Diffraction characteristics of general dielectric planar (slab) gratings and surface-relief (corrugated) gratings are reviewed. Applications to laser-beam deflection, guidance, modulation, coupling, filtering, wavefront reconstruction, and distributed feedback in the fields of acoustooptics, integrated optics, holography, and spectral analysis are discussed. An exact formulation of the grating diffraction problem without approximations (rigorous coupled-wave theory developed by the authors) is presented. The method of solution is in terms of state variables and this is presented in detail. Then, using a series of fundamental assumptions, this rigorous theory is shown to reduce to the various existing approximate theories in the appropriate limits. The effects of these fundamental assumptions in the approximate theories are quantified and discussed.

Analysis and applications of optical diffraction by gratings

The statistical properties of dynamic speckles produced by a moving diffuse object were reviewed by providing the space–time correlation function and the power spectrum of speckle-intensity fluctuation for five combined cases of both the optical configuration and the illumination light. In the optical configuration, three kinds of geometry (free-space, single-lens, and double-lens) were taken, and three kinds of illumination light (a Gaussian beam, a plane-wave beam, and a Gaussian Schell-model beam) were used. Consequently, it was shown that the cross-correlation function and the power spectrum are both Gaussian under some assumptions. From the dynamic properties, two types of speckle motion, boiling and translation, were also evaluated for various conditions of object motion, optical configuration, and illumination light.

Statistical properties of dynamic speckles

It is generally accepted among neuroscientists that the sensory cortex of the brain is arranged in a layered structure. Based on a unified quantum holographic approach to artificial neural network models implemented with coherent, hybrid optoelectronic, or analog electronic neurocomputer architectures, the present paper establishes a novel identity for the matching polynomials of complete bichromatic graphs which implement the intrinsic connections between neurons of local networks located in neural layers.

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Quantum holography and neurocomputer architectures

As seen in Chap. 3, the principal property of holograms is the storage of wave fields which may be reconstructed at any later time. As was already mentioned in the introduction, it is for this reason that two slightly different wave fields, which do not exist simultaneously, may be brought to interfere. Analysis of the resulting interference fringes (Fig. 4.1) constitutes the principal problem in holographic interferometry, for which the first experiments were performed around 1965 [4.1–14]. In particular, if both wave fields are recorded successively on the same hologram (with the same reference source) and later reconstructed together, we obtain the well-known double exposure or frozen fringe effect. Using this technique, measurements are almost completely insensitive to small modifications of the optical set-up at the reconstruction, since both wave fields undergo the same small changes. Thus, the fringes disclose information about the difference of relative positions of the two (stationary) configurations from which these wave fields emanate. In this chapter, we shall investigate two cases of special interest in engineering. First, we present the elements concerning holographic determination of the deformation of an opaque body with a diffusely reflecting surface. Here, the concepts of Sect. 2.3 will be combined with those outlined in Sect. 3.1.1. Secondly, we intend to study holographic interferometry of phase objects, i.e., the determination of the spatial variation of the index of refraction of a transparent medium. This topic relates Sects. 2.2 to 3.1.1.

Holographic Interferometry or Fringe Interpretation

The development of faster and more efficient computers in recent years has been driven by a seemingly unending thirst for communication, interaction, automation, control issues, information availability, and a yearning for new understanding of the self-organization principles of ourselves and our environment.The challenges of the future force us to create and study new concepts of adaptive information processing and to implement for faster communication novel computer architectures based on fundamental quantum theoretical principles.

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We present a solution for the theoretical first-order probability density function of laser speckle measured with a finite aperture. A two-dimensional Kac-Siegert analysis is made. This involves the solution of an eigenvalue problem. For the spatial speckle correlation function and the spatial profile of the detector we assume gaussian models. The eigenvalues are then exactly expressed by simple formulae, and the probability density is calculated for slit apertures and a two-dimensional aperture. Experimental results are presented, and they agree well with the theory.

On the First-order Probability Density Function of Integrated Laser Speckle

Interferometry with Miniature Format Volume Reflection Holograms

A theoretical formula for the first-order probability density function of polychromatic speckle is presented, based on recent results for integrated laser speckle. We consider both completely and partially coherent incident light. An experimental set-up for accurate measurements of speckle statistics is described. Experimental results for the constrast and the probability density of polychromatic speckle in the far field show a significant dependence on surface roughness. Except from some high contrast values they agree fairly well with the theory.

Carl Trygve Stansberg

Papers

On the First-order Probability Density Function of Integrated Laser Speckle

Interferometry with Miniature Format Volume Reflection Holograms

Surface Roughness Dependence of the First-order Statistics of Polychromatic Speckle Patterns