2698 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 44, NO. 10, OCTOBER 2006 Electromagnetic Scattering From Foliage Camouflaged Complex Targets Mojtaba Dehmollaian, Student Member, IEEE, and Kamal Sarabandi, Fellow,IEEE Abstract—In this paper, a hybrid target–foliage model based on existing electromagnetic techniques is developed to investigate the scattering behavior of hard targets embedded inside a forest canopy at high frequencies. The proposed model is composed of two basic scattering models, one for foliage and the other for the hard targets. The connection between these two models, which accounts for the interaction between the foliage scatterers and the target and vice versa, is accomplished through the application of the reciprocity theorem. Wave penetration through the forest canopy and near-field and far-field scattering from the canopy’s constituents is calculated using a coherent discrete scattering model that makes use of realistic tree structures. Calculation of scattering from a hard target illuminated by the reduced inci- dent field and the scattered field of nearby vegetation is carried out using an iterative physical optics (PO) method formulated for fast computation of foliage–target interaction. To reduce the number of iterations, geometrical optics (GO) approximation is initially used for determining the shadowed areas over the hard target when illuminated by individual foliage scatterers. Fur- thermore, using a scaled measurement system at millimeter-wave frequency, the accuracy of the iterative PO model is demonstrated, employing a complex target that occupies a volume as big as 86λ × 33λ × 20λ. Index Terms—Electromagnetic (EM) scattering, hybrid solution methods. I. I NTRODUCTION D ETECTION and identification of hard targets camou- flaged inside vegetation canopies are among the most challenging problems in remote sensing [1], [2]. Recent ad- vanced capabilities of synthetic aperture radar (SAR) and inter- ferometric SAR sensors such as multifrequency, multibaseline, and multipolarization features have made a wide range of both civilian and military applications possible. Civilian applications include search and detection of archaeological sites, crashed airplanes in forested environments, and foliage attenuation measurements using trihedrals placed under forest canopies. Military and law enforcement applications include detection and identification of foliage-camouflaged vehicles and facil- ities. To develop effective detection and identification meth- ods for such purposes, the phenomenology of electromagnetic (EM) wave interaction with foliage and hard targets embedded in forest canopies must be thoroughly understood. Basically, Manuscript received September 7, 2005; revised March 8, 2006. This work was supported by the Army Research Office under Contract DAAD19-02-1- 0262. The authors are with the Radiation Laboratory, Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109 USA (e-mail: saraband@eecs.umich.edu). Digital Object Identifier 10.1109/TGRS.2006.879109 a complete sensitivity study of backscattered fields to different parameters such as different realizations of the forest, different incidence angles, polarizations, and frequencies of the incident field will allow for investigation of applicability of novel detec- tion and identification algorithms, as reported in [3]–[5]. EM scattering from targets inside foliage may be studied using three basic approaches, namely: 1) analytical; 2) exact numerical; and 3) experimental/empirical. At very low frequen- cies, scattering from the forest itself may be rather small, and scattering behavior from the hard target is not much different from that of the target without the forest. In this case, the foliage can simply be modeled as layered homogeneous di- electric media with different effective dielectric constants. EM scattering in stratified media can be analytically solved, and consequently, closed-form expressions for low-frequency scat- tering from foliage can simply be obtained. At microwave frequencies, on the other hand, scattering and attenuation from foliage are rather significant, and their effects on total backscatter and foliage-covered target backscatter must be carefully accounted for. For the problem at hand, modeling the forest by randomly distributed particles and solving the problem of scattering from obscured targets inside random media is not sufficiently accurate. It has been observed that backscattering from and attenuation through the forest is sig- nificantly affected by the tree structures [6], [7]. Next, exact numerical simulations such as the finite- difference time-domain (FDTD) technique have been suggested for evaluation of scattering from objects inside random media [8] and scattering from forest [9]. The application of brute- force numerical methods is, however, limited to very high frequencies (VHFs) and lower [9]. At microwave frequencies, overall dimensions of a tree are much larger than a wavelength, and therefore, computation of the scattered field from a number of trees and their interaction with the target becomes computa- tionally intractable. Finally, scattering from targets inside forest can be studied experimentally using radar systems. Experimental and empir- ical approaches for phenomenological studies are oftentimes rather limiting due to the lack of comprehensive data sets and the accompanying ground truth. Such methods are, however, very useful for proof of concept and demonstrations [10]–[12]. In this paper, we propose an accurate EM model for scatter- ing from foliage-camouflaged targets at microwave frequencies that accounts for first-order near-field foliage and hard target interactions. This model is constructed from a number of an- alytic EM tools assembled in a unique fashion for fast and accurate computation of scattered fields using well-known EM theorems. To simplify the problem, the scattering domain is 0196-2892/$20.00 © 2006 IEEE