Generation of Talbot-like fields.

We present an integral of diffraction based on particular eigenfunctions of the Laplacian in two dimensions. We show how to propagate some fields, in particular a Bessel field, a superposition of Airy beams, both over the square root of the radial coordinate, and show how to construct a field that reproduces itself periodically in propagation, i.e.

Simple techniques to generate binary periodical polarization fields.

We report two new, to the best of our knowledge, methods to generate polarization gratings, whose basic cells are formed by sections that are orthogonally polarized. One of the methods employs a spatial filtering setup that modulates the diffraction orders in the Fourier domain of a Ronchi grating, with two orthogonal polarizations. In the second method, a binary phase modulation, generated by a liquid crystal device, is converted into orthogonal polarizations in different zones of an incident beam.

Efficient generation of Hermite-Gauss and Ince-Gauss beams through kinoform phase elements.

We discuss the generation of Hermite-Gauss and Ince-Gauss beams employing phase elements whose transmittances coincide with the phase modulations of such beams. A scaled version of the desired field appears, distorted by marginal optical noise, at the element's Fourier domain. The motivation to perform this study is that, in the context of the proposed approach, the desired beams are generated with the maximum possible efficiency.

Optimum generation of annular vortices using phase diffractive optical elements.

An annular vortex of arbitrary integer topological charge q can be obtained at the Fourier domain of appropriate phase diffractive optical elements. In this context we prove that the diffractive element that generates the vortex with maximum peak intensity has the phase modulation of a propagation-invariant qth order Bessel beam. We discuss additional advantages of this phase element as annular vortex generator.

Comparing efficiency and accuracy of the kinoform and the helical axicon as Bessel-Gauss beam generators.

We compare two phase optical elements that are employed to generate approximate Bessel-Gauss beams of arbitrary order. These elements are the helical axicon (HA) and the kinoform of the desired Bessel-Gauss beam. The HA generates a Bessel beam (BB) by free propagation, and the kinoform is employed in a Fourier spatial filtering optical setup.

Efficient generation of periodic and quasi-periodic non-diffractive optical fields with phase holograms.

The superposition of multiple plane waves with appropriate propagation vectors generates a periodic or quasi-periodic non-diffractive optical field. We show that the Fourier spectrum of the phase modulation of this field is formed by two disjoint parts, one of which is proportional to the Fourier spectrum of the field itself. Based on this result we prove that the non-diffractive field can be generated, with remarkable high accuracy and efficiency, in a Fourier domain spatial filtering setup, using a synthetic phase hologram whose transmittance is the phase modulation of the field.

Efficient generation of an arbitrary nondiffracting Bessel beam employing its phase modulation.

We report a highly efficient method for generation of any high-order nondiffracting Bessel beam employing a phase hologram whose transmittance coincides with the phase modulation of such a beam. It is remarkable that the Bessel beam generated by this hologram, at the plane of this device, has peak amplitude higher than the amplitude of the beam employed to illuminate it.

Accurate encoding of arbitrary complex fields with amplitude-only liquid crystal spatial light modulators.

We show that computer generated holograms, implemented with amplitude-only liquid crystal spatial light modulators, allow the synthesis of fully complex fields with high accuracy. Our main discussion considers modified amplitude holograms whose transmittance is obtained by adding an appropriate bias function to the real cosine computer hologram of the encoded signal. We first propose a bias function, given by a soft envelope of the signal modulus, which is appropriate for perfect amplitude modulators.

Common-path interferometry with one-dimensional periodic filters.

We discuss a spatial filtering interferometry setup that employs a periodic spatial filter with either cosine transmittance or binary phase modulation. The setup's input plane is formed by two separate windows, one of which supports a phase object and the other, a reference beam. Using the appropriate frequency and orientation of the filter produces an interference pattern of the two input fields at the output plane of the system.

Nonlinear common-path interferometer: an image processor.

A single-lens optical setup with a nonlinear medium placed in its geometrical focal plane is used to contrast a phase disturbance. This setup blends the robustness of phase-contrast methods with an optical nonlinear intensity-dependent medium and the usefulness of traditional interferometric techniques. We show that the ratio of the total illumination area to the phase-object area determines an adequate phase-disturbance contrast.

Double-phase holograms implemented with phase-only spatial light modulators: performance evaluation and improvement.

We propose modified hologram cells (or macropixels) for the computer-generated double-phase holograms (DPHs), based on pixelated phase-only spatial light modulators (SLMs). Such modified DPHs exhibit a substantially improved signal-to-noise ratio, in comparison with the conventional ones. The modified macropixels are formed by arrays of either 1 x 2 or 2 x 2 SLM pixels.

Influence of illuminating beyond the object support on Zernike-type phase contrast filtering.

A general analysis of the image fill-factor influence on Zemike-type phase contrast filtering is presented. We define image fill factor as the ratio of the object support area over the illuminating area. We first consider binary-phase objects and then generalize to arbitrarily quantized and continuous-phase objects.