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Rapid full-field surface topography measurement for large-scale wafers remains challenging due to limitations in speed, system complexity, and scalability. This work presents a interferometric system based on thin-film interference for high-precision wafer profiling. An optical flat serves as the reference surface, forming a parallel air-gap structure with the wafer under test. A large-aperture collimated beam is introduced via an off-axis parabolic mirror to generate high-contrast interference fringes across the entire field of view. Once the wafer is fully illuminated, topographic information is directly extracted from the fringe pattern. Comparative measurements with a commercial interferometer show relative deviations below 3% in bow and warp, confirming the system’s accuracy and stability. With its simple optical layout, low cost, and robust performance, the proposed method shows strong potential for industrial applications in wafer inspection and online surface monitoring.

For asymmetric laser beams, the values of beam quality factor M x 2 and M y 2 are inconsistent if one selects a different coordinate system or measures beam quality with different experimental conditionals, even when analyzing the same beam. To overcome this non-uniqueness, a new beam quality characterization method named as M2-curve is developed. The M2-curve not only contains the beam quality factor M x 2 and M y 2 in the x-direction and y-direction, respectively; but also introduces a curve of M x α 2 versus rotation angle α of coordinate axis. Moreover, we also present a real-time measurement method to demonstrate beam propagation factor M2-curve with a modified self-referencing Mach-Zehnder interferometer based-wavefront sensor (henceforth SRI-WFS). The feasibility of the proposed method is demonstrated with the theoretical analysis and experiment in multimode beams. The experimental results showed that the proposed measurement method is simple, fast, and a single-shot measurement procedure without movable parts.

At present, most wavefront sensing methods analyze the wavefront aberration from light intensity images taken in dark environments. However, in general conditions, these methods are limited due to the interference of various external light sources. In recent years, deep learning has achieved great success in the field of computer vision, and it has been widely used in the research of image classification and data fitting. Here, we apply deep learning algorithms to the interferometric system to detect wavefront under general conditions. This method can accurately extract the wavefront phase distribution and analyze aberrations, and it is verified by experiments that this method not only has higher measurement accuracy and faster calculation speed but also has good performance in the noisy environments.

A new operator named “probability metric” (PM) for defining the distance between random values or random vectors is proposed. Although the PM is a generalisation of the metric operator it does not satisfy the first metric axiom. Two particular forms of PM, for normal and uniform probability distributions are presented. Numerical example demonstrates the efficiency of PM in Shepard-Liszka approximation of residual stresses state discrete data, obtained from a strain gauge experiment. Possible applications of PM include fringe pattern analysis. The PM can be also employed in quantum mechanics issues to estimate the distance of two quantum particles expressed by their wave functions.

In conventional optical nondestructive evaluation (NDE) of structures using shearography or electronic speckle pattern interferometry (ESPI), results are typically provided in the form of fringe patterns or deformation contour plots. However, in order to fully automate the process of defect detection, it is desirable to obtain simpler results which are easier to interpret. We present here one such optical system based on additive–subtractive shearography/ESPI. This system processes additive–subtractive fringe patterns and provides the sizes and locations of defects such as disbonds in adhesively-bonded composite structures. This is achieved by exciting the structure under inspection using an acoustic stressing mechanism which sweeps a range of vibration frequencies of the structure. Since the defective areas of the structure have different mechanical properties from their neighboring regions, varying and complex fringe patterns are obtained at different stressing frequencies. We propose an algorithm which enables the automatic identification and selection of relevant additive–subtractive fringe patterns that pertain only to localized deformations associated with defects, and which excludes images that pertain to any overall modes of the entire structure. The algorithm also includes a pixel-by-pixel adjustable thresholding scheme which compensates for intensity variations due to nonuniform reflectivity from unpainted and dirty test objects. Morphological processing is then performed to extract the shapes of the defect from the processed fringe clusters. Various structures, from simple aluminum specimens with simulated defects to a complex honeycomb-based aviation repair patch specimen, have been successfully evaluated using this system.

In many optical metrology techniques, fringe pattern analysis is the central algorithm for recovering the underlying phase distribution from the recorded fringe patterns. Despite extensive research efforts for decades, how to extract the desired phase information, with the highest possible accuracy, from the minimum number of fringe patterns remains one of the most challenging open problems. Inspired by recent successes of deep learning techniques for computer vision and other applications, we demonstrate for the first time, to our knowledge, that the deep neural networks can be trained to perform fringe analysis, which substantially enhances the accuracy of phase demodulation from a single fringe pattern. The effectiveness of the proposed method is experimentally verified using carrier fringe patterns under the scenario of fringe projection profilometry. Experimental results demonstrate its superior performance, in terms of high accuracy and edge-preserving, over two representative single-frame techniques: Fourier transform profilometry and windowed Fourier transform profilometry.

The optical 3D surface measurement technique aligns the optical axis of the projector with that of the camera, enabling the measurement of objects with significant height variations, such as deep holes and grooves. This technique encodes the height of the object into the modulation of the fringe pattern, eliminating the requirement for phase unwrapping and avoiding issues such as shadow occlusion. To further enhance the noise reduction capability of fringe analysis and reconstruct objects with high-frequency detail, this paper introduces the two-dimensional generalized S-transform (2D-GST) method for modulation extraction. By incorporating two additional parameters p x and p y to adjust the resolution in the time domain/frequency domain, 2D-GST can provide higher reconstruction precision. The root mean square (RMS) for tested plane with 2D-GST is 4.35 μ m, whereas for the traditional 1D S-transform (1D-ST), the RMS is 4.97 μ m.

The rapid and significant expansion of urban areas is observed worldwide; however, considerable differences are detected within the characteristics of the process. The rural–urban fringe is changing most dynamically from the aspect of land use and this tends to be relevant in the case of post-socialist cities in Central Europe even with a stagnating or decreasing population. Debrecen (Hungary) and its hinterland adequately represent the migration trends of Hungarian cities and the great administrative area provided wide intra-urban suburbanization processes. The current study put the emphasis on the analysis of the spatial pattern of built-up areas and the distribution of residents. In order to discover the processes of the post-socialist transition period, detailed point layers were created to illustrate every built-up parcel in the rural–urban fringe of Debrecen (for the years 1980, 2000, and 2020). The most important characteristics were discovered with the help of GIS methods—Kernel-density, grid pattern analysis of the object density, and analysis of land cover/land use changes using Corine Land Cover Change (CLCC) databases. The dynamic and extended expansion of built-up areas was seen until 2000, in which the outskirts (including hobby gardens) densified spectacularly. The urban sprawl has been less intensive since the millennium and the increase in built-up areas has become more concentrated. As a consequence of the transition period, extended territories—primarily the least dense parts of the rural–urban fringe—are faced with the disappearance of buildings due to agricultural cultivation reasons.

Electronic speckle pattern interferometry (ESPI) is a non-contact, full field, real-time measurement technology, which judges the position and size of the internal defects of the object through the external deformation caused by the internal defects under certain loading conditions. We present the effect of loading mode and loading parameters to the defect detection. Firstly, the finite element analysis method is used to establish models to simulate the defect detection of aluminum plates under different loading conditions. Mechanical models are established to simulate different loading mode, loading sizes, defect depth and defect sizes. Secondly, the interpolation method based on partial differential equation is applied to obtain the whole field out-of-plane displacement after finite element analysis. Thirdly, by analyzing the interference fringe patterns obtained from the out-of-plane displacement caused by different defects, the deformation rules in the detection of internal defects of aluminum plates are obtained under different loading conditions. Finally, the loading mode and loading range suitable for the internal defect detection of aluminum materials are summarized. This method can provide a basis for the selection of loading mode and parameters in the ESPI experimental system.

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.