Near-field diffraction of gratings with surface defects

Diffraction gratings produce self-images in the near field. Defects on the surface of the grating may occur due to the manufacturing process. These devices are often placed in dirty industrial environments. Dust particles or drops of liquid can be deposited over their surface. In this work, we analyze the effect of surface defects placed over the grating on the self-imaging process. We analytically show how the self-images gradually recover as we separate from the grating when one defect is present. Also a random distribution of surface defects over the grating is analyzed. In particular, we focus on how the contrast of the self-images decreases in terms of the density of the defects. Analytical expressions for the near field are derived, considering a stochastic description of the spatial distribution of defects. In addition, numerical simulations based on the Rayleigh-Sommerfeld formulation are performed to validate the analytical results. (C) 2010 Optical Society of America