Presented here is a characterization of aberration in medical ultrasound imaging. The characterization is optimal in the sense of maximizing the expected energy in a modified beamformer output of the received acoustic backscatter. Aberration correction based on this characterization takes the form of an aberration correction filter. The situation considered is frequently found in applications when imaging organs through a body wall: aberration is introduced in a layer close to the transducer, and acoustic backscatter from a scattering region behind the body wall is measured at the transducer surface. The scattering region consists of scatterers randomly distributed with very short correlation length compared to the acoustic wavelength of the transmit pulse. The scatterer distribution is therefore assumed to be delta correlated. This paper shows how maximizing the expected energy in a modified beamformer output signal naturally leads to eigenfunctions of a Fredholm integral operator, where the associated kernel function is a spatial correlation function of the received stochastic signal. Aberration characterization and aberration correction are presented for simulated data constructed to mimic aberration introduced by the abdominal wall. The results compare well with what is obtainable using data from a simulated point source.