Search

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]

Copyright of Methods in Ecology & Evolution is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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]

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]

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]

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]

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]

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]

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]

Copyright of Revista Salud UIS is the property of Universidad Industrial de Santander and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Revista Numismática Hécate is the property of Revista Numismatica Hecate and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Performance and lifetime analysis of electrospray thrusters requires accurate knowledge of the mass and charge distributions of the plume. Mass flux and current density distributions were measured for a single capillary electrospray emitter using EMI-Im and found to be substantially different across a wide range of flow rates and emission voltages. Mass flux measurements yield an n ∼ 3 super-Gaussian profile across all flow rates and voltages, while current density measurements change shape from n ∼ 1.5 – 2.5 super-Gaussian profiles monotonically with decreasing flow rate, where n = 1 is Gaussian and higher n values correspond to increasingly more flat-top "super-Gaussian" profiles with steeper drop-off toward higher angles. For increasing flow rate, the mass flux profile grows while maintaining its shape, whereas the current density profile exhibits higher kurtosis, i.e., plumes that distribute proportionately more charge to higher angles. Additionally, higher extraction voltages exhibited tilted emission that led to highly off-axis plumes, ∼ 10 ° , for both mass flux and current density. Lifetime and performance assessments of electrospray thrusters must consider that mass flux and current density in the plume display different distribution shapes and trends in shape across changes in extraction voltage and flow rate. [ABSTRACT FROM AUTHOR]

Close-range photogrammetry methods are widely used for non-contact and accurate measurements of surface shapes. These methods are based on calculating the three-dimensional coordinates of an object from two-dimensional images using special digital processing algorithms. Due to the relatively complex measurement principle, the accurate estimation of the photogrammetric measurement error is a non-trivial task. Typically, theoretical estimations or computer modelling are used to solve this problem. However, these approaches cannot provide an accurate estimate because it is impossible to consider all factors that influence the measurement results. To solve this problem, we propose the use of physical modelling. The measurement results from the photogrammetric system under test were compared with the results of a more accurate reference measurement method. This comparison allowed the error to be estimated under controlled conditions. The test object was a flexible surface whose shape could vary smoothly over a wide range. The estimation of the measurement accuracy for a large number of different surface shapes allows us to obtain new results that are difficult to obtain using standard approaches. To implement the proposed approach, a laboratory system for the error estimation of close-range photogrammetric measurements was developed. The paper contains a detailed description of the developed system and the proposed technique for a comparison of the measurement results. The error in the reference method, which was chosen to be phasogrammetry, was evaluated experimentally. Experimental testing of the stereo photogrammetric system was performed according to the proposed technique. The obtained results show that the proposed technique can reveal dependencies that may not be detected by standard approaches. [ABSTRACT FROM AUTHOR]

Particle characterization is critical in industries that are influenced by particle size distribution. Understanding particle behavior is crucial for product quality control and manufacturing process optimization. Particle characteristics significantly affect material performance and properties. This review paper examines the importance of particle characterization in many industries and focuses on particle size and shape measurement. This paper begins by delving into particle size and size distribution analysis, emphasizing the impact of particle size on material properties and the many methodologies used for particle size analysis. This paper then examines particle shape characterization and its impact on material characteristics. It gives an overview of particle characterization techniques and the criteria for selecting the best technique for a given sample. Particle characterization in ceramics, food, cosmetics, medicines, and metallurgy are also thoroughly discussed. Overall, this work emphasizes the importance of particle characterization in numerous industries and provides insights into particle size and shape measurement. [ABSTRACT FROM AUTHOR]

Fringe projection profilometry (FPP) has been widely used for 3D reconstruction, surface measurement, and reverse engineering. However, if the surface of an object has a high reflectivity, overexposure can easily occur. Image saturation caused by overexposure can lead to an incorrect intensity of the captured pattern images, resulting in phase and measurement errors of FPP. To address this issue, we propose a phase retrieval method for the 3D shape measurement of high-reflectivity surfaces based on π phase-shifting fringes. Our method only requires eight images to be projected, including three single-frequency three-step phase-shifting patterns and one pattern used to provide phase unwrapping constraints, called conventional patterns, as well as the π phase-shifting patterns corresponding to the four conventional patterns, called supplemental patterns. Saturated pixels of conventional fringes are replaced by unsaturated pixels in supplemental fringes to suppress phase retrieval errors. We analyzed all 16 replacement cases of fringe patterns and provided calculation methods for unwrapped phases. The main advantages of our method are as follows: (1) By combining the advantages of the stereo phase unwrapping (SPU) algorithm, the number of projected fringes is reduced. (2) By utilizing the phase unwrapping constraint provided by the fourth fringe pattern, the accuracy of SPU is improved. For highly reflective surfaces, the experimental results demonstrate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

The advent of consumer spaceflight raises the issue of individuals with health conditions being exposed to periods of microgravity. Terrestrial lung function is gravitationally dependent, so it is important to understand the key lung functional changes currently understood to occur with a change in gravitational load. The aim of this systematic review was to summarise the effects of a microgravity (0G) environment on various volume, capacity and shape measurements on the human lung relative to normal Earth gravity (1G). Thirty studies including parabolic flights (10–25 s), short-duration spaceflight (≤30 days) and long-duration spaceflight (>30 days) were analysed. Parameters including lung shape, volumes and capacities reported in 1G (before flight) and 0G (in-flight) were extracted from these sources. While no change was seen in lung volume and capacity measurements between 0G and 1G in long-duration spaceflight, there were slight or no changes in parabolic and short-duration spaceflight. Additionally, no consistent effects were observed in lung shape in microgravity compared to 1G. • According to the current evidence available, no change is observed in lung volume and capacity measurements between 0G and 1G in long-duration spaceflight. • There are either no or slight changes in lung volume and capacity measurements between 0G and 1G in parabolic and short-duration spaceflight. • No consistent effects are observed in lung shape and physical dimensions in 0G compared to 1G. [ABSTRACT FROM AUTHOR]

We update the full set of B ¯ s → K form factors using light-cone sum rules with an on-shell kaon. Our approach determines the relevant sum rule parameters — the duality thresholds — from a Bayesian fit for the first time. Using a modified version of the Boyd-Grinstein-Lebed parametrisation, we combine our sum rule results at low momentum transfer q2 with more precise lattice QCD results at large q2. We obtain a consistent description of the form factors in the full q2 range. Applying these results to a recent LHCb measurement of branching ratios for the decays B s 0 → {K−, D s − }μ+νμ, we determine the ratio of Cabibbo-Kobayashi-Maskawa elements V ub V cb q 2 < 7 GeV 2 = 0.0681 ± 0.0040 and V ub V cb q 2 > 7 GeV 2 = 0.0801 ± 0.0047 , which are mutually compatible at the 1.9σ level. We further comment on the sensitivity to Beyond the Standard Model effects through measurements of the shape of B s 0 → K−μ+νμ decays, in light of recent limits on such effects from other exclusive b → uℓν processes. [ABSTRACT FROM AUTHOR]

Traditional non-coplanar calibration methods, represented by Tsai's method, are difficult to apply in multi-camera-based stereo vision measurements because of insufficient calibration accuracy, inconvenient operation, etc. Based on projective theory and matrix transformation theory, a novel mathematical model is established to characterize the transformation from targets' 3D affine coordinates to cameras' image coordinates. Then, novel non-coplanar calibration methods for both monocular and binocular camera systems are proposed in this paper. To further improve the stability and accuracy of calibration methods, a novel circular feature points extraction method based on region Otsu algorithm and radial section scanning method is proposed to precisely extract the circular feature points. Experiments verify that our novel calibration methods are easy to operate, and have better accuracy than several classical methods, including Tsai's and Zhang's methods. Intrinsic and extrinsic parameters of multi-camera-systems can be calibrated simultaneously by our methods. Our novel circular feature points extraction algorithm is stable, and with high precision can effectively improve calibration accuracy for coplanar and non-coplanar methods. Real stereo measurement experiments demonstrate that the proposed calibration method and feature extraction method have high accuracy and stability, and can further serve for complicated shape and deformation measurements, for instance, stereo-DIC measurements, etc. [ABSTRACT FROM AUTHOR]

This work proposes a systematic assessment of measuring type A uncertainty (caused by random errors) used in RF power sensor calibration. To reduce A type uncertainty, several successive measurements are repeated. The uncertainty arises from repeatability errors in connectors caused by changes in their electrical properties during repeated mating. The suitability of the METAS UncLib software was analysed and we concluded that software should be developed to take into account the shape of probability density function (PDF) using a Monte Carlo method (MCM), which was lacking in METAS UncLib. The self-developed software was then tested on an example taken from the literature and the superiority of the MCM over the analytical method (GUM) was confirmed. During the calibration of the RF sensor using a vector network analyzer (VNA), a series of repeated measurements were performed and, after applying our MCM software, it was found that the measurement uncertainties calculated by the MCM method were several times larger than those by the GUM. The reason for this was that the correlation between the measured input quantities was not taken into account. When this was done using a covariance matrix and assuming a normal PDF of the input quantities, the results obtained with the GUM and the MCM converged. Our main objective was to investigate the influence of the PDF shape of the input measurement samples on the measurement uncertainty. Taking more than a dozen measurements is too costly, on the other hand, the small sample size prevents a reliable determination of the PDF shape. Finally, to overcome this inconvenience, we have developed a special method that uses the histograms of standardized input data taken at all measurement frequencies under fixed conditions without disconnecting the connectors, to increasing the total number of results which were needed to create the PDF histograms of input quantities. [ABSTRACT FROM AUTHOR]

Objective: This study presents an extended evaluation of a numerical approach to simulate artifacts of metallic implants in an MR environment. Methods: The numerical approach is validated by comparing the artifact shape of the simulations and measurements of two metallic orthopedic implants at three different field strengths (1.5 T, 3 T, and 7 T). Furthermore, this study presents three additional use cases of the numerical simulation. The first one shows how numerical simulations can improve the artifact size evaluation according to ASTM F2119. The second use case quantifies the influence of different imaging parameters (TE and bandwidth) on the artifact size. Finally, the third use case shows the potential of performing human model artifact simulations. Results: The numerical simulation approach shows a dice similarity coefficient of 0.74 between simulated and measured artifact sizes of metallic implants. The alternative artifact size calculation method presented in this study shows that the artifact size of the ASTM-based method is up to 50% smaller for complex shaped implants compared to the numerical-based approach. Conclusion: In conclusion, the numerical approach could be used in the future to extend MR safety testing according to a revision of the ASTM F2119 standard and for design optimization during the development process of implants. [ABSTRACT FROM AUTHOR]

Digital fringe projection (DFP) is widely applied in three-dimensional (3D) shape measurements. However, its performance is severely disturbed while measuring complex surfaces with an extensive range of reflectivity. In this paper, to enhance the underexposed regions and reduce the saturated regions, an automatic and effective method is proposed for the multi-exposure determination of the DFP system. During the whole process, only one unsaturated image must be captured preliminarily, which could establish an adaptive strategy based on the intensity value distribution function. Raw absolute phase maps captured with different exposure times are synthesized at the pixel level for phase retrieval and 3D reconstruction. To evaluate the effectiveness of our method, a high dynamic range method and a global optimal exposure method are introduced for comparison. Verification experiments demonstrate that our method performs better for the 3D reconstruction results of complex surfaces with a large reflectivity range. [ABSTRACT FROM AUTHOR]

Abstract From a 2D video of a person in action, human mesh recovery aims to infer the 3D human pose and shape frame by frame. Despite progress on video‐based human pose and shape estimation, it is still challenging to guarantee high accuracy and smoothness simultaneously. To tackle this problem, we propose a Video2mesh, a temporal convolutional transformer (TConvTransformer) based temporal network which is able to recover accurate and smooth human mesh from 2D video. The temporal convolution block achieves the sequence‐level smoothness by aggregating image features from adjacent frames. The subsequent multi‐attention transformer improves the accuracy due to its multi‐subspace for better middle‐frame feature representation. Meanwhile, we add a TConvTransformer discriminator which is trained together with our 3D human mesh temporal encoder. This TConvTransformer discriminator further improves the accuracy and smoothness by restricting the pose and shape in a more reliable space based on the AMASS dataset. We conduct extensive experiments on three standard benchmark datasets and show that our proposed Video2mesh outperforms other state‐of‐the‐art methods in both accuracy and smoothness.

Riming is a key precipitation formation process in mixed-phase clouds by efficiently converting 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 were collecting spatially and temporally closely collocated radar and in situ measurements over the Fram Strait west of Svalbard in spring 2022. The first method is based on an inverse Optimal Estimation algorithm to retrieve 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, by 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 0.018 and 0.016 (mean values of 0.027 and 0.028) for combined and in situ method, respectively. Assuming particles with a normalized rime mass smaller 0.01 to be unrimed, we obtain average rimed fractions of 77% and 75%. Although in situ measurement volumes are in the range of a few cm³ and therefore much smaller than the radar volume (about 45 m footprint diameter), 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 compare normalized rime mass results with meteorological and cloud parameters and show the performance of the methods in two case studies, 1) a collocated segment in cold air outbreak conditions and 2) an in situ only flight close to a polar low.We find that higher normalized rime masses correlate with streaks of higher radar reflectivity.We also observe rimed particles in regions without liquid water, suggesting that particles were rimed in a liquid layer above and precipitated. The methods presented improve our ability to quantify riming from aircraft observations. [ABSTRACT FROM AUTHOR]

Riming is a key precipitation formation process in mixed-phase clouds by efficiently converting 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 were collecting spatially and temporally closely collocated radar and in situ measurements over the Fram Strait west of Svalbard in spring 2022. The first method is based on an inverse Optimal Estimation algorithm to retrieve 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, by 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 0.018 and 0.016 (mean values of 0.027 and 0.028) for combined and in situ method, respectively. Assuming particles with a normalized rime mass smaller 0.01 to be unrimed, we obtain average rimed fractions of 77 % and 75 %. Although in situ measurement volumes are in the range of a few cm3 and therefore much smaller than the radar volume (about 45 m footprint diameter), 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 compare normalized rime mass results with meteorological and cloud parameters and show the performance of the methods in two case studies, 1) a collocated segment in cold air outbreak conditions and 2) an in situ only flight close to a polar low. We find that higher normalized rime masses correlate with streaks of higher radar reflectivity. We also observe rimed particles in regions without liquid water, suggesting that particles were rimed in a liquid layer above and precipitated. The methods presented improve our ability to quantify riming from aircraft observations. [ABSTRACT FROM AUTHOR]

Two thione‐coordinated dinuclear bismuth(III) halides were isolated with a rare geometry and characterized using FT‐IR, NMR, and single‐crystal X‐ray diffraction techniques. The sterically less crowded N‐heterocyclic thione ligand gave bismuth(III) chloride‐thione complex in cis isomeric form, while the sterically more crowded N‐heterocyclic thione ligand gave dinuclear bismuth(III) bromide‐thione complex in facial isomeric form. Continuous shape measurement (CShM) revealed that the bismuth centres in cis‐bismuth(III) chloride‐thione complex adopts distorted octahedral geometry with the CShM values of 2.103, which is remarkably different compared to the facial‐dinuclear bismuth(III) bromide‐thione complex (1.071 and 0.391). [ABSTRACT FROM AUTHOR]

Pulmonary fissure segmentation in computed tomography (CT) images can be treated as important ancillary information in the diagnosis and treatment of pulmonary diseases, yet it poses a nontrivial uncertainty for the segmentation task due to complex structures such as indistinguishable pulmonary vessels, blurring pulmonary fissures and unpredictable pathological deformation. To address these challenges, a useful approach based on an oriented derivative of stick (ODoS) filter and shape features is presented for pulmonary fissure segmentation. Here, we adopt an ODoS filter by fusing its orientation and magnitude information to highlight structural features for fissure enhancement, which can effectively distinguish between pulmonary fissures and undesirable clutter. Motivated by the fact that pulmonary fissures appear as linear structures in 2D space and planar structures in 3D space in the orientation field, an orientation curvature criterion and an orientation partition scheme are fused to separate fissure patches and other structures in different orientation partitions, which is expected to achieve more complete fissure detection and suppress other structures. Considering the shape difference between pulmonary fissures and tubular structures in the magnitude field, a shape measurement approach and a 3D skeletonization model are combined to remove clutter for pulmonary fissure segmentation. When applying our scheme to 55 chest CT scans acquired from publicly available LOLA11 datasets, the median F1-score, false discovery rate (FDR), and false negative rate (FNR) were 0.90, 0.11, and 0.10, respectively, which indicates that our scheme has satisfactory pulmonary fissure segmentation performance. [ABSTRACT FROM AUTHOR]

When introducing a nanoparticle into an optical trap, its mass and shape are not immediately apparent. We combine a charge-based mass measurement with a shape determination method based on light scattering and an analysis of the damping rate anisotropy, all on the same set of silica nanoparticles, trapped using optical tweezers in vacuum. These methods have previously only been used separately, and the mass determination method has not been applied to asymmetric particles before. We demonstrate that the combination of these classification techniques is required to distinguish particles with similar mass but different shape, and vice versa. The ability to identify these parameters is a key step for a range of experiments on precision measurements and sensing using optically levitated nanoparticles. [ABSTRACT FROM AUTHOR]

In the absence of gravity, surface tension dominates over the behavior of liquids. While this often poses a challenge in adapting Earth-based technologies to space, it can also provide an opportunity for novel technologies that utilize its advantages. In particular, surface tension drives a liquid body to a constant-mean-curvature shape with extremely smooth surfaces, properties which are highly beneficial for optical components. We here present the design, implementation and analysis of parabolic flight experiments demonstrating the creation and in-situ measurement of optical lenses made entirely by shaping liquids in microgravity. We provide details of the two experimental systems designed to inject the precise amount of liquid within the short microgravity timeframe provided in a parabolic flight, while also measuring the resulting lens' characteristics in real-time using both resolution target-imaging and Shack-Hartmann wavefront sensing. We successfully created more than 20 liquid lenses during the flights. We also present video recordings of the process, from the lenses' creation during microgravity and up until their collapse upon return to gravity. The work thus demonstrates the feasibility of creating and utilizing liquid-based optics in space. [ABSTRACT FROM AUTHOR]

The advance of minimally invasive interventional surgeries has accelerated the iterative upgrading of continuum surgical robots. High compatibility with robotic applications and high precision are key features of sensors for robot navigation. In this paper, a spun multi-core fibre (SMCF) 3D shape sensor for continuum surgical robots is proposed. The sensor is fabricated by ultraviolet (UV) light inscribing fibre Bragg gratings (FBGs) in the SMCF, showing good spectra characteristics. Shape reconstruction is realized by the Frenet–Serret (F–S) frame and sensing characteristics such as twisting, strain and temperature are systematically analyzed. Especially, the twisting characteristics of SMCF and MCF are compared and the feasibility of self-torsional compensation of SMCF is demonstrated. In addition, shape measurement experiments with three known shapes are performed. The mean relative error (MRE) for each shape is 0.49%, 1.90% and 5.13%, respectively. These results show that the proposed sensor can accurately measure 3D shapes with temperature and twisting compensation, enabling its application prospects in the online shape feedback of continuum surgical robots. [ABSTRACT FROM AUTHOR]

We measure the galaxy-ellipticity (GI) correlations for the Sloan Digital Sky Survey Data Release 12 LOWZ and CMASS samples with the shape measurements from the DESI Legacy Imaging Surveys. We model the GI correlations in an N -body simulation with our recent accurate stellar–halo mass relation from the Photometric object Around Cosmic webs (PAC) method. The large data set and our accurate modeling turns out an accurate measurement of the alignment angle between central galaxies and their host halos. We find that the alignment of central elliptical galaxies with their host halos increases monotonically with galaxy stellar mass or host halo mass, which can be well described by a power law for the massive galaxies. We also find that central elliptical galaxies are more aligned with their host halos in LOWZ than in CMASS, which might indicate an evolution of galaxy–halo alignment, though future studies are needed to verify this is not induced by the sample selections. In contrast, central disk galaxies are aligned with their host halos about 10 times more weakly in the GI correlation. These results have important implications for intrinsic alignment (IA) correction in weak lensing studies, IA cosmology, and theory of massive galaxy formation. [ABSTRACT FROM AUTHOR]

Annular lithography is a recently introduced, flexible technique that has been tailored to the fabrication of rotationally symmetric optical structures in the meso and micro range. The optical concept for the exposure tool is based on a combination of axicons with movable components that create a ring-shaped light distribution with variable diameter in the image plane. This contribution demonstrates for the first time the use of gray tone exposure in annular lithography to fabricate continuous relief structures, overcoming the previous limitation using binary structures. For the controlled exposure of the continuous relief structures, the sensitivity curve of the resist, the exposure dose decreasing with increasing ring diameter, and the exposure time have to be considered. A control and simulation tool is introduced to provide radius-dependent exposure data and, furthermore, to control and iteratively improve the fabricated structures. To demonstrate the gray tone capabilities, various diffractive elements as well as refractive spherical and aspherical elements with a maximum diameter of ~6 mm and a maximum height of 4 µm are shown as examples. Profile shape measurements of fabricated elements show good agreement with the expectations. [ABSTRACT FROM AUTHOR]

Phase-shift profilometry (PSP) holds great promise for high-precision 3D shape measurements. However, in the case of measuring moving objects, as PSP requires multiple images to calculate the phase, the movement of the object causes artifacts in the measurement, which in turn has a significant impact on the accuracy of the 3D surface measurement. Therefore, we propose a method to reduce motion artifacts using feature information in the image and simulate it using the six-step term shift method as a case study. The simulation results show that the phase of the object is greatly affected when the object is in motion and that the phase shift due to motion can be effectively reduced using this method. Finally, artifact optimization was carried out by way of specific copper tube vibration experiments at a measurement frequency of 320 Hz. The experimental results prove that the method is well implemented. [ABSTRACT FROM AUTHOR]

In this work we built up and tested diffusion cells designed to obtain polysaccharide hydrogels by ionotropic gelation. The objective was to obtain gel samples that emulated the wall material of encapsulation beads but, unlike them, have appropriate size and shape for measurement of their structural properties, since these are of paramount importance for the protection, carry and delivery of bioactive compounds. Three polysaccharides widely used for encapsulation and with different gelation mechanisms were tested: kappaliota-carrageenan (which gels mainly in the presence of K+ ions), and sodium alginate and low methoxyl pectin (which both gel in the presence of Ca2+ ions). The diffusion cells consisted of two nitrocellulose membrane filters supported between three rings made by 3D printing. They were filled with the polysaccharide solution, hermetically tightened with screws and nuts, and submerged into the saline solution. The membrane filters effectively avoided the loss of the polysaccharide solution but allowed the diffusion of the ions (either Ca24 or K+) into the polysaccharide solutions to promote their gelation. Firm, self-standing gels were obtained, and their rheological and mechanical properties were successfully measured. Samples of different shapes and sizes could be obtained with this technique, for other types of measurement. [ABSTRACT FROM AUTHOR]

We propose a novel hybrid FPP-DIC technique to measure an object's shape and deformation in 3D simultaneously by using a single 3CCD color camera, which captures the blue fringe patterns and red fluorescent speckles within the same image. Firstly, red fluorescent speckles were painted on the surface of the specimen. Subsequently, 12 computer-generated blue fringe patterns with a black background were projected onto the surface of the specimen using a DLP projector. Finally, both the reference and deformed images with three different frequencies and four shifted phases were captured using a 3CCD camera. This technique employed a three-chip configuration in which red–green–blue chips were discretely integrated in the 3CCD color camera sensor, rendering independent capture of RGB information possible. Measurement of out-of-plane displacement was carried out through the implementation of Fringe Projection Profilometry (FPP), whereas the in-plane displacement was evaluated using a 2D Digital Image Correlation (DIC) method by leveraging a telecentric-lens-based optical system. In comparison to the traditional FPP-DIC hybrid methodology, the present approach showed a lower incidence of crosstalk between the fringe patterns and speckle patterns while also offering a corrective for the coupling of the in-plane displacement and out-of-plane displacement. Experimental results for the in-plane cantilever beam and out-of-plane disk comparisons with the traditional 3D-DIC method indicated that the maximum discrepancy obtained between FPP-DIC and 3D-DIC was 0.7 μm and 0.034 mm with different magnifications, respectively, validating the effectiveness and precision of the novel proposed FPP-DIC method. [ABSTRACT FROM AUTHOR]

In industry and architecture, real-time and complete measurement of structures has become a research frontier since it is directly related to the safety of life and property. Optical fibers have the potential to monitor constructions due to advantages such as small size, anti-electromagnetic interference, etc. However, existing research on optical fiber sensors pays attention to the sensing fiber itself and ignores the layout of the optical fibers. As a result, currently available fiber sensors are only suitable for monitoring one-dimensional rigid structures such as surgical robots and puncture needles. They may face challenges when measuring the freeform surfaces encountered in industrial and architectural scenarios. In this paper, a cross-orthogonal measurement method based on optical fiber shape sensors is proposed to meet the shape measurement requirements of freeform surfaces. The cross-orthogonal network allows global measurement and performs surface reconstructions more easily as compared to single-fiber arrays. It also divides the sensing fiber into several segments that are reconstructed separately (with different initial frames), avoiding the cumulative error at the end of the sensing fiber. Results of verification experiments using four-core fibers indicate that the presented method can improve measurement accuracy. [ABSTRACT FROM AUTHOR]

Free-form optical elements are more and more broadly used in modern optical systems due to their distinctive characteristics. In order to realize the high-precision manufacturing of free-form optical element, the constraints on parameters of manufacture and measurement were established based on the designing parameters of free-form optical element. Meanwhile, the evaluation system for the machinability and detectability of free-form optical element was obtained by means of the corresponding mathematical model. Furthermore, the White Light Interference (WLI) stitching detection technology, coupled with the least square multi-parameter optimization algorithm, was used to solve shape-error measurement of free-form optical element. Additionally, a free-form surface compensation manufacturing mechanism of asymmetric shape error was established. Based on the above methods, the polynomial free-form optics were processed and measured. According to the surface shape measurement results, the same element was processed with compensation manufacturing twice. The surface shape precision was obviously improved from PV = 2553 nm and RMS = 481 nm to PV = 214 nm and RMS = 19.9 nm, which verified the effectiveness of the method. A significant value was unfolded in the engineering application of this method. [ABSTRACT FROM AUTHOR]

Divergence in body shape is one of the most widespread and repeated patterns of morphological variation in fishes and is associated with habitat specification and swimming mechanics. Such ecological diversification is the first stage of the explosive adaptive radiation of cichlid fishes in the East African Rift Lakes. We use two hybrid crosses of cichlids (Metriaclima sp. × Aulonocara sp. and Labidochromis sp. × Labeotropheus sp., >975 animals total) to determine the genetic basis of body shape diversification that is similar to benthic‐pelagic divergence across fishes. Using a series of both linear and geometric shape measurements, we identified 34 quantitative trait loci (QTL) that underlie various aspects of body shape variation. These QTL are spread throughout the genome, each explaining 3.2–8.6% of phenotypic variation, and are largely modular. Further, QTL are distinct both between these two crosses of Lake Malawi cichlids and compared to previously identified QTL for body shape in fishes such as sticklebacks. We find that body shape is controlled by many genes of small effect. In all, we find that convergent body shape phenotypes commonly observed across fish clades are most likely due to distinct genetic and molecular mechanisms. [ABSTRACT FROM AUTHOR]

Shape measurements are crucial for evolutionary and developmental biology; however, they present difficulties in the objective and automatic quantification of arbitrary shapes. Conventional approaches are based on anatomically prominent landmarks, which require manual annotations by experts. Here, we develop a machine-learning approach by presenting morphological regulated variational AutoEncoder (Morpho-VAE), an image-based deep learning framework, to conduct landmark-free shape analysis. The proposed architecture combines the unsupervised and supervised learning models to reduce dimensionality by focusing on morphological features that distinguish data with different labels. We applied the method to primate mandible image data. The extracted morphological features reflected the characteristics of the families to which the organisms belonged, despite the absence of correlation between the extracted morphological features and phylogenetic distance. Furthermore, we demonstrated the reconstruction of missing segments from incomplete images. The proposed method provides a flexible and promising tool for analyzing a wide variety of image data of biological shapes even those with missing segments. [ABSTRACT FROM AUTHOR]

Two-dimensional (2D) dynamic image analysis (DIA) is gaining acceptance in geotechnical engineering research. Three-dimensional (3D) DIA extracts features from 8–12 projections of a particle and thus it is believed to verge on the true particle morphology. DIA is fast, efficient and convenient for characterising thousands of particles quickly; nevertheless, it captures shapes that are fundamentally different from the 3D morphologies reconstructed using micro-computed tomography (μCT). In DIA, particle features are interpreted using external images of a particle, which fail to account for differences in imaging perspectives. In addition, 2D and 3D shape descriptors are influenced by differences in dimensionality projection owing to variations in definition, dimensionality and perspectives of the particle images employed, which causes them to differ from their 3D counterparts. In this study, the sand particle size and shape descriptors obtained using both DIA and μCT are compared for three natural sands having wide granulometries. Three-dimensional DIA offers significant advantages in terms of efficiency, while providing adequate representation of Feret dimensions, sphericity and convexity. However, the study demonstrates that 3D roundness is difficult to characterise using DIA and that shape measurements of complex irregular calcareous sands obtained from 3D DIA are not comparable to those obtained using μCT. [ABSTRACT FROM AUTHOR]

In fringe projection profilometry (FPP) based on temporal phase unwrapping (TPU), reducing the number of projecting patterns has become one of the most important works in recent years. To remove the $2\pi $ ambiguity independently, this paper proposes a TPU method based on unequal phase-shifting code. Wrapped phase is still calculated from $N$ -step conventional phase-shifting patterns with equal phase-shifting amount to guarantee the measuring accuracy. Particularly, a series of different phase-shifting amounts relative to the first phase-shifting pattern are set as codewords, and encoded to different periods to generate one coded pattern. When decoding, Fringe order with a large number can be determined from the conventional and coded wrapped phases. In addition, we develop a self-correction method to eliminate the deviation between the edge of fringe order and the $2\pi $ discontinuity. Thus, the proposed method can achieve TPU but need to only project one additional coded pattern (e. g. 3+1), which can significantly benefit dynamic 3D shape reconstruction. The theoretical and experimental analysis verify that the proposed method performs high robustness on the reflectivity of the isolated object while ensuring the measuring speed. [ABSTRACT FROM AUTHOR]

The uncertainty of crop phenological cycle is an important issue in crop classification with time series polarimetric synthetic aperture radar (PolSAR) data. The time series alignment algorithm represented by dynamic time warping (DTW) can supply a potential solution, which realigns curves based on shape matching, dealing with the distortion of feature curves caused by uncertain crop phenological development. However, previous studies mainly focused on shape characteristics of time-varying feature curves, which is hard to comprehensively evaluate the similarity degree of crop phenological cycles. Furthermore, it ignored the differences in scattering signal and polarimetric statistical distribution of crops, which limited the accuracy of crop classification. In this letter, a novel crop classification method based on phenology alignment is proposed. First, the dual-branch time series alignment method is proposed, including the time-weighted DTW (TWDTW) alignment and the Wishart distance-based TWDTW (WD-TWDTW) alignment, which combines the feature curve characteristics and the polarimetric statistical information to correctly describe the similarity degree of phenological cycles. Second, a multi-similarity measure (including shape similarity, feature similarity, and polarimetric similarity) is defined to improve capacity of crop discrimination. The multisimilarity measure can describe the differences of crop types from three aspects, including crop growth trend, growth status, and statistical distribution. The proposed method is evaluated with time series full-polarization Radarsat-2 data in Flevoland area. The results show that our method is superior to traditional method with single TWDTW alignment and shape similarity, and the corresponding overall accuracy (OA) is improved by 6%. [ABSTRACT FROM AUTHOR]

Arbitrary-oriented target detection is widely used in optical remote-sensing image processing, and there have been lots of anchor-based detectors using horizontal bounding boxes. However, the image targets of various scales and shapes make it difficult to tune optimal anchor parameters, whereas the complex background and nonmaximum suppression (NMS) require well-aligned bounding box to predict dense targets. In this letter, a scale-independent IoU (SIoU) loss is proposed for bounding box regression, which can adaptively adjust the shape of predicted boxes and speed up the convergence. Besides, the regression branch of the fully convolutional one-stage object detector (FCOS) is refined to implement the novel intersection over union (IoU) loss for rotated bounding box regression. Extensive experiments on HRSC2016 and a large-scale dataset for object detection in aerial images (DOTA) show that our method obtains 88.1% mean average precision (mAP) under an IoU threshold of 0.5 on HRSC2016, which is 1.1% higher than generalized IoU (GIoU) loss and 0.7% than complete IoU (CIoU) loss. [ABSTRACT FROM AUTHOR]

3D measurement of inside human body becomes important and several techniques have been proposed. Among them, ultra-small pattern projector with off-the-shelf endoscope is promising because of stability, accuracy and cost-effectiveness. One drawback of the system is that since 3D shape is reconstructed for each frame while endoscope head is moving, they are not registered. In addition, shapes are distorted independently, since the position of the projector cannot be fixed to the head. In this paper, we propose a novel bundle adjust (BA) algorithm to solve both distortion and shape registration problems for a 3D endoscope system based on pattern projection. By using the proposed method, multiple measurements that potentially have scale inconsistencies and shape distortions are registered, with simultaneous correction of inter-frame inconsistencies. The effectiveness of the technique is proved for measurements of concave shapes made of clay, phantom models, and a real stomach of a pig. [ABSTRACT FROM AUTHOR]

This paper presents an optimization method that aims to mitigate disturbances in the radial-feed system of the ring-pendulum double-sided polisher (RDP) during processing. We built a radial-feed system model of an RDP and developed a single-tube robust model predictive control system to enhance the disturbance rejection capability of the radial-feed system. To constrain the system states inside the terminal constraint set and further enhance the system's robustness, we added the ε-approximation to approach the single-tube terminal constraint set. Finally, the effectiveness of the proposed method for the RDP radial-feed system was verified through simulations and experiments. These findings demonstrate the potential of the proposed method for improving the performance of the RDP radial-feed system in practical applications. The polish processing results demonstrated a substantial improvement in the accuracy of the surface shape measurements obtained by applying the STRMPC method. Compared to the MPC method, the PV value decreased from 1.49 λ PV to 0.99 λ PV, indicating an improvement in the convergence rate of approximately 9.78%. Additionally, the RMS value decreased from 0.257 λ RMS to 0.163 λ RMS, demonstrating a remarkable 35.6% enhancement in the convergence rate. [ABSTRACT FROM AUTHOR]

To study the compressive properties of an elastomeric porous cylinder, a 360° 3D digital image correlation (DIC) system is proposed. This compact vibration isolation table system captures different segments of the object from four different angles and fields of view, enabling a comprehensive measurement of the full surface of the object. To increase the stitching quality, a coarse–fine coordinate matching method is presented. First, a three-dimensional rigid body calibration auxiliary block is employed to track motion trajectory, which enables preliminary matching of four 3D DIC sub-systems. Subsequently, scattered speckle information characteristics guide fine matching. The accuracy of the 360° 3D DIC system is verified through a three-dimensional shape measurement conducted on a cylindrical shell, and the maximum relative error of the shell's diameter is 0.52%. A thorough investigation of the 3D compressive displacements and strains exerted on the full surface of an elastomeric porous cylinder are investigated. The results demonstrate the robustness of the proposed 360° measuring system on calculating images with voids and indicate a negative Poisson's ratio of periodically cylindrical porous structures. [ABSTRACT FROM AUTHOR]

In three-dimensional (3D) shape measurement based on fringe projection, various factors can degrade the quality of the point cloud. Existing point cloud filtering methods involve analyzing the geometric relationship between 3D space and point cloud, which poses challenges such as complex calculation and low efficiency. To improve the accuracy and speed of point cloud filtering, this paper proposes a new point cloud filtering method based on image segmentation and the absolute phase for the 3D imaging obtained by fringe projection. Firstly, a two-dimensional (2D) point cloud mapping image is established based on the 3D point cloud obtained from fringe projection. Secondly, threshold segmentation and region growing methods are used to segment the 2D point cloud mapping image, followed by recording and removal of the segmented noise region. Using the relationship between the noise point cloud and the absolute phase noise point in fringe projection, a reference noise-free point is established, and the absolute phase line segment is restored to obtain the absolute phase of the noise-free point. Finally, a new 2D point cloud mapping image is reconstructed in 3D space to obtain a point cloud with noise removed. Experimental results show that the point cloud denoising accuracy calculated by this method can reach up to 99.974%, and the running time is 0.954 s. The proposed method can effectively remove point cloud noise and avoid complex calculations in 3D space. This method can not only remove the noise of the 3D point cloud but also can restore the partly removed noise point cloud into a noise-free 3D point cloud, which can improve the accuracy of the 3D point cloud. [ABSTRACT FROM AUTHOR]

Shear estimation bias from galaxy detection and blending identification is now recognized as an issue for ongoing and future weak-lensing surveys. Currently, the empirical approach to correcting for this bias involves numerically shearing every observed galaxy and rerunning the detection and selection process. In this work, we provide an analytical correction for this bias that is accurate to sub per cent level and far simpler to use. With the interpretation that smoothed image pixel values and galaxy properties are projections of the image signal onto a set of basis functions, we analytically derive the linear shear responses of both the pixel values and the galaxy properties (i.e. magnitude, size, and shape) using the shear responses of the basis functions. With these derived shear responses, we correct for biases from shear-dependent galaxy detection and galaxy sample selection. With the analytical covariance matrix of measurement errors caused by image noise on pixel values and galaxy properties, we correct for the noise biases in galaxy shape measurement and the detection/selection process to the second-order in noise. The code used for this paper can carry out the detection, selection, and shear measurement for ∼1000 galaxies per CPU second. The algorithm is tested with realistic image simulations, and we find, after the analytical correction (without relying on external image calibration) for the detection/selection bias of about |$-4~{{\ \rm per\ cent}}$|⁠ , the multiplicative shear bias is |$-0.12 \pm 0.10~{{\ \rm per\ cent}}$| for isolated galaxies; and about |$-0.3 \pm 0.1~{{\ \rm per\ cent}}$| for blended galaxies with Hyper Suprime-Cam observational condition. [ABSTRACT FROM AUTHOR]

We analyse the full shape of anisotropic clustering measurements from the extended Baryon Oscillation Spectroscopic Survey quasar sample together with the combined galaxy sample from the Baryon Oscillation Spectroscopic Survey. We obtain constraints on the cosmological parameters independent of the Hubble parameter h for the extensions of the Lambda cold dark matter (ΛCDM) models, focusing on cosmologies with free dark energy equation of state parameter w. We combine the clustering constraints with those from the latest cosmic microwave background data from Planck to obtain joint constraints for these cosmologies for w and the additional extension parameters – its time evolution w a, the physical curvature density ω K and the neutrino mass sum ∑ m ν. Our joint constraints are consistent with a flat ΛCDM cosmological model within 68  per cent confidence limits. We demonstrate that the Planck data are able to place tight constraints on the clustering amplitude today, σ12, in cosmologies with varying w and present the first constraints for the clustering amplitude for such cosmologies, which is found to be slightly higher than the ΛCDM value. Additionally, we show that when we vary w and allow for non-flat cosmologies and the physical curvature density is used, Planck prefers a curved universe at 4σ significance, which is ∼2σ higher than when using the relative curvature density ΩK. Finally, when w is varied freely, clustering provides only a modest improvement (of 0.021 eV) on the upper limit of ∑ m ν. [ABSTRACT FROM AUTHOR]