Abstract

In a conventional digital phase conjugation system, only the phase of an input light is time-reversed. This deteriorates phase conjugation fidelity and restricts application fields to specific cases only when the input light has uniformly-distributed scattered wavefront. To overcome these difficulties, we present a digital phase conjugate mirror based on parallel alignment of two phase-only spatial light modulators (SLMs), in which both amplitude and phase of the input light can be time-reversed. Experimental result showed that, in the phase conjugation through a holographic diffuser with diffusion angle of 0.5 degree, background noises decrease to 65% by our digital phase conjugation mirror.

© 2014 Optical Society of America

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  1. B. Y. Zeldovich, V. I. Popovichev, V. V. Ragulskii, and F. S. Faizullov, “Connection between the wave fronts of the reflected and exciting light in stimulated Mandel'-shtam-Brillouin scattering,” Sov. Phys. JETP Lett. 15, 109–113 (1972).
  2. H. Kogelnik and K. S. Pennington, “Holographic imaging through a random medium,” J. Opt. Soc. Am. 58(2), 273–274 (1968).
    [Crossref]
  3. S. MacCormack and J. Feinberg, “High-brightness output from a laser-diode array coupled to a phase-conjugating mirror,” Opt. Lett. 18(3), 211–213 (1993).
    [Crossref] [PubMed]
  4. M. Cui and C. Yang, “Implementation of a digital optical phase conjugation system and its application to study the robustness of turbidity suppression by phase conjugation,” Opt. Express 18(4), 3444–3455 (2010).
    [Crossref] [PubMed]
  5. C. Bellanger, A. Brignon, J. Colineau, and J. P. Huignard, “Coherent fiber combining by digital holography,” Opt. Lett. 33(24), 2937–2939 (2008).
    [Crossref] [PubMed]
  6. C. L. Hsieh, Y. Pu, R. Grange, and D. Psaltis, “Digital phase conjugation of second harmonic radiation emitted by nanoparticles in turbid media,” Opt. Express 18(12), 12283–12290 (2010).
    [Crossref] [PubMed]
  7. I. N. Papadopoulos, S. Farahi, C. Moser, and D. Psaltis, “Focusing and scanning light through a multimode optical fiber using digital phase conjugation,” Opt. Express 20(10), 10583–10590 (2012).
    [Crossref] [PubMed]
  8. T. Omatsu, A. Katoh, K. Okada, S. Hatano, A. Hasegawa, M. Tateda, and I. Ogura, “Investigation of photorefractive phase conjugate feedback on the lasing spectrum of a broad-stripe laser diode,” Opt. Commun. 146(1-6), 167–172 (1998).
    [Crossref]
  9. V. Wang and C. R. Giuliano, “Correction of phase aberrations via stimulated Brillouin scattering,” Opt. Lett. 2(1), 4–6 (1978).
    [Crossref] [PubMed]
  10. I. M. Vellekoop and A. P. Mosk, “Universal optimal transmission of light through disordered materials,” Phys. Rev. Lett. 101, 120601 (2008).
  11. A. V. Oppenheim and J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69(5), 529–541 (1981).
    [Crossref]
  12. L. B. Lesem, P. M. Hirch, and J. A. Jordan., “The kinoform: A new wavefront reconstruction device,” IBM J. Res. Develop. 13(2), 150–155 (1969).
    [Crossref]
  13. A. J. MacGovern and J. C. Wyant, “Computer generated holograms for testing optical elements,” Appl. Opt. 10(3), 619–624 (1971).
    [Crossref] [PubMed]
  14. J. M. Florence and R. D. Juday, “Full complex spatial filtering with a phase mostly DMD,” Proc. SPIE 1558, 487–498 (1991).
    [Crossref]
  15. A. Shibukawa, A. Okamoto, M. Takabayashi, and A. Tomita, “Spatial cross modulation method using a random diffuser and phase-only spatial light modulator for constructing arbitrary complex fields,” Opt. Express 22(4), 3968–3982 (2014).
    [Crossref] [PubMed]
  16. L. G. Neto, D. Roberge, and Y. Sheng, “Full-range, continuous, complex modulation by the use of two coupled-mode liquid-crystal televisions,” Appl. Opt. 35(23), 4567–4576 (1996).
    [Crossref] [PubMed]
  17. D. A. Gregory, J. C. Kirsch, and E. C. Tam, “Full complex modulation using liquid-crystal televisions,” Appl. Opt. 31(2), 163–165 (1992).
    [Crossref] [PubMed]
  18. R. D. Juday and J. M. Florence, “Full complex modulation with two one-parameter SLMs,” Proc. SPIE 1558, 499–504 (1991).
    [Crossref]
  19. A. Okamoto, K. Kunori, M. Takabayashi, A. Tomita, and K. Sato, “Holographic diversity interferometry for optical storage,” Opt. Express 19(14), 13436–13444 (2011).
    [Crossref] [PubMed]
  20. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22(16), 1268–1270 (1997).
    [Crossref] [PubMed]

2014 (1)

A. Shibukawa, A. Okamoto, M. Takabayashi, and A. Tomita, “Spatial cross modulation method using a random diffuser and phase-only spatial light modulator for constructing arbitrary complex fields,” Opt. Express 22(4), 3968–3982 (2014).
[Crossref] [PubMed]

2012 (1)

I. N. Papadopoulos, S. Farahi, C. Moser, and D. Psaltis, “Focusing and scanning light through a multimode optical fiber using digital phase conjugation,” Opt. Express 20(10), 10583–10590 (2012).
[Crossref] [PubMed]

2011 (1)

A. Okamoto, K. Kunori, M. Takabayashi, A. Tomita, and K. Sato, “Holographic diversity interferometry for optical storage,” Opt. Express 19(14), 13436–13444 (2011).
[Crossref] [PubMed]

2010 (2)

C. L. Hsieh, Y. Pu, R. Grange, and D. Psaltis, “Digital phase conjugation of second harmonic radiation emitted by nanoparticles in turbid media,” Opt. Express 18(12), 12283–12290 (2010).
[Crossref] [PubMed]

M. Cui and C. Yang, “Implementation of a digital optical phase conjugation system and its application to study the robustness of turbidity suppression by phase conjugation,” Opt. Express 18(4), 3444–3455 (2010).
[Crossref] [PubMed]

2008 (2)

C. Bellanger, A. Brignon, J. Colineau, and J. P. Huignard, “Coherent fiber combining by digital holography,” Opt. Lett. 33(24), 2937–2939 (2008).
[Crossref] [PubMed]

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

1998 (1)

T. Omatsu, A. Katoh, K. Okada, S. Hatano, A. Hasegawa, M. Tateda, and I. Ogura, “Investigation of photorefractive phase conjugate feedback on the lasing spectrum of a broad-stripe laser diode,” Opt. Commun. 146(1-6), 167–172 (1998).
[Crossref]

1997 (1)

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22(16), 1268–1270 (1997).
[Crossref] [PubMed]

1996 (1)

L. G. Neto, D. Roberge, and Y. Sheng, “Full-range, continuous, complex modulation by the use of two coupled-mode liquid-crystal televisions,” Appl. Opt. 35(23), 4567–4576 (1996).
[Crossref] [PubMed]

1993 (1)

S. MacCormack and J. Feinberg, “High-brightness output from a laser-diode array coupled to a phase-conjugating mirror,” Opt. Lett. 18(3), 211–213 (1993).
[Crossref] [PubMed]

1992 (1)

D. A. Gregory, J. C. Kirsch, and E. C. Tam, “Full complex modulation using liquid-crystal televisions,” Appl. Opt. 31(2), 163–165 (1992).
[Crossref] [PubMed]

1991 (2)

R. D. Juday and J. M. Florence, “Full complex modulation with two one-parameter SLMs,” Proc. SPIE 1558, 499–504 (1991).
[Crossref]

J. M. Florence and R. D. Juday, “Full complex spatial filtering with a phase mostly DMD,” Proc. SPIE 1558, 487–498 (1991).
[Crossref]

1981 (1)

A. V. Oppenheim and J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69(5), 529–541 (1981).
[Crossref]

1978 (1)

V. Wang and C. R. Giuliano, “Correction of phase aberrations via stimulated Brillouin scattering,” Opt. Lett. 2(1), 4–6 (1978).
[Crossref] [PubMed]

1972 (1)

B. Y. Zeldovich, V. I. Popovichev, V. V. Ragulskii, and F. S. Faizullov, “Connection between the wave fronts of the reflected and exciting light in stimulated Mandel'-shtam-Brillouin scattering,” Sov. Phys. JETP Lett. 15, 109–113 (1972).

1971 (1)

A. J. MacGovern and J. C. Wyant, “Computer generated holograms for testing optical elements,” Appl. Opt. 10(3), 619–624 (1971).
[Crossref] [PubMed]

1969 (1)

L. B. Lesem, P. M. Hirch, and J. A. Jordan., “The kinoform: A new wavefront reconstruction device,” IBM J. Res. Develop. 13(2), 150–155 (1969).
[Crossref]

1968 (1)

H. Kogelnik and K. S. Pennington, “Holographic imaging through a random medium,” J. Opt. Soc. Am. 58(2), 273–274 (1968).
[Crossref]

Bellanger, C.

C. Bellanger, A. Brignon, J. Colineau, and J. P. Huignard, “Coherent fiber combining by digital holography,” Opt. Lett. 33(24), 2937–2939 (2008).
[Crossref] [PubMed]

Brignon, A.

C. Bellanger, A. Brignon, J. Colineau, and J. P. Huignard, “Coherent fiber combining by digital holography,” Opt. Lett. 33(24), 2937–2939 (2008).
[Crossref] [PubMed]

Colineau, J.

C. Bellanger, A. Brignon, J. Colineau, and J. P. Huignard, “Coherent fiber combining by digital holography,” Opt. Lett. 33(24), 2937–2939 (2008).
[Crossref] [PubMed]

Cui, M.

M. Cui and C. Yang, “Implementation of a digital optical phase conjugation system and its application to study the robustness of turbidity suppression by phase conjugation,” Opt. Express 18(4), 3444–3455 (2010).
[Crossref] [PubMed]

Faizullov, F. S.

B. Y. Zeldovich, V. I. Popovichev, V. V. Ragulskii, and F. S. Faizullov, “Connection between the wave fronts of the reflected and exciting light in stimulated Mandel'-shtam-Brillouin scattering,” Sov. Phys. JETP Lett. 15, 109–113 (1972).

Farahi, S.

I. N. Papadopoulos, S. Farahi, C. Moser, and D. Psaltis, “Focusing and scanning light through a multimode optical fiber using digital phase conjugation,” Opt. Express 20(10), 10583–10590 (2012).
[Crossref] [PubMed]

Feinberg, J.

S. MacCormack and J. Feinberg, “High-brightness output from a laser-diode array coupled to a phase-conjugating mirror,” Opt. Lett. 18(3), 211–213 (1993).
[Crossref] [PubMed]

Florence, J. M.

J. M. Florence and R. D. Juday, “Full complex spatial filtering with a phase mostly DMD,” Proc. SPIE 1558, 487–498 (1991).
[Crossref]

R. D. Juday and J. M. Florence, “Full complex modulation with two one-parameter SLMs,” Proc. SPIE 1558, 499–504 (1991).
[Crossref]

Giuliano, C. R.

V. Wang and C. R. Giuliano, “Correction of phase aberrations via stimulated Brillouin scattering,” Opt. Lett. 2(1), 4–6 (1978).
[Crossref] [PubMed]

Grange, R.

C. L. Hsieh, Y. Pu, R. Grange, and D. Psaltis, “Digital phase conjugation of second harmonic radiation emitted by nanoparticles in turbid media,” Opt. Express 18(12), 12283–12290 (2010).
[Crossref] [PubMed]

Gregory, D. A.

D. A. Gregory, J. C. Kirsch, and E. C. Tam, “Full complex modulation using liquid-crystal televisions,” Appl. Opt. 31(2), 163–165 (1992).
[Crossref] [PubMed]

Hasegawa, A.

T. Omatsu, A. Katoh, K. Okada, S. Hatano, A. Hasegawa, M. Tateda, and I. Ogura, “Investigation of photorefractive phase conjugate feedback on the lasing spectrum of a broad-stripe laser diode,” Opt. Commun. 146(1-6), 167–172 (1998).
[Crossref]

Hatano, S.

T. Omatsu, A. Katoh, K. Okada, S. Hatano, A. Hasegawa, M. Tateda, and I. Ogura, “Investigation of photorefractive phase conjugate feedback on the lasing spectrum of a broad-stripe laser diode,” Opt. Commun. 146(1-6), 167–172 (1998).
[Crossref]

Hirch, P. M.

L. B. Lesem, P. M. Hirch, and J. A. Jordan., “The kinoform: A new wavefront reconstruction device,” IBM J. Res. Develop. 13(2), 150–155 (1969).
[Crossref]

Hsieh, C. L.

C. L. Hsieh, Y. Pu, R. Grange, and D. Psaltis, “Digital phase conjugation of second harmonic radiation emitted by nanoparticles in turbid media,” Opt. Express 18(12), 12283–12290 (2010).
[Crossref] [PubMed]

Huignard, J. P.

C. Bellanger, A. Brignon, J. Colineau, and J. P. Huignard, “Coherent fiber combining by digital holography,” Opt. Lett. 33(24), 2937–2939 (2008).
[Crossref] [PubMed]

Jordan, J. A.

L. B. Lesem, P. M. Hirch, and J. A. Jordan., “The kinoform: A new wavefront reconstruction device,” IBM J. Res. Develop. 13(2), 150–155 (1969).
[Crossref]

Juday, R. D.

J. M. Florence and R. D. Juday, “Full complex spatial filtering with a phase mostly DMD,” Proc. SPIE 1558, 487–498 (1991).
[Crossref]

R. D. Juday and J. M. Florence, “Full complex modulation with two one-parameter SLMs,” Proc. SPIE 1558, 499–504 (1991).
[Crossref]

Katoh, A.

T. Omatsu, A. Katoh, K. Okada, S. Hatano, A. Hasegawa, M. Tateda, and I. Ogura, “Investigation of photorefractive phase conjugate feedback on the lasing spectrum of a broad-stripe laser diode,” Opt. Commun. 146(1-6), 167–172 (1998).
[Crossref]

Kirsch, J. C.

D. A. Gregory, J. C. Kirsch, and E. C. Tam, “Full complex modulation using liquid-crystal televisions,” Appl. Opt. 31(2), 163–165 (1992).
[Crossref] [PubMed]

Kogelnik, H.

H. Kogelnik and K. S. Pennington, “Holographic imaging through a random medium,” J. Opt. Soc. Am. 58(2), 273–274 (1968).
[Crossref]

Kunori, K.

A. Okamoto, K. Kunori, M. Takabayashi, A. Tomita, and K. Sato, “Holographic diversity interferometry for optical storage,” Opt. Express 19(14), 13436–13444 (2011).
[Crossref] [PubMed]

Lesem, L. B.

L. B. Lesem, P. M. Hirch, and J. A. Jordan., “The kinoform: A new wavefront reconstruction device,” IBM J. Res. Develop. 13(2), 150–155 (1969).
[Crossref]

Lim, J. S.

A. V. Oppenheim and J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69(5), 529–541 (1981).
[Crossref]

MacCormack, S.

S. MacCormack and J. Feinberg, “High-brightness output from a laser-diode array coupled to a phase-conjugating mirror,” Opt. Lett. 18(3), 211–213 (1993).
[Crossref] [PubMed]

MacGovern, A. J.

A. J. MacGovern and J. C. Wyant, “Computer generated holograms for testing optical elements,” Appl. Opt. 10(3), 619–624 (1971).
[Crossref] [PubMed]

Moser, C.

I. N. Papadopoulos, S. Farahi, C. Moser, and D. Psaltis, “Focusing and scanning light through a multimode optical fiber using digital phase conjugation,” Opt. Express 20(10), 10583–10590 (2012).
[Crossref] [PubMed]

Mosk, A. P.

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

Neto, L. G.

L. G. Neto, D. Roberge, and Y. Sheng, “Full-range, continuous, complex modulation by the use of two coupled-mode liquid-crystal televisions,” Appl. Opt. 35(23), 4567–4576 (1996).
[Crossref] [PubMed]

Ogura, I.

T. Omatsu, A. Katoh, K. Okada, S. Hatano, A. Hasegawa, M. Tateda, and I. Ogura, “Investigation of photorefractive phase conjugate feedback on the lasing spectrum of a broad-stripe laser diode,” Opt. Commun. 146(1-6), 167–172 (1998).
[Crossref]

Okada, K.

T. Omatsu, A. Katoh, K. Okada, S. Hatano, A. Hasegawa, M. Tateda, and I. Ogura, “Investigation of photorefractive phase conjugate feedback on the lasing spectrum of a broad-stripe laser diode,” Opt. Commun. 146(1-6), 167–172 (1998).
[Crossref]

Okamoto, A.

A. Shibukawa, A. Okamoto, M. Takabayashi, and A. Tomita, “Spatial cross modulation method using a random diffuser and phase-only spatial light modulator for constructing arbitrary complex fields,” Opt. Express 22(4), 3968–3982 (2014).
[Crossref] [PubMed]

A. Okamoto, K. Kunori, M. Takabayashi, A. Tomita, and K. Sato, “Holographic diversity interferometry for optical storage,” Opt. Express 19(14), 13436–13444 (2011).
[Crossref] [PubMed]

Omatsu, T.

T. Omatsu, A. Katoh, K. Okada, S. Hatano, A. Hasegawa, M. Tateda, and I. Ogura, “Investigation of photorefractive phase conjugate feedback on the lasing spectrum of a broad-stripe laser diode,” Opt. Commun. 146(1-6), 167–172 (1998).
[Crossref]

Oppenheim, A. V.

A. V. Oppenheim and J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69(5), 529–541 (1981).
[Crossref]

Papadopoulos, I. N.

I. N. Papadopoulos, S. Farahi, C. Moser, and D. Psaltis, “Focusing and scanning light through a multimode optical fiber using digital phase conjugation,” Opt. Express 20(10), 10583–10590 (2012).
[Crossref] [PubMed]

Pennington, K. S.

H. Kogelnik and K. S. Pennington, “Holographic imaging through a random medium,” J. Opt. Soc. Am. 58(2), 273–274 (1968).
[Crossref]

Popovichev, V. I.

B. Y. Zeldovich, V. I. Popovichev, V. V. Ragulskii, and F. S. Faizullov, “Connection between the wave fronts of the reflected and exciting light in stimulated Mandel'-shtam-Brillouin scattering,” Sov. Phys. JETP Lett. 15, 109–113 (1972).

Psaltis, D.

I. N. Papadopoulos, S. Farahi, C. Moser, and D. Psaltis, “Focusing and scanning light through a multimode optical fiber using digital phase conjugation,” Opt. Express 20(10), 10583–10590 (2012).
[Crossref] [PubMed]

C. L. Hsieh, Y. Pu, R. Grange, and D. Psaltis, “Digital phase conjugation of second harmonic radiation emitted by nanoparticles in turbid media,” Opt. Express 18(12), 12283–12290 (2010).
[Crossref] [PubMed]

Pu, Y.

C. L. Hsieh, Y. Pu, R. Grange, and D. Psaltis, “Digital phase conjugation of second harmonic radiation emitted by nanoparticles in turbid media,” Opt. Express 18(12), 12283–12290 (2010).
[Crossref] [PubMed]

Ragulskii, V. V.

B. Y. Zeldovich, V. I. Popovichev, V. V. Ragulskii, and F. S. Faizullov, “Connection between the wave fronts of the reflected and exciting light in stimulated Mandel'-shtam-Brillouin scattering,” Sov. Phys. JETP Lett. 15, 109–113 (1972).

Roberge, D.

L. G. Neto, D. Roberge, and Y. Sheng, “Full-range, continuous, complex modulation by the use of two coupled-mode liquid-crystal televisions,” Appl. Opt. 35(23), 4567–4576 (1996).
[Crossref] [PubMed]

Sato, K.

A. Okamoto, K. Kunori, M. Takabayashi, A. Tomita, and K. Sato, “Holographic diversity interferometry for optical storage,” Opt. Express 19(14), 13436–13444 (2011).
[Crossref] [PubMed]

Sheng, Y.

L. G. Neto, D. Roberge, and Y. Sheng, “Full-range, continuous, complex modulation by the use of two coupled-mode liquid-crystal televisions,” Appl. Opt. 35(23), 4567–4576 (1996).
[Crossref] [PubMed]

Shibukawa, A.

A. Shibukawa, A. Okamoto, M. Takabayashi, and A. Tomita, “Spatial cross modulation method using a random diffuser and phase-only spatial light modulator for constructing arbitrary complex fields,” Opt. Express 22(4), 3968–3982 (2014).
[Crossref] [PubMed]

Takabayashi, M.

A. Shibukawa, A. Okamoto, M. Takabayashi, and A. Tomita, “Spatial cross modulation method using a random diffuser and phase-only spatial light modulator for constructing arbitrary complex fields,” Opt. Express 22(4), 3968–3982 (2014).
[Crossref] [PubMed]

A. Okamoto, K. Kunori, M. Takabayashi, A. Tomita, and K. Sato, “Holographic diversity interferometry for optical storage,” Opt. Express 19(14), 13436–13444 (2011).
[Crossref] [PubMed]

Tam, E. C.

D. A. Gregory, J. C. Kirsch, and E. C. Tam, “Full complex modulation using liquid-crystal televisions,” Appl. Opt. 31(2), 163–165 (1992).
[Crossref] [PubMed]

Tateda, M.

T. Omatsu, A. Katoh, K. Okada, S. Hatano, A. Hasegawa, M. Tateda, and I. Ogura, “Investigation of photorefractive phase conjugate feedback on the lasing spectrum of a broad-stripe laser diode,” Opt. Commun. 146(1-6), 167–172 (1998).
[Crossref]

Tomita, A.

A. Shibukawa, A. Okamoto, M. Takabayashi, and A. Tomita, “Spatial cross modulation method using a random diffuser and phase-only spatial light modulator for constructing arbitrary complex fields,” Opt. Express 22(4), 3968–3982 (2014).
[Crossref] [PubMed]

A. Okamoto, K. Kunori, M. Takabayashi, A. Tomita, and K. Sato, “Holographic diversity interferometry for optical storage,” Opt. Express 19(14), 13436–13444 (2011).
[Crossref] [PubMed]

Vellekoop, I. M.

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

Wang, V.

V. Wang and C. R. Giuliano, “Correction of phase aberrations via stimulated Brillouin scattering,” Opt. Lett. 2(1), 4–6 (1978).
[Crossref] [PubMed]

Wyant, J. C.

A. J. MacGovern and J. C. Wyant, “Computer generated holograms for testing optical elements,” Appl. Opt. 10(3), 619–624 (1971).
[Crossref] [PubMed]

Yamaguchi, I.

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22(16), 1268–1270 (1997).
[Crossref] [PubMed]

Yang, C.

M. Cui and C. Yang, “Implementation of a digital optical phase conjugation system and its application to study the robustness of turbidity suppression by phase conjugation,” Opt. Express 18(4), 3444–3455 (2010).
[Crossref] [PubMed]

Zeldovich, B. Y.

B. Y. Zeldovich, V. I. Popovichev, V. V. Ragulskii, and F. S. Faizullov, “Connection between the wave fronts of the reflected and exciting light in stimulated Mandel'-shtam-Brillouin scattering,” Sov. Phys. JETP Lett. 15, 109–113 (1972).

Zhang, T.

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22(16), 1268–1270 (1997).
[Crossref] [PubMed]

Appl. Opt. (3)

A. J. MacGovern and J. C. Wyant, “Computer generated holograms for testing optical elements,” Appl. Opt. 10(3), 619–624 (1971).
[Crossref] [PubMed]

L. G. Neto, D. Roberge, and Y. Sheng, “Full-range, continuous, complex modulation by the use of two coupled-mode liquid-crystal televisions,” Appl. Opt. 35(23), 4567–4576 (1996).
[Crossref] [PubMed]

D. A. Gregory, J. C. Kirsch, and E. C. Tam, “Full complex modulation using liquid-crystal televisions,” Appl. Opt. 31(2), 163–165 (1992).
[Crossref] [PubMed]

IBM J. Res. Develop. (1)

L. B. Lesem, P. M. Hirch, and J. A. Jordan., “The kinoform: A new wavefront reconstruction device,” IBM J. Res. Develop. 13(2), 150–155 (1969).
[Crossref]

J. Opt. Soc. Am. (1)

H. Kogelnik and K. S. Pennington, “Holographic imaging through a random medium,” J. Opt. Soc. Am. 58(2), 273–274 (1968).
[Crossref]

Opt. Commun. (1)

T. Omatsu, A. Katoh, K. Okada, S. Hatano, A. Hasegawa, M. Tateda, and I. Ogura, “Investigation of photorefractive phase conjugate feedback on the lasing spectrum of a broad-stripe laser diode,” Opt. Commun. 146(1-6), 167–172 (1998).
[Crossref]

Opt. Express (5)

M. Cui and C. Yang, “Implementation of a digital optical phase conjugation system and its application to study the robustness of turbidity suppression by phase conjugation,” Opt. Express 18(4), 3444–3455 (2010).
[Crossref] [PubMed]

C. L. Hsieh, Y. Pu, R. Grange, and D. Psaltis, “Digital phase conjugation of second harmonic radiation emitted by nanoparticles in turbid media,” Opt. Express 18(12), 12283–12290 (2010).
[Crossref] [PubMed]

I. N. Papadopoulos, S. Farahi, C. Moser, and D. Psaltis, “Focusing and scanning light through a multimode optical fiber using digital phase conjugation,” Opt. Express 20(10), 10583–10590 (2012).
[Crossref] [PubMed]

A. Okamoto, K. Kunori, M. Takabayashi, A. Tomita, and K. Sato, “Holographic diversity interferometry for optical storage,” Opt. Express 19(14), 13436–13444 (2011).
[Crossref] [PubMed]

A. Shibukawa, A. Okamoto, M. Takabayashi, and A. Tomita, “Spatial cross modulation method using a random diffuser and phase-only spatial light modulator for constructing arbitrary complex fields,” Opt. Express 22(4), 3968–3982 (2014).
[Crossref] [PubMed]

Opt. Lett. (4)

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22(16), 1268–1270 (1997).
[Crossref] [PubMed]

C. Bellanger, A. Brignon, J. Colineau, and J. P. Huignard, “Coherent fiber combining by digital holography,” Opt. Lett. 33(24), 2937–2939 (2008).
[Crossref] [PubMed]

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[Crossref]

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[Crossref]

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Figures (11)

Fig. 1
Fig. 1

Dual-phase modulation method. (a) Conceptual diagram, (b) Modulation curve of phase-only SLM1, (c) Modulation curve of phase-only SLM2, (d) Accessible complex values in complex plane.

Fig. 2
Fig. 2

Experimental setup for dual-phase modulation method. Reference light is interfered with generated light for measurement of complex amplitude with holographic diversity interferometer (HDI). The HDI consists of two CCDs, PBS, and QWP. QWP makes phase difference of π/2 between transmitted light and reflected lights after PBS2, which is necessary for phase measurement with the HDI. Phase-only SLM provided by Hamamatsu can modulate the phase in the range [0, 2π] without any change of intensity. PSLM1 and PSLM2 offer phase modulation of 2π when gray levels are 85 and 157.

Fig. 3
Fig. 3

Initial deformations of two PSLMs, each of which is measured by displaying blank image (no modulation) onto each PSLM.

Fig. 4
Fig. 4

Complex modulation using a complex image consisting of a multi-level amplitude image and a multi-level phase image. Each data pixel consists of 16 × 16 SLM pixels. (a) Desired amplitude image. Each data pixel in the amplitude image randomly takes either of three values: 1, 0.6, and 0.3. (b) Desired phase image. Each data pixel in the phase image has either of four values: π/2, π, 3π/2, and 2π. (c) Phase image displayed on PSLM1. (d) Phase image displayed on PSLM2. (e) Measured amplitude image. (f) Measured phase image.

Fig. 5
Fig. 5

Independent modulation of amplitude image and phase image with the same resolution as that of PSLM. Each image consists of 256 × 256 SLM pixels. (a) Desired amplitude image. This is represented by 256 gray levels and includes all gray levels. (b) Desired phase image. This is represented by 256 gray levels and includes all gray levels. (c) Measured amplitude image. SNR was 6.25 dB. (d) Measured phase distribution when only the amplitude image is modulated. (e) Measured phase image. SNR was 5.85 dB. This low value is mainly due to phase wrapping. (f) Measured amplitude distribution when only the phase image is modulated.

Fig. 6
Fig. 6

Demonstration of full complex modulation using the result of Fig. 5.

Fig. 7
Fig. 7

Conceptual diagram of digital phase conjugate mirror.

Fig. 8
Fig. 8

Experimental setup for digital phase conjugate mirror. A OHP sheet is overhead projector sheet used for the correct mapping between SLMs and CCDs. The amplitude object is USAF resolution target (Edmund) and it is arranged at the focal plane of L1. A phase object is a plane-convex lens with f = 500mm or a holographic diffuser with diffusion angle of 0.5 degree (Edmund) and it is arranged at a distance of 30 mm from an amplitude object.

Fig. 9
Fig. 9

Several parameters used for precise mapping from wavefront sensor (HDI) to wavefront modulator (DPMM). (a) Image size printed on OHP sheet. (b) Image size displayed on SLM. (c) Spatial positions of OHP image on CCD1 and CCD2. (d) Spatial positions of OHP image and two SLM images on CCD3.

Fig. 10
Fig. 10

Focusing through plane-convex lens with f = 500 mm using digital phase conjugate mirror. (a) Measured intensity distribution with USAF target. (b) Measured phase distribution in a concentric fashion. (c) Widened intensity distribution on CCD4 when the blank image is displayed on the PSLM1. (d) Phase conjugated intensity distribution on CCD3 when the digital phase conjugate mirror works. (e) Phase conjugated focus spot on CCD4 when the digital phase conjugate mirror works. (f) Profile and FWHM of phase conjugated focus spots.

Fig. 11
Fig. 11

Focusing through random diffuser with the diffusion angle of 0.5 degree using digital phase conjugate mirror. (a) Measured intensity distribution. (b) Measured phase distribution. (c) Scattered intensity distribution on CCD4 when the blank image is displayed on the PSLM1. (d) Phase conjugated focus spot on CCD4 when conventional digital phase conjugation works, that is, conjugated phase distribution is displayed on PSLM1. (e) Phase conjugated focus spot on CCD4 when our digital phase conjugate mirror works. (f) Highlighted background noise on CCD4 when conventional digital phase conjugation works. (g) Highlighted background noise on CCD4 when our digital phase conjugate mirror works. (h) Profile and FWHM of phase conjugated focus spots.

Equations (6)

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Aexp( iφ )=exp( i θ 1 )+exp( i θ 2 ).
θ 1 (x,y)=φ(x,y)+ cos 1 [ A(x,y) 2 ],
θ 2 (x,y)=φ(x,y) cos 1 [ A(x,y) 2 ],
θ 1 (x,y)=φ(x,y)+ cos 1 [ A(x,y) 2 ]α(x,y)l(z),
θ 2 (x,y)=φ(x,y) cos 1 [ A(x,y) 2 ]β(x,y).
SNR(dB)=10 log 1 0 m=1 N dx n=1 N dy f ( mΔx,nΔy ) 2 m=1 N dx n=1 N dy { f ( mΔx,nΔy ) 2 g ( mΔx,nΔy ) 2 } ,

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