Self-adaptive phased array C scanning imaging method for surface thread curved surface

Abstract

The invention belongs to the technical field of image processing, and particularly relates to a self-adaptive phased array C scanning imaging method for a surface thread curved surface, which sequentially comprises the following steps of: (1) establishing a curved surface coordinate; step (2), generating propagation prior; step (3), executing a step of cTFM imaging; and step (4), executing a step of RPCA decomposition imaging. According to the method, thread appearance point cloud is synchronously collected through a contourgraph and an encoder, a spiral expansion coordinate domain and a curved surface coordinate index table are established through double quaternion spiral expansion, and geometric continuous modeling of the rotating and feeding process is achieved; in the coordinate domain, a propagation prior lookup table containing refraction time intervals is generated based on a rapid propulsion method, and the refraction propagation path of sound waves between the wedge block and the detected body is accurately described.

Description

Technical Field

[0001] This invention belongs to the field of image processing technology, specifically relating to a phased array C-scan imaging method for adaptive surface thread curvature. Background Technology

[0002] As a key connection structure in cylindrical metal components, threaded surfaces, including internal and external threads, exhibit complex helical surfaces, periodic tooth profiles, and localized high curvature variations. This places significantly higher demands on ultrasonic testing than on conventional planar welds or cylindrical surfaces. Existing phased array ultrasonic testing systems widely used in industry primarily rely on planar or axisymmetric models for imaging, such as traditional planar full-focusing methods, sector scanning, and linear C-scan. These methods generally assume that the inspected surface is approximately planar along the beam propagation direction or achieves fixed-angle incidence through fixed geometric wedges. However, when the inspected object is a threaded surface, the localized normal variation caused by the helical teeth causes periodic deflections in the sound wave incident angle and propagation path. Fixed geometric models cannot accurately describe the true propagation behavior of the sound beam, leading to focal point shifts, accumulated delay calculation errors, and inconsistent amplitude attenuation. Consequently, defect images exhibit misalignment, blurring, and artifacts.

[0003] Among the improved techniques for surface inspection, some researchers have proposed using surface point cloud measurement results to compensate for ultrasonic time delay. For example, one type of method uses laser scanning or structured light measurement to obtain the shape point cloud, then derives the normal direction of the incident point through plane fitting or 3D surface reconstruction, and then corrects the propagation path during time-delay focusing. This type of method works well on regular curved surfaces such as cylinders or spheres, but for threaded surfaces, because the tooth profile has periodic protrusions and depressions on the micrometer scale, the surface normal changes rapidly, and the local curvature is high. Conventional surface reconstruction easily smooths out details, resulting in significant time delay correction errors. In addition, the continuity of the helical structure requires strict matching of the angular displacement and axial displacement acquired by the encoder during scanning; otherwise, the point cloud and acoustic data cannot be registered in the same coordinate system, affecting subsequent imaging.

[0004] At the data processing level, existing C-scan imaging methods mostly employ conventional time-delay superposition or full-focusing algorithms, assuming uniform sound velocity and a straight or single-refractive path. When there is a significant sound velocity difference between the wedge and the object under test, or a complex refractive interface, this assumption no longer holds, especially in the surface thread root region, where the refraction angle varies greatly and local sound path differences are significant. Previous studies have attempted to simulate the sound field using ray tracing or the finite difference method, but these methods are computationally intensive and lack real-time performance, making it difficult to achieve rapid response in production testing. Furthermore, some algorithms use empirical time-distance correction tables or fixed sound path compensation factors. These methods rely on empirical parameters and cannot adapt to scenarios with different pitches, wedge angles, or material combinations. Summary of the Invention

[0005] Therefore, the main objective of this invention is to provide a phased array C-scan imaging method for adaptive surface threading, which significantly improves focusing accuracy and signal-to-noise ratio under high curvature and periodic structures. Compared to traditional planar models or empirical correction methods, this invention can generate geometrically equidistant high-resolution C-scan images in real time, effectively eliminating thread artifacts and refractive distortion, improving the accuracy and automation level of defect detection, and is suitable for high-reliability non-destructive testing of complex curved surface components such as surface threads.

[0006] The technical solution adopted in this invention is as follows: A phased array C-scan imaging method for adaptive surface thread curvature, comprising the following steps in sequence: Step (1), the steps to establish surface coordinates, include: based on the continuous point cloud of the thread shape collected by the profilometer under the trigger of the encoder, a spiral expansion coordinate domain and a surface coordinate index table are established by using double quaternion spiral expansion. Step (II), the step of generating propagation priors, includes: generating a lookup table containing refraction time distances in the spiral unfolding coordinate domain according to the fast propagation method; Step (3), the steps of performing cTFM imaging, include: performing time-delay superposition on the raw data stream acquired by the array according to the refraction time-distance lookup table to generate a result matrix; Step (iv), the steps of performing RPCA decomposition imaging, include: performing low-rank sparse decomposition on the result matrix to extract sparse components, thereby obtaining dentin-removed C-scan imaging.

[0007] Furthermore, the steps for establishing surface coordinates also include: determining the numerical ranges of the rotation axis, radial runout, and axial runout through two or more idle runs and one reference circle measurement to generate an attitude calibration table; and recording the three-dimensional position of the surface element center to the device coordinate system, the surface element normal, and the relative attitude with the wedge incident surface in the surface coordinate index table, and associating the spatial position of each array element with the surface coordinate index table item by item to form a surface element to array element mapping relationship.

[0008] Furthermore, the steps for generating propagation priors also include: establishing a layered medium mesh in the spiral unfolding coordinate domain and setting the contact surface between the wedge and the object under test as the refractive boundary; and when the propagation path crosses the refractive boundary, calling the boundary solver to determine the refractive angle in a binary search manner so that the incident angle and the refractive angle satisfy the refractive condition of the medium velocity ratio.

[0009] Furthermore, the steps for generating propagation priors also include: while generating the refraction time-distance lookup table, recording the grid sequence of the first-arrival path for use as a consistency constraint for subsequent cTFM imaging.

[0010] Furthermore, the steps for performing cTFM imaging also include: performing signal preprocessing on the raw data stream to form an analytical envelope sequence; and for each surface element in the spiral unfolding coordinate domain, calling the refraction time-distance lookup table to obtain the arrival time index, and using cubic interpolation to sample the amplitude of the analytical envelope sequence.

[0011] Furthermore, the steps for performing cTFM imaging also include: using the angular and axial displacement records of the encoder to align the row and column indices of the cTFM imaging accumulator to integers, and performing linear interpolation resampling according to the grid size of the spiral unfolded coordinate domain to obtain geometrically equidistant intermediate imaging frames; and extracting the maximum envelope pixel by pixel from the intermediate imaging frames according to a preset depth gate to write it into the result matrix, while saving the arrival time index map where the maximum value is located.

[0012] Furthermore, the steps for performing cTFM imaging also include: mapping the grid sequence of the first path to the result matrix, retaining the original values ​​of pixels that are consistent with the direction of the first path, and performing amplitude suppression on pixels whose directional deviation exceeds the preset angle tolerance, so as to obtain a result matrix with consistent direction.

[0013] Furthermore, the steps for performing cTFM imaging also include: marking the critical incident region and the curvature abrupt change region based on the relative orientation of the surface element normal and the wedge incident surface in the surface coordinate index table, and smoothing these regions by performing small window value operation on the result matrix with consistent orientation.

[0014] Furthermore, the steps for performing RPCA decomposition imaging also include: calculating the row mean curve along the axial direction of the spiral unfolding coordinate domain and using peak-valley detection to find periodic stripes to construct a tooth mark mask; and in the iterative process of low-rank-sparse alternating decomposition, performing singular value decomposition on the result matrix minus the current sparse matrix and performing a soft threshold operation to update the low-rank matrix, while forcing the use of the low-rank matrix value at the tooth mark mask position.

[0015] Furthermore, the steps for performing RPCA decomposition imaging also include: during the iteration process, calculating the residual of the result matrix minus the current low-rank matrix, and performing a soft threshold operation on the residual element by element to update the sparse matrix, while retaining the updated value outside the tooth pattern mask; and after the iteration process is completed, performing small connected component deletion and morphological opening and closing operations on the sparse matrix.

[0016] By adopting the above technical solutions, this invention achieves the following beneficial effects: By introducing a surface-adaptive phased array C-scan imaging system into the field of surface thread detection, this invention realizes integrated and coordinated geometric modeling, propagation path calculation, signal focusing, and thread removal processing, thereby significantly improving the ultrasonic imaging quality of complex helical surfaces. Its beneficial effects are reflected in several aspects. First, by adopting a surface coordinate establishment method based on double quaternion helical unfolding, the continuous point cloud of the thread shape acquired by the profilometer can be seamlessly unfolded under conditions of synchronous rotation and axial feed, accurately establishing a helical unfolding coordinate domain consistent with the actual geometry. This method eliminates the geometric distortion caused by traditional planar unfolding, ensuring strict consistency between delay calculation and imaging coordinates, effectively improving the spatial positioning accuracy of the helical surface region. Second, a rapid propagation method is introduced during the propagation prior generation process to establish a layered medium mesh, and a binary search is used to determine the refraction angle at the refraction boundary, ensuring that each propagation path satisfies the medium refraction condition, thereby obtaining a high-precision refraction time-distance lookup table. Compared to the traditional linear path assumption, this strategy accurately handles the propagation nonlinearity caused by the difference in sound velocity between the wedge and the inspected object, making the imaging focus more consistent with the actual reflection point and significantly improving defect resolution and signal-to-noise ratio. Furthermore, in the imaging stage, a cTFM cumulative delay superposition combined with a spiral coordinate resampling strategy is employed, ensuring that each pixel is reconstructed in a geometrically equidistant expanded domain. First-arrival path consistency constraints and directional amplitude suppression effectively reduce multipath reflections and scattering artifacts. This design allows the image to remain continuous and clear in the thread valleys and high curvature areas, solving the problems of tortuosity and shadowing caused by unstable incident angles. Finally, after imaging, this invention uses RPCA low-rank-sparse decomposition combined with a thread mask to separate periodic thread reflections from the real defect signal. This algorithm can adaptively remove stripe interference based on the geometric periodic characteristics of the thread without losing the local high-amplitude features of the defect, resulting in a C-scan image with a smooth background and clear contours. In summary, this invention forms a closed-loop adaptive mechanism in the stages of data acquisition, geometric modeling, sound path calculation and post-processing, which transforms surface thread detection from offline analysis that relies on manual experience to an automated, real-time, and high-precision imaging process, providing a stable and reliable technical approach for on-site non-destructive testing. Attached Figure Description

[0017] Figure 1 This is a schematic flowchart of a phased array C-scan imaging method for adaptive surface thread curvature provided in an embodiment of the present invention; Figure 2 This is a schematic diagram comparing the imaging effects before and after RPCA decomposition provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of the ultrasonic echo signal processing experimental curve provided in an embodiment of the present invention; Figure 4This is a schematic diagram of the real-time monitoring curve of the coupling layer thickness provided in an embodiment of the present invention; Figure 5 This is a diagram of the phased array arrangement structure provided in an embodiment of the present invention; Figure 6 This is a schematic diagram of the wedge coupling structure provided in an embodiment of the present invention; Figure 7 This is a schematic diagram of the principle of profilometer line structured light measurement provided in an embodiment of the present invention. Detailed Implementation

[0018] All features disclosed in this specification, or all steps in all disclosed methods or processes, may be combined in any way, except for mutually exclusive features and / or steps.

[0019] Any feature disclosed in this specification (including any appended claims and abstract) may be replaced by other equivalent or similar features, unless specifically stated otherwise. That is, unless specifically stated otherwise, each feature is merely one example of a series of equivalent or similar features.

[0020] Example 1: Reference Figure 1 A phased array C-scan imaging method for adaptive surface thread curvature is implemented through a device comprising an array, a wedge, a profilometer, an encoder, and an FPGA module.

[0021] In one embodiment, the entire device is equipped with an integrated support frame, on which an array and a wedge are fixed sequentially from top to bottom. The array is fixed to the wedge via a repeatable dovetail groove and a fine-tuning mechanism. The fine-tuning mechanism provides a fine displacement range of approximately ±2.0 mm in each of three orthogonal directions, facilitating fine-tuning of the bundle direction after assembly. The lower surface of the wedge faces the threaded area of ​​the surface being inspected, and a transparent observation window and a coupling agent injection port are provided on the outer side of the wedge. The profilometer is placed on one side of the wedge, with a field of view covering the area from the crest to the root of the thread. The reference planes of the profilometer and the array are established with a stable relative positional relationship through two pins and a stop surface. The pin hole spacing is preferably 60.0 mm, and the positioning repeatability is preferably better than 0.02 mm. The encoder is connected to a rotary chuck via a rigid coupling. The chuck clamps the drill pipe joint and achieves coaxiality control with a linear guide rail, with the coaxiality preferably better than 0.05 mm.

[0022] The array is a linear phased array with a selectable number of elements between 64 and 128, an element spacing between 0.50 mm and 0.80 mm, a center frequency between 5.0 MHz and 10.0 MHz, and a preferred straightness error of less than 0.02 mm for the effective aperture of the elements. The front end of the array is covered with a polyurethane film with a thickness between 0.30 mm and 0.60 mm to improve wear resistance and sealing. The rear end of the array uses a differential coaxial connection and is internally shielded, with the shielding layer connected to the device ground. The interface tension relief structure can withstand a tensile force of no less than 30 N. After array installation, a factory conformity verification is performed, including channel amplitude uniformity error no greater than ±1.0 dB, channel phase uniformity error no greater than ±3.0 degrees, and single-channel echo noise root mean square value no higher than 0.5% of full scale. These values ​​are chosen to ensure that the main lobe energy concentration and side lobe suppression are maintained in high curvature areas such as the tooth root, thus achieving stable contrast in subsequent imaging.

[0023] like Figure 5As shown, the phased array of this invention adopts a linear arrangement, with all array elements evenly spaced along a straight line. The outer shell of the phased array has a rectangular structure, indicated by a thick solid line border. This shell serves as mechanical support, electromagnetic shielding, and environmental sealing. The lateral length of the shell is determined by the number of array elements and the spacing between them, while the longitudinal height must meet the requirements for array element installation, electrical connection, and structural strength. Inside the shell, multiple independent array element units are evenly arranged horizontally. The figure schematically shows 15 array elements, each represented by a rectangle filled with gray to distinguish it from the white background of the shell. In practical applications, the number of array elements can be selected between 64 and 128, depending on the size of the object being detected, the required beam control accuracy, and the imaging resolution. The lateral width of each array element is closely related to the element spacing, while the longitudinal height is determined by the effective vibration dimension of the piezoelectric ceramic wafer. Adjacent array elements are arranged with precise equal spacing, which is called the element spacing or pitch, and its value is preferably in the range of 0.50 mm to 0.80 mm. The diagram clearly indicates the measurement method of the element spacing, i.e., the distance between the center lines of one element and the center lines of adjacent elements, using two vertical lines and a horizontal line. The selection of element spacing must follow the spatial sampling theorem to avoid grating lobe effects during beam deflection and focusing. At higher operating frequencies, a smaller element spacing is required; when the detection depth is greater and stronger acoustic penetration is needed, the element spacing can be appropriately increased to improve the transmission power of a single element. The elements are numbered sequentially from left to right as 1, 2, 3, 4, with ellipses used in the middle and N on the far right, where N represents the total number of elements. This numbering method facilitates indexing and management of data from each channel during signal processing. Each element corresponds to an independent transmit / receive channel. In phased array imaging, by applying different delays and weighting coefficients to each channel, electronic deflection, dynamic focusing, and sidelobe suppression of the acoustic beam can be achieved. Below the element array, a protective thin film layer is placed close to the element's emitting surface; the cross-section of this film is represented by a thin black rectangle in the diagram. The protective film is made of polyurethane material, with a thickness preferably in the range of 0.30 mm to 0.60 mm. The main functions of this film include: improving the array's abrasion resistance and preventing damage to the element surfaces during long-term contact with the wedges; providing sealing protection to prevent coupling agents or other liquids from seeping into the element gaps and causing electrical short circuits; and improving acoustic impedance matching to reduce interface reflection losses. The thickness of the film needs to be balanced between mechanical strength and acoustic transmittance; too thin a film will reduce abrasion resistance, while too thick a film will increase acoustic energy loss and introduce multiple reflections. Figure 5Below the image is a technical parameter table, represented by a rectangular border and divided into multiple rows by horizontal lines. The system lists the key technical specifications of the phased array. The first row indicates the number of array elements, ranging from 64 to 128, meaning it can be selected within this range according to application requirements. The second row indicates the element spacing, ranging from 0.50 to 0.80 mm, corresponding to the aforementioned geometric markings. The third row indicates the center frequency range, ranging from 5.0 to 10.0 MHz. This frequency range is selected considering both detection resolution and penetration depth requirements; higher frequencies provide better near-field resolution, while lower frequencies provide stronger penetration capabilities. The fourth row indicates the protective film thickness, ranging from 0.30 to 0.60 mm, consistent with the film layer markings in the image. The fifth row indicates the amplitude consistency index, ±1.0 dB. This index characterizes the balance of receiving sensitivity and transmission intensity across channels and is a key performance parameter for ensuring the imaging quality of the phased array. Poor amplitude consistency can lead to main lobe distortion and side lobe lift, reducing defect detection capability. After assembly, phased arrays require factory conformity verification, which includes channel amplitude uniformity error not exceeding ±1.0 dB, channel phase uniformity error not exceeding ±3.0 degrees, and single-channel echo noise root mean square value not exceeding 0.5% of full scale. Strict control of these indicators ensures that the phased array can maintain main lobe energy concentration and side lobe suppression even in high curvature regions such as tooth roots, thereby achieving stable contrast and reliable defect identification capabilities in subsequent imaging processes.

[0024] The wedge is made of a material with low acoustic loss and high mechanical strength, preferably polymethyl methacrylate or polycarbonate. The contact surface between the wedge and the array is a precision-machined plane, with a flatness preferably better than 0.02 mm. A flexible contact layer is provided on the side of the wedge in contact with the surface being inspected. The flexible contact layer is made of thermoplastic elastomer with a hardness between Shore A60 and A80 and a thickness between 0.50 mm and 1.50 mm. The function of the flexible contact layer is to conform to the undulations of the threads to maintain stable coupling, and at the same time eliminate air film caused by gaps at local abrupt changes in curvature. A coupling agent guide channel is provided inside the wedge. The width of the guide channel is between 2.0 mm and 3.0 mm, and the depth is between 1.0 mm and 1.5 mm. The guide channel is equipped with a needle valve on the inlet side to achieve micro-continuous replenishment of the coupling agent to maintain a stable coupling layer thickness. A temperature sensor is provided on the outside of the wedge. The accuracy of the sensor is preferably better than ±0.5 degrees Celsius. It is used to monitor the temperature rise of the wedge during long-term continuous scanning and guide the adjustment of the coupling agent flow rate. The combination of a flexible contact layer and continuous fluid replenishment is adopted because the surface threads are three-dimensional curved surfaces with periodic undulations. The flexible contact layer can adapt to small height differences while maintaining the stability of the array's incident attitude, and continuous fluid replenishment can suppress the coupling viscosity changes caused by friction and ambient temperature, thereby reducing the amplitude drift of the reflected wave on the front surface.

[0025] refer to Figure 6The wedge coupling structure of this invention mainly includes a wedge, a flexible contact layer, a coupling agent layer, and a threaded surface of the surface being inspected. The wedge is made of a material with low acoustic loss and high mechanical strength, preferably polymethyl methacrylate (PMMA) or polycarbonate, with a longitudinal wave velocity of 2730 m / s. The wedge has a trapezoidal structure, with its upper surface precisely fitted to the emitting surface of the phased array, and a flatness preferably better than 0.02 mm to ensure effective acoustic energy transmission. The main body area of ​​the wedge is shaded to distinguish it from other components. A coupling agent channel is provided inside the wedge, extending from the top of the wedge to near the lower surface. The width of the channel is preferably between 2.0 mm and 3.0 mm, and the depth is preferably between 1.0 mm and 1.5 mm. A needle valve is provided at the top of the channel; the needle valve has a circular structure, and by controlling the opening of the needle valve, a small amount of coupling agent can be continuously replenished to maintain the stability of the coupling layer thickness. A supply line is connected above the needle valve to continuously supply coupling agent to the channel. A temperature sensor, circular in shape and marked with the letter "T" inside, is installed on the outer side of the wedge to indicate its temperature measurement function. The temperature sensor's measurement accuracy is preferably better than ±0.5 degrees Celsius, used to monitor the temperature rise of the wedge in real time during long-term continuous scanning and to guide the automatic adjustment of the coupling agent flow rate based on temperature changes. A flexible contact layer is provided between the lower surface of the wedge and the surface thread. This flexible contact layer is represented by a wavy curve to reflect its flexible deformation characteristics. The flexible contact layer is made of thermoplastic elastomer with a hardness ranging from Shore A60 to A80 and a thickness ranging from 0.5 mm to 1.5 mm. The function of the flexible contact layer is to conform to the periodic undulations of the thread surface, maintaining the stability of the array's incident posture while accommodating minor height differences and eliminating air gaps that may form at local curvature abrupt changes. A coupling agent layer is filled between the flexible contact layer and the surface thread surface; the area covered by the coupling agent is indicated by an elliptical dashed box in the figure. The thickness of the coupling agent layer is preferably controlled at approximately 1.0 mm. This thickness avoids hard contact wear between the wedge and the thread tip while ensuring effective near-field acoustic energy transmission. The surface of the thread is represented by a periodic sawtooth curve, exhibiting the alternating distribution of thread crests and valleys. The thread height dimensions are marked in the figure, indicating the geometric parameters of the thread. The entire coupling structure, through the deformability of the flexible contact layer and the continuous fluid replenishment mechanism, ensures a stable acoustic coupling state during the dynamic scanning process of drill pipe rotation and axial feed.

[0026] The profilometer employs a line structured light scheme, projecting a line laser onto the threaded surface and using an industrial camera for high-frame-rate acquisition. The working distance of the profilometer is preferably between 80.0 mm and 140.0 mm, with a measurement range covering a width of at least 20.0 mm and a height of at least 8.0 mm, and a point spacing of at least 0.05 mm. After installation, the profilometer undergoes geometric calibration using ceramic stepped blocks and cylindrical standard parts as calibration targets. The calibration process includes intrinsic parameter calibration, extrinsic parameter alignment, and distortion correction, with a calibration residual preferably less than 0.03 mm. During online acquisition, the profilometer uses the angular and axial displacements provided by the encoder as triggers, with the trigger interval set to a combination of fixed angular and axial step sizes, for example, an angular step size of 0.10 degrees and an axial step size of 0.10 mm. The point cloud output by the profilometer is filtered in real time to form a single continuous spiral line. The filtering rule is to delete scattered points with an intensity less than three times the background noise and to remove isolated spikes based on three-point curvature judgment. The reason for using a trigger step size combined with a continuous spiral is that this allows each tooth line to become approximately a straight line after unfolding, thus providing a stable reference for subsequent coordinate unfolding and echo alignment. The profilometer uses a "near-side strong reflection priority" strategy to identify the contact interface, that is, it selects the first reflection peak with the strongest intensity closest to the wedge side on each scan line as the coupling interface. The reason is that the abrupt change in refractive index at the coupling interface leads to strong reflection and stable position. Selecting this peak can ensure that the coupling thickness estimation remains consistent under rotation and feed dynamics.

[0027] refer to Figure 7The profilometer of this invention employs a line structured light scheme for measuring the three-dimensional topography of threaded surfaces. The profilometer has a rectangular housing and integrates two core components: a laser and an industrial camera. The laser, located in the left cavity of the profilometer (shown in gray), generates a line laser and projects it onto the measured surface. The industrial camera, also shown in gray, is located in the right cavity of the profilometer. An optical lens is positioned at the front of the camera, with the optical axis indicated by a solid black circle in the figure. The laser emits a line laser beam downwards, and the beam's path is represented by multiple straight lines radiating from the laser's emission point to the threaded surface. The line laser forms a fan-shaped light plane in space, which intersects the threaded surface to form a laser line. This laser line is represented by a thick solid curve, exhibiting a wavy shape along the undulations of the threaded surface, accurately reflecting the height variations of the thread crests and valleys. The projection width of the laser line is preferably not less than 20 mm to ensure complete coverage of one or more complete tooth profile cycles. When the laser line irradiates the threaded surface, diffuse reflection occurs. The reflected light returns to the lens of the industrial camera along multiple paths, with typical reflected light paths represented by dashed lines in the figure. Using the principle of triangulation, the camera can calculate the three-dimensional coordinates of each point based on the imaging position of the laser line on the image sensor. The working distance of the profilometer, i.e., the vertical distance from the bottom surface of the profilometer to the thread surface, is represented by a labeled vertical line segment in the figure; this distance is preferably within the range of 80 mm to 140 mm. The selection of this working distance comprehensively considers the balance between field of view coverage, depth of field, and measurement resolution. The surface of the thread is represented by a periodic sawtooth waveform curve, clearly showing the geometric characteristics of the thread teeth. The figure indicates a measurement width of not less than 20 mm and a measurement height range of not less than 8 mm; the latter indicates the maximum height difference that the profilometer can measure, sufficient to cover the entire range from the tooth crest to the tooth root. In actual measurement, the profilometer performs high-frame-rate continuous acquisition via encoder triggering. The trigger interval is jointly determined by the angular step distance of the rotary encoder (preferably 0.1 degrees) and the axial step distance of the linear encoder (preferably 0.1 mm). The acquired point cloud data, after intensity filtering and geometric filtering, forms a continuous helical profile. The point spacing should preferably be no greater than 0.05 mm to ensure high-density sampling. The profilometer requires geometric calibration after installation, with the calibration residual preferably less than 0.03 mm to ensure measurement accuracy meets the requirements of subsequent coordinate transformation and imaging processing. Figure 7 The key technical parameters of the profilometer were also demonstrated, including point spacing, calibration residual, angular step distance, and axial step distance. These parameters together determine the accuracy and density of three-dimensional topography measurement, providing a reliable geometric benchmark for subsequent surface coordinate establishment and propagation of prior generation.

[0028] The encoders include rotary encoders and linear encoders. The rotary encoder is mounted on the spindle end holding the drill pipe, with a preferred resolution of 16384 equal divisions per revolution, providing a zero-point index signal to establish an absolute angle reference. The linear encoder is mounted on the axial feed guide, with a preferred resolution of 1.0 micrometer, providing an origin signal to establish the axial zero point. Signals from both types of encoders are connected to the control unit via anti-interference shielded cables, with timestamps superimposed on the signals; the difference between the two-channel timestamps is preferably less than 1.0 microsecond. The rotary and linear encoders jointly perform the "pitch consistency monitoring" function, calculating whether the axial displacement corresponding to adjacent angular divisions maintains a constant step size during operation. When a step size change exceeds the set tolerance (e.g., ±0.02 mm), triggering is paused, and a check of coupling and mechanical transmission is prompted. This monitoring mechanism eliminates accumulated errors caused by belt elongation or lead screw thermal expansion at the source, ensuring that the data for each revolution is strictly aligned on the unfolded grid.

[0029] After assembly, a no-load rotation test is performed. First, rotate the device two full rotations without load, acquiring encoder angle and profilometer point cloud data. Calculate the clamping eccentricity and runout magnitude. Then, using a fine-tuning mechanism on the support, align the array centerline with the spindle centerline, with an overlap error preferably less than 0.05 mm. Next, install a reference piece with standard threads. The profilometer acquires a point cloud for one rotation and fits it to standard geometry. If the fitting residual exceeds 0.05 mm, adjust the relative position of the profilometer and array until the target is achieved. Then, spread a coupling agent between the wedge and the reference piece. The coupling agent can be a glycerol aqueous solution or a dedicated ultrasonic coupling adhesive, with an initial thickness controlled at approximately 1.0 mm. This initial thickness is chosen because too thin a layer will cause hard contact between the wedge and the thread tip, leading to wear, while too thick a layer will cause near-surface energy diffusion and reduce near-field resolution. Finally, perform a test scan at a low speed, such as 10.0 revolutions per minute, to check whether the shape of the reflection peak on the front surface is continuous and stable. If periodic loss occurs, slightly increase the coupling agent flow rate or decrease the downpressure until the peak amplitude changes within ±2.0 dB along one revolution.

[0030] During operation, the spindle zero point is first aligned with the zero position of the rotary encoder, and then the feed start position is aligned with the origin of the linear encoder. The ratio of rotational speed to axial feed speed is set to equal the target pitch, typically set to a rotational speed of 30.0 to 60.0 revolutions per minute, with the axial feed speed automatically determined based on the pitch. This ratio ensures the array always performs a single-track helical scan along the same thread, reducing the time overhead of repeated coverage. The triggering rule is "angle priority, axial synchronization," meaning a trigger is generated based on each equally divided angle of the rotary encoder, while simultaneously verifying whether the current displacement of the linear encoder has reached the corresponding step size. If not, it waits; if it has, it triggers immediately. The advantage of this rule is that it ensures each ultrasonic transmission and reception corresponds to a fixed grid point in the unfolded coordinate system, simplifying subsequent interpolation and reducing registration errors.

[0031] The array's incident orientation is determined by the wedge geometry. After the array is emitted, it first receives a strong reflection from the coupling interface. The system uses the arrival time of this strong reflection as an instantaneous estimate of the coupling thickness. This peak is chosen as a reference because its amplitude and position are less affected by material and surface condition fluctuations, and it has a monotonic relationship with the actual coupling thickness, facilitating continuous monitoring without complex solutions. If the change in arrival time between adjacent triggers exceeds a set threshold, such as ±50.0 nanoseconds, a small amount of coupling agent is added via a needle valve or the rotation speed is reduced to restore stable coupling. After coupling stabilizes, the array continuously acquires data at a preset pulse repetition frequency, preferably at a sampling rate of 100.0 megasamples per second or higher to ensure high-frequency fidelity. In the root region, the incident angle of the array relative to the surface normal is ensured to be close to the design value by the wedge shape. At this point, the main lobe energy is concentrated in the target area, the profilometer synchronously provides the surface topography, and the encoder ensures the repeatability of each sampling position, thereby reducing geometric distortion and intensity fluctuations in subsequent image synthesis.

[0032] To improve data quality, three online measures were implemented. The first is near-surface interference suppression, specifically adaptive baseline subtraction of a short window near the front surface in each trigger cycle. The baseline is referenced to the average waveform at the same angular position in the previous revolution. This approach reduces the background caused by periodic structural textures while preserving the true defect echo. The second is mechanical vibration isolation, where a damping layer is added between the support and the base, with a natural frequency designed below 15.0 Hz. The rotational speed is designed to avoid this frequency, thus preventing stripe noise throughout the entire revolution. The third is temperature stabilization, where a temperature sensor on the outside of the wedge triggers a fine-tuning of the coupling agent flow rate. For every 1.0 degree Celsius increase in temperature, the flow rate is increased by approximately 5.0% to offset the trend of coupling layer thickness changes caused by viscosity reduction.

[0033] Figure 3The graph shows the experimental curves of ultrasonic echo signal processing, illustrating the temporal characteristics and envelope extraction effect of the array-received signal in this invention. The horizontal axis represents time in microseconds (μs), ranging from 0 to 12 microseconds, with a main scale interval of 2 microseconds. The vertical axis represents signal amplitude in volts (V), ranging from -1.0 V to 1.0 V, with a scale interval of 0.5 V. The solid line in the graph represents the original ultrasonic echo signal received by a single array element, which exhibits typical pulse modulation characteristics. A strong oscillating packet appears around 2.5 microseconds, with a peak amplitude of 0.9 V. This packet corresponds to the reflection from the front surface of the interface between the wedge and the object under test, and its arrival time is proportional to the coupling layer thickness. This invention utilizes this characteristic for real-time monitoring of the coupling state. A second oscillating packet appears around 8.5 microseconds, with a peak amplitude of approximately 0.6 V. This packet corresponds to the scattered echo from an internal defect in the object under test, and its arrival time reflects the defect depth information. The dashed line represents the envelope curve after full-wave rectification and moving average processing. This curve smoothly encloses the oscillation peaks of the original signal, effectively suppressing carrier frequency components and preserving amplitude modulation information. Envelope extraction uses a moving average with a window width of 15 sampling points, ensuring both envelope smoothness and maintaining temporal resolution. As shown in the figure, the envelope curve accurately tracks the amplitude changes of the two echo packets, providing a stable amplitude reference for subsequent time-delay stacking processing. Envelope processing avoids the superposition loss caused by phase cancellation, improving the signal-to-noise ratio of cTFM imaging.

[0034] Figure 4This graph shows the real-time monitoring curve of the coupling layer thickness, illustrating the dynamic changes in the coupling state during thread inspection. The horizontal axis represents the rotation angle in degrees, ranging from 0 to 300 degrees, with 60-degree increments, corresponding to the angular displacement of the drill pipe rotation during inspection. The vertical axis represents the coupling layer thickness in millimeters (mm), ranging from 0 to 2.0 mm, with 0.5 mm increments. The solid curve in the graph represents the coupling layer thickness calculated in real-time based on the arrival time of the echo from the front surface. This curve exhibits quasi-periodic fluctuations, with the fluctuation period consistent with the angular interval corresponding to the thread pitch. The peak of the curve corresponds to the thread crest region, where the distance between the wedge bottom and the inspected surface is larger, indicating a thicker coupling layer; the trough corresponds to the thread root region, where the distance is smaller, indicating a thinner coupling layer. The thickness variation is approximately ±0.15 mm, reflecting the geometric undulations of the thread surface. The horizontal dashed line in the graph represents a target coupling thickness of 1.0 mm, a value determined based on a combination of near-field resolution and coupling stability. The gray shaded area represents the permissible thickness variation range, with an upper limit of 1.05 mm and a lower limit of 0.95 mm, a tolerance of ±0.05 mm. When the measured thickness exceeds the tolerance range, the system compensates by adjusting the couplant flow rate or correcting the scanning speed. As can be seen from the curve, apart from the inherent undulations of the thread, the coupling layer thickness is basically maintained within the target range, indicating that the coupling control strategy of this invention can adapt to the complex geometry of the thread surface, ensuring the continuity and stability of acoustic coupling and providing a fundamental guarantee for high-quality imaging.

[0035] The array front-end diaphragm is designed as a replaceable component, to be replaced when the cumulative scanning length reaches 3000.0 meters or the surface wear exceeds 30% of the original thickness. The wedge block flexible contact layer is designed with a quick-release structure, secured with two positioning screws, and the replacement time is less than 10.0 minutes. The profilometer protective window uses hardened glass with an oleophobic coating to reduce transmittance loss caused by coupling agent adhesion. The encoder coupling adopts a clamping structure with anti-loosening plates, and its coaxiality retention capability after long-term operation is superior to that of a screw-driven structure. The purpose of these durability arrangements is to reduce downtime and maintenance costs, and ensure stable operation of the production line.

[0036] In one alternative implementation, for large-diameter drill pipe applications, the array element count can be set to 128, the element spacing to 0.60 mm, and the wedge length increased to over 100.0 mm to obtain a longer effective delay line, thereby maintaining resolution in deep regions. For small-diameter or internal thread applications, the profilometer can be replaced with a white light confocal type to obtain higher near-field height resolution, and the flexible contact layer of the wedge can be replaced with an ultra-soft silicone material with a hardness close to Shore A20 to achieve a good fit at the tooth groove. For high-speed online inspection applications, the rotation speed can be increased to 90.0 rpm, while the trigger step distance can be reduced to 0.05 degrees, and the resolution of the linear encoder can be increased to 0.5 micrometers. A coupling agent thermostatic unit can be used to maintain the temperature difference within ±1.0 degrees Celsius to ensure geometric accuracy and amplitude stability even at high cycle times.

[0037] The FPGA module is configured to work in conjunction with the array, wedge, profilometer, and encoder to execute an imaging pipeline. This pipeline includes: a surface coordinate establishment unit for establishing a spiral unfolded coordinate domain and a surface coordinate index table based on the continuous point cloud of the thread profile acquired by the profilometer under encoder triggering, using a dual quaternion spiral unfolding method; a propagation prior generation unit for generating a lookup table containing refraction time intervals within the spiral unfolded coordinate domain using a fast-progression method; a cTFM imaging unit for performing time-delayed superposition on the raw data stream acquired by the array based on the refraction time interval lookup table to generate a result matrix; and an RPCA decomposition unit for performing low-rank sparse decomposition on the result matrix to extract sparse components, thereby obtaining de-threaded C-scan imaging.

[0038] In one implementation, the surface coordinate establishment unit receives the continuous point cloud of the thread profile output by the profilometer under encoder triggering, as well as the angular and axial displacements from the encoder. To ensure consistency in position and time, the triggering cycle is defined by an angular displacement priority strategy, i.e., the profilometer is immediately triggered to sample after a fixed angular step, and the axial displacement is checked during sampling to see if it reaches the target step size; if not, it waits for the next extremely short cycle for re-verification. The angular step size can be set to 0.10 degrees, and the axial step size can be set to 0.10 millimeters. This strategy ensures that each sample falls into a stable grid point in the spiral unfolding coordinate domain, reducing subsequent registration errors. The point cloud of the profilometer is first filtered using both intensity and geometry thresholds. The intensity threshold can be set to three times the mean of the background noise to remove low-reflectivity particles; the geometry threshold estimates isolated spikes through three-point curvature estimation, and points exceeding the set curvature are deleted. The reason for using dual thresholds is that relying solely on intensity will retain noise scattering points at high-curvature roots, while relying solely on curvature will mistakenly delete the true boundaries of weak reflections. The combination of dual thresholds can maintain boundary continuity at both the crest and root of the thread.

[0039] To establish a stable attitude reference, the surface coordinate establishment unit performs two idle runs and one reference measurement during its first run after power-on. During the idle run, only the encoder sequence is recorded to estimate rotational uniformity; during the reference measurement, a point cloud is acquired to calculate clamping eccentricity and runout. The obtained eccentricity and runout are used to generate an attitude calibration table, which is then superimposed as a compensation term on the pose of each frame during subsequent projection. This approach is necessary because clamping eccentricity causes periodic drift in the unfolded toothed wires; early compensation avoids tilted stripes in the resulting matrix. The dual quaternion spiral unfolding chain-combines the rotations and translations of each frame sequentially. Each frame yields an attitude description, which, along with the point cloud of that frame, is projected onto the unfolding plane. The unfolding plane defines a pair of orthogonal axes: the horizontal axis corresponds to angular displacement, and the vertical axis corresponds to axial displacement. The grid step size is consistent with the trigger step size, with a recommended combination of 0.10 degrees and 0.10 millimeters. The point clouds of all frames are projected onto this plane to form the spiral unfolding coordinate domain. A surface coordinate index table is then generated. The surface coordinate index table is a two-dimensional record table, corresponding one-to-one with the helical unfolding coordinate domain. Each record contains six types of fields: the three-dimensional position of the location in the device coordinate system, the local normal of the location, the relative attitude of the location to the wedge incident surface, the integer index of the geometric distance from the location to each element of the array, the original pixel index of the location in the profilometer image, and the estimated coupling interface height of the location. The coupling interface height is determined by selecting the dominant reflection peak near the wedge side. The dominant reflection peak near the wedge side is chosen because it corresponds to the location of the refractive index abrupt change, with a large reflection amplitude and stable position. Using this peak, the coupling layer thickness can be stably estimated under dynamic changes in rotation and feed, thus maintaining the consistency of time-delay superposition. The surface coordinate index table is stored in row-major order, with a single record size of 64 bytes, containing fixed-point numbers and integer indices arranged in the above order. The total capacity when fully covering the data of each revolution is in the hundreds of megabytes, suitable for direct addressing of on-board memory.

[0040] The propagation prior generation unit establishes a layered medium mesh within the spiral unfolding coordinate domain. The lateral and longitudinal step sizes of the mesh are consistent with the surface coordinate index table to avoid subsequent interpolation errors. The upper layer of the spiral unfolding coordinate domain represents the wedge, and the lower layer represents the object under test. The contact boundary between them is given by the coupling interface height estimation in the surface coordinate index table. After mesh initialization, a source point is set at the radiation center of each element. The propagation arrival time is calculated point by point using a fast-push method, and the propagation arrival time is written into a lookup table containing the refraction time distance. The execution of the fast-push method includes three core steps. The first step is candidate set management. The propagation prior generation unit maintains three states for each mesh point: unvisited, candidate, and confirmed. The source point is marked as confirmed, the neighborhood of the source point is marked as candidate, and the candidates are placed in a priority queue sorted by propagation arrival time. The priority queue ensures that propagation always proceeds along the shortest arrival time direction, thus obtaining a monotonic arrival time field. The second step is boundary processing. When the propagation crosses the contact boundary between the wedge and the object under test, the propagation prior generation unit calls the boundary solver to determine the optimal refraction direction of the incident path at the boundary. The boundary solver searches for the direction that minimizes the overall propagation time within the allowed directional range using a bisection search. The termination condition for the bisection search can be set to an angular resolution better than 0.10 degrees or a propagation time variation less than 10.0 nanoseconds. This search scheme is adopted because, under actual material combinations, the propagation time exhibits a unimodal characteristic with respect to the boundary direction, and the bisection search can converge to a usable solution in a few steps. The third step is field updating. Each candidate grid point is popped from the priority queue, marked as confirmed, and the propagation arrival time estimates of its adjacent grid points are updated. If the new estimate is earlier than the existing values ​​of adjacent grid points, the priority of that node is overwritten and updated in the priority queue. This process continues until all valid grid points in the spiral unfolding coordinate domain are covered. To serve the cTFM imaging unit, the propagation prior generation unit also records the grid sequence index of the first-arrival path, which can be used later for directional consistency constraints or edge region protection of the result matrix. The lookup table containing the refraction time distance is organized with the channel as the outer layer and the spiral unfolding coordinate domain position as the inner layer. It uses fixed-point storage, with a bit width of up to 24 bits and a time resolution of up to 5.0 nanoseconds, which ensures both dynamic range and control of bandwidth and capacity.

[0041] The cTFM imaging unit receives the raw data stream acquired by the array and aligns it with a lookup table containing the refraction time interval. The raw data stream is delivered one frame per trigger, with each frame containing the sampling sequence of all received channels. To reduce subsequent interpolation errors, the cTFM imaging unit performs a three-step preprocessing for each channel. The first step is bandpass filtering using a linear-phase finite impulse response filter with a bandwidth covering more than 80% of the array's center frequency band to retain the main energy and suppress power frequency and high-frequency noise. The second step is zero-point alignment, using the arrival time of the strong peak on the front surface as a reference to shift the waveform of each channel along the time axis to a unified reference. This approach can offset minor delay differences between channels, making the main lobe more concentrated after delay superposition. The third step is envelope extraction, using full-wave rectification followed by moving average. The window width can be set to ten to twenty sampling points corresponding to the sampling rate to obtain a smooth analytical envelope sequence. Full-wave rectification plus moving average is chosen instead of complex analytical transformation because it is computationally stable and easy to implement pipelinedly in an FPGA module.

[0042] Pixel-level time-lapse stacking is performed according to the grid order of the spiral unfolded coordinate domain. For each grid position, the cTFM imaging unit reads the arrival time index of each transmit channel and each receive channel corresponding to that position from a lookup table containing refraction time distances, and then performs cubic interpolation sampling in the corresponding envelope sequence. The cubic interpolation uses a four-point sample fitting method: two points are taken on each side of the arrival time index, and a smooth curve is fitted with four points, and the amplitude is read at the target position of the fitted curve. Four-point interpolation is used instead of linear interpolation because it is more stable in suppressing aliasing effects and maintaining peak positions, especially at high-slope rising edges, where systematic underestimation does not occur. The interpolation results of all channels are added item by item at the grid position to obtain a cumulative amplitude. After traversing the grid in order, the cTFM imaging unit forms an intermediate amplitude frame. Subsequently, the intermediate amplitude frame is resampled at equal intervals and aligned with rows and columns according to the grid positions recorded in the surface coordinate index table, so that the data of each ring are seamlessly stitched in the same coordinate system. Finally, the cTFM imaging unit searches for the maximum envelope pixel-by-pixel within a preset depth range, writes the maximum value into the result matrix, and stores the arrival time index corresponding to the occurrence of the maximum value for subsequent localization. The preset depth range is selected with reference to the tooth profile height and coupling interface height provided by the profilometer. In root detection tasks, the near-superficial range below the coupling interface is preferentially selected. The advantage of selecting this range is that it minimizes the influence of strong echoes from the back wall on the C-scan, making the result matrix more sensitive to minor discontinuities in the root.

[0043] The RPCA decomposition unit receives the result matrix and outputs a de-grooved C-scan image. To make the decomposition more targeted to groove strips, the RPCA decomposition unit first constructs a groove mask. The mask generation process calculates the row mean curve along the axial direction of the spiral unfolding coordinate domain, and identifies approximately periodic strip positions through peak-valley detection. The strip width can be adaptively adjusted within a few pixels based on the actual spiral pitch. These strip positions are marked as mask regions. The purpose of constructing the mask is to guide the low-rank-sparse decomposition to absorb periodic structures into the low-rank part, while leaving non-periodic defect responses in the sparse part.

[0044] refer to Figure 2 , Figure 2 This is a schematic diagram comparing the imaging effects before and after RPCA decomposition, used to demonstrate the suppression effect of low-rank sparse decomposition on thread groove interference in this invention. Figure 2 The image is divided into two sub-image areas. The upper sub-image represents the original cTFM imaging result. The horizontal axis represents angular displacement, ranging from 0 to 360 degrees, with scales marked in 60-degree intervals. The vertical axis represents axial displacement, ranging from 0 to 20 millimeters, with scales marked in 5-millimeter intervals. In the original imaging result, a horizontal stripe pattern with alternating light and dark areas is presented. This stripe corresponds to the periodic tooth structure of the surface thread, and the stripe spacing corresponds to the thread pitch, approximately 2.5 millimeters. There are three circular areas in the stripe background, located at 250 degrees angular displacement and 10 millimeters axial displacement, 450 degrees angular displacement and 15 millimeters axial displacement, and 550 degrees angular displacement and 7 millimeters axial displacement, respectively. These circular areas represent actual defect signals, but due to the strong interference of the tooth stripes, their contrast is low, appearing semi-transparent, making them difficult to accurately identify and locate. The lower sub-image represents the sparse component extracted after RPCA decomposition, i.e., the tooth-removed C-scan imaging result, with its coordinate system set consistent with the upper sub-image. In this image, the original periodic bands have been completely suppressed, the background exhibits a uniform low-intensity distribution, and the three defect signals are clearly displayed as high-contrast black solid circles with sharp defect boundaries, facilitating automatic identification and quantitative analysis. The comparison demonstrates that RPCA decomposition can effectively separate periodic thread structure responses from non-periodic defect responses, significantly improving the defect detection rate.

[0045] The low-rank sparse decomposition employs an alternating minimization process. Initially, both the low-rank and sparse matrices are set to zero. Then, iterative iterations are performed, each containing three deterministic steps. The first step is low-rank update. Singular value decomposition is performed on the resulting matrix minus the current sparse matrix. Smaller singular values ​​are soft-cut using a fixed threshold, while larger singular values ​​are retained to reconstruct the low-rank matrix. The values ​​of the low-rank matrix are then forced at the tooth-pattern mask positions. Using a fixed threshold instead of adaptive weights ensures simplicity and predictable behavior, facilitating fixed-point computation on an FPGA module. The second step is sparse update. The residual between the resulting matrix and the current low-rank matrix is ​​calculated. A fixed threshold is applied to each element of the residual, resulting in a sparse matrix. Updated values ​​are retained outside the tooth-pattern mask, thus concentrating energy that does not conform to the striping pattern into the sparse components. The third step is convergence determination. The change in the total residual between two adjacent iterations is compared. The iteration stops when the change is less than a very small fixed threshold or when the number of iterations reaches a preset upper limit. After iteration, small connected component deletion and morphological opening and closing operations are performed on the sparse matrix to remove discrete isolated points with areas smaller than a few pixels and fill in small breaks, making the defect region boundaries in the de-grooving C-scan imaging more continuous. The reason for choosing this process is that singular value decomposition naturally tends to capture strong periodic structures, while soft reduction lowers noise without smoothing out sharp local peaks. Combined with a groove mask, it can effectively separate regular grooves from irregular defects.

[0046] To ensure real-time operation, the four units operate in a strictly pipelined manner within the FPGA module. The surface coordinate establishment unit generates the corresponding surface coordinate index table record for each trigger after a delay of no more than one frame. The propagation prior generation unit pre-calculates a lookup table containing the refraction time distance during the first loop, and then triggers a local update only when there is a significant change in the coupling interface height. The cTFM imaging unit completes the delay superposition and intermediate amplitude update for each trigger within one trigger cycle. The RPCA decomposition unit processes the row bands of the result matrix using a sliding window, with the window height set to 64 or 128 rows, covering the current row band and its adjacent row bands, and updates the de-serration C-scan imaging within two to three window delays. To balance accuracy and throughput, all time and amplitude values ​​are expressed in fixed-point form, with time represented by 24 bits and amplitude by 16 bits. Key thresholds are given in the form of table entries in read-only memory for easy rapid loading during process switching.

[0047] In one alternative implementation, for coarse pitch and large diameter scenarios, the angular step size of the helical unfolding coordinate domain can be reduced to 0.05 degrees, and the axial step size to 0.05 millimeters, to increase the spatial sampling density at the tooth root. To accommodate the higher density mesh, the lookup table containing the refraction time distance can be stored in blocks, each block covering several rows and columns. Within each block, a shorter fixed-point number relative to the block's starting point is used, thereby reducing the table size by more than one-third without sacrificing resolution. In high-temperature environments, a column of temperature sampling values ​​can be added to the surface coordinate index table. The propagation prior generation unit performs a small-range linear correction on the lookup table containing the refraction time distance, using a fixed correction step size based on the temperature increment to ensure deterministic implementation. In small diameter or internal thread scenarios, the peak and valley detection sensitivity of the row mean curve can be increased, and the upper limit of the strip width can be halved to accommodate more compact tooth profiles; simultaneously, the envelope sliding window width of the cTFM imaging unit can be reduced to retain higher near-surface details.

[0048] Example 2: A method for a phased array C-scan imaging system for adaptive surface threading, the method being executed by a device including an array, wedges, a profilometer, an encoder, and an FPGA module, comprising the following steps: Step 1: Establishing surface coordinates. The profilometer acquires continuous point clouds of the thread shape under the triggering of the encoder's angular and axial displacements. The FPGA module rotates and translates the continuous point cloud using a combination of double quaternion sequences to generate a rigid body transformation in the device coordinate system, and projects the continuous point cloud onto the unfolding plane according to the rigid body transformation to form a spiral unfolding coordinate domain, and then establishes a surface coordinate index table within the spiral unfolding coordinate domain; Step 2: Generating propagation... First, within the spiral unfolding coordinate domain, the FPGA module uses each array element as the source point and employs a fast-advance process to calculate the refraction time distance of the sound wave from the wedge to each element of the curved surface coordinate index table, and generates a refraction time distance lookup table. Second, cTFM imaging is performed. The array completes continuous spiral scanning and outputs the raw data stream. The FPGA module calls the refraction time distance lookup table to perform pixel-level delay superposition on the raw data stream to obtain an intermediate imaging frame. The maximum envelope is extracted from the intermediate imaging frame to generate the result matrix. Third, decomposition and imaging are performed. The FPGA module performs robust principal component analysis decomposition on the result matrix, extracts sparse components, and obtains a texture-free C-scan imaging.

[0049] Example 3: In this example, the spiral unfolding coordinate domain covers a circumferential and 20.0 mm axial range. The circumferential grid step size is set to... ( (Angular grid step size), axial grid step size is ( (This refers to the axial grid step size). This gives the number of circumferential grid columns. 3600 ( (Number of columns in the resulting matrix) and number of axial grid rows ( (This represents the number of rows in the resulting matrix). The sampling rate is set to... ( (Number of sampling points per second), the number of time samples in a single trigger sampling is ( (Number of sampling points per channel A-scan). The start and end times of the preset depth gate are set to... ( (the start time of the gate) and (This refers to the end time of the door).

[0050] For each trigger sample, the encoder provides angle and axial readings. Let the first... The angle and axis of the second trigger are respectively and ( For the first The absolute angle of the second trigger. For the first The absolute axial position of the next trigger), the zero position is respectively and At angle zero, (Axial zero position). This sample is written to the integer grid index of the CTFM imaging accumulator. The calculation is as follows: ;in Indicates rounding to the nearest integer. Numerical example: When hour, ;when hour, To eliminate jagged edges caused by discretization and obtain geometrically equidistant intermediate imaging frames, the accumulator is resampled using linear interpolation based on the grid size of the coordinate domain after spiral expansion. Let the continuous coordinates of the target to be resampled be... ( For column indices of continuous circumferential coordinates, (Row index of continuous axial coordinates), which is located at the four vertices of an integer grid cell. Within. Define interpolation coefficients. ;in This represents the fractional offset in the circumferential direction. The fractional offset along the axis, all located within the interval Let the cumulative magnitudes of these four vertices be respectively... , The magnitude of the top left vertex. The magnitude of the top right vertex. The magnitude of the lower left vertex. (where the amplitude is the value at the bottom right vertex), then the amplitude after resampling The amplitude of the resampling result is: Numerical example: Take ,get After completing global interpolation, geometrically equidistant intermediate imaging frames are obtained.

[0051] First, each channel A is scanned through bandpass and envelope processing to obtain the resolved envelope sequence. Assume the intermediate imaging frame is at a certain grid point. The time series is ( For grid points The The envelope amplitude of each time sample. (For time sample index). Time gate. Converted to sample index range ,in Substituting the values ​​from this example, we have: Search for the maximum envelope pixel-by-pixel within this interval. Define the resulting matrix as follows. (The C scan amplitude after writing), define the arrival time index graph as follows: To generate the time sample index of the maximum envelope, then Numerical example: If a certain point of exist If we take the maximum value of 1.24, then... .

[0052] The propagation prior generation unit has recorded the grid sequence of the first-arrival path for each source point when calculating the lookup table including the refraction time distance. This sequence is mapped to the same coordinate system as the resulting matrix. The orientation deviation of each pixel is calculated and suppressed according to a threshold. Let's assume that at pixel... At that point, the local tangent vector of the first path is ( It is a unit vector, derived from the first path in (Neighboring grid difference in the neighborhood), let the dominant direction vector obtained from the local magnitude gradient of the resulting matrix be... ( For unit vectors, use the central difference in (Neighborhood calculation). The angle between the two is... ; in Let be the directional deviation angle, in degrees. Assume a preset angle tolerance of . ( (Assuming the maximum permissible directional deviation), let the maximum effective suppression angle be... ( (The upper limit angle from the start to complete suppression). Define the amplitude suppression factor as... ;in For pixels The retention coefficients. The result matrix with consistent direction is denoted as... (where the amplitude is after directional constraints) Numerical example: If a certain pixel of ,but ,get Keep the original value. If the dot product of another pixel is 0.7660, then... Between and Above, therefore The pixel is suppressed.

[0053] The relative orientation of each surface element's normal to the wedge's incident surface is obtained from the surface coordinate index table. Defined in pixels... At this location, the normal direction of the face element is ( (where is a unit vector), the propagation direction vector from the effective radiation center of the wedge to this pixel is defined as . ( (This is a unit vector, which can be obtained by normalizing the geometric position difference vector). The critical incidence criterion uses the angle of incidence: ;in Let be the angle between adjacent horizontal normals. Let the curvature abrupt change threshold be... ( (to mark the threshold for curvature abrupt changes), when At that time, the pixels Regions marked as abrupt changes in curvature. For critical incident or curvature abrupt change regions, smoothing is performed using a small window averaging operation. The window size is defined as... (where the side length of the median filtering window is the window coverage) The smoothed amplitude is denoted as... ( (The smoothed amplitude), which is taken from the value within this window. The median; unmarked regions are directly set to... Numerical example: If the nine neighboring values ​​of a certain marked pixel are... The fifth value after sorting by size from smallest to largest is 1.04. .

[0054] Define the input matrix as ( Let be the two-dimensional magnitude matrix to be decomposed, with rows. The number of columns is The low-rank matrix is ( (For fitting the low-rank part of the periodic structure), the sparse matrix is ( (To accommodate defects and isolated strong echoes in the sparse portion). Construction of the tooth groove mask: Average the value for each row along the axial direction. Define the first... The row mean of the row is ,in For the first The mean of the rows, For matrix The Line number Column elements. For sequences Peak and valley detection is performed to find the set of approximate periodic strip center locations. ( (This is the set of row indices for the center of the stripe). Let the half-width of the stripe be... ( (where half the width along the axis is in pixels), then the tooth pattern mask (For a binary mask, where 1 represents a tooth pattern stripe) is defined as follows: .

[0055] Initialization and iteration of low-rank sparse alternating decomposition: Let the initial low-rank and sparse matrices be... ;in Indicates and A zero matrix of the same dimension. Let the singular value soft threshold be... ( (where is the reduction constant for singular values ​​during low-rank updates), and the sparse soft threshold is . ( (where is the reduction constant for residual magnitude during sparse updates), and the convergence threshold is... ( (where the stopping threshold is the relative residual change), and the maximum number of iterations is... ( (This is the upper limit of the number of iteration rounds). For the th... Round iteration, execution: low-rank update: for Perform singular value decomposition. ;in and These are the left and right singular vector matrices, respectively. This is a diagonal matrix with singular values. A soft threshold is applied to the singular values: ;in These are post-threshold singular values. These are the original singular values. We obtain... Forced low-rank priority within the tooth pattern mask: for all satisfying At the position, set the sparse matrix to zero. .

[0056] Sparse Update: Calculating Residuals ;in This is the residual after removing low-rank elements in the current round. Element-by-element soft threshold: ;like ,in For symbolic functions; Maintain position Convergence criterion: Calculate the relative change. ,in It is the F-norm. If or If the iteration fails, the iteration stops. After the iteration ends, the sparse matrix is ​​taken. ( (For the final round) as the amplitude base map for de-dentalized C-scan imaging.

[0057] Morphological post-processing: Define the minimum connected component area threshold as... (For the number of pixels threshold), the area to be deleted is less than The connected components are then subjected to morphological opening and closing operations. Let the structuring element be the radius. The disk ( (where is the radius of the structuring element, in pixels). First, perform an opening operation, then a closing operation, to remove noise and fill in small breaks.

[0058] Select a specific pixel Its envelope's maximum value inside the gate appears Amplitude Write The first path mapping is obtained (Unit vector), local gradient direction ( (Unit vector), dot product is ; Directional deviation angle .and By comparison, the inhibitory factor was obtained. Therefore .

[0059] The surface coordinate index table provides ,but This point is marked as the critical incident region. The median of the nine neighboring values ​​is taken. If the median is 1.08, then... During the RPCA stage, the row containing the pixel within the window is covered by a texture mask to appear as a non-strip. The residual after the first iteration is Execute sparse soft threshold: When the iteration reaches Then, if the pixel remains in the sparse matrix... If a pixel is not filtered out by connected components after morphological opening and closing, it is retained with an amplitude of 0.78 in the de-textured C-scan imaging, completing the full chain calculation from the intermediate imaging frame to the final pixel. When it is necessary to improve geometric alignment accuracy, the following can be used: Change to ,Will Change it to 0.05mm, and accordingly... and Increase proportionally; to control real-time performance, linear interpolation can be replaced with block vectorization to maintain... and Unchanged. For applications with extremely fine tooth patterns and short cycles, the half-width of the strip can be adjusted. Set it to 1, and set the sparse soft space The threshold value is reduced to 0.10 to avoid excessive absorption of small defect energy into the low-rank region. In high-noise conditions, the singular value soft threshold can be used. Increasing it to 0.30 allows the low-rank portion to absorb the periodic background more strongly, and then the continuity of the defect boundary is restored through morphological opening and closing.

[0060] While specific embodiments of the present invention have been described above, those skilled in the art should understand that these specific embodiments are merely illustrative. Those skilled in the art can omit, substitute, and modify the details of the above methods and systems in various ways without departing from the principles and essence of the present invention. For example, combining the above method steps to perform substantially the same function and achieve substantially the same result according to substantially the same method falls within the scope of the present invention. Therefore, the scope of the present invention is defined only by the appended claims.

Claims

1. A phased array C-scan imaging method for adaptive surface thread curvature, characterized in that, The method includes the following steps in sequence: Step (1), the steps to establish surface coordinates, include: based on the continuous point cloud of the thread shape collected by the profilometer under the trigger of the encoder, a spiral expansion coordinate domain and a surface coordinate index table are established by using double quaternion spiral expansion. Step (II), the step of generating propagation priors, includes: generating a lookup table containing refraction time distances in the spiral unfolding coordinate domain according to the fast propagation method; Step (3), the steps of performing cTFM imaging, include: performing time-delay superposition on the raw data stream acquired by the array according to the refraction time-distance lookup table to generate a result matrix; Step (iv), the steps of performing RPCA decomposition imaging, include: performing low-rank sparse decomposition on the result matrix to extract sparse components, thereby obtaining dentin-removed C-scan imaging.

2. The method according to claim 1, characterized in that, The steps for establishing surface coordinates also include: determining the numerical range of rotation axis, radial runout, and axial runout through two or more idle runs and one reference circle measurement to generate an attitude calibration table; and recording the three-dimensional position of the surface element center to the device coordinate system, the surface element normal, and the relative attitude with the wedge incident surface in the surface coordinate index table, and associating the spatial position of each array element with the surface coordinate index table item by item to form a surface element to array element mapping relationship.

3. The method according to claim 1, characterized in that, The steps for generating propagation priors also include: establishing a layered medium mesh in the spiral unfolding coordinate domain and setting the contact surface between the wedge and the object under test as the refraction boundary; and when the propagation path crosses the refraction boundary, calling the boundary solver to determine the refraction angle in a binary search manner so that the incident angle and the refraction angle satisfy the refraction condition of the medium velocity ratio.

4. The method according to claim 3, characterized in that, The steps for generating propagation priors also include: while generating the refraction time-distance lookup table, recording the grid sequence of the first arrival path for use as a consistency constraint for subsequent cTFM imaging.

5. The method according to claim 1, characterized in that, The steps for performing cTFM imaging also include: performing signal preprocessing on the raw data stream to form an analytical envelope sequence; and for each surface element in the spiral unfolding coordinate domain, calling the refraction time-distance lookup table to obtain the arrival time index, and using cubic interpolation to sample the amplitude of the analytical envelope sequence.

6. The method according to claim 1, characterized in that, The steps for performing cTFM imaging also include: using the angular and axial displacement records of the encoder to align the row and column indices of the cTFM imaging accumulator to integers, and performing linear interpolation resampling according to the grid size of the spiral unfolded coordinate domain to obtain geometrically equidistant intermediate imaging frames; and extracting the maximum envelope pixel by pixel from the intermediate imaging frames according to a preset depth gate to write it into the result matrix, while saving the arrival time index map where the maximum value is located.

7. The method according to claim 4, characterized in that, The steps for performing cTFM imaging also include: mapping the grid sequence of the first path to the result matrix, retaining the original values ​​of pixels that are consistent with the direction of the first path, and performing amplitude suppression on pixels whose directional deviation exceeds the preset angle tolerance, so as to obtain a result matrix with consistent direction.

8. The method according to claim 7, characterized in that, The steps for performing cTFM imaging also include: marking the critical incident region and the curvature abrupt change region according to the relative orientation of the surface element normal and the wedge incident surface in the surface coordinate index table, and smoothing these regions by performing small window value operation on the result matrix with consistent orientation.

9. The method according to claim 1, characterized in that, The steps for performing RPCA decomposition imaging also include: calculating the row mean curve along the axial direction of the spiral unfolding coordinate domain and using peak-valley detection to find periodic stripes to construct a tooth mark mask; and in the iterative process of low-rank-sparse alternating decomposition, performing singular value decomposition on the result matrix minus the current sparse matrix and performing a soft threshold operation to update the low-rank matrix, while forcing the use of the low-rank matrix value at the tooth mark mask position.

10. The method according to claim 9, characterized in that, The steps for performing RPCA decomposition imaging also include: during the iteration process, calculating the residual of the result matrix minus the current low-rank matrix, and performing a soft threshold operation on the residual element by element to update the sparse matrix, while retaining the updated value outside the tooth mark mask; and after the iteration process is completed, performing small connected component deletion and morphological opening and closing operations on the sparse matrix.

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