Off-axis Distance Research Articles

Propagation dynamics of symmetric Pearcey-Gaussian beam with optical vortices

The propagation dynamics of symmetric Pearcey-Gaussian beam embedded with on-axis and off-axis optical vortices (OVs) is investigated. Based on the extended Huygens-Fresnel diffraction integral, influences of embedded location, the off-axis distance and topological charge (TC) of OVs on the autofocusing dynamics of the symmetric Pearcey-Gaussian vortex beam (SPGVB) are explored analytically and numerically. The results show that, the embedded location, the off-axis distance and TC of OVs can significantly affect the initial intensity distribution, the propagation trajectory, the autofocusing length and the peak intensity at the focal plane. Interestingly, the fitted expression describing the relationship between the peak intensity of SPGVB and the off-axis distance of OVs with different TC is obtained, which would provide a method to determine the off-axis distance or the TC of OV based on the intensity distribution. The results indicate that SPGVB holds potential applications in biomedical treatment, optical manipulation and optical communication.

A simplified and effective off-axis Winston-Lutz for single-isocenter multi-target SRS.

To safely perform single-iso multi-target (SIMT) stereotactic radiosurgery (SRS), clinics must demonstrate SRS delivery accuracy for off-axis targets. The traditional Winston-Lutz (W-L) was widely adopted because it provides a simple and accurate solution for testing radiation-isocenter coincidence that uses a static target, enables testing arbitrary treatment angles, and does not require expensive commercial phantoms. The current noncommercial tests are cumbersome and insufficiently accurate. For an off-axis Winston-Lutz (OAWL) test, one must design MLC fields centered on off-axis targets. Unfortunately, because MLC leaf-interfaces are often misaligned with the target center, accomplishing this presents a nontrivial geometry problem that has not been previously solved in the literature. We present a solution for evaluating SIMT SRS accuracy that provides a straightforward method for creating OAWL test fields and offers all the benefits of the standard W-L test. We have developed a method to use any gantry, table, and initial collimator angles to create OAWL fields. This method calculates a series of nested coordinate transformations that produce a small collimator angle adjustment to align the MLC and create a symmetric field around an off-axis target. For an 8cm off-axis target, the described method yields OAWL results within 0.07mm of standard isocentric W-L results. Our six most recent isocentric W-L tests show max and mean errors of 0.59 and 0.37mm, respectively. For six runs of our proposed OAWL test, the average max and mean errors are 0.66 and 0.40mm, respectively. This method accurately evaluates SRS delivery accuracy for off-axis distances that span the majority of a typical human brain for a centered SIMT arc. We have made this method publicly available, so that physicists can employ it within their clinics, foregoing the need for expensive phantoms and improving access to the state-of-the-art SIMT SRS technique.

Comparison of 126 MeV antiproton and proton—a FLUKA-based microdosimetric approach

Objective. This study aims at comparing dosimetric parameters of 126 MeV antiprotons and protons using microdosimetric approach. Approach. Microdosimetric distributions of 126 MeV proton and antiproton beams at 1 μm site size are calculated using the Monte Carlo-based FLUKA code. The distributions are calculated at various depths along the central axis in water phantom as well as at different off-axis locations. The study also includes calculations of secondary radiations produced by antiprotons and protons. Mean quality factor, is calculated using the ICRP 60 and ICRU 40 recommendations. The Relative Biological Effectiveness (RBE) of HSG tumour cell at 10% survival level is calculated based on Microdosimetric Kinetic Model. Main results. and RBE for antiprotons are higher by a factor of about 3.60, 3.41 and 1.24, respectively, at Bragg-peak and higher by a factor of about 1.41, 1.76 and 1.05, respectively, at plateau region of depth-dose profile when compared to protons. At 15 cm depth along the central axis, and RBE for protons are higher by a factor of about 1.42, 1.66 and 1.26, respectively, when compared to antiprotons. At the off-axis distance (Ld ) of 6 cm (at 11.5 cm depth in water), and of protons are higher than that of antiproton whereas the trend is opposite at off-axis distance of 4 cm. At Ld = 4 cm (at 11.5 cm depth in water), RBE of antiprotons is higher by about 4% than protons whereas at Ld = 6 cm, RBE of protons is higher by about 13% than antiprotons. Significance. The study shows that antiproton radiotherapy is advantageous as compared to protons considering enhancements in the absorbed dose and RBE-weighed dose values at the Bragg-peak.

Generation of off-axis phased Gaussian optical array along arbitrary curvilinear arrangement

Vortex beams can potentially be used in optical communication, imaging, and processing applications, herein, we propose a method to generate a phased Gaussian optical array (PGOA) by arranging an aperture-bounded Gaussian optical array along arbitrary curves and using a discontinuous phase to form a controllable vortex phase. The phase difference between adjacent sub-beams is constant, and the total phase increment is 2πl. The experimental limitations of this technique are discussed, including the aperture radius, off-axis distance, number of sub-beams, and maximum topological charges. The coaxial interference characteristics of the PGOA in free space were examined numerically by using a split-step Fourier transform algorithm. We theoretically and experimentally proved the feasibility of a coherent beam combination scheme to generate a PGOA, which is of particular significance for particle manipulation and free-space optical communication applications.

Effect of blade profile on the efficiency of a waterfall cross-flow hydro turbine

The effect of blade profile on the efficiency of a waterfall cross-flow hydro turbine was investigated numerically using the non-uniform, thin, and standard blades. Each efficiency of the blade profile was evaluated by varying the tip-speed ratio (=0.3–0.9) and off-axis distance (=0.26–0.48), which are the influential parameters for characterizing the performance of the cross-flow turbine. Although a minor improvement was observed in the peak efficiency 62–63 % by the blade-profile effect, the off-peak efficiency was highly improved up to 8 % on the non-uniform blade and 11 % on the thin blade. The examination of the local and average torque distribution in reference to the flow fields showed that an increased torque on the non-uniform blade was observed at small blade angles due to the increased waterfall impingement, while that on the thin blade was observed at large blade angles caused by increased rebounding flow. This suggests the different torque enhancement mechanism of the cross-flow turbine on the non-uniform and thin blades in comparison with the standard blade.

Superimposed Hermite-Gaussian-correlated Schell-model beam with multiple off-axis vortices.

We first introduce a class of a superimposed Hermite-Gaussian-correlated Schell model with a multiple off-axis vortices beam, with the side lobe of the beam carrying one to four vortex singularities at the source plane. Subsequently, the variation laws of this beam after being focused by a thin lens are studied theoretically to obtain the optimal beam parameters. The numerical simulation results show that the beam possesses a unique multiple vortex structure, phase structure, and orbital angular momentum. Its intensity resembles a spiral staircase rotating around the axes. The rotational symmetry property of the transverse energy flow along the z axis was broken by the vortices. The hot spot position can be adjusted flexibly by changing the off-axis distance of vortices. This study is of great significance for nondestructive capture and manipulation of multiple particles or cells.

Detection of rotational errors in single-isocenter multiple-target radiosurgery: Is a routine off-axis Winston-Lutz test necessary?

PurposeRecently the use of linear accelerator (linac)‐based stereotactic radiosurgery (SRS) has increased, including single‐isocenter multiple‐target SRS. The workload of medical physicists has grown as a result and so has the necessity of maximizing the efficiency of quality assurance (QA). This study aimed to determine if measurement‐based patient‐specific QA with a high‐spatial‐resolution dosimeter is sensitive to rotational errors, potentially reducing the need for routine off‐axis Winston–Lutz (WL) testing.MethodsThe impact of rotational errors along gantry, couch, and collimator axes on dose coverage of the gross tumor volume (GTV) and planning target volume (PTV) was determined with a 1‐mm GTV/PTV expansion margin. Two techniques, the off‐axis WL test using the StereoPHAN MultiMet‐WL Cube (Sun Nuclear Corporation, Melbourne, Florida, USA) and patient‐specific QA using the SRS MapCHECK (Sun Nuclear Corporation, Melbourne, Florida, USA), were assessed on their ability to detect introduced errors before target coverage was compromised. These findings were also considered in the context of routine machine QA of rotational axis calibrations.ResultsRotational errors significantly impacted PTV dose coverage, especially in the couch angle. GTV dose coverage remained unaffected except for with large couch angle errors (≥1.5°). The off‐axis WL test was shown to be sensitive to rotational errors with results consistently exceeding tolerance levels when or before coverage fell below departmentally accepted limits. Although patient‐specific QA using the SRS MapCHECK was previously validated for SRS, this study showed inconsistency in detection of rotational errors.ConclusionsIt is recommended that off‐axis WL testing be conducted regularly to supplement routine monthly machine QA, as it is sensitive to errors that patient‐specific QA may not detect. This frequency should be determined by individual departments, with consideration of GTV–PTV margins used, limitations on target off‐axis distances, and routine mechanical QA results for particular linacs.

Calculating off-axis efficiency of coaxial HPGe detectors by Monte Carlo simulation

In beam geometries where a directed γ-ray beam hits the surface of a coaxial high purity germanium detector (HPGe), the detector efficiency is sensitive to the position where γ-rays initially hit the detector surface because the structure of the detector is nonuniform. This may cause inaccuracy of the detector efficiency when measured using standard sources that are point-like sources emitting γ-rays isotropically. Obtaining a precise estimation of the full energy peak efficiency of the coaxial HPGe detector in the beam geometry for on-axis and off-axis measurements requires a Monte Carlo simulation. We performed Monte Carlo simulations that calculate the detector efficiency in the beam geometry. The effects of the off-axis distance and γ-ray beam size on the efficiency are quantitatively analyzed. We found that the intrinsic efficiency in the beam geometry is maximized when the beam hits the detector at specific off-axis distances. Our Monte Carlo calculations have been supported by nuclear resonance fluorescence experiments using laser Compton scattering γ-ray beams.

A publicly available dataset of out-of-field dose profiles of a 6 MV linear accelerator.

An increase in radiotherapy-induced secondary malignancies has led to recent developments in analytical modelling of out-of-field dose. These models must be validated against measurements, but currently available datasets are outdated or limited in scope. This study aimed to address these shortcomings by producing a large dataset of out-of-field dose profiles measured with modern equipment. A novel method was developed with the intention of allowing physicists in all clinics to perform these measurements themselves using commonly available dosimetry equipment. A standard 3D scanning water tank was used to collect 36 extended profiles. Each profile was measured in two sections, with the inner section measured with the beam directly incident on the tank, and the outer section with the beam incident on a water-equivalent phantom abutted next to the tank. The two sections were then stitched using a novel feature-matching approach. The profiles were compared against linac commissioning data and manually inspected for discontinuities in the overlap region. The dataset is presented as a publicly accessible comma separated variable file containing off-axis ratios at a range of off-axis distances. This dataset may be applied to the development and validation of analytical models of out-of-field dose. Additionally, it may be used to inform dose estimates to radiosensitive implants and anatomy. Physicists are encouraged to perform these out-of-field measurements in their own clinics and share their results with the community.

Two-Dimensional Ultrafast X-ray Imager for Inertial Confinement Fusion Diagnosis

A two-dimensional ultrafast X-ray imager (UXI) composed of a time-dilation device, an electron-beam imaging unit, a gated microchannel plate (MCP) framing tube, and a pulser was developed. The time-dilation device extends the time spread of the electron signal generated by the pulsed photocathode (PC), and the electron-beam imaging unit images the electron pulse from PC to MCP. Finally, the gated MCP framing tube samples the dilated electron pulse. The time resolution and image size of the UXI were measured with an X-ray generated by a terawatt laser targeting device. When a driving pulse with a 2 V/ps slope is applied to the PC, the measured time resolution is 21 ps, and the image size is 12 mm × 3.9 mm. Furthermore, the image size varies with the time resolution. The results show that as the time resolution improves, the image size decreases. The use of two opposite-transmission PC driving pulses could improve the image size. Moreover, the measured UXI spatial resolution is 5 lp/mm, and the spatial resolution will be worse with the increasing off-axis distance.

Angular spectrum representation of the Bessel-Gauss beam and its approximation: A comparison with the localized approximation

The angular spectrum representation of the vector Bessel-Gauss beam is used for discussing the connection between the angular spectrum decomposition (ASD) method and the quadrature method of the generalized Lorenz-Mie theory (GLMT). Under the paraxial condition, the beam shape coefficients (BSCs) obtained in the ASD method can be approximated to the same expressions as those obtained in the localized approximation method. The validity of the approximate method for evaluating the BSCs is numerically studied, based on both the beam's angular spectrum and the off-axis distance.

Femtosecond laser point-by-point inscription of helical-sampled fiber Bragg gratings

In this Letter, a helical-sampled fiber Bragg gratings (HSFBGs) fabrication using a femtosecond laser point-by-point (PBP) technique is proposed. The unique helical structure generates sampled gratings owing to its periodicity. A simple, single-step method for inscription of the sampled gratings is described. The effects of geometrical parameters, including length of grating, helical diameter, helical pitch, and off-axis distance on the resonances are studied, and a series of comb-like spectra are obtained.

Grouping design method dependence on an illumination system and large off-axis distance for an anamorphic extreme ultraviolet lithography objective

High-numerical-aperture (NA) anamorphic extreme ultraviolet lithography (EUVL) is the next-generation technology to achieve a 3 nm node and below. Current EUVL anamorphic projection objectives in publications are designed with small off-axis distance of the field of view (FOV). Further, the ray path of the illumination system will be obscured by the last mirror of the objective. In fact, as the NA increases, the diameter of the last mirror of the objective becomes larger. Thus, the off-axis distance of the FOV should be larger to ensure that the ray path of the illumination system is not obscured by the objective. It is well known that the design of an anamorphic EUVL objective with large off-axis distance is very challenging. In this paper, a high-NA anamorphic EUVL objective with large off-axis distance is designed. The value of the large off-axis distance that satisfies the unobscured constraint is first analyzed. Then an 8× demagnification isomorphic objective with large off-axis distance is designed by a grouping design process. Finally, the XY polynomial surface is adopted to achieve a 4× demagnification perpendicular to the scanning direction. This method is implemented to design a NA 0.55 anamorphic EUVL objective with large off-axis distance. The performance of the designed objective demonstrates that this design method is very effective and will provide a good structure of the objective for the illumination system design.

Evaluating Mobius3D Dose Calculation Accuracy for Small-Field Flattening- Filter-Free Photon Beams.

Purpose: We aimed to investigate the dose calculation accuracy of Mobius3D for small-field flattening-filter-free x-rays, mainly utilized for stereotactic body radiation therapy (SBRT). The accuracy of beam modeling and multileaf collimator (MLC) modeling in Mobius3D, significantly affecting the dose calculation is investigated. Methods: The commissioning procedures of Mobius3D were performed for unflattened 6 MV and 10 MV x-ray beams of the linear accelerator, including beam model adjustment and dosimetric leaf gap (DLG) optimization. An experimental study with artificial plans was conducted to evaluate the accuracy of small-field modeling. The dose calculation accuracy of Mobius3D was also evaluated for retrospective SBRT plans with multiple targets. Results: Both studies evaluated the dose calculation accuracy through comparisons with the measured data. Relatively large differences were observed for off-axis distances over 5 cm and for small fields less than 1 cm field size. For the study with artificial plans, the maximum absolute error of 9.96% for unflattened 6 MV and 9.07% for unflattened 10 MV was observed when the field size was 1 cm. For the study with patient plans, the mean gamma passing rate with 3%/3 mm gamma criterion was 63.6% for unflattened 6 MV and 82.6% for unflattened 10 MV. The maximum of the average dose difference was -19.9% for unflattened 6MV and -10.1% for unflattened 10MV. Conclusions: The dose calculation accuracy uncertainties of Mobius3D for small-field flattening-filter-free photon beams were observed. The study results indicated that the beam and MLC modeling of Mobius3D must be improved for use in SBRT pretreatment QA in clinical practice.

Parametric Mid-Spatial Frequency Surface Error Synthesis

Standard mid-spatial frequency tooling mark errors were parameterized into a series of characteristic features and systematically investigated. Diffraction encircled and ensquared energy radii at the 90% levels from an unpowered optical surface were determined as a function of the root-mean-square surface irregularity, characteristic tooling mark parameters, fold mirror rotation angle, and incident beam f-number. Tooling mark frequencies on the order of 20 cycles per aperture or less were considered. This subset encompasses small footprints on single-point diamond turned optics or large footprints on sub-aperture tool polished optics. Of the characteristic features, off-axis fabrication distance held the highest impact to encircled and ensquared energy radii. The transverse oscillation of a tooling path was found to be the second highest contributor. Both impacts increased with radial tooling mark frequency.

Electron and Photon Energy Spectra Outside of 6 MV X-ray Small Radiotherapy Field Edges Produced by a Varian iX Linac

Due to the increase in the survival probability for patients treated with modern radiotherapy techniques to live enough for experimenting the late radiation effect, low dose outside the treatment volume becomes a concern. However, besides the absorbed dose, the beam quality outside the field edge should be taken into account. This work aimed at investigating the photon and electron fluence spectra outside the field edges for several small radiotherapy fields for determining the quality of the beams in order to better evaluate the secondary effect after modern radiotherapy treatments. Phase-space files of a 6 MV X-ray beam produced by a Varian iX linac for eight small fields of 0.7 × 0.7 cm2, 0.9 × 0.9 cm2, 1.8 × 1.8 cm2, 2.2 × 2.2 cm2, 2.7 × 2.7 cm2, 3.1 × 3.1 cm2, 3.6 × 3.6 cm2, and 4.5 × 4.5 cm2 and for the reference 10 × 10 cm2 field at SSD = 100 cm were generated using the BEAMnrc code. The photon and electron fluences in each field were calculated at 0.15, 1.35, and 9.85 cm water depth and several off-axis distances using FLURZnrc. The number of low-energy electrons between 1 and 10 keV at 2 cm outside the field edge increases by 60% compared to the central axis. Due to the relatively high linear energy transfer (LET) of these electrons, the results of this work should help to better evaluate the possible late effect of secondary radiation on healthy organs close to the tumor volume after radiotherapy treatment. We also observed high-energy electrons outside the field edge that are attributed to the leakage of the primary electron beam from the head of the linac. From a standpoint of radiological protection, these electrons should be taken into account when evaluating the dose delivered to the patient’s skin.

Experimental and numerical studies on the performance of a waterfall-type cross-flow hydraulic turbine

The performance of a waterfall-type cross-flow hydraulic turbine was investigated via experiment and numerical simulation. The experiment was carried out using a cross-flow hydraulic turbine operating in a two-dimensional waterfall, and the result was compared with a corresponding numerical result analyzed by the volume of fluid method. The experimental results show that the maximum efficiency reached approximately 60%, higher than that of previous experiments in the literature. It was also confirmed that the recorded experimental efficiency was well reproduced in a two-dimensional numerical simulation, suggesting the validity of the numerical results. Furthermore, flow fields of the turbine were studied based on phase-averaged particle image velocimetry measurement and the numerical simulation. These results indicate that the flow and torque mechanisms of the cross-flow hydraulic turbine studied are explained by stagnation pressure on the concave side of blades and a Coanda-like flow on the convex side of the blades at small angle of blade position, followed by the formation of a high-velocity region within the turbine and flow impingement on the downstream blades at large angle. These flow field variations generated an increased local torque at small angle and a moderate torque at large angle. The improved efficiency was obtained by optimizing the off-axis distance to the waterfall and the tip-speed ratio of the hydraulic turbine, which were examined by a visualization of the flow through the turbine and the local torque distribution with respect to the angle of blade position, respectively.

Splitting, generation, and annihilation of phase singularities in non-coaxial interference of Bessel–Gaussian beams

Based on the non-coaxial interference of Bessel–Gaussian (BG) beams, a new complex-structured light field is formed. By varying the off-axis distance, phase difference, separation angle, and topological charges (TCs) of the component beams, we observed the splitting, generation, and annihilation of phase singularities. The net TCs of the composite light field is not always equal the sum of the TCs of the original beams. Different from the general single-ringed vortex beams, because BG beams have infinitely many rings, alternately positive and negative unit vortex chains arise in the interference region. Furthermore, the edge dislocations are unstable, by modulating the phase difference and separation angle, we observe controllable transitions between edge dislocations and vortex singularities. Beyond providing an effective method for studying composite vortex beam interference, our results are significant for laser calibration and complex particle manipulation.

Neutron and photon out-of-field doses at cardiac implantable electronic device (CIED) depths

The accuracy of an out-of-field dose from an Elekta Synergy accelerator calculated using the X-ray Voxel Monte Carlo (XVMC) dose algorithm in the Monaco treatment planning system (TPS) for both low-energy (6 MV) and high-energy (15 MV) photons at cardiac implantable electronic device (CIED) depths was investigated through a comparison between MCNPX simulated out-of-field doses and measured out-of-field doses using three high spatial and sensitive active detectors. In addition, total neutron equivalent dose and fluence at CIED depths of a 15-MV dose from an Elekta Synergy accelerator were calculated, and the corresponding CIED relative neutron damage was quantified. The results showed that for 6-MV photons, the XVMC dose algorithm in Monaco underestimated out-of-field doses in all off-axis distances (average errors: −17% at distances X < 10 cm from the field edge and −31% at distances between 10 < X ≤ 16 cm from the field edge), with an increasing magnitude of underestimation for high-energy (15 MV) photons (up to 11%). According to the results, an out-of-field photon dose at a shallower CIED depth of 1 cm was associated with greater statistical uncertainty in the dose estimate compared to a CIED depth of 2 cm and clinical depth of 10 cm. Our results showed that the relative neutron damage at a CIED depth range for 15 MV photon is 36% less than that reported for 18 MV photon in the literature.

Vector magnetic field measurement based on magnetic fluid and high-order cladding-mode Bragg grating

An optical fiber-based vector magnetic field sensor combining fiber Bragg gratings (FBGs) and magnetic fluids (MFs) is proposed and experimentally demonstrated. The Bragg gratings are inscribed on the core and the cladding of a multi-clad fiber (MCF). Splicing the MCF with a standard single-mode fiber (SMF) via core mismatch provides a cladding-mode generation mechanism. Then, the high-order cladding mode is excited with the increasing off-axis distance. There are two kinds of resonant modes in the reflection spectrum of the sensor, which are the high-order cladding mode and the fundamental core mode. The intensity of the first mode shows an excellent response to the magnetic field intensity and the direction. The intensity sensitivity of the magnetic field sensor is −0.143 dB/Oe in a linear range of 60–110 Oe. Furthermore, the second mode intensity is quite stable and varies with the ambient temperature. Thus, the proposed magnetic field sensor can simultaneously measure the magnetic field and the temperature.