Effect of random grating pit displacements on the Talbot image

An analysis of diffraction images in the deep Fresnel region produced by gratings with random pit displacements around a nominal value is performed in this paper. Such pit displacements can be produced while developing a grating with etchers since the process can be slightly unpredictable. A theoretical prediction to describe the intensity distribution is obtained, produced by the grating at the near field, showing that smoothing of self-images is produced in the Talbot plane. In addition, random pit displacements produce different diffraction behaviors for cosine and binary gratings. It is shown that if the standard deviation of pit displacements is less than 30% of the grating period, the pit image, observed in the Talbot plane, shows some additional intensity fluctuation that leads to its displacement by meaning of the mass center for binary gratings and pit displacements for cosine gratings with some additional structural changes. Theoretical conclusions taken from a direct integration method based on the Rayleigh–Sommerfeld equation are in good agreement with the simulation results.