Theoretical scattering coefficient for near vertical incidence from contour maps

Abstract

In calcul ation of t he t heoretica l scatterin g coeffici ent for a te rrai n, p revious a u t hors tentatively assumed t hc normali zed a utocova riance func t io n p(r ) =e-A , 2 fo r the gro und elevation as a fun ction o f di stance from a given point. R ecently a utoco rrelatio n st ud ies were madc using map with co nto urs ranging from one to t wcn ty-fiv c feet. These I'rs ul ted in curves of p (I'), which are a pproxim ated b~' exp ( -lrIIB ) . The t hco retical scatte rill g cross sect ion (uo ) of ma ny such terra ins can be ex presscd as ( 1 ) where u, A, k, an d e a rc standa rd d eviatio n o f t he ta rget tc rra ill , wavele ngt h, wiLv e numbe r(2 7f' /'!I.) a nd t he a ngle of in cid ence res pectively. For t he case whe re JI B is s ma ll as co mpa red to k, t he a bove exp ressio n becomes 4u2 uO= AB (Bcot'e )( 2)These express ions, whell norm a li zed , arc in agree men t with ex perim ental rcsulLs of oLl'e r a u tho rs. It is a lso notewor t hy t hat the res ul ts obtained wi t h an aco llst ic simulato r mod e l co mpa red vc ry well with t his t heo re Lieal expression . T h is work is based 0 11 Lhc '" "operLy th;1t t he grou nd is co ndu ctin g a nd ha s ra nd om elevation variation s. Theon'tical res ults calcul ated o n t he basis o f vary ing gro und impedall ce ra the r tha n its elevatioll >l .. e a lso ill agreemen t with this expressio n.

Remote Probing of the Moon by Infrared and Microwave Emissions and by Radar

“…Other forms than Gaussian for the autocorrelation function p(ar) have been explored. These include the exponential, 9(Ar) = exp (--At/l) (37) [Daniels, 1961;Hayre and Moore, 1961;Hughes, 1962], which closely approximates many terrestrial surfaces. Fung and Moore [1964] and Beckmann [1965] have employed a sum of such terms.…”

The scattering behavior of the Moon at wavelengths of 3.6, 68, and 784 centimeters

“…We feel, therefore, that the theory presented by Senior and Siegel is based on a -12 ' ' '] ', I ,i , t, , ,, , , , -4o i,, A ,': ', ',' ' ', ' ' • ,•, I , ', ,"x,•o false premise, one that is in direct conflict with the experimental evidence. Hughes [1960] and Hayre [1961] as well as one of us [Evans, 1962b] have criticized Senior and Siegel's theory at length, and hence there seems little to be gained by discussing it further. It suiTices to say that we do not accept the value k = 1.1 for the dielectric constant of the lunar surface obtained by these authors.…”

Post Mixer Spectra of Periodic FM Altimeters with Area Target Returns

“…The computational model employs the radar scattering coefficient concept to facilitate its use with various types of terrain, and accepts almost all the usual models for the scattering coefficient ao, such as that used above, due to Cooper [7], and also that of Hayre and Moore [9]. Any periodic modulating function can be used also, provided the corresponding post mixer spectrum for a point target return can be found.…”

“…i.e., a weighted sum of the spectral contributions of all the individual scatterers, each weighting, in general, being dependent on the antenna coordinates of the scatterer W(ri,Oi, i) G_____________ (3) and the frequency effects in each spectral contribution being dependent on the waveform geometry of the (9) 2T 2ri) ) (4)…”