Time-reversed ultrasonically encoded (TRUE) optical focusing is an emerging technique that focuses light deep into scattering media by phase-conjugating ultrasonically encoded diffuse light. In previous work, the speed of TRUE focusing was limited to no faster than 1 Hz by the response time of the photorefractive phase conjugate mirror, or the data acquisition and streaming speed of the digital camera; photorefractive-crystal-based TRUE focusing was also limited to the visible spectral range. These time-consuming schemes prevent this technique from being applied in vivo, since living biological tissue has a speckle decorrelation time on the order of a millisecond. In this work, using a Tedoped Sn_2P_2S_6 photorefractive crystal at a near-infrared wavelength of 793 nm, we achieved TRUE focusing inside dynamic scattering media having a speckle decorrelation time as short as 7.7 ms. As the achieved speed approaches the tissue decorrelation rate, this work is an important step forward toward in vivo applications of TRUE focusing in deep tissue imaging, photodynamic therapy, and optical manipulation

Grabar, Alexander A.

Lai, Puxiang

Liu, Yan

Ma, Cheng

Suzuki, Yuta

Wang, Lihong V.

Xu, Xiao

Caltech Authors - Main

PROCEEDINGS OF SPIE
SPIEDigitalLibrary.org/conference-proceedings-of-spie
High-speed time-reversed
ultrasonically encoded (TRUE)
optical focusing inside dynamic
scattering media at 793 nm
Yan  Liu, Puxiang  Lai, Cheng  Ma, Xiao  Xu, Yuta  Suzuki,
et al.
Yan  Liu, Puxiang  Lai, Cheng  Ma, Xiao  Xu, Yuta  Suzuki, Alexander A.
Grabar, Lihong V. Wang, "High-speed time-reversed ultrasonically encoded
(TRUE) optical focusing inside dynamic scattering media at 793 nm," Proc.
SPIE 8943, Photons Plus Ultrasound: Imaging and Sensing 2014, 894339 (3
March 2014); doi: 10.1117/12.2039815
Event: SPIE BiOS, 2014, San Francisco, California, United States
Downloaded From: https://www.spiedigitallibrary.org/conference-proceedings-of-spie on 9/4/2018  Terms of Use: https://www.spiedigitallibrary.org/terms-of-use
High-Speed Time-Reversed Ultrasonically Encoded (TRUE) 
Optical Focusing inside Dynamic Scattering Media at 793 nm 
 
Yan Liu1,†, Puxiang Lai1,†, Cheng Ma1, Xiao Xu1, Yuta Suzuki1, Alexander A. Grabar2 and Lihong 
V. Wang1,* 
1 Optical Imaging Laboratory, Department of Biomedical Engineering, Washington University, 
Saint Louis, Missouri 63130, USA 
2 Institute of Solid State Physics and Chemistry, Uzhgorod National University, 88 000 Uzhgorod, 
Ukraine 
† Equal contribution  *Corresponding author: lhwang@wustl.edu 
 
                                      ABSTRACT 
 
Time-reversed ultrasonically encoded (TRUE) optical focusing is an emerging technique that focuses light deep into 
scattering media by phase-conjugating ultrasonically encoded diffuse light. In previous work, the speed of TRUE 
focusing was limited to no faster than 1 Hz by the response time of the photorefractive phase conjugate mirror, or the 
data acquisition and streaming speed of the digital camera; photorefractive-crystal-based TRUE focusing was also 
limited to the visible spectral range. These time-consuming schemes prevent this technique from being applied in vivo, 
since living biological tissue has a speckle decorrelation time on the order of a millisecond. In this work, using a Te-
doped Sn2P2S6 photorefractive crystal at a near-infrared wavelength of 793 nm, we achieved TRUE focusing inside 
dynamic scattering media having a speckle decorrelation time as short as 7.7 ms. As the achieved speed approaches the 
tissue decorrelation rate, this work is an important step forward toward in vivo applications of TRUE focusing in deep 
tissue imaging, photodynamic therapy, and optical manipulation. 
 
Keywords: Time-Reversed Ultrasonically Encoded (TRUE) optical focusing, optical phase conjugation, optical time 
reversal, light scattering, turbid media, optical focusing. 
 
 
1. INTRODUCTION 
Light focusing plays a central role in biomedical imaging, optical manipulation and therapy. However, in scattering 
media, direct light focusing deeper than around 10 scattering mean free path (typically ~1 mm in biological tissue) 
becomes infeasible due to light scattering1-3. Overcoming this optical diffusion limit has been extensively studied within 
the past decades. For example, wavefront shaping4, 5 has demonstrated that light can be focused through scattering 
media by compensating the scattering-induced phase distortions along the optical paths. Obtaining the best phase 
correction, however, is usually a time-consuming process (seconds to hours) limited by the refreshing speed of the 
spatial light modulators and the iterative nature of optimization. A solution to this speed limitation, termed time-
reversed ultrasonically encoded (TRUE) optical focusing6-11, uses either an analog (photorefractive material) or a digital 
(a digital camera plus a spatial light modulator) phase conjugate mirror to selectively record and time-reverse the 
ultrasound-modulated light emitted from the virtual guide-star formed by acoustic focus inside the tissue. TRUE 
focusing is inherently faster than wavefront shaping since it measures the desired phase map directly, avoiding the time-
consuming exhaustive search for the optimum wavefront in wavefront shaping. However, the speed of TRUE focusing 
was limited to no faster than 1 Hz by the response time of the photorefractive phase conjugate mirror (for the analog 
approach6, 12), or the data acquisition and streaming speed of the digital camera (for the digital approach8, 9). Moreover, 
photorefractive-crystal-based TRUE focusing was also limited to the visible spectral range, limiting its capability to 
focus even deeper. So far, there has been no report of studies on optical focusing deep inside dynamic scattering media 
or living biological tissue, mainly because the time needed to achieve focusing in previous work was much longer than 
the speckle decorrelation time of the scattering media, which is on the order of 1 ms for living tissue as determined by 
motions such as blood flow, breathing and heartbeat. In this work, we present our latest explorations, using a fast Te 
Seno Medical Best Poster Award
Photons Plus Ultrasound: Imaging and Sensing 2014, edited by Alexander A. Oraevsky, Lihong V. Wang, 
Proc. of SPIE Vol. 8943, 894339 · © 2014 SPIE · CCC code: 1605-7422/14/$18 · doi: 10.1117/12.2039815
Proc. of SPIE Vol. 8943  894339-1
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doped Sn2P2S6 photorefractive crystal (provided by Prof. Alexander A. Grabar) as a phase conjugate mirror, to focus 
light inside dynamic scattering media with a speckle decorrelation time as short as 7.7 ms.  
 
2. METHODS 
2.1 Experimental set-up for TRUE optical focusing inside dynamic scattering media 
Fig. 1 shows a diagram of the main parts of the set-up. The detailed layout is similar to that in Ref. 13. A continuous-
wave Ti:Sapphire laser (MBR110, Coherent) operating at 793 nm was used as the light source. A reference beam R and 
ultrasonically tagged signal light S wrote a holograph in the Sn2P2S6:Te photorefractive crystal (PRC) for 10 ms. Then, 
the writing beams were blocked by a mechanical shutter and the holograph was read by another reference beam R* 
(conjugate of R) for 2 ms, which produces a phase-conjugated signal light S* that converges back to the acoustic focus 
and was detected by a photodiode (PDA-36A, 70 dB gain, Thorlabs). The ultrasound was on only during the writing of 
the holograph. The Sn2P2S6:Te crystal was a 6×6×6 mm
3 cube and the intensity of the writing beams on the crystal was 
1.1 W/cm2. 
An absorptive target (made by adding black ink in gelatin) was sandwiched between two scattering media – a diffuser 
(DG10-120, Thorlabs), and an intralipid-gelatin phantom with a thickness of 2 mm (equivalent to 7 mean free paths at 
793 nm). The intralipid-gelatin phantom, mounted on a motorized linear stage, translates along the x-direction at a 
controllable speed during the recording and reading of the holograph. The movement of the intralipid-gelatin phantom 
causes the interference pattern formed by S and R beams on the PRC to decorrelate, and we can control the speckle 
decorrelation time by translating the phantom at different speeds.  
 
24 mm
R
S
UT
D ABT
IGPPD
L2 L3
Sn2P2S6:Te
crystal
L1
z
x
v
R*
PBS
     
 
Figure 1. Diagram for the experiment on TRUE optical focusing inside dynamic scattering media. An absorptive 
target was sandwiched between a diffuser and an intralipid-gelatin phantom which moves along x direction at 
speed v. PBS, polarizing beam splitter; PD, photodiode; Li, ith lens; PD, photodiode; D, diffuser; ABT: 
absorptive bar target; UT, ultrasonic transducer; IGP, intralipid-gelatin phantom; S, signal light; R, reference 
beam; R*, conjugated reference beam. 
2.2 Characterizing the relationship between speckle decorrelation time and phantom moving speed 
We characterized the relationship between speckle decorrelation time and phantom moving speed using the set-up 
shown in Fig. 2. The distance between the rear surface of the phantom and the focal plane of the objective was 22 mm, 
which was limited by the dimensions of the phantom mount. At each phantom moving speed v, we recorded a sequence 
of speckle patterns using a finite conjugate microscope objective [10×, numerical aperture (NA) = 0.1, tube length = 
160 mm, Leica] and a CMOS camera (208 frame per second, 320×108 pixels, Firefly MV, Point grey). We calculated 
the correlation coefficient between the first and each of the ensuing frames of the recorded speckle patterns. By fitting 
Proc. of SPIE Vol. 8943  894339-2
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the curve of speckle correlation coefficient versus time using a Gaussian function, we obtained the speckle decorrelation 
time Td, defined here as the time when the speckle correlation coefficient decreases to 0.1, for this speed.  
LT
24 mm
D
IGP
v
PBS
Obj Camera
z
x
Figure 2. Experimental set-up to measure the speckle decorrelation time. PBS, polarizing beam splitter; D, 
diffuser; IGP, intralipid-gelatin phantom; Obj, microscope objective; LT, lens tube.  
3. RESULTS
A sequence of speckle patterns when the intralipid-gelatin phantom was moving at a speed of 0.55mm/s was shown in 
Video 1. We can see there are translations and transformations of the speckle patterns.  
Video 1. A sequence of speckle patterns when the intralipid-gelatin phantom was moving at a speed of 0.55mm/
s. The video has a playback frame rate of 15 fps. http://dx.doi.org/0.1117/12.2039815.1 
The speckle correlation coefficient vs. time when the phantom moving speed is 0.055mm/s is shown in Fig. 3, from 
which we can obtain Td = 72 ms for this speed. The value of Td as a function of phantom moving speed v is shown in 
Fig. 4. By fitting the experimental data with Td = a/v, we obtain a = 4.23 ± 0.12 µm  (R
2 = 0.9987 for the fitting). Using
Td = 4.23µm /v, we obtained Td = 7.7 ms when v = 0.55 mm/s (at this speed, it is impossible to measure the speckle 
decorrelation time accurately by camera since the frame rate is 208 fps). 
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0 20 40 60 80 100 1200
0.2
0.4
0.6
0.8
1
Time (ms)
S
pe
ck
le
 c
or
re
la
tio
n 
co
ef
fic
ie
nt
 
Fig. 3 The speckle correlation coefficient vs. time when the phantom moving speed was 0.055mm/s. 
0 0.02 0.04 0.06 0.08 0.10
200
400
600
800
1000
Phantom moving speed (mm/s)
S
pe
ck
le
 d
ec
or
re
la
tio
n 
tim
e 
(m
s)
 
 
Experimental data
Fit by Td = 4.23 µm / v
 
Fig. 4 The relationship between speckle decorrelation time and phantom moving speed. 
 
When the phantom was moving at a speed of v = 0.55 mm/s, the signals detected by the photodiode, when the 
ultrasound was on and off during writing the holograph, are shown in Fig.5. It can be seen that the maximum signal 
amplitude was always higher when the ultrasound was on than that when the ultrasound was off, which suggests that we 
could detect phase-conjugated light when Td = 7.7 ms. We did not observe the phase conjugated light when we shifted 
the ultrasound frequency by 100 kHz. 
To acquire an image of the absorptive target with a width of 3.6 mm, we scanned the gelatin phantom containing the 
target along the x-direction. At each scanning position, 10 TRUE procedures were performed and the signals were 
averaged. The one dimensional images of the target are shown in Fig. 6, for two cases – when the intralipid-gelatin 
phantom was static (Td > 300 ms) and when it moved at a speed of 0.55 mm/s (Td = 7.7 ms). It can be seen that the 
image acquired when Td = 7.7 ms has a similar quality as the one acquired when Td > 300 s, demonstrating that our 
system is fast enough to overcome the speckle decorrelation caused by the movement of the scattering medium. The 
resolution of the image is about 1 mm, which is close to the theoretical value of 0.87 mm determined by the ultrasonic 
transducer (3.5 MHz, NA = 0.25).               
 
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0
0.02
0.04
0.06
0.08
0.10
0.12
A
m
pl
itu
de
 (V
)
0 0.4
Time (ms)
ON OFF ON OFF ON OFF
50.4 50.8
 
Fig. 5 The signal detected by the photodiode when the ultrasound was on and off during the writing of 
the holograph. 
0 2 4 6 8 10
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Lateral position [mm]
N
or
m
al
iz
ed
 T
R
U
E
 s
ig
na
l
 Td > 300 s
Td = 7.7 ms
 
Fig. 6 One dimensional images of the absorptive target, when the intralipid-gelatin phantom was static 
(Td > 300 ms) and when the phantom was moving at a speed of 0.55 mm/s (Td = 7.7 ms). Solid and 
dashed lines represent smoothed data computed by a 4-point moving average of the raw data. The step 
size of scanning is 0.2 mm.                                               
 
 
                                  4. CONCLUSIONS 
 
Using a Te-doped Sn2P2S6 photorefractive crystal at a near-infrared wavelength, we achieved high-speed TRUE 
focusing inside moving scattering media with a speckle decorrelation time as short as 7.7 ms. As the demonstrated 
speed approaches the tissue decorrelation rate, this work is an important step forward toward in vivo applications of 
TRUE focusing in deep tissue imaging, photodynamic therapy, and optical manipulation. 
 
 
 
 
 
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   ACKNOWLEDGEMENT 
 
This work was sponsored in part by National Institute of Health grants DP1 EB016986 (NIH Director’s Pioneer Award) 
and R01 CA186567 (NIH Director’s Transformative Research Award) as well as National Academies Keck Futures 
Initiative grant IS 13. L. W. has a financial interest in Microphotoacoustics, Inc. and Endra, Inc., which, however, did 
not support this work. 
 
 
  REFERENCES 
 
[1] Y. Liu, C. Zhang and L. V. Wang, "Effects of light scattering on optical-resolution photoacoustic microscopy," J 
Biomed Opt 17(12), 126014 (2012). 
[2] L. V. Wang and G. Liang, "Absorption distribution of an optical beam focused into a turbid medium," Appl Optics 
38(22), 4951-4958 (1999). 
[3] V. Ntziachristos, "Going deeper than microscopy: the optical imaging frontier in biology," Nat Methods 7(8), 603-
614 (2010). 
[4] I. M. Vellekoop and A. P. Mosk, "Focusing coherent light through opaque strongly scattering media," Opt. Lett. 
32(16), 2309-2311 (2007). 
[5] A. P. Mosk, A. Lagendijk, G. Lerosey and M. Fink, "Controlling waves in space and time for imaging and focusing 
in complex media," Nat Photon 6(5), 283-292 (2012). 
[6] X. Xu, H. Liu and L. V. Wang, "Time-reversed ultrasonically encoded optical focusing into scattering media," Nat 
Photon 5(3), 154-157 (2011). 
[7] P. Lai, X. Xu, H. Liu and L. V. Wang, "Time-reversed ultrasonically encoded (TRUE) optical focusing in 
biological tissue," J Biomed Opt 17(3), 030506 (2012). 
[8] Y. M. Wang, B. Judkewitz, C. A. DiMarzio and C. Yang, "Deep-tissue focal fluorescence imaging with digitally 
time-reversed ultrasound-encoded light," Nat Commun 3(928 (2012). 
[9] K. Si, R. Fiolka and M. Cui, "Fluorescence imaging beyond the ballistic regime by ultrasound-pulse-guided digital 
phase conjugation," Nat Photon 6(10), 657-661 (2012). 
[10] P. Lai, Y. Suzuki, X. Xu and L. V. Wang, "Focused fluorescence excitation with time-reversed ultrasonically 
encoded light and imaging in thick scattering media," Laser Physics Letters 10(7), 075604 (2013). 
[11] Y. Suzuki, X. Xu, P. Lai and L. V. Wang, "Energy enhancement in time-reversed ultrasonically encoded optical 
focusing using a photorefractive polymer," J Biomed Opt 17(8), 080507 (2012). 
[12] P. Lai, X. Xu, H. Liu, Y. Suzuki and L. V. Wang, "Reflection-mode time-reversed ultrasonically encoded optical 
focusing into turbid media," J Biomed Opt 16(8), 080505 (2011). 
[13] H. Liu, X. Xu, P. Lai and L. V. Wang, "Time-reversed ultrasonically encoded optical focusing into tissue-
mimicking media with thickness up to 70 mean free paths," J Biomed Opt 16(8), 086009 (2011). 
 
 
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High-speed time-reversed ultrasonically encoded (TRUE) optical focusing inside dynamic scattering media at 793 nm

PROCEEDINGS OF SPIE
SPIEDigitalLibrary.org/conference-proceedings-of-spie
High-speed time-reversed
ultrasonically encoded (TRUE)
optical focusing inside dynamic
scattering media at 793 nm
Yan  Liu, Puxiang  Lai, Cheng  Ma, Xiao  Xu, Yuta  Suzuki,
et al.
Yan  Liu, Puxiang  Lai, Cheng  Ma, Xiao  Xu, Yuta  Suzuki, Alexander A.
Grabar, Lihong V. Wang, "High-speed time-reversed ultrasonically encoded
(TRUE) optical focusing inside dynamic scattering media at 793 nm," Proc.
SPIE 8943, Photons Plus Ultrasound: Imaging and Sensing 2014, 894339 (3
March 2014); doi: 10.1117/12.2039815
Event: SPIE BiOS, 2014, San Francisco, California, United States
Downloaded From: https://www.spiedigitallibrary.org/conference-proceedings-of-spie on 9/4/2018  Terms of Use: https://www.spiedigitallibrary.org/terms-of-use
High-Speed Time-Reversed Ultrasonically Encoded (TRUE) 
Optical Focusing inside Dynamic Scattering Media at 793 nm 
 
Yan Liu1,†, Puxiang Lai1,†, Cheng Ma1, Xiao Xu1, Yuta Suzuki1, Alexander A. Grabar2 and Lihong 
V. Wang1,* 
1 Optical Imaging Laboratory, Department of Biomedical Engineering, Washington University, 
Saint Louis, Missouri 63130, USA 
2 Institute of Solid State Physics and Chemistry, Uzhgorod National University, 88 000 Uzhgorod, 
Ukraine 
† Equal contribution  *Corresponding author: lhwang@wustl.edu 
 
                                      ABSTRACT 
 
Time-reversed ultrasonically encoded (TRUE) optical focusing is an emerging technique that focuses light deep into 
scattering media by phase-conjugating ultrasonically encoded diffuse light. In previous work, the speed of TRUE 
focusing was limited to no faster than 1 Hz by the response time of the photorefractive phase conjugate mirror, or the 
data acquisition and streaming speed of the digital camera; photorefractive-crystal-based TRUE focusing was also 
limited to the visible spectral range. These time-consuming schemes prevent this technique from being applied in vivo, 
since living biological tissue has a speckle decorrelation time on the order of a millisecond. In this work, using a Te-
doped Sn2P2S6 photorefractive crystal at a near-infrared wavelength of 793 nm, we achieved TRUE focusing inside 
dynamic scattering media having a speckle decorrelation time as short as 7.7 ms. As the achieved speed approaches the 
tissue decorrelation rate, this work is an important step forward toward in vivo applications of TRUE focusing in deep 
tissue imaging, photodynamic therapy, and optical manipulation. 
 
Keywords: Time-Reversed Ultrasonically Encoded (TRUE) optical focusing, optical phase conjugation, optical time 
reversal, light scattering, turbid media, optical focusing. 
 
 
1. INTRODUCTION 
Light focusing plays a central role in biomedical imaging, optical manipulation and therapy. However, in scattering 
media, direct light focusing deeper than around 10 scattering mean free path (typically ~1 mm in biological tissue) 
becomes infeasible due to light scattering1-3. Overcoming this optical diffusion limit has been extensively studied within 
the past decades. For example, wavefront shaping4, 5 has demonstrated that light can be focused through scattering 
media by compensating the scattering-induced phase distortions along the optical paths. Obtaining the best phase 
correction, however, is usually a time-consuming process (seconds to hours) limited by the refreshing speed of the 
spatial light modulators and the iterative nature of optimization. A solution to this speed limitation, termed time-
reversed ultrasonically encoded (TRUE) optical focusing6-11, uses either an analog (photorefractive material) or a digital 
(a digital camera plus a spatial light modulator) phase conjugate mirror to selectively record and time-reverse the 
ultrasound-modulated light emitted from the virtual guide-star formed by acoustic focus inside the tissue. TRUE 
focusing is inherently faster than wavefront shaping since it measures the desired phase map directly, avoiding the time-
consuming exhaustive search for the optimum wavefront in wavefront shaping. However, the speed of TRUE focusing 
was limited to no faster than 1 Hz by the response time of the photorefractive phase conjugate mirror (for the analog 
approach6, 12), or the data acquisition and streaming speed of the digital camera (for the digital approach8, 9). Moreover, 
photorefractive-crystal-based TRUE focusing was also limited to the visible spectral range, limiting its capability to 
focus even deeper. So far, there has been no report of studies on optical focusing deep inside dynamic scattering media 
or living biological tissue, mainly because the time needed to achieve focusing in previous work was much longer than 
the speckle decorrelation time of the scattering media, which is on the order of 1 ms for living tissue as determined by 
motions such as blood flow, breathing and heartbeat. In this work, we present our latest explorations, using a fast Te 
Seno Medical Best Poster Award
Photons Plus Ultrasound: Imaging and Sensing 2014, edited by Alexander A. Oraevsky, Lihong V. Wang, 
Proc. of SPIE Vol. 8943, 894339 · © 2014 SPIE · CCC code: 1605-7422/14/$18 · doi: 10.1117/12.2039815
Proc. of SPIE Vol. 8943  894339-1
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doped Sn2P2S6 photorefractive crystal (provided by Prof. Alexander A. Grabar) as a phase conjugate mirror, to focus 
light inside dynamic scattering media with a speckle decorrelation time as short as 7.7 ms.  
 
2. METHODS 
2.1 Experimental set-up for TRUE optical focusing inside dynamic scattering media 
Fig. 1 shows a diagram of the main parts of the set-up. The detailed layout is similar to that in Ref. 13. A continuous-
wave Ti:Sapphire laser (MBR110, Coherent) operating at 793 nm was used as the light source. A reference beam R and 
ultrasonically tagged signal light S wrote a holograph in the Sn2P2S6:Te photorefractive crystal (PRC) for 10 ms. Then, 
the writing beams were blocked by a mechanical shutter and the holograph was read by another reference beam R* 
(conjugate of R) for 2 ms, which produces a phase-conjugated signal light S* that converges back to the acoustic focus 
and was detected by a photodiode (PDA-36A, 70 dB gain, Thorlabs). The ultrasound was on only during the writing of 
the holograph. The Sn2P2S6:Te crystal was a 6×6×6 mm3 cube and the intensity of the writing beams on the crystal was 
1.1 W/cm2. 
An absorptive target (made by adding black ink in gelatin) was sandwiched between two scattering media – a diffuser 
(DG10-120, Thorlabs), and an intralipid-gelatin phantom with a thickness of 2 mm (equivalent to 7 mean free paths at 
793 nm). The intralipid-gelatin phantom, mounted on a motorized linear stage, translates along the x-direction at a 
controllable speed during the recording and reading of the holograph. The movement of the intralipid-gelatin phantom 
causes the interference pattern formed by S and R beams on the PRC to decorrelate, and we can control the speckle 
decorrelation time by translating the phantom at different speeds.  
 
24 mm
R
S
UT
D ABT
IGPPD
L2 L3
Sn2P2S6:Te
crystal
L1
z
x
v
R*
PBS
     
 
Figure 1. Diagram for the experiment on TRUE optical focusing inside dynamic scattering media. An absorptive 
target was sandwiched between a diffuser and an intralipid-gelatin phantom which moves along x direction at 
speed v. PBS, polarizing beam splitter; PD, photodiode; Li, ith lens; PD, photodiode; D, diffuser; ABT: 
absorptive bar target; UT, ultrasonic transducer; IGP, intralipid-gelatin phantom; S, signal light; R, reference 
beam; R*, conjugated reference beam. 
2.2 Characterizing the relationship between speckle decorrelation time and phantom moving speed 
We characterized the relationship between speckle decorrelation time and phantom moving speed using the set-up 
shown in Fig. 2. The distance between the rear surface of the phantom and the focal plane of the objective was 22 mm, 
which was limited by the dimensions of the phantom mount. At each phantom moving speed v, we recorded a sequence 
of speckle patterns using a finite conjugate microscope objective [10×, numerical aperture (NA) = 0.1, tube length = 
160 mm, Leica] and a CMOS camera (208 frame per second, 320×108 pixels, Firefly MV, Point grey). We calculated 
the correlation coefficient between the first and each of the ensuing frames of the recorded speckle patterns. By fitting 
Proc. of SPIE Vol. 8943  894339-2
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the curve of speckle correlation coefficient versus time using a Gaussian function, we obtained the speckle decorrelation 
time Td, defined here as the time when the speckle correlation coefficient decreases to 0.1, for this speed.  
LT
24 mm
D
IGP
v
PBS
Obj Camera
z
x
Figure 2. Experimental set-up to measure the speckle decorrelation time. PBS, polarizing beam splitter; D, 
diffuser; IGP, intralipid-gelatin phantom; Obj, microscope objective; LT, lens tube.  
3. RESULTS
A sequence of speckle patterns when the intralipid-gelatin phantom was moving at a speed of 0.55mm/s was shown in 
Video 1. We can see there are translations and transformations of the speckle patterns.  
Video 1. A sequence of speckle patterns when the intralipid-gelatin phantom was moving at a speed of 0.55mm/
s. The video has a playback frame rate of 15 fps. http://dx.doi.org/0.1117/12.2039815.1 
The speckle correlation coefficient vs. time when the phantom moving speed is 0.055mm/s is shown in Fig. 3, from 
which we can obtain Td = 72 ms for this speed. The value of Td as a function of phantom moving speed v is shown in 
Fig. 4. By fitting the experimental data with Td = a/v, we obtain a = 4.23 ± 0.12 µm  (R2 = 0.9987 for the fitting). Using
Td = 4.23µm /v, we obtained Td = 7.7 ms when v = 0.55 mm/s (at this speed, it is impossible to measure the speckle 
decorrelation time accurately by camera since the frame rate is 208 fps). 
Proc. of SPIE Vol. 8943  894339-3
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0 20 40 60 80 100 1200
0.2
0.4
0.6
0.8
1
Time (ms)
S
pe
ck
le
 c
or
re
la
tio
n 
co
ef
fic
ie
nt
 
Fig. 3 The speckle correlation coefficient vs. time when the phantom moving speed was 0.055mm/s. 
0 0.02 0.04 0.06 0.08 0.10
200
400
600
800
1000
Phantom moving speed (mm/s)
S
pe
ck
le
 d
ec
or
re
la
tio
n 
tim
e 
(m
s)
 
 
Experimental data
Fit by Td = 4.23 µm / v
 
Fig. 4 The relationship between speckle decorrelation time and phantom moving speed. 
 
When the phantom was moving at a speed of v = 0.55 mm/s, the signals detected by the photodiode, when the 
ultrasound was on and off during writing the holograph, are shown in Fig.5. It can be seen that the maximum signal 
amplitude was always higher when the ultrasound was on than that when the ultrasound was off, which suggests that we 
could detect phase-conjugated light when Td = 7.7 ms. We did not observe the phase conjugated light when we shifted 
the ultrasound frequency by 100 kHz. 
To acquire an image of the absorptive target with a width of 3.6 mm, we scanned the gelatin phantom containing the 
target along the x-direction. At each scanning position, 10 TRUE procedures were performed and the signals were 
averaged. The one dimensional images of the target are shown in Fig. 6, for two cases – when the intralipid-gelatin 
phantom was static (Td > 300 ms) and when it moved at a speed of 0.55 mm/s (Td = 7.7 ms). It can be seen that the 
image acquired when Td = 7.7 ms has a similar quality as the one acquired when Td > 300 s, demonstrating that our 
system is fast enough to overcome the speckle decorrelation caused by the movement of the scattering medium. The 
resolution of the image is about 1 mm, which is close to the theoretical value of 0.87 mm determined by the ultrasonic 
transducer (3.5 MHz, NA = 0.25).               
 
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0
0.02
0.04
0.06
0.08
0.10
0.12
A
m
pl
itu
de
 (V
)
0 0.4
Time (ms)
ON OFF ON OFF ON OFF
50.4 50.8
 
Fig. 5 The signal detected by the photodiode when the ultrasound was on and off during the writing of 
the holograph. 
0 2 4 6 8 10
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Lateral position [mm]
N
or
m
al
iz
ed
 T
R
U
E
 s
ig
na
l
 Td > 300 s
Td = 7.7 ms
 
Fig. 6 One dimensional images of the absorptive target, when the intralipid-gelatin phantom was static 
(Td > 300 ms) and when the phantom was moving at a speed of 0.55 mm/s (Td = 7.7 ms). Solid and 
dashed lines represent smoothed data computed by a 4-point moving average of the raw data. The step 
size of scanning is 0.2 mm.                                               
 
 
                                  4. CONCLUSIONS 
 
Using a Te-doped Sn2P2S6 photorefractive crystal at a near-infrared wavelength, we achieved high-speed TRUE 
focusing inside moving scattering media with a speckle decorrelation time as short as 7.7 ms. As the demonstrated 
speed approaches the tissue decorrelation rate, this work is an important step forward toward in vivo applications of 
TRUE focusing in deep tissue imaging, photodynamic therapy, and optical manipulation. 
 
 
 
 
 
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   ACKNOWLEDGEMENT 
 
This work was sponsored in part by National Institute of Health grants DP1 EB016986 (NIH Director’s Pioneer Award) 
and R01 CA186567 (NIH Director’s Transformative Research Award) as well as National Academies Keck Futures 
Initiative grant IS 13. L. W. has a financial interest in Microphotoacoustics, Inc. and Endra, Inc., which, however, did 
not support this work. 
 
 
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High-speed time-reversed ultrasonically encoded (TRUE) optical focusing inside dynamic scattering media at 793 nm

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