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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 this work we find a lower bound on the energy required for synchronizing a Wireless Sensor Network (WSN) based on clock estimation techniques. The energy required for synchronizing a WSN is specified by both the transmit power and the required number of messages in order to achieve a desired estimation error level. This paper brings two main contributions: 1. A general relationship between the energy spent in the transmission and the clock offset estimation error by means of the number of transmitted messages, for both large-scale and small-scale wireless channel fading. 2. An optimal lower bound on the required energy and the number of messages by minimizing their product.

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