Counterfeit Deterrent Features for the Next-Generation Currency Design(1993)

Chapter: Appendix D: Induced Moire Pattern Background

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Page 115
Suggested Citation:"Appendix D: Induced Moire Pattern Background." National Research Council. 1993. Counterfeit Deterrent Features for the Next-Generation Currency Design. Washington, DC: The National Academies Press. doi: 10.17226/2267.
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INDUCED MOIRE PATTERN BACKGROUND

Large-scale moiré patterns occur when two regularly repeating patterns with slightly different periods are superimposed. The spacing of the resulting moiré pattern is most striking when the frequencies are in the ratio of small integers.

A simple illustration of induced moiré can be seen using the concentric-circle pattern shown in Figure D-1. To observe an induced moiré pattern, place a pocket comb one to two inches above the concentric-circle pattern. In this example, the comb serves a sampling function which analogous to the sampling that occurs in digital imaging systems.

FIGURE D-1 Concentric-circle pattern.

Page 116
Suggested Citation:"Appendix D: Induced Moire Pattern Background." National Research Council. 1993. Counterfeit Deterrent Features for the Next-Generation Currency Design. Washington, DC: The National Academies Press. doi: 10.17226/2267.
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The mathematical formulation of the moiré phenomenon can be done in several ways. A Fourier series representation can be made of the object and the sampling function in frequency space. The presence of a sampling function leads to the generation of aliased frequencies, which, when reconstructed, represent the moiré pattern. The same calculation can be performed in the spatial domain using discrete sampling. If there exists a certain ratio relationship between the period of an object and the sampling function, then false data (moiré pattern) will be generated that are fixed in space and related to the sampling ratio.

Page 115
Suggested Citation:"Appendix D: Induced Moire Pattern Background." National Research Council. 1993. Counterfeit Deterrent Features for the Next-Generation Currency Design. Washington, DC: The National Academies Press. doi: 10.17226/2267.
×
Page 116
Suggested Citation:"Appendix D: Induced Moire Pattern Background." National Research Council. 1993. Counterfeit Deterrent Features for the Next-Generation Currency Design. Washington, DC: The National Academies Press. doi: 10.17226/2267.
×
Next: Appendix E: Methods for Authentication of Unique Random Patterns »
Counterfeit Deterrent Features for the Next-Generation Currency Design Get This Book
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Traditionally, counterfeit deterrent features restricted counterfeiting to only the dedicated craftsman. With the advent of highly sophisticated reprographic systems, this is no longer true. Redesign of U.S. banknotes is necessary in order to incorporate additional features aimed at discouraging counterfeiting using advanced copiers-scanners-printers. This volume evaluates a large number of such features while recommending a comprehensive national strategy for anticipating and responding to counterfeiting threats.

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