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Optical image processing using an optoelectronic feedback system with electronic distortion correction

Yoshio Hayasaki, Ei-ichiro Hikosaka, Hirotsugu Yamamoto, and Nobuo Nishida

Open Access Open Access

Abstract

Spontaneous pattern formation in an optoelectronic system with an optical diffractive feedback loop exhibits a contrast enhancement effect, a spatial filtering effect, and filling-up of vacant space while maintaining surrounding structures. These effects allow image processing with defect tolerance. Aberrations and slight misalignments that inevitably exist in optical systems distort the spatial structures of the formed patterns. Distortion also increases due to a small aspect ratio difference between a display device and an image sensor. We experimentally demonstrate that the spatial distortion of the optoelectronic feedback system is reduced by electronic distortion correction and the initial structure of a seed optical pattern is preserved for a long time. We also demonstrate image processing of a fingerprint pattern based on seeded spontaneous optical pattern formation with electronic distortion correction.

©2005 Optical Society of America

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Figures (8)
Fig. 1.
Fig. 1. Schematic representation of a model of an OEFS. CCD: charge-coupled device image sensor, LCD: liquid crystal display.

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Fig. 2.
Fig. 2. Experimental setup. See text the description.

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Fig. 3.
Fig. 3. Temporal evolution of (a) patterns whose operating center coincides with the optical axis of the system (on-axis region), and (b) patterns whose operating center is shifted from the optical axis (off-axis region) by 100 pixels in the x-axis and 100 pixels in the y-axis on the LCD. These patterns are observed at 1/30 s, 5/30 s, 10/30 s, 15/30 s, and 20/30 s from the left, respectively.

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Fig. 4.
Fig. 4. Temporal evolutions of patterns (a) in the on-axis region, and (b) in the off-axis region in the OEFS with electronic distortion correction.

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Fig. 5.
Fig. 5. Temporal changes of the SSDs between each temporally evolving pattern and the pattern at the 1st frame (a) in the on-axis region and (b) in the off-axis region in the OEFS with electronic distortion correction. The dotted and the solid lines indicate the SSDs of the pattern evolutions in the OEFS (a) without and (b) with the electronic distortion correction, respectively.

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Fig. 6.
Fig. 6. (a) An original fingerprint pattern A and (b) the same pattern A′ with an artificial defect.

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Fig. 7.
Fig. 7. Temporal evolutions at 1/30 s, 10/30 s, and 22/30 s when the fingerprint patterns without and with the artificial defect are initially supplied to the OEFS with the electronic distortion correction.

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Fig. 8.
Fig. 8. The bold dashed curve and the bold solid curve indicate the temporal changes of the SSDs between the temporal evolutions of the original fingerprint pattern and those of the fingerprint pattern with the artificial defect, when the OEFS was used without and with the electronic distortion correction, respectively. The thin dashed curve and the thin solid curve indicate the temporal changes of the SSDs between two trials starting from same initial pattern in the OEFS without and with the electronic distortion correction, respectively.

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Equations (13)

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τ ∂ u ( x , y , t ) ∂ t = − u ( x , y , t ) + l 2 ∇ ⊥ 2 u ( x , y , t ) + p ( x , y , t ) ,
I ( x , y , t ) = ∣ A ( x , y , t ) ∣ 2 = F [ u ( x , y , t ) ] .
p ( x , y , t ) = G [ I d ( x , y , Z , t ) ] ,
∇ ⊥ 2 A d ( x , y , Z , t ) − 2 ik ∂ A d ∂ z = 0 ,
x 1 = A 0 + A 1 x
y 1 = B 0 + B 1 y .
x 2 = x 1 cos Θ + y 1 sin Θ ,
y 2 = − x 1 sin Θ + y 1 cos Θ .
r = r 2 ( 1 + Cr 2 2 ) ,
u = r 2 cos θ 2 ,
v = r 2 sin θ 2 ,
I ( u , v ) = ( 1 − q ) { ( 1 − p ) I ( i , j ) + pI ( i + 1 , j ) } + q { ( 1 − p ) I ( i , j + 1 ) + pI ( i + 1 , j + 1 ) } ,
D ( t ) = ∑ i ∑ j { [ I 1 ( i , j , t ) − μ 1 ( t ) ] ⁄ σ 1 ( t ) − [ I 2 ( i , j , t ) − μ 2 ( t ) ] ⁄ σ 2 ( t ) } 2 ⁄ N ,
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