Elliptical Aperture Research Articles

Sound penetration through an arbitrarily shaped aperture in a soft screen: Analytical approach

Van Bladel has reduced the problem of low-frequency scattering through an aperture in a soft screen to a sequence of static integral equations. Analytical solutions are known at the moment for a circular and an elliptic aperture only. A new analytical method is proposed here which is valid for the apertures of arbitrary shape. The method is based on an integral representation for the reciprocal distance between two points obtained by the author earlier. Specific approximate formulae are derived for evaluating the average value of the zeroth-order term in the low-frequency expansion for an aperture in the shape of a polygon, a triangle, a rectangle, a rhombus, a circular sector and a circular segment. All the formulae are checked against the numerical solutions known in the literature, and a good agreement is confirmed.

Relations between electric and magnetic polarizabilities and other related quantities

The magnetic polarizability tensor, the demagnetization tensor, and the depolarization tensor of an ellipsoid are all related to its electric polarizability tensor. The four tensors are completely described by two scalars. The relationship between the electric and magnetic polarizabilities of an ellipsoid can be applied directly to an elliptic aperture. The total cross section of an antenna integrated over wavelength is given by the antenna's polarizabilities.

New line integral expressions for Fraunhofer diffraction

New expressions for Fraunhofer diffraction at an arbitrary shape aperture are presented. These are expressed in the simple form of the line integral over the rim of the aperture. Far field patterns for various shaped apertures are easily derived from these expressions which are well suited for numerical calculation. As examples, Fraunhofer diffraction fields for elliptical, polygonal, and sinusoidal apertures are shown.

Jacobi-Bessel analysis of reflector antennas with elliptical apertures

Although many reflector antennas possess circular projected apertures, there are recent satellite and ground antenna applications for which it is desirable to employ reflectors with elliptical apertures. Here a modification of the Jacobi-Bessel expansion is presented for the diffraction analysis of reflectors with elliptical apertures. A comparative study is also performed between this modified Jacobi-Bessel algorithm and the one which uses the Jacobi-Bessel expansion over a circumscribing circular region. Numerical results are presented for offset reflectors with elliptical and circular apertures and the improved convergence properties of the modified algorithm are highlighted.

Fresnel and Far-field Diffraction of a Truncated Elliptical Gaussian Beam Due to an Elliptical Aperture

Abstract Using the Hopkins algorithm, expressions are derived for the intensity patterns, in both the Fresnel and far-field regions, associated with the diffraction of a plane-wave elliptical Gaussian beam truncated by an elliptical aperture. This is accomplished by evaluating the diffraction integral subject to the Fresnel approximation. Numerical results are presented that indicate how the truncation parameter affects the side-lobe level in the Fresnel and far-field regions.

A further research on the Jacobi-Bessel series method in analysis of reflector antenna

Based on the work developed by R. Mittra and others (1979), this paper carries on the Jacobi-Bessel series method to compute far-field patterns of a paraboloid reflector antenna with elliptical aperture by means of recursion of the series coefficients p B m n about indicesp andm respectively and enhances the computational efficiency to a great extent.

Sound transmission through an arbitrarily shaped aperture in a rigid screen: Analytical approach

Van Bladel has reduced the problem of low-frequency scattering through an aperture in a rigid screen to a sequence of static integral equations. Analytical solutions are known at the moment for a circular and an elliptic aperture only. A new analytical method is proposed here which is valid for apertures of arbitrary shape. The method is based on an integral representation for the reciprocal distance between two points, which was previously obtained by the author. Specific approximate formulae are derived for evaluating the average value of the first term in the low-frequency expansion for an aperture in the shape of a polygon, a triangle, a rectangle, a rhombus, a circular sector and a circular segment. All the formulae are checked against the numerical solutions known in the literature, and a good accuracy is confirmed. The second and the third terms of the low-frequency expansion can be derived in a similar manner, and the related formulae are to be publlshed later.

Sound penetration through an arbitrarily shaped aperture in a rigid screen: Analytical determination of the quadratic terms in low-frequency expansion

Van Bladel has reduced the problem of low-frequency scattering through an aperture in a rigid screen to a sequence of static integral equations. Analytical solutions are known at the moment for a circular and an elliptic aperture only. A new analytical method is proposed here which is valid for the nonelliptical apertures. The method is based on an integral representation for the reciprocal distance between two points obtained earlier by the author. Specific approximate formulae are derived for evaluating the average value of the quadratic term in the low-frequency expansion for an aperture in the shape of a polygon, a rectangle, a rhombus, and a cross. All the formulae are checked against the solutions known in the literature, and a good accuracy is confirmed in a sufficiently wide range of the aspect ratio.

Cold radiation shield design for a linear detector array II

This communication reports the results of calculation of cold shield shading effects in a linear detector array for an elliptical aperture geometry with varying major-to-minor axis ratio. The results suggest that an elliptical aperture geometry is a better design than a rectangular aperture.

The cortical representation of gradient-adapted multiple-stimulus perimetry.

Some stimuli, if scaled in proportion to the reciprocal of inter ganglion cell receptive field separation (M-scaled) exhibit an isosensitivity profile. Perimetric profiles which are isosensitive across the extent of the normal visual field facilitate multiple stimulus perimetry and provide a convenient method for the detection of abnormality. The purpose of the investigation was to establish whether the stimulus diameters necessary to produce an isosensitive perimetric profile were scaled in proportion to M. Sensitivity profiles for a sample of 15 age-matched observers were obtained with the Friedmann VFA Mk II. The stimulus aperture diameters were then measured under 100 X magnification. The observed elliptical apertures, corrected for obliquity of viewing, plate thickness and distance from the eye were represented as diameters of circles possessing an equivalent area to that of the ellipse. The apparent diameters were then M-scaled relative to stimulus pattern h using the equations of Rovamo and Virsu (1979). An overestimation of the M-scaled diameters relative to the apparent diameters was noted which increased with eccentricity for all four cardinal meridians by a factor of up to 3.5 times. It is suggested that the over compensation indicates that the cortical representation of perimetric spot targets at low photopic adaptation levels depends not only upon retinal ganglion cell density but also upon the variation of ganglion cell characteristics with eccentricity. The implications of this finding for perimetric instrument design are discussed.

Use of an Elliptical Aperture to Control Saturation in Closely-Coupled, Cold Iron, Superconducting Dipole Magnets

The high fields permitted by superconducting windings result in saturation of closely-coupled iron in dipole and quadrupole beam transport magnets. Coupland1 suggested using a triangular cutout at the poles to reduce the change in the sextupole (b2) term due to saturation. The use of an elliptical aperture in a close-coupled dipole for the Relativistic Heavy Ion Collider (RHIC) has been studied using the BNL computer program MDP (a version of GFUN). The ellipse aspect ratio was varied while holding the horizontal (minor) radius constant. The proper aspect ratio gives no shift in b2 due to saturation, and a reduction in the b4 shift. A modification of the ellipse also reduces b4. The elliptical aperture introduces a large b2 term at low field which must be compensated for by the coil design. A practical coil design which does this for the RHIC magnet is presented.

Fresnel and far-field diffraction due to an elliptical aperture

Based on the Hopkins [ Proc. Phys. Soc. London Sect. B70, 1002 ( 1957)] algorithm, theoretical and experimental investigations of the Fresnel and far-field diffraction of a coherent light beam that is due to an elliptical aperture with the axial ratio ∊ between 0 and 1 are presented. Perspective plots of the intensity distribution patterns and their cross section across the major and minor axes are generated with the help of an IBM-370/168 computer. Experimental results presented in photographs and in densitograms are compared with the theoretical prediction. A close agreement between them has been obtained. Also given are the plots of the intensity distribution along the optical axis.

Radiation patterns of an elliptical aperture in the Fresnel region

The Fresnel diffraction of a coherent light beam due to an elliptical aperture with the axial ratio ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\epsilon</tex> ) between 1.0 and 0.5 is investigated. The computations are based on an procedure due to Hopkins. Perspective plots of the intensity distribution diagrams are generated for Fresnel number <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(F) = 5</tex> and the axial ratio <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(\epsilon) = 1.0, 0.5</tex> , respectively. The results are compared with the corresponding diagrams for the circular aperture. With the decreasing axial ratio, it is observed that the central maxima and minima disappear in contrast to that of the circular aperture, whereas one finds a modulation in the central region along with the side maxima. Also given are the plots of the intensity distribution on the optical axis.

Mathematical model of emission from a multichannel laser

A mathematical model is proposed of emission from a multichannel laser regarded as a system of N identical sources with field distributions differing in respect of the phase. A study of far-field distributions of the intensity and of the radiation energy is used to formulate certain general conclusions. The example of a pair of ideal radiators which are not phase locked and have elliptic or rectangular apertures is used to analyze the characteristics of the angular divergence of the radiation.

Systematic design of a dual offset reflector antenna with an elliptical aperture

Systematic design of a dual offset reflector antenna with an elliptical aperture

Far-field radiation patterns of elliptical apertures and its annulli

A Fourier transform technique is applied to derive expressions for the diffraction field due to elliptical apertures and its annulli. Perspective plots of the intensity distribution diagrams are generated for various values of the axis ratio with the help of an IBM-370/168 computer. All possible cases are discussed briefly.

Symmetrical crossed rectangular horn for a circularly polarized multiple-beam reflector antenna

Radiation characteristics of a symmetrical crossed rectangular horn using a solution of an integral eigenvalue equation given by Lin is described. E - and H -plane pattern symmetry and two-dimensional radiation patterns for circular polarization are studied comparing with those of a square horn, with specific emphasis on cross-polarization levels. Using a symmetrical crossed rectangular horn as a circularly polarized primary feed gain and cross-polarization characteristics of offset paraboloidal reflector antennas with circular and elliptical apertures have been investigated. A practical example of a circularly polarized multiple-beam antenna with contoured pattern using three symmetrical-crossed rectangular horns is shown.

Iridopteris eriensis from the Middle Devonian of North America, with Systematics of Apparently Related Taxa

A reinvestigation of the permineralized axis Iridopteris eriensis Arnold, from type and new material, was conducted as part of a comprehensive study of all members of the Iridopteridineae of Arnold. The information presented here suggests that Iridopteris was a highly distinctive Middle Devonian plant with (1) a five-ribbed, mesarch, primary xylem column and apparent bilateral symmetry; (2) simple protoxylem strands, or cavities representing protoxylem strands, grouped in multiples near the tips of primary xylem ribs; (3) traces of two distinct sizes; (4) whorled order of trace departure; (5) metaxylem tracheids with circular to elongate elliptical bordered pit pairs with elliptical apertures; and (6) a distinct boundary between stele and cortex apparently comprised of a single layer of cells with dark materials in their lumina. Accumulating evidence suggests that a taxonomically distinct group of Middle and lower Upper Devonian plants has only partially been recognized. The Iridopteridales is here established to include the central concept of Arnold's Iridopteridineae, except for Reimannia, combined with directly comparable components of the Ibykales of Skog and Banks. Members of this new order include Arachnoxylon, Iridopteris, Ibyka, and Asteropteris.

Mode cutoff frequencies in elliptical and large numerical aperture optical fibres

It is shown that by perturbation of the weakly-guiding, circular fibre, it is possible to obtain, in a straightforward way, accurate information about the cutoff characteristics of the higher-order modes in optical fibres having either an elliptical cross-section (with aspect ratios as large as 2∶1) or a relatively large numerical aperture.

Radiation from unsymmetrically excited elliptical apertures

Expressions are derived for the field radiated by an unsymmetrically excited elliptical aperture which also encompass the special case of an unsymmetrically excited circular aperture. Tables and figures are presented for the ease of symmetrical excitation and for a specific example of unsymmetrical excitations.