Elementary Beams Research Articles

Shaping of arbitrary dose distributions by dynamic multileaf collimation

Traditionally, the shaping of non-uniform dose distributions has been performed by using wedges or compensating filters. The advent of high resolution multileaf collimators may largely eliminate the need for material attenuators for modification of the beam. This is achieved by a new technique for the shaping of arbitrary dose distributions by dynamic motion of the collimator leaves. By employing narrow elementary slit beams that correspond to the smallest possible opening of the multileaf collimator, the optimal density of such slit beams, i.e. opening density, can be determined automatically using a newly developed inversion algorithm. The present method has two major advantages: (1) internal structures in the field can be created, controlled solely by steering the collimator leaves, (2) the opening density determined by the algorithm never gives rise to underdosage: this is important from a radiobiological point of view.

Gabor’s expansion of an optical field in Cauchy elementary beams

Gabor’s expansion of an optical field in a discrete two-dimensional superposition of Gaussian elementary beams is extended here to incorporate the so-called Cauchy beams. The resultant expansion scheme has an advantage over the commonly used Gaussian beam representation in situations involving critical-angle refraction of light beams at a dielectric interface.

Gabor's expansion of an aperture field in exponential elementary beams

Gabor's expansion of an aperture field in a discrete two-dimensional superposition of Gaussian elementary beams is extended here to incorporate exponential beams. The resultant expansion scheme has an advantage over the commonly used Gaussian beam representation in situations involving an exponential aperture distribution such as the modal field in a thin slab laser amplifier.

Numerical implementation of the Gabor representation

Gabor's expansion of an electromagnetic field in a discrete two-dimensional superposition of elementary beams is an extended spectral representation having relevance to wave propagation problems. The computational implications of the expansion scheme are investigated within the context of aperture theory, leading to an efficient Gabor's expansion numerical processor.

Radiotherapeutic computed tomography with scanned photon beams

Radiotherapeutic computed tomography is a powerful technique to generate anatomical transversal tomograms of the patient in treatment position by using the therapy beam from the treatment unit. For this purpose the treatment unit has to be equipped with a detector array that can detect the beam transmitted through the patient and a computer that analyzes the data and performs the back projection. When the treatment unit uses scanned elementary photon beams, the only practical technique available for generating high quality high energy photon beams, the operation principle and, to some extent, the image quality is similar to that of a 3rd generation CT-scanner. The optimum choice of detection geometry and type of radiation detectors for radiotherapeutic computed tomography particularly at high photon energies are discussed indicating the merits of BGO (bismuthgermanate) or CWO (cadmiumtungstate) photo diod arrays. The first tomographic images of a thorax phantom at an acceleration potential of 50 MV using such detectors are presented. The image contrast is similar to that for 300 kV X rays mainly because the considerable influence of pair production at 50 MV. Line spread and modulation transfer functions are presented indicating a resolution of the order of two millimeters using a crystal thickness of 5 mm. The advantages with radiotherapeutic computed tomography, beside forming a new general communication channel between different diagnostic techniques, dose planning, and radiation delivery, are the elimination of position errors and the provision of exact attenuation data for dose planning.

Gabor representation and aperture theory

The analytical properties and computational implications of the Gabor representation are investigated within the context of aperture theory. The radiation field in the pertinent half-space is represented by a discrete set of linearly shifted and spatially rotated elementary beams that fall into two distinct categories, the propagating (characterized by real rotation angles) and evanescent beams. The representation may be considered a generalization in the sense that both the classical plane wave and Kirchhoff’s spatial-convolution forms are directly recoverable as limiting cases. The choice of a specific window function [w(x)] and the corresponding characteristic width (L) are, expectedly, cardinal decisions affecting the analytical complexity and the convergence rate of the Gabor series. The significant spectral compression achievable by an appropriate selection of w(x) and L is demonstrated numerically, and simple selection guidelines are derived. Two specific window functions possessing opposite characteristics are considered, the uniformly pulsed and the Gaussian distributions. These are studied analytically and numerically, highlighting several outstanding advantages of the latter. Consequently, the primary attention is focused on Gaussian elementary beams in their paraxial and their far-field estimates. Although the main effort is devoted to aperture analysis, demonstrating the advantages and limitations of the proposed approach, reference is also made to its potential when applied to aperture-synthesis and spatial-filtering problems. The quantitative effects of basic filtering in the discrete Gabor space are depicted.

Electron beam dose planning using discrete Gaussian beams. Mathematical background.

A general method for computerized electron beam dose planning is proposed based on the use of a square or hexagonal grid or matrix of discrete Gaussian elementary beams. Using this method the distribution of absorbed dose in an electron beam of arbitrary cross-section incident on an irregular patient surface can be calculated taking the influence of tissue inhomogeneities into account. The derived expressions for the absorbed dose in narrow and broad uniform beams are compared with experimental data and Monte Carlo calculations. Good agreement is obtained over the clinically significant portion of the absorbed dose distribution at a fairly wide grid spacing of about 0.5 cm.

Electron and photon beams from a 50 MeV racetrack microtron.

The quality of broad high energy photon and electron beams can be improved considerably by the scanning of elementary narrow beams. Dose distributions produced in this way have advantages with respect to improved dose gradients and therapeutic ranges for electrons and lower surface doses, increased depth doses and half value depths for photons. The possibility of giving the whole therapeutic dose in a single local pulse of short duration is discussed as a new method to protect superficial tissues.

Dielectric loaded waveguides as particle separators

Rectangular and circular dielectric loaded waveguides support propagating modes which have transverse deflecting fields which enable them to be used as rf particle separators for elementary particle beams. Electric fields in excess of 4.0 MV/m have been achieved in sample structures. The spark limit of these structures is as yet undetermined. Possible applications include traveling wave separators for beams of 1.0 to 5.0 GeV/ c and “quasi”-point deflectors for beams in excess of 20 GeV/ c.

�ber die Jeanssche Zahl und die W�rmestrahlung in anisotropen und absorbierenden K�rpern

Jeans' number gives the number of vibration modes of electromagnetic equilibrium radiation. By application ofJeans' original method, a formula for this quantity is derived, valid for an anisotropic and dispersive medium. This derivation is followed by a discussion of different points of view of equilibrium radiation as built up by elementary beams. Finally, for an absorbing uniaxial crystal in thermal equilibrium, a relationship is derived, giving the number of quantum transitions related to emission and absorption of light.

Continuous beam steering and null tracking with a fixed multiple-beam antenna array system

This paper describes how continuous null tracking of a target may be achieved with a fixed pattern multiple-beam forming network with a resulting improvement in tracking accuracy when compared to beam interpolation techniques. Continuous null tracking is accomplished by cascading a hybrid phasing matrix with a beam combining networks called a steering box. The steering box combines three elementary beams in the proper ratio to form a composite sum-and-difference beam which may be continuously steered throughout the coverage angle. The change in the sum-and-difference patterns as a function of steering angle is derived for different steering loci. It is shown how pattern asymmetry may be minimized or sidelobe fall-off rate maximized by the proper choice of a steering locus. Several physical realizations of steering boxes are discussed including the steering box employed in an experimental electronic scanning radar system.

On the guided propagation of electromagnetic wave beams

Any field in a half-space can be described by a continuous spectrum of cylindrical waves. If this spectrum comprises substantially only waves whose propagation constant is very close to the plane wave propagation constant, the field can be resolved into a set of elementary wave beams which are characterized by Laguerre polynomials. They satisfy orthogonality relations like the wave modes in a waveguide. The elementary beams or "beam modes" can be reiterated and guided by reconstituting the cross-sectional phase distribution at certain intervals. Reiterative beams are utilized in the beam waveguide. The finite size of the phase resetting devices effects a modification of the reiterative beam modes and causes diffraction losses. These losses decrease very rapidly with increasing diameter of the phasing devices.