COL 11(2), 021104(2013) CHINESE OPTICS LETTERS February 10, 2013
Colored object encoding scheme in ghost imaging system
using orbital angular momentum
Yongqiang Li (
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), Hua Yang (
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), Jiao Liu (
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), Longyan Gong (
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Yubo Sheng (
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), Weiwen Cheng (
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), and Shengmei Zhao (
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∗
Institute of Signal Processing and Transmission, Nanjing University of Posts and Telecommunications,
Nanjing 210003, China
∗
Corresponding author: zhaosm@njupt.edu.cn
Received June 18, 2012; accepted August 13, 2012; posted online January 21, 2013
A colored object encoding scheme in a ghost imaging (GI) system using orbital angular momentum is in-
vestigated. A colored object is decomposed into three components and then each component is obtained in
the idler arm using a multiple grayscale encoding scheme. Afterward, we synthesize the three reconstructed
components into a colored image. The scheme is conducted and then presented through numerical simula-
tions and experiments. The simulation result shows that the average peak signal-to-noise ratio (PSNR) is
at 21.636 for the reconstructed color of the “Lena” image with 255 gray scales. The experiment also shows
that the PSNR is 8.082 for the reconstructed color of the “NUPT” characters. The successful imaging of
colored objects extends the further use of the GI technique.
OCIS codes: 110.1650, 070.6120, 270.0270.
doi: 10.3788/COL201311.021104.
Ghost imaging (GI), also known as c oincidence imaging,
is a novel imaging technique that has become increas-
ingly popular over the last decade
[1−4]
. In this system,
photons are spatially separated and propagated along a
distinct optical path. The path including object is usu-
ally called the “signal arm,” and the other one is named
the “idler ar m.” The intensity correlation between the
signal beam, which encounters the target, and the idler
beam, which impinges on the hig h spatial reso lution de-
tector, imparts the information of the target into the idler
arm. This phenomenon is named GI. The GI technique
offers great potential with regard to standard imaging.
The technique allows the imaging of objects that are lo-
cated in optically harsh or noisy environment, such as in
military, astronomical, and medical X-ray imaging fields.
Recently, the GI technique has been re ported to be ap-
plicable in wireless communication technologies
[5]
.
The GI technique was first demonstrated by utilizing
a biphoton source to entangle s ource photons
[6]
. Sub-
sequently, theoretical
[7,8]
and exp erimental
[9−11]
works
demonstrated that GI can be per fo rmed using pseudo -
thermal light or true thermal light
[12,13]
. Other studies
regarding GI include co mputational GI
[14,15]
, compres-
sive GI
[16]
, differential GI
[12,17]
, and reflective GI
[18,19]
.
Recently, Jack et al. implemented holographic GI (HGI)
using orbital angular momentum (OAM), whereby the
contrast of the edge imaging is enhanced
[20]
. The OAM
state with one photon carries mor e than one bit of infor-
mation compared with the polarization state encoded in
the polarization degr e e s of freedo m. A multiple grayscale
encoding scheme with OAM was prop osed according
to the strong time and spatial correlation of entangled
photons
[20−22]
. In this scheme, different grayscales are
represented by differ e nt phase matrixes. This develop-
ment has led to the possibility of presenting GI for col-
ored objects. Compared with grayscale objects, colored
objects have more information and provide better data
for object recognition. In this letter, we investigate a GI
scheme for colored objects using OAM.
In holographic GI systems, the mode of the pump, sig-
nal, and idler can be described by nor malized transverse
mode functions: Φ
(~x
i
)
(i=s, i, p), where ~x is a vector in
the plane p e rpe ndicula r to the propagation direction of
light, and subscripts p, s, and i denote the pump, sig-
nal, and idler beam, respectively. The two-photon wave
function of the signal and idler generated by spontaneous
parametric down-conversion (SPDC)
[23,24]
is expressed as
|ψi =
Z
d
~
k
p
Z
d
~
k
s
Z
d
~
k
i
Φ
p
(
~
k
p
)
⌢
a
+
i
(
~
k
i
)
⌢
a
+
s
(
~
k
s
)
× ∆(
~
k
s
−
~
k
i
)δ
(2)
(
~
k
p
−
~
k
s
−
~
k
i
) |0i, (1)
where
⌢
a
+
is the creation operator, |0 i is the initial vac-
uum state, k is the transverse component of the mode
function wave vector, Φ
p
(k) is the Fourier transformation
of the transverse function, δ
(2)
is the two-dimensional
(2D) delta function, and ∆(·) is the pure geometrical
function. Through Four ie r trans fo rmation, Eq. (1) is
written as
|ψi =
Z
d~x
s
Z
d~x
i
Φ
p
~x
s
+ ~x
i
2
· ∆(~x
s
−~x
i
)
⌢
a
+
s
(~x
s
)a
+
i
(~x
i
) |0i. (2)
The coincidence probability of photons both in the signal
mode Φ
s
and the idler mode Φ
i
is then expressed by
P (Φ
s
, Φ
i
) = [hψ
i
, ψ
s
|ψi]
2
=
h
Z
d~x
s
Z
d~x
i
Φ
∗
s
(~x
s
)Φ
∗
i
(~x
i
)
· Φ
~x
s
+ ~x
i
2
∆(~x
s
−~x
i
)
i
2
. (3)
For normalized Laguerre-Gaussian modes, the transverse
1671-7694/2013/021104(4) 021104-1
c
2013 Chinese Optics Letters