Moiré fringe techniques have expanded considerably over the past decade and are now established as important metrological tools. The main reason for this flourishing expansion is the use of the moiré fringe method in the common availability of the laser light. This book covers the major theoretical aspects and applications of the moiré technique. A concise description of the formation of moiré fringes and their interpretation is presented. A comprehensive review of the most important applications of the moiré phenomenon is given. Although some of them are still being refined there are already well established applications to moiré displacement and alignment sensors, grating interferometry, moiré processing of interferograms, moiré topography and strain analysis. There is also a discussion on the influence of the types of superimposition on structures and of the type of illumination used on the intensity distribution in moiré patterns.

An understanding of moiré fringes and of the characteristics of moiré patterns, which depend on various optical configurations, is essential for the proper use and control of moiré methods. The physical and practical attributes of each technique are clarified throughout. The book will prove most appropriate in meeting the needs of newcomers to the field, as well as those of researchers and technicians who want to acquire a broader view and assessment of particular techniques.

Table of Contents

1. Theoretical Interpretation of Formation of Moiré Fringes. A Fourier series approach to the description of Moiré patterns. The parametric equation method. Description of moiré in terms of vectorial sums in Fourier space. Moiré as an aliasing phenomenon by undersampling. 2. Incoherent Methods of Superimposition of Structures. Moiré types: Additive, subtractive, multiplicative. Examples of two-structure superimpositions. Special techniques: Use of structures with orthogonal transmittances. 3. Coherent Methods of Superimposition. Fringe pattern formation by filtering of the double diffraction orders. Overlapping real time interference fringes with a recorded pattern. 4. Influence of the Type of Illumination and Separation of Gratings on the Intensity Distribution in Moiré Fringes. The case of: coherent illumination; incoherent illumination; partially coherent illumination. 5. Moiré Displacement Transducers. Basic concepts. Grating reading heads. Accuracy of moiré fringe transducers. 6. Moiré Fringe Alignment Methods. Optical alignment by whole-field detection of moiré fringes. Moiré patterns for three point alignment technique. Submicron alignment methods for lithography. 7. Moiré Photography. Principles. Implementation. Fringe pattern recording and processing. Examples of applications. 8. Moiré Methods in Interferometry. In two-beam interferometry. In two-beam interferometry with conjugate wavefronts. In grating shearing interferometry. 9. Shadow Moiré Topography. Principles. Theoretical description. Localization and contrast of moiré fringes. Fringe order determination: Absolute; Relative. Instrumental considerations. Applications. 10. Projection Moiré Topography. Principles and basic con


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© 1993
Elsevier Science
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About the authors

M. Kujawinska

Affiliations and Expertise

Warsaw, Poland