also be used for focusing imaging of multilayer structures. This algorithm was referred as multilayer SFM (RML-SFM).


## 2.1. TFM in a Single Medium

Consider the typical FMC setup shown in Figure1. Each transducer is excited in turn along a line in the x direction, and all transducers (including transmitting transducer) receive echo signals from a scatterer. Finally, a full-matrix data is obtained. The TFM is defined by(1)Ipxp,zp=∑i=1N∑j=1NAijtijxp,zp,where xp,zp is coordinates of scatterer P, Aij is a amplitude intensity of scatterer P excited by transducer i and received by transducer j,tijxp,zp is the time of flight staring from the transducer i, passing through to the scatterer P and arriving at the transducer j, and Nis the number of transducers. The time of flight is calculated by(2)tijxp,zp=xi−xp2+zp2+xj−xp2+zp2c,where c is ultrasonic velocity in the single medium and xi,0 and xj,0 are the Cartesian coordinates of the transmitting transducer and the receiving transducer, respectively. Assume that t0zp=zp/c is the normal incidence one-way flight time from ith ultrasonic transducer to the scatterer P in the single medium. The time of flight can be modified as(3)tijxp,zp=t02zp+xi−xp2c2+t02zp+xj−xp2c2.Figure 1
Schematic diagram of FMC and TFM.Consider the energy of weight of different transducers to the imaging area, and Equation (1) can be modified by(4)Ipxp,zp=∑i=1N∑j=KMAijtijxp,zp,1<K,M<N.Since the amount of postprocessing data is part of the full-matrix data, theoretically, the calculation time of this simplified matrix focusing method (SFM) will also be reduced. To superimpose and offset the random noise of positive and negative values, it is necessary to normalize the captured full-matrix data [18, 19]. The amplitude is normalized by(5)Ipxp,zp=Ipxp,zpImaxxp,zp×128,Ipxp,zp≥0,Ipxp,zp=−Ipxp,zpIminxp,zp×127,Ipxp,zp<0.


## 2.2. Traditional Multilayer Structure TFM (TML-TFM)

The principle of traditional multilayer structure TFM [29] is shown in Figure2. The height of layer 1 is h. The propagation speed of ultrasonic waves in layer 1 and layer 2 are c1 and c2, respectively. Assuming that the incident point of the ith element at the interface of the double-layer structure is S1, the incident angle and refraction angle are θ1 and θ2, respectively, and P represents any point in the imaging area.Figure 2
The principle of traditional multilayer structure TFM.In Figure2, the following equation can be obtained by(6)xp=htanθ1+zp−htanθ2.According to Snell’s law, the following equation can be obtained by(7)sinθ1sinθ2=c1c2.Then, the flight time of the ultrasonic wave reflected from theith element through point P to the jth element in the double-layer structure can be expressed as(8)tijxp,zp=xi−xit2+zit2+xj−xjr2+zit2c1+xp−xit2+zp−zit2+xp−xjr2+zp−zjr2c2.In the double-layer structure, because the acoustic impedances of the two materials are different, the ultrasonic waves are reflected and refracted at the interface. According to Fermat’s principle, the speed of sound always travels along the path with the shortest flight time. Therefore, the minimum value oftijxp,zp needs to be solved as the time index value of the full-matrix data processing.


## 2.3. Multilayer TFM Based on the RMS Velocity (RML-TFM)

In the case of multilayer structures, the ultrasonic propagation path becomes a bit more complicated. The ultrasonic propagation path is illustrated in Figure3. Because these layers have different sound velocities, reflection and refraction occur at the interfaces. In this case, the precise time of flight and delay between the scatterer and the each transducer cannot be calculated analytically [20]. In seismic signal processing technology, the RMS velocity is often adopted to calculate the migration imaging velocity in the geological layers of the Earth [30–32]. And, some seismic signal processing methods [33] are also suitable for ultrasonic data processing. Therefore, the RMS velocity model derived from seismic data processing can approximately calculate the time delay of ultrasonic propagation in multilayer structures.Figure 3
Wave propagation through multilayer with different sound velocities.In Figure3, it is assumed that the ultrasound array transducer is placed on top of layer 1, and the layers are, respectively, named 1, 2, …, L. The normal incidence one-way flight time from ithultrasonic transducer to the scatterer P in layer number L is calculated by(9)t0zp=∑k=1L−1hkck+ΔzcL,where hk and ck are the thickness and wave velocity of layer k, respectively, and Δz=zp−∑k=1L−1hk is vertical distance from the scatterer P to the interface between the last two layers. The RMS velocity of multilayer structures is defined by(10)crmszp=∑k=1L−1ck2tk+cL2t0zp−∑k=1L−1tkt0zp,where tk=hk/ck is the normal incidence one-way flight time of layer k. Substituting equation (9), Δz=zp−∑k=1L−1hk, and hk=cktk into equation (10), the RMS velocity can be modified as(11)crmszp=∑k=1L−1ckhk+cLΔzt0zp.Based on the law of RMS velocity, it is possible that the time of flight starting from the transduceri, passing through to the scatterer P, and arriving at the transducer j is derived.In multilayer structures, the flight time in a multilayer structure is similar to that in the single medium case:(12)tzp,xp,xi,xj=t02zp+xi−xp2crms2zp+t02zp+xj−xp2crms2zp.The conclusion can be obtained from [30] that expression (equation (12)) for t is equivalent to ignoring the higher-order part of the Taylor series expansion of xp−xi=0 for t. Therefore, this corresponding flight time is an approximate analytical solution. Using the imaging equation that was applied for TFM in a single medium (equation (1)), the modified equation (equation (12)) for t can be adopted for full focusing in multilayer structures. We call this algorithm multilayer TFM (RML-TFM). If the expression (equation (4)) is combined with the expression (equation (12)), this method can also be used for focusing imaging of multilayer structures. This algorithm was referred as multilayer SFM (RML-SFM).


## 3. Experiments and Results

### 3.1. Experimental Conditions

To further verify the performance of our proposed imaging method, ultrasonic TFM of three two-layer structures are conducted in finite element method (FEM) simulation. These three two-layer structures are composed of acrylic material and aluminum. For clarity, their geometry and the corresponding defects are depicted in Figure4. These three multilayer structures are numbered model 1, model 2, and model 3, respectively. A 32-element linear phased array is configured for imaging simulation, and the array specifications are shown in Table 1. In the simulation process, only the ultrasonic longitudinal wave generated by the array is considered, and the shear wave is ignored. In acrylic and aluminum materials, the ultrasonic longitudinal wave propagation velocity approximately is 2720 m/s and 6260 m/s, respectively.Figure 4
The geometry of two-layer structure. (a) Model 1. (b) Model 2. (c) Model 3.
(a)(b)(c)Table 1
The specifications of the ultrasonic phased array.
ParameterValueNumber of elements32Element width0.4 mmElement pitch0.1 mmSampling time interval2e − 8 sCenter frequency5 MHzIn this simulation, the finite element software ABAQUS (Dassault, Velizy-Villacoublay, France) was used to generate the full-matrix data. According to the principle of FMC, each array element is separately excited by a sinusoidal signal modulated by the Hanning window, and all array elements receive echo signals. As a result, the full-matrix data of32×32 were captured with a sampling frequency of 50MHz and imported into MATLAB R2016a (Math-Works, Natick, MA, USA) for postprocessing with different imaging algorithms. In this paper, the full matrix data are postprocessed by TML-TFM, RML-TFM, and RML-SFM.


### 3.2. Results and Discussion

#### 3.2.1. Imaging Results of Single Medium

This paper uses the experimental setup described in [19] to focus imaging on a single-layer medium, and the imaging results are shown in Figure 5. It can be seen that the imaging quality of the simplified matrix is the same as that of the full matrix. Compared with TFM, the imaging efficiency by using SFM is greatly improved.Figure 5
Focused imaging of a single medium. (a) TFM. (b) SFM-1 (in equation (4), j=7:23). (c) SFM-2 (in equation (4), j=1:i).
(a)(b)(c)


#### 3.2.2. Imaging Results of Multilayer Composite Structure

Figure6 presents the amplitude data for full matrix of model 2. It can be observed from Figure 6 that the full-matrix data has symmetry. In other words, the upper or lower triangle data can also be used for postprocessing focused imaging. In this article, the full-matrix imaging and simplified-matrix imaging are conducted on these three multilayer structures with different defects. The imaging results of different algorithms are shown in Figures 7–9.Figure 6
The captured full-matrix data of model 2.Figure 7
Focused imaging of model 1: (a) ML-TFM; (b) ML-SFM-1 (in equation (4), j=7:23); (c) ML-SFM-2 (in equation (4), j=1:i); (d) TML-TFM.
(a)(b)(c)(d)Figure 8
Focused imaging of model 2: (a) ML-TFM; (b) ML-SFM-1 (in equation (4), j=7:23); (c) ML-SFM-2 (in equation (4), j=1:i); (d) TML-TFM.
(a)(b)(c)(d)Figure 9
Focused imaging of model 3: (a) ML-TFM; (b) ML-SFM-1 (in equation (4), j=7:23); (c) ML-SFM-2 (in equation (4), j=1:i); (d) TML-TFM.
(a)(b)(c)(d)In order to prevent aliasing in space and time, according to the spatial sampling theorem [28], the imaging pixel density in the x and z directions are both 0.1 mm. In Figures 7–9, using traditional methods, there is obvious noise in the near-field area of the ultrasound image. However, using ML-TFM, ML-SFM-1, and ML-SFM-2, it can be observed that there is a pseudointerface at the interface of the two media. Compared with the total focus image based on the root-mean-square velocity, the false defects around every defect in the traditional total focus image are more prominent. Moreover, using ML-SFM-2, these defects display brightness is poor.The above imaging results show that the imaging quality of the full matrix of a single medium is consistent with the imaging quality of the simplified matrix. However, the imaging quality of the full matrix of the double-layer composite structure based on the root-mean-square velocity is higher than that of the simplified matrix. And, in the full-matrix image of the double-layer structure, the integrity of the defects is poor.


#### 3.2.3. Imaging Signal-to-Noise Ratio (SNR)

To quantitatively analyze the performance of different imaging methods, the image signal-to-noise ratio is used to express the relationship between the defect signal and the noise. The signal-to-noise ratio for a defect can be expressed [18, 19] by(13)SNR=20×log10Vp−pVave,where Vp−p is the peak-to-peak value of the defect signal in the surrounding region and Vaveis the average of noise signal. Except for the defects, the rest of the image is regarded as noise signal.In this paper, model 1 is used as the research object to calculate the defect signal-to-noise ratio of different imaging methods. In Model 1, the defect signal-to-noise ratios of the four different imaging methods are shown in Figure10. It can be observed that ML-TFM has the best signal-to-noise ratio. And, the SNR of ML-SFM-1 and ML-SFM-2 are relatively low. Moreover, the SNR of TML-TFM is between ML-TFM and ML-SFM.Figure 10
SNR of different algorithms.


#### 3.2.4. Imaging Efficiency

The entire experimental computing platform configuration in this article is presented in Table2. Figure 11 shows the imaging time of these three models using different imaging algorithms, respectively. It can be observed that ML-TFM has the lowest imaging efficiency.Table 2
Platform configuration.
SpecificationsRelated configurationOperating systemsWindowsCPU/GHzInter Core I5 9300H, 2.4Ram/GB8GPUNVIDIA GeForce GTX1650Figure 11
Imaging time of different algorithms.And, the imaging time of ML-SFM-1 and ML-SFM-2 are relatively close. Moreover, the imaging time of TML-TFM is between ML-TFM and ML-SFM.


## 3.1. Experimental Conditions

To further verify the performance of our proposed imaging method, ultrasonic TFM of three two-layer structures are conducted in finite element method (FEM) simulation. These three two-layer structures are composed of acrylic material and aluminum. For clarity, their geometry and the corresponding defects are depicted in Figure4. These three multilayer structures are numbered model 1, model 2, and model 3, respectively. A 32-element linear phased array is configured for imaging simulation, and the array specifications are shown in Table 1. In the simulation process, only the ultrasonic longitudinal wave generated by the array is considered, and the shear wave is ignored. In acrylic and aluminum materials, the ultrasonic longitudinal wave propagation velocity approximately is 2720 m/s and 6260 m/s, respectively.Figure 4
The geometry of two-layer structure. (a) Model 1. (b) Model 2. (c) Model 3.
(a)(b)(c)Table 1
The specifications of the ultrasonic phased array.
ParameterValueNumber of elements32Element width0.4 mmElement pitch0.1 mmSampling time interval2e − 8 sCenter frequency5 MHzIn this simulation, the finite element software ABAQUS (Dassault, Velizy-Villacoublay, France) was used to generate the full-matrix data. According to the principle of FMC, each array element is separately excited by a sinusoidal signal modulated by the Hanning window, and all array elements receive echo signals. As a result, the full-matrix data of32×32 were captured with a sampling frequency of 50MHz and imported into MATLAB R2016a (Math-Works, Natick, MA, USA) for postprocessing with different imaging algorithms. In this paper, the full matrix data are postprocessed by TML-TFM, RML-TFM, and RML-SFM.


## 3.2. Results and Discussion

### 3.2.1. Imaging Results of Single Medium

This paper uses the experimental setup described in [19] to focus imaging on a single-layer medium, and the imaging results are shown in Figure 5. It can be seen that the imaging quality of the simplified matrix is the same as that of the full matrix. Compared with TFM, the imaging efficiency by using SFM is greatly improved.Figure 5
Focused imaging of a single medium. (a) TFM. (b) SFM-1 (in equation (4), j=7:23). (c) SFM-2 (in equation (4), j=1:i).
(a)(b)(c)


### 3.2.2. Imaging Results of Multilayer Composite Structure

Figure6 presents the amplitude data for full matrix of model 2. It can be observed from Figure 6 that the full-matrix data has symmetry. In other words, the upper or lower triangle data can also be used for postprocessing focused imaging. In this article, the full-matrix imaging and simplified-matrix imaging are conducted on these three multilayer structures with different defects. The imaging results of different algorithms are shown in Figures 7–9.Figure 6
The captured full-matrix data of model 2.Figure 7
Focused imaging of model 1: (a) ML-TFM; (b) ML-SFM-1 (in equation (4), j=7:23); (c) ML-SFM-2 (in equation (4), j=1:i); (d) TML-TFM.
(a)(b)(c)(d)Figure 8
Focused imaging of model 2: (a) ML-TFM; (b) ML-SFM-1 (in equation (4), j=7:23); (c) ML-SFM-2 (in equation (4), j=1:i); (d) TML-TFM.
(a)(b)(c)(d)Figure 9
Focused imaging of model 3: (a) ML-TFM; (b) ML-SFM-1 (in equation (4), j=7:23); (c) ML-SFM-2 (in equation (4), j=1:i); (d) TML-TFM.
(a)(b)(c)(d)In order to prevent aliasing in space and time, according to the spatial sampling theorem [28], the imaging pixel density in the x and z directions are both 0.1 mm. In Figures 7–9, using traditional methods, there is obvious noise in the near-field area of the ultrasound image. However, using ML-TFM, ML-SFM-1, and ML-SFM-2, it can be observed that there is a pseudointerface at the interface of the two media. Compared with the total focus image based on the root-mean-square velocity, the false defects around every defect in the traditional total focus image are more prominent. Moreover, using ML-SFM-2, these defects display brightness is poor.The above imaging results show that the imaging quality of the full matrix of a single medium is consistent with the imaging quality of the simplified matrix. However, the imaging quality of the full matrix of the double-layer composite structure based on the root-mean-square velocity is higher than that of the simplified matrix. And, in the full-matrix image of the double-layer structure, the integrity of the defects is poor.


### 3.2.3. Imaging Signal-to-Noise Ratio (SNR)

To quantitatively analyze the performance of different imaging methods, the image signal-to-noise ratio is used to express the relationship between the defect signal and the noise. The signal-to-noise ratio for a defect can be expressed [18, 19] by(13)SNR=20×log10Vp−pVave,where Vp−p is the peak-to-peak value of the defect signal in the surrounding region and Vaveis the average of noise signal. Except for the defects, the rest of the image is regarded as noise signal.In this paper, model 1 is used as the research object to calculate the defect signal-to-noise ratio of different imaging methods. In Model 1, the defect signal-to-noise ratios of the four different imaging methods are shown in Figure10. It can be observed that ML-TFM has the best signal-to-noise ratio. And, the SNR of ML-SFM-1 and ML-SFM-2 are relatively low. Moreover, the SNR of TML-TFM is between ML-TFM and ML-SFM.Figure 10
SNR of different algorithms.


### 3.2.4. Imaging Efficiency

The entire experimental computing platform configuration in this article is presented in Table2. Figure 11 shows the imaging time of these three models using different imaging algorithms, respectively. It can be observed that ML-TFM has the lowest imaging efficiency.Table 2
Platform configuration.
SpecificationsRelated configurationOperating systemsWindowsCPU/GHzInter Core I5 9300H, 2.4Ram/GB8GPUNVIDIA GeForce GTX1650Figure 11
Imaging time of different algorithms.And, the imaging time of ML-SFM-1 and ML-SFM-2 are relatively close. Moreover, the imaging time of TML-TFM is between ML-TFM and ML-SFM.


## 3.2.1. Imaging Results of Single Medium

This paper uses the experimental setup described in [19] to focus imaging on a single-layer medium, and the imaging results are shown in Figure 5. It can be seen that the imaging quality of the simplified matrix is the same as that of the full matrix. Compared with TFM, the imaging efficiency by using SFM is greatly improved.Figure 5
Focused imaging of a single medium. (a) TFM. (b) SFM-1 (in equation (4), j=7:23). (c) SFM-2 (in equation (4), j=1:i).
(a)(b)(c)


## 3.2.2. Imaging Results of Multilayer Composite Structure

Figure6 presents the amplitude data for full matrix of model 2. It can be observed from Figure 6 that the full-matrix data has symmetry. In other words, the upper or lower triangle data can also be used for postprocessing focused imaging. In this article, the full-matrix imaging and simplified-matrix imaging are conducted on these three multilayer structures with different defects. The imaging results of different algorithms are shown in Figures 7–9.Figure 6
The captured full-matrix data of model 2.Figure 7
Focused imaging of model 1: (a) ML-TFM; (b) ML-SFM-1 (in equation (4), j=7:23); (c) ML-SFM-2 (in equation (4), j=1:i); (d) TML-TFM.
(a)(b)(c)(d)Figure 8
Focused imaging of model 2: (a) ML-TFM; (b) ML-SFM-1 (in equation (4), j=7:23); (c) ML-SFM-2 (in equation (4), j=1:i); (d) TML-TFM.
(a)(b)(c)(d)Figure 9
Focused imaging of model 3: (a) ML-TFM; (b) ML-SFM-1 (in equation (4), j=7:23); (c) ML-SFM-2 (in equation (4), j=1:i); (d) TML-TFM.
(a)(b)(c)(d)In order to prevent aliasing in space and time, according to the spatial sampling theorem [28], the imaging pixel density in the x and z directions are both 0.1 mm. In Figures 7–9, using traditional methods, there is obvious noise in the near-field area of the ultrasound image. However, using ML-TFM, ML-SFM-1, and ML-SFM-2, it can be observed that there is a pseudointerface at the interface of the two media. Compared with the total focus image based on the root-mean-square velocity, the false defects around every defect in the traditional total focus image are more prominent. Moreover, using ML-SFM-2, these defects display brightness is poor.The above imaging results show that the imaging quality of the full matrix of a single medium is consistent with the imaging quality of the simplified matrix. However, the imaging quality of the full matrix of the double-layer composite structure based on the root-mean-square velocity is higher than that of the simplified matrix. And, in the full-matrix image of the double-layer structure, the integrity of the defects is poor.


## 3.2.3. Imaging Signal-to-Noise Ratio (SNR)

To quantitatively analyze the performance of different imaging methods, the image signal-to-noise ratio is used to express the relationship between the defect signal and the noise. The signal-to-noise ratio for a defect can be expressed [18, 19] by(13)SNR=20×log10Vp−pVave,where Vp−p is the peak-to-peak value of the defect signal in the surrounding region and Vaveis the average of noise signal. Except for the defects, the rest of the image is regarded as noise signal.In this paper, model 1 is used as the research object to calculate the defect signal-to-noise ratio of different imaging methods. In Model 1, the defect signal-to-noise ratios of the four different imaging methods are shown in Figure10. It can be observed that ML-TFM has the best signal-to-noise ratio. And, the SNR of ML-SFM-1 and ML-SFM-2 are relatively low. Moreover, the SNR of TML-TFM is between ML-TFM and ML-SFM.Figure 10
SNR of different algorithms.


## 3.2.4. Imaging Efficiency

The entire experimental computing platform configuration in this article is presented in Table2. Figure 11 shows the imaging time of these three models using different imaging algorithms, respectively. It can be observed that ML-TFM has the lowest imaging efficiency.Table 2
Platform configuration.
SpecificationsRelated configurationOperating systemsWindowsCPU/GHzInter Core I5 9300H, 2.4Ram/GB8GPUNVIDIA GeForce GTX1650Figure 11
Imaging time of different algorithms.And, the imaging time of ML-SFM-1 and ML-SFM-2 are relatively close. Moreover, the imaging time of TML-TFM is between ML-TFM and ML-SFM.


## 4. Conclusions

In this paper, a multilayer structures ultrasonic full-matrix imaging method based on root-mean-square (RMS) velocity is proposed. The experimental results show that full-matrix imaging based on RMS velocity has the best signal-to-noise ratio and the lowest imaging efficiency. However, the simplified matrix imaging based on RMS velocity has the worst imaging performance and the highest imaging efficiency. The imaging performance and efficiency of the traditional full-matrix imaging method are between the above two. For the multilayer structure, how to maintain high-performance imaging while improving imaging efficiency needs to be studied further.



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