Ignasi Labastida

Full complex Fresnel holograms displayed on liquid crystal devices

We propose a method to display full complex Fresnel holograms by adding the information displayed on two analogue ferroelectric liquid crystal spatial light modulators. One of them works in real-only configuration and the other in imaginary-only mode. The Fresnel holograms are computed by backpropagating an object at a selected distance with the Fresnel transform. Then, displaying the real and imaginary parts on each panel, the object is reconstructed at that distance from the modulators by simple propagation of light. We present simulation results taking into account the specifications of the modulators as well as optical results. We have also studied the quality of reconstructions using only real, imaginary, amplitude or phase information. Although the real and imaginary reconstructions look acceptable for certain distances, full complex reconstruction is always better and is required when arbitrary distances are used.

Wavefront reconstruction by adding modulation capabilities of two liquid crystal devices

We analyze the behavior of complex information in the Fresnel domain, taking into account the limited capability to display complex values of liquid crystal devices when they are used as holographic displays. To do this analysis we study the reconstruction of Fresnel holograms at several distances using the different parts of the complex distribution. We also use the information adjusted with a method that combines two configurations of the devices in an adding architecture. The results of the error analysis show different behavior for the reconstructions when using the different methods. Simulated and experimental results are presented.

A simple method for displaying Fresnel holograms on liquid crystal panels

In this paper we present a method for reconstructing Fresnel holograms using two liquid crystal devices, one to display the amplitude information and the other to display the phase. The theoretical approach has been adapted to real configurations of VGA panels removed from a commercial video projector. The optical setup is based on the projection of the phase plane into the amplitude plane by means of an imaging lens. Simulated and experimental results are presented.

On-axis joint transform correlation based on a four-level power spectrum

We propose a method to obtain a single centered correlation with use of a joint transform correlator. We analyze the required setup to carry out the whole process optically, and we also present experimental results.

Optical correlation by use of partial phase-only modulation with VGA liquid-crystal displays

The development of liquid-crystal panels for use in commercial equipment has been aimed at improving the pixel resolution and the display efficiency. These improvements have led to a reduction in the thickness of such devices, among other outcomes, that involves a loss in phase modulation. We propose a modification of the classical phase-only filter to permit displays in VGA liquid-crystal panels with a constant amplitude modulation and less than a 2pi phase modulation. The method was tested experimentally in an optical setup.

Generalization of the Jared and Ennis method of complex transmittance objects for the generation of synthetic discriminant function filters

We present a simple method of constructing synthetic discriminant function filters optimized to take into account the modulation of liquid-crystal devices. This relaxation algorithm, a generalization of the Jared and Ennis method, is an iterative method that includes arbitrary modulations for both scene and filter, extending the problem to the complex plane. Simulated and experimental results obtained in a VanderLugt correlator are presented for a two-class recognition problem. The optimal number of images needed to describe an object in a filter generated in this way is discussed, and the influence of the spatial light modulation resolution on the correlation is studied.

On-axis interferometric detection using a binary joint transform correlator

Recently, we proposed an approach to obtain a single on-axis correlation with use of a joint transform correlator. That method required a displaying device with a determinate configuration, however, in this work we introduce a modification to be used with a modulator without a full 2π phase modulation. This variation is based on a binary joint power spectrum and it requires an interferometric process to obtain a single detection peak. We present a setup to carry out the whole process optically and we show experimental results that validate this new approach.

Generalization of the Jared-Ennis method to complex transmittance objects for the generation of synthetic discriminant function filters

In this work we present a generalization to complex transmittance objects of the Jared-Ennis algorithm for the generation of Synthetic Discriminant Function filters (SDFs). The original algorithm consists of the resolution of a nonlinear system of equations by means of an iterative procedure, including a phase adaptation of the filter. The method shown here takes into account the modulation of liquid crystal displays (LCD) both for scene and filter, generalizing the problem to the complex plane. Considering this new method gives a more realistic picture as the LCD modulation gives a complex distribution of the scenes instead of only real values as considered before. For instance, we use a high contrast configuration to display the scenes. Moreover, the addition of new parameters to the problem allows us to consider filters other than the phase-only one. In our case, we use a phase-mostly configuration to display the filter and the metric optimized is the maximum correlation intensity, as in the original method. Simulated results are presented for a two-class problem, as well as experimental results obtained in a VanderLugt correlator. The filters produce the desired correlation response in both cases.

Reconstruction of Fresnel holograms using partial wavefront information

In this work we analyze the behavior of complex information in Fresnel domain taking into account the limited capability to display complex transmittance values of current liquid crystal devices, when used as holographic displays. In order to do this analysis we compute the reconstruction of Fresnel holograms at several distances using the different parts of the complex distribution (real and imaginary parts, amplitude and phase) as well as using the full complex information adjusted with a method that combines two configurations of the devices in an adding architecture. The RMS error between the amplitude of these reconstructions and the original amplitude is used to evaluate the quality of the information displayed. The results of the error analysis show different behavior for the reconstructions using the different parts of the complex distribution and using the combined method of two devices. Better reconstructions are obtained when using two devices whose configurations densely cover the complex plane when they are added. Simulated and experimental results are also presented.

On-line applet-based optics course for undergraduate students

We present an educational resource based in a virtual optical laboratory for undergraduate students. It consists in a web-based textbook with several applets to illustrate the theory and simplify the teaching tasks in the classroom. These programs can also be used as a method for self-learning in an on-line environment. Applets are written in Java language using the Java Network Launching Protocol (JNPL) for avoiding problems related with the use of specific browsers or Java interpreters versions.