## Abstract

A new type of diffusion pattern is proposed. The proposed patterns are composed
of 2D diffusion dots. The diffusion dots are created on a photoresist
plate by recording the image of a local area of a piece of ground glass dot by dot. An
imaging lens covered by a mask with a slit aperture is used to form the image. By
changing the orientation of the slit aperture on the mask plane, the diffusion dots can
have different microintensity distributions for the same incident light beam.
Therefore the diffusion dots created by the same slit aperture orientation show the
same brightness, and the diffusion dots created by different slit orientations show
different brightness for the same illuminating and viewing conditions. Thus a proposed
diffusion pattern can show dynamic images by changing its illuminating or viewing
directions. By applying the double-exposure technique to the diffusion dots of a
pattern, the pattern not only can show dynamic effects but also can possess several
hidden features for identifying the pattern. Therefore the proposed patterns are
dynamic and anticounterfeiting.

© 2007 Optical Society of America

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### Equations (7)

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(1)
$${U}_{3}\left({x}_{3},{y}_{3}\right)=h\left({x}_{3},{y}_{3}\right)\otimes {U}_{g}\left({x}_{3},{y}_{3}\right)\text{,}$$
(2)
$$h\left({x}_{3},{y}_{3}\right)={\displaystyle {\int}_{-\infty}^{\infty}{\displaystyle {\int}_{-\infty}^{\infty}P\left({x}_{2},{y}_{2}\right)\times \mathrm{exp}\left[-j2\pi \left({x}_{3}\tilde{x}+{y}_{3}\tilde{y}\right)\right]d\tilde{x}d\tilde{y}}}\text{,}$$
(3)
$${U}_{g}\left({x}_{3},{y}_{3}\right)=\frac{1}{M}\text{\hspace{0.17em}}{U}_{1}\left(-\frac{{x}_{3}}{M},\text{\u2212}\frac{{y}_{3}}{M}\right),$$
(4)
$${I}_{3}\left({x}_{3},{y}_{3}\right)={\left|{U}_{3}\left({x}_{3},{y}_{3}\right)\right|}^{2}.$$
(5)
$$t\left({x}_{3},{y}_{3}\right)=\mathrm{exp}\left\{j\left[{c}_{1}+{c}_{2}{I}_{3}\left({x}_{3},{y}_{3}\right)\right]\right\}\text{,}$$
(6)
$${\tilde{U}}_{t}\left(u,v;\text{\hspace{0.17em}}\xi ,\eta \right)={c}_{3}F{\left\{\mathrm{exp}\left[j{c}_{2}{I}_{3}\left({x}_{3},{y}_{3}\right)\right]\right\}}_{u\to u-\xi \text{,}v\to v-\eta}={\tilde{U}}_{t}\left(u-\xi ,v-\eta ;\text{\hspace{0.17em}}0,0\right),$$
(7)
$${\tilde{U}}_{t}\left(u,v;\text{\hspace{0.17em}}\xi ,\eta \right)={c}_{3}\delta \left(u-\xi ,v-\eta \right)+{c}_{4}\left\{\left[\tilde{H}\left(u-\xi ,v-\eta \right)\times {\tilde{U}}_{g}\left(u-\xi ,v-\eta \right)\right]\oplus \left[\tilde{H}\left(u-\xi ,v-\eta \right)\times {\tilde{U}}_{g}\left(u-\xi ,v-\eta \right)\right]\right\}\text{,}$$