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High-efficiency time-reversed
ultrasonically encoded optical
focusing using a large-area
photorefractive polymer
Yuta Suzuki, Puxiang Lai, Xiao Xu, Lihong V. Wang
Yuta Suzuki, Puxiang Lai, Xiao Xu, Lihong V. Wang, "High-efficiency time-
reversed ultrasonically encoded optical focusing using a large-area
photorefractive polymer," Proc. SPIE 8581, Photons Plus Ultrasound: Imaging
and Sensing 2013, 85811G (4 March 2013); doi: 10.1117/12.2005021
Event: SPIE BiOS, 2013, San Francisco, California, United States
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High-efficiency time-reversed ultras
onically encoded optical focusing
using a large-area pho
torefractive polymer
Yuta Suzuki
*
, Puxiang Lai, Xiao Xu, and Lihong Wang
*
Optical Imaging Laboratory, Departme
nt of Biomedical Engineering,
Washington University in St. Loui
s, St. Louis, Missouri, 63130, USA
ABSTRACT
Time-reversed ultrasonically encode
d (TRUE) optical focusing focuses light beyond one transport mean free
path by phase-conjugating the ultrasonically tagged light. However, in previous works, only a small portion of the tagged
light was phase-conjugated by using a photorefractive Bi
12
SiO
20
crystal, due to its small active area (1×1 cm
2
). In this
work, we report high-efficiency TRUE focusing using a large-area photorefractive polymer (5×5 cm
2
), which
demonstrated ~40 times increase in focu
sed energy. Further, we imaged absorbers embedded in a turbid sample of
thickness of ~12 transport mean free paths.
Keywords:
optical focusing, ultrasound modulation, optical imaging, phase conjugation, time reversal,
photorefractive material.
1. Introduction
Localization of optical energy at desired locations inside
biological tissue is of essential interest in optical
applications for biomedicine. However, beyond one transport mean free path (
l
t
'), delivering optical energy with good
spatial control becomes more and more difficult due to the multiple scattering in tissue. One way to overcome the limit is
iterative wavefront shaping of the incident beam through maximizing a feedback signal from embedded visible targets
[1]. However, this approach is not suitable for many biom
edical applications, because
the limited speed of iterative
calculations suffers from microstructural movement of biological tissue. Further, the use of visible targets is not only
invasive, but also limits the focusing locations to predetermined positions.
In addressing the need to concentrate optical energy at the desired positions inside biological tissue beyond 1
l
t
',
Xu et al. developed a technique named time-reversed ultrasonically encoded (TRUE) optical focusing [2]. The technique
is a two-step method. In its recording phase, a focused ultrasound beam spectrally modulates, or tags, the diffuse light
inside a scattering medium. Such tagged photons are selectively recorded as a hologram onto an updatable holographic
film outside the sample. In the subsequent readout phase, optical focusing into the medium is achieved by phase
conjugating (or time reversing, for monochromatic light) the tagged light. As a phase conjugate mirror (PCM), Xu et al.
[2] used a photorefractive Bi
12
SiO
20
(BSO)
crystal. Recently, digital versions of the technique were demonstrated, which
employed a complementary-metal-oxide-semiconductor camera and a spatial light modulator to achieve digital optical
phase conjugation [3, 4]. The photorefractive PCM-based analog TRUE method has an important advantage over the
digital version in its faster operation speed and finer record
able grating resolution. However, inorganic photorefractive
crystals can only be fabricated up to a few centimeters in
the transverse dimension, which restricts the diffuse light
collection from a turbid sample. Further, there are other inferi
or figure-of-merits of photorefr
active crystals, such as their
diffraction efficiency, ho
logram persistency, and slow response time, that make the analog TRUE method infeasible for
in vivo
applications.
Recent research on photorefractive po
lymers (PRPs) shows exciting poten
tial to improve the TRUE focusing
ability. Unlike their inorganic counterparts, PRPs
can be made with large area (>30×30 cm
2
, [5]). Moreover, choosing
*
Further author information
Yuta Suzuki,
ysuzuk@wustl.edu
, 1-314-935 9587
Lihong V. Wang,
lhwang@wustl.edu
, 1-314- 935 6152
Photons Plus Ultrasound: Imaging and Sensing 2013, edited by Alexander A. Oraevsky, Lihong V. Wang,
Proc. of SPIE Vol. 8581, 85811G · © 2013 SPIE · CCC code: 1605-7422/13/$18 · doi: 10.1117/12.2005021
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proper composites allows high diffraction efficiency, long holographic persistency, and/or fast response times [6, 7, 8].
Here, by using a large-area PRP (~5×5 cm
2
), we show an increase in delivered
optical energy in TRUE focusing over
previous BSO crystal. Also, in terms of diffraction efficiency, we show that the experimental photorefractive behaviors
of the PRPs and a BSO crystal agree with the theoretical expectations in the case of holographic recording using diffuse
tagged light. Finally, by using a PRP, we show a prelimin
ary imaging result from a turbid medium, validating the
applicability of PRPs for this technique.
2. Experimental system
Operation of the optical setup used in this study is sc
hematically illustrated in Figure 1(a). As in the previous
photorefractive phase-conjugation experiments, the optical system has three light beams originating from the same laser
source: a sample beam (S), a reference beam (R), and a r
eadout beam (R*). The frequency
of S was adjusted to 2 MHz
higher than original laser output by the sequential acousto-optic modulators.
The hologram of the ultrasound-modulated light was recorded, and then its wavefront was reconstructed in the
holographic readout phase. In the 800-ms recording phase,
S with 3-mm diameter was switched on to illuminate an
optically turbid sample which mimics biological tissue. To si
mulate a biological tissue, we used an intralipid doped gel-
based phantom made by dissolving porcine gelatin into water and then adding intralipid to the mixture before it
solidified. A focused ultrasound beam
with 1-MPa focal pressure was generated by a 2-MHz transducer (Sonic
BS
Sample
PRP/BSO
R
R*
S
S2
PD1
UST
L1
L2
n
θ
PD2
F
PRP
10 mm
BSO
S1
AOM1&2
(a)
Z
Y
X
BS
Sample
PRP/BSO
R
R*
S
S2
PD1
UST
L1
L2
n
θ
PD2
F
PRP
10 mm
BSO
PRP
10 mm
BSO
S1
AOM1&2
(a)
Z
Y
X
Z
Y
X
(b)
~30
°
n
G
l
a
s
s
I
T
O
I
T
O
G
l
a
s
s
P
o
l
y
m
e
r
R
R*
V
(b)
~30
°
n
G
l
a
s
s
I
T
O
I
T
O
G
l
a
s
s
P
o
l
y
m
e
r
G
l
a
s
s
I
T
O
I
T
O
G
l
a
s
s
P
o
l
y
m
e
r
R
R*
V
Figure 1. (a) Schematic of the optical setup us
ed in this study. The back surface normal (
n
) of the PR materials was
rotated by angle
θ
. Either a BSO crystal or PRP was used as the PCM. HWP
i
,
i
th halfwave plate; PBS
i
,
i
th polarizing
beamsplitter; M
i
,
i
th mirror; AOM
i
,
i
th acousto-optic modulator; BS, beamsplitter; S
i
,
i
th shutter; BE
i
,
i
th beam expander;
UST, ultrasound transducer; L
i
,
i
th lens; F, neutral density filter.
X
is
the
sample scanning axis,
Y
is the acoustical axis,
and
Z
is the
optical axis. The inset shows a photograph of the PRP
and BSO crystal, demonstr
ating the advantageously
greater area of the PRP. (b) Schematic of high-voltage applic
ation to PRP. The voltage was applied across the indium-tin-
oxide (ITO) coated glass electrodes, which sandwiched the 100-
μ
m thick polymer film. The PRP's surface normal was
horizontally tilted from the optical axis by
θ
~30 degrees.
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Concepts, H106) to spectrally modulate th
e diffuse light propagating in
side the sample. The diffuse light exiting the back
of the sample (hereafter called "scattered S") was collected
to illuminate the photorefractive material. The reference
beam R had a 3-cm diameter. The beam angle between th
e scattered S and R was approximately 20°. R formed a
stationary interference pattern only with the ultrasound-modulated light in the scattered S, which contributed to a
hologram, while the unstationary interference patterns between
R and the other frequency components in the scattered S
resulted in a uniform background. Thus, the information of the tagged-light wavefront was selectively recorded in the
photorefractive material. Once S
was switched off after the holographic record
ing, shutter S2 was opened to start the
readout phase. Then shutter S1 was opened to turn on 50-ms R* pulse. R* is a counter propagating reference beam with
a 3-cm diameter. Through holographic diffraction, R* generated the phase-conjugated light (S*) of the tagged light from
the photorefractive material. After transmitting through the turb
id sample for the second time, S* was partially split by a
beamsplitter and detected as the TRUE signal. The repetition rate of the cycle was 1 Hz.
As a photorefractive material that serves as the upda
table holographic film, we used either a PRP film, supplied
by Nitto Denko, or a BSO crystal as used in our previous
experiments. The composite of the PRP film was the same as
the polymer device reported in [7]. The transverse dimensions of the PRP film and the BSO crystal were 5×5 cm
2
and
1×1 cm
2
, respectively, as shown in the inset
of Figure 1(a). As seen, the PRP film
offers an advantageous large area
compared to a BSO crystal, which increas
ed collection of the diffuse light from the turbid sample. The PRP film has a
thickness of 100
μ
m and is sandwiched between two indium-tin-oxide
coated glass slides, while
the BSO crystal has a
thickness of 0.5 cm. We applied 4-kV dc voltage across th
e front and back surfaces of the PRP film to enable
photorefractivity, as shown in Fig. 1(
b). The surface normal of the PRP film was tilted by ~30° from the propagation
direction of R to increase the diffractio
n efficiency from the recorded gratings. Although such a tilted configuration of
the film reduces its usable transverse area by a factor of
(
)
θ
cos
, where
θ
is defined in Fig. 1(a), the effective area of the
polymer was ~21 cm
2
, still far exceeding the area of a BSO crystal of 1 cm
2
. Under our experimental conditions, the
measured TRUE signal reached its stead
y state value after ~5 s, which potentially can be shortened by increasing the
intensity of the two writing beams (scatterd
S and R). When we used the BSO crystal,
θ
was ~10°, and we applied an 8-
kV
peak-to-peak
square wave electric field at 2.1 kH
z across the surface of the crystal as in
the previous work
s [2, 9, 10], to
increase the holographic diffraction efficien
cy [11]. Whenever we replaced PR materials, we adjusted mirrors M4 and
M5 to maximize the TRUE signal at the photode
tector before taking any measurement.
3. Theory
To examine the diffraction efficienci
es of PRPs and BSO crystals, it is
helpful to compare the experimental
results with the expected behaviors in
theory. According to the theory of p
hotorefractive crystals, the diffraction
efficiency of a recorded grating is proportional to the contrast (or modulation) squared of the interference grating, when
the two writing beams are plane waves and the reference beam is much stronger than the signal beam. In the case of
TRUE focusing, however, the problem is less trivial, because th
e signal beam is the diffuse tag light which is buried in a
strong untagged background light.
To extend the theory to the case of diffuse and tagged signal beams, let us denote the complex amplitude of the
plane reference beam R as E
R
(
f
0
), that of the unmodulated scattered S as E
S
(
f
0
–
f
a
;
x
,
y
),
and
that of the tagged light as
E
T
(
f
0
;
x
,
y
). Note that the spatial dependency of the scattere
d light, and the frequency associated with each of the
electrical fields are explicitly spelled out inside the brackets, where
f
0
is the original laser output frequency, and
f
a
is the
acoustic frequency applied to the sample. Then, the complex
amplitude of the electrical field that impinges on the
photorefractive material may be written as
()
(
)
(
)
(
)
y
x
f
E
y
x
f
f
E
f
E
x,y
E
T
a
S
,
;
,
;
0
0
0
R
+
−
+
=
. (1)
Therefore, the time-averaged intensity distribution can be expressed as the square of eq. (1), and becomes
()
()
()( )
[
]
()
⎪
⎭
⎪
⎬
⎫
⎪
⎩
⎪
⎨
⎧
+
−
+
=
y
x
f
E
E
y
x
f
E
f
E
m
E
y
x
f
f
E
E
y
x
I
T
R
T
R
R
a
s
R
,
;
,
;
Re
,
;
1
,
0
0
0
*
2
2
0
2
, (2)
where cross talks between the electrical fields of different
frequencies are dropped, by taking the time average of the
intensity. Also, by assuming that the tagged light is much
weaker than R, its contribution to the offset of the
interferogram is neglected.
m
in eq. (2) is the local contrast (or modulation) of the hologram, defined by
()
(
)
R
T
E
y
x
f
E
y
x
m
,
;
,
0
=
. (3)
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For simplicity, let us assume that |E
R
|
2
>> |E
S
|
2
, and neglect the second term in (2). This condition can be easily met in
the real experiment, since only a small po
rtion is collected as the scattered S
after the diffuse medium. Following the
knowledge of photorefractive diffraction
efficiency, we expect that the diffractio
n efficiency should be proportional to
the
m
(
x,y
) squared, |
E
T
(
f
0
;
x
,
y
)|
2
/|E
R
|
2
, which is the local intensity ratio of tagged light to R. In the experiment, we measure
the spatially averaged diffraction efficiency of the hologram, which is our interest. By taking the spatial average of
m
(
x,y
), we see that the holographic diffraction efficiency is proportional to the average intensity ratio of tagged light to
R. Further, because
E
T
is proportional to the scattered S, the diffractio
n efficiency of the hologr
am is expected to be
proportional to the intensity ratio of the scattered S to R, when |
E
R
|
2
>> |
E
S
|
2
.
4. Experimental Results
To see the phase-conjugation performance by using a
PRP film as a PCM instead of a BSO crystal, we
compared the R-to-signal conversion efficien
cy for both of the scenarios. In the first experiment, we fixed the S intensity
while increasing both the R* and R intensities at the fixed R*-to-R intensity ratio of 17, and observed the changes in the
TRUE signal intensities. The used sample was a 1-cm-thick gelatin-intralipid sample having a reduced scattering
coefficient
μ
s
'=5 cm
-1
. The diffraction efficiency was calculated by dividing the peak intensity of the TRUE signal by
that of R*. Figure 2(a) shows the measured variations of th
e diffraction efficiencies for th
e different intensity ratios of
(a)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
Intensity ratio of scattered S to R
Diffraction efficiency (a.u.)
PRP,
φ
3cm
PRP,
φ
1cm
BSO
(c)
0
0.02
0.04
0.06
0.08
0.1
0.12
0
0.02
0.04
0.06
0.08
0.1
0.12
Intensity ratio of scattered S to R
Diffraction efficiency (a.u.)
PRP,
φ
3cm
PRP,
φ
1cm
BSO
Time (s)
TRUE signal (mV)
0
0.02
0.04
0.06
0
4
8
12
16
PRP
BSO
-0.02
0
0.02
0.04
0.06
0.08
0.1
-2
-1
0
1
2
3
4
5
Time (s)
TRUE signal (mV)
(b)
(d)
PRP
BSO
(a)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
Intensity ratio of scattered S to R
Diffraction efficiency (a.u.)
PRP,
φ
3cm
PRP,
φ
1cm
BSO
(c)
0
0.02
0.04
0.06
0.08
0.1
0.12
0
0.02
0.04
0.06
0.08
0.1
0.12
Intensity ratio of scattered S to R
Diffraction efficiency (a.u.)
PRP,
φ
3cm
PRP,
φ
1cm
BSO
Time (s)
TRUE signal (mV)
0
0.02
0.04
0.06
0
4
8
12
16
PRP
BSO
PRP
BSO
-0.02
0
0.02
0.04
0.06
0.08
0.1
-2
-1
0
1
2
3
4
5
Time (s)
TRUE signal (mV)
(b)
(d)
PRP
BSO
PRP
BSO
Figure 2. (a) Plot of diffraction efficiencies
versus intensity ratio of scattered S to R
for PRP1. (b) Representative
temporal profiles of TRUE signals acquired using the PRP1
and BSO crystal. (c) Plot of
diffraction efficiencies versus
intensity ratio of scattered S to R
for PRP2. Linear fitting curves are also s
hown. (d) Representative temporal profiles o
f
TRUE signals acquired using the PRP2 and BSO crystal.
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the scattered S to R in both scenarios, by using a PRP (PRP
1). We see that, when we limite
d the polymer aperture size to
1-cm diameter, which is comparable to th
e area of the BSO crystal,
the diffraction efficiency
increased by ~3 times over
that of the BSO crystal. Moreover, when
we increased the aperture size to 3-cm
diameter, the efficien
cy increased by ~5
times. The improvement by increasing the
aperture size is not the same as the in
crement of the PRP area, because of the
non-uniform photorefractive properties of PRP over its area.
It was expected to see a linear relationship when the
intensity ratio of scattered S to R is small enough, but while conducting the experiment, the dielectric breakdown of the
PRP1 prohibited the measurement. The strong R and R* intensities led to the dielectric breakdown, which was used to
create a low intensity ratio of scattered S to R. Figure 2(b) shows TRUE signal waveforms acquired by using a BSO
crystal and the PRP1 under the same conditions of R and R*. As seen in Fig. 2(b), PRP offered a stronger signal peak for
a longer duration.
By using another PRP (PRP2), we conducted a further experiment to see the linear relationship when R is much
stronger than scattered S intensity. To prevent the polymer da
mage caused by the strong R and R* intensities, we varied
the S intensity while fixing R and R* intensities at 10 mW/cm
2
and 140 mW/cm
2
, respectively. In this way, low intensity
ratio of scattered S to R can be achieved when the S intensity
is low enough, without causing dielectric breakdown of the
polymer. The result is shown in Figure 2(c), where we s
ee the explained linear relations
hip of the photorefractive
diffraction efficiencies.
Using PRP2, we increased the dif
fraction efficiency by ~2 times
with an aperture size of 1-cm
diameter, and ~8 times with an aperture
size of 3-cm diameter. A pair of signal waveforms obtained by using the BSO
crystal and PRP2 is shown in Figure 2(d), which further validates the advantages of PRP of longer persistency and ~8
times higher diffraction efficiency.
Further, to demonstrate the PRP applicability for TRUE focusing, we obtained images from a turbid phantom,
by embedding two absorbers at its middle plane. Th
e sample had the reduced scattering coefficient
μ
s
' = 12 cm
-1
, and the
geometrical thickness
d
= 1 cm, which is equivalent to ~1.2 cm human tissue. The photograph of the sample middle
5 mm
X
Y
Z
4
6
8
10
12
14
16
18
20
22
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
X [mm]
Normalized signal
5 mm
X
Y
Z
4
6
8
10
12
14
16
18
20
22
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
X [mm]
Normalized signal
Figure 3. 1-D image demonstrating TRUE optical focusing us
ing PRP2. (a) Photograph of the imaging plane, which was
set middle plane of the sample. (b) Normalized TRUE
signal, TRDC signal, and DC signal versus the
X
axis.
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plane that contained the two absorbers is
shown in Figure 3(a). We scanned the sample in the X direction and the TRUE
signal was averaged for 32 times at each sample position. We
also acquired the image by us
ing the scattered S intensity
from the sample when the ultrasound is off (DC image),
and by using the time-reversed dc light (TRDC image). The
sample scanning step size was 0.32 mm. As seen in Figure
3(b), the TRUE image resolv
ed the two absorbers embedded
inside the sample, while the DC and TRDC images did not resolve the absorbers, which validates the TRUE focusing
ability by using PRP2.
5. Discussion and Conclusions
Towards
in vivo
TRUE focusing, there are several issues that mu
st be addressed. First,
the slow photorefractive
response time of ~5 s is an issue because of the fast speckle
decorrelation time of tissue (~ms). Such fast photorefractive
performance is possible by using PRPs wi
th different composites, and by short pu
lse lasers, as reported in some recent
works on PRPs [8]. Second, we noticed
that phase-conjugation
performance of our PRP fl
uctuated over a long time
period (~30 min). This issue also may be addressed by using fast polymers, by shortening the measurement of imaging
experiments. Also, using the two-wave mixing signal as a
reference signal to normalize
the acquired phase-conjugated
signal is another approach. Thirdly, our PRP had a relatively lower damage threshold compared to that of a BSO crystal.
By expanding the R and R* beam, we can overcome this issue while maintaining the same optical powers for both beams
and observable signal strength.
In summary, we showed a phase-co
njugation efficiency increase in TRUE
focusing by using a PRP. Also, for
the diffuse tagged light case, we showed
that diffraction efficien
cies of PRPs and a BSO crystal match the presented
photorefractive theory. Further, using a PRP, we resolved
two optical absorbers embedded
in a turbid medium with
μ
s
' =
12 cm
-1
, and geometrical thickness
d
= 1 cm, which is equivalent to 1.2-cm-thick human tissue. Although there are
several difficulties for
in vivo
applications, it is likely to be able to solv
e these step-by-step. Th
e presented efficiency
increase of TRUE focusing is an encouraging step
towards the future applications of this technique.
6. References
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