Resumen: We investigate the far field diffraction process produced by diffraction gratings with two roughness levels, such as steel tape gratings, which are used in environments where diffraction gratings made of glass are not possible. We obtain the analytical formulation describing the formation of diffraction orders in terms of the roughness parameters. Since roughness is stochastic, we use the mutual coherence function to propagate the field to the Fraunhofer regime. We conclude that diffraction orders exists when at least one correlation length of both roughness is larger than the period of the grating and the standard deviation on heights is around or larger than the illumination wavelength. Finally, we corroborate the analytical results with numerical simulations based on the fast Fourier transform, showing a high agreement. Idioma: Inglés DOI: 10.1088/2040-8986/ab2bdf Año: 2019 Publicado en: Journal of Optics (United Kingdom) 21, 8 (2019), 085605 [6 pp] ISSN: 2040-8978 Factor impacto JCR: 2.379 (2019) Categ. JCR: OPTICS rank: 40 / 97 = 0.412 (2019) - Q2 - T2 Factor impacto SCIMAGO: 1.167 - Electronic, Optical and Magnetic Materials (Q1) - Atomic and Molecular Physics, and Optics (Q1)