2072 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 44, NO. 8, AUGUST 2006 Hybrid FDTD and Single-Scattering Theory for Simulation of Scattering From Hard Targets Camouflaged Under Forest Canopy Kamal Sarabandi, Fellow,IEEE, Mojtaba Dehmollaian, StudentMember,IEEE, and Hossein Mosallaei, SeniorMember,IEEE Abstract—A hybrid target-foliage model is developed to inves- tigate the scattering behavior of hard targets embedded inside a forest canopy. The proposed model is composed of two existing electromagnetic-scattering models, one for the foliage and the other for the hard targets that are coupled in a computationally efficient manner. The connection between these two models, which accounts for the interaction between the foliage scatterers and the target, is accomplished through the application of Huygens’ prin- ciple. Wave penetration through the forest canopy and near-field and far-field scattering from its constituents is calculated using a coherent single-scattering theory, which makes use of realistic tree structures. Defining a Huygens’ surface enclosing the hard target and calculating the illuminating field (the scattered fields from the nearby vegetation scatterers and reduced incident field), the interaction between the foliage and the hard target is accounted for. Computing the scattered field from target on the Huygens’ surface and using a reciprocity theorem target-foliage interaction is captured very efficiently. Calculation of scattering from a hard target is carried out using a finite-difference time-domain (FDTD) technique. For a typical vehicle dimensions, the required time and memory for the FDTD computation and exact field calculation inside the foliage limits the simulation frequency to upper very high frequency (VHF) band. Index Terms—Electromagnetic (EM) scattering, finite- difference time-domain (FDTD) method, hybrid solution methods. I. I NTRODUCTION D ETECTION and identification of hard targets inside veg- etation canopies have long been a challenging problem in the area of remote sensing. Development of theoretical and numerical models for this problem has a wide range of both civilian and military applications. The ability of electromag- netic (EM) waves to penetrate through the foliage at low fre- quencies has made synthetic aperture radars (SARs) operating at the very high frequency (VHF) band ideal tools for detection Manuscript received May 26, 2005; revised November 3, 2005. This work was supported by the Army Research Office under Contract DAAD19-02- 1-0262. K. Sarabandi and M. Dehmollaian are with the Radiation Laboratory, Depart- met of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109 USA (e-mail: saraband@umich.edu). H. Mosallaei was with the Radiation Laboratory, Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109 USA. He is now with the Department of Electrical and Computer Engineering, College of Engineering, Northeastern University, Boston, MA 02115 USA. Digital Object Identifier 10.1109/TGRS.2006.872091 of targets in the foliage [1], [2]. However, the scattering effect of the tree constituents can distort the signal phase front, reducing the SAR resolution and changing the target signature. In this regard, a comprehensive phenomenological study is needed to accurately investigate the EM interaction of the foliage and an arbitrary hard target and vice versa. The literature concerning modeling the propagation through and scattering from forest canopies are many [3]–[7]. However, the problem of accurate modeling of scattering from hard targets embedded inside tree canopies remains an unsolved problem [8], [9]. The difficulties associated with developing such model are threefold: one is the accurate computation of the field inside a forest; the sec- ond is characterization of the scattered field from the target illuminated by the field inside the forest; and the third is the computation of the scattered-field interaction with the foliage, and the total scattered field outside the forest at the observation point. Considering the size of tree structures, the aspect ratio of the dimension of its constituent particles, the variability in dielectric constant of scatterers, and the relatively large number of trees around a target, brute force computational methods are not suitable for this problem. In addition, applicability of exact numerical methods is limited to very low frequencies where scattering from leaves and branches can be totally ignored. However, vegetation canopies can be viewed as a sparse random medium, having a volume fraction typically less than 1%. For such media, multiple scattering among constituent scatterers is of secondary importance and can be ignored. In this case, EM scattering from vegetation canopies can be simplified in terms of problems of scattering from individual dielectric cylin- ders and thin dielectric disks, modeling branches and leaves, arranged in a semideterministic fashion. The formulations for calculating the scattering and attenuation caused by vegetation particles have been derived analytically, using high- and low- frequency techniques [3], [4]. The effect of the ground plane is also accounted for, through the application of image theory maintaining only the saddle point contribution. For precise prediction of the field behavior inside the canopy, the structure of the trees is preserved in the forest model. This is done using a fractal-based model [known as Lindenmayer systems (L- systems)], which can generate very complex tree structures with a finite number of structural and botanical parameters. Monte Carlo coherent single-scattering model, which makes use of fractal-generated trees, has been proposed in [10] and [11] 0196-2892/$20.00 © 2006 IEEE