1 edition of **Mathematical Theory of Diffraction** found in the catalog.

- 29 Want to read
- 11 Currently reading

Published
**2004**
by Birkhäuser Boston, Imprint: Birkhäuser in Boston, MA
.

Written in English

- Mathematics,
- Mathematical physics

Arnold Sommerfeld"s Mathematical Theory of Diffraction marks a milestone in optical theory, full of insights that are still relevant today. In a stunning tour de force, Sommerfeld derives the first mathematically rigorous solution of an optical diffraction problem. Indeed, his diffraction analysis is a surprisingly rich and complex mix of pure and applied mathematics, and his often-cited diffraction solution is presented only as an application of a much more general set of mathematical results. The body of Sommerfeld"s work is devoted to the systematic development of a method for deriving solutions of the wave equation on Riemann surfaces, a fascinating but perhaps underappreciated topic in mathematical physics. This complete translation, reflecting substantial scholarship, is the first publication in English of Sommerfeld"s original work. The extensive notes by the translators are rich in historical background and provide many technical details for the reader. A detailed account of the previous diffraction analyses of Kirchhoff and Poincaré provides a context for the striking originality and power of Sommerfeld"s ideas. The availability of this translation is an enriching contribution to the community of mathematical and theoretical physicists.

**Edition Notes**

Statement | by Arnold Sommerfeld |

Series | Progress in Mathematical Physics -- 35, Progress in mathematical physics -- 35. |

Classifications | |
---|---|

LC Classifications | T57-57.97 |

The Physical Object | |

Format | [electronic resource] / |

Pagination | 1 online resource (ix, 157 p.) |

Number of Pages | 157 |

ID Numbers | |

Open Library | OL27073336M |

ISBN 10 | 1461264855, 0817681965 |

ISBN 10 | 9781461264859, 9780817681968 |

OCLC/WorldCa | 853262209 |

Introduction. The previous post in this series, Understanding Diffraction Grating, explained why iridescence occurs on some is a wave, and it bends every time it finds an obstacle in its path. If a material presents a microscopic slit or a bump, . Mathematical Theory of Diffraction: Sommerfeld, Arnold, Nagem, Raymond J., Zampolli, Mario, Sandri, Guido: Books -

The geometrical theory of diffraction is an extension of geometrical optics which accounts for diffraction. It introduces diffracted rays in addition to the usual rays of geometrical optics. These rays are produced by incident rays which hit edges, corners, or vertices of boundary surfaces, or which graze such surfaces. Various laws of diffraction, analogous to the laws of reflection and. Lectures by distinguished physicist examine geometrical optics, theory of interference and diffraction, Maxwell's Theory, crystal optics, and molecular optics. Peerless resource for students and professionals. Numerous helpful figures. Category: Science An Introduction To The Theory Of Optics.

Diffraction Gratings: Theory and Applications 3 What is a diffraction grating? zIt is a device that reflects or refracts light by an amount varying according to the wavelength. zIt works in analogy to the prism. zBasically, a diffraction grating performs a Fourier Transform, separating a waveform in the time domain into a number of waveforms in the. This is the first comprehensive book on the dynamical diffraction of x-rays since the development of synchrotron radiation. There is an introduction to the subject presenting early developments and the basic results, followed by a detailed development of the diffraction and propagation properties of x-rays in perfect crystals and by an extension of the theory to the case of .

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Arnold Sommerfeld's Mathematical Theory of Diffraction marks a milestone in optical theory, full of insights that are still relevant today. In a stunning tour de force, Sommerfeld derives the first mathematically rigorous solution of an optical diffraction problem. Indeed, his diffraction analysis is a surprisingly rich and complex mix of pure Cited by: Arnold Sommerfeld's Mathematical Theory of Diffraction marks a milestone in optical theory, full of Mathematical Theory of Diffraction book that are still relevant today.

In a stunning tour de force, Sommerfeld derives the first mathematically rigorous solution of an optical diffraction problem. Indeed, his diffraction analysis is a surprisingly rich and complex mix of pure and applied mathematics, and his often-cited.

Arnold Sommerfeld's Mathematical Theory of Diffraction marks a milestone in optical theory, full of insights that are still relevant today. In a stunning tour de force, Sommerfeld derives the first mathematically rigorous solution of an optical diffraction problem. "Based on the original German edition, Mathematische Theorie der Diffraction, appearing in Mathematische Annalen 47 (),Springer-Verlag."--Title page verso.

Description: vii, pages: illustrations ; 24 cm. Contents: Mathematical Theory of Diffraction.- 1. General problem formulation.- 2. Expansions in Bessel functions.- 3. Equations of Mathematical Diffraction Theory focuses on the comparative analysis and development of efficient analytical methods for solving equations of mathematical diffraction theory.

Following an overview of some general properties of integral and differential operators in the context of the lin. Mathematical Modeling in Diffraction Theory: Based on A Priori Information on the Analytical Properties of the Solution provides the fundamental physical concepts behind the theory of wave diffraction and scattered wave fields as well as its application in radio physics, acoustics, optics, radio astronomy, biophysics, geophysics, and astrophysics.

The theory of diffraction, as it was founded by Fresnel and made more precise analytically by Kirchhoff, does not satisfy the requirements of mathematical rigor for various reasons.

I have already expressed some objections of this type previously†).Cited by: In these two books, Ufimtsev presented the further development and application of PTD and its validation by mathematical theory.

In particular, a new version of PTD, based on the concept of elementary edge waves, is presented in his book Fundamentals of the Physical Theory of Diffraction.

In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when the diffraction pattern is viewed at a long distance from the diffracting object, and also when it is viewed at the focal plane of an imaging lens.

The equation was named in honour of Joseph von Fraunhofer although he was not actually involved in the development of the theory. The book presents a new and original method for the solution of boundary value problems in angles for second-order elliptic equations with constant coefficients and arbitrary boundary operators.

It enables the reader to master the modern techniques of the theory of diffraction. The book reviews the general considerations of thermodynamics, such as the first and second laws of thermodynamics, the van der Waals equation, and Nernst's third law of thermodynamics.

The text also discusses the application of thermodynamics to special systems, the theory of phase equilibria, the electromotive force of galvanic cells, and the.

matical physics appeared - the mathematical theory of diffraction. Using it, rigorous solutions to the problem of diffraction by a wedge, sphere, and infinite cylinder were obtained. Subsequently, other rigorous solutions were added; however, the total number of solutions was relatively small.

Discover the best Diffraction books and audiobooks. Learn from Diffraction experts like Alexander G. Kyurkchan and Max Born. Read Diffraction books like Mathematical Modeling in Diffraction Theory and Principles of Optics with a free trial. An important role in the mathematical theory of diffraction is played by solutions that depend harmonically on time, i.e.

solutions of equation (1) of the form (4) The parameter corresponds to the circular frequency. The functions, and (see formulas (1) and (3)) should also show a harmonic dependence on time.

Buy Mathematical Theory of Diffraction (Progress in Mathematical Physics) by Arnold Sommerfeld, Raymond J. Nagem, Mario Zampolli (ISBN: ) from Amazon's Book Store.

Everyday low prices and free delivery on eligible : Arnold Sommerfeld. It includes the mathematical background needed for risk management, such as probability theory, optimization, and the like.

The goal of the book is to expose the reader to a wide range of basic problems, some of which emphasize analytic ability, some requiring programming techniques and others focusing on statistical data analysis. diffraction theory will be treated in a forthcoming review by Claus Muller.

It is worth while to mention that a second and revised edition of Baker and Copson’s standard work on The Mathematical Theory of Huygens’ Principle (Baker and Copson ) has been met with great enthusiasm by workers in the field. For an introduction in diffraction. diffraction by a disk, etc., to illustrate it.

Agreement is shown be-tveen the predictions of the theory and various other theoretical analyses of some of these problems. Experimental confirmation of the theory is also presented. The mathematical justification of the theory on the basis of electromagnetic theory.

Bouwkamp C J Diffraction theory, a critique of some recent developments New York University, Mathematics Research Group, Research Report No EM Braumann H Z. Naturforsch. 3a Braunbek W Ann. Phys., Lpz.

6 Sommerfeld's Theory of Diffraction: 1 Sommerfeld's many-valued wave-functions; 2 The diffraction of plane-polarized light by a reflecting half-plane; 3 Diffraction of plane-polarized light by a black half-plane.

For example, the first mathematical theory of light diffraction is due to Fresnel. He reaffirmed the wave nature of light and gave a theory of half-period zones with which he could calculate diffraction patterns in simple geometries.

This gave remarkable agreement with experiments.2 Fundamendals of the geometrical theory of diffraction + Show details-Hide details p. 7 –28 (22) Fundamentals of the geometrical theory of diffraction is reported.

GTD is an extension of geometrical optics (GO). They divide in two groups [11]: the GO laws in boundless media where they allow the construction of rays and wavefronts and the calculation of the field and its polarisation along.The new wavefront at some later time can be constructed by summing up the wavefronts from all of the radiated spherical waves.

Joseph Fresnel formed a mathematical theory of diffraction by turning this summation into an integral and including the phase of the light when adding together the propagating spherical waves. This scalar diffraction.