Focal Radius Research Articles

Quasimonoenergetic proton beam from ultraintense-laser irradiation of a target with holed backside

A scheme for producing quasimonoenergetic proton beams is presented. In the scheme, a thin solid target with a tiny hole on its backside is employed. The optimal hole diameter is of the order of the laser spot size so that a localized uniform sheath field can be generated in the hole. Particle-in-cell simulations demonstrate that the highly localized uniform fields can produce monoenergetic target normal sheath acceleration protons in the hole. The transverse electric fields can well suppress the transverse divergence of the protons. The dependence of the proton beam quality on the focal radius and hole structure is also investigated. This special tailed target together with optimized laser parameters can serve as sources for collimated as well as quasimonoenergetic proton beams.

Numerical Analysis on the Feasibility of Laser Microwelding of Metals by Femtosecond Laser Pulses Using ABAQUS

Ultrafast lasers of subpicosecond pulse duration have the potential for laser microwelding of micronscale fusion zone. Due to the extremely short pulse duration, laser-metal interaction involving ultrafast laser pulses should be analyzed using the two-temperature model. In this study, the two-temperature model is analyzed using ABAQUS to study the feasibility of laser microwelding with ultrafast laser. A material model is constructed using material properties and the subsurface boiling model. The model is validated using experimental results from the literature. Laser processing parameters of repetition rate, pulse duration, and focal radius are then investigated, in terms of molten pool generated in the material and requirements on those parameters for laser microwelding using ultrafast lasers are discussed.

Possible temperature effects computed for acoustic microscopy used for living cells

Imaging of living cells or tissues at a microscopic resolution, where GHz frequencies are used, provides a foundation for many new biological applications. The possible temperature increase causing a destructive influence on the living cells should be then avoided. However, there is no information on possible local temperature increases at these very high frequencies where, due to strongly focused ultrasonic beams, nonlinear propagation effects occur. Acoustic parameters of living cells were assumed to be close to those of water; therefore, the power density of heat sources in a water medium was determined as a basic quantity. Hence, the numerical solution of temperature distributions at the frequency of 1 GHz was computed for high and low powers generated by the transducer equal to 0.32 W and 0.002 W. In the first case, typical nonlinear propagation effects were demonstrated and, in the second one, propagation was almost linear. The focal temperature increase obtained in water equaled 14°C for the highest possible theoretical repetition frequency of f r = 10 MHz and for the thermal insulation at the sapphire lens-water boundary. Simultaneously, the scanning velocity of the tested object was assumed to be incomparably low in respect to the acoustic beam velocity. The maximum temperature increase in water occurred exactly at this boundary, being equal there to 20°C. It was shown that, first of all, the very high absorption of water was significant for the temperature distribution in the investigated region, suppressing the focal temperature peaks. Because the temperature increases are proportional to the repetition frequency, so for example, at its practical value of f r = 0.1 MHz, all temperature increases will be 100 times lower than listed above. For the low transducer power of 0.002 W, the corresponding temperature increases were about 140 times lower than those for the high power of 0.32 W. The presented solutions are devoted mainly to the reflection pulse mode; however, they can be also applied for the transmitting (continuous-wave) mode, as shown in an example. Pressure distributions were computed for the acoustic field of the microscope for the first and higher harmonics. Hence, at the frequency of 1 GHz, the effective focal radius in water measured as the −6-dB amplitude pressure drop was found to be 1,1 μm, and 0.7 μm for the second harmonic, independently of the assumed transducer power. So the width of the beam, scanning the living cells in the focal region, was equal to 2.2 μm at the fundamental frequency of 1 GHz. (E-mail: lfilipcz@ippt.gov.pl)

Performance of submillimeter square hollow waveguides.

Propagation losses are determined for 100 microm x 100 microm square, hollow waveguides constructed from glass capillaries. The small size makes it possible to observe optical effects not easily seen with larger waveguides. The depletion of higher-order even modes creates a large, nonlinear loss. Over a distance of a meter the loss approaches the smaller, linear value expected for the fundamental mode. Additionally, the lowest two even modes beat to produce an oscillatory loss with a period of approximately 2 cm. Making the focal radius 0.35 the waveguide width minimizes these two effects. In a related study, 50-microm waveguides embossed in polydimethylsiloxane are shown to have losses similar to glass capillaries.

Local characterisation of inhomogeneous Cu surfaces by surface-enhanced Raman scattering

An attempt was made to compare surface-enhanced Raman spectra (SERS) of the probe molecules adsorbed on highly dispersed Cu surfaces of both real catalyst and various model systems produced from pure Cu. In particular, we searched for the Cu clusters with adsorption properties significantly differing from the properties of the clusters produced from pure copper on the surface of highly active copper-containing catalysts. The SERS spectra of pyridine used as a probe molecule were collected with a Raman spectrometer connected to a microscope having a focal radius of less than 10 −6 m. It was found, for example, that for the very active catalyst produced from 50Cu–50Zr amorphous precursor by high-pressure hydrogen charging, the relative intensities of pyridine bands are considerably different at some places to those observed for copper. At other areas on the sample, however, the spectrum is similar to that observed for pure Cu. This indicates that the local SERS technique has the potential to investigate adsorbate properties that are usually hidden by averaging if the signal is collected from a larger surface area.

Investigation of 90/spl deg/ dual-camera half-fanbeam collimation for myocardial SPECT imaging

This study investigated several aspects of the use of half-fanbeam collimation with a 90/spl deg/ dual-camera system for myocardial single photon emission computed tomography (SPECT) imaging. The detection efficiency, relative to parallel-hole collimation, was evaluated for a range of focal lengths and radii of rotation (ROR) to determine if there was an optimum focal length, which maximized the detection efficiency. In addition, sinograms were constructed and a simulation study was performed to determine if there was an optimal camera system rotation that maximized the total acquired myocardial counts while providing sufficient angular sampling for the myocardial region. Finally, artifacts in images reconstructed from data acquired over various system rotations were evaluated using simulated and experimental data. There existed an optimal collimator focal length for a given ROR; but it varied with ROR. Relative to parallel-hole collimation, the detection efficiency for half-fanbeam collimation was roughly 20% greater, for cast collimators constructed using the same pins and thickness. The theoretical minimum system rotation for sufficient sampling of the myocardial region ranged from 124/spl deg/ to 148/spl deg/ for RORs ranging from 13 to 25 cm, respectively. The total number of acquired myocardial counts was relatively constant for system rotations of 90/spl deg/ to 360/spl deg/. Myocardial SPECT images reconstructed iteratively with attenuation compensation from half-fanbeam data collected over system rotations ranging from 135/spl deg/ to 360/spl deg/ showed no artifacts in the myocardial region. Based on these results, the authors concluded that there was no single optimum system rotation, but that a system rotation of 180/spl deg/ centered at 45/spl deg/ left anterior oblique was a good, practical minimum rotation. Half-fanbeam collimation is a useful alternative system configuration for myocardial SPECT imaging.

Crystal Spectrometers and Monochromators in Microanalysis

An x-ray spectrometer is actually a scanning monochromator because two conditions must be satisfied, namely: (1) nλ, = 2d sinθ and (2) θI{= θR to within the rocking curve of the crystal 2Δθ. Before Castaing (B.C.) there were four known types of focussing monochromators, namely: Johann, Johansson, Cauchois, and von Hamos. Castaing was fortunate in having Andre Guinier (well known for his work in x-ray crystallography) as his thesis advisor. Thus, he wisely chose to use a spectrometer of the Johansson type. Had he used a flat crystal spectrometer, the result would have been unsatisfactory and the history of microanalysis would have been significantly different. Many of the spectrometers that were used in the early instruments were either of the Johansson type, in which the crystal planes are curved to a radius of 2R and the surface has a radius of R, the focal circle radius. This is sometimes called exact focussing because rays in the plane of the focal circle converge exactly to a point focus. For simpler construction, the Johann crystal which has the surface parallel to the atomic planes (also curved to a radius of 2R) was sometimes used. While both types provide one-dimensional focussing, the Johansson type is preferred because the effective width of the crystal can be greater.In addition to the type of geometry used, early instruments developed after Castaing (A.C) also had variations in the mechanism of the crystal movement. Many used a relatively simple mechanism with the crystal and detector moving about a fixed center for the focal circle as shown in Fig. 1A. Some later instruments used curved crystals that were fixed in position, and scanning was accomplished either by rotating the crystal as in Fig. 1B or by a mechanism that flexed the crystal and changed the radius of the focal circle as in Fig. 1C. The most satisfactory arrangement and the one subsequently adopted by most manufacturers of commercial microprobes utilized a linear motion of the crystal carriage with a provision for tilting the crystal so that the focal circle always passed though the x-ray source as shown in Fig. 1D. If the detector moves so that it remains on this focal circle, its motion is along a leaf-shaped curve. With this design it is easy to have a readout proportional to wave length.

Dictionary of Ophthalmic Optics

How to Use This Dictionary List of Figures Vocabulary Selected References Appendixes: Index of Refraction of Common Ophthalmic Materials Focal Power Converted to Focal Length Radius of Curvature of Standard Surface Grinding Tools Power of a One-Diopter Cylinder Lens at 1 Degree Intervals from The Axis True Surface Power of Various Refractive Index Lenses Center or Edge Thickness Comparison Chart for Select Powers for Various Index Lenses Thickness Difference of Sharp-Edged Prism for Various Indexes

Stability analysis of relativistic and charge-displacement self-channelling of intense laser pulses in underdense plasmas

The stability against small azimuthal perturbations of confined modes of propagation of intense short-pulse radiation governed by relativistic and charge-displacement nonlinearities in underdense plasmas is examined theoretically. In the plane of the dimensionless parameters rho 0 identical to r0 omega p,0/c and eta identical to P0/Pcr, defined by the critical power (Pcr) and the initial conditions represented by the focal radius (r0) of the incident radiation, the unperturbed plasma frequency ( omega p,0), and the peak incident power (P0), zones corresponding to stable (single-channel) and unstable (strong filamentation) regimes of propagation are established. The general finding is that large regions of stable propagation exist. The results show that for values of rho 0 sufficiently close to the dimensionless radius of the zeroth eigenmode rho c,0, the self-channelling is stable for all values of eta >1, a condition of exceptional robustness. It is also found that for the region 1< eta <or approximately=10, the propagation is stable for a very wide range of values of rho 0. In addition, the location of the boundary separating the stable and unstable zones is largely independent of the curvature of the phase front of the incident wave and weakly influenced both by the magnitudes of the azimuthal perturbations and the detailed radial profile of the incident radiation. Since self-focusing generated solely by relativistic mechanisms tends strongly to unstable behaviour in the eta >>1 regime, these results demonstrate the crucial role of the ponderomotively driven charge displacement in stabilizing the propagation. Physically, the ponderomotive radial displacement of the electrons and the contrasting inertial confinement of the ions simultaneously produce the two chief characteristics of the channels. They are the refractive self-focusing of the propagating energy arising from the displaced electrons and the spatial stability of the channels produced by the immobile electrostatic spine formed by the ions.

A new method to estimate the effective geometric focal length and radius of ultrasonic focused probes : Review of Progress in Quantitative Nondestructive Evaluation, La Jolla, California (United States), 15–20 Jul. 1990. Vol. 10A, pp. 861–865. Edited by D.O. Thompson, and D.E. Chimenti. Plenum Press (1991). ISBN 0-306-43903-4

A new method to estimate the effective geometric focal length and radius of ultrasonic focused probes : Review of Progress in Quantitative Nondestructive Evaluation, La Jolla, California (United States), 15–20 Jul. 1990. Vol. 10A, pp. 861–865. Edited by D.O. Thompson, and D.E. Chimenti. Plenum Press (1991). ISBN 0-306-43903-4

An Alternative Perspective on the Optical Property of Ellipses

If a ray of light passes through one focus of an ellipse and reflects off the ellipse, then it passes through the other focus. This phenomenon occurs because the tangent line at a point on an ellipse makes equal angles with the focal radii at that point, (See fig. 1.) This well-known property of ellipses, which is discussed by almost every textbook on calculus and analytic geometry, is usually derived by computing angles from the slopes of the tangent line and the focal radii. The following proof is based on the reflection principle, used in the game of billiards, and may be more interesting and motivating than the standard approaches.

Heavy ion inertial fusion: Initial survey of target gain versus ion-beam parameters

Inertial-fusion targets have been designed for use with heavy-ion accelerators as drivers in fusion energy power plants. We have made an initial survey of target gain versus beam energy, power, focal radius, and ion range. This provides input for understanding the trade-offs among accelerator designs.

Seismic source parameters of large earthquake in Vrancea

The seismic source parameters for five large Vrancea earthquakes are calculated : corner frequency, focal radius, seismic moment and stress drop. The multiplicity character of some events is put in evidence, using spectral and time domain analysis.

Passive Acoustic Beamforming with Spherical Liquid Lenses

The acoustic field within a spherical liquid lens due to plane-wave excitation is numerically computed by evaluation of the Helmholtz integral equation and compared to the exact boundary value solution over a lens diameter to wavelength range of 2 to 25. It is shown that rear hemisphere reradiation dominantly accounts for the computed differences, nearly exclusively affecting only the front-to-back spatial discrimination ratio. Lens focal radius as estimated by (1) minimum residual of the aperture phase and (2) ray (energy) considerations is compared and shown to be in excellent agreement with the computed field. Sidelobe and pressure gain degradation due to geometric aberration is evaluated and shown along with experimental data. Normalized beam patterns are presented showing this effect to be a negligibly weak function of refractive index. Finally, the lens passive sensitivity is developed and shown to be superior to an array of the same directive index.

On the Loci of Intersections of Certain Focal Radii in two Confocal Ellipses

On the Loci of Intersections of Certain Focal Radii in two Confocal Ellipses

Powered-Flight Trajectories of Rockets Under Constant Transverse Thrust

The second-order nonlinear differential equations of motion in the case of a rocket in drag-free powered-flight under constant transverse (normal to the focal radius) thrust are solved by series expansion developed to the seventh power of the independent variable “time.” The coefficients of the powers of time are in terms of given boundary conditions. The truncation errors of the series are estimated, hence the accuracy for any practical problem based on the analysis presented in this paper could be well established. The case of constant transverse thrust acceleration, which may be conceived as a special case of the present analysis, is also solved.

Generation of earthquakes by a volume source with moment

abstract The theory developed in paper I* has been used to determine the influence of the focal radius on the P and S wave radiation from a spherical source on which the stress τz=Tyr0eivt acts. The result has been applied to two earthquakes of which the P and S wave distribution around the focus was studied in paper II. † In an appendix, the present model of the focus is compared with similar models that are described in literature. * This bulletin p. 711 † This bulletin p. 723

A Simple Blackboard Ellipsograph

The simplest and best known method of drawing an ellipse is based on the fundamental theorem in conics that in any ellipse the sum of the focal radii is constant and equal to the major axis of the ellipse. This method is widely used by gardeners in laying out elliptical beds, by pattern-makers, metal workers, artists, and others.

THE REFRACTIVE INDICES OF WHOLE CELLS

Refractive indices of intact sporangiophores of Phycomyces were computed from measurements of focal length and radius of curvature of the cells. For the six cells studied, effective values of n were obtained ranging from 1.35 to 1.40. The average effective n was 1.38. Senn's determination of refractive indices of other plants cells gave much higher values: n = 1.37 to 1.52. The precision of the method and possible sources of this discrepancy are discussed.

The Polar Equation of the Tangent and Normal to a Conic

The property of a conic: “if the projections of K, any point on a tangent, on the directrix and the focal radius of the point of contact be I and U respectively, SU = e. KI,” is known as Adams's Property. The statement of the above property in terms of the polar coordinates of K is the equation of the tangent. Hence, if the eccentric angle of the point of contact is aor = cos (θ — α) + e cos θ is the equation of the tangent.