P. Chavel

2-D generation of random numbers by multimode fiber speckle for silicon arrays of processing elements

Abstract We investigate a random-number array generator based on the statistical properties of speckle patterns and we compare the use of (i) two moving diffusers, and (ii) multimode optical fiber model noise. Energy requirement, reliability and feasability argue in favour of the fiber system for microsecond generation so allowing implementation of stochastic algorithms on a massively parallel silicon array of processing elements.

A complement to the theory of Lohmann-type computer holograms

Abstract The introduction by Lohmann and co-workers of the detour phase method in realizing synthetic holograms has been an important step in the history of computer generated holography. In 1969, Brown and Lohmann proposed an improvement to their method: they used true phase and amplitude coding at the center of the diffracting aperture instead of periodically sampled phases and amplitudes. We present a mathematical analysis of this procedure and examine the approximation related to its practical realization.

Spatial filtering using Newton rings

Abstract The theory of spatial frequency filtering shows that any division of amplitude interferometric setup can be used as a spatial filter. We illustrate this idea by the example of Newton rings, which are convenient to implement, and demonstrate the main features of the theory: double images through the interferometer, Fresnel diffraction of these images, selectable shift between these images and selectable plane for the filtered image. All these parameters modify the resulting MTF. The interpretation of the experimental results in the case of a radial test target taken as an object shows that with such MTFs care must be exercised when using the intuitive idea of filtering of local spatial frequencies. The setup studied is also suitable for spatial frequency pseudocoloring.

Fresnel detour-phase circular computer generated holograms

Abstract When a circularly symmetric wavefront has to be encoded onto a computer generated hologram, it is highly desirable to preserve the symmetry. The coding scheme must therefore be circularly symmetric itself. This paper introduces a particular kind of computer generated hologram which extends circular symmetry to the detour phase technique; this is obtained by working in Fresnel diffraction. The wavefront should be sampled using a circular sampling theorem such as the one derived from the Dini-Bessel expansion. The hologram then consists of weighted unit masses distributed on a set of circles, which in practice are replaced by annuli of suitable inner and outer radii. The approximations due to the detour phase method and to the annuli widths are discussed and an experimental example is shown.

TWO-WAVE DIFFRACTION OF QUASI-MONOCHROMATIC LIGHT BY A VOLUME GRATING DEPOSITED ON A THICK TRANSPARENT PLATE

Abstract The diffraction by a Bragg volume grating deposited on a transparent parallel plate is analysed in the case of reduced temporal coherence. When the grating is thinner, and the substrate is thicker than the coherence length, the summation of multiple-beam series, involving coherent diffraction coefficients of the periodic film and incoherent multiple reflected intensities inside the plate, is shown to given simple analytic expressions of the diffraction efficiencies of the device. Numerical results of this model are compared with those obtained by spectral integration. The multiple-beam model provides an accurate representation of the energy balance between the diffracted orders, and is particularly useful for determining the energy losses due to spurious reflections.

A proposed generalization of Hopfield's algorithm

Abstract We generalize Hopfields algorithm by studying the influence on the capacities of associative memories of an additional nonlinearity which stresses the importance of the correlation between input and stored vectors. We show that the nonlinearity has a beneficial effect on the signal to noise ratio. Several simulation results indicate that on the one side it is possible to store a larger number of states for a given number of “formal neurons”, and on the other side that the convergence radius of each state is increased. It is expected that a nonlinear medium in an optical correlation plane allows to implement our model on any “inner product” version of an optical Hopfield machine.

An Extension Of The Hopfield Model Suitable For Optical Implementation

The analysis of neural models as associative memories has proven a fruitful domain of research. Two principal directions may be put forward : models tending to investigate learning processes in the human brain, and algorithms tending to increase the efficiency of associative memories.

Le facteur de qualite N/τ dans les deflecteurs de faisceaux lasers: Comparaison entre deflecteurs holographiques et acousto-optiques

Abstract N /τ (number of addressable points divided by access time) is a valuable figure of merit for laser scanners. It is shown that N /τ has the same theoretical expression for both acousto-optic and holographic scanners, and that it depends on the bandwidth of the temporal phenomenon “displacement of the fringes in the pupil” as well as on the nature of the scanning (continuous or discontinuous, with or without focusing). The comparison between acousto-optic and holographic scanners show clearly the interest of the latter. The bidimensional character of holographic scanning is probably its main advantage, for it is very convenient and it augments the number of points N : for holographic scanners, N and even N /τ can reach higher values than for acousto-optic scanners.

Optics In Image Processing : Prospects And Illustrations

Optics is necessary to analyze and realize imaging processes, but it is also a possible tool in image processing. Since the concepts of coherent and incoherent optical image processing including the formalism of spacial frequency filtering, the laser, and holography, were developed, computer science went through revolutionary developments. The past and present situation of optical image processing is critically examined, and three subject to which we have recently contributed are used as illustrations. The first is the use of interference phenomena as spatial frequency filters, which can be a useful complement to the more conventional use of diffraction. The second is the use of white light illumination in spatial frequency filtering setups to obtain spatial frequency pseudocoloring. Finally, a texture discrimination experiment involving optical preprocessing by a set of interference spatial frequency filters Followed by computer classification is described.

Optical preprocessing for texture classification using specialized binary black and white pseudocoloring masks

Abstract Image texture is a neighborhood information which is time consuming to analyze by computer. Optical processing can be used as a preprocessor to reveal some of the texture information in parallel on the whole image before classification of the preprocessed image by computer. Pseudocoloring allows an easy discrimination of texture information. A specialized binary black and white mask is introduced which selects at one particular wavelength one peak of the diffracted power spectrum of each texture considered. The method is applicable to textures showing some periodicity. The resolution, selectivity and difficulties of the method are described qualitatively and an experimental example including a problem of partial cross talk between different textures is presented.