{"id":1198,"date":"2026-07-21T13:57:00","date_gmt":"2026-07-21T20:57:00","guid":{"rendered":"https:\/\/chuckrino.com\/?p=1198"},"modified":"2026-07-22T12:15:23","modified_gmt":"2026-07-22T19:15:23","slug":"overview-2","status":"publish","type":"post","link":"https:\/\/chuckrino.com\/?p=1198","title":{"rendered":"Overview"},"content":{"rendered":"

The Theory of Scintillation with Applications in Remote Sensing<\/em> was published in 2011.\u00a0 This website was established as a forum for discussing the book and its applications, anticipating new insights and refinements of computational procedures.\u00a0 The book has served its original purpose well.\u00a0 However, computational resources have improved considerably, and the implied completeness of the theory needs elaboration.<\/p>\n

Developing a theory of scintillation starts with Maxwell\u2019s equations, which characterize the interaction of electromagnetic (EM) fields with material media.\u00a0 In free space <\/em>Maxwell\u2019s equations can be reduced to a \u00a0single vector equation that predicts the propagation of EM waves at the speed of light.\u00a0 In a transparent \u00a0homogeneous medium Maxwell\u2019s equations predict propagating vector waves comprised of two orthogonal circularly polarized characteristic modes.<\/p>\n

Exploiting the predictions of Maxwell\u2019s equations started with Marconi\u2019s demonstration of long-range communication with transmissions in\u00a0 the \u00a0kilohertz (HF) range. \u00a0Unknown to Marconi, the fields he was detecting were refracted by the earth\u2019s ionosphere, which is an inhomogeneous propagation medium.\u00a0 Manipulating Maxwell\u2019s equations to characterize propagation in an inhomogeneous medium remains a challenging task to this day.<\/p>\n

The textbook Waves and Fields in Inhomogeneous Media<\/em> treats a class of media comprised of homogeneous subregions isolated by discontinuous boundaries.\u00a0 A region defined by a closed boundary is formally a scatterer.\u00a0 Scattering theory treats the interaction of EM waves with collections of scatterers.\u00a0 Boundary integral equations reconcile fields intercepting each scatterer.\u00a0 The complexity of the problem is manifested by the fact that every scatterer potentially interacts with every other scatterer. \u00a0Discretizing the interactions leads to solving a very large system of coupled linear equations.<\/p>\n

Scintillation theory addresses one of the most challenging applications of Maxwell’s equations, namely propagation in a transparent inhomogeneous medium. Forward propagation assumes that in a plane slicing the medium a two-dimensional spatial Fourier decomposition can isolate a set of propagating\u00a0plane waves constrained to the forward hemisphere, which excludes the source field.\u00a0 No additional constraint is imposed on the propagation directions of the propagating waves.\u00a0 The forward propagation equation (FPE) developed in Chapter 2 of The Theory of Scintillation…<\/em> is based on a forward propagation equation (FPE). \u00a0The parabolic wave equation (PWE) is structurally similar to the FPE.\u00a0 However, the square root propagation operator is replaced by a quadratic approximation, which constrains the angular extent and introduces the Fresnel scale. \u00a0Free-space PWE propagation is unchanged if the propagation distance and the frequency are varied while keeping the Fresnel scale constant.<\/p>\n

The fact that the FPE imposes no constraint on the range of propagation angles suggested that it was more general than the PWE.\u00a0 However, when the FPE was applied to the HF propagation of a beam systematic differences between the trajectory of \u00a0a refracted narrow beam and ray-theory predictions were found.\u00a0 The approximations made in developing the geometric ray equations are not constrained by propagation angles.\u00a0 Agreement with ray theory predictions is a necessary condition.\u00a0 Consequently,\u00a0 solutions to the FPE are no more accurate than their PWE counterparts.<\/p>\n

The development in The Theory of Scintillation…<\/em> is constrained to near line-of-sight propagation.\u00a0 As a general rule propagation calculations that separate free propagation and the media interaction, which allows efficient discrete Fourier transformation implementation are similarly constrained.\u00a0 \u00a0Severe scintillation may develop but the angular extend of the propagating field cannot exceed more than a few degrees.\u00a0 A review with demonstrations of more accurate but computationally demanding FPE calculations are presented in \u00a0Scintillation Theory Revisited.<\/a><\/em><\/p>\n

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The Theory of Scintillation with Applications in Remote Sensing was published in 2011.\u00a0 This website was established as a forum for discussing the book and its applications, anticipating new insights and refinements of computational procedures.\u00a0 The book has served its … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[10,13,14],"tags":[],"class_list":["post-1198","post","type-post","status-publish","format-standard","hentry","category-ionospheric-scintillation","category-propagation-models","category-scintillation-theory-book"],"_links":{"self":[{"href":"https:\/\/chuckrino.com\/index.php?rest_route=\/wp\/v2\/posts\/1198","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/chuckrino.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/chuckrino.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/chuckrino.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/chuckrino.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1198"}],"version-history":[{"count":7,"href":"https:\/\/chuckrino.com\/index.php?rest_route=\/wp\/v2\/posts\/1198\/revisions"}],"predecessor-version":[{"id":1211,"href":"https:\/\/chuckrino.com\/index.php?rest_route=\/wp\/v2\/posts\/1198\/revisions\/1211"}],"wp:attachment":[{"href":"https:\/\/chuckrino.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1198"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/chuckrino.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1198"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/chuckrino.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1198"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}