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Minimizing the Bright/Shadow Focal Spot Size with Controlled Side-Lobe Increase in High-Numerical-Aperture Focusing Systems
S. N. Khonina,S. G. Volotovskiy
Advances in Optical Technologies , 2013, DOI: 10.1155/2013/267684
Abstract: Minimizing the bright/shadow focal spot size for differently polarized incident waves through the additional apodization of the focusing system output pupil by use of an optical element with the vortex phase dependence on angle and the polynomial amplitude dependence on radius is studied. The coefficients of the radial polynomial were optimized with the aim of fulfilling certain conditions such as the energy efficiency preservation and keeping the side lobes under control. The coefficients were chosen so as to minimize the functional using Brent’s method. 1. Introduction Recent years have seen the publication of a large number of articles dealing with obtaining a smaller transverse size of the focal spot using a high focusing system [1–5]. The smallest transverse size of the focal spot has been obtained for a radially polarized beam in which the longitudinal component makes the maximal contribution to the total intensity. There is a variety of techniques to gain the contribution of the longitudinal component to the total intensity, including the use of an annular aperture which allows only the peripheral part of radiation to pass through the lens [1, 2] and the use of additional phase optical elements, which provides a higher energy efficiency [3–5]. However, this study is concerned with not simply controlling the contribution of different electric field components into the focal spot region [5], but rather minimizing the (bright/dark) focal spot size by optimally selecting the pupil’s transmission function. In [6], it was proposed that the focal spot formed by a high focusing system should be reduced in size using radially polarized Laguerre-Gauss modes of higher radial order, devoid of vortex phase component. The positive role of the vortex phase function which allows obtaining a smaller focal spot in individual components of the sharply focused electric field at different polarization types was analyzed in [4], whereas the possibility of obtaining a smaller focal spot in terms of total intensity by introducing additional variations of radius was shown in [5]. The use of the transmission functions in the form of Zernike polynomials, including those containing vortex phase dependence, was considered in [7]. Thus, it has become possible to simultaneously introduce vortex phase dependence and amplitude variations on radius. Note that it has also been shown that it is possible to reduce not only the bright spot but the shadow region as well. In areas such as optical trapping and micromanipulation [8], STED-microscopy [9], and shadow microscopy [10], there
Analyzing the Symmetry Properties of a Distribution in the Focal Plane for a Focusing Element with Periodic Angle Dependence of Phase
Svetlana N. Khonina,Andrey V. Ustinov
Advances in Optical Technologies , 2012, DOI: 10.1155/2012/918298
Abstract: We analyze the symmetry properties of the focal plane distribution when light is focused with an element characterized by a periodic angular dependent phase, sin ( ) or cos ( ). The majority of wave aberrations can be described using the said phase function. The focal distribution is analytically shown to be a real function at odd values of m, which provides a simple technique for generating designed wave aberrations by means of binary diffractive optical elements. Such a possibility may prove useful in tight focusing, as the presence of definite wave aberrations allows the focal spot size to be decreased. The analytical computations are illustrated by the numerical simulation, which shows that by varying the radial parameters the focal spot configuration can be varied, whereas the central part symmetry is mainly determined by the parity of m: for even the symmetry order is 2m and for odd is m. 1. Introduction Various aberrations in the focusing system are known to result in a wider, distorted focal spot with disturbed axial symmetry [1]. Such an effect is normally considered to be a negative factor. However, it has been shown [2, 3] that some types of wave aberrations enable the central focal spot size to be decreased, providing tight focusing. Note that while only primary (axisymmetric) aberrations were dealt with in [2], aberrations associated with vortex phase components on the basis of Zernike polynomials were also discussed in [3]. In Zernike polynomials, the radius dependence is polynomial and the angle dependence is trigonometric (periodic). Optical elements characterized by periodic angular changes were considered in [4, 5]. In [4], such an element was shown to form the zero central intensity, whereas [5] also looked into diffraction-free properties of the generated light beams. Based on the decomposition of a cosine angular dependent phase function in terms of angular harmonics, the transmission function was shown [5] to produce a diffraction pattern composed of light spots arranged on a circumference. The coaxial interference of two vortex beams with identical topological charges and opposite signs was shown to produce a similar result [6, 7]. At the same time, the odd-order aberrations, such as distortion and coma, have been known to appear in distribution patterns with odd symmetry [1, 8, 9]. In particular, the presence of coma ( ) results in distributions with the third-order symmetry [10], similar to the 2D Airy beams [11]. It was also shown that the product of three 1D Airy functions, rotated by the angle of 120° relative to each other
Sharper Focal Spot for a Radially Polarized Beam Using Ring Aperture with Phase Jump
Svetlana N. Khonina,Andrei V. Ustinov
Journal of Engineering , 2013, DOI: 10.1155/2013/512971
Abstract: We study analytically and numerically in which way the width of ring aperture containing a phase jump affects the size and intensity of the focal spot generated with a radially polarized beam. It is shown that by means of destructive interference of beams coming from the different-phase rings it becomes possible to overcome the scalar diffraction limit corresponding to the first zero of the zero-order Bessel function. The minimal focal spot size (FWHM ) is found to be attained when the annular aperture width amounts to 20% of the full-aperture radius. In this case, the side-lobe intensity is not larger than 30% of the central peak. A wider annular aperture with the phase jump introduced is also shown to form a focal spot not exceeding the diffraction limit for a narrow annular aperture, simultaneously providing a nearly six times higher intensity. In this case, the side lobes amount to 35% of the central peak. 1. Introduction A narrow annular pupil that blocks the light from propagating practically through the entire central part of the lens [1–3] is a simple, albeit low-efficiency technique to generate narrow-extended beams in the focal plane. More complicated techniques for the full-aperture apodization of the pupil’s function that employ both purely phase and amplitude-phase distributions have also been reported [4–9]. In this case, a tighter focal spot is normally obtained at a sacrifice of the energy redistribution from the central peak to the side lobes. This situation is in full compliance with the Toraldo di Francia theory [10], which states that the central focal spot can be made as small as one likes but at a sacrifice of increasing side lobes, which sometimes become several times [11], or even orders [8, 9], larger than the central peak. The presence of the substantial side lobes limits the use of “superresolution” elements in the imaging and optical data recording systems, in which the acceptable side-lobe level is 30% of the central peak [12]. The optimization procedures aimed at controlling the growth of the side lobes inevitably lead to a widened central spot [12, 13]. With the side lobes’ intensity being less than 30% of the central peak intensity, they can be filtered out [14] or leveled as a result of nonlinear light interaction with the recording medium [15]. The focal spot can be made tighter without an essential increase in the side lobes by introducing a radial phase jump which leads to the destructive interference between two light beams generated by each of the pupil’s rings [15, 16]. The destructive action of the π-phase jump is
Thin Light Tube Formation by Tightly Focused Azimuthally Polarized Light Beams
Svetlana N. Khonina,Andrey V. Ustinov
ISRN Optics , 2013, DOI: 10.1155/2013/185495
Abstract: Theoretical and numerical analysis of the transmission function of the focusing system with high numerical aperture was conducted. The purpose of the study was to form a thin light tube in a focal area using the azimuthally polarized radiation. It was analytically shown that, due to destructive interference of two beams formed by two narrow rings, it is possible to overcome not only the full aperture diffraction limit but also the circular aperture limit. In this case, however, the intensity at the center of the focal plane is significantly reduced, which practically leads to the tube rupture. It was numerically shown that long thin one-piece tubes may be formed through the aperture apodization with diffractive axicon phase function or with complex transmission function of Laguerre-Gaussian or Airy-Gaussian beams. 1. Introduction Introducing a narrow annular aperture to the tightly focused cylindrical beams with radial or azimuthal polarization, the blocking light in almost all central parts of the lens [1–3] is a simple but energetically expensive way of forming long narrow beams in the focal region. In the case of radial polarization a thin thread of light is formed, while in the azimuthal polarization a light tube is formed. Moreover, the transverse dimension corresponds to the scalar diffraction limit. In other types of polarization the focal spot (or ring) is larger because of the contribution of the various components of the electromagnetic field to the focal region. To increase the efficiency and overcome the diffraction limit more sophisticated ways of full aperture apodization of function are used. It can be either a pure phase or an amplitude-phase distribution [4–9]. Thus, as a rule, reducing the focal spot size is accompanied by the redistribution of energy from the central part to the sidelobes. This situation is consistent with the Toraldo di Francia theory [10], according to which possible to obtain infinitely narrow central spot due to the growth of sidelobes. But this growth is sometimes several times [8, 9] or even orders [11] higher than the reducing of central light spot. The presence of significant sidelobes limits the use of “super-resolution” elements in representing systems and optical data recording, when the acceptable intensity level in the sidelobes is less than 30% with respect to the central peak [12]. However, the optimization procedures controlling the growth of the sidelobes lead to the inevitable broadening of the central spot size [12, 13]. It was shown in [14] that the introduction of the radial phase jump on radians
Analysis of Instantaneous and Continuous Migration of Radionuclides from Disposal Facility  [PDF]
N. S. Mahmoud
Open Journal of Safety Science and Technology (OJSST) , 2011, DOI: 10.4236/ojsst.2011.11001
Abstract: Many disposal sites have been suffered from radionuclide release problems, which lead to land contamination. Various remediation procedures have been developed during the past decade. Selection of remediation techniques is dependant mainly on quantity and quality of radioactive contamination. For that reason, the understanding of the factors that control the degree of contamination of any land should be the start of this problem. The present work aimed to construct the base of a new mandatory chapter in the safety analysis report that discuss and predict quantatively and qualitively the possible release from disposal site. The objective of this chapter is to prevent, restrict, and/or remediate economically the contamination that can be occurred. In the present work, a generic disposal system was evaluated. The radio-elements, which can contaminate the area before their decays, are determined by a screening process. Knowing that the mode of radionuclide migration from a disposal site is one from the important factors that control the contamination problem; migration activity of the selected radionuclides is assessed by considering instantaneous and continuous modes release of radionuclides from the disposal site. Finally, the elementary analysis steps demonstrated in this study will be concluded as the proposed items in the new chapter.
Ionization of Metastable 2P-State Hydrogen Atoms by Electron Impact for Coplanar Asymmetric Geometry  [PDF]
S. Dhar, N. Nahar
Open Journal of Microphysics (OJM) , 2014, DOI: 10.4236/ojm.2014.44007
Abstract: The triple differential cross-sections of First Born approximation have been calculated for ionization of metastable 2P-state hydrogen atoms by electron impact in the asymmetric coplanar geometry. In this study a multiple scattering theory of ionization of hydrogen atoms is used. The latest results of the present method are compared with other calculations. It will be added for new experimental study of ionization of hydrogen atoms in their metastable states.
A Hybrid Associative Classification Model for Software Development Effort Estimation  [PDF]
S. Saraswathi, N. Kannan
Circuits and Systems (CS) , 2016, DOI: 10.4236/cs.2016.76071
Abstract: A mathematical model that makes use of data mining and soft computing techniques is proposed to estimate the software development effort. The proposed model works as follows: The parameters that have impact on the development effort are divided into groups based on the distribution of their values in the available dataset. The linguistic terms are identified for the divided groups using fuzzy functions, and the parameters are fuzzified. The fuzzified parameters then adopt associative classification for generating association rules. The association rules depict the parameters influencing the software development effort. As the number of parameters that influence the effort is more, a large number of rules get generated and can reduce the complexity, the generated rules are filtered with respect to the metrics, support and confidence, which measures the strength of the rule. Genetic algorithm is then employed for selecting set of rules with high quality to improve the accuracy of the model. The datasets such as Nasa93, Cocomo81, Desharnais, Maxwell, and Finnish-v2 are used for evaluating the proposed model, and various evaluation metrics such as Mean Magnitude of Relative Error, Mean Absolute Residuals, Shepperd and MacDonell’s Standardized Accuracy, Enhanced Standardized Accuracy and Effect Size are adopted to substantiate the effectiveness of the proposed methods. The results infer that the accuracy of the model is influenced by the metrics support, confidence, and the number of association rules considered for effort prediction.
Efficient Dynamic Economic Load Dispatch Using Parallel Process of Enhanced Optimization Approach  [PDF]
S. Hemavathi, N. Devarajan
Circuits and Systems (CS) , 2016, DOI: 10.4236/cs.2016.710278
Abstract: In Dynamic Economic Load Dispatch (DELD), optimization and evolution computation become a major part with the strategy for solving the issues. From various algorithms Differential Evolution (DE) and Particle Swarm Optimization (PSO) algorithms are used to encode in a vector form and in sharing information and both approaches are based on the master-apprentice mechanism for the Dual Evolution Strategy. In order to overcome the challenges like the clustering of PSO, optimization problems and maximum and minimum searching, a new approach is developed with the improvement of searching and efficient process. In this paper, an Enhanced Hybrid Differential Evolution and Particle Swarm Optimization (EHDE-PSO) is proposed with Dynamic Sigmoid Weight using parallel procedures. A hybrid form of the proposed approach combines the optimizing algorithm of Enhanced PSO with the Differential Evolution (DE) for the improvement of computation using parallel process. The implementation and the parallel process are analyzed and discussed to gather relevant data to show the performance enhancement which is better than the existing algorithm.
The Power of an Arbitral Tribunal to Determine Its Own Jurisdiction in International Commercial Arbitration  [PDF]
Patricia N. S. Kamanga
Beijing Law Review (BLR) , 2021, DOI: 10.4236/blr.2021.122021
Abstract: This article discusses the powers of an arbitral tribunal to determine its own jurisdiction. The determination of the question of the jurisdiction of a tribunal lies in its own domain at least in the first instance by virtue of the principle of competence-competence. The principle enables a tribunal to test its own jurisdiction and confirm the extent of its power. This is one of the pillars of arbitration as it promotes party autonomy. The positive aspect of this power of the tribunal is that it cures the excesses of jurisdiction or any lack of it by granting an objecting party with immediate remedy thereby saving costs and time. The downside of this power is that an objecting party may still be permitted under the English Act and the Model Law to revert to court during the proceedings if he is not happy. However, time is of the essence. The article rests on an accumulation of case law, current and secondary literature. It takes cognizance of the fact that parties to an arbitration agreement have, by virtue of their autonomy a choice of subjecting the arbitration proceedings to rules of arbitration. As such, this article uses the ICC Rules of Arbitration and the UNCITRAL Rules of Arbitration as reference sets of rules. An arbitral tribunal’s power to rule on its own jurisdiction is unique in the sense that it is a test of its jurisdiction. It is indeed an exceptional power as it helps define the extent a tribunal’s powers and therefore becomes its own judge when queried. This power is important as it enables the arbitration proceedings to progress as scheduled.
Beyond Biological Aging: Table Analysis  [PDF]
Jorge Barragán, Sebastián Sánchez
Advances in Aging Research (AAR) , 2022, DOI: 10.4236/aar.2022.112003
Abstract: Keeping in mind the relationship between the basal metabolic rate and the change in weight in the aging process, we propose to verify the holographic description of the same. For this we set ourselves the following objectives: Verify the correlation between total energy dissipation and energy dissipation per unit body mass, and verify the correlation between the total energy dissipation and the body mass. As a result of the data analysis, we obtained a coherent representation of our proposal. A high degree of correlation between the total energy dissipation in an organism and the basal metabolic rate/dry kg was found. Such a condition implies that the stated biological system satisfies the Holographic Principle.
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