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In this paper, the detection of a small reflector in a randomly heterogenousmedium using second-harmonic generation is investigated. The medium isilluminated by a time-harmonic plane wave at frequency omega. It is assumedthat the reflector has a non-zero second-order nonlinear susceptibility, andthus emits a wave at frequency two omega in addition to the fundamentalfrequency linear scattering. It is shown how the fundamental frequency signaland the second-harmonic signal propagate in the medium. A statistical study ofthe images obtained by migrating the boundary data is performed. It is provedthat the second-harmonic image is more stable with respect to medium noise thanthe one obtained with the fundamental signal. Moreover, the signal-to-noiseratio for the second-harmonic image does not depend neither on the second-ordersusceptibility tensor nor on the volume of the particle.

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