COL 9(8), 081102(2011) CHINESE OPTICS LETTERS August 10, 2011
Performance of third-order ghost imaging with
second-order intensity correlation
Bin Cao (
ùùù QQQ
)
∗
, Chunxi Zhang (
ÜÜÜ
SSS
), and Pan Ou (
îîî
)
School of Instrumentation Science and Opto-Electronics Engineering, Beihang University, Beijing 100191, China
∗
Corresponding author: cao bb@hotmail.com
Received November 16, 2010; accepted March 15, 2011; posted online May 31, 2011
The third-order ghost imaging with the second-order intensity correlation is theoretically and experi-
mentally demonstrated. The resolution and visibility of the reconstructed image are discussed, and the
relationship between resolution and visibility is analyzed. The theoretical results show t hat a tradeoff
exists between the visibility and resolution of the reconstructed image; the better the image resolution, the
worse the image visibility. N umerical simulations are carried out to verify this theory, and a ghost imaging
experiment is conducted to validate our calculations. The experimental results agree with the theoretical
predictions.
OCIS codes: 100.4994, 110.2960.
doi: 10.3788/COL201109.081102.
Correlated imaging, also known as “intensity correla -
tion”, was first introduced by Hanbury Brown et al. in
1956
[1]
. The principle of correlated optical imaging is
based on classical and quantum coherent theory
[2]
. Ghost
imaging and ghost diffraction are typical practical appli-
cations of optical intensity correlatio n
[3−19]
.
Ghost imaging, proposed in 1995
[6]
, is a novel imag-
ing method that indirec tly retrieves information about
an unknown object. In the principal setup of the second-
order ghost imaging, the seminal light beam is split into
two separated daughter beams that are spatially corre-
lated. Each of the correlated beams passes through a
different imaging system. O ne beam path, usually called
the “test arm”, is sent through an unknown object and
detected by a bucket detector that co llec ts all the in-
coming light. Meanwhile, the other one that travels in a
sp e cific path called the “reference arm”, is detected by
a scanning point-like detector on the transverse plane.
The object can be reco nstructed from the spatial cross-
correla tio n between the intensity fluctuations of the two
detectors. The correlogram indicates the object image.
The bottleneck of the second-order ghost imaging in
which a fully incoherent light source is use d lies in low
visibility, which never exceeds 33.3%
[16]
. Visibility can be
enhanced w ith a high-order intensity corr e lation
[16−18]
.
In the principal setup of the high-order ghost imaging,
the light source is split into several separa ted light paths
and detected by N detectors
[15]
. Cao et al.
[17]
proposed
that a high-order intensity correlation can be imple-
mented by two detectors, i.e., one intensity is comp osed
of an n-fold inte nsity product and the other intensity is
an (N − n)-fold product.
In this letter, the third-order ghost imaging is realized
using two detectors with a fully incoherent light source .
The resolution and visibility of the obtained image are in-
fluenced by the optical transverse coherent length at the
object. A comparison o f the second-order and third-order
ghost imaging shows that b oth yield the same resolution;
however, the visibility in the third-order ghost imaging is
higher than that in the second-order ghost imaging when
their optical transverse coherent lengths a re e qual. In
addition, a tradeoff be tween the resolution and visibility
of the third-order ghos t imaging continues to ex ist, sim-
ilar to that observed in the second-order ghost imaging.
To validate our theoretical analysis, a novel ghost imag-
ing experimental configuration is proposed and investi-
gated. With the propose d ghost imaging experimental
setup, any arbitrary-order ghost imaging can be re alized,
and its resolution and visibility can be adjusted conve-
niently.
To exploit the properties of the third-order ghost ima g-
ing performed with the second-order intensity correla-
tion, the setup depicted in Fig. 1 is considered. The
imaging system uses a fully inco herent light as light
source. The incoherent light beam is split into two spa-
tially correlated daughter light beams by a beam split-
ter. The two daughter light beams propa gate in the test
arm and reference arm, as previously mentioned. An
unknown object is placed in the test arm and a bucket
detector is located immediately after the object, so that
all the light passing through the object is collected. The
other daughter beam, which travels through the refer-
ence a rm, is detected by a scanning point-like detector.
Both the bucket detector a nd the point-like detector are
located in the optical far field of the light source. Then,
the optical intensity correlation is measured using an in-
tensity correlation calcula tio n system. The two detector s
are spatially resolved; hence, the second-order intensity
correla tio n function is registered as a function of the po-
sition of the two detectors. By scanning the point-like
detector, the image of the object can be reconstr ucted.
A detailed theoretical analysis of the third-order ghost
imaging is necessary. For simplicity, only a one-
dimensional case is considered in the following analysis.
According to Ref. [15] and the experimental configu-
ration shown in Fig. 1, the third-order ghost imaging
function can be expressed as
g
(3)
(x
1
, x
2
) = 2 +
4
l
o
Z
x
2
|t(x
2
)|
2
sin c
2
h
π(x
1
− x
2
)
l
c
i
dx
2
,
(1)
where l
o
is the transversal transmission light size of
the imaged object; l
c
is the optical transverse c oherent
length on the detection plane defined as l
c
= λz/l
s
[19]
,
with l
s
as the transverse size of the light source; z is
1671-7694/2011/081102(4) 081102-1
c
2011 Chinese Optics Letters