Stochastic Time-Averaged Moiré Fringes
This Demonstration illustrates the formation of time-averaged Moiré fringes. The horizontal axis represents the amplitude of harmonic oscillation ; the vertical axis, the longitudinal coordinate . The stationary Moiré grating is shown at . Time-averaged images of the Moiré grating are shown at increasing amplitudes of oscillation. The parameter controls the number of discrete time nodes in a period of the oscillation used to integrate the dynamical process. Double-exposure fringes are produced at ; time-averaged fringes are produced at . You can choose the type of the Moiré grating—it can be harmonic, stepped, or stochastic. Moreover, you can observe two digital images. The first is the time-averaged Moiré image and the second is the filtered image in which time-averaged fringes are shown in high contrast. Interesting time-averaged patterns can be observed whenever a regular Moiré grating is replaced by a set of random numbers uniformly distributed in the interval . Those patterns can reveal certain properties of the random number generator used to construct the stochastic Moiré grating.
Contributed by: Algiment Aleksa, Vilma Petrauskiene, and Minvydas Ragulskis (March 2011)
(Research Group for Mathematical and Numerical Analysis of Dynamical Systems)
Open content licensed under CC BY-NC-SA
Theoretical relationships governing the formation of time-averaged Moiré fringes are discussed in the references.
 M. Ragulskis, "Time-Averaged Patterns Produced by Stochastic Moiré Gratings," Computers and Graphics, 2009, 33(2), pp. 147–150.
 M. Ragulskis, L. Saunoriene, and R. Maskeliunas, "The Structure of Moiré Grating Lines and Influence to Time-Averaged Fringes," Experimental Techniques, 33(2), 2009 pp. 60–64.
 M. Ragulskis and Z. Navickas, "Time-Average Moiré—Back to the Basics," Experimental Mechanics, 49(8), 2009 pp. 439–450.
 M. Ragulskis, A. Aleksa, and R. Maskeliunas, "Contrast Enhancement of Time-Averaged Fringes Based on Moving Average Mapping Functions," Optics and Lasers in Engineering, 47(7-8), 2009 pp. 768–773.
 M. Ragulskis and A. Aleksa, "Image Hiding Based on Time-Averaging Moiré," Optics Communications, 282, 2009 pp. 2752–2759.
 M. Ragulskis, A. Aleksa, and Z. Navickas, "Image Hiding Based on Time-Averaged Fringes Produced by Non-Harmonic Oscillations," Journal of Optics A: Pure and Applied Optics, 11(12), 2009. doi:10.1088/1464-4258/11/12/125411.