By Alexei A. Maradudin, Eugenio R. Méndez, Tamara A. Leskova
This publication offers an method of the layout and fabrication of optical parts which are in accordance with using one- or two-dimensional randomly tough surfaces to mirror or transmit gentle in special methods. The reader is supplied with an creation to analytical tools for the answer of direct difficulties in tough floor scattering, and fabrication concepts. those could be invaluable in contexts outdoors the scope of this e-book. the benefits and downsides of this stochastic procedure in comparison to the diffractive optics strategy are mentioned. eventually, experimental effects that be sure the predictions of the theories built during this booklet are provided. - authority of authors- the single publication at the subject- derivations are given intimately, with many figures illustrating effects
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60) can now be evaluated. 86b) 26 One-Dimensional Surfaces = 2Ns b 2π sin θ0 − sin θs f . 87) If we now use the fact that the length L1 is equal to 2Ns b, then on combining Eqs. 88) where we have indicated explicitly that the mean differential reflection coefficient depends on both θs and θ0 . We now make the change of variable sin θ0 − sin θs = −γ . 90b) we can rewrite Eq. 91) θs = θ0 + 2 tan−1 γ . 92) so that From Eq. 89) we obtain the useful results cos θs = (1 − γ 2 ) cos θ0 − 2γ sin θ0 , 1+γ2 sin θs = (1 − γ 2 ) sin θ0 + 2γ cos θ0 .
In tackling this problem, it is good to know at the outset what kinds of surfaces can produce a mean scattered intensity of a prescribed form or, what is equally important, what kinds of surfaces cannot produce a mean scattered intensity of a desired form, so as to avoid starting the solution of the inverse problem on the basis of invalid assumptions about the nature of the surface we seek. In this section we address these questions. As noted in Chapter 1, an optical element that has a variety of potential applications is a band-limited uniform diffuser.
The results obtained for Np = 100 000 realizations of the surface profile function were used in calculating the average in Eq. 132). From the results presented in Fig. 6 we see that the random surface generated from the pdf f (γ ) given by Eq. 139) behaves as a band-limited uniform diffuser. 1. 7. The mean differential reflection coefficient ∂R/∂θs estimated from Np = 20 000 realizations of the surface profile function for the case of a band-limited uniform diffuser for which f (γ ) is given by Eq.