A new print-based security strategy for the protection of valuable documents and products using moire intensity profiles

In response to the ever increasing need for new anticounterfeiting methods, a new integrated print-based authentication and security strategy is proposed for the protection of valuable documents and products, based on moire intensity profiles. This strategy combines the advantages of microstructure artistic screening for the halftoning of black-and-white or color images, the application of specially designed mathematical transformations on the microstructure, and the possibility of using non-standard color separation for printing the microstructured image with non-standard custom inks. Using our moire-based method, the overt (or covert) microstructured information from which the halftoned image is composed can be made clearly visible in the form of black-and-white of full-color moire intensity profiles with varying displacements, magnification rates and orientations, generating an attractive, dynamic visual effect which is very difficult to counterfei

Spin- and band-ferromagnetism in trilayer graphene

We study the ground state properties of an ABA-stacked trilayer graphene. The low energy band structure can be described by a combination of both a linear and a quadratic particle-hole symmetric dispersions, reminiscent of monolayer- and bilayer-graphene, respectively. The multi-band structure offers more channels for instability towards ferromagnetism when the Coulomb interaction is taken into account. Indeed, if one associates a pseudo-spin 1/2 degree of freedom to the bands (parabolic/linear), it is possible to realize also a band-ferromagnetic state, where there is a shift in the energy bands, since they fill up differently. By using a variational procedure, we compute the exchange energies for all possible variational ground states and identify the parameter space for the occurrence of spin- and band-ferromagnetic instabilities as a function of doping and interaction strength.Comment: 9 pages/ 8 figure

Moire patterns between aperiodic layers: quantitative analysis and synthesis

Moire effects that occur in the superposition of aperiodic layers such as random dot screens are known as Glass patterns. Unlike classical moiré effects between periodic layers, which are periodically repeated throughout the superposition, a Glass pattern is concentrated around a certain point in the superposition, and farther away from this point it fades out and disappears. I show that Glass patterns between aperiodic layers can be analyzed by using an extension of the Fourier-based theory that governs the classical moire patterns between periodic layers. Surprisingly, even spectral-domain considerations can be extended in a natural way to aperiodic cases, with some straightforward adaptations. These new results allow us to predict quantitatively the intensity profile of Glass patterns; furthermore, they open the way to the synthesis of Glass patterns that have any desired shapes and intensity profile

Glass patterns as moire effects: new surprising results

It is well known that the superposition of two identical random dot patterns may give rise to a particular form of moire effect known as a Glass pattern. Surprisingly, new research results show that if one chooses appropriate dot shapes for each of the two random dot patterns, while keeping the random dot locations in both layers identical, it is possible to synthesize in the superposition a Glass pattern having any desired shape and intensity profil

Unified approach for the explanation of stochastic and periodic moires

Moire phenomena of different types are frequently encountered in electronic imaging. Most common are moire effects that occur between periodic structures. These effects have been intensively investigated in the past, and their mathematical theory is today fully understood. The same is true for moire effects between repetitive layers (i.e., between geometric transformations of periodic layers). However, although moire effects that occur between random layers (Glass patterns) have long been recognized, only little is known today about their mathematical behavior. In this work we study the behavior of such moires, and compare it with analogous results from the periodic case. We show that all cases, periodic or not, obey the same basic mathematical rules, in spite of their different visual properties. This leads us to a unified approach that explains both the behavior of Glass patterns in the stochastic case, and the well-known behavior of the moire patterns in periodic or repetitive case

The Fourier-spectrum of circular sine and cosine gratings with arbitrary radial phases

The Fourier spectra of circular gratings having sine or cosine radial profiles are derived, and their particular properties are discussed. These results are then extended to the most general form of circular sinusoidal gratings, namely: circular sine or cosine gratings with any arbitrary radial phas

Fourier spectrum of curvilinear gratings of the second order

The class of second-order curvilinear gratings consists of all the curvilinear gratings that are obtained by second-order spatial transformations of periodic gratings. It includes, for example, circular, elliptic, and hyperbolic gratings as well as circular, elliptic, and hyperbolic zone plates. Such structures occur quite frequently in optics, and their Fourier transforms may arise, for instance, in connection with the Fraunhofer diffraction patterns generated by these structures. I present the two-dimensional Fourier spectra of the most important second-order curvilinear gratings for gratings having any desired intensity profile (cosinusoidal, sawtooth wave, square wave, etc.). These analytic results are also illustrated by figures showing the various gratings and their spectra as they are obtained on a computer by two-dimensional fast Fourier transfor

Fourier spectra of radially periodic images with a non-symmetric radial period

It has been previously shown that a radially periodic image having a symmetric radial period can be decomposed into a circular Fourier series of circular cosine functions with radial frequencies of f=1/T, 2/T, ..., and that its Fourier spectrum consists of a series of half-order derivative impulse rings with radii f=n/T (which are the Fourier transforms of the circular cosines in the sum). In the present paper these results are extended to the general case of radially periodic images, where the radial period does not necessarily have a symmetric profile. Such a general radially periodic function can be decomposed into a circular Fourier series which is a weighted sum of circular cosine and sine functions with radial frequencies of f=1/T, 2/T, .... In terms of the spectral domain, the Fourier spectrum of a general radially periodic function consists of half-order derivative impulse rings with radii f=n/T (which are the Fourier transforms of the weighted circular cosines and sines in the sum

Scattered data interpolation methods for electronic imaging systems: a survey

Numerous problems in electronic imaging systems involve the need to interpolate from irregularly spaced data. One example is the calibration of color input/output devices with respect to a common intermediate objective color space, such as XYZ or L*a*b*. In the present report we survey some of the most important methods of scattered data interpolation in two-dimensional and in three-dimensional spaces. We review both single-valued cases, where the underlying function has the form f:R2→R or f:R3→R, and multivalued cases, where the underlying function is f:R2→R2 or f:R3→R3. The main methods we review include linear triangular (or tetrahedral) interpolation, cubic triangular (Clough-Tocher) interpolation, triangle based blending interpolation, inverse distance weighted methods, radial basis function methods, and natural neighbor interpolation methods. We also review one method of scattered data fitting, as an illustration to the basic differences between scattered data interpolation and scattered data fittin

Shear-strain-induced Spatially Varying Super-lattice Structures on Graphite studied by STM

We report on the Scanning Tunneling Microscope (STM) observation of linear fringes together with spatially varying super-lattice structures on (0001) graphite (HOPG) surface. The structure, present in a region of a layer bounded by two straight carbon fibers, varies from a hexagonal lattice of 6nm periodicity to nearly a square lattice of 13nm periodicity. It then changes into a one-dimensional (1-D) fringe-like pattern before relaxing into a pattern-free region. We attribute this surface structure to a shear strain giving rise to a spatially varying rotation of the affected graphite layer relative to the bulk substrate. We propose a simple method to understand these moire patterns by looking at the fixed and rotated lattices in the Fourier transformed k-space. Using this approach we can reproduce the spatially varying 2-D lattice as well as the 1-D fringes by simulation. The 1-D fringes are found to result from a particular spatial dependence of the rotation angle.Comment: 14 pages, 6 figure