Self-imaging of gratings with rough strips

Abstract

We analyze the self-imaging process produced by a transmission grating whose strips present two different roughness levels. This kind of grating periodically modulates the transmitted light owing only to the different microtopographic properties of the strips. In spite of the fact that the grating is not purely periodic, it produces a kind of self-image at Talbot distances. These self-images gradually appear as light propagates, but they are not present just after the grating, as occurs in amplitude or phase gratings. There exists a distance from the grating, which depends on the stochastic properties of roughness, from which the contrast of the self-images becomes stable. Important cases are analyzed in detail, such as low-and high-roughness limits. We assume for the calculations that the grating can be used in a mobile system. Simulations using the Rayleigh-Sommerfeld regime have been performed, which confirm the validity of the theoretical approach proposed in this work

Far field diffraction of gratings with two roughness levels

“…This fact has been reported for some approximations in [610]. Particularly, in [8,11] the near eld diraction of rough gratings with one or two roughness levels is reported. Analytical equations showing the dependence of the self-imaging phenomenon on the parameters of the roughness are obtained.…”

Diffraction by gratings with random fill factor

“…Particularly, in optics, the most common kinds of diffraction gratings are amplitude-based and phase-based gratings that modulate the amplitude and the phase of the incident beam respectively, [5], but other types of gratings such as polarization gratings or rough gratings have been introduced in recent years. Rough gratings can be understood as a modulation of the coherence state of the beam, [6][7][8].…”

Self-imaging with curved gratings

“…This model has been progressively improved introducing new concepts: finite spectral width [6], Gaussian illumination [7], total incoherence [8] or partially coherent light [9][10][11][12][13]. Also non-ideal gratings have been studied: as for example, the effects of surface roughness, [14][15][16][17], or surface defects, [18], have been described. These works took into account only flat surfaces.…”