We present a study of the variations of a speckle pattern passing through a grating that can be displaced. This study is described theoretically by a simple model based on the scalar diffraction theory in the Fresnel zone. The intensity correlation of the modified speckle as a function of the grating displacement is obtained and compared with experimental results. The possibilities of metrological applications in optical encoders are suggested.

Optical encoders are used in industrial and laboratory motion equipment to measure rotations and linear displacements. We introduce a design of an optical encoder based on a nondiffractive beam. We expect that the invariant profile and radial symmetry of the nondiffractive beam provide the design with remarkable tolerance to mechanical perturbations. We experimentally demonstrate that the proposed design generates a suitable output sinusoidal signal with low harmonic distortion. Moreover, we present a numerical model of the system based on the angular spectrum approximation whose predictions are in excellent agreement with the experimental results.

In a previous work, we introduced the design of an optical encoder based on a nondiffractive beam and demonstrated that it generates a suitable output sinusoidal signal [Appl. Opt.47, 2201-2206 (2008)]. In this work, we experimentally, analytically, and numerically study the dependence of the system performance on its parameters (grating pitch, photodetector size, etc.) and propose three different optimization criteria for which the tolerance to variations in the system parameters is also analyzed. We conclude that the proposed design generates a suitable output signal, with high contrast and very low harmonic distortion, while having a remarkable tolerance to variations in its parameters and to mechanical perturbations.

In two preceding works (Appl. Opt.47, 2201-2206, 2008; Appl. Opt.48, 414-424, 2009) we introduced the design of an optical encoder based on a nondiffractive beam and studied the dependence of its performance on its parameters (e.g., grating pitch, photodetector size). In those works we proposed different optimization criteria and concluded that the proposed design provides an output sinusoidal signal with high contrast and very low harmonic distortion, while having remarkable tolerance to variations in its parameters and to mechanical perturbations. In this work we (1) study how to improve the system performance by means of selecting appropriate photodetector geometry, (2) study the system performance for different nondiffractive beam geometries, and (3) quantify the output signal tolerance to vertical and lateral misalignment between the centers of the nondiffractive beam and the photodetector. As a consequence, we obtain new sets of optimal parameters that significantly improve the system performance and enhance its tolerance to mechanical perturbations and fabrication errors.

The speckle grain close to a diffuser medium carries information about the angles at which light is scattered. We propose the extension of a technique that allows obtaining the angular distribution of the scattered intensity in the far-field speckle pattern from the near-field speckle pattern produced by strong diffusers (whose roughness is greater than the illuminating wavelength). To illustrate this technique we applied it to the light scattered from ground glass diffusers. The experimental results are compared with those obtained by direct measurement of the angular distribution of the mean scattered intensity in the far field showing good agreement with each other. The advantages over the classical far-field methods are outlined.