Controlling light in scattering media

different focusingdifferent conditions. focusing The linear conditions. relation Thebe-
tween the enhancement tween the andenhancement the number and of segments the number of segments
linear relation bebjective
the demagnifying experiment.
with a lens 1:3 demagnifying system dent (not lens wavefront. system (not
ent. dent wavefront.
n). overfilled; we use only segments
by The the objective sample is overfilled; we The use algorithm only segmentsthat constructs the inverse diffusion
. all ple The inside shaped the wavefront pupil. algorithm Theishaped focused
that is evident constructs is focused untilis the evident inverse enhancement until diffusion thesaturates enhancement at saturates at
eThe
g strongly [Fig.
sample
1(a)].
(S), scattering andThe
wavefront a CCD sample camera
wavefront
uses (S), the and alinearity =1000. CCDuses camera All measured the linearity
of the
=1000.
scattering enhancements All measured of the scattering
process. were enhancements slightlyprocess.
be-werlow /4, the quarter-
theoretical field low maximum. in the the theoretical target, This maximum. isEunderstand-
Acknowledgements (2)
slightly be-
sintensity the totransmitted thepattern. sample intensity /4, quarterveple
plate; M,
The pattern. transmitted
The
mirror;
transmitted
BS, 50% nonfielable
in since the alltarget, perturbations E m , is move a linear m , This a linear is understandable
since
plate; d in/2, a specified
half-wave plate; M, the system away
fied
combination
mirror; BS, 50%
of
nonizing
P, polarizer. beam combination splitter; P, polarizer. of the fields from the coming global maximum. from the the global The N different main maximum. reasonThe formain de-
reason for de-
the fields coming
all perturbations
from the Nmove different
the system away
ental setup for
for
segments
viations
of the
frommodulator:
segments of the modulator: theviations optimal August from wavefront 15, 2007 the/ Vol. optimal is 32, residual No. 16 wavefront / OPTICS am-LETTERplitude themodulation optiplitude
inNthemodulation phase modulator, in the phase whichmodulator, in-
which in-
is residual 2309am-
npropagation own the sample in Fig. through and propagation 2. the opti-througby spatially the iselements described modu-
t mn
. 2.
N
stem by of the the elements
Focusing
unatrix.
Clearly, the magnitude E m to= 14% of t mn theA total
ttroduced mn of the
coherent an un-uncontrollen transmission matrix. Clearly, the magnitude m = n, intensity. 14% t
light
troduced
through bias in the opaque field amounting
dused
will be the highest when all terms inThe Eq. n=1 (1) saturation are
strongly
st when all terms in Eq. (1) are
scattering n e i an uncontrolled bias the field amounting
E
of mn A
the n e i n,
1
total intensity.
ator and focused
1
n=1
ofThe thesaturation enhancement mediaof the is the enhancement result of is the result of
hase. ine mple.
um-thced WeThe optimal determine num-
segment by cycling is its phase from 0 effectively limited
phase the for optimal a slow phase changes for a in the slowspeckle changes pattern. in the speckle This instability pattern. This instability
me elator I. M. Vellekoop* number
and A. P.
of
Mosk
segments for which
Complex Photonic Systems, Faculty of Science and Technology and MESA Research Institute,
nt
where at reduced a time Aby n and cycling
where
its n are, phase
A n and
respectively, from n 0
are, respectively, the amplitude and
effectively the amplitude limited theand
number of segments for which
.
number
For we each storesegment the phase at which the optimal phase could be measured. We estimate
University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
the of
phase N of
we store phase the phase of the at which light reflected the optimal from phase segment could be measured. n. Scatter- We estimate
the light reflected from segment n. Scatterargethighest.
intensity Atisthat the point highest. theAt that thatpoint the*Corresponding effective that author: enhancement the i.m.vellekoop@utwente.nl
effectivedecreases enhancement to eff
decreases to
nitors
tenan
one
ibution ment isof the
inthe phase
intenfeedback
diffuse After forbackground. the an measure-
After posted June 28, 2007 (Doc. ID 80762); published August 2, 2007
eff
segment with is theinal-
ackground. present
phase=/1+NT/T with the al-
Received March 6, 2007; p , where =/1+NT/T revised June T=1.2 14, 2007; s p accepted , iswhere theJune time T=1.2 21, 2007; needed s is the for time needed for
the measures
odulator.
have been for all performed segments, forthe
all segments, the
measurement one and measurement the persistence and the timepersistence T
We report focusing of coherent light through opaque scattering materials by control of the incident p
time T p
wavefront.
The multiply =5400 scattereds light is forms the atime focus =5400 with scalea sbrightness isatthe which that time is up the scale to a speckle factor atof which 1000pat-
higher the thanspeckle patformed
s is of set theto segments their stored is setvalues.
the tobrightness their stored of the normal values. diffuse transmission. © 2007 Optical Society of America
e tern of the
OCIS codes: 290.1990, 290.4210, 030.6600.
TiO 2 sample remains stable. Depending
sions the
wave
fromcontributions diffusion
tern of the TiO 2 sample remains stable. Depending
all segments frominterfere
all segments interfere
ructively
on the environmental theconditions, environmental T
target intensity and theis target at the intensity glotimizatioaximum.
n. TheAwith sample preoptimization a small num-
with a small num-
is at the glo-
p can conditions, be consider-
T p can be consider-
one of the most
ost
f Random scattering of light is what makes materials In Fig. 3 we show the intensity pattern of the
cantly ple segments improves significantly
such theassignal-to-
hod tile ratio.
improves the signal-to-
k white paint, milk, or human tissue opaque. transmitted light. In Fig. 3(a) we see the pattern that
layer
is generally This
of
method
rutile
Inapplicable these
ismaterials, generally to repeated
applicable
scatteringtoand interference
m time distort not reversal rely the incident on time wavefront reversal so strongly that the sample. The light formed a typical random
was transmitted when a plane wave was focused onto
of oes r systems 0.55±0.10 not rely and ondoes m
all spatial coherence
Fig. 1.
is
(Color
lost [1]. Incident
online)
coherent
Designspeckle of thepattern experiment.
with a low intensity.
(a) A plane
We then optimized
the wavefront so that the transmitted light fo-
of this etry absorption. sample absence Fig. Although 1. of(Color absorption.
light thediffuses maththically
the isthis the wave algorithm most ume is efficient, focused is the wave
online) Although Design math-
of the experiment. (a) A plane
through the medium and forms a vol-
speckle field on inmost is focused
thata disordered efficient, onina disordered medium, and a speckle pattern
dreds has no correlations medium, on a distance
learning larger
and cused a speckle to a targetpat-
tern is transmitted. (b) The wavefront of the incident light
area with the size of a single
nditions experimental
of times,
es, adaptive conditions than adaptive al-thmore iswavelength transmitted. learning of light. alhmplete
scrambling of the field makes it impossible to individually controlled segments is seen in Fig. 3(b),
The
(b)
com-
The wavefront speckle. The result of the for a wavefront incident composed light of 3228
e incident [9]
ve-
effective, mightwave-
be
is shaped and more
control
an effective,
so light
investi-
is shaped and an soinvesti-
n of such algorithms is on that propagation
that scattering makes the light focus at a predefined
its way. scattering using the makes well-established the light where focus a single at abright pre-
spot stands out clearly against
].
target.
ms is on its way. wavefront correction methods of adaptive optics (see
esity maximum defined
enhancement intensity target.
e.g., that [2]). enhancement can be that can be
We demonstrate focusing A new of coherent paradigm lightfor through light control in complex media!
162309-3/$15.00 eednumber is related of segments to the number that
disordered© scattering
2007 are of segments
Optical
that
media by the
Society
are
construction
of America
00 to of
cident
describe © wavefront. 2007 the incident Optical
wavefronts For a
wavefront.
disorstants
Society of For America a disormedium
that invert diffusion of light. Our method
t
the
mn are
constants
statistically relies interference t mn in-
are statistically and universally in-applicable to
the diffuse background. The focus was over a factor of
1000 more intense than the nonoptimized speckle
pattern. By adjusting the target function used as
feedback it is also possible to optimize multiple foci
simultaneously, as is shown in Fig. 3(c) where a pattern
of five spots was optimized. Each of the spots