scholarly journals Off-axis Fresnel numbers in laser systems

2014 ◽  
Vol 2 ◽  
Author(s):  
Yudong Yao ◽  
Junyong Zhang ◽  
Yanli Zhang ◽  
Qunyu Bi ◽  
Jianqiang Zhu
Keyword(s):  
Correction Factor ◽  
Intensity Distribution ◽  
Physical Meaning ◽  
Analytical Formula ◽  
Numerical Calculations ◽  
Optical Systems ◽  
Circular Aperture ◽  
Fresnel Number ◽  
Laser Systems ◽  
Simple Analytical Formula

Abstract The physical meaning and essence of Fresnel numbers are discussed, and two definitions of these numbers for off-axis optical systems are proposed. The universal Fresnel number is found to be $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}N=(a^{2}/\lambda z ) \ast C_{1} +C_{2} $ . The Rayleigh–Sommerfeld nonparaxial diffraction formula states that a simple analytical formula for the nonparaxial intensity distribution after a circular aperture can be obtained. Theoretical derivations and numerical calculations reveal that the first correction factor $C_{1} $ is equal to $\cos \theta $ and the second factor $C_{2} $ is a function of the incident wavefront and the shape of the diffractive aperture. Finally, some diffraction phenomena in off-axis optical systems are explained by the off-axis Fresnel number.

Pre-Impact Configuration Designing of a Robot Manipulator for Impact Minimization

2017 ◽  
Vol 9 (3) ◽  
Author(s):  
Jingchen Hu ◽  
Tianshu Wang
Keyword(s):  
Impact Force ◽  
Robot Manipulator ◽  
Analytical Formula ◽  
Joint Space ◽  
Collision Problem ◽  
Spatial Operator ◽  
Inertia Ellipsoid ◽  
The Impact ◽  
Maximum Minimum ◽  
Simple Analytical Formula

This paper studies the collision problem of a robot manipulator and presents a method to minimize the impact force by pre-impact configuration designing. First, a general dynamic model of a robot manipulator capturing a target is established by spatial operator algebra (SOA) and a simple analytical formula of the impact force is obtained. Compared with former models proposed in literatures, this model has simpler form, wider range of applications, O(n) computation complexity, and the system Jacobian matrix can be provided as a production of the configuration matrix and the joint matrix. Second, this work utilizes the impulse ellipsoid to analyze the influence of the pre-impact configuration and the impact direction on the impact force. To illustrate the inertia message of each body in the joint space, a new concept of inertia quasi-ellipsoid (IQE) is introduced. We find that the impulse ellipsoid is constituted of the inertia ellipsoids of the robot manipulator and the target, while each inertia ellipsoid is composed of a series of inertia quasi-ellipsoids. When all inertia quasi-ellipsoids exhibit maximum (minimum) coupling, the impulse ellipsoid should be the flattest (roundest). Finally, this paper provides the analytical expression of the impulse ellipsoid, and the eigenvalues and eigenvectors are used as measurements to illustrate the size and direction of the impulse ellipsoid. With this measurement, the desired pre-impact configuration and the impact direction with minimum impact force can be easily solved. The validity and efficiency of this method are verified by a PUMA robot and a spatial robot.

Study of Fraunhofer Diffraction Pattern from a Circular Aperture Using an Optical Fiber Microprobe

2011 ◽  
Vol 378-379 ◽  
pp. 565-568
Author(s):  
Wan Maisarah Mukhtar ◽  
P. Susthitha Menon ◽  
Sahbudin Shaari
Keyword(s):  
Optical Fiber ◽  
Diffraction Pattern ◽  
Light Propagation ◽  
Optical Power ◽  
Transverse Motion ◽  
Circular Aperture ◽  
Fraunhofer Diffraction ◽  
Fresnel Number ◽  
Function Profile ◽  
Effect Of Light

Fraunhofer diffraction pattern from a circular aperture with the diameter of 10µm was observed using an optical fiber microprobe. The optical fiber microprobe started to detect optical power when the distance between the probe and the circular aperture was more than 292µm. When the probe was moved in a lateral motion, the light propagation showed a Bessel function profile. When the optical fiber microprobe was moved from 293µm to 309µm from the centre of the circular aperture in a transverse motion, the power detected was not consistent with a continuation of maxima and minima due to the effect of light propagation from the circular aperture. We also observed that the distance between the probe and the centre of the circular aperture was directly proportional with the radius of focused spot and inversely proportional with the Fresnel number.

scholarly journals Analytical Formula for the Ratio of Central to Minimum Film Thickness in a Circular EHL Contact

Lubricants ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 80 ◽  
Author(s):  
Petr Sperka ◽  
Ivan Krupka ◽  
Martin Hartl
Keyword(s):  
Experimental Data ◽  
Film Thickness ◽  
Analytical Formula ◽  
Numerical Calculations ◽  
Constant Ratio ◽  
Viscosity Coefficients ◽  
Wide Range ◽  
Minimum Film Thickness ◽  
Film Parameter ◽  
Ehl Contact

Prediction of minimum film thickness is often used in practice for calculation of film parameter to design machine operation in full film regime. It was reported several times that majority of prediction formulas cannot match experimental data in terms of minimum film thickness. These standard prediction formulas give almost constant ratio between central and minimum film thickness while numerical calculations show ratio which spans from 1 to more than 3 depending on M and L parameters. In this paper, an analytical formula of this ratio is presented for lubricants with various pressure–viscosity coefficients. The analytical formula is compared with optical interferometry measurements and differences are discussed. It allows better prediction, compared to standard formulas, of minimum film thickness for wide range of M and L parameters.

Influence of optimum balanced linear coma on disk spread functions

1978 ◽  
Vol 56 (1) ◽  
pp. 12-16
Author(s):  
A. K. Gupta ◽  
R. N. Singh ◽  
K. Singh
Keyword(s):  
Intensity Distribution ◽  
Point Spread Function ◽  
Optical Systems ◽  
Point Spread ◽  
Spread Function ◽  
Special Case ◽  
Optimum Balance

Disk spread functions are evaluated to study the performance of optical systems in the presence of linear coma. Optimum balance among various coma terms based on Strehl intensity criterion is used and the applicability of this balance to imaging of extended objects is examined. Graphical results of intensity distribution in the paraxial receiving plane for the diffraction images of extended circular targets for various sizes and azimuths are presented. Results for the point spread function in presence of optimum balanced linear coma come out as a special case and are also included.

Group Theoretic Approach to the Exponential Cosine Screened Coulomb Potential

1985 ◽  
Vol 40 (5) ◽  
pp. 453-455 ◽  
Author(s):  
Barnana Roy
Keyword(s):  
Perturbation Method ◽  
Coulomb Potential ◽  
Analytical Formula ◽  
Theoretic Approach ◽  
Energy Eigenvalues ◽  
Screened Coulomb Potential ◽  
Simple Analytical Formula

Perturbation method, using the properties of SO (2,1) algebra is applied to get a simple analytical formula for energy eigenvalues of the exponential cosine screened Coulomb potential.

Comparison between different proximity potentials and the double-folding model for spherical–deformed interacting nuclei

2016 ◽  
Vol 94 (1) ◽  
pp. 102-111 ◽  
Author(s):  
M. Ismail ◽  
I.A.M. Abdul-Magead
Keyword(s):  
Coulomb Barrier ◽  
Analytical Formula ◽  
Orientation Angle ◽  
Heavy Ion ◽  
Folding Model ◽  
Deformation Parameters ◽  
Double Folding Model ◽  
Double Folding ◽  
Coulomb Part ◽  
Simple Analytical Formula

The Coulomb barrier parameters have been calculated for a spherical–deformed interacting pair of nuclei using 14 different versions of the proximity approaches and a simple analytical formula for the Coulomb part of the heavy ion potential. The results of these proximity versions have been compared with more accurate results obtained from the double-folding model (DFM). We have considered the interacting pair 48Ca + 238Pu as an example and assumed the presence of the quadrupole, octupole, and hexadecapole deformation parameters for 238Pu. The orientation angle dependence of the Coulomb barrier parameters has been computed for different sets of deformation parameters. We found that the proximity types named Prox77, BW Prox91, AW Prox95, Bass Prox77, and Bass Prox80 are the best ones of the available 14 versions of the proximity approaches for calculating the nuclear part of the interaction potential for a spherical–deformed pair of nuclei.

Four-probe Magnetoresistance of Current-perpendicular-to-plane Structures

2005 ◽  
Vol 906 ◽  
Author(s):  
Hua Zhou ◽  
Mark W. Covington ◽  
Michael A. Seigler
Keyword(s):  
Finite Element ◽  
Current Flow ◽  
Three Dimensional ◽  
Analytical Formula ◽  
Unified Approach ◽  
Uniform Current ◽  
Current Perpendicular To Plane ◽  
Numerical Finite Element ◽  
Simple Analytical Formula ◽  
Probe Geometry

AbstractThe resistance and magnetoresistance (MR) of three-dimensional current-perpendicular-to-plane (CPP) structures have been calculated via numerical finite element solutions of the Laplace equation. This model accounts for the non-uniform current paths in a four-probe geometry that can yield MR that differs from the intrinsic MR of the isolated CPP pillar with spatially uniform current flow. We calculated the four-probe MR for various geometries and resistivities of both the normal metal leads and the magnetoresistive pillar. From a single, unified approach, we are able to consistently account for the disparate behavior that has been previously published. In particular, we identify conditions that produce four-probe MR that differs from the intrinsic MR of the CPP pillar and highlight those situations where the four-probe resistance is negative. Finally, we present a simple analytical formula for the MR ratio that is applicable to narrow CPP pillars with wide, thin leads.

An analytical formula for estimating the bending angle by laser forming

2006 ◽  
Vol 220 (2) ◽  
pp. 243-247 ◽  
Author(s):  
H Shen ◽  
Z Yao ◽  
Y Shi ◽  
J Hu
Keyword(s):  
Experimental Data ◽  
Solid Mechanics ◽  
Present Model ◽  
Analytical Formula ◽  
Laser Forming ◽  
Compatibility Conditions ◽  
Bending Angle ◽  
Metal Plates ◽  
External Forces ◽  
Simple Analytical Formula

Laser forming of metal plates offers the advantages of requiring no external forces and thus reduced cost and increased flexibility. It also enables forming of some materials and shapes that are impossible by using the traditional methods. Based on the conventional equilibrium and compatibility conditions used in solid mechanics, a simple analytical formula for predicting the bending angle is derived. The present model is compared with other models and available experimental data, from which the superiority of the present model is demonstrated.

An Analysis of Temporal Diffraction of a Chirped Femtosecond Laser Pulse by a Circle Aperture

2012 ◽  
Vol 263-266 ◽  
pp. 360-364
Author(s):  
Huai Sheng Wang
Keyword(s):  
Laser Pulse ◽  
Femtosecond Laser ◽  
Femtosecond Laser Pulse ◽  
Intensity Distribution ◽  
Diffraction Intensity ◽  
Central Frequency ◽  
Fresnel Number ◽  
Gaussian Curve ◽  
Central Direction ◽  
Temporal Intensity

An equation is put forward to calculate the temporal diffraction intensity distribution of a chirped femtosecond laser pulse when it incites a circle aperture. In the aperture central direction an analytic expression is given to calculate the temporal intensity distribution. Many factors such as the width of the laser pulse, the radius of the circle aperture, the Fresnel number at central frequency, time and the chirped coefficient of the laser pulse affect the temporal intensity. Number calculation shows that if the width of laser pulse is within a few tens of femtoseconds and Fresnel number at central frequency is much than twenty, the temporal diffraction intensity outline is not a Gaussian curve. While when the Fresnel number is less than ten and the chirped coefficient is small, the temporal intensity is an approximate Gaussian curve. If the chirped coefficient is large, the temporal intensity is not Gaussian distribution.

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