Stochastic Time-Averaged Moiré Fringes

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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.


[1] M. Ragulskis, "Time-Averaged Patterns Produced by Stochastic Moiré Gratings," Computers and Graphics, 2009, 33(2), pp. 147–150.

[2] 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.

[3] M. Ragulskis and Z. Navickas, "Time-Average Moiré—Back to the Basics," Experimental Mechanics, 49(8), 2009 pp. 439–450.

[4] 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.

[5] M. Ragulskis and A. Aleksa, "Image Hiding Based on Time-Averaging Moiré," Optics Communications, 282, 2009 pp. 2752–2759.

[6] 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.

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