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.
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.
We propose an implementation to display full complex information using two ferroelectric liquid crystals spatial light modulators. We compare the simulated and experimental results obtained.
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.
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.
Optical correlators process two-dimensional images that come from a three-dimensional world. Filters designed for object recognition of three-dimensional scenes must have the information of all possible views. This implies a large quantity of filters, especially when the object is moving with respect to the observer. Although filters designed through the synthetic discriminant functions formalism can encode information of several images, there is a practical limit imposed by the noise appearing at the correlation plane. Fast correlators are one way of solving this problem. In this work we propose a global process for detecting 3-D objects based on fast sequential correlations with filters derived from the different possible views of the target. The acquisition of these views is accomplished in a fast and simple way by means of a three-dimensional scanner based on stereovision techniques. The 3-D model of the object thus obtained is then used to compute synthetic plane views from any desired viewpoint. A compact correlator has been developed which uses fast CCD cameras for input and output, and ferroelectric SLMs (spatial light modulators) to display the scene and the sequence of filters. The process of digitizing the 3-D coordinates is described in detail, from the acquisition of the stereopair of images, the stereo-matching algorithm we use and the final integration of all data sets into a common object-centered coordinate system. Also, general engineering problems involved in the design and construction of the correlator are analysed and discussed.
In this work we propose a method to obtain single centered correlations with an optical setup based on a joint transform correlator. This approach is a modification of a previous procedure that required displaying devices with a full 2(pi) phase modulation. The displaying requirements are less restrictive than before, allowing the use of many modulators and configurations. This new method is based on a binary power spectrum and it needs an interferometric process to obtain a single detection peak. To validate our new procedure, we propose an optical setup and we present the experimental results achieved.
The inclusion of optoelectronic displays has enabled optical correlators to improve radically and maintain the competitive edge of optical processors among information processing fields. In this work, an optical correlator has been implemented by using two VGA liquid crystal displays as spatial light modulators, both at the input and Fourier planes. These devices have been removed from a commercial videoprojector and have been characterized in order to operate in different configurations. This characterization is based on an interferometric procedure which includes amplitude and phase modulation measurements. For a phase-only modulation we have compared the use of linearly and elliptically polarized light. In this latter case we have found an operating curve with phase-only modulation which takes values from 0 to π radians. This is a limitation when a pure phase filter is required as in data security and encryption, in wavelet-based systems, and in optical pattern recognition, among others. An application in this latter field is presented in our work as a solution to overcome this limited phase depth. We propose a modification of the classical phase-only filter based on the use of the absolute value of the phase. Experimental correlation results using the optical setup and the modified filter have been obtained.
The proposal of this work is the study of a method for characterization of the focal of ophthalmic lenses whose surface refraction index has been modified by diffusion techniques based on thermal ion exchange in glass. In particular the aim is the measurement of the variations in focal length of ophthalmic lenses after undergoing a diffusion process. An interferometric technique has been used and computer simulations have also been carried out.
In this work we present the developments for the simulation of image formation through an ophthalmic lens. The procedure is, essentially an exact ray tracing taking into account the particular mobility conditions of the exit pupil. This leads to the computation of astigmatism as a function of the field angle considered. In the computer program, the use of a commercial glass with a gradient in the refractive index (GRIN material) is foreseen. This latter feature proves to be useful for two practical objectives: modifying the power and the astigmatism of the lens. To illustrate these points, an example based on a lens made by deforming a plane parallel plate of GRIN material will be presented.
The reduction of geometrical distances in optical correlators, in order to build miniaturized systems, has become a necessity for realistic applications [1]. In general, the scope of the studies carried out is only focused in some parts of the problem. Nowadays, liquid crystal devices (LCD), usually removed from commercial videoprojectors, are used to display images in optical setups. As a result of using pixelated panels, the viability study of building an optical correlator in a reduced space should not be only limited to a design of optical systems. It must include an analysis of the behaviour of the displaying devices. Another issue that has not been raised yet is the reduction of the material needed to control simultaneously two LCDs in a Vander Lugt correlator, which involves a duplication in the driving electronics. We analyze in depth several engineering problems regarding the construction of a Vander Lugt correlator with LCDs at the input and Fourier planes. In order to reduce the length of the setup we have designed two telephoto systems. An original method to control both devices with a single 8-bit frame grabber and a single videoprojector electronics is presented. We have solved the problems related to pixel-by-pixel control when displaying the data from the frame grabber on the LCDs. An accurate analysis of the phase modulation capability of the panels is also discussed. Experimental results obtained with this setup are presented.
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