Near field diffraction of steel tape gratings illuminated with finite-size incoherent sources

Steel tape gratings are diffraction gratings engraved on a steel substrate, whose slits are commonly manufactured by laser ablation. They behave as amplitude diffraction gratings, since the engraved slits act as strong scatters. Here, we extend previous works to the case of finite-size illumination sources, as they are used in applications such as optical encoders, where LEDs are commonly used as illumination sources. We obtain an analytical formulation for the near field behavior of this kind of gratings. When the light source increases its size, a decreasing in the contrast of the self-images is added to the effect of the surficial roughness. The agreement between analytical and numerical results is high, validating the obtained formulation. Besides, these results could be crucial in metrological applications in which steel tape gratings or other diffractive optical elements engraved on steel substrates are used, providing with a theoretical formalism to analyze the near field propagation of light after reflecting in them.