Publisher Summary This chapter describes the self-imaging phenomenon and its applications. The self-imaging phenomenon requires a highly spatially coherent illumination. It disappears when the lateral dimensions of the light source are increased. When the source is made spatially periodic and is placed at the proper distance in front of the periodic structure, a fringe pattern is formed in the space behind the structure. The chapter discusses the theoretical and applicational aspects of the self-imaging phenomenon—that is, the property of the Fresnel diffraction field of some objects illuminated by a spatially coherent light beam. The applications of self-imaging are summarized in four main groups—namely, (1) image processing and synthesis, (2) technology of optical elements, (3) optical testing, and (4) optical metrology. The chapter describes the double diffraction systems using spatially incoherent illumination. The first periodic structure plays the role of a periodic source composed of a multiple of mutually incoherent slits. Depending on whether the periods of two periodic structures are equal, the Lau or the generalized Lau effect is discussed. Various applications of incoherent double-grating systems are described in the fields of optical testing, image processing, and optical metrology. After examining some cases of coherent and incoherent illumination, the general issue of spatial periodicities of optical fields and its relevance to the replication of partially coherent fields in space is discussed.

I The Self-Imaging Phenomenon and its Applications

The authors discuss application of the modern concept on rock mass structure as a hierarchy of blocks and the phenomenological basis of the pendulum wave theory in the context of source areas of destructive events in natural and nature-and-production systems. The phenomenological relationship is set between Zhurkov’s concentration criterion of fracture, experimental criterion of underground excavation “collapse,” canonical structure of spectrum of pendulum waves by Oparin and the long-range action of heavy explosion impacts in geomedia by Sadovsky-Adushkin. The article validates the energy approach to describing transformation of elastic energy of destructive event source areas into kinetic energy of structural elements of these areas. The authors introduce a new notion of “interference seismic emission events.”

From the alternating-sign explosion response of rocks to the pendulum waves in stressed geomedia. Part II

Attention is drawn to the changes in the Fraunhofer diffraction patterns encountered when the planar objects become titled with respect to the optical axis. The differences between the far-field images observed in the well-known untilted case and the one investigated are shown and discussed using examples of familiar objects, such as square or rectangular apertures and linear diffraction gratings.

Fraunhofer Diffraction Patterns of Titled Planar Objects

Volume optical storage systems suffer from numerous sources of noise and interference, the effects of which can seriously degrade retrieved data fidelity and produce unacceptable bit-error rates (BERs). We examine the problem of reliable two-dimensional data retrieval in the context of recently developed soft-decision methods for iterative decoding. We describe a novel near-optimal algorithm in which each pixel on the page is treated as a starting point for a simple iterative procedure so that a highly parallel, locally connected, distributed computational model emerges whose operation is well suited to the page-oriented memory (POM) interface format. We study the use of our two-dimensional distributed data detection (2D/sup 4/) algorithm with both incoherent (linear) and coherent (nonlinear) finite-contrast POM channel models. We present BER results obtained using the 2D/sup 4/ algorithm and compare these with three other typical methods [i.e., simple thresholding (THA), differential encoding (DC) and the decision feedback Viterbi algorithm (DFVA)]. The BER improvements are shown to have a direct impact on POM storage capacity and density and this impact is quantified for the special case of holographic POM. In a Rayleigh resolved holographic POM system with infinite contrast, we find that 2D/sup 4/ offers capacity improvements of 84%, 56%, and 8% as compared with DC, THA, and DFVA respectively, with corresponding storage density gains of 85%, 26%, and 9%. In the case of finite contrast (C=4), similar capacity improvements of 93%, 18%, and 4% produce similar density improvements of 98%, 21%, and 6%. Implementational issues associated with the realization of this new distributed detection algorithm are also discussed and parallel neural and focal plane strategies are considered. A 2 cm/sup 2/ /spl lambda/=0.1 /spl mu/m digital VLSI real estate budget will support a 600/spl times/600 pixel 2D/sup 4/ focal plane processor operating at 40 MHz with less than 1.7 W/cm/sup 2/ power dissipation.

Near-optimal parallel distributed data detection for page-oriented optical memories

Explicit expressions for Fraunhofer diffraction patterns (spectra) of absolutely black bodies of constant thickness have been derived from the model of equivalent diaphragms in the Kirchhoff–Fresnel approximation. The expressions can be interpreted as results of interference between generalized point sources with corresponding amplitudes and Fresnel radiation diagrams located at boundary points of the object. Approximation of the Fresnel radiation diagrams by elementary functions is suggested for analytical estimation. For essential simplification of calculations, the quasi-geometrical approach has been developed, according to which the light diffraction by faces of the object is taken into account and propagation of diffracted waves in free space is described in the geometrical-optics approximation. The extension of objects is shown to result in Fresnel modulation of their spectra and also in disturbance of the equidistant position of diffraction minima. There is agreement between theoretical and experimental results.

Fraunhofer diffraction by volumetric bodies of constant thickness

The possibility of applying an ordinary quasi-geometrical technique for Fraunhofer diffraction calculations on absolutely absorbing three-dimensional (3-D) bodies of constant thickness is investigated. It is shown that such an application can lead to results that are inadequate for finding the physical diffraction pattern of 3-D bodies. A modified version of the technique is suggested that, to a greater degree, takes into account secondary diffraction and thus permits a more exact presentation of characteristic features of the light diffracted by 3-D bodies. Some examples of this approach applied to the light-diffraction analysis of simple 3-D bodies are given. It is shown experimentally and with calculations that this approach permits description of the diffraction effects of 3-D bodies of the class mentioned in rather simple form and with good accuracy.

Quasi-geometrical method for Fraunhofer diffraction calculations for three-dimensional bodies

Optical dimensional metrology for 3D objects of constant thickness

A method for measuring diameters of circular reflecting cylinders is discussed. The method consists in processing a diffraction pattern that is formed in the near-field zone by illuminating the object edges by a plane monochromatic beam. An equivalent mathematical model of forming a diffraction field is developed and experimentally validated. The model makes it possible to obtain analytical functions describing the distribution of the field from the circular reflecting cylinder. The influence of the cylinder reflecting surface on the diffraction pattern parameters is studied. A highly accurate algorithm is proposed for calculating the diameter of the cylindrical article by its Fresnel diffraction pattern with an error under 1 µm.

Precision dimensional inspection of diameters of circular reflecting cylinders

The most important results of the development and manufacturing of unique optoelectronic measurement and laser technologies and systems for various purposes aimed at solving urgent problems in industry and academic research, which are obtained at the Technological Design Institute of Scientific Instrument Engineering of the Siberian Branch of the Russian Academy of Sciences, are reviewed. Technical characteristics of developed devices and systems and results of their testing at industrial enterprises and research institutes of the Siberian Branch of the Russian Academy of Sciences are reported.

Yu. V. Chugui

Papers

Fraunhofer diffraction by volumetric bodies of constant thickness

Quasi-geometrical method for Fraunhofer diffraction calculations for three-dimensional bodies

Optical dimensional metrology for 3D objects of constant thickness

Precision dimensional inspection of diameters of circular reflecting cylinders

Three-dimensional optoelectronic measurement systems and laser technologies for scientific and industrial applications