Backpropagation Imaging in Nonlinear Harmonic Holography in the Presence of Measurement and Medium Noises

In this paper, the detection of a small reflector in a randomly heterogeneous medium using secondharmonic generation is investigated. The medium is illuminated by a time-harmonic plane wave at frequency ω. It is assumed that the reflector has a nonzero second-order nonlinear susceptibility, and thus emits a wave at frequency 2ω in addition to the fundamental frequency linear scattering. It is shown how the fundamental frequency signal and the second-harmonic signal propagate in the medium. A statistical study of the images obtained by migrating the boundary data is performed. It is proved that the second-harmonic image is more stable with respect to medium noise than the one obtained with the fundamental signal. Moreover, the signal-to-noise ratio for the second-harmonic image does not depend either on the second-order susceptibility tensor or on the volume of the particle.