E. Wolf (ed.)'s Progress in Optics, Vol. 23 PDF

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By E. Wolf (ed.)

ISBN-10: 0444869824

ISBN-13: 9780444869821

Growth in Optics is a well-established sequence of volumes of overview articles facing theoretical and utilized optics and comparable matters. largely acclaimed via quite a few reviewers as representing an authoritative and up to date resource of knowledge in all branches of optics, the sequence maintains to fulfil a real want in the clinical group. Articles are contributed by way of major scientists (including Nobel Prize winners) selected through the Editor, with the recommendation of a world panel of specialists constituting the Editorial Advisory Board. some of the articles showing in those volumes have due to the fact that been demonstrated as simple references of their respective fields. Vols. I-X: Out of print

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If we define the bracket average ( * * ) as the average over the ensemble of surface realizations, then, in order to find, say, the coherent scattered field ( f) we must know the ensemble average of products of interaction functions of the form 40 MULTIPLE SCAlTERING FROM ROUGH SURFACES [I, § 7 which are related to the n-point characteristic function of the surface. The general case has been done for a surface satisfying multivariate homogeneous Gaussian statistics (ZIPFEL and DESANTO [ 19721).

31) which we refer to as version (A) of the theory. Version (B) again uses Green’s theorem but now on QSc and Gf, the former field satisfying the sourceless, homogeneous Helmholtz equation. Using the same boundary conditions eqs. 30) we now find that + Gy(x:, x,,) a an 1 Gy(x, x i ) dS’ . 32) Version (C) uses Green’s theorem applied to aSc and a Green’s function G which vanishes on the surface: C(X, X i ) = 0. 34) where @,‘ is the image Green’s function. 41) where A‘ is the unit normal to the surface.

The result is, with r, = x; - x,, given by where the correlation function C and rms height 0 were defined in eq. 8). 21) is a boundary condition solely on the coherent wave, but whereas the stochastic boundary condition was local, this condition is nonlocal. In the flat surface limit 0 = 0 and we recover locality. We have also used the statistical translational invariance in the correlation function. Note that in the limit L 4 x (C(r,)-, 1) locality is not recovered in perturbation theory. The coherent wave in eq.

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Progress in Optics, Vol. 23 by E. Wolf (ed.)

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