Focusing light deep inside living tissue has not been achieved despite its promise to play a central role in biomedical imaging, optical manipulation and therapy. To address this challenge, internal-guide-star-based wavefront engineering techniques—for example, time-reversed ultrasonically encoded (TRUE) optical focusing—were developed. The speeds of these techniques, however, were limited to no greater than 1 Hz, preventing them from in vivo applications. Here we improve the speed of optical focusing deep inside scattering media by two orders of magnitude, and focus diffuse light inside a dynamic scattering medium having a speckle correlation time as short as 5.6 ms, typical of living tissue. By imaging a target, we demonstrate the first focusing of diffuse light inside a dynamic scattering medium containing living tissue. Since the achieved focusing speed approaches the tissue decorrelation rate, this work is an important step towards in vivo deep tissue noninvasive optical imaging, optogenetics and photodynamic therapy

Grabar, Alexander A.

Lai, Puxiang

Liu, Yan

Ma, Cheng

Wang, Lihong V.

Xu, Xiao

Caltech Authors - Main

1 
 
Supplementary Figures 
 
Supplementary Figure 1. Schematic of the experimental set-up for imaging an absorptive 
target inside a dynamic scattering medium with TRUE optical focusing. Abbreviations: AOM, 
acousto-optic modulator; AT, absorptive target; BB, beam block; BC, beam condenser; BE, beam 
expander; EOM, electro-optic modulator; 0f , frequency of the laser light; af , frequency detuning 
applied by AOMs, which was also the frequency used to drive the ultrasonic transducer; GD, 
ground glass diffuser; HWP, half-wave plate; IP, intralipid-gelatin phantom, mounted on a 
motorized linear stage; L, lenses; L3 & L4 were combined as L drawn in Fig. 2a, 2d of the main 
text, and were combined as L1 drawn in Fig. 2i and Fig. 3c of the main text; LS, linear stage; M, 
mirror; PBS, polarizing beamsplitter; PD, photodiode; PRC, photorefractive crystal; R, reference 
beam; R*, reading beam, phase conjugate to R; S, sample light; S , frequency-down-shifted sample 
light (signal light); *S , time-reversed signal light; MS, mechanical shutter; UT, ultrasonic 
transducer. 
HWP4
PBS2
HWP1
PBS1
BC
BE2
BB1
HWP2
AOM1
Laser EOM
HWP3
BE1
PD
M1
BB2
AOM2
L1
PBS3
L2
HWP5
GD
MS1
AT
UT(fa)
IP
L3 L4
BB3PRC
M2
M3
M4
M5
M6
MS2
f0 = c / 793 nm
R*(f0)
R(f0)
S_(f0)S(f0+fa)
LS2
LS1
S_(f0)
*
2 
 
 
Supplementary Figure 2. Photodiode signal amplitudes of the detected 
*
S  light diffracted 
from the holograms that were recorded when the focused ultrasonic modulation was on and 
off. The frequency of the focused ultrasonic modulation was 3.5 MHz (equal to the difference 
between the frequency of the light that illuminated the sample and the frequency of the reference 
beam) in (a), and shifted to 3.4 MHz in (b). A constant offset was subtracted in both figures. 
  
Time (ms)
ON OFF ON OFF
0 0.4 50.0 50.4 100.0 100.4 150.0 150.4
A
m
p
lit
u
d
e
 (
m
V
)
0
20
40
60
80
100
120
a
Time (ms)
ON OFF ON OFF
0 0.4 50.0 50.4 100.0 100.4 150.0 150.4
A
m
p
lit
u
d
e
 (
m
V
)
0
20
40
60
80
100
120
b
3 
 
 
Supplementary Figure 3. Light intensity distributions on the focal plane of an objective 
(Obj1) before and after a living-mouse ear was inserted as a scattering medium. (a) The 
experimental set-up. The focal plane of objective 1 (AC080-020-B-ML, Thorlabs Inc., USA. 
Working distance = 18 mm, NA = 0.2) was imaged by objective 2 (Leica, E1 ACHRO, 10×, NA 
= 0.25) and a CMOS camera (FMVU-03MTM, Point Grey, Canada). (b) The light intensity 
distribution on the focal plane of objective 1. The full width at half maximum focal spot size was 
2.4 µm on the object plane, which was close to the diffraction-limited focal spot size (2.0 µm). (c) 
A living-mouse ear (E) was inserted between objective 1 and its focal plane. The distance between 
the mouse ear and the focal plane was 14 mm, which was the same as the distance between the 
mouse ear and the ultrasonic focus in the TRUE focusing experiment illustrated in Fig. 3c. (d) The 
light intensity distribution on the focal plane of objective 1. The focus in (b) could no longer be 
observed due to scattering of the mouse ear. Abbreviations: E, mouse ear; IMP, image plane; Obj, 
objective; OBP, object plane. Scale bar, 1 mm. 
Without a mouse ear With a mouse ear
Obj1 Obj2 Camera
a
b d
Obj1 Camera
c
21 mm
Obj2
14 mm18 mm
21 mm
E
IMPOBP IMPOBP
N
o
rm
a
liz
e
d
 i
n
te
n
s
it
y
1
0
4 
 
 
Supplementary Figure 4. A photo of the set-up used to measure the speckle correlation time 
after blocking the blood flow in the mouse ear. A metal bar pressed the ear against a stiff acrylic 
wall to block its blood flow. 
 
 
 
 
 
 
5 
 
 
Supplementary Figure 5. Simulation of TRUE optical focusing inside a dynamic scattering 
medium with a speckle correlation time of 5.2 ms. (a) The correlation coefficients between 
different speckle patterns. The ith speckle pattern is the speckle pattern on the PRC (formed by 
signal light S ) at the time of i ms. (b) The correlation coefficients between the speckle pattern at 
0 ms, and each of the ensuing speckle patterns, from which c  = 5.2 ms was determined. (c) The 
correct hologram formed by the interference between S  and the reference beam R at 10 ms. The 
partially blurred hologram within the hologram writing time (10 ms) (d) can be decomposed into 
a partially blurred hologram within c  ((e), formed by the integration of the interference patterns 
between the S  and R at 5
 – 10 ms) and an incorrect hologram ((f), formed by the integration of 
the interference patterns between S  and R at 0
 – 4 ms). (g–j) The light intensity distributions on 
Plane A (i.e., the x-z plane intersecting the acoustic axis in Fig. 1a) when the corresponding 
holograms in (c−f) were read. (k) The ultrasonic modulation efficiency distribution. All the images 
were normalized by their own maximum values.  
 
 
0
1
c d e f
g h i j
a b
0
0.2
0.4
0.6
0.8
1
S
p
e
c
k
le
 c
o
rr
e
la
ti
o
n
 
c
o
e
ff
ic
ie
n
t
Time (ms)
0 1 2 3 4 5 6 7 8 9 100 1 2 3 4 5 6 7 8 9 10
Speckle pattern index
S
p
e
c
k
le
 p
a
tte
rn
 in
d
e
x
C
o
rr
e
la
ti
o
n
 c
o
e
ff
ic
ie
n
t
N
o
rm
a
liz
e
d
 i
n
te
n
s
it
y
1
0
N
o
rm
a
liz
e
d
 i
n
te
n
s
it
y
1
0
k0
1
2
3
4
5
6
7
8
9
1
0
6 
 
Supplementary Notes 
Supplementary Note 1: The required number of independent control elements increases 
quadratically with focusing depth. 
In wavefront shaping, the focusing efficiency   is defined as the ratio of the energy deposited at 
the targeted location (where a guide star is placed) to that reflected by a SLM (with pixel number 
N). Due to reciprocity1, the efficiency is equal to the ratio of the number of optical modes on the 
SLM to the total number of output modes that emanate from the guide star. The total number of 
optical modes, TotalN , can be estimated by 
2 2
Total 4 / ( / 2)N l  , where l  is the depth of the 
targeted location and   is the wavelength of the laser light in the scattering medium;  /2 is the 
approximated speckle size. So, 2 2Total( / 4) / / 16 / ( / 2)N N N l       , which is proportional 
to 
2/N l . Thus, in order to keep the focusing efficiency, the number of independent control 
elements N  should increase quadratically with focusing depth l .  
It should be noted that the above conclusion does not hold if we consider from the 
perspective of focusing quality. The focusing quality, in terms of peak to background ratio2 (PBR), 
can be calculated by  (N+1)/(4M), where M is the number of modes in the focus. M  = 
2
x y / ,d d d  where xd , yd  are the dimensions of the focus perpendicular to the optical axis z, and 
d is the speckle size. If we focus light inside scattering media beyond a certain depth (denoted as 
L) where speckle is fully developed, the speckle size can be approximated as / 2  and it no longer 
decreases with depth, so the PBR will stay unchanged beyond L.  
 
7 
 
Supplementary Note 2: Remarks on the speckle patterns (shown in Supplementary Movie 
1a) formed by light passing through a living-mouse ear. 
The light intensity at each position on the camera has contributions from both blood-scattered 
photons and non-blood-scattered photons. So, the output of each pixel of the camera, ( , )V r t , can 
be expressed as:  
/2 /2 22
s d
/2 /2
( , ) ( , ) ( )exp( ) ( , )exp( )
t T t T
t T t T
V r t E r d E r i E r i d     
 
 
      . 
Here, s ( )E r  is the complex amplitude of the net electric field (E-field) of non-blood-scattered light 
at position r , which does not change over time; d ( , )E r   is the complex amplitude of the net E-
field of blood-scattered light at position r  and time  ;   is the frequency of the laser light; and 
T is the camera’s exposure time. The intensities of the bright speckle grains in the seemingly-static 
background pattern fluctuate over time at small amplitudes, which can be explained as follows. In 
these speckle grains, the phasor s d( , ) ( ) ( , )E r t E r E r t   is a vector sum of a large constant vector 
in the complex plane and a small vector which rotates randomly over time and changes its length. 
Since s ( )E r  is much larger than d ( , )E r t , the resulting amplitude of the phasor ( , )E r t  can be 
approximated by s ( )E r , thus the intensity ( , )I r t  appears to be constant in these speckle grains. 
 
 
 
8 
 
Supplementary Note 3: Simulation of TRUE optical focusing inside a dynamic scattering 
medium with a speckle correlation time of 5.6 ms.  
Similar to the procedures described in Methods, the E-field of the ultrasonically encoded light on 
the PRC can be calculated by b Ta , where T is the transmission matrix (dimension = 625625) 
and a is the ultrasonically encoded light field (dimension = 6251) on the x-z plane intersecting 
the acoustic axis (denoted as plane A, see Fig. 1a). In our phantom experiment, since the speckle 
pattern 
2
b  had a speckle correlation time ( c ) of 5.6 ms when the phantom was moved at 0.100 
mm/s, we simulated 11 transmission matrices 
iT  (i = 0, 1, 2,⋯, 10, representing the scattering 
medium at the time of i ms), whose elements  
jki
T  were correlated because they were sampled 
from 9-point moving averaging of a sequence of random complex numbers. Specifically, 
4
4
[ ] [ ] / 9
p i
jk jk
p i
 
 
 i pT M  (i = 0, 1, 2,⋯, 10), where pM  (p = 4, 3, ⋯, 14) are 19 independent 
random matrices whose elements follow the circular Gaussian distribution, and † ˆp pM M I  , where 
“ † ” denotes conjugate transpose and Iˆ  is the identity matrix. The speckles at different time,
i ib = Ta , were correlated with a c  = 5.2 ms (see Supplementary Fig. 5a–5b), similar to the 
measured value ( c  = 5.6 ms) in our experiments. ib  interfered with a reference beam R (whose 
E-field was represented by a vector R (dimension = 6251) in which all elements were 1) and 
formed an interference pattern 
2
i ibI = + R . The hologram recorded within the writing time ( wt  
= 10 ms) was proportional to a weighted summation of iI  (see Supplementary Fig. 5d) as in: 
1010 ms 2
w r
0
0
( 10 ms) (t )exp( / )d ,i
t
i
wt t    


      wt ih h I b  R   
9 
 
          r(10e p / .)xi iw     
Here, r  = 7 ms is the response time of the PRC at 1 W cm
−2. If the response time of the PRC was 
much shorter than c , h(t = 10 ms) ≜ Correcth  10I  (see Supplementary Fig. 5c). It can be seen 
that although 
wt
h  was partially blurred compared with 
Correcth , it was still highly correlated with 
Correcth  (r = 0.74). wth  could be further decomposed into cτh and Wrongh . 
10
2
5
i
i
w

 cτ ih b  R  was 
the hologram integrated over a duration of c  starting at time w ct  . Compared with wth , cτh  
was expected to resemble Correcth  more closely due to reduced blurring (r = 0.81, see 
Supplementary Fig. 5e). Wrongh
4
2
0
 ib  R
i
iw  was the hologram integrated from time 0 to 
w ct  . Since ib  (i = 0 – 4) was poorly correlated with 10b , Wrongh  was expected to be poorly 
correlated with 
Correcth  (r = 0.12, see Supplementary Fig. 5f).  
In the time-reversal step, the hologram 
wt
h  was read by a reading beam R* (whose E-field 
was represented by a vector *R ) at t = 10 ms, and the −1st order diffracted light was generated, 
which was proportional to 
10
0
i
i
w

 *ib . At this time, the dynamic scattering medium (i.e. the 
intralipid-gelatin phantom) was represented by the transmission matrix 
10T , and the light field 
distribution on plane A in Fig. 1a, 

wt
a , was proportional to 
10
0
T
i
i
w

 *10 iT b  (see Supplementary Fig. 
5h for the intensity distribution 
2

wt
a  ), where the superscript “T ” denotes matrix transpose. If 
Correcth  was read, the field distribution on plane A, 

Correcta , was proportional to 
T *10 10T b a  
10 
 
(assuming 
† ˆ10 10T T I ), representing the ideal TRUE focus (see Supplementary Fig. 5g for 
2

Correct
a ). The background in 
2

Correct
a  was due to partial time-reversal2 (i.e. not all the output 
modes were detected and time-reversed). Compared with 
2

Correct
a , there was a stronger 
background in 
2

wt
a . This elevated background could be better understood by studying the readout 
of the hologram 
cτ
h  and Wrongh  (   w ct τ Wrongh h h ), simulated by 
10
5
T
i
i
w 

 cτ 10 ia T b  and 

Wronga  
4
0
T
i
i
w

 10 iT b , respectively (see Supplementary Fig. 5i−5j for the intensity distributions 
2

cτ
a  and  
2

Wrong
a ). It can be seen that the little-blurred hologram 
cτ
h  generated a TRUE focus with good 
fidelity, while the incorrect hologram 
Wrongh  generated a background 
2

Wrong
a  with no focus. For 
the background 
2

Wrong
a , the energy of light was broadly distributed in space so that the intensity 
at each position was much lower than the intensity in the TRUE focus in 
2

cτ
a . Because of this, 
the background in 
2

wt
a  is only slightly stronger than the background in 
2

Correct
a , and thus the 
quality of the TRUE focus in 
2

wt
a  is comparable with that in 
2

Correct
a  (r = 0.93).  
11 
 
References 
1. McMichael, I., Ewbank, M.D. & Vachss, F. Efficiency of phase conjugation for highly 
scattered light. Opt. Commun. 119, 13-16 (1995). 
2. Wang, Y.M., Judkewitz, B., DiMarzio, C.A. & Yang, C. Deep-tissue focal fluorescence 
imaging with digitally time-reversed ultrasound-encoded light. Nat. Commun. 3, 928 (2012). 
 
 
 


Optical focusing deep inside dynamic scattering media with near-infrared time-reversed ultrasonically encoded (TRUE) light

https://authors.library.caltech.edu/67911/2/ncomms6904-s1.pdf

Optical focusing deep inside dynamic scattering media with near-infrared time-reversed ultrasonically encoded (TRUE) light

Abstract

Similar works

Full text

Available Versions

Caltech Authors - Main