Near-field diffraction of chirped gratings.

In this Letter, we analyze the near-field diffraction pattern produced by chirped gratings. An intuitive analytical interpretation of the generated diffraction orders is proposed. Several interesting properties of the near-field diffraction pattern can be determined, such as the period of the fringes and its visibility. Diffraction orders present different widths and also, some of them present focusing properties. The width, location, and depth of focus of the converging diffraction orders are also determined. The analytical expressions are compared to numerical simulation and experimental results, showing a high agreement.

Self-imaging technique for beam collimation.

A simple collimation technique based on measuring the period of one self-image produced by a diffraction grating is proposed. Transversal displacement of the grating is not required, and then automatic single-frame processing can be performed. The self-image is acquired with a CMOS camera, and the period is computed using the variogram function. Analytical and experimental results are obtained, which show the simplicity and accuracy of the proposed technique.

Collimation method using a double grating system.

We present a collimation technique based on a double grating system to locate with high accuracy an emitter in the focal plane of a lens. Talbot self-images are projected onto the second grating producing moiré interferences. By means of two photodetectors positioned just behind the second grating, it is possible to determine the optimal position of the light source for collimation by measuring the phase shift between the signals over the two photodetectors. We obtain mathematical expressions of the signal in terms of defocus. This allows us to perform an automated technique for collimation. In addition, a simple and accurate visual criterion for collimating a light source using a lens is proposed. Experimental results that corroborate the proposed technique are also presented.

Correlation technique for the compensation of diffraction widening of optical reference signals.

Two-grating measurement systems are routinely employed for high-resolution measurements of angular and linear displacement. Usually, these systems incorporate zero reference codes (ZRCs) to obtain a zero reference signal (ZRS), which is used as a stage-homing signal. This signal provides absolute information of the position to the otherwise relative information provided by the two-grating incremental subsystems. A zero reference signal is commonly obtained illuminating the superposition of two identical pseudorandom codes and registering the transmitted light by means of a photodiode. To increase the resolution of the system, a reduction of the grating period and the ZRC widths is required. Due to this reduction, the diffractive effects produce a widening of the ZRS and, in turn, a loss of the measuring accuracy. In this work, we propose a method to narrow the distorted signal obtained with a Lau-based encoder, reinstating the accuracy of the ZRS. The method consists of the inclusion of a correlation mask on the detector. A theoretical model to design the mask has been developed, and experimental results have been obtained that validate the proposed technique.