Random volume scattering
1964; The National Institute of Standards and Technology; Volume: 68D; Issue: 9 Linguagem: Inglês
10.6028/jres.068d.096
ISSN2376-5771
Autores Tópico(s)Computational Geometry and Mesh Generation
ResumoThe di sturbances produ ccd by a sli gh tly inhomogeneo us r a ndom m cdium o n a pass in g wave can be classified in to co ntr ibu tions d epe ndin g on a n inCl'easing llu mber of successive scatterings.The indi vidu al co nt ribu t ions a ppear in an expansion of t he Ro lu t io n of a n integr al eq uation.The fir st te r m, the Born approximation , o ill y acco u nts for a sin g le scattering.Convenient expressions for t hi s approx imat ion res ult from a sad dl e poi li t t reatm ent for s h or t di stances, a nd from a Fraun h ofer a pproximation for la rg e r di sta nces .Th e evalu a\ ion of t he higher-o rder co ntr ibu t ions, describi ng plura l-scatterin g eff ects, leads to mat he mati cal d iffi cul t ies wh ich a re evaded by co nsiderin g t he scat terill g; mecha ni s m as a M a rk ov ia n p rocess .The correspond in g t heory can be developed wit h t he a id of an integ ro-dir-fer ent ial diffu sion eq uation ; t he latte r r efers to t he join t probabili ty de nsity of t he lateral and ang u la r d eviations suffered by t he trajecto ry of t he passi ng w'tve .Th e equat ion in quest ion can be solved w ith t he a id of fo ur-d imensio na l o perat io na l calc ulu s ; i t r ed uces to t he simp le d iffere nt ial eq uat ion of Fok ker-Pla nck u nd cr s pecial co nd itio ns .Th e a ppl ication of t h e ge neral eq uat ion to t ro pospheri c point-to-poi nt rad io comm uni cation is work ed out.It is sh own t hat t he fa r-d istance fi eld, associated i n t hi s case w ith multip le scatterin g, docs dec rease proportio na ll y to t he second or t hird powe r of t h e in verse di stance.
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