Gabriel Y. Sirat

Conoscopic holography. I: Basic principles and physical basis

Conoscopic holography is an incoherent holographic technique based on the properties of crystal optics. More precisely, for each point of the object, the interference pattern between the ordinary and the extraordinary rays is presented. The pattern is a Gabor-zone-lens pattern, with a scale parameter that is a function of the distance of the point. The superposition of the Gabor zone lens from each point of the object is the hologram, which contains information on the shape of the object through the scale-parameter dependence of each point is presented. I present a simplified version of the theory of conoscopic holography. The point-spread function and the transfer function of the conoscopic system are presented by using simple arguments, and the conoscopic hologram is defined. The basic schemes for reconstruction, i.e., retrieving, optically or numerically, this three-dimensional information about the object from the recorded hologram, are presented. Finally, the resolution of the system is quantified.

Conoscopic holography. II. Rigorous derivation

Conoscopic holography was discussed with simplifying assumptions in a companion paper [ J. Opt. Soc. Am. A.9, 70 ( 1992)]. These assumptions are removed, and the conclusions of the simplified analysis of the companion paper are proved by more exact calculations.

Frequency multiplexed raster neural networks. 1: Theory.

In the first part of this paper we present frequency multiplexed raster (FMR) optical implementation of neural networks. A hidden difficulty for hardware (optical and electronic) implementation is that the dimension of the synaptic matrix is twice that of the input and output matrices or vectors. For 2-D images, which is we believe one of the greatest potentialities of neural networks, the synaptic matrix is 4-D and cannot be directly implemented in optics. We propose FMR as a method to fold this matrix into a 2-D format. In the second part of this paper we describe the system built in our laboratory showing the feasibility of FMR optical neural networks. The system is built from an optical input module, a fixed synaptic matrix coded on a transparency, a CCD camera, and a microcomputer which performs the thresholding and feedback operations. In a later stage the fixed matrix will be replaced by a programmable matrix.

Reconstruction of a three-dimensional object from its conoscopic hologram

Conoscopic holography is a method for recording holograms with incoherent light, first presented in 1985. Its applications range from 3D microscopy to 3D satellite imaging and include robotics. The Point Spread Function (PSF) is a Gabor Zone Pattern, which is known to have zeros in Fourier space. We present an experimental technique to obtain an invertible PSF with an experimental image reconstruction, and an original algorithm to find the object shape, validated with both simulations and first experimental results.

3-D camera based on conoscopic holography

The principle and the firstresults of a new 3D camera will be presented. This camera is based on a holographic technique named conoscopic holography. The simplicity of the technique, using only a crystal, waves plates and polarizers, and its compatibility with CCD sensors make possible the fabrication of low cost and flexible conoscopic vision systems. The first prototype is an tive rangefmder which will be developed into a profilometer and a 3D camera a resolution of 1 jnn and a precision of a 2-3 jim have already been obtained. The numerical processing is based on Fourier Transforms, quickly performed by available dedicied hardware.

Optoelectronic implementation of a neural network

We present a hybrid opto-electronic implementation of a neural network. In our system the linear part of the algorithm (calculation intensive) is performed optically. The non4inear feedback is controlled by a microcomputer which takes the system output detected using a CD camera, thresholds this output and then uses the thresholded signal to commtnd the spatial light modulator which provides the input to the optical part of the system. One of the major advantages of optics in this type of architecture is its ability to work in parallel on two•dimensional data structures. However, a four-dimensional synaptic matrix is required to stoie the connections between two images. We recall and explain the Frequency Multiplexed Raster (FMR) coding scheme we have developed to enable us to store this four..dimensional array on a planar component (CGH). In addition we present some modifications to the basic synaptic matrix algorithm which improve its performance with correlated images. Finally, after presenting some first experimental results we extend the FMR coding scheme for use in generalized optical interconnections.

Invariance in an optoelectronic implementation of neural networks

Two dimensional jmuem recognition related tasks require the introduction of invariant recognition ftors such as shift, rotation, scale and deformation. In a preliminary work we showed the inherent capability of our FMR coding to perform shift-invariant retrieval. This capability is essential for other invariances which can be transformed into translated representations. In this paper we propose using this translation invariant coding in a general scheme, whereby a we-processor handles the invariance issues and aligns the input probe to a fixed baseline utilized by the recognition mechanism. This higher order layer includes S validation switches, each switch corresponding to a position index of translated objects. A validation switch will be eon f the stimulus matches one of the objects, translated to the position handled by this switch. These switches condition the search, and where a search is needed, they supply the required transformation for stimulus alignment. Several proximity measures, needed for the realization of these switches, are presented and compared, in the context of different weight prescription algorithms.