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., a field that renders the Talbot effect. Additionally, it is shown that the superposition of Airy beams produces self-focusing.

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. The analysis of the generated polarization states is made at 1/4 of the Talbot distance of the generated gratings. The experimental results are in good agreement with the theoretical description.

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. A disadvantage of the method is the distortion of the desired beams by the influence of several nondesired beam modes generated by the phase elements. We evaluate such distortion employing the root mean square deviation as a figure of merit.

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. As the main result, it is obtained that the error in the BBs generated with the kinoform is smaller than the error in the beams obtained with the HA. On the other hand, it is obtained that the efficiencies of the methods are approximately 1.0 (HA) and 0.7 (kinoform).

Electro-optical processor for measuring displacement employing the Talbot and the nonsteady-state photo-electromotive force effects

We present a device for measuring displacement based on the Talbot and the nonsteady photo-electromotive force effects. The proposed device does not require any numerical signal processing since its output signal is, in appropriate regions, linearly related to the measured displacement. The proposed system requires an illuminating field with a sinusoidal amplitude distribution and low fringe visibility. The dynamic range can be adjusted according to the illuminating field spatial period or wavelength. Displacements with an estimated resolution better than 10 μm in a dynamic range of 1.5 mm were detected using a sinusoidal amplitude grating with a period d=100 μm.

Holographic generation of a class of nondiffracting fields with optimum efficiency

We discuss the accurate generation of complex optical fields using phase holograms that provide the optimum diffraction efficiency. In each considered case, the phase modulation of the employed hologram is identical to the phase of the desired optical field. We show that periodic and quasiperiodic nondiffracting optical fields, mathematically obtained through the superposition of multiple plane waves, can be generated with high fidelity using this approach.

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.

Polarization-controlled contrasted images using dye-doped nematic liquid crystals

We explore the polarization dependence of the nonlinear response of a planar nematic liquid crystal cell doped with 1% wt of methyl red dye. The results obtained show that the refractive index change can be switched from a positive value to a negative one as the polarization of the beam changes from parallel to perpendicular with respect to the rubbing direction. This property is exploited in a phase contrast system, where a dynamic phase filter is photoinduced in a liquid crystal cell placed in the system's Fourier plane. Real-time contrast inversion in the resulting images is demonstrated.

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. The main attributes and advantages of the setup are discussed and experimentally illustrated with the example of a binary phase periodic filter implemented with a spatial light modulator.

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.

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. Numerical simulations are presented for binary- and quadratic-phase objects, where the contrast of the output image is evaluated as a function of the image fill factor, image phase variations, and filter phase. The results obtained show that the image fill factor can significantly modify the contrast and irradiance of the contrasted image.

Incoherent-to-coherent conversion and square-law transmission based on photoinduced birefringence in bacteriorhodopsin films

We review the main optical properties of bacteriorhodopsin that are relevant to its use as a spatial light modulator. A model is described for the transmittance of a film placed between crossed polarizers in which photoinduced birefringence occurs. We show when the transmittance is proportional to the write intensity. We use this property in a joint transform correlator for incoherent-to-coherent conversion and effective square-law modulation in the Fourier plane.