Everybody who ever has looked at a high quality optical hologram will be fascinated by the three-dimensional spatial perspective it offers to the observer. At a level of aesthetic appeal similar to that of central perspective during the Italian Renaissance are the fractalization phenomena studied by computer scientists and the intriguing geometric patterns which appear at the intersection of repetitive structures such as the folds of curtains. The superposition of repetitive structures present a fascinating geometrical phenomenon of abelian Fourier analysis known as the Moiré effect [K. Patorski, Handbook of the Moiré fringe technique. Elsevier Science, Amsterdam, New York (1993)]. As a technique applicable to high sensitive measuring of in-plane displacements, the modality of Moiré interferometry combines the concepts of geometrical Moiré with the techniques of optical interferometry [D. Post, B. Han and P. Ifju, High Sensitivity Moiré: Experimental Analysis for Mechanics and Materials. Springer-Verlag, New York, Berlin, Heidelberg (1994)].
The monograph under review forms the first textbook which is completely devoted to the abelian Fourier analysis of the Moiré phenomenon. It is based on the author’s Ph.D. thesis entitled “Analysis of Moiré Patterns in Multi-Layer Superpositions” (# 1341, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland 1995). Due to Fourier-based tools such as the theory of almost-periodic functions and the theory of geometry of numbers, the book offers a unified and coherent approach to the superposition for any number of layers provided the line spacing in each grating is coarse enough for diffraction effects to be ignored. Abelian Fourier spectral analysis and its practical applications to micro- and macrostructures are illustrated in a convincing and attractive manner. Moiré phenomena such as moirés between random screens and temporal moirés can be considered as natural extensions of the abelian Fourier spectral approach presented in the book. Knowledge of abelian harmonic analysis at the level of standard engineering textbooks such as [R. N. Bracewell, The Fourier Transform and Its Applications. Second Edition, McGraw-Hill, New York, St. Louis, San Francisco (1978; Zbl 0502.42001); J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics. John Wiley & Sons, New York, Chichester, Brisbane (1978)] are sufficient to follow the mathematical development because the author prefers a pictorial, intuitive approach supported by abelian Fourier spectral analysis over a rigorous mathematical treatment.