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Contribution to diffraction theory; Contribution a la theorie de la diffraction

Abstract

In a first part, we have given a general and detailed treatment of the modern theory of diffraction. The rigorous theory is formulated as a boundary value problem of the wave equation or Maxwell equations. However, up to the present time, such a program of treating diffraction by optical systems, even for simple optical instruments, has not been realized due to the complicated character of the boundary conditions. The recent developments show clearly the nature of the approximation of the classical theories originally due to Fresnel and Young, later formulated in a rigorous manner by Kirchhoff and Rubinowicz, respectively and, at the same time the insufficiency of these theories in explaining a number of diffraction phenomena. Furthermore, we have made a study of the limitations of the approximate theories and the recent attempts to improve these. The second part is devoted to a general mathematical treatment of the theory of diffraction of optical systems including aberrations. After a general and specific analysis of geometrical and wave aberrations along classical and modern (Nijboer) lines, we have been able to evaluate the diffraction integrals representing the image field at any point in image space explicitly, when the aberrations are small. Our formulas  More>>
Authors:
Chako, N [1] 
  1. Commissariat a l'Energie Atomique, Saclay (France). Centre d'Etudes Nucleaires
Publication Date:
Nov 01, 1966
Product Type:
Thesis/Dissertation
Report Number:
CEA-R-3151
Resource Relation:
Other Information: 129 refs
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUNDARY CONDITIONS; DIFFRACTION; GEOMETRICAL ABERRATIONS; INTEGRAL EQUATIONS; MATHEMATICAL MODELS; MAXWELL EQUATIONS; SCHROEDINGER EQUATION; WAVE EQUATIONS
OSTI ID:
20650681
Research Organizations:
CEA Saclay, 91 - Gif-sur-Yvette (France); Faculte des Sciences de l'Universite de Paris - 75 (France)
Country of Origin:
France
Language:
French
Other Identifying Numbers:
TRN: FR05R3151090294
Availability:
Available from INIS in electronic form
Submitting Site:
FRN
Size:
181 pages
Announcement Date:
Nov 28, 2005

Citation Formats

Chako, N. Contribution to diffraction theory; Contribution a la theorie de la diffraction. France: N. p., 1966. Web.
Chako, N. Contribution to diffraction theory; Contribution a la theorie de la diffraction. France.
Chako, N. 1966. "Contribution to diffraction theory; Contribution a la theorie de la diffraction." France.
@misc{etde_20650681,
title = {Contribution to diffraction theory; Contribution a la theorie de la diffraction}
author = {Chako, N}
abstractNote = {In a first part, we have given a general and detailed treatment of the modern theory of diffraction. The rigorous theory is formulated as a boundary value problem of the wave equation or Maxwell equations. However, up to the present time, such a program of treating diffraction by optical systems, even for simple optical instruments, has not been realized due to the complicated character of the boundary conditions. The recent developments show clearly the nature of the approximation of the classical theories originally due to Fresnel and Young, later formulated in a rigorous manner by Kirchhoff and Rubinowicz, respectively and, at the same time the insufficiency of these theories in explaining a number of diffraction phenomena. Furthermore, we have made a study of the limitations of the approximate theories and the recent attempts to improve these. The second part is devoted to a general mathematical treatment of the theory of diffraction of optical systems including aberrations. After a general and specific analysis of geometrical and wave aberrations along classical and modern (Nijboer) lines, we have been able to evaluate the diffraction integrals representing the image field at any point in image space explicitly, when the aberrations are small. Our formulas are the generalisations of all anterior results obtained by previous investigators. Moreover, we have discussed the Zernike-Nijboer theory of aberration and generalised it not only for rotational systems, but also for non-symmetric systems as well, including the case of non circular apertures. The extension to non-circular apertures is done by introducing orthogonal functions or polynomials over such aperture shapes. So far the results are valid for small aberrations, that is to say, where the deformation of the real wave front emerging from the optical system is less than a wave length of light or of the electromagnetic wave from the ideal wave front. If the aberrations are large, then one must employ the method of stationary phase. A complete mathematical treatment of this method of evaluating multiple integrals containing a large parameter will be found in our second thesis, including applications. Finally, we have given a detailed development of the diffraction theory of corpuscular waves by an electron optical system, satisfying a Schroedinger equation. (author) [French] Dans une premiere partie nous presentons un expose general de la theorie moderne de la diffraction. La theorie rigoureuse est formulee a partir de l'equation d'onde scalaire et aussi des equations de Maxwell, comme un probleme aux valeurs limites. Cependant, un tel programme n'a pas encore ete realise jusqu'a present, meme pour les plus simples des systemes optiques, a cause de la complexite de ces conditions aux limites. Les developpements recents montrent clairement le caractere approximatif des theories classiques de Fresnel et Young, formulees rigoureusement par Kircnhoff et Rubinowicz. Elles montrent aussi l'insuffisance de ces theories, pour expliquer un certain nombre de phenomenes de diffraction. Nous avons fait l'etude de ces differentes theories approximatives, y compris une tentative recente, pour les ameliorer et nous en avons montre les limites. La deuxieme partie contient une analyse mathematique generale de la diffraction des aberrations. Apres un expose des aberrations geometriques et ondulatoires selon les developpements classiques et modernes (Nijboer), les integrales representant le champ dans l'espace image, ont ete evaluees. Les formules obtenues generalisent tous les resultats des chercheurs anterieurs. Pour la comparer avec la theorie de Zernike-Nijboer, nous avons developpe et generalise notre theorie dans le cas des ouvertures non-circulaires et pour des systemes optiques qui ne sont pas de revolution. La fonction d'aberration est developpee en polyn es orthogonaux sur l'ouverture de la pupille de sortie. La fonction d'image a ete calculee, pour des ouvertures triangulaires et elliptiques, dans le cas d'une seule aberration du troisieme ordre. Tous ces resultats sont valables, quand les aberrations sont tres petites, c'est-a-dire quand la deformation de l'onde reelle est inferieure a la longueur d'onde. Mais nous avons etudie le probleme de la diffraction, quand les aberrations sont plus grandes que la longueur d'onde, par l'application de la methode de phase stationnaire qui permet l'evaluation des inegrales multiples a grand parametre et qui a ete developpee en detail dans notre deuxieme these. Enfin, les methodes ont ete appliquees au probleme de la diffraction par des ondes corpusculaires, dans un systeme d'optique electronique, ou elles satisfont a l'equation de Schroedinger. (auteur)}
place = {France}
year = {1966}
month = {Nov}
}