Multi-parameter identification of gratings measurement by Experimental Ray Tracing

2021 ◽  
Vol 21 (11) ◽  
pp. 283
Author(s):  
Li-Si Chen ◽  
Zhong-Wen Hu ◽  
Hai-Jiao Jiang ◽  
Hui-Min Kang ◽  
Chen-Zhong Wang

Abstract A simple method for measuring grating groove density as well as its position and orientation is proposed based on the idea of ERT (Experimental Ray Tracing). Conventional methods only measure grating groove density with accuracy limited by its rotary stage and goniometer. The method proposed in the paper utilizes linear guides which could be calibrated to much higher accuracy. It is applicable to gratings of arbitrary surface profile or mosaic of a group of various gratings. Various measurement error sources are simulated by the Monte Carlo method and the results show high accuracy capability of grating parameters identification. A verification testing is performed. The accuracy dependency on main configuration parameters is evaluated. A method to expand measurement range by double wavelength is also discussed.

2006 ◽  
Vol 128 (9) ◽  
pp. 945-952 ◽  
Author(s):  
Sandip Mazumder

Two different algorithms to accelerate ray tracing in surface-to-surface radiation Monte Carlo calculations are investigated. The first algorithm is the well-known binary spatial partitioning (BSP) algorithm, which recursively bisects the computational domain into a set of hierarchically linked boxes that are then made use of to narrow down the number of ray-surface intersection calculations. The second algorithm is the volume-by-volume advancement (VVA) algorithm. This algorithm is new and employs the volumetric mesh to advance the ray through the computational domain until a legitimate intersection point is found. The algorithms are tested for two classical problems, namely an open box, and a box in a box, in both two-dimensional (2D) and three-dimensional (3D) geometries with various mesh sizes. Both algorithms are found to result in orders of magnitude gains in computational efficiency over direct calculations that do not employ any acceleration strategy. For three-dimensional geometries, the VVA algorithm is found to be clearly superior to BSP, particularly for cases with obstructions within the computational domain. For two-dimensional geometries, the VVA algorithm is found to be superior to the BSP algorithm only when obstructions are present and are densely packed.


Author(s):  
Barton L. Smith ◽  
William L. Oberkampf

Measurement uncertainty of quantities that are functions of more than one measured variable are usually determined using propagation methods; either the Taylor Series Method or the Monte Carlo Method. Each of these requires critical assumptions that are more sweeping and potentially dangerous than commonly realized. The implications of these assumptions is explained along with some examples of how violation of these assumptions invalidates the uncertainty estimate. A new perspective based on consideration of potential error sources is presented ranging from the physical system being measured, the measurement system, the data reduction system, to the final experimental measurement result. An alternative approach that relies on sampling of error sources, whether known or unknown, is demonstrated through several examples. These examples demonstrate that the alternative approach can provide a more realistic estimate of total experimental uncertainty; one which is commonly much larger than that provided by traditional propagation methods.


Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. V83-V97 ◽  
Author(s):  
Yongna Jia ◽  
Siwei Yu ◽  
Jianwei Ma

Acquisition technology advances, as well as the exploration of geologically complex areas, are pushing the quantity of data to be analyzed into the “big-data” era. In our related work, we found that a machine-learning method based on support vector regression (SVR) for seismic data intelligent interpolation can fully use large data as training data and can eliminate certain prior assumptions in the existing methods, such as linear events, sparsity, or low rank. However, immense training sets not only encompass high redundancy but also result in considerable computational costs, especially for high-dimensional seismic data. We have developed a criterion based on the Monte Carlo method for the intelligent reduction of training sets. For seismic data, pixel values in each local patch can be regarded as a set of statistical data and a variance value for the patch can be calculated. A high variance means that there are events centered around its corresponding patch or the pixel values in the patch range obviously. The patches with high variances are regarded as more representative patches. The Monte Carlo method assigns the variance as constraint and selects only the representative patches with a higher probability through a series of random positive numbers. After the training set is intelligently reduced through the Monte Carlo method, only these representative patches, constituting the new training set, are input to the SVR-based machine learning frame to construct a continuous regression model. Meanwhile, the patches with lower variances can be readily interpolated using a simple method and only present a minor influence in the construction of the regression model. Thus, the representative patches are called effective patches. Finally, the missing traces can be generated from the learned regression model. Numerical illustrations on 2D seismic data and results on 3D or 5D data show that the Monte Carlo method can intelligently select the effective patches as the new training set, which greatly decreases redundancy and also keeps the reconstruction quality.


Author(s):  
С.А. Желтов ◽  
Н.Н. Чупятов

Процесс нанесения покрытий на поверхности является одним из важнейших при нанесении защитных слоев. Особенно актуальным является метод молекулярно-лучевой эпитаксии, который применяют, например, для нанесения покрытий металлов и полимеров на металлические поверхности. Однако при производстве установок необходимо провести много предварительных экспериментов для получения максимально однородных напыленных поверхностей: размеры кювет, уровень расплава в кювете, расстояния до напыляемой поверхности и расположения системы кювет. Упрощением проведения этих реальных экспериментов является метод Монте-Карло. Моделируя компьютерные эксперименты с предполагаемыми параметрами установки, можно быстро получить необходимый результат с высокой точностью. В каждом компьютерном эксперименте разыгрывался вылет N = 108 частиц (атомов, молекул), что обеспечивало получение всех результатов с высокой точностью. Было установлено, что результаты расчетов не зависят от масс частиц. Анализ полученных данных позволил установить, что частицы, испарявшиеся с поверхности расплава по равновероятному закону и по закону косинуса, имеют близкие распределения, отличающиеся не более чем на 10%. Увеличение расстояния от верхнего края пластины до напыляемой плоскости с расстояния G = 0,01 м до расстояния G = 0,05 м приводит к тому, что плотность распределения для первого случая, имеющая значительный максимум около середины кюветы, становится практически равномерным распределением во втором случае. Применение метода Монте-Карло для процессов напыления в вакууме эффективно использовать не только для плоских поверхностей, но и на поверхности произвольных форм, например, цилиндрических. The coating process on surfaces is one of the most important in the application of protective layers. Particularly relevant is the method of molecular beam epitaxy, which is used, for example, for the deposition of coatings of metals and polymers on metal surfaces. However, in the manufacture of installations, it is necessary to carry out many preliminary experiments to obtain the most homogeneous sprayed surfaces: the dimensions of the cuvettes, the level of the melt in the cuvette, the distance to the sprayed surface and the location of the cuvette system. A simplification of these real-world experiments is the Monte Carlo method. By simulating computer experiments with the expected parameters of the installation, it is possible to quickly obtain the required result with high accuracy. In each computer experiment, the emission of N = 108 particles (atoms, molecules) was played, which ensured obtaining all results with high accuracy. It was found that the calculation results do not depend on the particle masses. An analysis of the data obtained made it possible to establish that the particles evaporated from the surface of the melt according to the equiprobable law and according to the cosine law have similar distributions differing by no more than 10%. An increase in the distance from the upper edge of the plate to the sprayed plane from a distance of G = 0.01 m to a distance of G = 0.05 m leads to the fact that the distribution density for the first case, which has a significant maximum near the middle of the cell, becomes an almost uniform distribution in the second case. ... The use of the Monte Carlo method for vacuum deposition processes can be effectively used not only for flat surfaces, but also on surfaces of arbitrary shapes, for example, cylindrical ones.


2020 ◽  
Vol 2020 (4) ◽  
pp. 25-32
Author(s):  
Viktor Zheltov ◽  
Viktor Chembaev

The article has considered the calculation of the unified glare rating (UGR) based on the luminance spatial-angular distribution (LSAD). The method of local estimations of the Monte Carlo method is proposed as a method for modeling LSAD. On the basis of LSAD, it becomes possible to evaluate the quality of lighting by many criteria, including the generally accepted UGR. UGR allows preliminary assessment of the level of comfort for performing a visual task in a lighting system. A new method of "pixel-by-pixel" calculation of UGR based on LSAD is proposed.


Author(s):  
V.A. Mironov ◽  
S.A. Peretokin ◽  
K.V. Simonov

The article is a continuation of the software research to perform probabilistic seismic hazard analysis (PSHA) as one of the main stages in engineering seismic surveys. The article provides an overview of modern software for PSHA based on the Monte Carlo method, describes in detail the work of foreign programs OpenQuake Engine and EqHaz. A test calculation of seismic hazard was carried out to compare the functionality of domestic and foreign software.


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