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'Perfect' imaging in left-handed meta-materials (LHMs) is constrained by evanescent wave losses. A multi-layer LHM structure can be deployed to reduce the losses, particularly in near field imaging. In this paper, we demonstrate using dispersive FDTD simulation how the multiple-layer LHM structure is used to 'guide' evanescent waves with very little attenuation over large stack thickness in near field imaging at microwave frequencies. Effect of the multi-layer structure on far field imaging is also presented. The theoretical prediction is verified by FDTD simulation with good agreement.