FDTD method incorporating the Doppler effect

In one former paper [1] the author reported about a comprehensive physical analysis of the Doppler effect of electromagnetic waves. The paper contains an analytical description of one dimensional (1-D) wave propagation in layered media with moving boundaries and an approximate method to calculate backscattering signals from moving objects of arbitrary shape with the help of full wave simulations of motionless, stationary objects. Both approaches are matching well for the shown kind of applications. In this publication the author presents the deviations between both approaches and their origin. Furthermore a new FDTD approach is presented for the one-dimensional case to consider the Doppler effect of moving boundaries in layered media. An outlook for the three-dimensional approach is given.