Diffraction by gratings with random fill factor

In this work, we analyze the diffraction produced by Ronchi gratings where the fill factor is not constant, but presents random fluctuations around its nominal value. This effect can be produced while developing the grating with etchers since the process can be slightly unpredictable. We obtain the theoretical formalism to describe the intensity produced by the grating at near and far field, showing that smoothing of the self-images is produced at the near field and, consequently, cancellation of higher diffraction orders is obtained at the far field. In addition, different nominal fill factors produce different diffraction behaviors in terms of the randomness. We corroborate the analytical formalism using a direct integration method based on the Rayleigh-Sommerfeld formula and conclude that the numerical results are in high agreement with the theoretical predictions.