Effective Beam Size Research Articles

Technical note: TERMA scaling as an effective heterogeneity correction model for convolution-based external-beam photon dose calculations.

In highly heterogeneous medium, such as one with lung tissue or air cavities, the dose in the low-density region or after it, as calculated by the conventional methods based on convolution with an energy-spreading kernel, is usually overestimated in comparison with measurements or more accurate predictions. To correct the overestimation, we propose a method of scaling the total energy released per mass (TERMA). The scaling depends on both the density distribution and the effective beam size in the lateraldirection. The corrected convolution method achieved a significantly improved accuracy in both the lung-like tissue and the water-like region after air, compared to the uncorrected method. The TERMA correction only adds about 10% to the overall computationalcost. Due to the improvement in accuracy and the preservation of computational efficiency, the proposed dose calculation method will be valuable for inverse treatmentplanning.

Analyzing the spreading properties of vortex beam in turbulent biological tissues

Presenting the intensity development of a circular Laguerre-cosh-Gaussian (CLChG) beam in turbulent mouse biological tissues is the major goal of the current work. Using the power spectrum refractive index from Schmitt's model and the extended Huygens-Fresnel integral, the propagation formula of the CLChG beam is produced. In order to determine the spreading properties of the studied beam, analytical expressions of the CLChG beam's effective beam size in turbulent mouse biological tissues are constructed. Some graphical representations have to be carried out in order to discover the impacts of beam and biological turbulence parameters on this sort of beam. The findings show that the transformation of the CLChG beam into a Gaussian-like beam in the far field occurs more quickly when the beam passes through the deep dermis of the mouse. The shape of the CLChG beam can also be changed by choosing a specific value for the parameter linked to the cosh-part. Because the effective beam spot radius along the x- and y-axis are equal, we also see that the beam spot in biological tissues takes on a circular shape.

Flattening filter for Gaussian-shaped monochromatic X-ray beams: an application to breast computed tomography.

The vertical intensity distribution of synchrotron-based X-ray beams usually has a Gaussian profile encompassing large intensity variations. For biomedical imaging applications this may entail sub-optimal dose distributions and large fluctuations in terms of image noise. Commonly, planar metallic filters coupled with absorbing slits systems are applied to adjust the delivered flux and to limit intensity variations, respectively. The latter results in a reduction of the effective beam size. A flattening filter that counterbalances the transverse inhomogeneity, while retaining a sufficient flux, has been developed in the context of a monochromatic phase-contrast breast computed tomography application, ongoing at the Elettra synchrotron facility. The implementation of the new filtration system results in homogeneous intensity (hence dose) distribution and signal-to-noise ratio across the imaged volume. Finally, and most importantly, it allows a wider portion of the beam to be used, directly translating into a major (∼40%) reduction of the overall scan time for samples requiring a field of view larger than the beam size (i.e. multiple translation steps).

Propagation of Cosh-Airy and Cos-Airy Beams in Parabolic Potential

The analytical expressions of one-dimensional cosh-Airy and cos-Airy beams in the parabolic potential are derived in the general and the phase transition points. The expression in the phase transition point shows a symmetric Gaussian intensity profile and is independent of any Airy features, which is completely different from that in the general point. The intensity, the center of gravity, and the effective beam size of the cosh-Airy and cos-Airy beams in the parabolic potential are periodic and have the same period. The effects of the transverse displacement, the cosh factor, and the cosine factor on these periodic behaviors are also investigated. The direction of self-acceleration reverses every half-period. The phase transition point is also the inversion point of the intensity distribution, which indicates that the intensity distributions before and after the phase transition point are mirror symmetrical. The periodic behaviors of the normalized intensity, the center of gravity, and the effective beam size of the cosh-Airy and cos-Airy beams in the parabolic potential are attractive and well displayed. The results obtained here may have potential applications in particle manipulation, signal processing, and so on.

Generation of an Adjustable Optical Cage through Focusing an Apertured Bessel-Gaussian Correlated Schell-Model Beam

An adjustable optical cage generated by focusing a partially coherent beam with nonconventional correlation function named the Bessel–Gaussian correlated Schell-model (BGCSM) beam is investigated in detail. With the help of the generalized Huygens–Fresnel integral and complex Gaussian function expansion, the analytical formula of the BGCSM beam passing through an apertured ABCD optical system was derived. Our numerical results show that the generated optical cage can be moderately adjusted by the aperture radius, the spatial coherence width, and the parameter β of the BGCSM beam. Furthermore, the effect of these parameters on the effective beam size and the spectral degree of coherence were also analyzed. The optical cage with adjustable size can be applied for particle trapping and material thermal processing.

Propagation of an Airy beam through atmospheric turbulence with optical vortex under fractional Fourier transforms

In this paper, we have theoretically investigated the behaviour of an Airy beam (AiB) with an optical vortex (OV) in atmospheric turbulence. The obtained splitting on each line of the phase pattern indicates the OV. The results show that the OV position changes when the power of the fractional Fourier transforms (FrFT) (p) changes. Moreover, uniformity of the spot beam disappears with the presence of the vortex in the AiB. The characteristics of an AiB, such as the effective beam size, number, width, height, and uniformity of the spot beam, change by changing the value of p. The position of the OV in the beam with scintillation and without scintillation was changed by changing the value of p.

Effects of liver tissue turbulence on propagation of annular beam

Effects of tissue turbulence on the propagation properties of an annular laser beam is examined. In this respect, the average intensity profile and the beam spread at the observation plane are formulated and evaluated after the annular laser beam propagates through the turbulent liver tissue. In our formulation, the extended Huygens-Fresnel method is utilized with the involvement of the turbulence power spectrum of the liver tissue. Results obtained from the performed simulations include the variations of the received average intensity and the effective beam size of the annular beam against the changes in the liver tissue turbulence and the laser beam parameters, i.e., against the laser wavelength, tissue length, primary and secondary source sizes of the annular laser beam. Our work in this paper will prove to be helpful in obtaining clues to diagnose abnormalities such as cancer and tumor in a liver tissue.

Study on the Mainardi beam through the fractional Fourier transforms system

In this paper, we introduced the Mainardi beam and indicated its attributes under the Fractional Fourier transform for power variations of Fractional Fourier transform. The results represent that the behavior of the Mainardi beam is similar to that of the Airy beam. The obtained formula is a very powerful tool to describe propagation of a Mainardi beam through the FFT and the FrFT systems. An analytical expression of the Mainardi beam passing through an Fractional Fourier transform system presented. The influences of the Fractional Fourier transform, rational order of the Mittag-Leffler function (Fourier transform of the Mainardi function) on the normalized intensity distribution and characteristics of the Mainardi beam in the Fractional Fourier transform system examined. Power of the Fractional Fourier transform (p) and rational order of the Mittag-Leffler function (q) control characteristics of the Mainardi beam such as effective beam size, number, width, height, and orientation of the beam spot.

Focusing of radially polarized Lorentz–Gauss beams with the power–exponent–phase vortex

Using the vector diffraction theory, the optical field of the focusing radially polarized Lorentz–Gauss beam with the power–exponent–phase vortex is derived. The normalized intensity distributions of the focusing radially polarized Lorentz–Gauss beam with the power–exponent–phase vortex are numerically demonstrated. The influences of the power order n and the topological charge m on the normalized intensity distribution are examined. The beam centre and the effective beam size, which are defined by the first- and the second-order moments of the intensity distribution, are the important parameters for focus. Therefore, the quantitative effects of the power order n and the topological charge m on the beam centre and the effective beam size are further investigated. This research is beneficial to the optical manipulation which is involved in the radially polarized Lorentz–Gauss beam with the power–exponent–phase vortex.

Theory and optical design of x-ray echo spectrometers

X-ray echo spectroscopy, a space-domain counterpart of neutron spin echo, is a recently proposed inelastic x-ray scattering (IXS) technique. X-ray echo spectroscopy relies on imaging IXS spectra, and does not require x-ray monochromatization. Due to this, the echo-type IXS spectrometers are broadband, and thus have a potential to simultaneously provide dramatically increased signal strength, reduced measurement times, and higher resolution compared to the traditional narrow-band scanning-type IXS spectrometers. The theory of x-ray echo spectrometers presented in [1] is developed here further with a focus on questions of practical importance, which could facilitate optical design and assessment of the feasibility and performance of the echo spectrometers. Among others, the following questions are addressed: spectral resolution, refocusing condition, echo spectrometer tolerances, refocusing condition adjustment, effective beam size on the sample, spectral window of imaging and scanning range, impact of the secondary source size on the spectral resolution, angular dispersive optics, focusing and collimating optics, and detector's spatial resolution. Examples of optical designs and characteristics of echo spectrometers with 1-meV and 0.1-meV resolutions are presented.

Orbit and dispersion tool at European XFEL injector

Trajectory and electron beam size play an essential role in Free Electron Laser (FEL) obtainment. Since transverse dispersion changes off-energy particle trajectories and increases the effective beam size, dispersion and orbit must constantly be controlled and corrected along the whole lattice. In this paper the principles underlying the orbit and dispersion correction tool, developed at DESY, are described. The results of its testing on European XFEL injector are presented.

A theoretical investigation on the propagation properties of Hollow Gaussian beams passing through turbulent biological tissues

Hollow Gaussian beam (HGB) is a new mathematical model to describe a dark hollow beam with circular and noncircular symmetry. By expanding the HGB as a superposition of a series of Hermite-Gaussian mode, the analytical formulae of the considered beam passing through turbulent biological tissues are investigated and developed, based on the extended Huygens-Fresnel integral. Our results indicate the effect of the turbulent biological tissues on the propagation properties of the HGB. The present study shows that the circular and the elliptical HGB propagating in biological tissues will evolve into Gaussian like beam in the far field, and the central irradiance of the HGB propagating in biological tissues rises more rapidly with lager constant of refraction index structure Cn2. We also calculate the formulae of the effective beam size of the HGB in turbulent biological tissues which provide a convenient way to learn the spreading properties of the considered beam.

Average intensity and spreading of an astigmatic sinh-Gaussian beam with small beam width propagating in atmospheric turbulence

Propagation properties of astigmatic sinh-Gaussian beams (ShGBs) with small beam width in turbulent atmosphere are investigated. Based on the extended Huygens–Fresnel integral, analytical formulae for the average intensity and the effective beam size of an astigmatic ShGB are derived in turbulent atmosphere. The average intensity distribution and the spreading properties of an astigmatic ShGB propagating in turbulent atmosphere are numerically demonstrated. The influences of the beam parameters and the structure constant of atmospheric turbulence on the propagation properties of astigmatic ShGBs are also discussed in detail. In particular, for sufficiently small beam width and sinh-part parameter as well as suitable astigmatism, we show that the average intensity pattern converts into a perfect dark-hollow profile from initial two-petal pattern when ShGBs with astigmatic aberration propagate through atmospheric turbulence.

Effective X-ray beam size measurements of an X-ray tube and polycapillary X-ray lens system using a scanning X-ray fluorescence method

Size measurements of an X-ray beam produced by an integrated polycapillary X-ray lens (PXL) and X-ray tube system were performed by means of a scanning X-ray fluorescence (SXRF) method using three different metallic wires. The beam size was obtained by fitting the SXRF data with the analytical convolution between a Gaussian and a constant functions. For each chemical element in the wire an effective energy was calculated based on the incident X-ray spectrum and its photoelectric cross section. The proposed method can be used to measure the effective X-ray beam size in XRF microscopy studies.

The SESAME materials science beamline for XRD applications

We present a detailed description of the SESAME Materials Science (MS) beamline for X-ray diffraction (XRD) applications, presently under construction in Allan, Jordan. The beamline is based on components previously installed at the Swiss Light Source, but modifications in the beamline design have been introduced to match the characteristics of the SESAME storage ring. The SESAME MS beamline will accommodate XRD experiments in the energy range between 5 and 25 keV. The beamline ray tracing analysis at 10 keV estimates the flux at the sample to be of the order of 1013 (photons s−1), the energy resolution is about 2 eV and the effective beam size at the sample of 300 × 2800 µm2. Investigations of microstruture will be possible as the instrumental broadening, resulted from simulating the diffraction pattern for a standard material, is of the order of 0.01° at 15 keV. A wide range of applications will be possible at the beamline, such as powder diffraction studies, single crystals and in situ XRD. The commisioning of the beamline is expected to be in the second half of 2017.

Effects of biological tissues on the propagation properties of anomalous hollow beams

We derived analytical formulae of anomalous hollow beams (AHBs) passing through the turbulent biological tissues based on the extended Huygens–Fresnel integral formula. With the help of these formulae, we investigate the propagation properties of AHBs in turbulent biological tissues, the irradiance and spreading properties of AHBs in turbulent biological tissues are studied numerically. It is found that the circular and elliptical AHBs eventually become Gaussian beams in the far field and the central irradiance of the AHB rises more rapidly as the value of Cn2 grows. We also calculate the formulae of the effective beam size of AHB and find that finally Wxz becomes equal to Wyz in turbulent biological tissues which can be used to explain the beam spot eventually becomes circular under the influence of turbulence of biological tissues.

Propagation of an Airy beam in a strongly nonlocal nonlinear media

An analytical expression of an Airy beam propagating in a strongly nonlocal nonlinear media is derived. The analytical expressions of the corresponding characteristic parameters for the Airy beam, such as the centre of gravity, the effective beam size, the curvature radius, the kurtosis parameter, and the linear momentum, have also been presented, respectively. The normalized intensity distribution and these characteristic parameters are pictorially demonstrated in the strongly nonlocal nonlinear media, respectively. It shows all the characteristic parameters versus the axial propagation distance are periodic. The period of the linear momentum versus the axial propagation distance is The period of other characteristic parameters and the normalized intensity is The periodic behavior of the Airy beam in the strongly nonlocal nonlinear media has promising application in optical switch and optical micromanipulation.

PROPERTIES OF AIRY-GAUSS BEAMS IN THE FRACTIONAL FOURIER TRANSFORM PLANE

An analytical expression of an Airy-Gauss beam passing through a fractional Fourier transform (FRFT) system is derived. The normalized intensity distribution, phase distribution, centre of gravity, effective beam size, linear momentum, and kurtosis parameter of the Airy-Gauss beam are demonstrated in FRFT plane, respectively. The influence of the fractional order p on the normalized intensity distribution, phase distribution, centre of gravity, effective beam size, linear momentum, and kurtosis parameter of the Airy-Gauss beam are examined in FRFT plane. The fractional order p controls the normalized intensity distribution, phase distribution, centre of gravity, effective beam size, the linear momentum, and kurtosis parameter. The period of the normalized intensity, phase, and centre of gravity versus the fractional order p is 4. The period of effective beam size, linear momentum, and kurtosis parameter versus the fractional order p is 2. The periodic behaviors of the normalized intensity distribution, phase distribution, centre of gravity, effective beam size, linear momentum, and kurtosis parameter can bring novel applications such as optical switch, optical micromanipulation, and optical image processing.

Propagation of a Hermite–Laguerre–Gaussian beam in a turbulent atmosphere

The propagation and spreading of a Hermite–Laguerre–Gaussian (HLG) beam in a turbulent atmosphere has been investigated. Based on the extended Huygens–Fresnel integral and some mathematical techniques, analytical expressions for the average intensity, the effective beam size, and the kurtosis parameter of an HLG beam in a turbulent atmosphere are derived, respectively. The average intensity distribution and the spreading properties of HLG beams in a turbulent atmosphere are numerically demonstrated. Upon propagation in a turbulent atmosphere, the central lobes in the beam spot of the HLG beam will evolve into the dominant lobes, and the peripheral lobes around the central lobes will evolve into the subdominant lobes. The influences of the additional angle parameter and the transversal mode numbers on the propagation of HLG beams in a turbulent atmosphere are also discussed. As the coherence length of the turbulence is determined by the propagation distance, the effect of the additional angle parameter on the effective beam size is related to the propagation distance. The kurtosis parameter generally increases with increasing the additional angle parameter. The influence of the transversal mode numbers on the kurtosis parameter is related to the additional angle parameter and the propagation distance. According to the practical need of free-space optical communications and remote sensing, the HLG beam in a turbulent atmosphere can be controlled by choice of the additional angle parameter and the transversal mode numbers.

Fractional Fourier transform of Airy beams

An analytical expression of an Airy beam passing through a fractional Fourier transform (FRFT) system is presented. The effective beam size of the Airy beam in the FRFT plane is also derived. The influences of the order of FRFT, the modulation parameter, and the transverse scale on the normalized intensity distribution and the effective beam size of an Airy beam in the FRFT plane are examined. The order of FRFT controls the effective beam size and the orientation of the beam spot. The modulation parameter affects the effective beam size and the number of lateral side lobes. The normalized intensity distribution and the effective beam size are both proportional to the transverse scale.