.AN nIDOOR l-fB:l'nOD FOR liiEP.sURE1·iEtJT OF BACK-.sCATTERHm COEFFICIENT,s by David Clarence Roee A thesis s'J.bmi tted in partial fulfilment of the requirements of Doctor of Philosophy in the Faculty of Graduate Studies and Research Ea.ton Electronics Research Laborat.ory He Gill Uni ver si ty, Hontreal April, 1953 TABLE OF CONT&"'IJTS Pace ABSTRliCT Ci) J.CKHOHLEDm~S Cii) INTRODUCTION l l A LABORATORY 11EI'HOD l"OR Iv:1EliSUREHENT OF BACK-SGATTERING COEFFICI:E:f-.ITS ••••••••••••••••••••••••••••••••••••••••••• 5 2 LENS INVESTIG~~TIOl'JS 2.1 Lens Requirements •••••••••••••••••••••••••••••••••••••• 9 2.2 Lens Construction •••••••••••••••••••••••••••••••••••••• 10 2.3 Design of the Lens Feed •••••••••••••••••••••••••••••••• 14 2.L.,. Incident Fields and Aperture Fields •••••••••••••••••••• 16 2.5 Heur Fields of Lenses: Theory and l'1easurement •••••••••• 21 3 THEORY OF BACX-SCli.TTERDm THROUGH ~~ LENS 3.1 Statement of the Problem ••••••••••••••••••••••••••••••• 31 3.2 Errors in the Eack-scattering Coefficient due to Diffraction •••••••••••••••••••••••••••••••••••••••••• 31 a. Nuti1atior: and Lens &rors •••••••••••••••••••••••••• 32 b. IJon-uniform Il1wnination •••••••••••••••••••••••••••• 41 4 EXPERIHENTAL ARRAHGEl'Œl'lT .t'tm PREIJIHINARY l>1Ej~URE1vlENTS 4.1 l\.pparatus •••••••••••••••••••••••••••••••••••••••••••••• ~.5 /." .• 2 Preliminary Heasurements ••••••••••••••••••••••••••••••• 49 5 HEASUREHENTS .4JID IYIEASUREivjJ!!NT ~l.NALYSIS •••••••••••••••••••••• 55 6 SUl·'1HA.-qy iùID CONCLUSIONS •••••••• ~ •• • • • • • • •• • • • • • • • • •• • • • • • • • 65 llPPENDIX 1: DEVELOPt"lENT OF AN .iffiTIFICIAL DIELECTRIC FOR l-'lICROHAVE L~\ SES ••••••••••••••••••••••••••••••••••••••••••••••• 67 BIBLIOGR~œHY ••••••••••••••••••••••••••••••••••••••••••••••• 77 (; \ \~ , ABSTR.il.CT An indoor method for measurement of the back-scatterin,:; of short radio waves is described. The scatterer is illuminated by a quasi-plane \oJave generated by collimating the field froID a point source by a micro- loJave lens. It is 5hO\-;'}1 that the back-scattering coefficients of metal discs of radii one to six \-Iavelensths can be ffieasurec1 w"Ï th considerable accuracy using 8. lens thirty-three Havelengths in d.i.ameter. Baclc- scatterinz by circl.ùar cylinders also is discussed. Perturbations of the baclc-scattered fields, due to diffraction by the fini te lens aperture are evaluCl.ted theoretice.lly. T",O neu features of the diffraction fields associated ,·Ii th lenses are explained: the field in the plane of a c.ircular aperture, due ta incident spherical ",aves, is predicted b:{ an empirical eCiuationj the field neé~r the surface of a dielectric lens is explained qualito.tively. Investizations on an isotropie artificial dielectric, and on a le115 construct.ed from it, are described. The author is indebted to 11.1.3 director, Professor 8- •.ù .• ::oonton for expert guidance throushout t.he investigation. DiscussioDc Hi th Drs H.E.<T. Neuc;ebauer and G. Bel-cefi concernine; electroma:.=;netic problems have been moci t helpful. The critic8.1 remarks of t.he author's colleaeue, ]'-fr'. G.C. HcCor:rnick, have he1ped to c1éxify the mat.heI'l.a.tical l,·Jork. Hany of the 8.ri thr.18tica1 computations Here madA by J1iss E. l1ajor. Br. V. Avar1aid <o'.1:.d his [;roup of teclï.nicians have contri buted valuable sl1scestions, especial1y vIi th reGard to 1ens crinà.ins t.echni~:ues. The research l,-JaS financed, in part, by the Defence Research Board of Canada through Contract D.R.B. No. 176. A studentship from the National Research COlIDcil 0f Camlc~ a for the 1952-53 session is e;rate- f ully aclmo',-Iled eed. -1- INTRODUCTION The investigation of back-scattering coefficients, or radar cross- sections, occupies one part of the broad field of diffraction studies. When electromagnetic energy irradiates an object, sorne of the energy is absorbed and dissipated as heat, the remainder being distributed in space in a manner that depends on the geometry and electrical constants of the object, and the characteristics of the incident radiation. This modi- fication of the incident energy is referred to as scattering, or diffraction by the obstacle. Since the advent of radar, considerable interest has been stimulated in the nature of scattered fields at that point in space where the incident energy originates. These are called the back-scattered fields; their magnitude, for steady state conditions, is specified by a constant, 0', characteristic of the obstacle. The back-scattered energy in such a measurement is often interpreted as being set up by specular reflection from the scatterer; in general, this interpretation is incorrect. The back-scattered field which results from a plane incident wave is the type that is of practical interest and in addition, i t is of great theoretical interest. The plane wave field can be obtained experimentally by placing the scatterer at a large distance from the radiating source since the phase variation over a given scattering area is inversely pro- portional to the source distance. Investigations, utilizing this fact have been carried out at YcGill University1,2 and elsewhereJ ,4. For a given size of scatterer, the condition on phase variation also stipulates 1. H.D. Griffiths, "Br.ck Scatterine of HicroltTaves by a Conducting Cylinder", Thesis, McGill Uni versi ty, 1950. 2. G.A. Woonton, D.R. Hay and D.C. Hogg, Report No. 1 on Contract D.R.B. X-27 to the Defence Research Board of Canada; Baton Electronics Research Laboratory, 1951. 3. Ohio State Research Foundation Report No. 302-5. 4. Naval Research Laboratory Reports Nos. C-3460-94A, 1951 and C-3460-lJ8A, 1951. -2- that distance from scatterer to source increase as the YTavelength decreases, therefore, at microwave frequencies, the scattering sites, of necessity, are out of doors. Experience has shown that many difficulties are inherent in outdoor back-scattering experiments. For example, high towers are required in order to avoid multiple path transmission due to reflections from the earth. The towers, in turn, produce undesirable secondary fields that are often dependent on wind and weather conditions. Rain, snow and wind also prevent measura~ent because of their effect on the antennas and apparatus, and because of transmission and reflection difficulties. These objectionable features led to consideration of the possibility of performing back-scattering measurements within the laboratory. It \.n.ll be seen in the text that an indoor measurement involves several fundamental problems in microwave optics. Briefly, the quasi-plane wave that illuminates the scatterer is produced by the Fresnel field of a lens. Of necessity, the lens must be isotropic wi th regard to polarization and have 10\-1 reflection properties; it must therefore be a dielectric lens. This requirement prompted an extensive investigation of an artificial dielectric that also possessed other desirable properties from the point of view of the back-scattering experiment. A new fonn of artificial dielectric has been tested and a lens const~Qcted from it. It is necessary to know the nature of the field in \-lhich the scatterer is placed, therefore the problem of obtaining a mathematical expression for the diffraction field of a lens arises. The magnitude of this problem will be appreciated when it is recalled that relatively few rigorous solutions of electromagnetic diffraction problems exist even when no -3- lens is involved. It is important, nevertheless, to have workable solutions, not necessarily rigorous, which ,dll predict diffraction fields wi th an accuracy sufficient that experiments in microwave optics can be perfonned with confidence. During the present investigation, two new features of diffraction fields have been observed. Bath are of importance in deter- mining the behaviour of a lens. One of them has been predicted wi th con- siderable accuracy by an empirical forffiula. The influence of lens action on back-scattering measurements will be evident throughout the thesis. It is also necessary to have sorne theoretical information on back- scattered fields, considered as a distinct class of diffraction problem. Scattering by a sphere and an infinite cylinder, for example, can be evaluated rigorously. Moreover, since one is concerned with the distant field in evaluating scattering coefficients, optical approximations are fairly reliable in certain instances. The indoor method was tested by comparing experimental results with these theories. Errors in the scattering coefficient, introduced by the lens diffraction have been evaluated. Other errors, due to limitations in the technique of microwave optics are also discussed. It is found that agreement between indoor and outdoor measurements exists, for scatterers with simple geometrical shapes, over a limited range of size of scatterer and over a limited angle of back-scattering. The lens method was suggested by G.A. Uoonton5 several years ago. Recently6, an outdoor back-scattering experiment, utilizing a 1ens of very low refractive index to partial1y correct a spherical wavefront, 5. G.A. Woonton, J.A. Carruthers, A.R. Elliot and E.C. Rigby, J. App1. Phys., ~, pp 390-397, 1951. 6. J.R. Mentzer, Proc. I.R.E., ~, pp 252-256, 1953. -4- was described by J.R. Mentzer; this will be referred to in section 4.2 of the texte The indoor method to be described has proven superior in sensitivity and stab11ity to equivalent outdoor methods within the knowledge and experience of the author. -5- 1. A LABORATORY NEI'HOD FOR MEASUREMENT OF BACK-SCATTERING COEFFICIENTS.