Near field diffraction of cylindrical convex gratings

Abstract

We analyze the field produced by a cylindrical convex diffraction grating at the Fresnel regime for several kinds of light sources, including a monochromatic quasipunctual source, finite size, and polychromatic sources. These results can help one understand the functioning of rotary optical encoder technology. A decrease in the self-image contrast is produced for finite nonpunctual sources. In addition, the polychromaticity of the source affects the smoothness of the self-images, making them quasicontinuous from a certain distance from the grating forward. Finally, we experimentally validate the obtained analytical predictions.

A diffraction experiment at the near field: the homemade Talbot effect

“…In the same fashion, by taking zeroth and third diffraction orders, constructive interference appears at distances z = (2m − 1)z T /4 but with a periodicity half of that of the diffraction grating [3]. We show in figure 2 four examples of Talbot effect obtained analytically from the intensity calculated by means of the propagation of the grating transmittance by using the Fresnel kernel with plane wave illumination, in a similar way as it is made in [4]. The period of the gratings, placed at z = 0, is p = 20 µm, and the Talbot distance results z T = 1.26 mm and z T = 1.5 mm for λ = 632 nm and λ = 532 nm, respectively.…”

“…It appears when a diffraction grating is illuminated with a collimated monochromatic beam. This effect has been found also for other types of waves, besides electromagnetic, such as mechanical waves in water [3], and it has been analysed under many configurations, for cylindrical gratings [4], with non-collimated beams, with polychromatic illumination [5,6], with rough diffraction gratings [7], all of them resulting in very interesting properties and behaviours. Besides, it has applications in many different branches of science and technology such as machine tool, optical encoders, dimensional metrology, and so on [8].…”

“…Now, the illumination beam is slightly divergent. With diverging or converging light, the period of the self-images increases or decreases, respectively, as we separate from the grating plane [4]. In addition, the source is no longer monochromatic but it has a wide spectrum.…”

Near-field diffraction-based focal length determination technique

“…As can be observed, Talbot self-images converge to the focal plane. It is important to notice that the period of the self-images must be calculated under paraxial approximation since the lens also curves the self-images far from the optical axis in a similar way to that is shown in [18,19]. Theoretically, the period has a linear dependence with z, p az b ′ = + .…”