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Fresnel Integral

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Fresnel Integral 

Integrals of the form

are called Fresnel integrals. They were introduced by A. J. Fresnel for the solution of problems of the diffraction of light. In the case of improper Fresnel integrals, we have S(∞) = C(∞) = ½. Tables of Fresnel integrals are given in many handbooks (for example, E. Jahnke, F. Emde, and F. Lösch, Spetsial’nye funktsii, 2nd ed., 1968 [translated from German]).
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In either case, the diffraction pattern due to the principal aperture A can be evaluated using a generalized Fresnel integral derived by this author from the general equations for the propagation of cross-spectral density in a partially coherent optical field (3).
Issues in optical diffraction theory by Mielenz, Klaus D. / Journal of Research of the National Institute of Standards and Technology
In the Fresnel limit on either side of the aperture plane (|z| [much greater than] [lambda]) the forward and reverse fields are unidirectional, and the forward field is reduced to the standard expressions in terms of Fresnel integrals for slits and Lommel functions for circular apertures [8] for z > 0, and to the unperturbed geometrical field for z < 0.
Optical diffraction in close proximity to plane apertures. III. ... by Mielenz, Klaus D. / Journal of Research of the National Institute of Standards and Technology
1 Analysis of Fresnel Integral Consider the purely mathematical problem of obtaining a variable spaced grating from self-assembled tiles.
Diffractive optics from self-assembled DNA by Levine, Zachary H. / Journal of Research of the National Institute of Standards and Technology
 
 
 
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