Who has not noticed, on one o~casion or another, those intriguing geometric patterns which appear at the intersection Of repetitive structures such as two far picket fences on a hill, the railings on both sides of a bridge, superposed layers of fabric, or folds of a nylon curtain? This fascinating phenomenon, known as the moire effect, has found useful applications in several fields of science and technology, such as metrology, strain analysis or even document authentication and anti-counterfeiting. However, in other situations moire patterns may have an unwanted, adverse effect. This is the case in the printing world, and, in particular, in the field of colour reproduction: moire patterns which may be caused by the dot-screens used for colour printing may severely deteriorate the image quality and tum into a real printer's nightmare. The starting point of the work on which this book is based was, indeed, in the research of moire phenomena in the context of the colour printing process. The initial aim of this research was to understand the nature and the causes of the superposition moire patterns between regular screens in order to find how to avoid, or at least minimize, their adverse effect on colour printing. This interesting research led us, after all, to a much more far reaching mathematical understanding of the moire phenomenon, whose interest stands in its own right, independently of any particular application.

Since the first edition of this book was published several new developments have been made in the field of the moiré theory. The most important of these concern new results that have recently been obtained on moiré effects between correlated aperiodic (or random) structures, a subject that was completely absent in the first edition, and which appears now for the first time in a second, separate volume. This also explains the change in the title of the present volume, which now includes the subtitle “Volume I: Periodic Layers”. This subtitle has been added to clearly distinguish the present volume from its new companion, which is subtitled “Volume II: Aperiodic Layers”. It should be noted, however, that the new subtitle of the present volume may be somewhat misleading, since this book also treats (in Chapters 10 and 11) moiré effects between repetitive layers, which are, in fact, geometric transformations of periodic layers, that are generally no longer periodic in themselves. The most suitable subtitle for the present volume would therefore have been “Periodic or Repetitive Layers”, but in the end we have decided on the shorter version.

Since the first edition of this book was published several new developments have been made in the field of the moiré theory. The most important of these concern new results that have recently been obtained on moiré effects between correlated aperiodic (or random) structures, a subject that was completely absent in the first edition, and which appears now for the first time in a second, separate volume. This also explains the change in the title of the present volume, which now includes the subtitle “Volume I: Periodic Layers”. This subtitle has been added to clearly distinguish the present volume from its new companion, which is subtitled “Volume II: Aperiodic Layers”. It should be noted, however, that the new subtitle of the present volume may be somewhat misleading, since this book also treats (in Chapters 10 and 11) moiré effects between repetitive layers, which are, in fact, geometric transformations of periodic layers, that are generally no longer periodic in themselves. The most suitable subtitle for the present volume would therefore have been “Periodic or Repetitive Layers”, but in the end we have decided on the shorter version.

Moiré Fringes in Strain Analysis provides a comprehensive description of the entire spectrum of techniques and methods using the moiré fringe phenomenon for the measurement of strains in engineering structures and in deformed bodies. This book presents several examples of applications of each technique to particular metrological problems. Organized into 12 chapters, this book begins with an overview of the interference fringes between two beams of monochromatic light. This text then discusses the theory of moiré patterns developed by various types of gratings based on the indicial representation method. Other chapters consider the experimental and theoretical investigation of the properties of moiré fringes that was primarily confined to moiré fringes formed by the interference of two-line gratings. This book discusses as well the major requisite for the application of moiré methods in the field of strain analysis. The final chapter deals with the advantages of the moiré methods. This book is a valuable resource for engineers, students and researchers.

This monograph explores the close relationship of variouswell-known pattern recognition problems that have so far beenconsidered independent. These relationships became apparent with thediscovery of formal procedures for addressing known problems and theirgeneralisations. The generalised problem formulations were analysedmathematically and unified algorithms were found. The main scientificcontribution of this book is the unification of two main streams inpattern recognition - the statistical one and the structuralone. The material is presented in the form of ten lectures, each ofwhich concludes with a discussion with a student."Audience: " The book is intended for both researchers and studentswho work in knowledge management and organisation, machine learning, statistics, and symbolic and algebraic manipulations. It provides newviews and numerous original results in their field. Written in aneasily accessible style, it introduces the basic building blocks ofpattern recognition, demonstrates the beauty and the pitfalls ofscientific research, and encourages good habits in readingmathematical text.

This one volume treatise presents a comprehensive discussion of moire metrology analysis. The authors work from a new point of view, treating the gratings used in moire analysis as an artificial analog to electromagnetic waves, thereby comparing moire analysis with conventional optical methods based on wave properties such as interferometry. It is shown that for every interferometric technique in metrology, there is an analogous technique in moire metrology and vice versa, and that scientists involved in optical metrology have a real choice between interferometric and moire methods.

Introduction to Optical Metrology examines the theory and practice of various measurement methodologies utilizing the wave nature of light. The book begins by introducing the subject of optics, and then addresses the propagation of laser beams through free space and optical systems. After explaining how a Gaussian beam propagates, how to set up a collimator to get a collimated beam for experimentation, and how to detect and record optical signals, the text: Discusses interferometry, speckle metrology, moiré phenomenon, photoelasticity, and microscopy Describes the different principles used to measure the refractive indices of solids, liquids, and gases Presents methods for measuring curvature, focal length, angle, thickness, velocity, pressure, and length Details techniques for optical testing as well as for making fiber optic- and MEMS-based measurements Depicts a wave propagating in the positive z-direction by ei(ωt – kz), as opposed to ei(kz – ωt) Featuring exercise problems at the end of each chapter, Introduction to Optical Metrology provides an applied understanding of essential optical measurement concepts, techniques, and procedures.