Fast high-precision center-of-gravity positioning method and system for distortion of an aero-insulation tile bottom keel

CN122671069APending Publication Date: 2026-09-01CHONGQING UNIV OF POSTS & TELECOMM
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Patent Information

Application Number
CN202610607328.2
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2026-05-06
Publication Date
2026-09-01

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Technical Problem

[0004]然而,将太赫兹反射成像技术实际应用于航空隔热瓦下龙骨畸变检测仍面临若干关键技术瓶颈

Benefits of technology

[0017]与现有技术相比,本发明提供的航空隔热瓦下龙骨畸变快速高精度质心定位方法及系统具有如下有益效果:

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Abstract

This invention discloses a rapid and high-precision centroid localization method and system for keel distortion under aircraft thermal insulation tiles, belonging to the field of terahertz nondestructive testing. Addressing the problems of slow imaging speed, low positioning accuracy, and limited working distance in existing terahertz imaging technologies, this invention constructs a reflective terahertz imaging system. Utilizing the penetration characteristics of terahertz waves through aircraft thermal insulation tiles and the reflection difference between the metal tag and the skin, based on the tag-skin echo interference effect, it only collects waveform features within a specific time window, without requiring a complete time-domain spectrum. Combined with image processing algorithms, it achieves centroid localization of the tag. The system extends the Rayleigh length of the terahertz beam by optimizing the off-axis parabolic mirror optical structure, improving the depth of focus and working distance tolerance. This invention has the advantages of being fast, nondestructive, high-precision, and having a wide depth-of-field tolerance, making it suitable for online nondestructive testing of keel distortion under aircraft thermal insulation tiles.
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Description

Technical Field

[0001] This invention belongs to the field of terahertz nondestructive testing, specifically to a method and system for rapid and high-precision centroid positioning of distortion under the keel of aviation thermal insulation tiles. Background Technology

[0002] As core equipment in the aerospace field, the structural integrity and safety of aircraft are of paramount importance. During high-speed flight, the interior of an aircraft requires thermal insulation tiles to withstand the harsh aerodynamic thermal environment. Minor distortions in the supporting structure beneath the thermal insulation tiles (i.e., the keel), such as millimeter-level deformations caused by thermal stress, vibration, or impact, may not initially affect flight, but over time can lead to loosening, detachment, or even structural failure of the thermal insulation tiles, seriously impacting flight safety. Currently, the detection methods for keel distortion mainly rely on destructive sampling inspection, such as removing the thermal insulation tiles and using a coordinate measuring machine or laser scanner for contact or optical inspection of the exposed keel. These methods are cumbersome, inefficient, and cause irreversible physical damage to the aircraft skin and thermal insulation layer, failing to meet the demands of modern aircraft for online, non-destructive, and rapid inspection.

[0003] Terahertz waves refer to electromagnetic waves with frequencies ranging from 0.1 THz to 10 THz. Their wavelengths are much shorter than microwaves but longer than infrared light, possessing the dual advantages of high penetration and high spatial resolution. Terahertz waves exhibit excellent penetration capabilities through non-polar dielectric materials such as ceramics, foams, and composite materials (e.g., the main components of aerospace thermal insulation tiles), while displaying strong reflection characteristics towards metals and highly conductive materials. Based on this physical characteristic, an emerging technique for non-destructive detection of keel distortion under aerospace thermal insulation tiles involves pre-attaching highly reflective terahertz tags to the aircraft skin (or corresponding locations of key keel nodes) to simulate distortion feature points (i.e., hidden points) of the keel structure. Subsequently, a terahertz reflection imaging system is used to perform a two-dimensional scan of the area covered by the thermal insulation tile. When a terahertz pulse penetrates the thermal insulation tile and illuminates the skin and metal tag, the system can receive echo signals carrying spatial location information due to the significant difference in their reflection characteristics. After obtaining a terahertz image through two-dimensional reconstruction of the signal, and combining edge detection and centroid localization algorithms in digital image processing, the centroid coordinates of the concealed tag can be accurately determined. By comparing the real-time measured centroid coordinates with the factory reference coordinates, the distortion displacement of the keel can be calculated. This technology provides an important technical path for achieving non-contact inspection of aircraft structural safety and future online service status monitoring.

[0004] However, the practical application of terahertz reflection imaging technology to the detection of distortion in the undercarriage of aerospace thermal insulation tiles still faces several key technical bottlenecks. First, the imaging speed is slow. Traditional terahertz time-domain spectral imaging systems rely on mechanical-optical delay lines for time-resolved measurements during point-by-point scanning. Each scan point acquisition requires a long mechanical reset operation of the delay line, typically taking several seconds to obtain a complete time-domain waveform. This results in imaging centimeter-level areas taking tens of minutes or even longer, failing to meet the timeliness requirements of engineering inspections. Second, imaging and positioning accuracy are limited. When terahertz waves penetrate relatively thick (e.g., centimeter-level) porous thermal insulation tile materials, the scattering effect and absorption loss within the medium are significant, leading to a sharp attenuation of the echo signal intensity at the receiving end and a reduced signal-to-noise ratio. This, in turn, blurs the edge features of the metal tag, directly restricting the sub-millimeter accuracy of subsequent centroid positioning algorithms. Third, the detection working distance is limited. According to electromagnetic wave propagation theory, path loss is positively correlated with electromagnetic wave frequency and transmission distance. Terahertz waves have extremely high frequencies, and the absorption by water vapor in the atmosphere and the loss due to spatial diffusion result in a short effective depth of focus for conventional terahertz imaging systems. The detection distance is usually limited to a short range, and the requirements for the distance tolerance between the probe and the sample are extremely stringent, which is not conducive to engineering adaptation in complex field environments.

[0005] To address the problems of low imaging efficiency, poor positioning accuracy, and limited working distance in the existing technologies, this invention proposes a method and system for rapid and high-precision centroid positioning of keel distortion under aviation heat insulation tiles. This invention has the following significant advantages: (1) Fast imaging and positioning speed: This invention abandons the traditional scanning mechanism of continuous reset of delay lines, and utilizes the interference effect between the skin background and the terahertz echo of the high-reflectivity tag. It only needs to collect the skin reflection waveform characteristics within a specific time window corresponding to each pixel point in the two-dimensional plane, without needing to obtain the complete time domain spectrum, thereby greatly shortening the single-point acquisition time. Actual verification shows that for a 2cm×2cm scanning area, the total time required to complete the imaging and positioning of the hidden point is only about 5-8 minutes. (2) High penetration resolution: This invention can effectively suppress the internal scattering noise of the heat insulation tile, and achieve clear imaging and identification of 2mm diameter metal tags covered by aviation heat insulation tiles with a thickness of up to 4cm. (3) High centroid positioning accuracy: By optimizing the signal processing and centroid extraction algorithm, the centroid positioning accuracy of the terahertz image of the 2mm metal tag is higher than 0.2mm. (4) Long detection range and wide depth-of-field tolerance: This invention fully utilizes the Rayleigh length characteristic of terahertz beams and expands the focal depth range of the focused spot through optimized optical system design. When the terahertz probe is 31.6 cm away from the reference distance of the skin surface, the probe can maintain the clarity of the concealed point image and the stability of the centroid positioning accuracy within a longitudinal range of ±5 cm before and after the focal plane, which greatly improves the robustness and operability of the system in actual aircraft field testing. Summary of the Invention

[0006] To address the shortcomings of existing terahertz reflective imaging technology in detecting concealed targets under aviation thermal insulation tiles, such as slow imaging speed, low positioning accuracy, and limited effective working distance, this paper proposes a method and system for rapid and high-precision centroid positioning of keel distortion under aviation thermal insulation tiles.

[0007] like Figure 1 The diagram shows the structure of a reflective terahertz imaging system. This system consists of a femtosecond laser, beam splitter, optical delay unit, high-reflectivity mirror, terahertz probe, heat-insulating tile sample, metal label, skin, stepper motor, adapter, and computer. The terahertz probe mainly comprises two photoconductive antennas (PCA1 and PCA2), two off-axis parabolic mirrors (OAP3 and OAP4) with a focal length of 5 cm, and two off-axis parabolic mirrors (OAP1 and OAP2) with a focal length of 35 cm.

[0008] A rapid and high-precision centroid localization method for under-keel distortion of aerospace thermal insulation tiles. Specifically, a high-reflectivity terahertz metal tag is placed on the skin beneath the aerospace thermal insulation tile as a feature point for keel distortion; a reflective terahertz imaging system is used to perform a two-dimensional scan of the thermal insulation tile area; based on the terahertz echo interference effect between the skin and the metal tag, the skin reflection waveform characteristics within a specific time window of each scanning point are acquired, without acquiring the complete terahertz time-domain spectrum; imaging is performed using the reflected terahertz pulse signal data. After imaging, the image is processed as follows:

[0009] Signal preprocessing involves peak-to-peak value correction and mirroring of the acquired metal tag signal intensity distribution data to eliminate distortion and asymmetry introduced by the acquisition system, resulting in a corrected original signal intensity distribution map. Data normalization linearly normalizes the preprocessed signal intensity data to the [0,1] interval, eliminating the influence of signal amplitude differences and providing a unified data scale for subsequent threshold segmentation. Threshold segmentation uses a set threshold (e.g., 0.96) to binarize the normalized signal intensity data, extracting the core target areas of the metal tags with signal intensities not lower than the set threshold, forming a binarized target area map. Subpixel-level edge extraction involves edge detection of the binarized target area, refining the edge contours using a subpixel interpolation algorithm to obtain high-precision contour coordinates of the metal tag, achieving subpixel-level edge localization. Weighted centroid calculation uses a weighted centroid algorithm based on the signal intensity distribution of the metal tag and the target area contour, with the signal intensity of each pixel as the weight, to calculate the centroid coordinates of the metal tag.

[0010] The formula is:

[0011]

[0012] in, The coordinates of the pixels within the target area. The signal strength of the corresponding pixel. The coordinates of the centroid of the metal tag obtained from the solution.

[0013] The calculated centroid coordinates are superimposed onto the original signal intensity distribution map to verify the consistency between the centroid position and the signal intensity center. Finally, high-precision centroid coordinates of the metal tag are output, achieving sub-pixel level positioning accuracy. The centroid coordinates of the metal tag are then compared with the factory reference coordinates to invert the keel distortion displacement.

[0014] The two-dimensional scanning adopts a Z-shaped trajectory, and the scanning area can be adjusted according to the detection requirements to complete the acquisition of imaging data. The working distance between the probe and the skin surface reference of the reflective terahertz imaging system is 31.6cm. When the probe moves within ±5cm before and after the focal plane, the imaging quality and centroid positioning accuracy remain stable.

[0015] The computer-controlled stepper motor drives the probe to complete two-dimensional scanning and performs signal processing, image reconstruction, and centroid coordinate calculation. The Rayleigh length of the terahertz beam is extended by optimizing the off-axis parabolic mirror optical structure, thereby increasing the system's depth of focus and working distance tolerance.

[0016] The advantages and beneficial effects of this invention are as follows:

[0017] Compared with existing technologies, the rapid and high-precision centroid positioning method and system for the under-keel distortion of aviation heat insulation tiles provided by this invention has the following beneficial effects:

[0018] First, the imaging and positioning speed is significantly improved. This invention does not employ the traditional terahertz time-domain spectral imaging system's reliance on continuous reciprocating reset of the mechanical-optical delay line and complete time-domain waveform acquisition. Instead, it utilizes the interference characteristic signal between the skin background and the highly reflective terahertz tag echo. It only needs to extract key feature parameters of the skin reflection waveform within a specific time window corresponding to each scanned pixel, drastically reducing the single-point data acquisition and processing time. Actual test results show that for a typical 2.0cm × 2.0cm scanning area, the total time for completing concealed tag imaging and centroid positioning is only about 5 to 8 minutes, which is more than an order of magnitude more efficient than existing point-by-point full-waveform acquisition methods, effectively meeting the timeliness requirements of rapid on-site detection in engineering projects.

[0019] Secondly, it boasts strong penetration and high imaging resolution. This invention, through optimized processing of terahertz echo signals and background scattering suppression methods, effectively overcomes the signal attenuation and noise interference problems caused by scattering and absorption of terahertz waves within centimeter-scale porous thermal insulation tile materials. Experimental verification shows that for aerospace thermal insulation tile coverings up to 4 cm thick, the method of this invention can achieve clear imaging and reliable identification of metal reflective tags with a diameter of only 2 mm. The imaging results exhibit complete edge features, and the signal-to-noise ratio meets the requirements for subsequent high-precision positioning analysis.

[0020] Third, the centroid positioning accuracy is high. This invention combines an optimized terahertz image reconstruction algorithm with sub-pixel-level edge detection and centroid extraction algorithms, significantly improving the accuracy of calculating the spatial position of concealed tags. Under the condition of being covered with 4cm heat insulation tiles, the centroid positioning accuracy for a 2mm diameter metal tag is higher than 0.2mm, providing high-precision data support for subsequent accurate inversion of keel distortion displacement by comparing with reference coordinates.

[0021] Fourth, it offers a long detection range and a wide depth-of-field tolerance. This invention fully utilizes the Rayleigh length characteristic of terahertz beams and extends the effective depth-of-field range of the focused spot through optimized optical system design. In typical applications, when the distance between the terahertz probe and the aircraft skin reference surface is set to 31.6 cm, the probe can be moved longitudinally within a range of ±5 cm before and after the focal plane, and the concealed label in the acquired terahertz image remains clearly discernible. This characteristic significantly reduces the requirements for precise adjustment of the probe's installation position and detection attitude, and significantly improves the system's operability under complex operating conditions in the aircraft's field.

[0022] Figure 1 Schematic diagram of a reflective terahertz imaging system.

[0023] Figure 2 Image of a 2 mm label under a 4 cm thick heat insulation tile.

[0024] Figure 3 Schematic diagram of the strong region interpretation principle of terahertz imaging: (a) Schematic diagram of the generation of reflected signals from the skin and tag; (b) Comparison of terahertz waveforms reflected from the tag and skin; (c) Spectral peak distribution diagram based on interference effect.

[0025] Figure 4 A schematic diagram illustrating the evolution of the terahertz light spot and the tag coverage area as the terahertz probe moves.

[0026] Figure 5 A schematic diagram illustrating the evolution mechanism of terahertz imaging images as the terahertz probe moves back and forth.

[0027] Figure 6 Image taken when the probe is 31.6 cm away from the skin surface.

[0028] Figure 7 Image taken when the probe is 33cm away from the skin surface.

[0029] Figure 8 Distribution of image coordinates and positioning errors from 10 tag scans. Detailed Implementation

[0030] This invention overcomes the bottleneck of long acquisition time per point due to mechanical delay line reset in traditional terahertz time-domain spectral imaging. It establishes a rapid scanning and feature extraction mechanism based on the echo interference effect of skin and high-reflectivity tags to achieve minute-level imaging and localization of hidden points in centimeter-level areas. It suppresses the high loss and scattering noise interference of terahertz waves in thick thermal insulation tile media, improving the penetration imaging resolution of millimeter-level metal tags. It expands the effective depth of focus range and working distance tolerance of the terahertz reflection imaging system, and optimizes optical parameters by utilizing the Rayleigh length characteristics of the terahertz beam to ensure stable imaging quality and sub-millimeter-level centroid positioning accuracy even within a large longitudinal offset range.

[0031] The system's workflow is as follows: The ultrashort pulse laser output from the femtosecond laser is split into a pump beam and a detection beam by a beam splitter. The pump beam is incident on the photoconductive antenna PCA2 via a high-reflectivity mirror, generating a terahertz pulse. This pulse is collimated and focused by OAP4 and OAP2, and then incident on the skin and label in reflection mode. The detection beam adjusts the optical path difference via an optical delay line composed of multiple high-reflectivity mirrors to achieve time synchronization with the terahertz signal. The terahertz signal reflected from the sample is collected by OAP1 and OAP3 and coherently detected by the photoconductive antenna PCA1. A stepper motor connects to the probe via a 3D-printed adapter, controlling the probe's movement in three-dimensional space and enabling scanning in the YZ plane. Simultaneously, it acquires the reflected terahertz time-domain signals at various locations. Finally, a computer processes the data and reconstructs the image, achieving non-destructive testing of the internal structural distortions of non-polar materials.

[0032] like Figure 2 The image shows the terahertz imaging results of a 2 mm tag under a 4 cm thick heat-insulating tile. This set of images demonstrates the processing from peak-to-peak correction of the original image to precise centroid localization, ultimately extracting the centroid coordinates of the tag. The horizontal and vertical axes of the image represent the horizontal and vertical positions, respectively, in mm; the color bars correspond to the intensity of the reflected terahertz signal, with higher intensity values ​​indicating a color closer to red and lower intensity values ​​indicating a color closer to blue. The original terahertz image exhibits a distribution characteristic of high signal intensity in the central region and low intensity in the edge region, accompanied by ring-shaped interference fringes with gradually changing intensity; Figure (c) shows the centroid localization result after image binarization processing. After algorithm calculation, the centroid coordinates of the tag under test are extracted as (6.98, 7.45).

[0033] like Figure 3 As shown in (a), terahertz waves simultaneously irradiate the label and the skin surface, with the label attached to the upper surface of the skin. The terahertz waves are incident on the label first, therefore the detector receives the terahertz waves reflected from the label first. The reflected waves from the skin surface have a time delay relative to the reflected waves from the label, as shown in (a). Figure 3 As shown in (b), the tag size is 2 mm × 2 mm, and the spot diameter is approximately 5 mm. During scanning, the area of ​​the spot covering the skin is larger than the area covering the tag; therefore, the terahertz reflection signal intensity on the skin surface is higher than that on the tag. Figure 3 As shown in (c), the intensity of the reflected signal gradually decreases as the frequency increases. Figure 3 (c) It can be seen that the intensity of the reflected signal gradually decreases with increasing frequency. The reflected terahertz waves from the tag and the skin originate from the same incident terahertz light source, and their spectral characteristics are consistent. Due to the distance between the two reflecting interfaces, an optical path difference is formed between the reflected pulses. Under perpendicular incidence conditions, this optical path difference is twice the tag thickness. At the same time, the polarization components of the two sets of reflected pulses satisfy the coherence condition, causing a significant wave field interference effect. Signal superposition and enhancement phenomena occur in different regions, manifested as a local increase in intensity of the terahertz image. When the tag is completely within the range of the terahertz light spot, the amplitude of the tag's reflected pulse reaches its peak value.

[0034] like Figure 4 The diagram shows the evolution of the light spot and the tag coverage area during the movement of the terahertz probe. Figure 4 (a)-(c) show the terahertz wave scanning along the top of the label. Figure 4 (d)-(f) correspond to scanning along the middle of the label. Figure 4 (g)-(i) involve scanning along the bottom of the label. When the light spot is located at the edge of the label, only a weak label reflection signal can be detected; when the light spot completely covers the label area, the label reflection signal intensity reaches its maximum. Therefore, the scanned image exhibits a distribution characteristic of a brighter central area (corresponding to the high-intensity area represented by red in the color bar) and a darker periphery (corresponding to the low-intensity area represented by blue in the color bar). The relative positional relationship between the light spot and the label during this process is shown in the figure. The label size is 2 mm × 2 mm, and the light spot diameter is 5 mm, meaning the light spot area is larger than the label area. Terahertz waves contain different frequency components. When one of the wavelengths is close to the 2 mm label aperture size, constructive interference occurs between the label reflection signal and the skin background reflection signal. When the area of ​​the terahertz wave irradiating the skin surface is large, the constructive interference effect is more significant, leading to a further increase in the intensity of the central area in the imaging result. Conversely, when the terahertz wave only partially irradiates the four corners of the tag, the tag reflects a weaker signal, and the interference effect is weakened accordingly, resulting in a terahertz image that presents an approximately elliptical outline rather than a strict square.

[0035] like Figure 5 The diagram shows the mechanism of how the horizontal movement of the terahertz probe affects imaging. The horizontal movement of the probe changes the distance from the OAP to the skin surface. Figure 5 (a) shows how a terahertz probe scans along a “Z” shaped trajectory. In this mode, parameters such as the scanning range, scanning step, and optical delay linear velocity can be set. Figure 5 (b) is a schematic diagram of the probe moving device. The probe can be adjusted back and forth based on a reference distance of 31.6 cm, thereby changing the distance between the probe surface and the skin surface. Figure 5 (c) shows the spatial arrangement of the OAP and the skin. As can be seen from the figure, after the terahertz wave is focused by the off-axis parabolic mirror, the spot diameter remains basically unchanged in the region near the focal point. The spot diameter at the focal point mainly depends on the focal length and aperture of the 2-inch off-axis parabolic mirror, as well as the center frequency of the terahertz wave. Figure 5 (d) describes the evolution of the terahertz Polley length under focusing conditions of the 2-inch off-axis parabolic mirror.

[0036] A brief calculation was performed on the spot diameter and Rayleigh length after passing through the off-axis parabolic mirror system. The terahertz wave frequency was set to 0.2 THz, the focal length of the off-axis parabolic mirror to be 35 cm, and the aperture to be 2 inches (approximately 5.08 cm). Under these conditions, the Rayleigh length was calculated:

[0037]

[0038] In the formula The speed of light in a vacuum; It is a terahertz frequency.

[0039] Formula for calculating the waist radius of a Gaussian beam:

[0040]

[0041] In the formula For the focal length of the parabolic mirror, The aperture of the optical element.

[0042] Rayleigh length determines the depth of focus range, expressed as:

[0043]

[0044] The waist radius of the focused terahertz wave Combining wavelength The Rayleigh length can be calculated from 1.5 mm. = 9.04 cm.

[0045] Figure 6 , Figure 7The probe scanned the label at distances of 31.6 cm and 33 cm from the skin to create images. Image data processing included peak-to-peak value correction and mirror correction of the original images, normalization, binarization segmentation, and centroid calculation. Results showed that the intensity distribution of the two sets of images was similar, with high intensity in the center and low intensity around the edges, and clear outlines of the high-intensity areas. After normalization and binarization, the shape and size of the target area showed no significant difference, indicating that the energy distribution structure of the light spot was stable within this distance range. Centroid localization results showed that the centroid coordinates of the two measurements were (6.03, 5.98) mm and (5.89, 6.07) mm, respectively, with a coordinate deviation of less than 0.2 mm, within the localization error range. Based on Rayleigh distance theory analysis, the light spot in both scans was within the Rayleigh distance of the terahertz beam, and the spot size and propagation direction did not change significantly. Therefore, the image features and centroid position remained highly stable, verifying the localization consistency and reliability of the imaging system within the experimental distance range.

[0046] Within the Rayleigh distance, statistical analysis was performed on 10 sets of two-dimensional positioning coordinate data obtained from scanning imaging. The horizontal coordinate range was 5.90–6.28 mm, with an average of 6.046 mm and a root mean square deviation of 0.107; the vertical coordinate range was 5.83–6.01 mm, with an average of 5.948 mm and a root mean square deviation of 0.054. The overall data distribution was relatively concentrated with low dispersion, indicating good repeatability and high data stability.

[0047] The above embodiments should be understood as illustrative only and not as limiting the scope of protection of the present invention. After reading the description of the present invention, those skilled in the art can make various alterations or modifications to the present invention, and these equivalent changes and modifications also fall within the scope defined by the claims of the present invention.

Claims

1. A method for rapid and high-precision centroid positioning of the under-keel distortion of aviation thermal insulation tiles, characterized in that, include: A high-reflectivity terahertz metal tag is set on the skin beneath the aviation heat insulation tile as a keel distortion feature point; a reflective terahertz imaging system is used to perform a two-dimensional scan of the heat insulation tile area. Based on the terahertz echo interference effect between the skin and the metal tag, the skin reflection waveform characteristics within a specific time window of each scanning point are collected. The reflected terahertz pulse signal data is processed, and the centroid coordinates of the metal tag are calculated by combining sub-pixel level edge detection and centroid extraction algorithms; the real-time centroid coordinates are compared with the factory reference coordinates to invert the keel distortion displacement.

2. The method according to claim 1, characterized in that, Two-dimensional scanning uses a Z-shaped trajectory, and the scanning area can be adjusted according to the detection requirements to obtain reflected terahertz pulse signal data at different locations.

3. The method according to claim 1, characterized in that, The working distance between the probe and the skin surface reference of the reflective terahertz imaging system is 31.6 cm. When the probe moves within ±5 cm before and after the focal plane, the imaging quality and centroid positioning accuracy remain stable.

4. The method according to claim 1, characterized in that, The surface of the metal tag is a 100 nm thick gold-plated film. The tag reflection pulse and the skin reflection pulse form coherent interference, which improves the imaging signal-to-noise ratio and the clarity of the tag edge.

5. The method according to claim 1, characterized in that, The processing of reflected terahertz pulse signal data, combined with sub-pixel level edge detection and centroid extraction algorithms, calculates the centroid coordinates of the metal tag. Specifically, this includes: signal preprocessing, data normalization, threshold segmentation, sub-pixel level edge extraction, and weighted centroid calculation.

6. A rapid and high-precision centroid positioning system for the distortion of the underframe of an aviation thermal insulation tile, characterized in that, It includes a femtosecond laser, beam splitter, optical delay line, high-reflectivity mirror, terahertz probe, stepper motor, adapter, and computer; the terahertz probe includes two photoconductive antennas (PCA) PCA1 and PCA2, as well as off-axis parabolic mirrors (OAP) OAP3 and OAP4 with a focal length of 5cm and off-axis parabolic mirrors OAP1 and OAP2 with a focal length of 35cm.

7. The system according to claim 6, characterized in that, The computer controls the stepper motor to drive the probe to complete two-dimensional scanning, and performs signal processing, image reconstruction and centroid coordinate calculation.

8. The system according to claim 6, characterized in that, The Rayleigh length of the terahertz beam is extended by optimizing the optical structure of the off-axis parabolic mirror, thereby increasing the system's depth of focus and working distance tolerance.