A Correction of Random Medium Motion Correlation Imaging Method

Imaging and communication are often disturbed in random medium due to random scattering. The correlation in a random scattering field provides a possible way to recover information. By using speckle intensity correlation, Newmann and Webb proposed a motion correlation imaging method to reconstruct the field incident on thick random medium. However, the size effect of a light intensity detector on the speckle intensity correlation is not fully understood. We investigate the size effect on the speckle intensity correlation. We find that if the size is too large or too small, the statistics of an electric field deviates from zero-mean circular complex Gaussian statistics, and the speckle intensity correlation deviates from magnitude square of the incident field autocorrelation. The deviation is due to the random fluctuation amplitude of the scattered electric field, which is different at spatial locations on an output plane.