Abstract

In this work, we report a novel high capacity (number of degrees of freedom) open loop adaptive optics method, termed digital optical phase conjugation (DOPC), which provides a robust optoelectronic optical phase conjugation (OPC) solution. We showed that our prototype can phase conjugate light fields with ~3.9 x 10−3 degree accuracy over a range of ~3 degrees and can phase conjugate an input field through a relatively thick turbid medium (μsl ~13). Furthermore, we employed this system to show that the reversing of random scattering in turbid media by phase conjugation is surprisingly robust and accommodating of phase errors. An OPC wavefront with significant spatial phase errors (error uniformly distributed from – π/2 to π/2) can nevertheless allow OPC reconstruction through a scattering medium with ~40% of the efficiency achieved with phase error free OPC.

© 2010 OSA

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2010 (1)

2009 (4)

D. Débarre, E. J. Botcherby, T. Watanabe, S. Srinivas, M. J. Booth, and T. Wilson, “Image-based adaptive optics for two-photon microscopy,” Opt. Lett. 34(16), 2495–2497 (2009).
[CrossRef] [PubMed]

M. Wenner, “The most transparent research,” Nat. Med. 15(10), 1106–1109 (2009).
[CrossRef] [PubMed]

L. V. Wang, “Multiscale photoacoustic microscopy and computed tomography,” Nat. Photonics 3(9), 503–509 (2009).
[CrossRef]

M. Cui, E. J. McDowell, and C. H. Yang, “Observation of polarization-gate based reconstruction quality improvement during the process of turbidity suppression by optical phase conjugation,” Appl. Phys. Lett. 95(12), 123702 (2009).
[CrossRef] [PubMed]

2008 (4)

I. M. Vellekoop and A. P. Mosk, “Universal optimal transmission of light through disordered materials,” Phys. Rev. Lett. 101(12), 120601 (2008).
[CrossRef] [PubMed]

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

I. M. Vellekoop, E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Demixing light paths inside disordered metamaterials,” Opt. Express 16(1), 67–80 (2008).
[CrossRef] [PubMed]

D. Débarre, E. J. Botcherby, M. J. Booth, and T. Wilson, “Adaptive optics for structured illumination microscopy,” Opt. Express 16(13), 9290–9305 (2008).
[CrossRef] [PubMed]

2007 (1)

2006 (1)

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. U.S.A. 103(46), 17137–17142 (2006).
[CrossRef] [PubMed]

2002 (1)

M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. U.S.A. 99(9), 5788–5792 (2002).
[CrossRef] [PubMed]

2001 (1)

A. Derode, A. Tourin, and M. Fink, “Random multiple scattering of ultrasound. Ii. Is time reversal a self-averaging process?” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(3), 036606 (2001).
[CrossRef] [PubMed]

1999 (1)

M. Fink, “Time-reversed acoustics,” Sci. Am. 281(5), 91–97 (1999).
[CrossRef]

1998 (1)

1997 (2)

1991 (1)

C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, and H. T. Barclay, “Compensation of atmospheric optical distortion using a synthetic beacon,” Nature 353(6340), 141–143 (1991).
[CrossRef]

1989 (1)

D. M. Pepper, “Observation of diminished specular reflectivity from phase-conjugate mirrors,” Phys. Rev. Lett. 62(25), 2945–2948 (1989).
[CrossRef] [PubMed]

1987 (1)

1981 (1)

1980 (1)

1978 (1)

A. Yariv and P. Yeh, “Phase conjugate optics and real-time holography,” IEEE J. Quantum Electron. 14(9), 650–660 (1978).
[CrossRef]

1976 (1)

Barclay, H. T.

C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, and H. T. Barclay, “Compensation of atmospheric optical distortion using a synthetic beacon,” Nature 353(6340), 141–143 (1991).
[CrossRef]

Booth, M. J.

Botcherby, E. J.

Cui, M.

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(1), 25–30 (2010).
[CrossRef] [PubMed]

M. Cui, E. J. McDowell, and C. H. Yang, “Observation of polarization-gate based reconstruction quality improvement during the process of turbidity suppression by optical phase conjugation,” Appl. Phys. Lett. 95(12), 123702 (2009).
[CrossRef] [PubMed]

Débarre, D.

Denk, W.

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. U.S.A. 103(46), 17137–17142 (2006).
[CrossRef] [PubMed]

Derode, A.

A. Derode, A. Tourin, and M. Fink, “Random multiple scattering of ultrasound. Ii. Is time reversal a self-averaging process?” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(3), 036606 (2001).
[CrossRef] [PubMed]

Feinberg, J.

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(2), 110–115 (2008).
[CrossRef] [PubMed]

Fink, M.

A. Derode, A. Tourin, and M. Fink, “Random multiple scattering of ultrasound. Ii. Is time reversal a self-averaging process?” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(3), 036606 (2001).
[CrossRef] [PubMed]

M. Fink, “Time-reversed acoustics,” Sci. Am. 281(5), 91–97 (1999).
[CrossRef]

M. Fink, “Time reversed acoustics,” Phys. Today 50(3), 34–40 (1997).
[CrossRef]

Goodman, J. W.

Hellwarth, R. W.

Juskaitis, R.

M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. U.S.A. 99(9), 5788–5792 (2002).
[CrossRef] [PubMed]

Lagendijk, A.

Lind, R. C.

Lindsay, I.

Mack-Bucher, J. A.

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. U.S.A. 103(46), 17137–17142 (2006).
[CrossRef] [PubMed]

McDowell, E. J.

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(1), 25–30 (2010).
[CrossRef] [PubMed]

M. Cui, E. J. McDowell, and C. H. Yang, “Observation of polarization-gate based reconstruction quality improvement during the process of turbidity suppression by optical phase conjugation,” Appl. Phys. Lett. 95(12), 123702 (2009).
[CrossRef] [PubMed]

Mosk, A. P.

Murphy, D. V.

C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, and H. T. Barclay, “Compensation of atmospheric optical distortion using a synthetic beacon,” Nature 353(6340), 141–143 (1991).
[CrossRef]

Neil, M. A. A.

M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. U.S.A. 99(9), 5788–5792 (2002).
[CrossRef] [PubMed]

Page, D. A.

C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, and H. T. Barclay, “Compensation of atmospheric optical distortion using a synthetic beacon,” Nature 353(6340), 141–143 (1991).
[CrossRef]

Pepper, D. M.

D. M. Pepper, “Observation of diminished specular reflectivity from phase-conjugate mirrors,” Phys. Rev. Lett. 62(25), 2945–2948 (1989).
[CrossRef] [PubMed]

Primmerman, C. A.

C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, and H. T. Barclay, “Compensation of atmospheric optical distortion using a synthetic beacon,” Nature 353(6340), 141–143 (1991).
[CrossRef]

Psaltis, D.

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

Rueckel, M.

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. U.S.A. 103(46), 17137–17142 (2006).
[CrossRef] [PubMed]

Srinivas, S.

Steel, D. G.

Tourin, A.

A. Derode, A. Tourin, and M. Fink, “Random multiple scattering of ultrasound. Ii. Is time reversal a self-averaging process?” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(3), 036606 (2001).
[CrossRef] [PubMed]

van Putten, E. G.

Vellekoop, I. M.

Wang, L. V.

L. V. Wang, “Multiscale photoacoustic microscopy and computed tomography,” Nat. Photonics 3(9), 503–509 (2009).
[CrossRef]

Watanabe, T.

Wenner, M.

M. Wenner, “The most transparent research,” Nat. Med. 15(10), 1106–1109 (2009).
[CrossRef] [PubMed]

Wilson, T.

Yamaguchi, I.

Yang, C.

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(1), 25–30 (2010).
[CrossRef] [PubMed]

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

Yang, C. H.

M. Cui, E. J. McDowell, and C. H. Yang, “Observation of polarization-gate based reconstruction quality improvement during the process of turbidity suppression by optical phase conjugation,” Appl. Phys. Lett. 95(12), 123702 (2009).
[CrossRef] [PubMed]

Yaqoob, Z.

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

Yariv, A.

A. Yariv and P. Yeh, “Phase conjugate optics and real-time holography,” IEEE J. Quantum Electron. 14(9), 650–660 (1978).
[CrossRef]

Yeh, P.

A. Yariv and P. Yeh, “Phase conjugate optics and real-time holography,” IEEE J. Quantum Electron. 14(9), 650–660 (1978).
[CrossRef]

Zhang, T.

Zollars, B. G.

C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, and H. T. Barclay, “Compensation of atmospheric optical distortion using a synthetic beacon,” Nature 353(6340), 141–143 (1991).
[CrossRef]

Appl. Phys. Lett. (1)

M. Cui, E. J. McDowell, and C. H. Yang, “Observation of polarization-gate based reconstruction quality improvement during the process of turbidity suppression by optical phase conjugation,” Appl. Phys. Lett. 95(12), 123702 (2009).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

A. Yariv and P. Yeh, “Phase conjugate optics and real-time holography,” IEEE J. Quantum Electron. 14(9), 650–660 (1978).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (1)

Nat. Med. (1)

M. Wenner, “The most transparent research,” Nat. Med. 15(10), 1106–1109 (2009).
[CrossRef] [PubMed]

Nat. Photonics (2)

L. V. Wang, “Multiscale photoacoustic microscopy and computed tomography,” Nat. Photonics 3(9), 503–509 (2009).
[CrossRef]

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

Nature (1)

C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, and H. T. Barclay, “Compensation of atmospheric optical distortion using a synthetic beacon,” Nature 353(6340), 141–143 (1991).
[CrossRef]

Opt. Express (3)

Opt. Lett. (6)

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

A. Derode, A. Tourin, and M. Fink, “Random multiple scattering of ultrasound. Ii. Is time reversal a self-averaging process?” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(3), 036606 (2001).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

I. M. Vellekoop and A. P. Mosk, “Universal optimal transmission of light through disordered materials,” Phys. Rev. Lett. 101(12), 120601 (2008).
[CrossRef] [PubMed]

D. M. Pepper, “Observation of diminished specular reflectivity from phase-conjugate mirrors,” Phys. Rev. Lett. 62(25), 2945–2948 (1989).
[CrossRef] [PubMed]

Phys. Today (1)

M. Fink, “Time reversed acoustics,” Phys. Today 50(3), 34–40 (1997).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A. (2)

M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. U.S.A. 99(9), 5788–5792 (2002).
[CrossRef] [PubMed]

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. U.S.A. 103(46), 17137–17142 (2006).
[CrossRef] [PubMed]

Sci. Am. (1)

M. Fink, “Time-reversed acoustics,” Sci. Am. 281(5), 91–97 (1999).
[CrossRef]

Other (2)

P. Yeh, Introduction to photorefractive nonlinear optics (John Wiley & Sons, Inc, New York, 1993).

D. P. M. Gower, Optical phase conjugation (Springer-Verlag, New York, 1994).

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Figures (8)

Fig. 1
Fig. 1

The two elements of the DOPC system, a wavefront measurement device (sensor) and a spatial light modulator (actuator), are optically combined with a beam splitter. They function as a single system which can both measure an input wavefront and generate a phase conjugate output wavefront. (a) shows the wavefront measurement process wherein a reference wave interferes with the input signal. Their relative phase is controlled by an EO phase modulator. (b) shows the phase shaping process wherein the SLM modulates the incident reference wave.

Fig. 2
Fig. 2

Experimental setup of the DOPC system. The laser is a solid state CW laser at 532nm (Spectra-Physics, Excelsior Scientific 200mW). SLM, LCOS reflective spatial light modulator (Holoeye, LC-R 2500); CCD, CCD camera (ImagingSource DFK41BF02); PBS, polarizing beam splitter; BS1 and BS 2, non-polarizing beam splitter, ND, neutral density filter.

Fig. 3
Fig. 3

The procedure for mapping between the CCD and the SLM. (a) A mask was placed at the symmetry plane of the SLM. The mask was illuminated and imaged on CCD 1. (b), a phase pattern was displaced on the SLM, which was imaged on CCD 2. (c) The mask was illuminated and was imaged on CCD 2. (d) Experimentally measured SLM image. (e) Experimentally measured mask image.

Fig. 4
Fig. 4

Setup for testing the accuracy of DOPC. The laser is a solid state CW laser at 532nm. SLM, LCOS reflective spatial light modulator (Holoeye, LC-R 2500); CCD, CCD camera (ImagingSource DFK41BF02); PBS, polarizing beam splitter; BS, non-polarizing beam splitter. EO, electro-optic phase modulator (Thorlabs, EO-PM-NR-C4). Lens 1 and 2, objective lenses (Olympus, UPLFLN 100XO2, NA1.3), ND, neutral density filter.

Fig. 5
Fig. 5

(a) Lens 1 was shifted in the lateral direction. The beam exiting Lens 2 deviated from the original propagation direction. (b) Lens 1 was shifted in the axial direction. The beam incident on the DOPC system was either a converging or a diverging beam.

Fig. 6
Fig. 6

(a) The phase shifting holography measured wavefront when lens 1 was shifted laterally from the center position by 50 microns. (b) The measured wavefront when Lens 1 was shifted axially from the center position by 50 microns. (c) The DOPC reconstructed focus position as Lens 1was shifted laterally. (d) The DOPC reconstructed focus diameter as Lens 1 was shifted axially. (e) The measured reflected focus position variation when Lens 1 was shifted laterally. (f) The reflected focus size variation when Lens 1 was shifted axially.

Fig. 7
Fig. 7

(a) The DOPC measured phase profile. (b) DOPC reconstructed signal. The field of view is ~12 μm. (c) Control measurement with the phase of the SLM set to 0.

Fig. 8
Fig. 8

Theoretical calculation and experimental measurements of the reconstructed OPC signal dependence on the amount of phase error.

Equations (1)

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R p o w e r = | E a E a | 2 = | b | t b a | 2 exp ( i ϕ b ) b | t b a | 2 | 2 .

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