Proceedings with Extended Abstracts (single PDF file) - Radio ...

externally perturbing generalized force of time f (t). In this system, the time correlationof the scattered field of the stationary nature will be,Φ ( t , t')= Φ(t − t')= A(t)A * ( t')(2)where A(t)is the complex amplitude of the scattered field at time t . We now make theassumption that the phase relaxation function can be taken as the generalizedsusceptibility function, α ( t)= φ(kB, t), of the fluctuation-dissipation theorem and that thescattered field is the linearized response of the system to the generalized force f (t),∫ ∞A ( t)= α(τ ) f ( t −τ)(3)0The above relation can also be expressed in terms of the Fourier components of the forceand the fluctuation,A ( ω)= α(ω)f ( ω)(4)where the generalized susceptibility is obtained as,∞∫0iωtα ( ω)= φ(k , t)e(5)BHaving specified this function, the behavior of the system under a given perturbation iscompletely determined [2,3].What we see in Eq. 2 is the radar backscatter autocorrelation function. The radarbackscatter spectra can be obtained by a Fourier Transform operation on theautocorrelation function. From the classical limit of the fluctuation dissipation theorem,the backscatter spectrum Φ(ω) can be related to the imaginary part of the generalizedsusceptibility function as [2],2T''Φ ( ω)= α ( ω)(6)ω''where α is the imaginary part of the generalized susceptance. T in the above equationcan be related to the mean square of the scattered field by,T α ωA tdωπ ∫ ∞ ''2 2 ( )( ) =(7)0ωThese formulae can be viewed as the equation for fluctuations of the scattered fieldA(t)from a closed system in equilibrium and under the action of a random force. Theformulation of the above thermodynamic fluctuation theory is valid for fluctuations ofarbitrary size [2,3]. The absence of restrictions on the permissible values of the scatteredfield amplitude allows us to apply the fluctuation-dissipation theorem to weak incoherentor Thompson scattering as well as strong coherent scattering.112