Stochastic Time-Averaged Moiré Fringes

time

2

128

grating

Harmonic

Random

Stepped

This Demonstration illustrates the formation of time-averaged Moiré fringes. The horizontal axis represents the amplitude of harmonic oscillation

a

; the vertical axis, the longitudinal coordinate

x

. The stationary Moiré grating is shown at

a=0

. Time-averaged images of the Moiré grating are shown at increasing amplitudes of oscillation. The parameter

n

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

n=2

; time-averaged fringes are produced at

n∞

. 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

[0,1]

. Those patterns can reveal certain properties of the random number generator used to construct the stochastic Moiré grating.