CN104898123A - Water immersion ultrasonic synthetic aperture focusing imaging method based on angular domain virtual source - Google Patents

Abstract

The invention discloses a water immersion ultrasonic synthetic aperture focusing imaging method based on an angular domain virtual source. The method is used for ultrasonic imaging of water-immersed workpieces and comprises four steps including water-immersed workpiece acoustic beam propagation modeling, echo signal acquisition in the angular domain, echo signal reconstruction in the virtual source, and synthetic aperture focusing imaging. The method has technical effects that it is no need to consider influences of an acoustic beam propagation path and a sound velocity change on delayed superposition computation to perform ultrasonic synthetic aperture focusing imaging on the water-immersed workpieces by using virtual source technology, thereby reducing imaging computation complexity; and a delayed superposition algorithm based on an angular domain virtual source model is provided which effectively combines synthetic aperture focusing imaging technology and spatial composite imaging technology such that an angular domain ultrasonic synthetic aperture focusing image can be acquired just by one-time delayed superposition computation, thereby improving synthetic aperture focusing imaging efficiency and precision and reducing influence of spot noise on imaging.

Description

Water Immersion Ultrasound Synthetic Aperture Focusing Imaging Method Based on Angle Domain Virtual Source

technical field

The invention relates to a water immersion ultrasonic imaging method, which includes angle-domain scanning technology, virtual source technology, synthetic aperture focusing imaging technology, and space composite imaging technology, and realizes efficient and high-precision ultrasonic synthetic aperture focusing imaging of water-immersed workpieces.

Background technique

As an important means of non-destructive testing, ultrasonic testing has been widely used in industrial product testing. It can detect defects without destroying the structural performance of workpieces. When the traditional ultrasonic detection method adopts a single probe detection, the imaging resolution is β _B = 0.84·λ/D, where D represents the aperture of the transducer, and λ represents the wavelength of the sound beam excited by the transducer. Therefore, it is necessary to improve the resolution of ultrasonic imaging. Increasing the transducer aperture or reducing the ultrasonic wavelength increases the operating frequency of the ultrasonic transducer. However, increasing the transducer aperture limits the detection range of the probe, which is not suitable for the detection of complex surface structures. Increase the operating frequency of the transducer. It will increase the attenuation of ultrasonic waves in the workpiece, which is not conducive to the detection of internal defects of the workpiece. Synthetic Aperture Focusing Technique (SAFT) is an important imaging method in the field of ultrasonic testing. Its imaging is not affected by the propagation characteristics of the sound field in the Fresnel zone. The imaging resolution β _saft = D/2, only with the transducer Higher resolution imaging can be obtained through small aperture and low operating frequency transducers.

However, for the ultrasonic detection of water-immersed workpieces, the traditional SAFT needs to consider the propagation path of the sound beam in the water and the workpiece, and the change of the sound velocity when performing delay superposition, resulting in low calculation efficiency of delay superposition. In order to improve the calculation efficiency of time-delay superposition, application publication number CN103018333A, the patent document published on April 3, 2013 discloses a synthetic aperture focused ultrasonic imaging method for layered objects, which uses linear scan conversion technology to reduce the time-delay superposition time. This method can reduce the calculation time of delay superposition to a certain extent, but it still needs to consider the change of the sound velocity of the sound beam propagating in the water and the workpiece.

In addition, ultrasonic detection is affected by the random noise of the system and structure, and speckle noise will be generated during imaging. After checking the angles, the ultrasonic imaging of each scanning angle is obtained, and the images of adjacent scanning angles are differentially processed and combined, and the speckle noise of the combined image is effectively suppressed. However, when using this method to spatially compound SFAT images, it is necessary to perform time-delayed superposition calculations on the echo signals of each scanning angle, and then perform spatial compound imaging after obtaining the SAFT image of each scanning angle. The imaging time is shortened, and the imaging efficiency is low.

In order to improve the time-delayed superposition calculation efficiency of SAFT in water immersion ultrasonic testing, the present invention introduces virtual source technology. The schematic diagram of the virtual source model is shown in Figure 3. Water immersion ultrasonic testing is taken as an example. When using a focusing probe to detect a workpiece, when the focusing probe is focused on the surface Q ₁ of the workpiece, the focusing point can be regarded as a virtual transducer that can generate spherical waves at a certain angle. The aperture of the focusing probe is set to is D, the unit energy generated by the transducer is p ₀ , for any point P inside the workpiece, its depth is z _s , and the imaging signal-to-noise ratio is When the virtual source technology is used, the imaging signal-to-noise ratio is It can be seen that the imaging signal-to-noise ratio of the traditional ultrasonic testing method decreases with the increase of the detection depth, but when the virtual source technology is used for imaging, if the attenuation of the ultrasonic wave inside the workpiece is not considered, the imaging signal-to-noise ratio does not change with the detection depth. Variety. In addition, when a virtual source is used for SAFT imaging, the sound beam can be considered to be focused on the virtual source on the surface of the workpiece during transmission and reception, so it is not necessary to consider the changes in the propagation path and sound velocity of the sound beam in water and in the workpiece.

In order to reduce the speckle noise in ultrasonic imaging and improve the imaging efficiency of the spatial composite imaging method when processing SAFT images, through the angle domain virtual source model, the schematic diagram of the model is shown in Figure 5, and a time-delay superposition algorithm based on this model is established, which can realize The combination of SAFT and spatial compound imaging method can obtain the angle-domain ultrasonic synthetic aperture focused image through a time-delay superposition calculation.

Contents of the invention

The object of the present invention is to propose a water immersion ultrasonic synthetic aperture focusing imaging method with high imaging efficiency and precision and less affected by speckle noise.

The present invention is characterized in that, through the virtual source technology, it is not necessary to consider the propagation path and propagation sound velocity of the sound beam in water and in the workpiece, thereby improving the calculation efficiency of delay and superposition.

The present invention is characterized in that the combination of synthetic aperture focusing imaging technology and space composite imaging technology is realized through the angle domain virtual source model, and the angle domain ultrasonic synthetic aperture focusing image can be obtained through a time-delay superposition calculation.

The technical solution of the present invention is a method for focusing imaging of water immersion ultrasonic synthetic aperture based on an angle-domain virtual source, comprising the following steps:

Step 1: Modeling of sound beam propagation of water-immersed workpiece. The acoustic beam propagation model of the water-immersed workpiece is established according to the workpiece geometry and material parameters, and the angular domain scanning range and scanning interval angle are determined according to the acoustic beam propagation model. The angle between the normal of the incident point of the workpiece and the scanning interval angle refer to the adjacent scanning angle interval when the focusing probe scans in the angular domain. Assuming that the sound velocity of the sound beam in water and in the workpiece is c _w and c _s respectively, the focal length of the focusing probe is d, and the diameter of the chip is φ, then the probe aperture angle θ _w = 2arctan(φ/2d). When the sound beam is refracted at the interface of the water-immersed workpiece, the wave mode conversion will occur. According to the first critical angle law, the scanning range in the angular domain is determined to be In order to further reduce the influence of shear wave on water immersion ultrasonic testing during wave mode conversion, the scanning range in the angular domain is finally determined as In order to ensure the continuous scanning of the acoustic beam along the direction of the angular domain in the workpiece, the scanning interval angle is determined to be |Δφ|≤θ _w according to Snell's law.

Step 2: Acquisition of echo signals in the angle domain. According to the angular domain scanning range and scanning interval angle determined in step 1, the workpiece to be measured is placed on a four-axis automatic ultrasonic testing platform with X/Y/Z/A, and the position of the focusing probe is adjusted through the motion control device to make it vertical and parallel. Focus on the workpiece surface, mark the starting point B(0,0) and then scan along the X-axis direction with a step distance of Δx to the end point B(n,0), and store the echo signal data(i,j,0° synchronously ), where the total number of virtual sources is n/Δx, where n represents the coordinates of the sound beam incident point along the X-axis direction, i represents the number of sampling points along the scanning direction of the X-axis, and j represents the number of sampling points along the detection direction of the Z-axis; define The clockwise direction of the A-axis is positive. The A-axis rotation and the Z-axis movement are controlled by the motion control device, so that the focusing probe rotates and scans the interval angle Δφ and focuses on the starting point B(0,0) on the workpiece surface, and then moves along the X-axis The direction is scanned to the end point B(n,0) with the step distance of Δx, and the echo signal data(i,j,Δφ) is stored synchronously. After repeating the above operations, all echo signals data( i,j,±N·Δφ), where N represents the number of scanning tilts of the focusing probe within half an angle domain.

Step 3: Reconstruction of the echo signal in the virtual source. Establish a virtual source model in the angle domain of the water-immersed workpiece, and obtain the beam divergence angle of the reconstructed virtual source in the water-immersed workpiece when the focusing probe scans at any scanning angle in the angle domain: Accordingly, the echo signal data(i,j,±N·Δφ) obtained in step 2 is reconstructed into data(i,j,±N·θ _t ) in the virtual source.

Step 4: synthetic aperture focusing imaging. Establish a time-delay superposition algorithm based on the angle-domain virtual source model, and perform time-delay superposition calculation on the reconstructed echo signal obtained in step 3 to obtain the superimposed voltage amplitude of each imaging point, and calculate the voltage amplitude of all points in the imaging area After the normalized calculation, the value is reassigned to realize the water immersion ultrasonic synthetic aperture focusing imaging based on the virtual source in the angle domain.

Said one method of water immersion ultrasonic synthetic aperture focusing imaging based on an angle-domain virtual source, said step 3 in which the reconstruction of the virtual source sound beam diffusion angle θ _t in the water-immersion workpiece is calculated as follows: establishing a water-immersion workpiece angle-domain virtual Source model, virtual source sound beam spread angle calculated by Snell's law Assuming that the scanning interval angle of the focusing probe is Δφ, when |Δφ|< _θw , the virtual source sound beams will overlap along the direction of the angular domain in the workpiece, and the overlapping part is processed by the mean value method to determine that the focusing probe is in the angular domain at any When scanning at the scanning angle, the beam divergence angle of the reconstructed virtual source in the water-immersed workpiece is Said a kind of water immersion ultrasonic synthetic aperture focusing imaging method based on angle-domain virtual source, said step 4 based on the time-delay superposition algorithm of angle-domain virtual source model comprises the following steps:

Step 1. For any point P(i,j) in the workpiece, its effective synthetic aperture length where z _s represents the depth of point P from the workpiece surface, The number of times the probe involved in the delay superposition calculation moves along the X-axis direction K=round(n) is obtained after rounding.

Step 2. When K in step 1>2, K is compensated to obtain K _n , so that K _n is an even number, that is, the number of probes participating in the delay superposition calculation is an odd number; when K≤2, no delay superposition is performed Calculate, go to step 9.

Step 3. Read the echo signal data data(i, j, 0°) when the scanning angle is 0°, and assign it as the initial value SUM ₀ .

Step 4. Define variable ii, which represents the ii-th virtual source participating in the delay superposition calculation, and assign an initial value of 1 to ii.

Step 5. Calculate the inclination angle θ _ii =atan(ii·Δx/z _s ) from the virtual source to point P(i,j) in step 4, and the delay time t=(z _s /cosθ _ii -z _s )/c , the number of time-delayed sampling points along the Z-axis detection direction T=round(t/dt), dt represents the sampling time interval along the detection direction, the apodization coefficient ε=0.5[1+cos(2·pi·η)], the formula Among them, η=ii·Δx/L.

Step 6. Divide the inclination angle θ _ii obtained in step 5 by the sound beam spread angle θ _t of a single virtual source, and round up the result N=ceil(θ _ii /θ _t ).

Step 7. Add the apodization coefficient ε in step 5 to the delay superposition calculation, and the calculation formula is:

SUM=SUM ₀ +ε(data(i−ii,j+T,−N·θ _t )+εdata(i+ii,j+T,N·θ _t )).

Step 8. Redefine the result obtained in step 7 as the initial value SUM ₀ , process the ii+1th virtual source, and continue to execute steps 3 to 7 until ii=K _n /2-1.

Step 9. Perform mean value processing on the SUM finally obtained in step 8, data(i,j)=SUM/(K _n +1), and assign the voltage amplitude of the processed data to P(i,j).

The technical effect of the present invention is that, for the ultrasonic synthetic aperture focusing imaging of the water-immersed workpiece, by adopting the virtual source technology, it is not necessary to consider the change of the propagation path and sound velocity of the sound beam in the water and the workpiece, thereby improving the calculation efficiency of delay superposition; The time-delay superposition algorithm based on the angle-domain virtual source model realizes the combination of synthetic aperture technology and spatial composite technology in ultrasonic imaging, and obtains the angle-domain ultrasonic synthetic aperture focused image through a time-delay superposition calculation, thereby improving imaging efficiency and accuracy. Reduce the impact of speckle noise on imaging.

The present invention will be further described below in conjunction with accompanying drawing.

Description of drawings

Fig. 1 is the flow chart of the water immersion ultrasonic synthetic aperture focusing imaging based on the angle-domain virtual source proposed by the present invention;

Fig. 2 is the schematic diagram of the sound beam propagation model of the water immersion workpiece of the present invention;

Fig. 3 is a schematic diagram of the virtual source model of the present invention;

Fig. 4 is a schematic diagram of echo signal acquisition in a virtual source of the present invention;

Fig. 5 is a schematic diagram of the angle domain virtual source model of the present invention;

Fig. 6 is the flow chart of the delay superposition calculation based on the angle domain virtual source model of the present invention;

Fig. 7 is the physical figure of detection test block in the specific embodiment of the present invention;

Figure 8 is a B-scan imaging diagram of the focusing probe of the present invention;

Fig. 9 is an imaging diagram of the present invention using a traditional synthetic aperture focusing method;

Fig. 10 is a water immersion ultrasonic synthetic aperture focusing imaging diagram based on an angle-domain virtual source in the present invention.

Detailed ways

The specific embodiment of the present invention takes the water immersion ultrasonic detection of aluminum test block as an example. The physical picture of the test block is shown in Figure 7. The size of the test block is 120mm×100mm, the size of the target imaging area is 15mm×30mm, and the diameter of the defect hole is 2mm. Water immersion ultrasonic synthetic aperture focusing imaging based on angle-domain virtual sources is performed on the target imaging area, and the steps include:

Step 1: Modeling the sound beam propagation of the water-immersed workpiece, and determining the scanning range and scanning interval angle in the angular domain. The propagation speed c _w of longitudinal wave in water is 1480m/s, and the propagation speed c _s in aluminum is 5840m/s. The center frequency is 5MHz, the chip diameter is 25mm, and the focal length is 125mm. Modeling the sound beam propagation of water-immersed aluminum workpieces, the angular domain scanning range is determined to be -4.5°<β _w <4.5°, and the scanning interval angle is Δφ≤11.4°. Combined with the actual detection needs, the angular domain scanning range is determined to be -4°≤β _w ≤4°, scan interval angle Δφ=1°, that is, the focus probe will be at -4°, -3°, -2°, -1°, 0°, 1°, 2° in the angle domain , 3°, 4° scan angle for scanning.

Step 2: Acquisition of echo signals in the angle domain. Place the test block on a four-axis automatic ultrasonic detection platform with X/Y/Z/A, adjust the position of the focusing probe through the motion control device to make it perpendicular to the surface of the workpiece, and ensure that the underwater sound distance is 125mm, mark the starting point B (0, 0) Then along the X-axis direction, the step distance Δx is 0.1mm, scan to the end point B(120,0), the number of sampling points along the X-axis scanning direction is 1200, and the number of sampling points along the Z-axis detection direction is 4096, The total number of virtual sources is 1200, and the echo signal data (1200,4096,0°) is stored synchronously; the A-axis rotation and the B-axis movement are controlled to make the probe rotate clockwise by 1°, and focus on the starting point B( 0,0), then scan along the X-axis direction with a step distance of 0.1mm to the end point B (120,0), and store the echo signal data (1200,4096,1°) synchronously, and repeat the above operations to obtain the angle All echo signals when the scan angles in the field are -4°, -3°, -2°, -1°, 0°, 1°, 2°, 3°, 4°.

Step 3, reconstructing the echo signal in the virtual source. Establish a virtual source model in the angle domain of the water-immersed workpiece, and obtain the reconstructed virtual source sound beam diffusion angle θ _t = 3.9° in the water-immersed workpiece when the focusing probe scans at any scanning angle in the angular domain. Based on this, step 2 The acquired echo data is reorganized in the angular domain as: data( _xi , 4096, N· _θt ), ( _xi =1...1000, N=-4,...0,...4).

Step 4, synthetic aperture focusing imaging. Through the time-delay superposition algorithm based on the virtual source model in the angle domain, the time-delay superposition calculation is performed on the reconstructed echo signal obtained in step 3, and the superimposed voltage amplitude of each imaging point is obtained, and the voltage amplitude of all points in the imaging area is calculated. After performing normalized calculations and reassigning values, water immersion ultrasonic synthetic aperture focusing imaging based on the virtual source in the angle domain is realized. The time-lapse superposition algorithm based on the virtual source model in the angle domain includes the following steps:

Step 1. For any point P(i,j) in the workpiece, its effective synthetic aperture length where z _s represents the depth of point P from the workpiece surface, The number of times the probe involved in the delay superposition calculation moves along the X-axis direction K=round(n) is obtained after rounding.

Step 2. When K in step 1>2, K is compensated to obtain K _n , so that K _n is an even number, that is, the number of probes participating in the delay superposition calculation is an odd number; when K≤2, no delay superposition is performed Calculate, go to step 9.

Step 3. Read the echo signal data data(i, j, 0°) when the scanning angle is 0°, and assign it as the initial value SUM ₀ .

Step 4. Define variable ii, which represents the ii-th virtual source participating in the delay superposition calculation, and assign an initial value of 1 to ii.

Step 5. Calculate the inclination angle θ _ii =atan(ii·Δx/z _s ) from the virtual source to point P(i,j) in step 4, and the delay time t=(z _s /cosθ _ii -z _s )/c , the number of time-delayed sampling points along the Z-axis detection direction T=round(t/dt), dt represents the sampling time interval along the detection direction, the apodization coefficient ε=0.5[1+cos(2·pi·η)], the formula Among them, η=ii·Δx/L.

Step 6. Divide the inclination angle θ _ii obtained in step 5 by the sound beam spread angle θ _t of a single virtual source, and round up the result N=ceil(θ _ii /θ _t ).

Step 7. Add the apodization coefficient ε in step 5 to the time-delay superposition calculation. The calculation formula is: SUM=SUM ₀ +ε(data(i-ii,j+T,-N θ _t )+εdata(i+ ii,j+T,N θ _t )).

Step 8. Redefine the result obtained in step 7 as the initial value SUM ₀ , process the ii+1th virtual source, and continue to execute steps 3 to 7 until ii=K _n /2-1.

Step 9. Perform mean value processing on the SUM finally obtained in step 8, data(i,j)=SUM/(K _n +1), and assign the voltage amplitude of the processed data to P(i,j).

Figure 8 shows the B-scan imaging of the focusing probe, Figure 9 shows the imaging image using the traditional synthetic aperture focusing method, and Figure 10 shows the water immersion ultrasonic synthetic aperture focusing imaging based on the virtual source in the angle domain. The characteristic information and imaging quality of the 2mm defect hole are shown in Table 1. From Table 1, it can be seen that the water immersion ultrasonic synthetic aperture focusing imaging based on the angle domain virtual source has a higher resolution and eliminates the influence of system and structural noise on imaging.

Table 1

Claims (3)

1., based on the ultrasonic Synthetic Aperture Focussing Imaging of water logging of angular domain virtual source, it is characterized in that, comprise the following steps:

Step one: water logging workpiece acoustic beam propagation modeling.Water logging workpiece acoustic beam propagation model is set up according to workpiece geometry and material parameter, and according to acoustic beam propagation model determination angular domain scanning scope and scanning angular interval, wherein angular domain refers to that focusing probe is with central axis during any scanning angle scanning and workpiece incidence point normal angle, and scanning angular interval refers to the scanning angular spacing that focusing probe is adjacent during scanning in angular domain.If the velocity of sound of acoustic beam in water and in workpiece is respectively c _w, c _s, the focal length size of focusing probe is d, and wafer diameter is φ, then pop one's head in aperture angle θ _w=2arctan (φ/2d).Acoustic beam can produce shape transformation when reflecting at water logging workpiece interface place, according to first critical angle law determination angular domain scanning scope is during for reducing shape transformation further, shear wave is on the impact of immersed ultrasonic test, and angular domain scanning scope is finally defined as for ensure acoustic beam in workpiece along the continuous scanning in angular domain direction, according to Snell's law determination scanning angular interval be | Δ φ |≤θ _w.

Step 2: echo wave signal acquisition in angular domain.The angular domain scanning scope determined according to step one and scanning angular interval, measured workpiece is placed in one and there is X/Y/Z/A four-spindle automatic Ultrasonic Detection platform, make it vertical by motion control device adjustment focusing probe position and focus on surface of the work, mark starting point B (0, 0) scanning B (n is to terminal carried out along X-direction with the step distance of Δ x after, 0), synchronous storage echoed signal data (i, j, 0 °), wherein virtual source total number is n/ Δ x, in formula, n represents that beam index is along X-direction coordinate, i represents the sampling number along X-axis scanning direction, j represent along Z axis detection side to sampling number, the clockwise direction of definition A axle is just, moved by the rotation of motion control device control A axle and Z axis, make focusing probe rotate scanning angular interval Δ φ and focus on the starting point B (0 of surface of the work, 0), then scanning B (n is to terminal carried out along X-direction with the step distance of Δ x, 0), synchronous storage echoed signal data (i, j, Δ φ), obtain whole echoed signal data (i, j within the scope of angular domain scanning after repeating aforesaid operations, ± N Δ φ), in formula, N represents at half angular domain inner focusing probe scanning inclination number of times.

Step 3: echoed signal reconstruct in virtual source.Set up water logging workpiece angular domain virtual source model, obtain focusing probe in angular domain with any scanning angle scanning time, the virtual source acoustic beam spread angle size of reconstruct is in water logging workpiece accordingly the echoed signal data (i, j, ± N Δ φ) that step 2 obtains is reconstructed into data (i, j, ± N θ in virtual source _t).

Step 4: synthetic aperture focusing imaging.Set up the time delay superposition algorithm based on angular domain virtual source model, time delay superposition calculation is carried out to the echoed signal after step 3 obtains reconstruct, obtain the voltage magnitude after the superposition of each imaging point, again assignment is normalized after calculating to point voltage amplitude whole in imaging region, realizes the ultrasonic synthetic aperture focusing imaging of water logging based on angular domain virtual source.

2. the ultrasonic Synthetic Aperture Focussing Imaging of a kind of water logging based on angular domain virtual source as claimed in claim 1, is characterized in that, the virtual source acoustic beam spread angle θ of reconstruct in water logging workpiece in described step 3 _tcomputing method are: set up water logging workpiece angular domain virtual source model, calculate virtual source acoustic beam expand calculation angle by snell law if focusing probe scanning angular interval is Δ φ, when | Δ φ | < θ _wtime, virtual source acoustic beam there will be overlap along angular domain direction in workpiece, adopts averaging method process to lap, determine focusing probe in angular domain with any scanning angle scanning time, in water logging workpiece, the virtual source acoustic beam spread angle size of reconstruct is ${\mathrm{\&theta;}}_t={\sin }^{-1}(\frac{c_s}{c_w}\&CenterDot;\sin \mathrm{\&Delta;\&phi;}).$

3. the ultrasonic Synthetic Aperture Focussing Imaging of a kind of water logging based on angular domain virtual source according to claim 1, is characterized in that, the time delay superposition algorithm based on angular domain virtual source model in described step 4 comprises the following steps:

Step 1, for arbitrfary point P (i, j) in workpiece, its effective length of synthetic aperture z in formula _srepresent the degree of depth of some P distance surface of the work, the probe participating in time delay superposition calculation moves number of times along X-direction k=round (n) is obtained after rounding.

Step 2, as K > 2 in step 1, K is compensated to obtain to K _n, make K _nfor even number, the probe number namely participating in time delay superposition calculation is odd number; When K≤2, do not carry out time delay superposition calculation, perform step 9.

Echo signal data data (i, j, 0 °) when step 3, reading scanning angle are 0 °, assignment is initial value SUM ₀.

Step 4, defining variable ii, represent the i-th i the virtual source participating in time delay superposition calculation, ii initialize 1.

The tiltangleθ that in step 5, calculation procedure 4, virtual source is put to P (i, j) _ii=atan (ii Δ x/z _s), delay time t=(z _s/ cos θ _ii-z _s)/c, along Z axis detection side to time delay sampling number T=round (t/dt), dt represent along detection side to sampling time interval, trace-changing coefficient ε=0.5 [1+cos (2pi η)], in formula, η=ii Δ x/L.

Step 6, the tiltangleθ that step 5 is obtained _iiwith single virtual source acoustic beam spread angle θ _tbe divided by, and result is rounded up N=ceil (θ _ii/ θ _t).

Step 7, the trace-changing coefficient ε in step 5 is added time delay superposition calculation, computing formula is:

SUM＝SUM ₀+ε(data(i-ii,j+T,-N·θ _t)+εdata(i+ii,j+T,N·θ _t))。

Step 8, result step 7 obtained are newly defined as initial value SUM ₀, process the i-th i+1 virtual source, continue to perform step 3 to 7, until ii=K _n/ 2-1.

Step 9, average value processing is carried out, data (i, j)=SUM/ (K to the SUM that step 8 finally obtains _n+ 1), and will process after data voltage magnitude give P (i, j).