Measurement Of Local Curvature Research Articles

A nano-radian precision absolute local slope measurement method for X-ray reflectors.

Ultra-precise reflectors in the advanced light source facilities urgently call for local slope error measurements with nano-radian precision. However, the existing methods currently utilized in the long trace profiler systems struggle to meet the requirements. In this paper, we present a weak-value amplification enhanced absolute local slope measurement scheme, in which the surface height difference between two adjacent points can be measured directly with precision on the pico-meter level. As a result, the absolute local slope measurement reaches a record precision level of 9.7 nrad (RMS) with a small lateral separation of 0.5 mm. Comparing to the existing methods, our scheme is more disturbance-resistant, more compact and cost-effective. The local curvature measuring capability is also validated with two synchronously parallel local slope measurement paths, between which the separation is set as 2mm. A local curvature measurement is obtained with precision of 3.4 × 10-6m-1 (RMS) and its corresponding slope variation is 6.8 nrad. Our method exhibits important application prospects in the field of ultra-precise surface fabrication inspection.

S-XCT experimental determination of local contact angle and meniscus shape in liquid moulding of composites

In-situ spontaneous wicking experiments were scanned using Synchrotron X-ray Computed Tomography (S-XCT) to study the meniscus shape at the fibre scale. To this end, a single tow of E-glass fibres was impregnated with a commercial epoxy resin by using a wicking fixture specially designed for such purpose. The high resolution of the S-XCT images recorded (0.325μm/pixel) allowed the direct access to the surface of the individual menisci formed between fibres and permitted a direct quantification of the contact angle as well as the local curvature measurement. The contact angle values measured were in good agreement with values reported in the literature. The experimental methodology employed was also compared with numerical results obtained using a surface minimization approach. The results obtained with the simulation tool, in terms of effective capillary pressure and meniscus shape, were in good agreement with the experimental data reported.

Local Slope and Curvature Tests via Wave Front Modulations in the Shack–Hartmann Sensor

To provide slope and full curvature measurements with a single image for each subaperture in zonal wave front sensing, we propose to introduce a wave front modulation to each subaperture of the Shack–Hartmann sensor. This idea is preliminarily realized on a new sensor, which uses a four-hole mask array to modulate the test wave front incident on the lenslet array. Centroid estimation for the local slope measurements can be performed with reduced variance, thanks to the reduced size of the central lobe offered by the four-hole mask modulation. Meanwhile, the side lobes in the focal image give three intensity-normalized differential signals for the local curvature measurements. Each of the three signals shows approximately linear response to the corresponding second order term of the local wave front. In this way, the full curvature information for each subaperture can be directly determined without any complicated post processing algorithms required in other focal plane sensing techniques. Accuracy of the sensor in a single subaperture is examined by simulation.

Characterization of Cracks and their Effects on the Effective Transport Pathways in Ni-YSZ Anodes after Reoxidation Using X-Ray Nanotomography

Reduction-oxidation (redox) cycling of Ni-based electrodes for solid oxide fuel/electrolysis cell irreversibly alters their microstructure and can cause the fracture of the electrolyte. Non-destructive 3-D imaging techniques enable tracking the microstructural changes that occur during the cycling [1]. Despite the recent advances, the understanding of how local 3-D geometrical features in the heterogeneous electrode material contribute to the material degradation remains incomplete. Absorption contrast X-ray nanotomography (XNT) of a same Ni(O)-yttria-stabilized zirconia (YSZ) sample was performed at the NiO K-edge white-line peak (8348 eV), before and after exposure to air at 800°C during 45 minutes. A complimentary XNT at 8376 eV confirmed a degree of oxidation in the range of 98%. The morphology of the Ni(O) phase was as expected completely different after re-oxidation. The spatial resolution in the range of 20 nm [2] further enabled the detection of cracks in the brittle YSZ phase. 3-D local curvature measurements were first performed to identify and characterize the crack initiation sites. Then, the capabilities of simple fracture mechanics models combined with curvature measurements were tested in the view of rapidly pinpointing the locations vulnerable to redox cycling. Finally, the detrimental effects of the cracks on the effective 3-D transport pathways in the Ni-YSZ anode under polarization was investigated using a skeleton-based discrete representation of the imaged volume and an analytical electrochemical fin model [3]. Topological properties, effective ionic conductivity and polarization resistance were calculated before and after oxidation. For the latter estimate, the effect of cracked YSZ network was considered first alone; that of the spatial re-distribution of triple-phase boundaries induced by re-oxidation will be included in the future. [1] A. M. Kiss, W. M. Harris, S. Wang, J. Vila-Comamala, A. Deriy and W. K. S. Chiu, Applied Physics Letters 102 (2013) 053902. [2] J. Vila-Comamala, Y. Pan, J. J. Lombardo, W. M. Harris, W. K. S. Chiu, C. David, Y. Wang, J. Synchrotron Rad. 19 (2012), 705–709. [3] G. J. Nelson, A. Nakajo, B. N. Cassenti, M. B. DeGostin, K. R. Bagshaw, A A. Peracchio, G. Xiao, S. Wang, F. Chen, W. K. S. Chiu, Journal of Power Sources 246 (2014) 322-334.

Local curvature measurements of a lean, partially premixed swirl-stabilised flame

A swirl-stabilised, lean, partially premixed combustor operating at atmospheric conditions has been used to investigate the local curvature distributions in lifted, stable and thermoacoustically oscillating CH4-air partially premixed flames for bulk cold-flow Reynolds numbers of 15,000 and 23,000. Single-shot OH planar laser-induced fluorescence has been used to capture instantaneous images of these three different flame types. Use of binary thresholding to identify the reactant and product regions in the OH planar laser-induced fluorescence images, in order to extract accurate flame-front locations, is shown to be unsatisfactory for the examined flames. The Canny-Deriche edge detection filter has also been examined and is seen to still leave an unacceptable quantity of artificial flame-fronts. A novel approach has been developed for image analysis where a combination of a non-linear diffusion filter, Sobel gradient and threshold-based curve elimination routines have been used to extract traces of the flame-front to obtain local curvature distributions. A visual comparison of the effectiveness of flame-front identification is made between the novel approach, the threshold binarisation filter and the Canny-Deriche filter. The novel approach appears to most accurately identify the flame-fronts. Example histograms of the curvature for six flame conditions and of the total image area are presented and are found to have a broader range of local flame curvatures for increasing bulk Reynolds numbers. Significantly positive values of mean curvature and marginally positive values of skewness of the histogram have been measured for one lifted flame case, but this is generally accounted for by the effect of flame brush curvature. The mean local flame-front curvature reduces with increasing axial distance from the burner exit plane for all flame types. These changes are more pronounced in the lifted flames but are marginal for the thermoacoustically oscillating flames. It is concluded that additional fuel mixture fraction and velocimetry studies are required to examine whether processes such as the degree of partial-premixedness close to the burner exit plane, the velocity field and the turbulence field have a strong correlation with the curvature characteristics of the investigated flames.

Ultra-sensitive, highly reproducible film stress characterization using flexible suspended thin silicon plates and local curvature measurements

Film stress is crucial for stringent MEMS/NEMS design. In this paper, novel micromachined flexible suspended thin silicon plates combined with a sub-nanometer optical interferometry measuring setup have been developed to detect stresses in nanometer-scale films as well as ultra low stresses in thin films. By measuring the local out-of-plane curvature of a thin silicon substrate of 15 µm, a bending sensitivity two orders larger than that of the wafer curvature method has been achieved. Residual stresses in LPCVD Si3N4 thin films are measured, which are in good agreement with those extracted by other methods. Since non-contact optical instruments are used to detect all the parameters and the boundary conditions are well characterized, reproducibility better than 1% has been realized. By reusing the testing structures, residual stresses in sputtered metal films are also determined, which vary in a broad range. A stress difference as small as 1.5 MPa within a 30 nm film can be resolved with this metrology, which is among the best in the present reports.

Implementing the Automatic Generation of 3D Statistical Shape Models with ITK

Statistical Shape Models are a popular method for segmenting three-dimensional medical images. To obtain the required landmark correspondences, various automatic approaches have been proposed. In this work, we present an improved version of minimizing the description length (MDL) of the model. To initialize the algorithm, we describe a method to distribute landmarks on the training shapes using a conformal parameterization function. Then, we introduce a novel procedure to modify landmark positions locally without disturbing established correspondences. We employ a gradient descent optimization to minimize the MDL cost function, speeding up automatic model building by several orders of magnitude when compared to the original MDL approach. The necessary gradient information is estimated from a singular value decomposition, a more accurate technique to calculate the PCA than the commonly used eigendecomposition of the covariance matrix. In this work, we first present a basic version where spatial locations are used in the MDL cost function; next, we introduce an extended version where any combination of features can be used as a metric. As an example application, we present results based on local curvature measurements. Finally, we present results for synthetic and real-world datasets demonstrating the efficiency of our procedures and give details about the implementation using the Insight Toolkit (ITK).

Three-dimensional skeletonization for computer-assisted treatment planning in radiosurgery

This paper describes a new algorithm for skeletonization of two- (2D) and three-dimensional (3D) objects based on ridge extraction. Ridges are formed when grassfire fronts collapse during grassfire propagation and they correspond to the locus of skeleton. The iso-distance contours/surfaces of a distance map are analogous to the grassfire fronts. They are locally smooth everywhere except at ridge locations. The new skeletonization algorithm extracts these ridge points based on local curvature measurement and is rotational invariant. It requires one scan of the image for curvature detection in any dimension, and is much faster than thinning methods. Connectivity checks are not required and the algorithm is extensible to higher dimensions. Our 3D skeletonization method is used in a novel algorithm to guide computerized planning of radiosurgical treatment of brain tumors.

Morphometric measurement of local curvature of the alveolar ducts in lung mechanics.

We have performed partial serial reconstructions of an acinus of the rabbit lung and determined the apparent existence of numerous heterogeneities in length, diameter, and local curvature in individual generation branches of the lung. We believe that structural changes during respiratory movements may include changes in the length and diameter of the whole duct. Alveoli are seen to be side differentiations secondary to the ducts in the gas-exchanging parenchyma of the rabbit lung. We have developed a technique for measuring local curvature in simple reconstructed ducts from the average of the integral curvation of the section contour. The contour curvature is measured from the chain code representation of the sampled contour from digital image analysis. The stereological requirements of an unbiased and random selection of contours is approached here by the random orientation of the individual alveoli of a single duct. Over 700 sections through the last four airway generations (alveolar ducts) at 3-micron intervals were analyzed. The average integral curvature ranges from 7.7 to 9.5 (mean 8.9) mm-1 for sixth- and seventh-generation branches from the start with volumes for the segments from 0.022 to 1.198 (mean 0.497) mm3.