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Transient reflectivity measurements are used to probe the strain waves induced by ultrashort laser pulses in bulk [100] germanium. The measurement signals are compared to purely analytical model functions based on the known material parameters for germanium. The modeling includes (i) a derivation of analytical solutions to the wave equation for strain waves coupled to the diffusion equation for heat and charge carriers and (ii) an expression for the impact on reflection coefficients that are caused by perturbations to the dielectric function but extended to cover a non-isotropic, uniaxial dielectric tensorial form. The model is held up against transient reflectivity measurements with an s- and a p-polarized probe and with a probe wavelength in the range of 502–710 nm. Excellent agreement is found when comparing the oscillatory shape of the measurement signals to the models. As for the magnitude of the oscillations, the models reproduce the overall trends of the experiment when using the previously published values for the elasto-optical tensor measured under static strain. [ABSTRACT FROM AUTHOR]

ObjectiveIdentify infants with abnormal suckling behavior from simple non-nutritive suckling devices.BackgroundWhile it is well known breastfeeding is beneficial to the health of both mothers and infants, breastfeeding ceases in 75 percent of mother-child dyads by 6 months. The current standard of care lacks objective measurements to screen infant suckling abnormalities within the first few days of life, a critical time to establish milk supply and successful breastfeeding practices.Materials and methodsA non-nutritive suckling vacuum measurement system, previously developed by the authors, is used to gather data from 91 healthy full-term infants under thirty days old. Non-nutritive suckling was recorded for a duration of sixty seconds. We establish normative data for the mean suck vacuum, maximum suck vacuum, suckling frequency, burst duration, sucks per burst, and vacuum signal shape. We then apply computational methods (Mahalanobis distance, KNN) to detect anomalies in the data to identify infants with abnormal suckling. We finally provide case studies of healthy newborn infants and infants diagnosed with ankyloglossia.ResultsIn a series of case evaluations, we demonstrate the ability to detect abnormal suckling behavior using statistical analysis and machine learning. We evaluate cases of ankyloglossia to determine how oral dysfunction and surgical interventions affect non-nutritive suckling measurements.ConclusionsStatistical analysis (Mahalanobis Distance) and machine learning [K nearest neighbor (KNN)] can be viable approaches to rapidly interpret infant suckling measurements. Particularly in practices using the digital suck assessment with a gloved finger, it can provide a more objective, early stage screening method to identify abnormal infant suckling vacuum. This approach for identifying those at risk for breastfeeding complications is crucial to complement complex emerging clinical evaluation technology.Clinical impactBy analyzing non-nutritive suckling using computational methods, we demonstrate the ability to detect abnormal and normal behavior in infant suckling that can inform breastfeeding intervention pathways in clinic.Clinical and Translational Impact Statement: The work serves to shed light on the lack of consensus for determining appropriate intervention pathways for infant oral dysfunction. We demonstrate using statistical analysis and machine learning that normal and abnormal infant suckling can be identified and used in determining if surgical intervention is a necessary solution to resolve infant feeding difficulties.

In the shape measurement of convex hyperboloid mirrors with large relative apertures, alignment deviations can significantly affect the accuracy of null test results owing to their sensitivity, resulting in inaccurate results. This paper introduces autocollimation and compensation methods. Subsequently, a shape detection experiment of a large relative aperture convex hyperboloid mirror with a diameter of 15 mm was conducted using the aforementioned methods. Further, a detailed simulation analysis was performed to address the inconsistencies between the two test results. The results suggested that the Hindle sphere method was highly sensitive to distance deviation. Furthermore, the distances in the optical path exerted a complementary effect, which easily obscured the true surface shape of the measured part. The computer-generated hologram (CGH) method could accurately determine the true surface shape deviation based on the alignment judgment provided by the aligned CGH part. These studies provide scientific guidance for more accurately obtaining the true surface shape error of the hyperboloid mirror under test, and have significant engineering application value. • Shape detection experiment of large relative aperture convex hyperboloid mirror. • Simulation analysis to address inconsistencies between two test results. • The larger relative aperture, the more distance sensitivity in Hindle sphere method. • The complementary effect in Hindle sphere method makes the test result inaccurate. • The higher alignment precision in CGH method makes the test result more accurately. [ABSTRACT FROM AUTHOR]

Objective: The aim of this study was to evaluate changes in shape of the palatal vault after maxillary expansion with hyrax expander (HE) and leaf expander (LE), using 3D Geometric Morphometric Analysis. Setting and Sample Population: Overall, 250 patients (110 M, 140 F) with maxillary transverse deficiency were selected for this study. In this study, 127 subjects were treated with HE, 123 with LE. Materials and Methods: Digital dental models were obtained pre‐treatment (T0) and after 12 months from the cementation of the device (T1) and processed by means of a digital scanner. Linear and morphometric analyses were conducted to determine the effects of each appliance on dental measurements and palatal shape, and a multiple linear regression was performed to analyse the influence of anchorage and appliance type on final shape. Results: Morphometric analysis showed that there was a lowering of the palatal vault in the HE group, while in the LE group it remained unchanged: the difference in palatal shape at time T0 and T1 was statistically significant in both treatments (HE vs. LE). In the HE group, the change in shape also included the upper part of the palatal vault in the vertical dimension, while in the LE group the change in shape interested mainly palatal shelves and the lower portion of the palate. Conclusions: Both LE and HE produce clinically significant changes in the morphology of the palatal vault. [ABSTRACT FROM AUTHOR]

The paper proposes and verifies a small-angle measurement method based on the defect spot mode of the position-sensitive detector (PSD). With the output characteristics of the PSD in the defect spot mode and the size transformation properties of a focused beam, the measurement sensitivity can be significantly improved. Calibration experiments with the piezoelectric transducer (PZT) indicate that compared with the current PSD-based autocollimation method, the proposed method can improve the sensitivity of small-angle measurement by 57 times, and the measurement sensitivity of the proposed method can be further improved by optimizing the system parameters, while the proposed method has the advantages of a simple system and high real-time performance. Therefore, the proposed method is expected to be used in high-precision motion error detection, as well as in shape and position measurement. [ABSTRACT FROM AUTHOR]

A fringe projection system, in special application scenarios, is used for three-dimensional (3D) shape measurement through a transparent medium. The light refraction caused by the medium gives rise to erroneous 3D data in conventional fringe projection methods. In this work, we propose ray-tracing-based 3D profilometry using fringe projection. The method uses phase information for seeking the homologous points between camera images and projector images pixel by pixel. Equations of light rays emitted from each point pair are identified with the law of flat refraction. A midpoint of skew lines common perpendicular algorithm is developed for calculating the intersections of these equations, which are 3D shape data without refraction error. For validation, a fringe projection system through a transparent glass was set up and applied for 3D shape measurements. The results verify the effectiveness and accuracy of the proposed ray-tracing-based 3D profilometry. [ABSTRACT FROM AUTHOR]

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This article proposes a computational method for finite element analysis with deformed shape constraints for analyzing constructed structures to account for deformations that occur before shape measurement by a terrestrial laser scanner (TLS). In this method, point clouds obtained by a TLS are considered as a partial surface of the deformed structure. An analysis model is assumed to be created from CAD data or drawings. The analysis is performed under deformed shape constraints, namely, the deformed surface constraints or the normal vector constraints, which are generated by the point clouds. These constraints are introduced to reproduce the current displacements and stresses for the structure through the analysis. This method was applied to analyses of a plate and a desk using point clouds, which were created virtually on a computer or obtained by a TLS in the numerical examples. The results showed that this method can consider unexpected deformations that occur before laser scanning. Although the computed stresses oscillated when the scanned point cloud was used due to measurement errors and conventional point cloud processing methods, the stress values were responsive enough to indicate unnatural shapes of the deformed structure. Moreover, the oscillation was observed only in areas with constraints, whereas it was not seen in areas without constraints. [ABSTRACT FROM AUTHOR]

Cold spray is a material deposition technology with a high deposition rate and attractive material properties that has great interest for additive manufacturing (AM). Successfully cold spraying free-form parts that are close to their intended shape, however, requires knowing the fundamental shape of the sprayed track, so that a spray path can be planned that builds up a part from a progressively overlaid sequence of tracks. Several studies have measured track shape using ex situ or quasi-in situ approaches, but an in situ measurement approach has, to the authors' knowledge, not yet been reported. Furthermore, most studies characterize the track cross section as a symmetric Gaussian probability density function (PDF) with fixed shape parameters. The present study implements a novel in situ track shape measurement technique using a custom-built nozzle-tracking laser profilometry system. The shape of the track is recorded throughout the duration of a spray, allowing a comprehensive investigation of how the track shape evolves as the deposit is built up. A skewed track shape is observed—likely due to the side-injection design of the applicator used—and a skewed Gaussian PDF—a more generalized version of the standard Gaussian PDF—is fit to the track profile. The skewed Gaussian fit parameters are studied across two principal nozzle path parameters: nozzle traverse speed and step size. Empirical relationships between the fit parameters and the nozzle path parameters are derived, and a physics-based inverse relationship between nozzle speed and powder mass deposition rate is obtained. One of the fit parameters is shown to be an effective means of monitoring deposition efficiency during spraying. Overall, the approach presents a promising means of measuring track shape, in situ, as well as modeling it using a more general shape function. [ABSTRACT FROM AUTHOR]

Compensating for the pitch error in the scanning movement is a fundamental issue when conducting large-scale surface shape measurements with deflectometric profilers. This paper presents a new long trace profiler employing a shearing measurement technique. In this setup, the optical head and the mirror under test are mounted on two independent parallel movable air-bearing carriages to enable shearing and scanning movements separately. The distance between the optical head and the tested mirror remains fixed, effectively minimizing the influence of system errors resulting from imperfections in optical devices. Simulation studies show that the double shear measurement method with a low-spatial-frequency filtering process can effectively mitigate high-frequency angular measurement errors introduced by the instability of the air-bearing stage. Experimental tests conducted on flat mirrors demonstrated a precision of less than 50 nrad rms, thereby confirming the robustness of the system. [ABSTRACT FROM AUTHOR]

Given the increasing application of eddy current sensors for measuring turbine tip clearance in aero engines, enhancing the performance of these sensors is essential for improving measurement accuracy. This study investigates the influence of coil shape on the measurement performance of planar eddy current sensors and identifies an optimal coil shape to enhance sensing capabilities. To achieve this, various coil shapes—specifically circular, square, rectangular wave, and triangular wave—were designed and fabricated, featuring different numbers of turns for the experiment at room temperature. By employing a method for calculating coil inductance, the performance of each sensor was evaluated based on key metrics: measurement range, sensitivity, and linearity. Experimental results reveal that the square coil configuration outperforms other shapes in overall measurement performance. Notably, the square coil demonstrated a measurement range of 0 mm to 8 mm, a sensitivity of 0.115685 μH/mm, and an impressive linearity of 98.41% within the range of 0 mm to 2 mm. These findings indicate that the square coil configuration enhances measurement capabilities. The conclusions drawn from this study provide valuable insights for selecting coil shapes and optimizing the performance of planar eddy current sensors, thereby contributing to the advancement of turbine tip clearance measurement techniques in aero engines. [ABSTRACT FROM AUTHOR]

Measurement methods based on photogrammetry are highly accurate and effective for large space structures. However, photogrammetry is difficult to use in a thermal vacuum chamber because a remote drive system is required for operating a camera, whose position and attitude must be constrained. The objective of this study is to evaluate the measurement accuracy of a photogrammetry system under camera constraints. We constructed a simplified rail-based measurement system that simulates the circular motion of a camera drive system in a chamber. The camera was constrained to moving on a circular rail that surrounded the specimen, taking photographs at regular intervals along the circumference. We conducted experiments at various camera heights and angles and determined the measurement error. A high measurement accuracy of about 0.02mm root-mean-square was achieved under appropriate camera conditions. Placing the camera nearly perpendicular to the target was found to improve the measurement accuracy. It was also found that markers were more easily detected on the curved surface of a parabolic antenna than on the flat surface of an aluminum honeycomb plate. The results indicate that accurate photogrammetric measurements in a thermal vacuum chamber are possible, even with constraints on the camera position and attitude. [ABSTRACT FROM AUTHOR]

Background: Stereo-DIC is a widely used optical measurement technique that provides a dense full-field 3D measurement of the shape, displacement, and strain of a solid sample. When compared with 2D-DIC, Stereo-DIC provides greater flexibility and expands its use beyond flat, planar specimens. Furthermore, the widespread availability of commercial systems has led to the adoption of the technique throughout industry, academia, and government research labs. Objective: Even though some research has been done to understand the effects of different experimental and stereo-DIC parameters, no reference is available to benchmark and compare the performance of current stereo-DIC algorithms to each other. Methods: This paper provides the description and analysis of a carefully controlled 3D experiment and associated images used to compare the results from five subset based DIC software packages. Both the images and analysis codes used in this paper to compare the results are described here and are available for download and use for continued research. Results: We show that over a very large range of motion, the 3D errors are very small, less than 80 μ m over a travel of ±20 mm out-of-plane and ±20 mm in-plane. While all codes performed similarly, there are important differences noted in the paper. Conclusion: The image sets and results comparison software are hosted by the International DIC Society (www.iDICs.org) and are freely available for download and analysis for comparison with results in this paper. Furthermore, it is hoped that this set of images can be used for future research in improving stereo-DIC by future authors. [ABSTRACT FROM AUTHOR]

In this work, a statistical model is constructed to forecast the possibility of lung nodules that may grow in the future. This study segments all potential lung nodule candidates using the Multi-scale 3D UNet (M-3D-UNet) method. 34 patients' CT scan series yielded an average of approximately 600 nodule candidates larger than 3 mm, which were then segmented. After removing the arteries, non-nodules and 3D shape variation analysis, 34 actual nodules remained. On actual nodules, the nodule growth Rate (NGR) was calculated in terms of 3D-volume change. Three of the 34 actual nodules had RNG values greater than one, indicating that they were malignant. Compactness, Tissue deficit, Tissue excess, Isotropic Factor and Edge gradient were used to develop the nodule growth predictive measure. [ABSTRACT FROM AUTHOR]

Purpose: We aimed to establish criteria for determining the deformed lateral torso type to identify individuals requiring measurement methods different from standard methods before extracting dimensions from three-dimensional (3D) scan data. Design/methodology/approach: We collected the 3D body scan data of 119 women aged 70–85 years collected in the 6th Size Korea. Three axes were defined to determine the deformation of the lateral shape, and the angle of each reference axis was used for the analysis. Additionally, to classify the lateral torso shape, 14 experts made visual judgments on the side-view images of the participants. Findings: To identify the axis that best represented the lateral torso shape, we used each angle value of the three reference axes as an independent variable and the expert's visual classification as a dependent variable. Each discriminant function was obtained and accuracy calculated. The whole torso axis exhibited the highest accuracy. Next, an assessment scale was developed to determine the shape of the lateral torso using the angular value of the whole torso axis. Originality/value: The scale developed in this study has the potential to reduce measurement errors arising from elderly deformed torso shapes, thereby enhancing data reliability. [ABSTRACT FROM AUTHOR]

We explore the principles, implementation details, and performance characteristics of a lensless multi-spectral digital holographic sensor and demonstrate its potential for quality assurance in semiconductor manufacturing. The method is based on capturing multi-spectral digital holograms, which are subsequently utilized to evaluate the shape of a reflective test object. It allows for a compact setup satisfying high demands regarding robustness against mechanical vibrations and thus overcomes limitations associated with conventional optical inspection setups associated with lens-based white light interferometry. Additionally, the tunable laser source enhances the versatility of the system and enables adaptation to various sample characteristics. Experimental results based on a wafer test specimen demonstrate the effectiveness of the method. The axial resolution of the sensor is ± 2.5 nm, corresponding to 1σ. [ABSTRACT FROM AUTHOR]

Three-dimensional(3D) shape measurement using point clouds has recently gained significant attention. Phase measuring profilometry (PMP) is widely preferred for its robustness against external lighting changes and high-precision results. However, PMP suffers from long computation times due to complex calculations and its high memory usage. It also faces a 2π ambiguity issue, as the measured phase is limited to the 2π range. This is typically resolved using dual-wavelength methods. However, these methods require separate measurements of phase changes at two wavelengths, increasing the data processing volume and computation times. Our study addresses these challenges by implementing a 3D shape measurement system on a System-on-Chip (SoC)-type Field-Programmable Gate Array (FPGA). We developed a PMP algorithm with dual-wavelength methods, accelerating it through high-level synthesis (HLS) on the FPGA. This hardware implementation significantly reduces computation time while maintaining measurement accuracy. The experimental results demonstrate that our system operates correctly on the SoC-type FPGA, achieving computation speeds approximately 11.55 times higher than those of conventional software implementations. Our approach offers a practical solution for real-time 3D shape measurement, potentially benefiting applications in fields such as quality control, robotics, and computer vision. [ABSTRACT FROM AUTHOR]

The absolute shape measurement of large aperture optical flats usually requires a standard mirror with the same or larger aperture as the element to be measured as the reference surface for calibration. However, the large aperture standard mirror is difficult to process, and the measurement resolution is limited. To solve this problem, a method of measuring the absolute surface shape of a large aperture optical flat is proposed. The aperture optical flat is divided into several sub-apertures using the sub-aperture stitching method. The reference mirror shape is obtained by the odd and even function four-step absolute measurement method and separated to obtain the absolute surface shape of the sub-aperture. The immune algorithm is optimized and applied to the adjacent sub-aperture stitching to obtain the complete absolute surface shape. The 210 mm long flat crystal was measured, and the closed-loop self-test was designed to verify the correctness of the obtained reference mirror shape. The peak and valley value (PV) of reference mirror B is 53.64 nm, and the root mean square (RMS) value is 9.96 nm. The results of the closed-loop self-test are 58.63 nm and 10.86 nm, and the data are basically consistent with the surface shape diagram. The surface shape test results pass the closed-loop self-test. The absolute surface shape results after stitches are compared with those measured by a large aperture interferometer. The deviation of the PV value is less than λ/135 (λ=632.8 nm), and the deviation of the RMS value is less than λ/75. The measurement resolution is 11 times that measured by a large aperture interferometer, which fully proves the accuracy and high resolution of the method. [ABSTRACT FROM AUTHOR]

To determine both the size of a satellite antenna and the thermal deformation of its surface shape, a novel high-accuracy close-range photogrammetric technique is used in this study. The method is also applied to assess the performance of the antenna in orbit. The measurement principle and solution method of close-range photogrammetry were thoroughly investigated, and a detailed measurement test scheme was developed. A thermal deformation measurement of the surface shape of a satellite antenna was then carried out. The results show that the measurement error using close-range photogrammetry was smaller than 0.04 mm, which meets the accuracy requirement. Thanks to the high accuracy, it was discovered that both the surface shape and the rib precision of the satellite antenna deteriorate with decreasing temperature. The accuracy of the surface shape and ribs was lowest when the temperature node was −60 °C. The maximum root mean square errors (RMSEs) reached 0.878 mm and 0.761 mm, respectively. This indicates that the surface shape deformation error of the antenna caused by high and low temperatures is relatively high. However, the requirement for the technical design index (RMSE ≤ 1 mm for the surface shape accuracy of the antenna) is still met. Furthermore, for temperature differences of 40 °C and 80 °C, the measured RMSEs for the surface shape deformation were 0.216 mm and 0.411 mm, respectively. Overall, the technical design indicators (RMSE ≤ 0.3 mm and RMSE ≤ 0.5 mm, respectively) for the surface shape deformation of the antennas are met. [ABSTRACT FROM AUTHOR]

As a non-contact method, vision-based measurement for vibration extraction and modal parameter identification has attracted much attention. In most cases, artificial textures are crucial elements for visual tracking, and this feature limits the application of vision-based vibration measurement on textureless targets. As a computation technique for visualizing subtle variations in videos, the video magnification technique can analyze modal responses and visualize modal shapes, but the efficiency is low, and the processing results contain clipping artifacts. This paper proposes a novel method for the application of a modal test. In contrast to the deviation magnification that exaggerates subtle geometric deviations from only a single image, the proposed method extracts vibration signals with sub-pixel accuracy on edge positions by changing the perspective of deviations from space to timeline. Then, modal shapes are visualized by decoupling all spatial vibrations following the vibration theory of continuous linear systems. Without relying on artificial textures and motion magnification, the proposed method achieves high operating efficiency and avoids clipping artifacts. Finally, the effectiveness and practical value of the proposed method are validated by two laboratory experiments on a cantilever beam and an arch dam model. [ABSTRACT FROM AUTHOR]

This paper proposes a 3D shape measurement method based on Res-Attention-Unet for deep learning, which effectively integrates single-frame fringe phase extraction and temporal phase unwrapping. The Res-Attention-Unet, trained with a large amount of data, is shown to be able to extract phase information directly from deformed fringe patterns with large frequency differences and to achieve high-precision and unambiguous 3D measurement using hierarchical phase unwrapping. We experimentally demonstrate that the method requires only three deformed fringe patterns with different frequencies to achieve accurate and 3D measurement, and Res-Attention-Unet has an absolute advantage over the traditional single-frame fringe phase extraction algorithm in terms of the phase extraction accuracy of low-frequency fringe patterns. Since only three fringe patterns need to be projected, this method is expected to be applied to project single-frame color fringe for dynamic 3D measurement. [ABSTRACT FROM AUTHOR]

Purpose: This study compared in vivo crystalline lens shape measurements using B‐scan images from the IOLMaster 700 with phakometry. Methods: Twenty‐four young adult participants underwent IOLMaster 700 and phakometry measurements under cycloplegia (1% cyclopentolate). The IOLMaster 700 generated B‐scan images along six meridians in 30° increments, which were analysed using custom MATLAB software to determine lens surface radii of curvature. Phakometry measurements were obtained using Purkinje images reflected from the lens surfaces. Results: The IOLMaster 700 image analysis method yielded a lower mean anterior lens surface spherical equivalent power (+6.20 D) than phakometry (+7.55 D); however, the two measurements were strongly correlated (R(21) = 0.97, p < 0.0001). The astigmatic power vectors (J0 and J45) for the anterior lens surface were significantly higher for the IOLMaster 700 measurements, with only J0 showing a significant moderate positive correlation (R(21) = 0.57, p = 0.005). For the posterior lens surface, the IOLMaster 700 measurements had a higher mean spherical power (+14.28 D) compared to phakometry (+13.70 D); however, a strong positive correlation (R(21) = 0.90, p < 0.0001) was observed. No significant correlations were noted for posterior lens surface astigmatic vectors (J0 and J45). The IOLMaster 700 estimates for the equivalent lens mean spherical power were slightly lower than those for phakometry, with a mean difference of −0.72 D, and both methods were positively correlated (R(21) = 0.94, p < 0.0001). Conclusions: The findings demonstrate that IOLMaster 700 B‐scan image analysis technique provides similar estimates of lens surface powers to phakometry. These results highlight the potential of the IOLMaster 700 to provide measurements of lens shape, informing future research and clinical use. [ABSTRACT FROM AUTHOR]

The vast array of dog breeds showcases a remarkable diversity that extends to osteological differences. Exploring these morphological distinctions and establishing reference data for various dog breeds are essential steps in comprehending the evolutionary changes that dogs have undergone. In this study, we conducted linear measurements of the calcaneus and performed shape analyses on selected dog breeds to elucidate distinctive characteristics among them. X‐ray images of the calcaneus from six different dog breeds—Maltese Terrier, Toy Poodle, Pomeranian, Cavalier King Charles Spaniel, French Bulldog and Golden Retriever—were utilized for this investigation. Radiological images were obtained from a medio‐lateral exposure, positioned 30 cm away from the x‐ray device. From these images, four linear length measurements and two angle values were extracted. Additionally, a 2D geometric morphometric analysis was conducted using 32 semi landmarks placed on the radiological images. Linear measurements were assessed using ANOVA, while principal component analysis was employed to examine shape variations across all individuals. Shape differences between species were further elucidated through canonical variates analysis. The results revealed that the Golden Retriever exhibited the highest values for linear measurements, while the Pomeranian showed the lowest. Maltese Terriers displayed the highest dorsal calcaneal angle value. Notably, there were significant differences in calcaneal body length among all breeds, except for the Toy Poodle and Cavalier King Charles Spaniel. Moreover, Maltese Terriers exhibited statistically distinct angular measurements compared to other breeds. Principal component analysis unveiled that the first principal component explained 32.69% of the total variation, with the cranial edge of the calcaneal body being closer to the body in individuals with higher values. Shape variations also indicated that Golden Retrievers displayed a broader range of shapes compared to French Bulldogs, which exhibited a more conservative distribution. While there was no clear breed‐specific distinction according to the first principal component, Cavalier King Charles Spaniels generally showed lower values. In canonical variates analysis, distinctions in calcaneal shape between species were apparent, with Golden Retrievers, Cavalier King Charles Spaniels and French Bulldogs displaying positive values for the first canonical variates. The highest Procrustes distance was observed between Maltese Terriers and Cavalier King Charles Spaniels. Notably, allometry was found to be statistically insignificant. This comprehensive study utilized both linear and geometric morphometric analyses based on x‐ray images, yielding promising results. The integration of imaging systems in veterinary anatomy research presents numerous opportunities for studying animal welfare and health, utilizing various materials such as bones and cadavers. These advancements hold the potential for further enhancing our understanding of animal morphology and well‐being. [ABSTRACT FROM AUTHOR]

It is imperative to achieve the co-phase state for large segmented mirrors of telescopes. This paper proposes a novel method for quantifying the co-phase errors of the segmented mirrors, as well as to detect any residual errors by analyzing the surface shape of segmented mirrors using conformal mapping after the correction of the co-phase errors, aiming to achieve a more precise co-phase state. This method applies a dual-wavelength phase-shifting interferometry based on optical vortex to measure the co-phase errors (i.e., tip, tilt, and piston), and measures the surface shape of segmented mirrors based on conformal mapping phase-shifting interferometry to identify which kind of co-phase errors still exist there, and then adjust the segmented mirrors to achieve a more precise co-phase state. The functional relationships between piston error or tip/tilt error and phase distribution in the image plane are derived, and the mathematical tool of conformal mapping is used for surface shape demodulation. The experiment results indicate that the resolution of the piston error measurements is 1.878 nm, and the resolution of the tip/tilt error measurements is 0.760″. Furthermore, the surface shape measurement after adjustment based on conformal mapping phase-shifting interferometry is 7.503 nm (RMS). [ABSTRACT FROM AUTHOR]

Concentrated solar power is a promising technique enabling renewable energy production with large scale solar power plants in the near future. Estimating quantitatively the reflectivity of a solar concentrator is a major issue, since it has a significant impact on the flux distribution formed at the solar receiver. Moreover, it is desirable that the mirrors can be measured during operation in order to evaluate environmental factors such as day/night thermal cycles or soiling and ageing effects at the reflective surfaces. For that purpose, a backward gazing method that was originally developed to measure mirror shape and misalignment error was developed. The method operates in quasi real-time without disturbing the heat production process. It was successfully tested at the Themis solar tower power plant in Targasonne, France. Its basic principle consists in acquiring four simultaneous images of a Sun-tracking heliostat, captured from different observation points located near the thermal receiver. The images are then processed with a minimization algorithm allowing the determination of the reflectance and slopes errors of the mirrors. In this communication, it is shown that the algorithm allows one to get quantitative reflectivity maps at the surface of the heliostat. The measurement is fully remote and is used to evaluate surface reflectivity that depends on optical coatings quality and soiling effects. Preliminary results obtained with a Themis heliostat are presented. They show that reflectivity measurements can be carried out within repeatability about ± 5% Peak-to-Valley (PTV) and 1% RMS. Ways to improving these numbers are discussed in the paper.

Spatial similarity provides an important basis for geographic information processing and is widely applied in multi-source data fusion and update, data retrieval and query, and cartographic generalization. To address the shape description and similarity measurement of polygon entities, this study presents a new hierarchical shape description approach and examines its application in similarity measurement of polygon entities. Using the rotation and segmentation methods, we first constructed a hierarchical shape description model for target polygon entities, followed by measurement of global and hierarchical shape description of polygon entities, respectively, using the farthest-point-distance and geometric feature description methods. Finally, we constructed a comprehensive similarity measurement model through a weighted integration of position, size, direction, and shape. The hierarchical shape description approach proposed in this paper can be applied to the shape similarity measurement of polygon elements, similarity measurement after spatial object simplification, and multi-scale polygon entity matching. The experimental results showed that the hierarchical shape description approach and similarity measurement model are able to effectively measure spatial similarity between different polygon entities, and have obtained good application results. [ABSTRACT FROM AUTHOR]

Microwave holographic measurement technology is a common method used in antenna measurement. This method has high measurement efficiency and high precision. To evaluate and enhance the antenna's performance, it is crucial to precisely determine the surface deformation. In this paper, the effects of feed offset error and scanning error on the antenna microwave holographic measurement results are investigated, and corresponding error compensation methods are proposed. The relationship between the influence of the error sources on the antenna gain loss and surface deformation accuracy is established. The reasons for holographic measurement errors, their characteristics, and their specific impact on system performance can be better understood. In order to improve the accuracy of the measurement, the compensation methods for the different measurement errors are given. They can provide the theoretical basis for maintaining and enhancing the performance of antenna system. [ABSTRACT FROM AUTHOR]

The continuous scanning laser Doppler vibrometry (CSLDV) technique is usually used to evaluate the vibration operational deflection shapes (ODSs) of structures with continuous surfaces. In this paper, an extended CSLDV is demonstrated to measure the non-continuous surface of the bladed disk and to obtain the ODS efficiently. For a bladed disk, the blades are uniformly distributed on a given disk. Although the ODS of each blade can be derived from its response data along the scanning path with CSLDV, the relative vibration direction between different blades cannot be determined from those data. Therefore, it is difficult to reconstruct the complete vibration mode of the whole blade disk. In order to measure the complete ODS of the bladed disk, a method based on ODS frequency response functions (ODS FRFs) has been proposed. While the ODS of each blade is measured by designing the suitable scanning paths in CSLDV, an additional response signal is obtained at a fixed point as the reference signal to identify the relative vibration phase between the blade and the blade of the bladed disk. Finally, a measurement is performed with a simple bladed disk and the results demonstrate the feasibility and effectiveness of the proposed extended CSLDV method. [ABSTRACT FROM AUTHOR]

For hot and shiny forging, rapid optical three-dimensional (3D) shape measurement can find the defects in time, improve manufacturing efficiency and reduce manufacturing cost. Optical 3D measurement of hot and shiny forging faces following three challenges. (a) Influence of blackbody radiation on the red band of visible light leads to saturation of captured fringe pattern. (b) Infrared band of blackbody radiation causes the camera to heat up. (c) Specular reflection of shiny forging leads to local saturation of captured fringe pattern. To address the above issues, we propose an effective optical 3D measurement scheme for hot and shiny forging in this paper. Firstly, the experiments demonstrate that the influence of blackbody radiation on visible light is concentrated in red light band and has no crosstalk in the blue light band, so we adopt blue light projection and blue light band-pass filter (BBF) to capture clear fringe pattern. Secondly, since the BBF cannot block the near-infrared component, we use an infrared light cutoff filter (ICF) to reduce the thermal effect of blackbody radiation. Finally, we analyze the Fourier transform (FT) spectrum of saturated fringe pattern caused by specular reflection, and propose an efficient Butterworth low-pass filtering (BLPF) method that does not require additional hardware, algorithm processing, and image assistance. The experimental results verify the effectiveness of the proposed scheme. • 3D measurement for hot and shiny forging based on blue light projection and blue light band-pass filter is proposed. • An effective infrared light cutoff filter is adopted to reduce the thermal effect on the camera. • Butterworth low-pass filter is adopted to suppress high-order harmonics introduced by shiny forging. [ABSTRACT FROM AUTHOR]

It has long been known that galaxy shapes align coherently with the large-scale density field. Characterizing this effect is essential to interpreting measurements of weak gravitational lensing, the deflection of light from distant galaxies by matter overdensities along the line of sight, as it also produces coherent galaxy alignments that we wish to interpret in terms of a cosmological model. Existing direct measurements of intrinsic alignments using galaxy samples with high-quality shape and redshift measurements typically use well-understood but sub-optimal projected estimators, which do not make good use of the information in the data when comparing those estimators to theoretical models. We demonstrate a more optimal estimator, based on a multipole expansion of the correlation functions or power spectra, for direct measurements of galaxy intrinsic alignments. We show that even using the lowest order multipole alone increases the significance of inferred model parameters using simulated and real data, without any additional modelling complexity. We apply this estimator to measurements of parameters of the non-linear alignment model using data from the Sloan Digital Sky survey, demonstrating consistent results with a factor of ∼2 greater precision in parameter fits to intrinsic alignments models. This result is functionally equivalent to quadrupling the survey area, but without the attendant costs – thereby demonstrating the value in using this new estimator in current and future intrinsic alignments measurements using spectroscopic galaxy samples. [ABSTRACT FROM AUTHOR]

Single-shot dual-wavelength interferometry offers a promising avenue for surface profile measurement of dynamic objects. However, current techniques employing pixel multiplexing or color cameras encounter challenges such as complex optical alignment, limited measurement range, and difficulty in measuring rough surfaces. To address these issues, this study presents a novel approach to single-shot dual-wavelength interferometry. By utilizing separated polarization illumination and detection, along with a monochromatic polarization camera and two slightly different wavelengths, this method enables the simultaneous recording of two frames of separated interferometric patterns. This approach facilitates straightforward optical alignment, expands measurement ranges, accelerates data acquisition, and simplifies data processing for dual-wavelength interferometry. Consequently, it enables online shape measurement of large dynamic samples with rough surfaces. [ABSTRACT FROM AUTHOR]

We have recently demonstrated that the 3D shape of micro-parts can be measured using LED illumination based on speckle contrast evaluation in the recently developed SPICE profilometry (shape measurements based on imaging with spatially partially coherent illumination). The main advantage of SPICE is its improved robustness and measurement speed compared to confocal or white light interferometry. The limited spatial coherence of the LED illumination is used for depth discrimination. An electrically tunable lens in a 4 f -configuration is used for fast depth scanning without mechanically moving parts. The approach is efficient, takes less than a second to capture required images, is eye-safe and offers a depth of focus of a few millimeters. However, SPICE's main limitation is its assumption of a small illumination aperture. Such a small illumination aperture affects the axial scan resolution, which dominates the measurement uncertainty. In this paper, we propose a novel method to overcome the aperture angle limitation of SPICE by illuminating the object from different directions with several independent LED sources. This approach reduces the full width at half maximum of the contrast envelope to one-eighth, resulting in a twofold improvement in measurement accuracy. As a proof of concept, shape measurements of various metal objects are presented. [ABSTRACT FROM AUTHOR]

The precision requirements for aeroengine blade machining are exceedingly stringent. This study aims to improve the accuracy of existing aeroengine blade measurement methods while achieving comprehensive measurement. Therefore, this study proposes a new concentric ring calibration method and designs a multi-layer concentric ring calibration plate. The effectiveness of this calibration method was verified through actual testing of standard ball gauges. Compared with the checkerboard-grid calibration method, the average deviation of the multilayer concentric ring calibration method for measuring the center distance of the standard sphere is 0.02352, which improves the measurement accuracy by 3–4 times. On the basis of multi-layer concentric ring calibration, this study builds a fringe projection profiler based on the three-frequency twelve-step phase shift method. Compared with the CMM, the average deviation of the blade chord length measured by this solution is 0.064, which meets the measurement index requirements of aeroengine fan blades. [ABSTRACT FROM AUTHOR]

Full-field three-dimensional (3D) measurement technology based on phase information has become an indispensable part of geometric dimension measurement in modern scientific research and engineering applications. This field has been developing and evolving for the study of highly reflective phenomena, diffuse reflections, and specular surfaces, and many novel methods have emerged to increase the speed of measurements, enhance data accuracy, and broaden the robustness of the system. Herein, we will discuss the latest research progress in full-field 3D shape measurement based on phase information systematically and comprehensively. First, the fundamentals of 3D shape measurement based on phase information are introduced, namely, phase-shifting and transform-based methods. Second, recent technological innovations are highlighted, including increases in measurement speed and automation and improvements in robustness in complex environments. In particular, the challenges faced by these technological advances in solving highly dynamic, composite surface measurement problems are presented, i.e., with multiexposure techniques proposed for high dynamics that extend the dynamic range of the camera to reduce the effects of overexposure but increase the cost of time and have high hardware requirements, fringe adaptive techniques that overcome light variations but are computationally complex, and multipolarized camera techniques that reduce the effects of light variations but are sensitive to the light source. Third, the phase-shifting method combined with coding is proposed to improve the measurement speed, but the accuracy is slightly reduced. Deep learning techniques are proposed to cope with measurements in complex environments, but the dataset computation process is cumbersome. Finally, future research directions are suggested, and the challenges are presented. Overall, this work provides a reference for researchers and engineers. Highlights: This paper reviews advancements in technology aimed at the high precision and high speed of measurements, ensuring more efficient and reliable full-field 3D shape measurements. The challenges related to the advancement of error compensation for phase calculations are outlined and discussed in various techniques with their advantages and trade-offs. The examination of future research directions and challenges in the field of full-field 3D measurements based on phase information culminates by providing insightful perspectives. [ABSTRACT FROM AUTHOR]

Background: Position verification and motion monitoring are critical for safe and precise radiotherapy (RT). Existing approaches to these tasks based on visible light or x‐ray are suboptimal either because they cannot penetrate obstructions to the patient's skin or introduce additional radiation exposure. The low‐cost mmWave radar is an ideal solution for these tasks as it can monitor patient position and motion continuously throughout the treatment delivery. Purpose: To develop and validate frequency‐modulated continuous wave (FMCW) mmWave radars for position verification and motion tracking during RT delivery. Methods: A 77 GHz FMCW mmWave module was used in this study. Chirp Z Transform‐based (CZT) algorithm was developed to process the intermediate frequency (IF) signals. Absolute distances to flat Solid Water slabs and human shape phantoms were measured. The accuracy of absolute distance and relative displacement were evaluated. Results: Without obstruction, mmWave based on the CZT algorithm was able to detect absolute distance within 1 mm for a Solid Water slab that simulated the reflectivity of the human body. Through obstructive materials, the mmWave device was able to detect absolute distance within 5 mm in the worst case and within 3.5 mm in most cases. The CZT algorithm significantly improved the accuracy of absolute distance measurement compared with Fast Fourier Transform (FFT) algorithm and was able to achieve submillimeter displacement accuracy with and without obstructions. The surface‐to‐skin distance (SSD) measurement accuracy was within 8 mm in the anterior of the phantom. Conclusions: With the CZT signal processing algorithm, the mmWave radar is able to measure the absolute distance to a flat surface within 1 mm. But the absolute distance measurement to a human shape phantom is as large as 8 mm at some angles. Further improvement is necessary to improve the accuracy of SSD measurement to uneven surfaces by the mmWave radar. [ABSTRACT FROM AUTHOR]

Understanding the quantitative responses of anisotropic dynamic properties in organic-rich shale with different kerogen content (KC) is of great significance in hydrocarbon exploration and development. Conducting controlled experiments with a single variable is challenging for natural shales due to their high variations in components, diagenesis conditions, or pore fluid. We employed the hot-pressing technique to construct 11 well-controlled artificial shale with varying KC. These artificial shale samples were successive machined into prismatic shape for ultrasonic measurements along different directions. Observations revealed bedding perpendicular P-wave velocities are more sensitive to the increasing KC than bedding paralleling velocities due to the preferential alignments of kerogen. All elastic stiffnesses except C13 are generally decreasing with the increasing KC, the variation of C11 and C33 on kerogen content are more sensitive than those of C44 and C66. Apparent dynamic mechanical parameters (n and E) were found to have linear correlation with the true ones from complete anisotropic equations independent of KC, which hold value towards the interpretation of well logs consistently across formations. Anisotropic mechanical parameters (DE and brittleness DB) tend to decrease with the reducing KC, with DB showing great sensitivity to KC variations. In the range of low KC (<10%), the VP/VS ratio demonstrated a linearly negative correlation with KC, and the VP/VS ratio magnitude of less than 1.75 may serve as a significant characterization for highly organic-rich (>10%) shale, compilation of data from natural organic rich-shales globally verified the similar systematic relationships that can be empirically used to predict the fraction of KC in shales. [ABSTRACT FROM AUTHOR]

We explore the principles, implementation details, and performance characteristics of a lensless multi-spectral digital holographic sensor and demonstrate its potential for quality assurance in semiconductor manufacturing. The method is based on capturing multi-spectral digital holograms, which are subsequently utilized to evaluate the shape of a reflective test object. It allows for a compact setup satisfying high demands regarding robustness against mechanical vibrations and thus overcomes limitations associated with conventional optical inspection setups associated with lens-based white light interferometry. Additionally, the tunable laser source enhances the versatility of the system and enables adaptation to various sample characteristics. Experimental results based on a wafer test specimen demonstrate the effectiveness of the method. The axial resolution of the sensor is ±2.5 nm, corresponding to 1σ.

Riming is a key precipitation formation process in mixed-phase clouds which efficiently converts cloud liquid to ice water. Here, we present two methods to quantify riming of ice particles from airborne observations with the normalized rime mass, which is the ratio of rime mass to the mass of a size-equivalent spherical graupel particle. We use data obtained during the HALO-(AC) 3 aircraft campaign, where two aircraft collected radar and in situ measurements that were closely spatially and temporally collocated over the Fram Strait west of Svalbard in spring 2022. The first method is based on an inverse optimal estimation algorithm for the retrieval of the normalized rime mass from a closure between cloud radar and in situ measurements during these collocated flight segments (combined method). The second method relies on in situ observations only, relating the normalized rime mass to optical particle shape measurements (in situ method). We find good agreement between both methods during collocated flight segments with median normalized rime masses of 0.024 and 0.021 (mean values of 0.035 and 0.033) for the combined and in situ method, respectively. Assuming that particles with a normalized rime mass smaller than 0.01 are unrimed, we obtain average rimed fractions of 88 % and 87 % over all collocated flight segments. Although in situ measurement volumes are in the range of a few cubic centimeters and are therefore much smaller than the radar volume (about 45 m footprint diameter at an altitude of 500 m above ground, with a vertical resolution of 5 m), we assume they are representative of the radar volume. When this assumption is not met due to less homogeneous conditions, discrepancies between the two methods result. We show the performance of the methods in a case study of a collocated segment of cold-air outbreak conditions and compare normalized rime mass results with meteorological and cloud parameters. We find that higher normalized rime masses correlate with streaks of higher radar reflectivity. The methods presented improve our ability to quantify riming from aircraft observations. [ABSTRACT FROM AUTHOR]

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Aircraft icing can cause severe aerodynamic and flight mechanical effects, thus threatening aircraft flight safety. Understanding of aircraft icing, e.g., geometry shape of the ice accretion, is significant for its aerodynamic analysis, control methodologies, and continued design. In this study, a laser sheet scanning approach is developed to achieve the time-resolved geometry shape measurements of the ice accretion. By using the tridimensional calibration board consisted of two special checkerboard plates, all laser plane coefficients during laser sheet scanning could be obtained in advance. Then, based on the two-stage laser line extraction scheme that combined the Steger method with gradient centroid calculation, accurate positioning of the laser lines projected on the ice accretion surface was realized. The proposed approach is demonstrated in the large-scale icing wind tunnel tests of an airfoil model, conducted at the 3 m × 2 m Icing Wind Tunnel of China Aerodynamics Research and Development Center. Temporal evolution of the rime, mixed, and clear ice accretion shapes on the leading edge of the airfoil model was measured throughout the tests, respectively. The measurement at the end of ice accretion was compared with the results by a commercial 3D laser scanner, which showed highly consistent. [ABSTRACT FROM AUTHOR]

Particle shape variability is a key to understanding the rich behavior of granular materials. Polyhedra are among the most common particle shapes due to their ubiquitous origins in nature such as rock fragmentation and mineral crystallisation. Because of their faceted shape, polyhedral particles tend to assemble in jammed structures in which face-face and face-edge contacts between particles control the packing-level properties. In this paper, we use tri-periodic particle dynamics simulations to derive for the first time a generic analytical expression of the elastic moduli of polyhedral and spherical particle packings subjected to triaxial compression as a function of two contact network variables: (1) a "constraint number" that accounts for the face-face and edge-face contacts between polyhedra and is reduced to the coordination number in the case of spherical particles, and (2) the contact orientation anisotropy induced by compression. This expression accurately predicts the simulated evolution of elastic moduli during compression, revealing thereby the origins of the higher elastic moduli of polyhedral particle packings. We show that particle shape affects the elastic moduli through its impact on the contact network and the level of nonaffine particle displacements is the same for the simulated shapes. Its nearly constant value during compression underlies the constant values of our model parameters. By connecting the elastic moduli to the contact network through parameters that depend on particle shape, our model makes it possible to extract both the connectivity and anisotropy of granular materials from the knowledge of particle shape and measurements of elastic moduli. [ABSTRACT FROM AUTHOR]

The title compound dipotassium gadolinium(III) phosphate(V) molybdate(VI), K2Gd(PO4)(MoO4), was synthesized from a high-temperature melt starting from GdF3 as a source of gadolinium. Its structure is isotypic with other MI2MIII(MVIO4)(PO4) compounds, where MI = Na, K or Cs, and MIII = rareearth cation, MVI = Mo orW. The three-dimensional framework is built up from [Gd(PO4)(MoO4)] anionic sheets, which are organized by adhesion of [GdPO4] layers and [MoO4] tetrahedra stacked above and below these layers. The interstitial space is occupied by K cations having eightfold oxygen coordination. The polyhedron of GdO8 was estimated to be a triangular dodecahedron by the continuous shape measurement method. [ABSTRACT FROM AUTHOR]

The title compound dipotassium gadolinium(III) phosphate(V) molybdate(VI), K2Gd(PO4)(MoO4), was synthesized from a high-temperature melt starting from GdF3 as a source of gadolinium. Its structure is isotypic with other MI2MIII(MVIO4)(PO4) compounds, where MI = Na, K or Cs, and MIII = rareearth cation, MVI = Mo orW. The three-dimensional framework is built up from [Gd(PO4)(MoO4)] anionic sheets, which are organized by adhesion of [GdPO4] layers and [MoO4] tetrahedra stacked above and below these layers. The interstitial space is occupied by K cations having eightfold oxygen coordination. The polyhedron of GdO8 was estimated to be a triangular dodecahedron by the continuous shape measurement method. [ABSTRACT FROM AUTHOR]

Dry body mass (DBM) is perhaps the most biologically informative variable describing body size in invertebrates. Unfortunately, obtaining species-specific indices of DBM is problematic because body mass inevitably changes during the course of the life of an individual. Here, we present a phylogenetically informed analysis of allometric relationships between body size and various linear measurements in the moth family Geometridae, which relies on DBM recorded at a fixed time point of adult life. We demonstrate that all measurements of wing size predict DBM with reasonable accuracy, with the distance between the most distal ends of the two forewings in traditionally mounted moths showing the best performance. Abdomen width provides independent morphometric information and can be used as a proxy of body plan, i.e. a measurement of shape that is not dependent on size. Incorporating abdomen width into the regression models considerably increases their predictive ability. We also show that the allometric relationships are reasonably consistent between the two sexes, between monophyletic clades of Geometridae and between the two geographical regions involved in the study (northern Europe and equatorial Africa). The derived equations thus appear to be general enough to be applied in various studies, from comparative phylogenetic analyses to applied projects monitoring insect biomass. [ABSTRACT FROM AUTHOR]

Designing an offset cable net in parabolic reflectors introduces several complexities compared to prime focus configurations. This study aims to develop a versatile cable net generation algorithm capable of adapting to the reflector's dimensions and the curvature of the paraboloid surface. In this regard, we propose a methodology that leverages specific paraboloid surface curves known as quasi-geodesic curves. Similar to geodesic curves on a sphere, quasi-geodesic curves visually resemble proper geodesic shapes but may follow distinct mathematical principles. We introduce two types of quasi-geodesic curves: primary curves that intersect the center point of the cable net and secondary curves that pass through any two points on the net. We present various solutions accommodating different cable net layouts and introduce a quality index based on an equilateral triangle cable net. Finally, we compare the quasi-geodesic-type cable net with the isogrid-type cable net to highlight tension distribution and surface accuracy improvements. • An iterative cable net design based on quasi-geodesic curves is proposed. • Interface nodes are integrated into the cable net generation process. • The best geometry minimizing the rms error of the reflector surface is calculated. • A method based on the triangular shape measurement of the cable net is introduced. [ABSTRACT FROM AUTHOR]

Phase-measuring deflectometry (PMD) with active display registration (ADR) is a ray-optics-based technique for the shape measurement of specular surfaces. To obtain quantitative results, the relative position of the cameras of the PMD–ADR setup needs to be determined by geometric calibration. Geometric calibration can be performed by inserting a planar mirror into the setup that brings all camera fields of view to overlap on an active pattern display. The mirror is tilted to multiple positions and each time the cameras capture the displayed images, which yields sufficient data to obtain the relative camera positions and the positions of the mirror. In this article, we give a more detailed description of PMD–ADR and its calibration. We also implement a laser-tracker-based reference method to measure the mirror positions and use its result to expose systematic errors in the geometric calibration. [ABSTRACT FROM AUTHOR]

To address the challenge of tracking irregular extended target while adapting to unknown measurement noise, this paper presents a novel tracking algorithm for irregular extended target. Considering the flexibility of the Gaussian process (GP) model for representing shape, in the proposed algorithm, we utilize the GP model to delineate the radial function of the tracked extended target's contour. Then, we incorporate the GP model into the variational Bayesian technique to formulate the posterior distribution for both the unknown measurement noise and the shape state of the tracked target. Subsequently, the square-root cubature Kalman filter is employed to tackle the nonlinearity filtering in the problem of irregular extended target tracking (ETT), enabling simultaneous estimation of intricate shape details and the unknown measurement noise covariance. Through extensive experiments using both simulated and real-time lidar data, the proposed algorithm demonstrates superior performance compared to the existing ETT algorithms for extended target tracking in both accuracy and robustness. • A method tracking an irregular extended target with unknown measurement noise. • The method represents the irregular target shape with GP model. • The method derives the posterior distribution based on VB method. • SCKF is used for the nonlinear system model. • The intricate shape and measurement are simultaneously estimated. [ABSTRACT FROM AUTHOR]