Properties of dynamic image displacements based on microstructure

Peng Huang; Chuanwang He; Bin Fan; Xiaochun Dong

doi:10.1364/AO.57.008187

Applied Optics
Vol. 57,
Issue 28,
pp. 8187-8192
(2018)
•https://doi.org/10.1364/AO.57.008187

Properties of dynamic image displacements based on microstructure

Peng Huang, Chuanwang He, Bin Fan, and Xiaochun Dong

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Peng Huang, Chuanwang He, Bin Fan, and Xiaochun Dong, "Properties of dynamic image displacements based on microstructure," Appl. Opt. 57, 8187-8192 (2018)

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Abstract

The superposition structure of dynamic moiré images contains a layer of micropattern array and a corresponding layer of microlens array. Dynamic moiré images can be observed without special eyeglasses and will shift with variation of the viewing angle. In this work, it is described as a presentation of a variety of the moiré. We chiefly investigate the motion effects of dynamic moiré images. Analytical models to describe the structures and methods to evaluate the displacement of dynamic moiré images are proposed. Experiments are conducted to validate the formula of the displacement. The results of this study are helpful to design dynamic moiré images, which can be applied for potential applications in anti-counterfeiting films, packaging, and authentication.

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Symbol	Definition	Symbol	Definition
$D$	Pitch of MLA	$h$	Thickness of PET substrate
$d$	Pitch of MPA	$f$	Focal length of MLA
$T$	Period of dynamic moiré images	$t$	Sag height of MLA
$L$	Displacement of dynamic moiré images	$n_{1}$	Refractive index of PET film
$θ$	Angle between MLA and MPA	$n_{2}$	Refractive index of UV MLA
$γ$	Angle between the dynamic moiré image and MLA	$n_{0}$	Refractive index of air
$φ$	Viewing angle	$r$	Radius of lens surface

Order	Pitch of MLA $D$ (μm)		Pitch of Dot Array $d_{1}$ (μm)		Pitch of “A” Array $d_{2}$ (μm)
Order	$D_{x}$	$D_{y}$	$d_{1 x}$	$d_{1 y}$	$d_{2 x}$	$d_{2 y}$
1	50	50	50.1	50.5	50.5	50.5
2	50	50	50.3	50.5	50.5	50.5
3			50.5

Viewing Angle		10°	20°	30°
$d = 50.1 μm$	Measured result (cm)	0.90	1.80	2.50
$d = 50.1 μm$	Calculated result (cm)	0.88	1.78	2.75
$d = 50.3 μm$	Measured result (cm)	0.25	0.55	0.90
$d = 50.3 μm$	Calculated result (cm)	0.29	0.59	0.92
$d = 50.5 μm$	Measured result (cm)	0.20	0.40	0.60
$d = 50.5 μm$	Calculated result (cm)	0.18	0.36	0.55

Symbol	Definition	Symbol	Definition
$D$	Pitch of MLA	$h$	Thickness of PET substrate
$d$	Pitch of MPA	$f$	Focal length of MLA
$T$	Period of dynamic moiré images	$t$	Sag height of MLA
$L$	Displacement of dynamic moiré images	$n_{1}$	Refractive index of PET film
$θ$	Angle between MLA and MPA	$n_{2}$	Refractive index of UV MLA
$γ$	Angle between the dynamic moiré image and MLA	$n_{0}$	Refractive index of air
$φ$	Viewing angle	$r$	Radius of lens surface

Order	Pitch of MLA $D$ (μm)		Pitch of Dot Array $d_{1}$ (μm)		Pitch of “A” Array $d_{2}$ (μm)
Order	$D_{x}$	$D_{y}$	$d_{1 x}$	$d_{1 y}$	$d_{2 x}$	$d_{2 y}$
1	50	50	50.1	50.5	50.5	50.5
2	50	50	50.3	50.5	50.5	50.5
3			50.5

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Applied Optics