Download or read book Diffraction by a Spheroid Classic Reprint written by Bertram R. Levy and published by Forgotten Books. This book was released on 2019-01-24 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Diffraction by a Spheroid Our first result, given in Section 2, is based upon the geometrical theory of diffractionei]. This is a theory which describes the field scattered by any object directly in terms of geometrical properties of the object and certain coefficients determined from a few canonical problems. 'we have previously applied this theory to diffraction by convex cylindersez] and convex solidstfi]. Whenever possible we compared the results of that theory with the asymptotic form (for wavelength small compared to object dimensions) of the solution of the corresponding boundary value problem. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Download or read book Diffraction by a Spheroid written by Bertram R. Levy and published by . This book was released on 1959 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Diffraction by a Spheroid written by Bertram R. Levy and published by . This book was released on 1959 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Diffraction by an Elliptic Cylinder Classic Reprint written by Bertram Levy and published by . This book was released on 2016-06-24 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Diffraction by an Elliptic Cylinder In Section 2 we formulate the boundary value prdblem.for the reduced wave equation corresponding to a cylindrical wave incident upon an acous tically soft or acoustically hard elliptic cylinder. The problem is than solved by the usual separation of variables technique, and an alternative representation for the field is presented. By using the asymptotic expansions for the special functions occurring in the solution the asymptotic expansion of the diffracted.field is found in Section 3. In.section h the diffracted field is constructed geometrically and this construction is shown to be in agreement with the asymptotic expansion of the exact solution. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Download or read book Diffraction by an Aperture II Classic Reprint written by J. B. Keller and published by Forgotten Books. This book was released on 2017-11-20 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Diffraction by an Aperture II The geometrical theory of diffraction used in Part I involves the concept of a diffracted ray. It enables us to express the singly diffracted field explicitly in terms of geometrical quantities. Similar geometrical expressions can also be obtained for the multiply diffracted field. In the Kirchhoff method and its modifications, on the other hand, the diffracted field is expressed as a double integral over the aperture. We will evaluate the double integrals given by all these methods asymptotically for small wavelengths l. We will find that each one leads to the formula deduced in Part I for the singly edge-diffracted field, with an appropriate diffraction coefficient in each case. This fact supports the theory used in Part I. Only the Braunbek method yields exactly the same edge diffraction coefficient, and therefore the same singly edge-diffracted field, as is obtained in Part I. This agreement between the Braunbek method and the geometrical theory of diffraction lends support to both of these methods, and shows that the simpler geometrical theory can be used instead of the more complicated Braunbek method. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Download or read book Diffraction Theory written by C. J. Bouwkamp and published by Forgotten Books. This book was released on 2017-11-23 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Diffraction Theory: A Critique of Some Recent Developments A number of important recent developments have not been treated in these lectures. Among these we can mention the exact solutions recently obtained for diffraction by circular apertures and disks, and the wiener-hopf technique which has proved its power in the solution of certain waveguide problems. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Download or read book Classical and Modern Diffraction Theory written by Kamill Klem-Musatov and published by SEG Books. This book was released on 2016-06-30 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing geophysicists with an in-depth understanding of the theoretical and applied background for the seismic diffraction method, “Classical and Modern Diffraction Theory” covers the history and foundations of the classical theory and the key elements of the modern diffraction theory. Chapters include an overview and a historical review of classical theory, a summary of the experimental results illustrating this theory, and key principles of the modern theory of diffraction; the early cornerstones of classical diffraction theory, starting from its inception in the 17th century and an extensive introduction to reprinted works of Grimaldi, Huygens, and Young; details of the classical theory of diffractions as developed in the 19th century and reprinted works of Fresnel, Green, Helmholtz, Kirchhoff, and Rayleigh; and the cornerstones of the modern theory including Keller’s geometrical theory of diffraction, boundary-layer theory, and super-resolution. Appendices on the Cornu spiral and Babinet’s principle are also included.

Download or read book Molecular Diffraction of Light Classic Reprint written by C. V. Raman and published by Forgotten Books. This book was released on 2015-08-05 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Molecular Diffraction of Light In the course of the work, references are made to cases in which the classical wave theory apparently fails to explain the facts relating to molecular scattering in a satisfactory manner, and in the final chapter an attempt is made to consider these cases in terms of the conception introduced by Einstein in 1905 that light is not continuous wave-motion but consists of discrete quanta moving through space. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Download or read book Diffraction by an Aperture I Classic Reprint written by Joseph B. Keller and published by Forgotten Books. This book was released on 2018-02-03 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Diffraction by an Aperture I The present treatment of diffraction of a wave by an aperture in a thin screen is based upon a new theory of wave propagation. This theory is called 'the geometrical theory of because it is an extension of geometrical optics which describes diffraction phenomena. It is like geometri cal optics inasmuch as it postulates that fields propagate along certain lines or curves called rays. However, it goes beyond geometrical optics, by intro ducing various new kinds of rays, called 'diffracted rays', in addition to the usual optical ones. It also assigns a field value to each point on a ray in a quantitative way and postulates that the total field at a point is the sum of the fields on all rays through that point. Thus the new theory not only provides a qualitative description of diffraction in terms of the diffracted rays, but it permits a quantitative determination of the field as well. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Download or read book Diffraction by an Elliptic Cone Classic Reprint written by Lester Kraus and published by Forgotten Books. This book was released on 2018-02-17 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Diffraction by an Elliptic Cone We will formulate our diffraction problems as follows. Let the domain R be the exterior or interior of a semi-infinite elliptic cone, or the exterior of a plane angular sector, and let C be the boundary of R. We wish to find the two Green's functions and defined for r r' About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Download or read book On a Fredholm Equation in Diffraction Theory Classic Reprint written by Irving J. Epstein and published by Forgotten Books. This book was released on 2018-02-21 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from On a Fredholm Equation in Diffraction Theory We consider here the problem of the diffraction of a plane scalar wave normally incident on a plane screen with a circular aperture. Let u be the solution of Au K2u O, which represents the diffracted wave, and let p, 9 be polar coordinates on the screen such that p 0 represents the center of the aperture. We assume that on the screen u 0. Let the radius of the aperture be a and let Q (p) be the value of u in the aperture, 0 5 p 5 a. Bomkamp [1] using the Levine and Schwinger [2] variational method, derived the following result. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Download or read book Diffraction by a Wide Slit Classic Reprint written by Samuel N. Karp and published by . This book was released on 2015-08-04 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Diffraction by a Wide Slit Since there already exist numerous investigations of the diffraction of scalar waves by a slit, the addition of another item to the literature requires some explanation. The purpose of the present note is to give an elementary and intuitive account of the diffraction by an infinite conducting plane with a slit. We consider specifically the case of electromagnetic waves whose electric field possesses only a single component, namely a component in the direction parallel to the edges of the slit. The results are also applicable to the acoustic problem, for soft screens. It is found that the results for large slit widths can be expressed approximately in terms of simple well-known functions and that these approximations are more accurate than those conveniently obtainable by previous procedures. The procedures that have hitherto been proposed and applied to this problem fall into three categories. First, there is the exact theory based upon separation of variables in elliptic coordinates. This procedure is useful only when the ratio of slit width to wavelength is small (that is, say, smaller than 3), Second, there are approximation procedures that are valid when the ratio of slit width to wavelength is small. Such procedures, based on the solution of related electrostatic problems, were indicated by Rayleigh and have been Ca developed further by, e.g., Sommerfeld, Groschwitz and Honl, and Bouwkamp. Finally, there are approximate treatments valuable particularly for large ratios of slit widths to wavelength; among these are calculations based on Kirchoff's procedures and their various modifications, and the work of Schwarzschild. A calculation related to that of Schwarzschild has recently been published by Fox in connection with diffraction by a pulse. It should be noted that variational techniques may be applied in conjunction with any of the approximate methods just mentioned. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Download or read book Diffraction Theory Three Papers written by Abe Shenitzer and published by Forgotten Books. This book was released on 2016-08-21 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Diffraction Theory Three Papers: Translated From the Russian On the basis of a critical survey of earlier papers it is shown that the results obtained in these papers are insufficiently justified. A rigorous solution of the problem is given. It is also shown that in the limiting case of very high frequencies the solution takes on a form which corresponds to the approximation yielded by geometrical Optics. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Download or read book Diffraction in Inhomogeneous Media Classic Reprint written by Bernard D. Seckler and published by Forgotten Books. This book was released on 2018-02-03 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Diffraction in Inhomogeneous Media This theory differs from ordinary geometrical optics by the inclusion of certain additional rays called diffracted rays and others called complex or imaginary rays. The former are associated with the boundaries or discontinuities of the medium while the latter are associated with refraction shadows which occur in the absence of boundaries. In addition to characterizing these new rays, the theory also provides a method for calculating the field associated with them. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Download or read book Diffraction by a Circular Aperture at High Frequencies Classic Reprint written by Harold Levine and published by Forgotten Books. This book was released on 2018-02-09 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Diffraction by a Circular Aperture at High Frequencies The mathematical analysis of diffraction phenomena has been significantly extended in recent years. A variety of methods, new and old, have proved their worth in enlarging the roster of problems amenable to calculation, particularly as regards configurations of geometrical complexity. It should be remarked, however, that the form of solutions thus Obtained may not always be well suited for describing certain features of the scattering problem, such as the high frequency or shortawavelength characteristics. The latter can be recognized in the zero-wavelength (or geometrical optics) limit, although without the inter esting distinction that is manifest at long wavelengths, say, between like scatterers of different composition. To exhibit a corresponding difference in the scattering at high frequencies one must refine the geometrical optics approxi mation. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Download or read book High Frequency Scattering by an Impenetrable Sphere Classic Reprint written by H. M. Nussenzveig and published by . This book was released on 2015-08-04 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from High-Frequency Scattering by an Impenetrable Sphere The scattering of a scalar plane wave by a totally reflecting sphere (hard-core potential) at high frequencies is treated by a modified Watson transformation. The behavior of the solution both in the near and far regions of space is discussed, as well as the accuracy and domain of applicability of the WKB approximation and classical diffraction theory. It is shown that different transformations are required in the forward and backward half-spaces, and corresponding integral representations for the primary wave are derived. The transformations are rigorously proved and the convergence of the residue series is discussed. In the shadow region, the physical interpretation of the complex angular momentum poles in terms of surface waves is in agreement with Keller's geometrical theory of diffraction. In the lit region, sufficiently far from the shadow boundary, the WKB expansion for the wave function is confirmed up to the second order. On the surface of the sphere, Kirchhoff's approximation is accurate, except in the penumbra region, where the behavior is described by Fock's function. The diffraction effects in the neighborhood of the shadow boundary are investigated and the corrections to classical diffraction theory are obtained. The shift of the shadow boundary is evaluated. The expression for the wave function in the Fresnel-Lommel region is derived and applied to the discussion of the Poisson spot and the behavior near the axis. The total scattering amplitude is evaluated for all angles, including the neighborhood of the forward and backward directions. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Download or read book On Diffraction by an Infinite Grating Classic Reprint written by Fritz Reiche and published by Forgotten Books. This book was released on 2019-01-11 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from On Diffraction by an Infinite Grating The diffraction of a plane wave by an infinite grating of identical circular cylinders is considered. It is shown that the various scattered cylindrical waves combine to form a finite number of plane waves and at: infinite number of surface waves. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.