Relationship between the near-field speckle pattern and the statistical properties of a surface

The scattering of light by a random rough surface is studied in the near field. We define a correlation function for the near-field intensity. Using a perturbative approach, we show that the power spectral density of the intensity is obtained by multiplying the power spectral density of the random rough surface by a transfer function. The explicit form of the transfer function is derived. We also show that the speckle contrast is proportional to the root mean square (rms) height of the surface. Finally, we present some simulations showing the modifications on the images produced when reducing either the temporal or the spatial coherence of the incident beam.