The Theory of the Moiré Phenomenon: Volume I: Periodic Layers (Computational Imaging and Vision, 38)

This is a new, revised and updated edition of the original book by Isaac Amidror. It presents the most comprehensive and methodical work on the theory of the moiré phenomenon, providing a full general-purpose and application-independent exposition of this fascinating effect. Based on the Fourier theory, it leads the reader through the various phenomena which occur in the superposition of repetitive layers, both in the image and in the spectral domains. The first chapters of the book present the basic theory which covers the superposition of monochrome, periodic layers. In later chapters the theory is extended to the even more interesting cases of polychromatic moirés and moirés between repetitive, non-periodic layers. Throughout the whole text the book favours a pictorial, intuitive approach which is supported by mathematics, and the discussion is accompanied by a large number of figures and illustrative examples, some of which are visually attractive and even spectacular. This book is intended for students, scientists, engineers and any readers who wish to widen their knowledge of the moiré effect. It also offers a beautiful demonstration of the Fourier theory and its relationship with other fields of mathematics and science. The prerequisite mathematical background is limited to an elementary familiarity with calculus and with the Fourier theory. This book presents the most comprehensive and methodical work on the theory of the moire phenomenon, providing a full general-purpose and application-independent exposition of this fascinating effect. Based on the Fourier theory, it leads the reader through the various phenomena which occur in the superposition of repetitive layers, both in the image and in the spectral domains. The first chapters of the book present the basic theory, covering the superposition of monochrome, periodic layers. In later chapters the theory is extended to the even more interesting cases of polychromatic moires and moires between repetitive, non-periodic layers. Throughout the whole text, the book favours a pictorial, intuitive approach which is supported by mathematics, and the discussion is accompanied by a large number of figures and illustrative examples, some of which are visually attractive and even spectacular. This book is intended for students, scientists, engineers and any readers who wish to widen their knowledge of the moire effect. It also offers a beautiful demonstration of the Fourier theory and its relationship with other fields of mathematics and science. The prerequisite mathematical background is limited to an elementary familiarity with the Fourier theory 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. Front Matter....Pages i-xviii Introduction....Pages 1-8 Background and basic notions....Pages 9-58 Moiré minimization....Pages 59-80 The moiré profile form and intensity levels....Pages 81-108 The algebraic foundation of the spectrum properties....Pages 109-148 Fourier-based interpretation of the algebraic spectrum properties....Pages 149-164 The superposition phase....Pages 165-190 Macro- and microstructures in the superposition....Pages 191-232 Polychromatic moiré effects....Pages 233-248 Moirés between repetitive, non-periodic layers....Pages 249-352 Other possible approaches for moiré analysis....Pages 353-374 Back Matter....Pages 375-529