Amidror The Theory of the Moiré Phenomenon

2000
ISBN: 978-94-011-4205-2
Verlag: Springer Netherland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 15, 474 Seiten, eBook

Reihe: Computational Imaging and Vision

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.

Zielgruppe

Research

Autoren/Hrsg.

Amidror, Isaac

Inhaltsverzeichnis

1. Introduction.- 2. Background and basic notions.- 3. Moiré minimization.- 4. The moiré profile form and intensity levels.- 5. The algebraic foundation of the spectrum properties.- 6. Fourier-based interpretation of the algebraic spectrum properties.- 7. The superposition phase.- 8. Macro- and microstructures in the superposition.- 9. Polychromatic moiré effects.- 10. Moirés between repetitive, non-periodic layers.- 11. Other possible approaches for moiré analysis.- Appendices.- A. Periodic functions and their spectra.- A.1 Introduction.- A.2 Periodic functions, their Fourier series and their spectra in the 1D case.- A.3 Periodic functions, their Fourier series and their spectra in the 2D case.- A.3.3 1-fold periodic functions in an arbitrary direction.- A.3.4 2-fold periodic functions in arbitrary directions (skew-periodic functions).- A.4 The period-lattice and the frequency-lattice (= spectrum support).- A.5 The matrix notation, its appeal, and its limitations for our needs.- B. Almost-periodic functions and their spectra.- B.1 Introduction.- B.2 A simple illustrative example.- B.3 Definitions and main properties.- B.4 The spectrum of almost-periodic functions.- B.5 The different classes of almost-periodic functions and their spectra.- B.6 Characterization of functions according to their spectrum support.- B.7 Almost-periodic functions in two variables.- C. Miscellaneous issues and derivations.- C.1 Derivation of the classical moiré formula (2.9) of Sec. 2.4.- C.2 Derivation of the first part of Proposition 2.1 of Sec. 2.5.- C.3.1 Invariance of the 2D Fourier transform under rotations.- C.4 Shift and phase.- C.4.1 The shift theorem.- C.4.2 The particular case of periodic functions.- C.4.3 The phase of a periodic function: the ? and the ? notations.- C.6 The2D spectrum of a cosinusoidal zone grating.- C.7 The convolution of two orthogonal line-impulses.- C.11 The spectrum of screen gradations.- C.12 Convergence issues related to Fourier series.- C.12.1 On the convergence of Fourier series.- C.12.2 Multiplication of infinite series.- C.13 Moiré effects in image reproduction.- D. Glossary of the main terms.- D.1 About the glossary.- D.2 Terms in the image domain.- D.3 Terms in the spectral domain.- D.4 Terms related to moiré.- D.5 Terms related to light and colour.- D.6 Miscellaneous terms.- List of notations and symbols.- List of abbreviations.- References.