Effective Beam Widths Research Articles

Evolution properties of a complex coherent square Gaussian-Schell-model beam in a uniaxial crystal orthogonal to the optical axis.

The analytical formulas for spectral density, degree of coherence, and effective beam widths of complex coherent square Gaussian-Schell-model (GSM) beams in a uniaxial crystal orthogonal to the optical axis are derived. Based on these analytical formulas, the evolution properties are investigated by a set of numerical examples. It is demonstrated that the complex coherent square GSM beams spread at different rates in the directions parallel and orthogonal to the optical axis due to the anisotropic crystal, but the self-shift effect of the light field is almost unaffected by the fact that the uniaxial crystal is anisotropic. The effect of anisotropy of the uniaxial crystal on the effective width of the beam in the x direction and that in the y direction is completely opposite. The results provide a way for the modulation of the complex coherent square GSM beams and enrich the propagation theory of uniaxial crystal.

The effective beam width of a partially coherent rectangular mul-ti-Gaussian Schell-model vortex beam propagating in a turbulent plasma

Based on the derived analytical formulae for the optical intensity and effective beam width of a partially coherent rectangular multi-Gaussian Schell-model (RMGSM) vortex beam, we analyzed the evolution of the effective beam width of a partially coherent RMGSM vortex beam propagating in an anisotropic turbulent plasma using numerical examples. The numerical results demonstrated that the effective beam widths in the x and y directions were similar. In studies on the influences of the source parameters, one can see that an RMGSM vortex beam with a larger topological charge and beam waist or a smaller correlation coefficient σ evolves into a beam with a larger effective beam width. However, the influence of beam order was not evident. In addition, numerical examples proved that the effective beam width increases with increasing propagation distance and refractive index fluctuation variance or decreasing anisotropy parameter , outer scale , and inner scale . This study's results will be beneficial for applications in free-space optical communications.

Calibration of the Dual-Frequency Precipitation Radar Onboard the Global Precipitation Measurement Core Observatory

This article describes four-year calibration results of the dual-frequency precipitation radar (DPR) onboard the Global Precipitation Measurement (GPM) Core Observatory. The calibration method basically follows the method that was used to calibrate the precipitation radar (PR) onboard the Tropical Rainfall Measuring Mission (TRMM) satellite. However, both the hardware and data processing method for calibration are improved by taking advantage of the lessons learned from the PR’s calibration. Since the response of the radar receivers was found to depend on the waveform, the active calibrator was improved in such a way that the external calibration can be performed with both continuous and pulse waves. The methods for evaluating the calibration data were also improved. Instead of assuming a Gaussian antenna pattern, the effective beamwidths were determined by assuming an antenna pattern created by the Taylor distribution that was used to design the antennas. The results of the calibration including these improvements provide the new precise parameters of DPR’s calibration. The new parameters increased the Ku-band precipitation radar’s (KuPR’s) radar reflectivity factor ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Z$ </tex-math></inline-formula> ) by about 1.3 dB and that of the Ka-band precipitation radar (KaPR) by about 1.2 dB from the precalibrated <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Z$ </tex-math></inline-formula> values, and the minimum detectable radar reflectivities were 15.46, 19.18, and 13.71 dBZ for KuPR, matched beam of KaPR, and high-sensitivity beam of KaPR, respectively. After applying the new calibration methods to both DPR and PR, normalized radar cross sections ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sigma ^{0}$ </tex-math></inline-formula> ) from the DPR and PR agree with each other.

Propagation of a rectangular multi-gaussian schell-model vortex beam in uniaxial crystal

The cross-spectral density of a rectangular multi-Gaussian Schell-model vortex beam propagating in uniaxial crystal orthogonal to the optical axis has been derived, and the normalized intensity and effective beam widths are investigated by using numerical analysis. The results indicate that the rectangular multi-Gaussian Schell-model vortex beam propagating in uniaxial crystal will evolve from circular dark hollow beam into an elliptical flat-topped beam due to the influences of uniaxial crystal. The effective beam width Wx will gradually increase as the propagation distance z increase, and the beam with larger M and N1=N2 or smaller σ will have a larger effective beam width Wx at the same propagation distance.

Propagation of rectangular multi-Gaussian Schell-model vortex beams in turbulent atmosphere

Based on the extended Huygens-Fresnel integral, the analytical expression of average intensity of a rectangular multi-Gaussian Schell-model vortex (RMGSMV) beam propagating in turbulent atmosphere is derived, the effects of turbulent atmosphere on the average intensity and effective beam widths of a RMGSMV beam are analyzed. The numerical results indicate that the RMGSMV beam propagating in turbulent atmosphere will gradually evolve from the dark hollow beam into a solid beam with Gaussian-like distribution, and the effective beam width Wxz of a RMGSMV beam propagating in turbulent atmosphere with larger Cn2 will have a larger beam width. The results also show that the effective beam width of a RMGSMV beam with smaller σ, larger M and N1=N2 will have a larger effective beam width as the propagation distance increases.

Effects of the turbulent atmosphere and the oceanic turbulence on the propagation of a rotating elliptical Gaussian beam

Based on the extended Huygens–Fresnel integral, the average intensity, the gradient force and the effective beam width in the x- and y-directions of a rotating elliptical Gaussian (REG) beam in the turbulent atmosphere and the oceanic turbulence are explored analytically and numerically. It is shown that the intensity patterns of the REG beam in the atmospheric and the oceanic turbulences spin anticlockwise within a certain propagation range and always keep unimodal distributions during the propagation. Meanwhile, the numerical experiments of the REG beam are carried out to verify the theoretical analytical results. By comparative analysis, the effective beam widths can be adjusted by varying the turbulent characteristic parameters and the initial beam waist of the REG beam. The intensity modulation of the REG beam through the turbulent atmosphere and the oceanic turbulence can be realized.

Propagation properties of the rotating elliptical chirped Gaussian vortex beam in the oceanic turbulence

Based on the extended Huygens–Fresnel integral, the analytical formulas for the average intensity of the rotating elliptical chirped Gaussian vortex beam (RECGVB) in the oceanic turbulence are derived in this paper. Meanwhile, the evolutions of the intensity, the effective beam widths in the x- and y-directions and the dynamic center of gravity for the RECGVB propagating through the oceanic turbulence are explored by numerical examples. Results show that the intensity pattern of the RECGVB which presents two light spots at the beginning deforms and spins within a certain propagation range. Moreover, the position of the dynamic center of gravity can be modulated by the first-order chirped parameters while the profile of the intensity pattern can be affected by the second-order chirped parameters. In addition, the effects of the oceanic turbulence parameters and the initial beam width on the normalized intensity and the effective beam width of the RECGVB are discussed in detail.

Effect of secondary organic aerosol coating thickness on the real-time detection and characterization of biomass-burning soot by two particle mass spectrometers

Abstract. Biomass burning is a large source of light-absorbing refractory black carbon (rBC) particles with a wide range of morphologies and sizes. The net radiative forcing from these particles is strongly dependent on the amount and composition of non-light-absorbing material internally mixed with the rBC and on the morphology of the mixed particles. Understanding how the mixing state and morphology of biomass-burning aerosol evolves in the atmosphere is critical for constraining the influence of these particles on radiative forcing and climate. We investigated the response of two commercial laser-based particle mass spectrometers, the vacuum ultraviolet (VUV) ablation LAAPTOF and the IR vaporization SP-AMS, to monodisperse biomass-burning particles as we sequentially coated the particles with secondary organic aerosol (SOA) from α-pinene ozonolysis. We studied three mobility-selected soot core sizes, each with a number of successively thicker coatings of SOA applied. Using IR laser vaporization, the SP-AMS had different changes in sensitivity to rBC compared to potassium as a function of applied SOA coatings. We show that this is due to different effective beam widths for the IR laser vaporization region of potassium versus black carbon. The SP-AMS's sensitivity to black carbon (BC) mass was not observed to plateau following successive SOA coatings, despite achieving high OA : BC mass ratios greater than 9. We also measured the ion fragmentation pattern of biomass-burning rBC and found it changed only slightly with increasing SOA mass. The average organic matter ion signal measured by the LAAPTOF demonstrated a positive correlation with the condensed SOA mass on individual particles, despite the inhomogeneity of the particle core compositions. This demonstrates that the LAAPTOF can obtain quantitative mass measurements of aged soot-particle composition from realistic biomass-burning particles with complex morphologies and composition.

Detection of the Presence of Tornadoes at the Center of Mesocyclones Using Simulated Doppler Velocity Measurements

Abstract Simulations were conducted to investigate the detection of the Doppler velocity tornado signature (TS) and tornadic vortex signature (TVS) when a tornado is located at the center of the parent mesocyclone. Whether the signature is a TS or TVS depends on whether the tornado’s core diameter is greater than or less than the radar’s effective beamwidth, respectively. The investigation included three radar effective beamwidths, two mesocyclones, and six different-sized tornadoes, each of which had 10 different maximum tangential velocities assigned to it to represent a variety of strengths. The concentric tornadoes and mesocyclones were positioned 10–150 km from the radar. The results indicate that 1) azimuthal shear at the center of the mesocyclone increases as the associated tornado gains strength before a TS or TVS appears, 2) smaller tornadoes need to be much stronger than larger tornadoes at a given range for a signature to appear within the mesocyclone, and 3) when the tornado diameter is wider than about one-quarter of the mesocyclone diameter, the TS or TVS associated with a given mesocyclone appears when the tornado has attained about the same strength regardless of range.

Radially polarized partially coherent beams propagation in uniaxial crystals orthogonal to the optical axis

The propagation of radially polarized partially coherent beams in uniaxial crystals orthogonal to the optical axis is investigated. The analytical formulae for the elements of the cross-spectral density matrix of radially polarized partially coherent beams propagating through uniaxial crystals orthogonal to the optical axis are derived. The effect of initial coherence and ratio of extraordinary and ordinary refractive indices on the intensity and effective beam widths is illustrated analytically and numerically. The results show that the propagation properties of radially polarized partially coherent beams in uniaxial crystals orthogonal to the optical axis are closely related to the initial coherence and the ratio of extraordinary and ordinary refractive indices.

Calibration of sound forces in acoustic traps

A two-dimensional or transverse acoustic trapping and its capability to noninvasively manipulate micrometersized particles with focused sound beams were experimentally demonstrated in our previous work. To apply this technique, as in optical tweezers, for studying mechanical properties of and interactions among biological particles such as cells, the trapping forces must be calibrated against known forces, i.e., viscous drag forces exerted by fluid flows. The trapping forces and the trap stiffness were measured under various conditions and the results were reported in this paper. In the current experimental arrangement, because the trapped particles were positioned against an acoustically transparent mylar membrane, the ultrasound beam intensity distribution near the membrane must be carefully considered. The total intensity field (the sum of incident and scattering intensity fields) around the droplet was thus computed by finite element analysis (FEA) with the membrane included, and it was then used in the ray acoustics model to calculate the trapping forces. The membrane effect on trapping forces was discussed by comparing effective beam widths with and without the membrane. The FEA results found that the broader beam width, caused by the scattered beams from the neighboring membrane and the droplet, resulted in the lower intensity, or smaller force, on the droplet. The experimental results showed that the measured forces were as high as 64 nN. The trap stiffness, approximated as a linear spring, was estimated by linear regressions and found to be 1.3 to 4.4 nN/μm, which was on a larger scale than that of optical trapping estimated for red blood cells, a few tenths of piconewtons/nanometer. The experimental and theoretical results were in good agreement.

A sub-micron metallic electrothermal gripper

We report the design, fabrication, and characterization of a multiple bent beam, sub-micron metallic electrothermal gripper. A bottom electroplating mold for electrodes was patterned using electron beam lithography in an SU-8, followed by nickel electroplating. A top electroplating mold for a sub-micron metallic gripper with high aspect ratio bent beams (thickness of 1 μm, width of 350 nm) was prepared using electron beam lithography in a polymethyl methacrylate (PMMA), followed by nickel electroplating and dry release of the top and bottom molds. The sub-micron gripper was characterized using a nanomanipulator system installed in a dual column scanning electron microscopy/focused ion beam system. The ability of the jaw to close up to 1.39 μm displacement with high precision and reliability has been reproducibly observed at an applied current of 28 mA, corresponding to the maximum power consumption of 11.2 mW. Finite element modeling displacement results performed using ANSYS for effective bent beam widths of 370 nm showed a good agreement with the measured displacement results. The sub-micron gripper demonstrated herein will enable the reproducible manipulations with nano-scale resolution displacement and could provide an effective means of interface between nano-scale objects and the micro/macro scale robotic systems.

Organ and effective doses in newborn patients during helical multislice computed tomography examination

In this study, two computational phantoms of the newborn patient were used to assess individual organ doses and effective doses delivered during head, chest, abdomen, pelvis, and torso examinations using the Siemens SOMATOM Sensation 16 helical multi-slice computed tomography (MSCT) scanner. The stylized phantom used to model the patient anatomy was the revised ORNL newborn phantom by Han et al (2006 Health Phys.90 337). The tomographic phantom used in the study was that developed by Nipper et al (2002 Phys. Med. Biol. 47 3143) as recently revised by Staton et al (2006 Med. Phys. 33 3283). The stylized model was implemented within the MCNP5 radiation transport code, while the tomographic phantom was incorporated within the EGSnrc code. In both codes, the x-ray source was modelled as a fan beam originating from the focal spot at a fan angle of 52° and a focal-spot-to-axis distance of 57 cm. The helical path of the source was explicitly modelled based on variations in collimator setting (12 mm or 24 mm), detector pitch and scan length. Tube potentials of 80, 100 and 120 kVp were considered in this study. Beam profile data were acquired using radiological film measurements on a 16 cm PMMA phantom, which yielded effective beam widths of 14.7 mm and 26.8 mm for collimator settings of 12 mm and 24 mm, respectively. Values of absolute organ absorbed dose were determined via the use of normalization factors defined as the ratio of the CTDI100 measured in-phantom and that determined by Monte Carlo simulation of the PMMA phantom and ion chamber. Across various technique factors, effective dose differences between the stylized and tomographic phantoms ranged from +2% to +9% for head exams, –4% to –2% for chest exams, +8% to +24% for abdominal exams, –16% to –12% for pelvic exams and –7% to 0% for chest–abdomen–pelvis (CAP) exams. In many cases, however, relatively close agreement in effective dose was accomplished at the expense of compensating errors in individual organ dose. Per cent differences in organ dose between the stylized and tomographic phantoms at 120 kVp and 12 mm collimator setting ranged from –25% (skin) to +164% (muscle) for head exams, –92% (thyroid) to +98% (ovaries) for chest exams, –144% (uterus) to +112% (ovaries) for abdominal exams, –98% (SI wall) to +20% (thymus) for pelvic exams and –60% (extrathoracic airways) to +13% (ovaries) for CAP exams. Better agreement was seen between the two phantom types for organs entirely within the scan field. In these cases, corresponding per cent differences in organ absorbed dose did not vary more than 17%. For all scans, the effective dose was found to range approximately 1–13 mSv across the scan parameters and scan regions. The largest effective dose occurred for CAP scans at 120 kVp.

Simulated Doppler Velocity Signatures of Evolving Tornado-Like Vortices

Abstract Exact solutions of the Navier–Stokes or Euler equations of motion and the continuity equation in cylindrical coordinates for 3D, axisymmetric, inviscid, or laminar flows are utilized to represent evolving vortices that roughly model tornado cyclones or misocyclones contracting to tornadoes. These solutions are unsteady versions of the diffusive Burgers–Rott vortex and the inviscid Rankine-combined vortex. They satisfy the free-slip condition at the ground. Different vortices are obtained by choosing different values of the constant eddy viscosity and uniform horizontal convergence while holding the circulation at infinity constant. A simulated Weather Surveillance Radar-1988 Doppler (WSR-88D) is employed to generate time-varying Doppler velocity signatures in uniform reflectivity of these analytical vortices at ranges of 25 and 50 km from the radar. Mean Doppler velocities are determined by computing 3D integrals over effective resolution volumes. Magnitudes of Doppler vortex signatures at different times in the evolution of the stationary vortices are computed for effective beamwidths of 1.02° and 1.39°, which correspond to azimuthal sampling intervals of 0.5° and 1.0°, respectively. Four tornado predictors—rotational velocity, shear, excess rotational kinetic energy, and circulation—are examined. Results of the simulations show that for smaller effective beamwidths, Doppler vortex signatures are stronger and exceed fixed threshold values of rotational velocity and shear earlier. With finer azimuthal resolution, tornado cyclone, misocyclone, or tornado signatures switch to tornadic vortex signatures later. Circulations of the vortex signatures give good estimates of the circulations of the simulated tornadoes and tornado cyclones with relative insensitivity to range, effective beamwidth, and stage of evolution. High circulation and convergence values of a rotation signature reveal the potential for a tornado earlier than all the other predictors, which increase significantly during tornadogenesis.

A method for effective beam widths of slabs in flat plate structures under gravity and lateral loads

Effective beam width models are commonly used to obtain the lateral stiffness of flat plate structures. In these models, an effective beam width is defined as the width when the flexural stiffness of the beam element equals the slab stiffness. In this present study, a method to obtain effective beam widths that considers the effects of connection geometry and slab cracking is analytically proposed. The rectangularity of the vertical member for the connection geometry and the combined effects of creep and shrinkage for the slab cracking are considered. The results from the proposed method are compared with experimental results from a test structure having nine slab-column connections.

The effect of bandwidth on the interpretation of the cross spectra of wave recordings from spatially separated sites

It is argued that the coherence between records from a triangle of stations can be used to deduce not only the effective beamwidths of gravity wave patterns but can also be used to obtain their velocity bandwidth throughout the wave spectrum and its effect on the apparent velocity of propagation. Relationships between the apparent velocity of wave propagation and the velocity bandwidth are derived; they are analogous to the cross correlation approach of Briggs, Phillips, and Shinn but are herein generalized to include the frequency domain. The significance of the similarity hypothesis which is essential to the Briggs, Phillips and Shinn approach is discussed. The effect of the frequency bandwidth corresponding to the sampling rate and digital methods of analysis is considered in relation to the apparent phase velocity. The analytical results are applied to experimental data on gravity wave motions in the D region of the ionosphere.

Focusing of Low-Energy Electron Beams

Conventional electrostatic and magnetic lenses were used to focus electron beams in the range of energies 30–70 v, produced by a specially designed experimental tube. The electron distribution in the focused beam was resolved by a series of concentric end collectors and a convention introduced to assess effective beam widths. With near-symmetrical lenses of the electrostatic type and for energies above 30 v, the beam, if inside the aberration limits of the lens, appears to be acted on as a whole by the field and a definite focus is obtained; for 30-v beams, on the other hand, there is no unique focus since maximum and minimum values of effective beam width were recorded as the focus voltage was varied. Such a periodic variation might arise from the existence of standing wave patterns in the space charge in front of the cathode. A characteristic feature of the focusing which is most marked in the magnetic case is the disappearance on focus of the Gaussian core of the incident beam distribution. With magnetic lenses having apertures in the ratio 2/1, it was remarkable to find that the smaller aperture lens was the most efficient in bringing beams to a focus. In general, the power of magnetic lenses had to be greatly increased (in the measurements, by a factor of 30) over any expected thin lens performance to achieve a focus. Space charge forces, nonhomocentricity, and potential depression are held to be responsible for the abnormal conditions of focus.