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In this paper, the cracking of concrete cover caused by steel bar corrosion was discussed and studied based on the three-period model of steel bar corrosion in concrete. In the analysis, the contour of the corrosion layer was simplified into a semi-ellipse according to the non-uniformity of steel bars in reinforced concrete under a natural environment. The steel bar corrosion was divided into three different periods by two corrosion points, namely, the void to be filled was exactly filled and the concrete cover was exactly cracked. Different assumptions are made for each corrosion period. Before the concrete cover cracks, it is developed into an elastic plate. Based on the theory of elastic mechanics, the maximum corrosion depth of steel bar when concrete cover cracks is predicted. After the concrete cover cracks, a model of the relationship between the crack width of the concrete cover and the maximum corrosion depth of steel bar was established by considering the filling of cracks by corrosion products. The rationality of the model was tested by employing experimental data from the literature, and it was found that the calculated value of the model was in good agreement with the experimental data in the literature.

We present a novel thin head atomic force microscope (AFM) that can be easily integrated with an upright optical microscope (OM). The optical beam detection unit in the AFM used an obliquely incident laser beam onto the cantilever, reducing the AFM head’s effective thickness to 7.3 mm. That allows an open space above the cantilever probe to accommodate the objective lens up to 0.6 numerical aperture (N.A.) without obstruction. A multi-function digital controller was developed to control the AFM and reserved interfaces to communicate with the OM. To assess the performance of the developed AFM, we first measured the noise level and bandwidths of the AFM system. Then, the imaging quality of the AFM was evaluated by both calibration grids and two-dimensional materials. Finally, the thin head AFM was integrated into a homemade white light interferometer as a demonstration of combined use with an advanced optical system. The experimental results demonstrated that our developed AFM is suitable for integration under upright OM and brings AFM high-resolution advantages to the existing OM system.

This paper proposed a multi-scale measurement methodology for turbine blade, which is able to evaluate the geometrical features of turbine surface in different scales. A turbine blade measurement system is designed by using LED illuminators in this work. To ensure the efficiency and the accuracy of our system during the scale transition, a fast light source calibration method is introduced with a special designed calibration target, where with only one camera snapshot, the position and the orientation of a LED can be calibrated precisely and simultaneously. A surface reconstruction algorithm via iteration is improved by analyzing the LED radiant intensity distribution. The simulation is carried out with a synthetic hyperboloid structure, where the root mean square error (RMSE) of rebuilding is lower than 1.7 µm, and the mean angular error(MAE) of normal estimation is 0.5°. System calibration is performed by using a USAF 1951 calibration target with 3 different scales with the minimum deviation below 4 µm. Experiments are implemented on the concave and the tenon of a turbine blade from civil aero engine, where the profile, the size of the cooling hole and the roughness are retrieved successfully in different scales, which shows the great potential of the proposed methodology in blade inspection applications.

As an important ultra-precision measurement method, white light interferometry is widely used in 3D measurements with nanometer resolution. In this paper, a white light interferometer is designed with a random phase noise insensitive algorithm. A discrete interferogram is established by analyzing the phase noise, which is modelized by the combination of random noise and systematic deviation. After Fourier analysis, the mathematical expression of the discrete interferogram in frequency domain is derived, where the random noise can be estimated by least square method and then be corrected. As a result, a more accurate relationship between phase distribution and surface height is established. To set up an stable system, the scanner of white light interferometer is driven by a precision step motor with scanning range 100 mm, and the travel range of the object stage in x and y directions is 60 mm. In the experiment, a step height standard (VLSI, 182.7±2.0 nm) and the end face of a multi-mode optical fiber are tested, where the repeatability error for the step height is less than 0.28%, which proves the measurement accuracy and robustness of the system.

We proposed and experimentally demonstrate a calibration method to estimate the position and the orientation of the anisotropic near point LED light source from a single view. In this work, a Lambertian sphere is used as the calibration target, where the reflection model of the Lambertian sphere under the illumination of LED with given radiant intensity distribution is analyzed theoretically to establish the relationship between the recorded image intensity and the observed surface. Based on this relationship, the geometrical principle of the calibration is researched and an iteration method is presented to calculate the LED position and orientation with a cost function through minimizing the estimation error. The accuracy of the proposed method is verified by simulations with the mean estimation error lower than 5.8mm and 1.7deg for near field lighting. The experiments are performed by measuring the plaster models using the presented system, which proves the effectiveness of the proposed calibration approach.

In this paper, a calibration method for non-isotropic point light source is developed, which is capable of calibrating position and orientation of the point light source with a single image synchronously. Based on the bidirectional reflectance distribution function (BRDF), the relationship between the shape of observed surface and the recorded grayscale image is firstly investigated in a more accurate way. Based on this model, a cost function is proposed to evaluate the estimation error, and a new cumulative, error-free iteration method is designed to recursively estimate the point light source parameters. The average simulation rebuilding root mean square error (RMSE) is below 0.9. The experiments are performed by calibrating a point light source in a photometric stereo measurement system, and the corresponding RMSE is below 1.2 in the unit of grayscale. Further analysis shows one image is enough to achieve the precision calibration using our proposed method.

When Gini coefficients are decomposed by class (e.g. occupation, sex, region, and so on, it is possible to examine how income inequality can be measured by its class components: intra-class, inter-class and overlapped. In the literature, there have been many studies on the decomposition methodology but most methods are either inflexible or too onerous for empirical analysis. This paper develops a new approach to overcome the shortcomings of existing studies. An example using the most recent Chinese rural income data is provided to demonstrate how this method can be applied to study regional income inequality.