Scattering by linearly vibrating objects

The scattering problem for a plane wave incident upon a perfectly conducting linearly oscillating object is investigated both theoretically and experimentally. The theoretical analysis, accurate to order
v/c
where
v
and
c
axe the velocities of object and light, respectively, shows that the target oscillation changes the scattered far field of a motionless target only in phase. The oscillation is assumed to be periodic, and this period is shown to be impressed on the scattered field. Spectral analysis of the modulation shows that the power distribution varies with the shape of the motion, wavelength of the incident field, and the magnitude of the projections of the oscillation in the direction of incidence and receiver. Power spectra have been calculated for square, triangular, and sinusoidal target motion and, in general, the power content in the higher harmonics is found to increase with cartier frequency and magnitude of oscillation. For backscattering from an object moving sinusoidally along the direction of incidence, the power in the first harmonic is shown to exceed that at the carrier frequency when
d > 0.23\lambda
where
d
is the magnitude of the oscillation. These calculations are shown to agree with experimental measurements of the phase modulation of the field scattered from a vibrating disk at the
X
-band. Experimental results were obtained with continuous wave backscatter equipment at 10 GHz that utilized separate tunnel antennas for transmitting and receiving. The receiving section of this equipment was modified to separately display phase modulation and amplitude modulation characteristics of the backscattered signal in both time and frequency, as well as characteristics of the overall modulation envelope. Phase modulations introduced by target oscillations as small as
\pm 0.001
in were readily detected, as were amplitude modulations of a few percent.