Abstract

The possibility of applying an ordinary quasi-geometrical technique for Fraunhofer diffraction calculations on absolutely absorbing three-dimensional (3-D) bodies of constant thickness is investigated. It is shown that such an application can lead to results that are inadequate for finding the physical diffraction pattern of 3-D bodies. A modified version of the technique is suggested that, to a greater degree, takes into account secondary diffraction and thus permits a more exact presentation of characteristic features of the light diffracted by 3-D bodies. Some examples of this approach applied to the light-diffraction analysis of simple 3-D bodies are given. It is shown experimentally and with calculations that this approach permits description of the diffraction effects of 3-D bodies of the class mentioned in rather simple form and with good accuracy.

© 1981 Optical Society of America

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  11. It is obvious that the quasi-geometric approach application is right when a true Fresnel image of the back face reduced to the input plane differs only slightly from the initial one g(x0). For this it is necessary that the Fresnel zone size ε =√λd be much less than the characteristic size D of the binary function g(x0), i.e., D≫ √λ d.

1979

1977

M. Kochsiek, H. Kunzmann, and J. Tantau, "Anwendung Beugungsoptischer Methoden zur Messung der Durchmesser von kleinen Wellen," PTB-Mitt. 87, 279–282 (1977).

G. Harburn, J. K. Ranniko, and R. P. Williams, "An aspect of phase in Fraunhofer diffraction patterns," Optik 48, 321–328 (1977).

1976

S. Schmidt, "Ein Beitrag zur Ekrlärung der Lichtbeugung am metallischen Kriszylinder," PTB-Mitt. 86, 239–247 (1976).

1973

1961

Arsenault, H.

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, London, 1965).

Brousseau, N.

Bytchkov, R. M.

Chugui, Yu. V.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Harburn, G.

G. Harburn, J. K. Ranniko, and R. P. Williams, "An aspect of phase in Fraunhofer diffraction patterns," Optik 48, 321–328 (1977).

Hönl, H.

H. Hönl, A. W. Maue, and K. Westpfahl, Theorie der Beugung (Springer-Verlag, Berlin, 1961).

Keller, J. B.

Kochsiek, M.

M. Kochsiek, H. Kunzmann, and J. Tantau, "Anwendung Beugungsoptischer Methoden zur Messung der Durchmesser von kleinen Wellen," PTB-Mitt. 87, 279–282 (1977).

Koronkevitch, V. P.

Kunzmann, H.

M. Kochsiek, H. Kunzmann, and J. Tantau, "Anwendung Beugungsoptischer Methoden zur Messung der Durchmesser von kleinen Wellen," PTB-Mitt. 87, 279–282 (1977).

Lugt, A. Vander

A. Vander Lugt, "Operational notation for the analysis and synthesis of optical data-processing systems," Proc. IEEE 54, 1055–1063 (1966).

Maue, A. W.

H. Hönl, A. W. Maue, and K. Westpfahl, Theorie der Beugung (Springer-Verlag, Berlin, 1961).

Ranniko, J. K.

G. Harburn, J. K. Ranniko, and R. P. Williams, "An aspect of phase in Fraunhofer diffraction patterns," Optik 48, 321–328 (1977).

Schmidt, S.

S. Schmidt, "Ein Beitrag zur Ekrlärung der Lichtbeugung am metallischen Kriszylinder," PTB-Mitt. 86, 239–247 (1976).

Tantau, J.

M. Kochsiek, H. Kunzmann, and J. Tantau, "Anwendung Beugungsoptischer Methoden zur Messung der Durchmesser von kleinen Wellen," PTB-Mitt. 87, 279–282 (1977).

Westpfahl, K.

H. Hönl, A. W. Maue, and K. Westpfahl, Theorie der Beugung (Springer-Verlag, Berlin, 1961).

Williams, R. P.

G. Harburn, J. K. Ranniko, and R. P. Williams, "An aspect of phase in Fraunhofer diffraction patterns," Optik 48, 321–328 (1977).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, London, 1965).

Appl. Opt.

J. Opt. Soc. Am.

Optik

G. Harburn, J. K. Ranniko, and R. P. Williams, "An aspect of phase in Fraunhofer diffraction patterns," Optik 48, 321–328 (1977).

PTB-Mitt.

M. Kochsiek, H. Kunzmann, and J. Tantau, "Anwendung Beugungsoptischer Methoden zur Messung der Durchmesser von kleinen Wellen," PTB-Mitt. 87, 279–282 (1977).

S. Schmidt, "Ein Beitrag zur Ekrlärung der Lichtbeugung am metallischen Kriszylinder," PTB-Mitt. 86, 239–247 (1976).

Other

M. Born and E. Wolf, Principles of Optics (Pergamon, London, 1965).

H. Hönl, A. W. Maue, and K. Westpfahl, Theorie der Beugung (Springer-Verlag, Berlin, 1961).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

A. Vander Lugt, "Operational notation for the analysis and synthesis of optical data-processing systems," Proc. IEEE 54, 1055–1063 (1966).

It is obvious that the quasi-geometric approach application is right when a true Fresnel image of the back face reduced to the input plane differs only slightly from the initial one g(x0). For this it is necessary that the Fresnel zone size ε =√λd be much less than the characteristic size D of the binary function g(x0), i.e., D≫ √λ d.

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