Abstract

We study the focusing of light through random photonic materials using wavefront shaping. We explore a novel approach namely binary amplitude modulation. To this end, the light incident to a random photonic medium is spatially divided into a number of segments. We identify the segments that give rise to fields that are out of phase with the total field at the intended focus and assign these a zero amplitude, whereas the remaining segments maintain their original amplitude. Using 812 independently controlled segments of light, we find the intensity at the target to be 75±6 times enhanced over the average intensity behind the sample. We experimentally demonstrate focusing of light through random photonic media using both an amplitude only mode liquid crystal spatial light modulator and a MEMS-based spatial light modulator. Our use of Micro Electro-Mechanical System (MEMS)-based digital micromirror devices for the control of the incident light field opens an avenue to high speed implementations of wavefront shaping.

© 2011 Optical Society of America

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References

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  1. I. M. Vellekoop, and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32, 2309–2311 (2007).
    [PubMed]
  2. I. M. Vellekoop, E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Demixing light paths inside disordered metamaterials,” Opt. Express 16, 67–80 (2008).
    [PubMed]
  3. I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4, 320–322 (2010).
  4. Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2, 110–115 (2008).
    [PubMed]
  5. M. Cui, E. J. McDowell, and C. Yang, “An in vivo study of turbidity suppression by optical phase conjugation (TSOPC) on rabbit ear,” Opt. Express 18, 25–30 (2010).
    [PubMed]
  6. M. Cui, and C. Yang, “Implementation of a digital optical phase conjugation system and its application to turbidity suppression by phase conjugation,” Opt. Express 18, 3444–3455 (2010).
    [PubMed]
  7. C.-L. Hsieh, Y. Pu, R. Grange, G. Laporte, and D. Psaltis, “Imaging through turbid layers by scanning the phase conjugated second harmonic radiation from a nanoparticle,” Opt. Express 18, 20723–20731 (2010).
    [PubMed]
  8. S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
    [PubMed]
  9. S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).
  10. D. Dudley, W. Duncan, and J. Slaughter, “Emerging Digital Micromirror Device (DMD) Applications,” Proc. SPIE 4985, 14 (2003).
  11. C. W. J. Beenakker, “Random-matrix theory of quantum transport,” Rev. Mod. Phys. 69, 731–808 (1997).
  12. J. W. Goodman, Statistical optics (Wiley, New York, 2000).
  13. M. Born, and E. Wolf, Principles of Optics (Cambridge University Press, 2003).
  14. E. G. van Putten, I. M. Vellekoop, and A. P. Mosk, “Spatial amplitude and phase modulation using commercial twisted nematic LCDs,” Appl. Opt. 47, 2076–2081 (2008).
    [PubMed]
  15. A. Derode, A. Tourin, and M. Fink, “Ultrasonic pulse compression with one-bit time reversal through multiple scattering,” J. Appl. Phys. 85, 6343–6352 (1999).
  16. F. van Beijnum, and M. Sc, Thesis, University of Twente (2009).

2010 (6)

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4, 320–322 (2010).

M. Cui, E. J. McDowell, and C. Yang, “An in vivo study of turbidity suppression by optical phase conjugation (TSOPC) on rabbit ear,” Opt. Express 18, 25–30 (2010).
[PubMed]

M. Cui, and C. Yang, “Implementation of a digital optical phase conjugation system and its application to turbidity suppression by phase conjugation,” Opt. Express 18, 3444–3455 (2010).
[PubMed]

C.-L. Hsieh, Y. Pu, R. Grange, G. Laporte, and D. Psaltis, “Imaging through turbid layers by scanning the phase conjugated second harmonic radiation from a nanoparticle,” Opt. Express 18, 20723–20731 (2010).
[PubMed]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[PubMed]

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).

2008 (3)

2007 (1)

2003 (1)

D. Dudley, W. Duncan, and J. Slaughter, “Emerging Digital Micromirror Device (DMD) Applications,” Proc. SPIE 4985, 14 (2003).

1999 (1)

A. Derode, A. Tourin, and M. Fink, “Ultrasonic pulse compression with one-bit time reversal through multiple scattering,” J. Appl. Phys. 85, 6343–6352 (1999).

1997 (1)

C. W. J. Beenakker, “Random-matrix theory of quantum transport,” Rev. Mod. Phys. 69, 731–808 (1997).

Beenakker, C. W. J.

C. W. J. Beenakker, “Random-matrix theory of quantum transport,” Rev. Mod. Phys. 69, 731–808 (1997).

Boccara, A. C.

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[PubMed]

Carminati, R.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[PubMed]

Cui, M.

Derode, A.

A. Derode, A. Tourin, and M. Fink, “Ultrasonic pulse compression with one-bit time reversal through multiple scattering,” J. Appl. Phys. 85, 6343–6352 (1999).

Dudley, D.

D. Dudley, W. Duncan, and J. Slaughter, “Emerging Digital Micromirror Device (DMD) Applications,” Proc. SPIE 4985, 14 (2003).

Duncan, W.

D. Dudley, W. Duncan, and J. Slaughter, “Emerging Digital Micromirror Device (DMD) Applications,” Proc. SPIE 4985, 14 (2003).

Feld, M. S.

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2, 110–115 (2008).
[PubMed]

Fink, M.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[PubMed]

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).

A. Derode, A. Tourin, and M. Fink, “Ultrasonic pulse compression with one-bit time reversal through multiple scattering,” J. Appl. Phys. 85, 6343–6352 (1999).

Gigan, S.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[PubMed]

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).

Grange, R.

Hsieh, C.-L.

Lagendijk, A.

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4, 320–322 (2010).

I. M. Vellekoop, E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Demixing light paths inside disordered metamaterials,” Opt. Express 16, 67–80 (2008).
[PubMed]

Laporte, G.

Lerosey, G.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[PubMed]

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).

McDowell, E. J.

Mosk, A. P.

Popoff, S. M.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[PubMed]

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).

Psaltis, D.

C.-L. Hsieh, Y. Pu, R. Grange, G. Laporte, and D. Psaltis, “Imaging through turbid layers by scanning the phase conjugated second harmonic radiation from a nanoparticle,” Opt. Express 18, 20723–20731 (2010).
[PubMed]

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2, 110–115 (2008).
[PubMed]

Pu, Y.

Slaughter, J.

D. Dudley, W. Duncan, and J. Slaughter, “Emerging Digital Micromirror Device (DMD) Applications,” Proc. SPIE 4985, 14 (2003).

Tourin, A.

A. Derode, A. Tourin, and M. Fink, “Ultrasonic pulse compression with one-bit time reversal through multiple scattering,” J. Appl. Phys. 85, 6343–6352 (1999).

van Putten, E. G.

Vellekoop, I. M.

Yang, C.

Yaqoob, Z.

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2, 110–115 (2008).
[PubMed]

Appl. Opt. (1)

J. Appl. Phys. (1)

A. Derode, A. Tourin, and M. Fink, “Ultrasonic pulse compression with one-bit time reversal through multiple scattering,” J. Appl. Phys. 85, 6343–6352 (1999).

Nat. Commun. (1)

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).

Nat. Photonics (2)

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4, 320–322 (2010).

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2, 110–115 (2008).
[PubMed]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[PubMed]

Proc. SPIE (1)

D. Dudley, W. Duncan, and J. Slaughter, “Emerging Digital Micromirror Device (DMD) Applications,” Proc. SPIE 4985, 14 (2003).

Rev. Mod. Phys. (1)

C. W. J. Beenakker, “Random-matrix theory of quantum transport,” Rev. Mod. Phys. 69, 731–808 (1997).

Other (3)

J. W. Goodman, Statistical optics (Wiley, New York, 2000).

M. Born, and E. Wolf, Principles of Optics (Cambridge University Press, 2003).

F. van Beijnum, and M. Sc, Thesis, University of Twente (2009).

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Figures (7)

Fig. 1
Fig. 1

(color) Graphical explanation of the binary amplitude modulation algorithm. (ac) Complex plane representation of the electric field at the target in successive steps of the algorithm. Small black vectors represent the electric field of each input channel as modified by traveling through the sample. The red vector is the total electric field at the target output channel. Dashed gray vector represents the electric field at the target position before optimization. (d–f) Evolution of the amplitude pattern on the SLM. (a,d) In this step, a segment which contributes negatively to the total amplitude is identified (circled). This segment will be turned off as algorithm proceeds to next segment. (b,e) Subsequently, other segments which contribute negatively are identified and will be turned off. (c,f) At the end of the algorithm, all of the segments which have a negative contribution to the total electric field at the target are turned off.

Fig. 2
Fig. 2

(color) Experimental setup. A HeNe laser beam with a wavelength of 632.8 nm and output power of 5 mW is expanded and passed through a half waveplate (λ/2 WP), a polarizer (pol.1) and a polarizing beam splitter (PBS) to be reflected off a Holoeye LC-R 2500 liquid crystal spatial light modulator (SLM). Phase and amplitude modulation is decoupled [14]. A high NA (NA=0.95) microscope objective projects the shaped wavefront on the sample and an identical microscope objective collects the light transmitted through the sample. The transmitted intensity pattern is passed through a polarizer (pol.2) and monitored with a CCD camera. The computer (PC) receives intensity pattern from the CCD and adjusts the SLM segments according to the algorithm. L1, 250 mm focal length lens. D, aperture. L2, 150 mm focal length lens. M, mirror. L3, 600 mm focal length lens.

Fig. 3
Fig. 3

(color) Experimental results of the optimization procedure. (a) Amplitude map written on the SLM before optimization. Active area of the SLM is divided into 812 segments, all of which are on. (b) Image captured by the CCD before optimization is performed. (c) Amplitude map on the SLM after the optimization procedure is complete. (d) Image captured after the optimization is complete. A single bright spot appears on the target point. Note the different color scale between (b) and (d).

Fig. 4
Fig. 4

Intensity enhancement at the target position versus the number of segments on the SLM. Black solid line: enhancements expected under ideal conditions, as obtained from Eq. (3). Each data point (black circles) is an ensemble average of 14–25 data points obtained from measurements. Bars represent the standard error of each measurement set. Black dotted curve: fit performed for the experimental enhancements using Eq. (4) with a single free parameter, SNR. Best curve fit yields SNR=24.

Fig. 5
Fig. 5

(color) Experimental setup for MEMS-based focusing. A HeNe laser beam that has a wavelength of 632.8 nm and output power of 2 mW is expanded and used to illuminate the SLM via a mirror (M). L1, L2 and L3 are planoconvex lenses with respectively 150 mm, 50 mm and 50 mm focal lengths. D is an aperture used for spatial filtering, and NA 0.25 is a microscope objective having 10X magnification and 0.25 numerical aperture. Light exiting the sample is converted to far field with L3, passed through a polarizer, pol. and projected on a CCD camera, which is connected to the SLM via a PC.

Fig. 6
Fig. 6

(color) (a) Image of an area of 121 by 121 pixels of the camera is presented just before the optimization process. (b) The same area is presented after the optimization process was finished. In both figures, the intensity is measured in counts/milliseconds and presented on the same scale. The SLM is divided into 3228 segments.

Fig. 7
Fig. 7

Numerically simulated intensity enhancement at the target position versus the number of segments that the SLM is divided into. Each data point represented by the black circles is an ensemble average of a set of data points obtained from simulations conducted with an intensity noise of SNR=165. Bars represent the standard error of each measurement set. The dashed line shows the enhancements obtained from Eq. (25), assuming 〈A2/〈A2〉 = 1 and using Eq. (19).

Equations (25)

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E m = n = 1 N t m n E n ,
η I opt I ref ,
η ideal 1 + 1 π ( N 2 1 ) .
η non–ideal = η ideal ( 1 2 + 1 π arctan ( S N R N ) ) A 2 A 2 ,
E n = A e i ϕ .
E m = n = 1 N | t m n | e i arg ( t m n ) E n .
I ref = E m * E m ,
I ref = k N A | t m k | e i ( arg ( t m k ) ) n N A | t m n | e i ( arg ( t m n ) ) ,
I ref = N t 2 A 2 ,
Δ I k = | E m | 2 | E m E k t m k | 2 .
f ( Δ I k ˜ ) = 1 σ 2 π e ( Δ I k ˜ μ ) 2 2 σ 2 ,
μ = A 2 t 2 ,
σ = t 4 A 4 + ( 2 N 3 ) t 2 A 2 2 .
N = N P ( x > 0 ) = 0 N σ 2 π e ( x μ ) 2 2 σ 2 d x ,
= N 2 erfc ( μ σ 2 ) .
I opt = E m * E m ,
= N A 2 t 2 + N ( N 1 ) A t 2 4 π 2 .
η ideal = I opt I ref = 1 + 1 π ( N 1 ) .
η ideal 1 + 1 π ( N 2 1 ) .
P wrong = P ( Δ I k > 0 Λ Δ I k exp < 0 ) + P ( Δ I k < 0 Λ Δ I k exp > 0 ) ,
P wrong = 0 f ( Δ I k ˜ ) 0 f ( Δ I k exp ˜ ) d Δ I k exp ˜ d Δ I k ˜ + 0 f ( Δ I k ˜ ) 0 f ( Δ I k exp ˜ ) d Δ I k exp ˜ d Δ I k ˜ .
f ( Δ I k exp ˜ ) = 1 ( 2 ) σ noise 2 π e ( Δ I k exp ˜ Δ I k ) 2 4 σ noise 2 ,
P wrong = 1 2 1 π arctan ( σ 2 σ noise ) .
P wrong = 1 2 1 π arctan ( S N R N ) .
η non–ideal = η ideal ( 1 2 + 1 π arctan ( S N R N ) ) A 2 A 2 .

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