THE INTERACTION OF ELECTROMAGNETIC WAVES WITH SOME NATURAL SURFACES DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By WILLIAM HELLER PEAKE, B.S., M.A. The Ohio State University 1959 Approved by: t ACKNOWLEDGEMENTS I would like to thank my adviser, Professor Dickey, and my colleagues in the Antenna Laboratory, particularly Professor R. Li. Cosgriff and M r. R. C. Taylor, for their encouragement and advice during the past several years. Some of the m easurem ents of complex dielectric constant reported in Chapter II were made by M r. Tet Pang, and some of the correlation functions were computed by M r. Byron Potts. A part of the work described in this dissertation was sponsored by the Air Research and Development Command, Wright Air Development Center, Wright Patterson Air Force Base, Ohio, under contracts AF 33( 616)-3649 and AF 33( 616)-61 58. ii TABLE OF CONTENTS Page CHAPTER I - THE PROBLEM OF SCATTERING BY NON-UNIFORM SURFACES 1 A. Introduction 1 B. The Taxonomic Problem and the Scattering P ro b le m 1 C. The Role of Models 3 D. General Approach 4 CHAPTER H - THE SCATTERING COEFFICIENTS 6 A. Introduction 6 B. The Slightly Rough Surface 1 2 C. The Surface of Long, Thin Lossy Cylinder! 21 CHAPTER IB - THE BACK-SCATTERING COEFFICIENTS. WITH APPLICATIONS TO THE RADAR RETURN FROM TERRAIN 34 A. Introduction 34 B. Models with Undetermined Parameter* 34 C. The Slightly Rough Surface 38 D. Surfaces Covered with Vegetation in the Form of Long Thin Loaay Cylinders 43 E. Other Theoretical Models 48 CHAPTER IV - APPLICATIONS TO THE RADIOMETRIC PROPERTIES OF TERRAIN 62 A. Introduction - Kirchhoff's Law 62 iii B. Apparent Surface Temperatures 68 C. Point Source Effects 75 D. Application to the Apparent Temperature of Some Natural Surfaces 77 CHAPTER V - CONCLUSIONS 86 REFERENCES 88 A P P E N D IX I 93 A P P E N D IX U 98 iv LIST OF FIGURES Page Fig. 1. Geometry of the scattering problem. 7 Fig. 2. Scattering from a slightly rough surface. 13 Fig. 3. Scattering by a cylinder. 23 Fig. 4. Back-scattering from a vegetation covered surface (15" grass in head) illustrating Eq. (51). 36 Fig. 5. Back-scattering from a vegetation covered surface (short grass) illustrating Eq. (52). 37 Fig. 6. Correlation functions for 3 asphalt surfaces. 40 Fig. 7. Correlation functions for 2 concrete surfaces. 40 Fig. 8. Effect of dielectric constant on return from a slightly rough surface (horizontal polarization). 41 Fig. 9. Effect of dielectric constant on return from a slightly rough surface (vertical polarization). 41 Fig. 10. Calculated and m easured return from a slightly rough asphalt surface (vertical polarization). 50 Fig. 11. Calculated and m easured return from a slightly rough asphalt surface (horizontal polarization). 50 Fig. 12. Calculated and m easured return from a slightly rough asphalt surface (vertical polarization). 51 Fig. 13. Calculated and m easured return from a slightly rough asphalt surface (horizontal polarization). 51 Fig. 14. Calculated and m easured return from a slightly rough asphalt surface (vertical polarization). 52 Fig. 15. Calculated and m easured return from a slightly rough asphalt surface (horizontal polarization). 52 v Calculated and m easured return from a slightly rough concrete surface (vertical polarization). 53 Calculated and m easured return from a slightly rough concrete surface (horizontal polarization). 53 Calculated and m easured return from a slightly rough concrete surface (vertical polarization). 54 Calculated and m easured return from a slightly rough concrete surface (horizontal polarization). 54 Calculated and m easured return from vegetation at 8.6 mm wavelength. Dependence on water c o n te n t. 55 Calculated and m easured return from vegetation at 3 cm wavelength. Dependence on water content. 55 Calculated and m easured return from vegetation at 8. 6 mm wavelength. Dependence on water c o n te n t. 56 Calculated and m easured return from vegetation at 3 cm wavelength. Dependence on water content. 56 Calculated and m easured return from vegetation at 8. 6 mm wavelength. Dependence on AN. 57 Calculated and m easured return from vegetation at 3 cm wavelength. Dependence on AN. 57 Calculated and m easured return from vegetation at 8. 6 mm wavelength. Dependence on AN. 58 Calculated and m easured return from vegetation at 3 cm wavelength. Dependence on AN. 58 Calculated return from vegetation at Ka-band. Ratio of return for vertical polarization to return for horizontal polarization for two values of water content and various densities of vegetation. 59 vi Fig. .19. Calculated return from vegetation at X-band. Ratio of return for vertical polarization to return for horizontal polarization for two values of water content and various densities of vegetation. 60 Fig. 30. Calculated and measured wavelength dependence of the return from vegetation, at 45° incidence angle. 61 Fig. 31. Geometry for derivation of Kirchhoff's law. 64 Fig. 32. Contributions to the apparent temperature of a surface. 70 Fig. 33. Measured and calculated apparent temperature of an asphalt surface. 79 Fig. 34. The functions Fx (r) and F?(r) vs r. 82 Fig. 35. Measured and calculated apparent temperature of a vegetation covered surface. 84 Fig. 36. Measured and calculated apparent temperature of a vegetation covered surface. 84 Fig. 37. Measured and calculated apparent temperature of a vegetation covered surface. 8 5 Fig. 38. Geometry for reciprocity theorem. 99 vii C H A P T E R I THE PROBLEM OF SCATTERING BY NON-UNIFORM SURFACES A. Introduction One of the m ajor unsolved problems of electromagnetic theory ss that of the interaction of electrom agnetic radiation with non-uniform surfaces, particularly those natural surfaces that constitute the sur­ face of the earth. Apart from its intrinsic interest, a genera] solution of this problem would have many applications, both scientific and technical. A complete solution for all frequencies and classes of sur­ face is out of the question at the present tim e. However, there exist ceriain general relations between the properties of the surface and those of the radiation in interaction with it. There are also certain restricted wavelength intervals and classes of surface for which detailed solutions of the scattering problem may be obtained. It is the purpose of this study to derive some of these general relations, and to carry out the detailed solution for two special surfaces of practical interest in the microwave region. B. The Taxonomic Problem and the Scattering Problem There are two m ajor difficulties that face the investigator of such problem s. The first is that of solving the electromagnetic sc steering problem for any particular, properly specified non- uniform surface. Unfortunately, present theories of scattering from 1 irregular surfaces are not sufficiently well developed to permit an exact solution of the scattering problem except in a few special cases. Thus approximate solutions must be used. The second, and in some respects the m ore difficult, problem is that of describing the surfaces of interest, or at least of classi­ fying them into categories that are significant for the scattering problem. These categories may be chosen intuitively, on the basis of the appearance of the surface; experimentally, on the basis of the observed characteristics of the interaction of the surface with radi­ ation; or on theoretical grounds, on the basis of the kind of model used to represent the surface when formulating the scattering prob­ lem . It is clear that in any useful taxonomy, all three approaches diould lead to the same grouping or association of terrains. A good idea of the rather prim itive state of the classification problem as it applies to the interaction of light waves with natural surfaces may be had from Penndorf's review1 of Krinov's reflectiv­ ity data. 2 At microwave frequencies, the situation is sim ilar.** Indeed even the relatively simple problem of describing the surface of the sea is only now, * after several decades of intensive research, approaching a state that is suitable for the solution of scattering p r o b le m s . 2 C. The Rale of Models As a consequence of these two difficulties, it has been cus tom ar) to approach the problem of calculating the interaction of electrom agnetic radiation with such surfaces by the use of models. That is, use has been made of idealized surfaces which are more or less amenable to theoretical treatm ent, and more or less rep­ resentative of the category of natural surface under consideration. Not all surfaces can be represented in this way at the present tim e, but for those which can, the specification of a few basic param eters of the surface (which may be chosen on the basis of theoretical con­ venience or experim ental evidence) will allow one to estim ate the interaction of the surface with radiation. In the past, most surface models have fallen into one of two classes, depending on which of these two principal difficulties their authors have wished to confront. In the first group4* S* 4 the models have been chosen so as to avoid the difficulties of the scattering problem, by representing the surface with assem blies of objects of known scattering properties (spheres, point scatterers, facets, etc. ). The number, size, etc* of these scatterers have provided the param ­ eters of the models, to be fitted by recourse to experim ent. Insofar as it has been the aim of such models to predict the statistical prop­ erties of the scattered radiation, and to provide em pirical formulas 3 for its angular dependence, they have been quite successful.