scholarly journals Engineering Aspheric Liquid Crystal Lenses by Using the Transmission Electrode Technique

Crystals ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. 835
Author(s):  
José Francisco Algorri ◽  
Dimitrios C. Zografopoulos ◽  
Luis Rodríguez-Cobo ◽  
José Manuel Sánchez-Pena ◽  
José Miguel López-Higuera
Keyword(s):  
Liquid Crystal ◽  
Numerical Simulations ◽  
Least Squares ◽  
Least Squares Method ◽  
Electric Circuit ◽  
Equivalent Electric Circuit ◽  
Novel Technique ◽  
Analytical Expressions ◽  
Manufacturing Parameters ◽  
Electrode Technique

The transmission electrode technique has been recently proposed as a versatile method to obtain various types of liquid-crystal (LC) lenses. In this work, an equivalent electric circuit and new analytical expressions based on this technique are developed. In addition, novel electrode shapes are proposed in order to generate different phase profiles. The analytical expressions depend on manufacturing parameters that have been optimized by using the least squares method. Thanks to the proposed design equations and the associated optimization, the feasibility of engineering any kind of aspheric LC lenses is demonstrated, which is key to obtain aberration-free lenses. The results are compared to numerical simulations validating the proposed equations. This novel technique, in combination with the proposed design equations, opens a new path for the design and fabrication of LC lenses and even other types of adaptive-focus lenses based on voltage control.

An efficient algorithm for incommensurate structure refinement

1987 ◽  
Vol 20 (1) ◽  
pp. 57-59 ◽  
Author(s):  
W. A. Paciorek ◽  
I. Uszynski
Keyword(s):  
Least Squares ◽  
Structure Factor ◽  
Efficient Algorithm ◽  
Least Squares Method ◽  
Structure Refinement ◽  
Partial Derivatives ◽  
Incommensurate Structure ◽  
Crystallographic Symmetry ◽  
Incommensurate Structures ◽  
Analytical Expressions

A least-squares algorithm to refine incommensurate structures in the framework of (3 + 1)-dimensional crystallographic symmetry is described in some detail. It is applicable to the cases of occupational and/or harmonic displacive modulation. Compact analytical expressions for the structure factor and its partial derivatives well suited for structure refinement by the least-squares method have been obtained. The efficiency of the algorithm is discussed.

Least squares method for liquid crystal display characterization

2017 ◽  
Vol 56 (5) ◽  
pp. 1438 ◽  
Author(s):  
Dafne Amaya ◽  
Daniel Actis ◽  
Gonzalo Rumi ◽  
Alberto Lencina
Keyword(s):  
Liquid Crystal ◽  
Least Squares ◽  
Least Squares Method ◽  
Liquid Crystal Display

‘Least squares’ method—theorem or law?

1980 ◽  
Vol 59 (9) ◽  
pp. 8
Author(s):  
D.E. Turnbull
Keyword(s):  
Least Squares ◽  
Least Squares Method

An Augmented Iteratively Re-weighted and Refined Least Squares Method for lp Minimization Problem in Inverse Modeling of Potential Field Magnetic Data

2020 ◽  
Vol 1 (3) ◽  
Author(s):  
Maysam Abedi
Keyword(s):  
Magnetic Field ◽  
Magnetic Susceptibility ◽  
Least Squares ◽  
Minimization Problem ◽  
Potential Field ◽  
Field Data ◽  
Least Squares Method ◽  
Porphyry Copper ◽  
Magnetic Data ◽  
Magnetic Field Data

The presented work examines application of an Augmented Iteratively Re-weighted and Refined Least Squares method (AIRRLS) to construct a 3D magnetic susceptibility property from potential field magnetic anomalies. This algorithm replaces an lp minimization problem by a sequence of weighted linear systems in which the retrieved magnetic susceptibility model is successively converged to an optimum solution, while the regularization parameter is the stopping iteration numbers. To avoid the natural tendency of causative magnetic sources to concentrate at shallow depth, a prior depth weighting function is incorporated in the original formulation of the objective function. The speed of lp minimization problem is increased by inserting a pre-conditioner conjugate gradient method (PCCG) to solve the central system of equation in cases of large scale magnetic field data. It is assumed that there is no remanent magnetization since this study focuses on inversion of a geological structure with low magnetic susceptibility property. The method is applied on a multi-source noise-corrupted synthetic magnetic field data to demonstrate its suitability for 3D inversion, and then is applied to a real data pertaining to a geologically plausible porphyry copper unit.  The real case study located in  Semnan province of  Iran  consists  of  an arc-shaped  porphyry  andesite  covered  by  sedimentary  units  which  may  have  potential  of  mineral  occurrences, especially  porphyry copper. It is demonstrated that such structure extends down at depth, and consequently exploratory drilling is highly recommended for acquiring more pieces of information about its potential for ore-bearing mineralization.

МАКРОМОДЕЛИРОВАНИЕ СХЕМЫ ФАПЧ С ИСПОЛЬЗОВАНИЕМ ПОЛНОЙ ПРИНЦИПИАЛЬНОЙ СХЕМЫ ФАЗОВОГО ДЕТЕКТОРА

2020 ◽  
Vol 96 (3s) ◽  
pp. 295-299
Author(s):  
М.М. Гурарий ◽  
М.М. Жаров ◽  
Л.П. Ионов ◽  
И.И. Мухин ◽  
С.Г. Русаков ◽  
...  
Keyword(s):  
Electric Circuit ◽  
Schematic Diagram ◽  
Equivalent Electric Circuit ◽  
Phase Frequency Detector ◽  
Frequency Detector ◽  
A Current

В работе рассмотрены проблемы анализа схем ФАПЧ с учетом наличия неидеальностей в схеме частотно-фазового детектора с токовым ключом. Для снижения затрат на моделирование предложено использовать эквивалентную электрическую схему, содержащую полную принципиальную схему ЧФД и схемные эквиваленты макромоделей остальных блоков ФАПЧ. The paper considers the problems of analyzing the PLL circuit taking into account the presence of nonidealities in the phase-frequency detector with a current key. To reduce the simulation efforts, it has been proposed to apply an equivalent electric circuit containing the complete schematic diagram of the PFD and circuit equivalents of the macromodels of other PLL blocks.

Theoretical accuracy of the last squares method in the isotope dilution analysis

1984 ◽  
Vol 49 (4) ◽  
pp. 805-820
Author(s):  
Ján Klas
Keyword(s):  
Least Squares ◽  
Isotope Dilution ◽  
Least Squares Method ◽  
Isotope Dilution Analysis ◽  
Straight Line ◽  
The One ◽  
Two Parameter ◽  
Theoretical Accuracy

The accuracy of the least squares method in the isotope dilution analysis is studied using two models, viz a model of a two-parameter straight line and a model of a one-parameter straight line.The equations for the direct and the inverse isotope dilution methods are transformed into linear coordinates, and the intercept and slope of the two-parameter straight line and the slope of the one-parameter straight line are evaluated and treated.

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