The task of transforming a given intensity distribution into a different, desired intensity distribution can be achieved either by diffractive optical elements or by beam shaping. The most essential difference between these two approaches is that with diffractive optics, the output amplitude results from a superposition of all contributions of the input plane, while in beam shaping there is a one-to-one correspondence between the Poynting-vectors in both planes. Consequently, beam shaping does not require temporal coherence. Applications of beam shaping are typically in the area of high power lasers, where the Gaussian beam shape leads to an inefficient use of the available laser power due to loss at the focusing lens. In the contribution, different techniques for designing beam shaping elements are discussed and an extension to analytic methods will be presented.

The advances in the design and fabrication of microlaser arrays, photodetectors and free­-space optical interconnection elements have driven the creation of ever more "real world" demonstrator systems. In this paper we review the progress made to date on two separate demonstrator projects which have been assembled at Heriot-Watt University. We shall describe some of the enabling technologies used in the creation of these systems and outline the potential for scaling the architectures described up to sizes where the computational advantages of the optics-in-computing paradigm become highly attractive.

Fourier analysis has been revealing itself as powerful for dealing with coherent optics and the fractional order Fourier transform is an extension of this tool. There exists a method of the fractional Fourier transform in coherent optics which legitimizes the name of fractional Fourier optics. This fact is illustrated by examples in light propagation, coherent imaging, image formation, and optical resonator theory. A fractional correlation operation is deduced and the designs of optical fractional correlators are proposed.

Diffraction-based optical correlators working under broadband illumination, in contrast to their coherent counterparts, allow us to exploit color information. However, the use of the wavelength as an additional parameter requires to take into account the chromatic dispersion inherent to the diffraction process. In this contribution, we describe a novel family of dispersion-compensated broadband optical correlators that operate some in the Fourier and some in the Fresnel region. In both cases, the chromatic compensation is achieved by a proper combination of a small number of commercially available optical elements, conventional diffractive and refractive lenses. In all cases, and with a single matched filter, the chromatic content of the correlation peak provides the spectral com­position of the detecting color signal. On top of that, some of our optical solutions work with point-source illumination and others with spatially-incoherent light. In this way, on the one hand, our spatially coherent optical designs permit to perform the color correla­tion in amplitude for each spectral channel. Accordingly, working in the Fresnel domain, we achieve a space-variant color pattern recognition setup. On the other hand, totally incoherent optical correlators, which are linear in irradiance, provide important practical advantages as they employ natural light and allow us to deal with diffuse, reflecting or self-luminous color objects.

Nonlinear optical processing techniques that produce space-time information processing are introduced and experimentally demonstrated. The basic concept of such space-time processors closely resembles conventional Fourier optical processors of the space domain. By using ultrafast short pulses and nonlinear optics, we can perform not only real-time optical information conversion between the space and time domains, but also the processing and imaging of temporal information.

Several methods for channel multiplexing are described and analyzed. The systems permit the use of a single optical setup for the processing of multichannel images or several channels of the same image. The definition of channels depends on the problem to be addressed, examples being RGB images, several orders of circular or radial harmonic extracted from a monochromatic image or resolution channels. The methods can rely on a time sequential multiplexing, spatial multiplexing in the input plane and wavelength multiplexing

This talk deals with correlation filtering techniques developed for finding patterns in Wavelet compressed imagery. It has been shown that the correlation filters can recognize patterns in IR and SAR imagery at very high compression rates in excess of I 00 to 1. The reason is partly due to the excellent information compaction capability of wavelets augmented by the zero-tree encoding technique, and partly because correlation filters do not require pixel level reconstruction of visual information, but rather the preservation of spectrally significant information which wavelet encoding may achieve very well.

As part of the presentation, we will describe a technique for merging the inverse wavelet compression and correlation filtering operations into a seamless process. In addition to being theoretically elegant, this has the added benefit of reducing the overall computations. Equally significant, it offers a method for obtaining the correlation result without requiring the full image to be reconstructed thus avoiding the need for large amounts of storage. We also show that it is indeed possible to design the compression filters and the correlation filter in a joint optimization process with added benefits. The notion of performing recognition by directly exploiting the Wavelet coefficients is also addressed. Here, we describe a technique which combines the information in different bands using a multi-channel correlation algorithm known as polynomial correlation filters. The optimization process must take into account the shift-sensitivity of wavelet coefficients. It is shown that simultaneous optimization of the sub-band QMFs and the correlation filters leads to promising results.

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.

We describe a number of new optoelectronic approaches to three-dimensional (3D) image recognition. In all the cases, digital holography is used to record the complex amplitude distribution of Fresnel diffraction patterns generated by 3D scenes illuminated with coherent light. This complex information is compared with that from a similar digital hologram of a 3D reference object using correlation methods. Pattern recognition techniques that are shift-variant or shift-invariant along the optical axis are described. In the latter case it is possible to detect the 3D position of the reference in the input scene with high accuracy. We use also a nonlinear composite correlation filter to achieve distortion tolerance. Experiments are presented to illustrate the recognition of a 3D object in the presence of out-of-plane rotation.

We define nonlinear correlations based on binary decompositions of gray level objects. Those correlations are expressed by means of a matrix representation. This matrix allows the investigation of some interesting properties, as common linear correlation, binary correlation and morphological correlation among others are described in terms of those nonlinear correlations. Those correlations have been implemented optically using a joint transform correlator and a time sequential technique in the joint power spectrum domain. The discrimination capability is studied for some pattern recognition operations like noisy scenes and rotation invariance.

The discrimination capability requirements of pattern recognition systems may vary depending on the application and the characteristics of the objects to analyse. Our goal is to obtain a single system with a wide and smooth control of its discrimination capability in two senses: the first one, a discrimination capability selective to different aspects of the target (for example, shape, intensity, colour, texture); the second one, a discrimination capability with variable level of sensitivity -or tolerance- to the differences between an object and the target in the aspect selected. This purpose lead us to consider higher levels of complexity in the sensitivity of the recognition system. Thus, we obtain pattern recognition with high discrimination capability for a given aspect along with certain tolerance for another aspect, or vice versa. In this work, we build an optoelectronic system for pattern recognition with selective and adjustable discrimination capability by applying a dual nonlinear correlation model to a joint­ transform correlator. Dual nonlinear correlation is achieved by means of two nonlinear operators that are applied to both the reference and input channels. A filtering function that limits the region of support in the Fourier plane is additionally introduced. The eventual capabilities of the real system strongly depend on some experimental conditions such as quantization, grey-level dynamic range, saturation and other technical characteristics of both the camera and the spatial light modulator used in the joint ­transform correlator. We explore these capabilities for a 8-bits and a 12-bits CCD camera and several available modulators. Experimental and simulated results for model and real objects - alphabetic characters, keys and screws- are presented and discussed. They demonstrate that the discrimination capability of the optical recognition system by dual nonlinear correlation can be controlled and adjusted with gradable tolerance to object variations in a given aspect.

We review correlation methods for pattern recognition that are invariant to a transformation af(x,y)+b of unsegmented targets. This linear transformation is an approximation to nonlinear image transformations such as those caused by detector nonlinearities. The case b=O corresponds to a change of illumination of the object with respect to the reference. Earlier methods had considered only the latter case; here we introduce a technique for the more general case. We show that two of the invariant methods are equivalent to measuring the angles between the reference and the targets in a multidimensional vector space. Experimental results that compare the various methods with and without noise show that the new method yields results that are much improved over the previous methods.

Polarization diversity active imaging techniques have the appealing fea­ture of revealing contrasts that do not appear in conventional intensity im­ages. However, the intensity images provided by the system are in general not useful due to their perturbation by atmospheric turbulence and spatial inhomogeneity of laser sources. It is thus preferable to process only the im­age that represents the degree of polarization (DOP) of the reflected light. In this chapter, the analysis will be devoted to the particular case of purely de­polarizing materials which are defined by their property of having diagonal coherency matrices whatever the incident state of polarization. We discuss some statistical results of the "Orthogonal State Contrast Image" (OSCI) which is nothing but the degree of polarization when the coherency matrix is diagonal. We also analyze some estimation properties useful for image processing. These results are illustrated on target detection and segmentation processing tasks. We demonstrate that simple but still very efficient algo­rithms can be developed.

We have demonstrated a morphological image processor composed of arrays of bistable optoelectronic transceivers which are connected in differential pairs and work as comparators. The use of differential pairs of optoelectronic thyristors suggested a dual rail architecture for this Photonic Morphological Image Processor (PMIP). The PMIP consists of a thresholding module, that decomposes grey level images into binary slices, and a binary morphological processing module. Morphological operations are performed within a neighbourhood defined by a structuring element implemented as a diffractive fan-out element. We demonstrate dilation and erosion operations performed at a 100 Hz frame rate for an image of 8x8 pixels and threshold decomposition of 6 grey level images is demonstrated at a 1,800 Hz rate. In this paper we also discuss the limitations of photonic morphological image processing with respect to speed, bandwidth, parallelism and architecture.

To be competitive with their electronic counterparts, correlation-based optical processors require very fast spatial light modulators (SLMs) that can perform simultaneously phase and amplitude modulation. Owing to their ultra-high speed, multiple quantum well (MQW) SLMs have been early identified as very good candidates. However, the coding domain of MQW SLMs is not widely known. We present here a study of available coding domains of MQW SLMs. We demonstrate that pure amplitude modulation, ternary { -1, 0, + 1} modulation and quaternary {0, + 1, e^i2π/3, e^i4π/3}, modulation are examples of coding domains that can be achieved by tuning a few parameters in the design of Fabry-Perot MQW modulators. We show that ternary and quaternary filters provide much better results than binary filters for the recognition of objects embedded in highly cluttered noise. Finally, we present a technique, the time-averaged pseudo-random encoding technique, which enables encoding of any complex filter onto a quaternary modulator. Combined with the time-­averaged pseudo-random encoding technique, MQW SLMs may pave the way to the development of new optoelectronic correlator systems with improved speed and accuracy performance.

In this paper we will revise the application of twisted nematic liquid crystal displays (TN-LCD) as spatial light modulators (SLM) for image processing and diffractive optics. In general two kind of responses are desired for the mentioned applications: amplitude­-only and phase-only modulation. In general the users of commercially available LCDs do not know the optical properties of the used material. Thus, a reverse-engineering approach is needed to optimize the LCD response. First, we show a simplified model, that we recently proposed, for the orientation of the LC molecules. The model allows the determination of the physical parameters of the LCD by means of simple intensity measurements. Second, we demonstrate the capability of the model to provide very accurate predictions of the optical transmission. Therefore, we can perform computer searches for the optimum orientation of the added polarizing elements to obtain the required optical transmission. We demonstrate the need to insert wave plates in front and behind the LCD to obtain either amplitude-only or phase-only regimes with the LCD. Finally, we show the application of the optimized LCD to display images and filters in optical image processing, as well as we show the design of diffractive optical elements and apodizers.

Spatial light Modulators (SLM) are key devices for the development of optical information processors. Low cost twisted nematic liquid crystal (TN-LC) SLM's are widely available and their characteristics have been extensively studied. Beside the fact that they exhibit a coupled amplitude and phase modulation, their speed is limited to approximately the video frame rate. An alternative to TN-LC devices can be the use of analog ferroelectric liquid crystal (FLC) devices. These devices now commercially available produce a gray level pure amplitude modulation at typical frame rates of 1 kHz. In order to determine its coding capabilities and its limitations, the characterization of such a device, manufactured by Boulder Nonlinear Systems Inc., is presented in this paper. This SLM has a resolution of 512 by 512 pixels with a pitch of 15 μm and has a reflective VLSI backplane. The study of its potential applications for the display of dynamic diffractive optical elements and also as a component of an optical processor for pattern recognition will be followed by experimental results and comparisons with TN­LC devices.

In response to the increasing demand of information systems, we need new materials with high performance for storage and processing applications. Available on the market optical storage materials present very useful characteristics but are still limited in the visible spectrum and are expansive. Recently, we have developed holographic polymer dispersed liquid crystal (H-PDLC) materials sensitive in the near infrared region (800 nm to 850 nm). These compounds are based on acrylate monomers and different liquid crystals (LC) and allow highly efficient in-situ recording of holographic optical elements using infra red lasers. Diffraction efficiency above 95% is demonstrated. Photosensitivity of the material, its dark ­development and photochemical stability of recorded gratings are investigated. The angular and spectral selectivities of gratings, recorded in these films are examined for recovering the refractive index modulation profile.