Lensless imaging based on coherent backscattering in random media

Lensless imaging based on coherent backscattering in random media
Lei Xu, Hao Yang, Peilong Hong, Fang Bo, Jingjun Xu, and Guoquan Zhang
Citation: AIP Advances 4, 087124 (2014); doi: 10.1063/1.4893471
View online: http://dx.doi.org/10.1063/1.4893471
View Table of Contents: http://scitation.aip.org/content/aip/journal/adva/4/8?ver=pdfcov
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AIP ADVANCES 4, 087124 (2014)
Lensless imaging based on coherent backscattering
in random media
Lei Xu, Hao Yang, Peilong Hong, Fang Bo, Jingjun Xu,
and Guoquan Zhanga
The MOE Key Laboratory of Weak Light Nonlinear Photonics, School of Physics and TEDA
Applied Physics Institute, Nankai University, Tianjin 300457, China
(Received 10 May 2014; accepted 7 August 2014; published online 15 August 2014)
We studied lensless imaging due to coherent backscattering in random media both
theoretically and experimentally. The point spread function of the lensless imaging
system was derived. Parameters such as the volume fraction of the scatterer in the
random scattering medium, the diameter of the scatterer, the distance between the
object to be imaged and the surface of the random scattering medium were optimized
to improve the image contrast and resolution. Moreover, for complicated objects,
high contrast and quality images were achieved through the high-order intensity correlation measurement on the image plane, which may propel this imaging technique
C 2014 Author(s). All article content, except where otherto practical applications. wise noted, is licensed under a Creative Commons Attribution 3.0 Unported License.
[http://dx.doi.org/10.1063/1.4893471]
I. INTRODUCTION
The phenomena and effects of light propagation in disordered media, such as coherent
backscattering1–3 and Anderson localization,4, 5 have been studied intensively.6–10 In recent years,
random scattering, which is always thought as noise and fundamental limit for an optical system in
the past,11–13 has been used for image formation.14–16 Furthermore, researchers found the random
scattering useful to overcome the diffraction limit and perform wide-area imaging.17, 18 By calculating the transmission matrix, Gigan et al. have achieved a rapid and accurate reconstruction of an
arbitrary image after transmitting through a complex medium.19 Lensless imaging has been demonstrated based on the coherent backscattering from random scattering media without the requirement
to know the inner properties of multiple scattering of light within such random media.14, 15 However,
for complicated objects, low image contrast makes this imaging technique almost impossible to be
put into practice (the image contrast is defined as γ = Iim /Ibg , where Iim and Ibg are the intensities
related to the image and background in the image plane, respectively). Therefore, efficient and
effective methods to improve the image contrast are urgently needed in practice.
In this paper, we carried out a detailed study on this lensless imaging due to coherent backscattering in random media. The point spread function (PSF) of the lensless imaging system was derived
theoretically. The image resolution and contrast were optimized by adjusting the parameters of
the random media and the imaging system. Finally, we demonstrated that the image quality can
be improved significantly by measuring the high-order intensity correlation function in the image
plane.
II. THEORETICAL ANALYSIS
When a light source illuminates a random scattering medium, the light waves scattered multiply
by the medium will form the image of the light source at the equivalent backward source position
a Electronic mail: [email protected]
2158-3226/2014/4(8)/087124/11
4, 087124-1
C Author(s) 2014
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FIG. 1. Geometry used for the calculation of PSF, showing two interfering light paths p1 and p2 . S is the point source. The
light is incident on the random scattering medium, and the backscattered light Si at different position is recorded.
due to coherent backscattering, as depicted in Fig. 1. In the simplest case with a point source S,
the fundamental features of the lensless imaging system are characterized by the PSF, which is
the intensity distribution in the image plane formed by the coherent backscattering from the semiinfinite random scattering medium. Therefore, the instantaneous PSF can be defined as the ratio
of the time-dependent emergent energy in the image plane to the incident energy flux of the point
source. According to Refs. 7 and 11, let’s first consider the dynamic case in which an energy pulse
from the point source impinges on a random scattering medium with random motion particles, the
associated PSF of the lensless imaging based on coherent backscattering from a semi-infinite random
scattering medium can be written as
c
r1 , rn ; t)
dz 1 dz n d 2r1 d 2 ρ P(
PSF(s , si ; t) = 2 2
l d r1
z
1 − μ(sz,1r )l − μ(szn,r )l
− 1 − zn i n
1
e
+ e μ(si ,r1 )l μ(s ,rn )l
×
2
z
z
1
−1
+ zn + 1 + zn
+e 2 μ(s ,r1 )l μ(si ,rn )l μ(si ,r1 )l μ(s,rn )l cos (s , si ; r1 , rn ) ,
(1)
where P(
r1 , rn ; t) is the Green’s function which describes the light transport from a pulse located at
r1 at time t0 = 0 to rn at time t. For a large number of random scatterers, it is well approximated by
the solution of a time-dependent diffusion equation,6, 7 and can be expressed approximately in the
2
−(z−z )2 /4D t
2
e−ρ /4Dd t
n
d
e
−e−(z+zn +2z0 ) /4Dd t . l is the elastic mean free path of the
form P(
r1 , rn ; t) = (4π
Dd t)3/2
random scattering medium, c is the light speed in vacuum, z0 = 2/3l, Dd is the diffusion constant,
r1 and rn are the positions of the first and the last nth scatterers in the random scattering medium,
ρ = (
r1 − rn )⊥ is the projection of r1 − rn on the interface plane, d 2 r1 and d 2 ρ depict the energy
integration over the incident and emergent surfaces, respectively. μ(si , r1,n ) are the projections of
→ −
→ −
→ −→ −→ −→ −→
−
→/|−
sr
1 sr 1 |, sr n /|sr n |, si r 1 /|si r 1 |, si r n /|si r n | on the z-axis, respectively. d is the distance between the
point source and the surface of the random scattering medium, r is the displacement of si from s,
(s , si ; r1 , rn ) is the net phase difference between two counterpropagating paths p1 and p2 , as shown
r1 ) and
in Fig. 1. In the case when r d, one can take the approximation μ(s , r1 ) = μ(si , r1 ) = μ(
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μ(s , rn ) = μ(si , rn ) = μ(
rn ). Thus, Eq. (1) is reduced as
c
PSF(s , si ; t) = 2
r1 , rn ; t)
dz 1 dz n d 2r1 d 2 ρ P(
l d 2r1
z
− 1 − zn ×e μ(r1 )l μ(rn )l 1 + cos (s , si ; r1 , rn ) .
(2)
According to Refs. 6, 7, and 11, the stationary PSF can be obtained by integrating Eq. (2) over
time, which, in fact, can be done by integrating P(
r1 , rn ; t) over time, and one gets
P(
r1 , rn , ρ)
=
P(
r1 , rn ; t)dt
1
=
4π Dd
1
1
−
|ρ|
2 + (z − z n )2
|ρ|
2 + (z + z n + 2z 0 )2
So the stationary PSF can be written as
PSF(s , si ) =
l2
×e
c
d 2r1
.
(3)
z
r1 , rn , ρ)
dz 1 dz n d 2r1 d 2 ρ P(
− μ(r1 )l − μ(zrnn )l
1
1 + cos (s , si ; r1 , rn ) ,
(4)
where μ(
r1 ) = cos θ1 and μ(
rn ) = cos θn . Such a stationary PSF can be experimentally evaluated
with a continuous wave incident light, just as the cases in Refs. 6 and 7.
The expression of stationary PSF can be further simplified when one considers the condition in
Ref. 6, where r1 and rn are located on the same plane at z = l. In this case, the PSF can be simplified
as
1
1
− 1
2
2
−
PSF(s , si ) = A d r1 d ρ
e cos θ1
2
2
|ρ|
|ρ|
+a
1
×e− cos θn 1 + cos (s , si ; r1 , rn ) ,
(5)
→+−
where A is a constant, a = 2(l + z0 ), and the net phase difference (s , si ; r1 , rn ) = 2π
[(−
sr
si→
rn ) −
1
λ
−
→
−
→
(srn + si r1 )]. Considering the on-axis condition (when r is far away from the axis, P → 0), and r d, the net phase difference can be written as
2π
rs − rsi )
(
r1 − rn ) · (
λd
2π
ρ · r ,
=
λd
(s , si ; r1 , rn ) =
(6)
and
d
cos θn = ,
d 2 + (d tan θ1 )2 + |ρ|
2 − 2d|ρ|
tan θ1 cos φ
→. Therefore, the stationary PSF can be written as
where φ is the angle between ρ and −
ss
i
1
1
− 1
2
2
−
PSF(s , si ) = A d r1 d ρ
e cos θ1
|ρ|
|ρ|
2 + a2
2π
− cos1θn
1 + cos
×e
ρ · r
.
λd
(7)
(8)
According to Eq. (8), a theoretical image profile of a point source at the equivalent backward
source position is shown in Fig. 2, showing the one-to-one correspondence between the point
source and its image. Suppose that there is an arbitrary object with
a transmission profile T (s ),
the intensity distribution in the image plane will be proportional to T (s )ds + (PSFnorm − 1)T (s ),
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FIG. 2. The theoretical image profile PSF (normalized to the background) of a point source calculated according to Eq. (8).
The wavelength of the incident light is set to be 532 nm, d = 23 cm, and l = 35.4 μm, respectively.
where T (s )ds represents the total background on the image plane and PSFnorm is the PSF of a
single point source normalized to its background as shown in Fig. 2. It is evident that the image
contrast will be extremely low and the image may even be indiscernible for a complicated object,
which should be overcome in practical application.
III. EXPERIMENTAL RESULTS AND DISCUSSIONS
In this section, we will give an experimental demonstration of the above theoretical analysis
about this lensless imaging technique. Then we will optimize the material parameters of the random
medium to optimize the image quality and contrast. Finally, we demonstrate a significant improvement on the image contrast by performing the high-order intensity correlation measurement at the
image plane.
A. Experimental scheme
Figure 3 shows the schematic diagram of the lensless image system based on the coherent
backscattering in a random medium. A 532-nm laser beam was focused by a lens with a focal length
of 6 cm onto a 10-μm pinhole template to mimic a 10-μm-diameter point source. The total power of
the light emerging from the object was set to be 100 mW in the following. Then the diverging light
passed through a 50:50 beam splitter and impinged on a random scattering medium, which was the
suspension of polystyrene spheres dispersed in deionized water in our experiments. The backward
scatterings from the random scattering medium were reflected by the beam splitter. A charge coupled
device (CCD) camera was placed at the equivalent backward source position to record the intensity
distribution of the backscattered light there. The exposure time of CCD was set to be 0.04 ms for each
image frame, which is much less than the characteristic time of 1 ms associated with the Brownian
motion of the scatters (polystyrene spheres).7 Considering the de-polarization effect of the multiple
scattering of light,1, 2, 6 a polarization analyzer (P) was placed just before the CCD camera so that
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FIG. 3. Experimental configuration for the observation of lensless imaging due to coherent backscattering in a random
medium. Here S stands for the object to be imaged, Si is the image, BS is beam splitter, P is the polarization analyzer,
respectively.
only the light scattering with its polarization parallel to that of the incident light was allowed to pass
through. In this way, one can get a higher image contrast. This is because the enhancement factor
is larger for the scattered light polarized parallel to the incident light than that polarized vertically
to the incident light, which may be due to the angular dependence of the light scattered from each
individual scatterer in the random scattering medium.1, 2, 6 The distance d between the object (point
source) and the surface of the random scattering medium was set to be 23 cm unless stated elsewhere.
In order to suppress the fluctuations due to random interference of light among multiply scattered
paths, the image profile, under the condition of ergodicity,7, 20 could be ensemble-averaged over
100,000 frames in the following.1–3
B. Characterization and optimization
A typical image of a point-source object, obtained through suspension of polystyrene spheres
with a 1.0-μm diameter and a volume fraction ϕ being 5 vol.%, is shown in Fig. 4(a). The thickness
of the random medium sample was 16 mm. The red curve in Fig. 4(b) is a theoretical fit to the
measured experimental data (the solid squares) according to Eq. (8). The elastic mean free path l
was measured to be 35.4 μm by the coherent backscattering experiment.21 Quantitative agreement
is achieved between the theoretical prediction and the experimental data, with the exception that the
measured enhancement factor is less than 2. This is due to several factors such as a non-ideal point
source, a finite sample cell size (which eliminates the possibility of long scattering paths), and the
presence of closed loop scattering paths.20, 21
The resolution and quality of the image depends on several factors, such as the volume fraction
of the scatterer ϕ, the diameter of the scatterer D, and the distance d. When the scatterer diameter
D is fixed, low volume fraction ϕ (corresponding to a low number content) reduces the possibility
of multiple scattering paths, and therefore resulting in a small enhancement factor. On the other
hand, when the volume fraction is too large (corresponding to a large number content), the recurrent
scattering leads to a reduction of the enhancement factor and an increase in the full width at halfmaximum (FWHM) of the PSF,22 which lead to a decreasing image resolution. The scattering
strength increases with increasing diameter D in general, meanwhile, the number content decreases
for a fixed volume fraction ϕ, thus reducing the possible paths of the multiple scattering of light
which forms the image at the equivalent backward source position. Therefore, one has to optimize
the scatterer diameter D to balance these two effects to improve the image contrast. Also, the FWHM
increases with increasing volume fraction of polystyrene spheres, which will result in a reduction in
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(a)
(b)
FIG. 4. The image of a one-point source at the equivalent backward source position. (a) is the 2-dimensional image and (b)
is the image profile across the image center. The solid squares in (b) are the measured data, while the red solid curve is a
theoretical fit to the experimental data according to Eq. (8).
FIG. 5. The normalized image profiles of a point-source object for suspensions of 1.0 μm-diameter polystyrene spheres with
ϕ being 2 vol.% (dark solid curve), 5 vol.% (red dashed curve), and 8 vol.% (blue dotted curve), respectively.
the image resolution. The corresponding experimental results are shown in Figs. 5 and 6. Here, Fig. 5
gives the image profiles of a point source with three different volume fraction of polystyrene spheres
of 1.0 μm-diameter, and Fig. 6 gives the dependence of the enhancement factor on the scatterer’s
diameter D with various volume fraction ϕ, respectively. One sees that the image contrast is relatively
high when the diameter of spheres ranging from 0.5 μm to 1.2 μm in general. Referring to these
results, in order to get better image resolution and quality, we chose a suspension of polystyrene
spheres with a sphere diameter of 1.0 μm and a volume fraction of 5 vol.% as the random scattering
medium in the following experiments. One should note that the above optimized conditions are valid
only for the suspension of polystyrene spheres used in our experiments because different scatterers
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FIG. 6. The dependence of the enhancement factor on the scatterer diameter D for suspensions of polystyrene spheres with
ϕ being 2 vol.% (black solid squares), 5 vol.% (red solid circles), and 8 vol.% (blue solid triangles), respectively. The lines
are guided by eyes.
or particles will have different scattering properties, nevertheless, the optimization procedure to get
the best performance is similar.
Figure 7 shows the image profiles of PSF at different distances d, which are not sensitive to
the distance d. This indicates that one can get images with unit magnification within a large range
of distance d. The slight decrease in the enhancement factor for large d may be due to the fact
that less light (emerging from the point source) is injected into the random scattering medium to
participate in the coherent backscattering effect with increasing d because of the finite sample size
in the experiment.
C. Image contrast improved by the high-order intensity correlation
As we have mentioned above, the image contrast for a complicated object will be extremely low
and even indiscernible because of the relatively high background, this puts a serious limitation on this
novel technique for practical applications. Here we employed the high-order intensity correlation
measurement on the equivalent backward source plane to improve the image contrast. Our results
show that this lensless imaging based on coherent backscattering with high-order intensity correlation
method is linear and the image contrast can be significantly improved for a complicated object, which
may propel this novel technique for potential image applications.
The Nth-order spatial intensity correlation function is defined as23–25
G (N ) (r1 , . . . , r N ) = I1 (r1 ) . . . I N (r N ) ,
(9)
where Ij (rj ) gives the intensity at position rj , and . . . stands for an ensemble average. In our case,
we consider the intensity correlation function under the condition r1 = r2 = . . . = rj = r, which is
also called as the Nth-order moment of intensity, and it can be written as
G (N ) (r ) = I (r ) N .
(10)
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FIG. 7. The normalized image profiles of a point-source object with distance d being 23 cm (black solid curve), 33 cm (red
dotted curve), 43 cm (blue dash-dotted curve), and 53 cm (pink dashed curve), respectively. A suspension of polystyrene
spheres with a sphere diameter of 1.0 μm and a volume fraction of 5 vol.% was used in the experiment.
As alreadyshown in Sec. II, the image of an arbitrary object with
a transmission profile T (s ) is
proportional to T (s )ds + (PSFnorm − 1)T (s ), where the first term T (s )ds corresponds to the total
background Ibg and the second term (PSFnorm − 1)T (s ) depicts the useful net image information
Iim − Ibg on the image plane. Here Iim depicts the averaged intensity distribution at the image
position, and Ibg is the averaged background intensity far away from the image position in the
image plane. The image contrast becomes
γN =
=
(N )
G im
)
G (N
bg
N
Iim
N
Ibg = 1+
N
N
− Ibg
Iim
N
Ibg
.
(11)
For complicated objects, the image will be submerged in the background noise in the image plane,
and the intensity difference between the image and the background is very small and both the
image and background beams experience the same statistically random scattering process so that the
corresponding normalized Nth-order intensity correlation functions in the image plane are the same,
namely
N
N
Ibg
Iim
=
= g,
N
Iim Ibg N
(12)
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FIG. 8. The normalized image profile of a three-point-source object (point1, point2, and point3 with an input intensity ratio
of 8 : 2 : 1).
which is also confirmed experimentally. By substituting Eq. (12) into Eq. (11), γ N can be further
written as
γN = 1 +
=
=
≈
=
N
N
− Ibg
Iim
N
Ibg
g Iim N − Ibg N
1+
gIbg N
Iim − Ibg N
1
N
N
1+
− Ibg Ibg 1 +
Ibg N
Ibg Iim − Ibg 1
N
N
Ibg 1 + N
− Ibg 1+
Ibg N
Ibg Iim − Ibg .
1+ N
Ibg (13)
It is seen from Eq. (13) that, by performing the Nth-order intensity correlation measurement, one
expects to amplify the intensity difference between the image and the background by N times.
Therefore, the image contrast γ N can be improved dramatically. Eq. (13) also shows that the net
image strength Iim − Ibg increases linearly with the increase of the correlation order N, which
clearly indicates that the imaging system is linear. One should also note that the imaging system is
nonlinear when the net image term is comparable to the background term.
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(a)
(b)
FIG. 9. (a) The 4th-order intensity correlation function of the image shown in Fig. 8, and (b) the net image strength of three
points as a function of the correlation order N. Note that the net image strength of point2 and point3 are multipled by a factor
of 10 in (b).
(a)
(b)
FIG. 10. Images of an object ‘2’. (a) is the normalized image profile, and (b) is the image formed by performing the 8th-order
intensity correlation measurement on the image plane, respectively.
In the following, we will measure the intensity correlation function G(N) for the images of two
objects: a three-point-source object and a number ‘2’ object. Note that, although we employed a
coherent laser to illuminate the object, the spatial coherence between different points of the object
will be totally washed out on the image plane because of the multiple scattering in the random
scattering media, which can be easily confirmed experimentally.
Figure 8 shows the normalized image profiles of the three point sources (point1, point2 and
point3) with an input intensity ratio of 8 : 2 : 1. The enhancement factors of these three point sources
on the image plane were measured to be 1.48, 1.11 and 1.06, respectively. The ratio of net image
strength among them is 8 : 1.8 : 1, which indicates that the imaging system based on coherent
backscattering itself is linear.
Figure 9(a) is the 4th-order intensity correlation function of the image shown in Fig. 8, and Fig.
9(b) is the net image strength of the Nth-order intensity correlation function as a function of the
intensity correlation order N. It is clearly seen that the strength of the strongest one (point1), in which
the strength of its image term in Fig. 8 is comparable to the background, increases nonlinearly with
the increase of the correlation order N. More interestingly, the strengthes of the two weak ones (point2
and point3), in which the image term itself is much less than the background, increase linearly with
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the increase of the correlation order N, indicating that the imaging system with high-order intensity
correlation method is linear as predicted theoretically. Note that the net image strengthes for the two
weak points (point2 and point3) are multiplied by a factor of 10 in Fig. 9(b) for comparison.
Figure 10(a) is the normalized image profile of a number ‘2’. It is seen that the image contrast is
very low and it is difficult for one to identify the number ‘2’ in the image plane. Figure 10(b) is the
result by measuring the 8th-order intensity correlation function on the image plane. One sees that the
image contrast increases greatly and the image of the number ‘2’ is clearly displayed. This proves
that the method is reliable for improving the quality of image based on coherent backscattering in a
random medium.
IV. CONCLUSIONS
In summary, we have studied the lensless imaging based on the coherent backscattering effect
of random scattering media, and gotten the PSF of this lensless imaging system. We have shown that
the image contrast and resolution depend on several factors such as the diameter of the scatterer, the
volume fraction of the suspension, the distance between the object and the surface of the random
scattering medium. The contrast is relatively higher for suspension of polystyrene spheres with the
sphere diameter between 0.5 μm to 1.2 μm dispersed in water. An increase in volume fraction of
scatterers may increase the possible paths of multiple scattering of light, but meanwhile it increases
the possibility of recurrent scattering, which may reduce the image contrast. Furthermore, we have
demonstrated that the lensless imaging based on coherent backscattering with high-order intensity
correlation method is linear for complicated objects, and the image quality can be significantly
improved by performing the high-order intensity correlation measurement on the image plane.
Therefore, this imaging technique could be practical even for complicated objects.
ACKNOWLEDGMENTS
This work is supported by the 973 program (2013CB328702), the NSFC (11174153 and
11374165), the 111 project (B07013), and the Fundamental Research Funds for the Central Universities.
1 P.
E. Wolf and G. Maret, Phys. Rev. Lett. 55, 2696–2699 (1985).
P. V. Albada and A. Lagendijk, Phys. Rev. Lett. 55, 2692–2695 (1985).
3 S. Etemad, R. Thompson, and M. J. Andrejco, Phys. Rev. Lett. 57, 575–578 (1986).
4 P. Anderson, Phil. Mag. B 52, 505–509 (1985).
5 S. John, Phys. Rev. Lett. 53, 2169–2172 (1984).
6 E. Akkermans, P. E. Wolf, and R. Maynard, Phys. Rev. Lett. 56, 1471–1474 (1986).
7 E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, J. Phys. France 49, 77–98 (1988).
8 P. Wolf, G. Maret, and R. Maynard, J. Phys. France 49, 63–75 (1988).
9 D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, Nature 390, 671–673 (1997).
10 A. A. Chabanov, A. Z. Genack, and M. Stoytchev, Nature 404, 850–853 (2000).
11 A. Ishimaru, Wave Propagation and scattering in Random Media (Academic Press, New York, 1978).
12 P. E. Sebbah, Waves and Imaging through Complex Media (Kluwer Academic, 2001).
13 C. K. Hayakawa, V. Venugopalan, V. V. Krishnamachari, and E. O. Potma, Phys. Rev. Lett. 103, 043903 (2009).
14 J. S. Preston, Nature 213, 1007–1008 (1967).
15 P. Rochon, D. Bissonnette, D. Bissonnette, C. Barsi, W. Wan, P. M. Mcculloch, and P. A. Hamilton, Nature 348, 708–710
(1990).
16 H. M. Escamilla, E. R. M´
endez, and A. Mart´ınez, J. Opt. Soc. Am. A 13, 1439–1447 (1996).
17 I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, Nat. Photon. 4, 320–322 (2010).
18 Y. Choi, T. Yang, C. Fang-Yen, P. Kang, K. Lee, R. Dasari, M. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
19 S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, Nat. Commun. 1, 81 (2010).
20 C. M. Aegerter and G. Maret, “Coherent backscattering and Anderson localization of light,” in Progress in Optics, edited
by E. Wolf (Elsevier, 2009), pp. 1–62.
21 R. Corey, M. Kissner, and P. Saulnier, Am. J. Phys. 63, 560–564 (1995).
22 D. Wiersma, M. van Albada, and B. van Tiggelen, Phys. Rev. Lett. 74, 4193–4196 (1995).
23 B. Picinbono and E. Boileau, J. Opt. Soc. Am. 58, 784–789 (1968).
24 D. Z. Cao, J. Xiong, S. H. Zhang, L. F. Lin, L. Gao, and K. Wang, Appl. Phys. Lett. 92, 201102 (2008).
25 J. Liu and Y. Shih, Phys. Rev. A 79, 023819 (2009).
2 M.
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