spatio-temporal control of light in complex media
DESCRIPTION
Ph.D. defense of Sebastien Popoff (ESPCI - Institut Langevin) 14/12/2011TRANSCRIPT
Spatio-temporal control of
light in complex media
SébastienPOPOFF
Directors : M. Fink et C. BoccaraSupervisors : S. Gigan et G. Lerosey
114/12/2011
Introduction
214/12/2011
Imaging in optics
Look smaller
Look furtherWhat are optical systems useful for?
Introduction
3
Imaging in optics
Aberrations
Atmospheric
aberrations
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Introduction
414/12/2011
Real-time correction of aberrations with adaptive opticsCourtesy: F. Lacombe/observatoire de Paris
Wavefront Sensor(ex: Hartmann-Schack)
Wavefront Sensor(ex: Hartmann-Schack)
Wavefront correction(ex: deformable mirror)Wavefront correction
(ex: deformable mirror)
Real-time control loop
Imaging device (CCD)
Imaging device (CCD)
Adaptive optics
Introduction
514/12/2011
AO convenient for wavefront perturbation :
Large spatial scale / small amplitude
Relevant for astronomy, free space optics, some biological applications…
Strong perturbations
What about stronger pertubations?
Multiple scattering, multiple reflections…
Techniques in Acoustics / Electromagnetism
Time reversal
Can we apply them in optics?
Introduction
614/12/2011
Hypothesis : linearity, reversibility of wave equation
Time reversal
Time reversal mirror
Spatial and temporal focusing
One-channel time reversal
Temporal focusing Spatial focusingC. Draeger and M. Fink, Phys. Rev. Lett., 79, 407 (1997)
(Ultrasound experiment)
A. Derode, P. Roux et M. Fink, Phys. Rev. Lett., 75, 4206 (1995)
importance of reflections
Introduction
714/12/2011
Time reversal
Monochromatic counterpart of TR: Phase conjugation
If no access to temporal details
Spatial focusing
Reverse time conjugate the phase
Introduction
814/12/2011
New techniques of light control
Spatial light modulators (SLM)
Deformable mirrors: up to 4000 elements – kHz – expensiveLiquid cristals technology: ~1 million pixels – ~100Hz – cheap
Temporal control:
- Pulse shaping
- Modulators
Acousto-optic modulators (up to GHz)
Electro-optic modulators ( > 10 GHz)
Allow a high degree of control on light propagation!
What about optics?
Outline
914/12/2011
I. Transmission matrix in scattering media
II. Reflection matrix and optical “DORT”
III. Complex envelope time reversal
Transmission matrix in scattering media
Introduction
1014/12/2011
In every day life…
…clouds… …white paint…
…biological tissues !
Transmission matrix in scattering media
Scattering: complex but coherent process
11
Simple caseYoung slits:Fringes : Two waves interference
Thick disordered media:Speckle- Multiple events of diffusion- Position of diffuser unknown
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Transmission matrix in scattering media
Multiple scattering: too complex
12
>108 particlesImpossible to simulate
100μm
1mm²
White paint(particle size ≤ 1 μm)
Only predictions accessible: Mesoscopic physicsStatistical properties on transport, correlations, fluctuationsNo knowledge of the field for a given realization
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Transmission matrix in scattering media
A pioneering experiment
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A speckle grain:• Interference of a great number of optical paths Sum of terms of random phases (phasors)• Contributions in phase constructive interferences of multiple paths
Transmission matrix in scattering media
A pioneering experiment
1414/12/2011
Transmission matrix in scattering media
Improve the resolution
λf1/D1
Acoustics: A. Derode, P. Roux and M. Fink , Phys. Rev. Lett., 75, 4206 (1995)Optics: I. M. Vellekoop, A. Lagendijk and A. P. Mosk, Nature Photonics 4, 320 - 322 (2010)
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λf2/D2
Transmission matrix in scattering media
First experiment
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Remarks:
- 1 optimization = 1 focal spot Need to optimize for each target- Optimization: only indirect information on the medium
Can we go further?
Transmission matrix in scattering media
Basic principle
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SLM : array of pixels Linear system CCD camera : array of pixels
= ==
Transmission matrix in scattering media
Linear media and matrices
inn
nmn
outm EhE
N..1
outE Output field
inE Input field.out inE H E
Ou
tpu
t k
Free space
Identity Matrix
Direct access to information
Input k
Scattering sample
Seemingly Random Matrix
Information shuffled but not lost!O
utp
ut
k
Input k
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Transmission matrix in scattering media
Setup
Objective : Measuring the Transmission MatrixHypothesis : Coherence of the illumination, Stability of the Medium, Linearity
Input ControlSpatial Light Modulator (SLM) in Phase Only Modulationmacropixel ↔ k vector
Output Detection
(Interferometry)1 macropixel ↔ k vector
Sample
ZnO L = 80 ± 25
μm l* = 6 ± 2 μm
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Transmission matrix in scattering media
Measurement of the Transmission Matrix
1..Nout inm mn n
n
E h E
Step by step reconstruction
Pixel off Pixel on
, , , etc…
In practice, we use Hadamard vectors
φ=+π/2
φ=-π/2
(Phase-only SLM,SNR)
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E. Herbert, M. Pernot, G. Montaldo, M. Fink and M. Tanter, IEEE UFFC, 56, 2388, (2009)
Transmission matrix in scattering media
Construction of the Transmission Matrix
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Transmission matrix (filtered to remove effect of the reference)
Transmission matrix in scattering media
Applications: Focusing
What can we do with the TM?Calculate the mask to display!
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Plane wave illumination
SL
MS
LM
SL
M
CC
DC
CD
CC
D
sample
sample
sample
Only one measurement of the TM
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Transmission matrix in scattering media
Applications: Focusing
* target.out tE H H E* targetin tE H E
N=256 modes (16x16 pixels on the CCD)
N=2
56 *tH H
Strong values in the diagonal We can focus everywhere
Non-diagonal elements not zero Imperfection inherent to PC
23
Which mask to focus?
?Phase conjugated mask
Put contributions in phase on one spot ↔ A. Mosk experiment
Transmission matrix in scattering media
14/12/2011 24
Can we go beyond phase conjugation?
Transfer of information (image) Statistical properties of the TM
Transmission matrix in scattering media
Statistical properties of the transmission matrix
Tool: Singular Value Decomposition (generalization of diagonalization for any Matrix)
We study the distribution of (normalized) singular values ρ(λ)
1
2
0 0 0
0 0 0
0 0 ... ...
0 0 ... N
--i >0 represents the amplitude transmission through the ith channel.
-Σλi2 corresponds to the total transmittance for a
plane wave
*H U V Output basis
Input basis
14/12/2011 25
Transmission matrix in scattering media
Statistical properties of the transmission matrix
Transmission matrix (filtered to remove effect of the
reference)
A general Random Matrix Theory prediction : quarter circle law distribution
14/12/2011 26
Signature of randomnessIn acoustics:A. Aubry et al., Phys. Rev. Lett., 102, 84301, (2009)
Transmission matrix in scattering media
Applications: Image transmission
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sample
SL
MC
CD
?
Finding Eobj knowing Eout Shaping
TM
. .img out objE O E OH E We want OH close to Identity
Transmission matrix in scattering media
Applications: Image transmission
What operator to reconstruct a complex image? (knowing the TM)
Inversion : 1O H Perfect reconstructionNot stable in presence of noise
OH I
1
2
0 0 0
0 0 0
0 0 ... ...
0 0 ... N
1
2
1/ 0 0 0
0 1/ 0 0
0 0 ... ...
0 0 ... 1/ N
low λi high 1/λi If noise, H-1 dominated by noise !
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Transmission matrix in scattering media
Applications: Image transmission
Very stableReconstruction perturbated when the image is complex
Phase Conjugation : *tO H*tOH H H
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What operator to reconstruct a complex image ?N
=100
N=100
*tH H
λi λiH *tH
Transmission matrix in scattering media
Applications: Image transmission
(Noiseless)0 1O H
Optimal Operator for σ = Noise variance
1* *.t tH H I HO
A tradeoff : Tikhonov Regularization(A.N.Tikhonov, Soviet. Math. Dokl., 1963)
(Noisy) *tO H
14/12/2011 30
Rec
on
stru
ctio
n
Transmission matrix in scattering media
Applications: Image transmission
Experimental Results :
Input Mask (Eobj)
Inversion
C = 11%
Phase Conjugation
C = 76%
Regularization
C = 95%
Output Speckle (Eout)
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Transmission matrix in scattering media
Applications: Image transmission
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Transmission matrix in scattering media
Conclusion and Perspective
- Focusing and information transfer through complex medium
We did:
- Develop a faster setup (micromirror arrays, ferromagnetic SLMs) for biological purposes
More:
References :- S.M. Popoff, G. Lerosey, R. Carminati, M. Fink, A.C. Boccara and S. Gigan, Phys. Rev. Lett 104, 100601, (2010)- S.M. Popoff, G. Lerosey, M. Fink, A.C. Boccara and S. Gigan, Nat. Commun., 1,1 ncomms1078 (2010)
Related papers :- I.M. Vellekoop and A.P. Mosk, Opt. Lett. 32, 2309 (2007).-Z. Yaqoob, D. Psaltis, M.S. and Feld and C. Yang, Nat. Phot., 2, 110 (2008).
And many many more !
- Study more complex media (Anderson localization, photonic cristals…)
- Studied statistical properties of a scattering medium
14/12/2011 33
From transmission matrix to reflection matrix
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SLM
Linear sample CCD camera
= ==
CCD camera : array of pixels
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SLM : array of pixels
Linear sample
From transmission matrix to reflection matrix
Reflection matrix and optical “DORT”
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I. Transmission matrix in scattering media
II. Reflection matrix and optical “DORT”
III. Complex envelope time reversal
Reflection matrix and optical “DORT”
Introduction
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Applications of the RM for multiply scattering media?
Measure of the CBS cone as in acoustics
Optics: M.P.V. Albada and A. Lagendijk, Phys. Rev. Lett., 55,2692 (1985)Acoustics: A; Tourin et al, Phys. Rev. Lett., 79, 3637, (1997)
A. Aubry et al., Phys. Rev. Lett., 102, 84301, (2009) Problem:Measurement in optics: noise, specular reflections…
Application in freespace / aberrating medium (simple scattering):The DORT method in optics (suggested by A. Aubry)
Reflection matrix and optical “DORT”
Introduction
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0KE
* *0KK E
*0KK KE
* *0K E
0E
*0K KE
Itera
tive
time
reve
rsal
Reflection matrix and optical “DORT”
Introduction
3914/12/2011
1
2
0 0 0
0 0 0
0 0 ... ...
0 0 ... N
21 0 0 0
2 0 0 0 0
0 0 ... ...
0 0 ... 0
n
n
2 *0
nn tE K K E
2 2 21 2 ...n n n
N
*K U V Output basis
Input basis
22 *0
nnE U V E
At step n:
SVD of K:
Reflection matrix and optical “DORT”
Introduction
4014/12/2011
1 strong singular value ↔ 1 scatterer ? DORT: - Mesure of the RM- SVD of the RM- Display the first singular vectors
Reflection matrix and optical “DORT”
Introduction
4114/12/2011
Works with an aberrating medium(single scattering only)
Hypothesis: linearity, single scattering regime
Reflection matrix and optical “DORT”
Setup
Control
Aberrating medium
Scatterers:100 nm isotropic gold particles on a glass slide
Cross Polarization
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Reflection matrix and optical “DORT”
Problems
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The energy measured should only come from the scatterers
Problem:- Important contributions of specular reflections !
Solutions:- Cross polarization - (Dark field)
x
y
k
inP
x
y
k
outP
Focal planeAberating
medium
100 nm gold beads
Reflection matrix and optical “DORT”
Selective Focusing
14/12/2011 44
Reflection
Control
Reflection matrix and optical “DORT”
Setup
Aberrating medium
Scatterers:100 nm isotropic gold particles on a glass slide
Cross Polarization
14/12/2011 45
Reflection matrix and optical “DORT”
Adaptive optics
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Aspect of the first input singular vector (phase mask)
Free space ~ lens With aberrating mediums
y component of the output field
Reflection matrix and optical “DORT”
Modes of a single particles
Particle ~ 3 orthogonal dipoles
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Need for sufficient NA to excite the dipoles with one input polarization
Reflection matrix and optical “DORT”
Modes of a single particleN
um
be
r o
f S
V
-
(vector diffraction theory)
Pz Dipole Px Dipole
Py Dipole
Theoretical singular value distribution
14/12/2011 48
Reflection matrix and optical “DORT”
Modes of a single particle
14/12/2011 49
Reflection matrix and optical “DORT”
Modes of a single particleN
um
be
r o
f S
V
-
Pz Dipole
Px Dipole
Py Dipole
Experimental singular value distribution
? Pz dipole Px dipole
14/12/2011 50
Reflection matrix and optical “DORT”
Conclusions and Perspectives
- Selective focusing through aberrating medium
We did:
- Reduce specular reflections (dark field)
More:
References :- S.M. Popoff, A. Aubry ,G. Lerosey, M. Fink, A.C. Boccara and S. Gigan, Phys. Rev. Lett. (in press)
- Develop a setup more stable (laser) Pattern analysis for characterization, plasmonic, …
- Radiation pattern analysis of a single nanobead
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Complex envelope time reversal
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I. Transmission matrix in scattering media
II. Reflection matrix and optical “DORT”
III. Complex envelope time reversal
Complex envelope time reversal
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Spatio-temporal focusing in complex media
J. Aulbach et al., Phys. Rev. Lett., 106,103901 (2011)
O. Katz et al., Nat. Photonics, 5, 372, (2011)
With spatial degrees of freedom
D. McCabe et al., Nat Commun., 2, 447, (2011)
With temporal degrees of freedom (pulse shaping)
Complex envelope time reversal
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Modulation for telecommunications
When only low frequencies accessible Modulation (Telecomunications)
=Detector
Use high frequency waves with ‘low’ frequency generator / oscilloscope
Independent modulation in phase and quadrature (IQ)
Modulators and demodulators widely available for telecommunications ($$$)
x
Propagation
Carrier wave Signal
Lower bandwidth but very high spectral resolution
Complex envelope time reversal
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Time reversal
TR = reverse modulation + conjugate carrier wave
G. Lerosey et al., Phys. Rel. Lett., 92, 193904 (2004)
Spatial and temporal focusing
( ) ( ). j tABh t E t e
-t( ) ( ). j tABh t E t e
Pulse in modulation at A (on one quadrature)
Time (μs)
Signal received at A after time reversal
Time (μs)
Complex envelope time reversal
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Setup
Setup
Modulation Part:- 10 GHz arbitrary waveform generator- Triple Mach-Zehnder modulator
Demodulation Part:- Interferometric detection of 2 quadratures- 50 GHz oscilloscope
Complex envelope time reversal
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Modulation / Demodulation
Demodulation Part:- Interferometric detection of 2 quadratures- 20 GHz oscilloscope
Modulation Part:- 10 GHz arbitrary waveform generator- Triple Mach-Zehnder modulator (Photline)
A
B
Complex envelope time reversal
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Bandwidth vs medium’s correlation frequency
Lifetime in system need to be >> 1/Δf modulation
G. Lerosey et al., Phys. Rev. Lett., 92, 193904 (2004)
Electromagnetism experiment:Huge cavity needed ( > 13m3) Huge number of modes (λ2.45GHz = 12cm )
Same problem in opticsNeed for strong dispersion / strong enough signal
Impulse response B
Time (μs)
Complex envelope time reversal
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Temporal focusing
input output
Evanescent coupling
Looped single mode cavity
Impulseresponse
Channel I Channel Q
Numerical time reversal(correlations)
Complex envelope time reversal
6014/12/2011
Temporal focusing
Numericaltime reversal(correlations)
Experimental time reversal
Channel I Channel Q
Demonstration of the compression of the impulse response by time reversal
Application : fiber optics telecommunication
Complex envelope time reversal
6114/12/2011
Towards spatio-temporal focusing
Problems : Weak signals / Need for very strong dispersion
Multimode fiber cavity
Still in progress!
Chaotic3D cavity
input output
Scattering medium
Conclusion
6214/12/2011
I. Transmission matrix in scattering media- Spatial focusing
- Image transmission
- Singular value analysis
II. Reflection matrix and optical “DORT”- Selective focusing through an aberrating medium
- Scattering pattern analysis
III. Complex envelope time reversal- Temporal focusing
- Towards spatial and temporal focusing...
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Remerciements :
Collaborateurs :Sylvain GiganGeoffroy LeroseyAlexandre AubryRemi CarminatiMathias FinkClaude Boccara
Préparation échantillons :Laurent BoitardGilles TessierBenoit MalherOlivier Loison
Aide au montage :Aurélien PeillouxSébastien BidaultThéorie :
Samuel Grésillon Caractérisation des échantillons :Matthieu LeclercSupport divers :
Marie Lattelais
Collaborateurs
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Sylvain GIGAN
Geoffroy LEROSEY
Mathias FINK
ClaudeBOCCARA
Rémi CARMINATI
AlexandreAUBRY
Transmission matrix in scattering media
Statistical properties of the transmission matrix
Artefact :« raster » effect
due to the amplitude of Sref
Observed Matrix
.obs refH H
Effect of ref
14/12/2011 65
Transmission matrix in scattering media
Setup
Objective : Measuring the Transmission MatrixHypothesis : Coherence of the illumination, Stability of the Medium, Linearity
Input ControlSpatial Light Modulator (SLM) in Phase Only ModulationA macropixel ↔ A k vector
Output Detection
CCD CameraA macropixel ↔ A k vector
Sample
ZnO L =
80 ± 25 μm l* = 6 ± 2
μm
14/12/2011 66
Matrice de Transmission Optique d’un Milieu Diffusant
Applications : Transmission d’Image
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Efficacité de la reconstruction en fonction de σ
σ
Filtrage inverse Filtrage adapté
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Matrice de Transmission et Milieu Diffusant
Propriétés Statistiques de la Matrice de Transmission
Filtrage de Hobs pour éliminer les effets de la référence
obsfil mnmn obs
mnm
hh
h
Matrice FiltréeMatrice Observée
Une prédiction générale des matrices aléatoires : “Loi du quart de cercle”
68
Transmission matrix in scattering media
Applications : Focusing
Expected focusing from measured matrix
Experimental focusing
Target
Theoretical focusing VS Experimental focusing
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Transmission matrix in scattering media
Stability and Measurement Time
TM Measurement Time (1024x1024 )
~ 15 min
Decorrelation Time of ZnO deposit
~ 1 hour
Decorrelation Time of Biological Tissues << 1s
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Reflection matrix and optical “DORT”
Introduction
7114/12/2011
The reflection matrix
nE
outE Output field
inE Input field
.out inE K E
1..Nout inm mn n
n
E k E
n
mmn nk E
Signal received at A
Optical time reversal in modulation
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Time reversal
Time reversal in modulation
Pulse in modulation at A (on one quadrature)
TR = reverse modulation + conjugate carrier wave
A
B
Signal received at B
G. Lerosey et al., Phys. Rel. Lett., 92, 193904 (2004)
Spatial and temporal focusing
Transmission matrix in scattering media
The matrix model : A conveniant model
Free space Multiply scattering sample
Matrix Description to link input / output k vectors
Detrimental to Conventional Optical Techniques
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Transmission matrix in scattering media
Measuring the Complex Output Field
uniform
2
outout EI
2
refi
out EeEI
refE
3 1
2 20 ioutE I I i I e I
3 1
2 20
*.
i
out ref
I I i I e I
E E
No phase information !
Interferometric stability for several minutes !
not uniformrefE
OK as long as ….. …. is constantrefE
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Transmission Matrix of an Optical Scattering Medium
Theoretical Focus Spot
λf1/D1
I. M. Vellekoop, A. Lagendijk & A. P. Mosk, Nature Photonics 4, 320 - 322 (2010)
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λf2/D2
Transmission Matrix of an Optical Scattering Medium
Theoretical Focus Spot
λF/D
F
D λl/LSLM
l
L
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A
B
Signal received at A
Complex envelope time reversal
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Time reversal
Time reversal in modulation in a reverberant cavity
Pulse in modulation at A (on one quadrature)
TR = reverse modulation + conjugate carrier wave
Signal received at B
G. Lerosey et al., Phys. Rel. Lett., 92, 193904 (2004)
Spatial and temporal focusing
Transmission matrix in scattering media
Linear media and matrices
Ou
tpu
t k
Free space
Identity Matrix
Direct access to information
Input k
Scattering sample
Seemingly Random Matrix
Information shuffled but not lost !O
utp
ut
kInput k
inn
nmn
outm EhE
N..1
outE Output field
inE Input field.out inE H E
7814/12/2011