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Th(B) = 1 + Rh(B) and Te(f)) = 1 + Re(B). For () greater than the critical angle Be, T( B) = O. The dense media radiative transfer equation (7.4.5) with boundary conditions (7.4.19)-(7.4.20) resembles that of conventional radiative transfer equation of independent scattering except that the expressions for "'e and w in terms of physical parameters are different from those of the conventional theory because of correlated scattering and the fact that the effective propagation constant K has been taken into account. The procedure of numerical solutions of the dense media transfer equation follow the same procedure as that of the conventional ones as described in Volume 1.

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Relations exist between the brightness temperatures of passive remote sensing and the bistatic coefficients of active remote sensing when the medium is of uniform temperature. The expressions were derived in Volume I, 3, Section 5. In this section, we derive a similar expression for nonuniform temperature distribution. An expression will be derived relating the thermal radiated field intensity of a medium with nonuniform temperature distribution to the electromagnetic fields in the problem of active remote sensing. Specifically, it is shown that the thermal radiated field intensity is equal to a constant times the integration of the product of the temperature distribution and the divergence of the Poynting's vector for the problem of active remote sensing. The derivation is based on the field equations of a medium of discrete scatterers and the fluctuation-dissipation theorem. The key quantity to utilize in the derivation is the dyadic Green's function of the random medium, which is common to both problems and is also reciprocal. In the following, active and passive remote sensing problems will be labeled as Problems A and B, respectively.

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In Section 3 we have seen the importance of the pair distribution function in calculating the lowest-order scattered intensity because the field and field conjugates originate from different scatterers. In some problems the scatterers occur in clusters. For example, in a vegetation canopy the branches and leaves can occur in clusters, so that they are locally densely distributed and not uniformly dense. In such a case the pair distribution function depends on whether the two scatterers arc in the same cluster or in different clusters. In 7 of Volume II, we have performed Monte Carlo simulations for collections of clusters of scatterers. In the following, we consider the scattering of a layer of thickness D of point scatterers when the scatterers can be in clusters. We assume that the particles may occur in clusters with N s particles in each cluster. Note that N., may not be a large number. For the case of nonclustering, N s = 1. The number of clusters in the layer is N c with N Nc = (3.6.1a) Ns and N, N c - t 00. The center of each cluster is at 'fa, Q = 1,2, ... , N c (Fig. 3.6.1). The N s scatterers in each cluster Q are labeled as secondary scatterers, with indices ja, ja = 1, ... , N s . The location of the ja scatterer is at

(3.6.1b)

Once the correct position was reached, a sequential operation of placing steel support columns between the cross steel to the foundation allowed for the removal of the track beams and main beams. Support columns were installed while the lighthouse was still elevated; setting the lighthouse to its proper elevation, and allowing the columns to support the load of the lighthouse, while the support frame was sequentially dismantled from the mains down.

with ja = 1, ... N s . The volume occupied by the clusters is Ve, where Vc does not have to be large compared with wavelength. Thus the single-particle

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