Phase-shift Migration Research Articles

Circular phase shift migration based photoacoustic computational tomography

Abstract In the recent several decades, photoacoustic technique has proved to be capable of noninvasive biomedical imaging with scalable spatial resolution and high penetration depth. To achieve faithful image reconstruction, various method has been proposed, such as back projection, phase shift migration, model-based method, etc. These methods have simple implementations in homogeneous media, whereas in the cases of heterogeneous media (e.g., layered media), complicated modifications with respect to wave propagation at layer interface are always necessary. Here, we propose a frequency domain algorithm extension of phase shift migration in polar coordinates, which is obtained by making second order approximation to the optoacoustic point spread function in cylindrical coordinates and thereafter step by step wavenumber-frequency domain wave field extrapolation along the axial direction. Theoretical simulation and phantom experimental results demonstrate that the proposed circular phase shift migration method can well solve the layered heterogeneous reconstructive problem without modifying the wave propagation model. The acoustic diffraction limited acoustic resolution (up to 225 μm) and high imaging SNR (at least 16 dB) are obtained.

Sparse-TFM imaging in frequency domain based on amplitude-squared parameter

Abstract The total focusing method (TFM) implemented in time domain has high complexity, limiting its large-scale engineering applications. In contrast, the frequency-domain TFM based on phase shift migration (PSM) is helpful to improve imaging efficiency. On this basis, partial data can be abandoned for imaging to save computing costs and shorten processing time without reducing imaging quality. In this paper, an adaptive sparse-TFM in the frequency domain is proposed by selecting desired signals from full matrix capture (FMC) data. The amplitude-squared parameter for all the received signals corresponding to each transmitting element is taken as the relevant weight, and sparse arrays are constructed adaptively according to the descending order of numerical values. Simulated and experimental results indicate that the proposed method has stable imaging quality under different sparsity ratios, rapidly improving imaging efficiency with good resolution for defect detection.

Ultrasonic Imaging of Deeper Bone Defect Using Virtual Source Synthetic Aperture with Phased Shift Migration: A Phantom Study.

Ultrasound imaging for bone is a difficult task in the field of medical ultrasound. Compared with other phase array techniques, the synthetic aperture (SA) has a better lateral resolution but a limited imaging depth due to the limited ultrasonic energy emitted by the single emitter in each transmission. In contrast, the virtual source (VS) synthetic aperture allows a simultaneous multi-element emission and could provide a higher ultrasonic incident energy in each transmission. Therefore, the VS might achieve a high imaging quality at a deeper depth for bone imaging than the traditional SA. In this study, we proposed the virtual source phase shift migration (VS-PSM) method to achieve ultrasonic imaging of the deeper bone defect featured in the multilayer structure. The proposed VS-PSM method was validated using standard soft tissue phantom and printed bone phantom with artificial defects. The image quality was evaluated in terms of contrast-to-noise ratios (CNR) and amplitudes of scatters and defects at different imaging depths. The results showed that the VS-PSM method could achieve a high imaging quality of the soft tissues with a significant improvement in the scattering amplitude and without a significant sacrifice of the lateral and axial resolution. The PSM was superior to the DAS in suppressing the background noise in the images. Compared with the traditional SA-PSM, the VS-PSM method could image deeper bone defects at different ultrasonic frequencies, with an average improvement of 50% in CNR. In conclusion, this study demonstrated that the proposed VS-PSM method could image deeper bone defects and might help the diagnosis of bone disease using ultrasonic imaging.

Defect detection and imaging using electromagnetic acoustic transducer with butterfly coil.

Electromagnetic ultrasonic detection technology utilizes the electromagnetic coupling method to generate and receive ultrasonic waves without a couplant, which is suitable for rapid detection. However, the detection can be affected by the spatial distribution of the acoustic field and the polarization direction of the shear wave, which can result in suboptimal detection performance. The acoustic field directivity of the shear wave generated by the butterfly coil electromagnetic acoustic transducer was measured using the transmission method. The data indicate that the acoustic pressure amplitude of the shear wave is maximized along the axis of the acoustic field, thereby meeting the requirements of synthetic aperture focusing technique imaging. We used the reflection method to detect the through-hole defects and investigated the effect of shear wave polarization direction. By comparing the experimental data and imaging results, it can be concluded that higher echo amplitudes are obtained when the polarization direction of the shear wave is perpendicular to the axis of the through-hole defects. Based on the explosive reflection model, the frequency domain phase shift migration (PSM) method converts the time-domain signal to the frequency domain for processing and uses a phase-shift factor for layer-by-layer imaging. We used the PSM method to process the experimental data, which not only produced high-resolution images but also had a high computational speed.

Towards real-time processing for UAV-mounted GPR-SAR imaging systems

Ground Penetrating Radar (GPR) systems mounted on Unmanned Aerial Vehicles (UAVs) are becoming a promising solution to inspect beneath the soil surface. In particular, resorting to Synthetic Aperture Radar (SAR) techniques, these systems are able to retrieve subsurface radar images, in which buried targets can be detected. However, one of the major bottlenecks of this technology is the significant amount of time required for computing the radar images (due to the usage of computationally expensive algorithms to handle non-regular acquisition domains). To face this challenge, this work proposes an efficient interpolation approach, combining a height shift operation with a 2D interpolation, that enables the adoption of a migration algorithm called Phase Shift Migration (PSM). As a result, the processing time is drastically improved, offering close to real-time operation. The proposed methodology has been validated in a realistic scenario for detecting buried explosive targets, comparing it with conventional backprojection techniques in terms of image quality and processing time.

An efficient ultrasonic full-matrix imaging method for industrial curved-surface components defect detection

Curved-surface components are ubiquitous in various industries. However, defects inside the components badly degenerate the mechanical properties and lead to premature failure. Ultrasonic full-matrix imaging is a prominent method in nondestructive testing, but there is still a lack of efficient imaging methods for cases with curved interfaces. To amend this problem, this article proposes an efficient ultrasonic full-matrix imaging method to detect the defects in the industrial curved-surface components. The wavefield extrapolation for full matrix capture (FMC) dataset is taken as the combined effect of the downward migration of the source and receiver wavefields in the wavenumber-frequency domain. Compensation terms corresponding to the source and receiver wavefields act on the wavefield of FMC in the spatial-frequency domain to make up for lateral variations of the sound speed. After the wavefield reconstruction, an efficient imaging condition is implemented to transform the wavefield into the defect image. The best compensation term is determined and the influence factors is investigated in the simulation experiments. Laboratory experiments furtherly validate the superiority of the proposed method over the existing methods, especially for the imaging efficiency which is twice of the phase shift migration (PSM) based method.

Laser ultrasonic frequency-domain imaging and phase weighted optimization based on full matrix capture

Far-field laser technology has greatly promoted the progress of nondestructive ultrasonic imaging of bulk structures. However, under thermoelastic excitation, the body waves exhibit a relatively low signal-to-noise ratio, resulting in images with low resolution and contrast. Based on the motivation, this paper developed a frequency-domain phase weighted imaging method to improve the quality of laser ultrasonic defect imaging. Firstly, laser ultrasonic scanning was performed on the sample with artificial transverse hole defects. The cylindrical lens focused line source was used to improve the intensity of the body wave signals, and ensure that there was no damage on the material surface under high laser energies. Then, the frequency-domain phase shift migration (PSM) algorithm was used to perform multimode imaging of defects, achieving frequency-domain synthetic aperture focusing technique (F-SAFT) and total focused method (F-TFM) imaging based on full matrix capture. Furthermore, the phase circular statistical vector (PCSV) was proposed for weighted optimization, which improved the image quality, suppressed the background noise and multimode artifacts. Finally, the imaging quality of several algorithms were discussed. The results indicate that frequency-domain images were superior to time-domain results. After phase weighting, the imaging quality can be further improved, and the detection blind zone was significantly reduced. This work will contribute to the rapid and high-quality defect imaging of laser ultrasonic.

Defect detection in additively manufactured AlSi10Mg and Ti6Al4V samples using laser ultrasonics and phase shift migration

Laser ultrasonics (LU) is a non-contact and non-destructive method with a high data acquisition rate, making it a promising candidate for in-situ monitoring of defects in different additive manufacturing (AM) processes, including laser powder bed fusion (LPBF) and directed energy deposition, as well as final part inspection. In order to see the effect of various artificial defect types on an LU sub-surface reconstruction, AlSi10Mg samples with side through-holes, as well as Ti6Al4V samples with bottom blind holes and trapped powder were printed using LPBF, and then ultrasound B-scans of the samples were obtained using an LU system. The resulting scan data was processed using a custom frequency domain phase shift migration (PSM) algorithm, to reconstruct the defects and their locations. Novel ways of pre-processing the B-scan, used as an input to PSM, and taking advantage of its frequency representation, are demonstrated. Newton’s method was used to find a stationary phase approximation, used to account in the frequency domain for the fixed offset emitter-receiver arrangement within the PSM calculation. The Newton’s method calculation time was reduced by 33%, by using an approximation of the phase function to find an initial guess. The smallest defects that were detected using this method were in the size range between 200 to 300μm for the bottom hole defects, using an 8 ns laser pulse duration. The effect of the laser on the surface of a part being built, and the challenges and further work needed to integrate LU in a LPBF machine for in-situ inspection are discussed.

Design and angular robustness test of chirped periodically poled lithium niobate crystal for 1064 nm second-harmonic generation experiment

A 532-nm solid-state laser, generated by second-harmonic generation (SHG) technology, has become one of the most extensively used lasers in various applications today. In the traditional scheme, the most prevalent SHG crystal of the 532-nm solid-state is lithium borate (LBO), and continues to exhibit insufficient angular robustness and SHG efficiency. In order to overcome these limitations and obtain SHG crystals with better angular robustness, this study starts with a comprehensive theoretical analysis of angular robustness. On this basis, the structure of a chirped periodically poled lithium niobate (CPPLN) crystal is designed by taking into account the desired properties for improving its performance, and then the theoretical simulations and experimental tests are implemented to validate the effectiveness of the designed crystal. The simulation results corroborate the superior angular robustness of the CPPLN crystal. In a range from <inline-formula><tex-math id="M4">\begin{document}$ - {3^ \circ } $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20240778_M4.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20240778_M4.png"/></alternatives></inline-formula> to <inline-formula><tex-math id="M5">\begin{document}$ + {3^ \circ } $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20240778_M5.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20240778_M5.png"/></alternatives></inline-formula>, the designed CPPLN crystal exhibits a maximum SHG efficiency of 0.80% and a minimum one of 0.51%, which indicates that the SHG efficiency of this crystal in this range can be maintained at 60% of the maximum efficiency. The experimental results show that the SHG efficiency can be more than 11 times that of LBO crystal. Moreover, the study indicates that the half width of the actual SHG efficiency near the incident angle of the designed CPPLN crystal can exceed <inline-formula><tex-math id="M6">\begin{document}$ {6^ \circ } $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20240778_M6.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20240778_M6.png"/></alternatives></inline-formula>, demonstrating its excellent tolerance for changes in incident angle. Furthermore, the output spot of the SHG light generated by the designed CPPLN crystal exhibits a standard Gaussian profile, which remains virtually unaffected by the incident angle. In summary, the findings of this research highlight the CPPLN crystal as a promising alternative to LBO, with markedly higher SHG efficiency and better angular robustness. These superior characteristics make the CPPLN crystal a highly attractive candidate for a wide range of laser applications.

3-D Millimeter Wave Fast Imaging Technique Based on 2-D SISO/MIMO Array

In this article, a novel three-dimensional (3-D) imaging method based on the range decomposing algorithm (RDA) is proposed for millimeter wave imaging. We combined it with binomial theory and we derive the theoretical formulation of RDA applied to single-input–single-output (SISO)/multiple-input–multiple-output (MIMO) array; meanwhile, its computational complexity and computational error are analyzed. Compared to the classical Fourier algorithm, such as the range migration algorithm (RMA) and the phase shift migration (PSM), the proposed algorithm can replace the time-consuming interpolation and accumulation operations with reasonable approximations and transformations offering a more efficient approach, while maintaining the image quality. In addition, a method based on RDA which is applicable to the transformation between MIMO and SISO, is proposed to further enhance the processing efficiency. Proof-of-principle simulation using echo data collected from a large number of antennas, verifies that the proposed algorithm has higher efficiency. In order to better verify the feasibility of the proposed algorithm, a scanning prototype located in the millimeter wave band is designed. The experimental results of different targets demonstrate that the proposed algorithm achieves significantly higher reconstruction efficiency when compared to the traditional algorithms.

MIMO-SA-Based 3-D Image Reconstruction of Targets Under Illumination of Terahertz Gaussian Beam—Theory and Experiment

For the 3-D terahertz (THz) holographic imaging, this work proposes an extended phase-shift migration (PSM) reconstruction algorithm based on multiple-input-multiple-output (MIMO) array with an orthogonal synthetic aperture (SA). For this MIMO-SA-based imaging mechanism, the accurate expression of the signal spatial spectrum can also be obtained by utilizing the method of stationary phase (MSP). Meanwhile, the analytical expression of the reconstructed 3-D point-spread function (PSF) for target under the illumination of MIMO-SA-based THz Gaussian beam is derived to provide the theoretical spatial resolutions quantitatively. A serial of simulation results with fairly good agreement were given to verify the accuracy of the proposed MIMO-SA-based PSM reconstruction algorithm. Meanwhile, due to the PSM’s characteristic of phase shift compensation along the range direction, the image reconstruction process can also be implemented and accelerated by a GPU solution. Finally, two types of MIMO-SA-based prototype imagers are applied for the proof-of-principle experiments. The first prototype imager is configured with one transmitter and two receivers in 0.3-THz band. The MIMO linear array including arbitrary number of transmitters/receivers can be realized by controlling their positions in a low-cost way with the help of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$x$</tex-math> </inline-formula> -axis of a 2-D scanner. The second prototype imager is configured with eight transmitters and eight receivers in 0.2-THz band. The experimental results from the two prototype imagers can validate the effectiveness on image reconstruction quality.

A safe power controlling method for a phase-shift migration inverter to drive a high-power ultrasonic transducer.

The aim of this work is to investigate and analyze the operation mechanism and power control principle of a bolted Langevin type (BLT)-loaded phase-shifted control inverter and to find a safe power control method for a phase-shifted control inverter used to drive a high-power BLT by preventing the differential current (shock current) from occurring in the right branches of a phase-shifted full-bridge circuit. In this paper, by allowing the inverter operating frequency to operate under inductive loads that coincide with the zero points of voltage and current rather than the resonant frequency of the BLT, which results in the generation of a shock current in the right branch of the full-bridge circuit, the switches of the right-branch also enabled zero-voltage, zero-current switching on (ZVZCS turn-on). The proposed method can fundamentally eliminate the generation of shock current by realizing ZVZCS turn-on on the right-branch switch elements of the inverter. The phase-shift angle control limit for power control by this scheme is 90° and the power control range is 20%-100%.

Phase shift migration based plane-wave imaging of cortical bone

Cortical bone, a highly attenuated, anisotropic, and multilayered biological medium with high acoustic impedance, presents significant challenges for high-frequency ultrasound to penetrate its complex structure and acquire high-quality images. The traditional method of using uniform sound velocity in ultrasonic dynamic focusing imaging is limited by emission energy and frame rate, which hinders the accurate and rapid reconstruction of multi-layer structures and clinical applications. In order to meet these challenges, this study proposes a novel method, called the phase shift migration-based plane-wave bone imaging via velocity inversion (PSM-PW-VI), that can accurately and quickly image the multi-layer structure of cortical bone. In the PSM-PW-VI method, two identical linear array probes are arranged in parallel on both sides of the cortical bone for data acquisition. First, the ultrasound velocity distribution in the imaging region is obtained by using ultrasound travel time inversion. Next, two images corresponding to the upper probe and lower probe are acquired in parallel in the frequency domain by employing a phase shift migration-based coherent plane-wave compounding method. Finally, the two images are merged to generate a complete ultrasound image of the cortical bone. Wave propagation in cortical bone is simulated by using the open source toolbox &lt;i&gt;k&lt;/i&gt;-wave in MATLAB. &lt;i&gt;Ex-vivo&lt;/i&gt; experiments are conducted on 2.5-mm-thick sawbones phantom and 2.45-mm-thick bovine bone plates to evaluate the feasibility of the proposed method, by using the Verasonics platform. Simulation, phantom (Sawbones), and &lt;i&gt;ex-vivo&lt;/i&gt; experiments validate the effectiveness of the method. Notably, the average error of the thickness is less than 0.2 mm, and the relative error is less than 7% for both three-layer and five-layer cortical bone. The influence of the number of plane wave compounding angles on imaging quality is investigated, revealing that only 15 angles are sufficient to produce high-quality images. The influence of the velocity model on imaging accuracy is also examined since accurate sound velocity estimation is crucial for obtaining high-quality images of cortical bone. Finally, the performances of PSM-PW-VI and PSM-SA in imaging depth and efficiency are compared. The results demonstrate that the proposed PSM-PW-VI method offers significant improvements in temporal resolution, data storage and processing quantity, emission energy, and imaging depth. The experimental findings validate the effectiveness of the proposed method as an accurate and efficient ultrasound imaging tool for cortical bone, and its substantial role in promoting ultrasound bone imaging technology and clinical applications.

Phase shift migration with absorbing boundary condition for full-matrix imaging heterogenous medium with high quality

Ultrasonic imaging with phased array has been widely employed for nondestructive testing in various fields. Phase shift migration (PSM) is a significant imaging method and shows great advantages for multilayer structures. However, the artifact reflections at the edges of the calculation region emerge in the wavefield reconstruction process, which greatly deteriorate the imaging quality of PSM. To overcome this problem, two absorbing boundary conditions for the wavefield extrapolation of PSM are proposed in this paper. The first absorbing boundary condition renders elements in the boundary regions lower weights in frequency-space domain. The second one follows a nonstationary phase shift scheme and filters the incident waves in the boundary regions in frequency-wavenumber domain. The implementing schemes of the absorbing boundary conditions for both homogenous and heterogenous medium are developed, and the full-matrix imaging method with absorbing boundary conditions is proposed. According to the simulation and experiment, the proposed boundary conditions have strong ability to suppress the background artifacts, and they can improve the signal-to-noise ratio (SNR) and resolution by 2 times when imaging heterogenous medium. Further experiments indicate that the boundary conditions are insensitive to the window functions, and a width of one-sixteenth the length of the scan line is recommended for the absorbing boundary conditions.

Terahertz 3-D Imaging for Non-Cooperative On-the-Move Whole Body by Scanning MIMO-Array-Based Gaussian Fan-Beam

This work proposes a novel terahertz (THz) 3-D imaging system that combines the Gaussian-fan-beam scanning and multiple-input–multiple-output (MIMO) array to create a high frame rate, large field of view (FoV), and high-resolution radar images for continuously noncooperative on-the-move personnel security screening. The main novelty of the present system is that the 3-D THz focused images of the noncooperative on-the-move whole body can be created in real time when the persons are illuminated by scanning the MIMO-array-based Gaussian fan beam. In this article, the 3-D image is composed of a serial of 2-D slice images that are reconstructed by the proposed MIMO-array-based phase shift migration algorithm under the illumination of the THz Gaussian fan beam. Meanwhile, an analytical expression of the reconstructed point-spread function is derived to provide the theoretical spatial resolutions quantitatively. One prototype imager was designed for the proof-of-principle experiments in the 0.2 THz band, and the image reconstruction process is implemented in real time by the proposed hybrid central processing unit (CPU)–graphics processing unit (GPU) solution. At this stage, an FoV of 500 cm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times200$ </tex-math></inline-formula> cm at a 10 m distance costs less than 0.1 s for 3-D imaging during 10 Hz mechanical Gaussian-fan-beam scanning. Finally, both simulation and experimental results validate the effectiveness of the proposed imaging algorithm on image reconstruction quality, including resolution, frame rate, and FoV.

Ultrasonic phased array phase shift migration imaging of irregular surface components using attenuation compensation and anti-aliasing technique

Extended non-stationary phase shift migration (ENPSM) is a promising imaging algorithm for ultrasonic phased array testing of components with irregular surfaces. In this paper, ENPSM is developed further by combining attenuation compensation (AC) with an anti-aliasing (AA) technique, in an approach called AC-AA-ENPSM, to address the negative effects of attenuation during ultrasonic wave propagation in metals and of jagged medium interface determined by traditional rectangular window. The attenuation term in AC-AA-ENPSM is measured by immersion testing with referenced samples. An anti-aliasing technique is used to smooth the spatial velocity distribution based on the weights of different velocities on a pixel grid. Experiments are performed on objects with irregular surfaces, varying attenuation characteristics and side-drilled hole (SDH) defects. A comparison of the results shows that the proposed AC-AA-ENPSM algorithm has the advantage of a higher signal-to-noise ratio (SNR) than traditional ENPSM. Moreover, the proposed algorithm has a computational efficiency at least 40 times higher than the total Focusing Method (TFM) algorithm, and the SNR difference of them is less than 2 dB.

Efficient phase shift migration for ultrasonic full-matrix imaging of multilayer composite structures

Multilayer composite structures are essential for various fields but void defects inside will greatly reduce its mechanical properties. Ultrasonic full-matrix capture (FMC) is a useful imaging modality to detect defects in multilayer structures, but it also brings heavy computational burden. Though great progress has been made in the full-matrix imaging for homogeneous medium, most of these methods are invalid or inefficient for the cases of multilayer structures. To amend it, an efficient phase shift migration for ultrasonic full-matrix imaging of multilayer structures is proposed in this paper. The method regards FMC as data in three dimensions: receiver position, transmitter position and time, and transforms it into frequency-wavenumber (f-k) space by a three-dimensional fast Fourier transform. By downward extrapolating the wavefield on the surface, the wavefield at arbitrary depth in the measuring region is reconstructed, with a firstly introduced double-square-root vertical wavenumber. Then the imaging condition t = 0 is directly applied in the f-k space to produce the defect image. Computational complexity was reduced greatly, and the calculation time of the proposed method was only 1/6 of that of the well-established extended phase shift migration, in the case of the same resolution. Therefore, the proposed method has great potential in on-line ultrasound defect detection, especially for cases of large multilayer structures.

Image reconstruction of immersed ultrasonic testing for strongly attenuative materials

With the development of industrial materials, the objects of ultrasonic non-destructive evaluation (UNDE) have been expanded from metals to composite and polymer materials. However, composite and polymer materials are elastoplastic. The elastoplastic induced strong acoustic attenuation and dispersion affect the phases and waveforms of ultrasound waves. If overlooking these effects, the ultrasound reconstruction image will generate position deviation, resolution degradation and detail loss. To overcome this kind of deficiency, this paper introduces an ultrasound reconstruction that takes account of attenuation and dispersion compensation for the UNDE applications. It is derived from phase shift migration (PSM) by modifying the phase shift term with compensations of the attenuation and dispersion. This method can resolve imaging of layered media with depth-variant attenuation, such as commonly used immersed ultrasonic testing cases, while inheriting the high computational efficiency of PSM. Based on simulation and experimental results, the proposed method corrects the reconstruction deviation, improves image resolution, and restore details caused by depth variant attenuation and dispersion which literature methods cannot. For reconstructing a 3D image data sized of 4000 × 140 × 300 pixels, the memory cost can be controlled under 300 MB using recursive implementation, and the time cost can be reduced to 0.4 s using parallelization implementation.

Phase Shift Migration with Modified Coherent Factor Algorithm for MIMO-SAR 3D Imaging in THz Band

In multiple-input-multiple-output synthetic aperture radar (MIMO-SAR) systems, sparse arrays are usually applied, resulting in increased sidelobes of the point spread function. In this paper, a phase shift migration (PSM) imaging algorithm based on the explosion reflection model with modified coherent factor was proposed for sidelobe suppression in MIMO-SAR three-dimensional (3D) imaging application. By defining the virtual difference wavenumber, reconstructing the raw echo by data rearrangement in wavenumber domain, the original coherent factor algorithm operating in spatial domain can be achieved by the PSM algorithm frame in the wavenumber domain, which means two orders of magnitude increase in computational efficiency. The correctness of the theory is verified by simulation. Finally, a bistatic prototype imaging system in the 0.3 THz band was designed for the proof-of-principle experiments. The experimental results show that the proposed algorithm has a 0.948 structural similarity value to the original coherent factor back-projection algorithm (CF-BPA) which means comparable image quality with much superior efficiency.

A Modified Wavenumber Algorithm of Multi-Layered Structures with Oblique Incidence Based on Full-Matrix Capture

Full-matrix capture (FMC)-based ultrasonic imaging provides good sensitivity to small defects in non-destructive testing and has gradually become a mainstream research topic. Many corresponding algorithms have been developed, e.g., the total focusing method (TFM). However, the efficiency of the TFM is limited, especially in multi-layered structures. Although the appearance of wavenumber algorithms, such as extended phase-shift migration (EPSM) methods, has improved imaging efficiency, these methods cannot be applied to cases with oblique incidence. Therefore, a modified wavenumber method for full-matrix imaging of multi-layered structures with oblique array incidence is proposed. This method performs a coordinate rotation in the frequency domain to adapt it to the oblique incidence. It then utilizes wave-field extrapolation to migrate the transmitting and receiving wave field to each imaging line, and a correlation imaging condition is used to reconstruct a total focused image. The proposed method can deal with any incident angle without precision loss. Moreover, it inherits the computational efficiency advantages of the wavenumber algorithms. The simulation and experimental results show that the proposed method performs better in terms of accuracy and efficiency than the TFM. Specifically, it is nearly 60 times faster than the TFM when processing an FMC dataset with a size of 4096 × 64 × 64.