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.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


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.


    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2017 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+