Abstract

Aberration correction within a free-space optical interconnect based on a spatial light modulator for beam steering and holographic wavefront correction is presented. The wavefront sensing technique is based on an extension of a modal wavefront sensor described by Neil et al. [J. Opt. Soc. Am. A 17, 1098 (2000)], which uses a diffractive element. In this analysis such a wavefront sensor is adapted with an error diffusion algorithm that yields a low reconstruction error and fast reconfigurability. Improvement of the beam propagation quality (Strehl ratio) for different channels across the input plane is achieved. However, due to the space invariancy of the system, a trade-off among the beam propagation quality for channels is obtained. Experimental results are presented and discussed.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef]

2006 (1)

D. Gil-Leyva, B. Robertson, C. J. Henderson, T. D. Wilkinson, D. C. O'Brien, and G. Faulkner, "Cross-talk analysis in a telecentric adaptive free-space optical relay based on a spatial light modulator," Appl. Opt. 45, 63-75 (2006).
[CrossRef] [PubMed]

2005 (1)

C. J. Henderson, B. Robertson, D. Gil-Leyva, T. D. Wilkinson, D. C. O'Brien, and G. Faulkner, "Control of a free space adaptive optical interconnect using a liquid crystal spatial light modulator for beam steering," Opt. Eng. 44, 075401 (2005).
[CrossRef]

2004 (2)

D. C. O'Brien, G. Faulkner, T. D. Wilkinson, B. Robertson, and D. Gil-Leyva, "Design and analysis of an adaptive board-to-board dynamic holographic interconnect," Appl. Opt. 43, 3297-3305 (2004).
[CrossRef] [PubMed]

D. Gil-Leyva, B. Robertson, C. J. Henderson, T. D. Wilkinson, D. C. O'Brien, and G. Faulkner, "Free space optical interconnect using a FLC SLM for active beam steering and wave front correction," in Micro-Optics, VCSELs and Photonic Interconnects, H. Thienpont, K. D. Choquette, and M. R. Taghizadeh, eds., Proc. SPIE 5453, 62-71 (2004).
[CrossRef]

2003 (1)

M. J. Booth, "Direct measurement of Zernike aberration modes with a modal wave-front sensor," in Advanced Wavefront Control: Methods, Devices, and Applications, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 5162, 79-90 (2003).
[CrossRef]

2002 (2)

M. A. A. Neil, R. Justakis, M. Booth, T. Wilson, T. Tanaka, and S. Kawata, "Active aberration correction for the writing of three-dimensional optical memory devices," Appl. Opt. 41, 1374-1379 (2002).
[CrossRef] [PubMed]

M. T. Gruneisen, T. Martinez, and D. L. Lubin, "Dynamic holography for high-dynamic-range for two-dimensional laser wave front control," in High-Resolution Wavefront Control: Methods, Devices, and Applications III, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 4493, 224-238 (2002).
[CrossRef]

2000 (3)

M. A. A. Neil, M. J. Booth, and T. Wilson, "New modal wave front-sensor: a theoretical analysis," J. Opt. Soc. Am. A 17, 1098-1107 (2000).
[CrossRef]

D. V. Plant and A. G. Kirk, "Optical interconnects at the chip and board level: challenges and solutions," Proc. IEEE 88, 806-818 (2000).
[CrossRef]

M. A. A. Neil, M. J. Booth, and T. Wilson, "Closed-loop aberration correction by use of a modal Zernike wave-front sensor," Opt. Lett. 25, 1083-1085 (2000).
[CrossRef]

1999 (1)

1998 (1)

M. A. A. Neil, M. J. Booth, and T. Wilson, "Dynamic wave-front generation for the characterization and testing of optical systems," Opt. Lett. 23, 1849-1851 (1998).
[CrossRef]

1996 (2)

F. A. P. Tooley, "Challenges in optically interconnecting electronics," IEEE J. Sel. Top. Quantum Electron. 2, 3-13 (1996).
[CrossRef]

D. T. Neilson and C. P. Barrett, "Performance trade-offs for conventional lenses for free-space digital optics," Appl. Opt. 35, 1240-1248 (1996).
[CrossRef] [PubMed]

1994 (1)

T. D. Wilkinson, D. C. O'Brien, and R. J. Mears, "Dynamic asymmetric binary holograms using a ferroelectric liquid crystal spatial light modulator," Opt. Commun. 109, 222-226 (1994).
[CrossRef]

1992 (3)

1991 (1)

1990 (1)

1989 (1)

S. Weissbach, F. Wyrowski, and O. Bryngdahl, "Digital phase holograms: coding and quantization with an error diffusion concept," Opt. Commun. 72, 37-41 (1989).
[CrossRef]

1987 (1)

1982 (1)

R. A. Gonsalves, "Phase retrieval and diversity in adaptive optics," Opt. Eng. 21, 829-832 (1982).

1979 (1)

W. H. Lee, "Binary computer-generated holograms," Appl. Opt. 18, 3661-3669 (1979).
[CrossRef] [PubMed]

1976 (1)

R. W. Floyd and L. Steinberg, "An adaptive algorithm for spatial grayscale," Proc. Soc. Inf. Disp. , 17, 75-77 (1976).

Allenbach, J. P.

Barnes, T. H.

Barrett, C. P.

D. T. Neilson and C. P. Barrett, "Performance trade-offs for conventional lenses for free-space digital optics," Appl. Opt. 35, 1240-1248 (1996).
[CrossRef] [PubMed]

H. J. White, N. A. Brownjohn, C. Stace, G. M. Proudley, A. C. Walker, M. R. Taghizadeh, B. Robertson, C. P. Barrett, and M. J. Birch, "Practical demonstration of a free space optical crossbar switch," in Photonics in Switching, J.W.Goodman and R.C.Alferness, eds., Vol. 146 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1993), pp. 129-132.

Birch, M. J.

H. J. White, N. A. Brownjohn, C. Stace, G. M. Proudley, A. C. Walker, M. R. Taghizadeh, B. Robertson, C. P. Barrett, and M. J. Birch, "Practical demonstration of a free space optical crossbar switch," in Photonics in Switching, J.W.Goodman and R.C.Alferness, eds., Vol. 146 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1993), pp. 129-132.

Blanchard, P. M.

Booth, M.

Booth, M. J.

M. J. Booth, "Direct measurement of Zernike aberration modes with a modal wave-front sensor," in Advanced Wavefront Control: Methods, Devices, and Applications, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 5162, 79-90 (2003).
[CrossRef]

M. A. A. Neil, M. J. Booth, and T. Wilson, "Closed-loop aberration correction by use of a modal Zernike wave-front sensor," Opt. Lett. 25, 1083-1085 (2000).
[CrossRef]

M. A. A. Neil, M. J. Booth, and T. Wilson, "New modal wave front-sensor: a theoretical analysis," J. Opt. Soc. Am. A 17, 1098-1107 (2000).
[CrossRef]

M. A. A. Neil, M. J. Booth, and T. Wilson, "Dynamic wave-front generation for the characterization and testing of optical systems," Opt. Lett. 23, 1849-1851 (1998).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2000).

Brownjohn, N. A.

H. J. White, N. A. Brownjohn, C. Stace, G. M. Proudley, A. C. Walker, M. R. Taghizadeh, B. Robertson, C. P. Barrett, and M. J. Birch, "Practical demonstration of a free space optical crossbar switch," in Photonics in Switching, J.W.Goodman and R.C.Alferness, eds., Vol. 146 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1993), pp. 129-132.

Bryngdahl, O.

S. Weissbach, F. Wyrowski, and O. Bryngdahl, "Digital phase holograms: coding and quantization with an error diffusion concept," Opt. Commun. 72, 37-41 (1989).
[CrossRef]

Dames, M. P.

Dowling, R. J.

Eiju, T.

Faulkner, G.

D. Gil-Leyva, B. Robertson, C. J. Henderson, T. D. Wilkinson, D. C. O'Brien, and G. Faulkner, "Cross-talk analysis in a telecentric adaptive free-space optical relay based on a spatial light modulator," Appl. Opt. 45, 63-75 (2006).
[CrossRef] [PubMed]

C. J. Henderson, B. Robertson, D. Gil-Leyva, T. D. Wilkinson, D. C. O'Brien, and G. Faulkner, "Control of a free space adaptive optical interconnect using a liquid crystal spatial light modulator for beam steering," Opt. Eng. 44, 075401 (2005).
[CrossRef]

D. C. O'Brien, G. Faulkner, T. D. Wilkinson, B. Robertson, and D. Gil-Leyva, "Design and analysis of an adaptive board-to-board dynamic holographic interconnect," Appl. Opt. 43, 3297-3305 (2004).
[CrossRef] [PubMed]

D. Gil-Leyva, B. Robertson, C. J. Henderson, T. D. Wilkinson, D. C. O'Brien, and G. Faulkner, "Free space optical interconnect using a FLC SLM for active beam steering and wave front correction," in Micro-Optics, VCSELs and Photonic Interconnects, H. Thienpont, K. D. Choquette, and M. R. Taghizadeh, eds., Proc. SPIE 5453, 62-71 (2004).
[CrossRef]

Floyd, R. W.

R. W. Floyd and L. Steinberg, "An adaptive algorithm for spatial grayscale," Proc. Soc. Inf. Disp. , 17, 75-77 (1976).

Gil-Leyva, D.

D. Gil-Leyva, B. Robertson, C. J. Henderson, T. D. Wilkinson, D. C. O'Brien, and G. Faulkner, "Cross-talk analysis in a telecentric adaptive free-space optical relay based on a spatial light modulator," Appl. Opt. 45, 63-75 (2006).
[CrossRef] [PubMed]

C. J. Henderson, B. Robertson, D. Gil-Leyva, T. D. Wilkinson, D. C. O'Brien, and G. Faulkner, "Control of a free space adaptive optical interconnect using a liquid crystal spatial light modulator for beam steering," Opt. Eng. 44, 075401 (2005).
[CrossRef]

D. C. O'Brien, G. Faulkner, T. D. Wilkinson, B. Robertson, and D. Gil-Leyva, "Design and analysis of an adaptive board-to-board dynamic holographic interconnect," Appl. Opt. 43, 3297-3305 (2004).
[CrossRef] [PubMed]

D. Gil-Leyva, B. Robertson, C. J. Henderson, T. D. Wilkinson, D. C. O'Brien, and G. Faulkner, "Free space optical interconnect using a FLC SLM for active beam steering and wave front correction," in Micro-Optics, VCSELs and Photonic Interconnects, H. Thienpont, K. D. Choquette, and M. R. Taghizadeh, eds., Proc. SPIE 5453, 62-71 (2004).
[CrossRef]

Gonsalves, R. A.

R. A. Gonsalves, "Phase retrieval and diversity in adaptive optics," Opt. Eng. 21, 829-832 (1982).

Greenaway, A. H.

Gruneisen, M. T.

M. T. Gruneisen, T. Martinez, and D. L. Lubin, "Dynamic holography for high-dynamic-range for two-dimensional laser wave front control," in High-Resolution Wavefront Control: Methods, Devices, and Applications III, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 4493, 224-238 (2002).
[CrossRef]

Guest, C. C.

Henderson, C. J.

D. Gil-Leyva, B. Robertson, C. J. Henderson, T. D. Wilkinson, D. C. O'Brien, and G. Faulkner, "Cross-talk analysis in a telecentric adaptive free-space optical relay based on a spatial light modulator," Appl. Opt. 45, 63-75 (2006).
[CrossRef] [PubMed]

C. J. Henderson, B. Robertson, D. Gil-Leyva, T. D. Wilkinson, D. C. O'Brien, and G. Faulkner, "Control of a free space adaptive optical interconnect using a liquid crystal spatial light modulator for beam steering," Opt. Eng. 44, 075401 (2005).
[CrossRef]

D. Gil-Leyva, B. Robertson, C. J. Henderson, T. D. Wilkinson, D. C. O'Brien, and G. Faulkner, "Free space optical interconnect using a FLC SLM for active beam steering and wave front correction," in Micro-Optics, VCSELs and Photonic Interconnects, H. Thienpont, K. D. Choquette, and M. R. Taghizadeh, eds., Proc. SPIE 5453, 62-71 (2004).
[CrossRef]

Ichikawa, H.

Justakis, R.

Kawata, S.

Kim, M. S.

Kirk, A. G.

D. V. Plant and A. G. Kirk, "Optical interconnects at the chip and board level: challenges and solutions," Proc. IEEE 88, 806-818 (2000).
[CrossRef]

Kostuk, R. K.

R. K. Kostuk, "Simulation of board-level free-space optical interconnects for electronic processing," Appl. Opt. 31, 2438-2445 (1992).
[CrossRef] [PubMed]

Lee, W. H.

W. H. Lee, "Binary computer-generated holograms," Appl. Opt. 18, 3661-3669 (1979).
[CrossRef] [PubMed]

Lubin, D. L.

M. T. Gruneisen, T. Martinez, and D. L. Lubin, "Dynamic holography for high-dynamic-range for two-dimensional laser wave front control," in High-Resolution Wavefront Control: Methods, Devices, and Applications III, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 4493, 224-238 (2002).
[CrossRef]

Martinez, T.

M. T. Gruneisen, T. Martinez, and D. L. Lubin, "Dynamic holography for high-dynamic-range for two-dimensional laser wave front control," in High-Resolution Wavefront Control: Methods, Devices, and Applications III, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 4493, 224-238 (2002).
[CrossRef]

Matsuda, K.

McKee, P.

Mears, R. J.

T. D. Wilkinson, D. C. O'Brien, and R. J. Mears, "Dynamic asymmetric binary holograms using a ferroelectric liquid crystal spatial light modulator," Opt. Commun. 109, 222-226 (1994).
[CrossRef]

Neil, M. A. A.

M. A. A. Neil, R. Justakis, M. Booth, T. Wilson, T. Tanaka, and S. Kawata, "Active aberration correction for the writing of three-dimensional optical memory devices," Appl. Opt. 41, 1374-1379 (2002).
[CrossRef] [PubMed]

M. A. A. Neil, M. J. Booth, and T. Wilson, "Closed-loop aberration correction by use of a modal Zernike wave-front sensor," Opt. Lett. 25, 1083-1085 (2000).
[CrossRef]

M. A. A. Neil, M. J. Booth, and T. Wilson, "New modal wave front-sensor: a theoretical analysis," J. Opt. Soc. Am. A 17, 1098-1107 (2000).
[CrossRef]

M. A. A. Neil, M. J. Booth, and T. Wilson, "Dynamic wave-front generation for the characterization and testing of optical systems," Opt. Lett. 23, 1849-1851 (1998).
[CrossRef]

Neilson, D. T.

D. T. Neilson and C. P. Barrett, "Performance trade-offs for conventional lenses for free-space digital optics," Appl. Opt. 35, 1240-1248 (1996).
[CrossRef] [PubMed]

O'Brien, D. C.

D. Gil-Leyva, B. Robertson, C. J. Henderson, T. D. Wilkinson, D. C. O'Brien, and G. Faulkner, "Cross-talk analysis in a telecentric adaptive free-space optical relay based on a spatial light modulator," Appl. Opt. 45, 63-75 (2006).
[CrossRef] [PubMed]

C. J. Henderson, B. Robertson, D. Gil-Leyva, T. D. Wilkinson, D. C. O'Brien, and G. Faulkner, "Control of a free space adaptive optical interconnect using a liquid crystal spatial light modulator for beam steering," Opt. Eng. 44, 075401 (2005).
[CrossRef]

D. C. O'Brien, G. Faulkner, T. D. Wilkinson, B. Robertson, and D. Gil-Leyva, "Design and analysis of an adaptive board-to-board dynamic holographic interconnect," Appl. Opt. 43, 3297-3305 (2004).
[CrossRef] [PubMed]

D. Gil-Leyva, B. Robertson, C. J. Henderson, T. D. Wilkinson, D. C. O'Brien, and G. Faulkner, "Free space optical interconnect using a FLC SLM for active beam steering and wave front correction," in Micro-Optics, VCSELs and Photonic Interconnects, H. Thienpont, K. D. Choquette, and M. R. Taghizadeh, eds., Proc. SPIE 5453, 62-71 (2004).
[CrossRef]

T. D. Wilkinson, D. C. O'Brien, and R. J. Mears, "Dynamic asymmetric binary holograms using a ferroelectric liquid crystal spatial light modulator," Opt. Commun. 109, 222-226 (1994).
[CrossRef]

Plant, D. V.

D. V. Plant and A. G. Kirk, "Optical interconnects at the chip and board level: challenges and solutions," Proc. IEEE 88, 806-818 (2000).
[CrossRef]

Proudley, G. M.

H. J. White, N. A. Brownjohn, C. Stace, G. M. Proudley, A. C. Walker, M. R. Taghizadeh, B. Robertson, C. P. Barrett, and M. J. Birch, "Practical demonstration of a free space optical crossbar switch," in Photonics in Switching, J.W.Goodman and R.C.Alferness, eds., Vol. 146 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1993), pp. 129-132.

Robertson, B.

D. Gil-Leyva, B. Robertson, C. J. Henderson, T. D. Wilkinson, D. C. O'Brien, and G. Faulkner, "Cross-talk analysis in a telecentric adaptive free-space optical relay based on a spatial light modulator," Appl. Opt. 45, 63-75 (2006).
[CrossRef] [PubMed]

C. J. Henderson, B. Robertson, D. Gil-Leyva, T. D. Wilkinson, D. C. O'Brien, and G. Faulkner, "Control of a free space adaptive optical interconnect using a liquid crystal spatial light modulator for beam steering," Opt. Eng. 44, 075401 (2005).
[CrossRef]

D. C. O'Brien, G. Faulkner, T. D. Wilkinson, B. Robertson, and D. Gil-Leyva, "Design and analysis of an adaptive board-to-board dynamic holographic interconnect," Appl. Opt. 43, 3297-3305 (2004).
[CrossRef] [PubMed]

D. Gil-Leyva, B. Robertson, C. J. Henderson, T. D. Wilkinson, D. C. O'Brien, and G. Faulkner, "Free space optical interconnect using a FLC SLM for active beam steering and wave front correction," in Micro-Optics, VCSELs and Photonic Interconnects, H. Thienpont, K. D. Choquette, and M. R. Taghizadeh, eds., Proc. SPIE 5453, 62-71 (2004).
[CrossRef]

H. J. White, N. A. Brownjohn, C. Stace, G. M. Proudley, A. C. Walker, M. R. Taghizadeh, B. Robertson, C. P. Barrett, and M. J. Birch, "Practical demonstration of a free space optical crossbar switch," in Photonics in Switching, J.W.Goodman and R.C.Alferness, eds., Vol. 146 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1993), pp. 129-132.

Seldowitz, M. A.

Stace, C.

H. J. White, N. A. Brownjohn, C. Stace, G. M. Proudley, A. C. Walker, M. R. Taghizadeh, B. Robertson, C. P. Barrett, and M. J. Birch, "Practical demonstration of a free space optical crossbar switch," in Photonics in Switching, J.W.Goodman and R.C.Alferness, eds., Vol. 146 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1993), pp. 129-132.

Steinberg, L.

R. W. Floyd and L. Steinberg, "An adaptive algorithm for spatial grayscale," Proc. Soc. Inf. Disp. , 17, 75-77 (1976).

Sweeney, D. W.

Taghizadeh, M.

Taghizadeh, M. R.

H. J. White, N. A. Brownjohn, C. Stace, G. M. Proudley, A. C. Walker, M. R. Taghizadeh, B. Robertson, C. P. Barrett, and M. J. Birch, "Practical demonstration of a free space optical crossbar switch," in Photonics in Switching, J.W.Goodman and R.C.Alferness, eds., Vol. 146 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1993), pp. 129-132.

Tanaka, T.

Tooley, F. A. P.

F. A. P. Tooley, "Challenges in optically interconnecting electronics," IEEE J. Sel. Top. Quantum Electron. 2, 3-13 (1996).
[CrossRef]

Turunen, J.

Tyson, R. K.

R. K. Tyson, Principles of Adaptive Optics, 2nd ed. (Academic, 1991).

Walker, A. C.

H. J. White, N. A. Brownjohn, C. Stace, G. M. Proudley, A. C. Walker, M. R. Taghizadeh, B. Robertson, C. P. Barrett, and M. J. Birch, "Practical demonstration of a free space optical crossbar switch," in Photonics in Switching, J.W.Goodman and R.C.Alferness, eds., Vol. 146 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1993), pp. 129-132.

Weissbach, S.

S. Weissbach and F. Wyrowski, "Error diffusion procedure: theory and applications in optical signal processing," Appl. Opt. 31, 2518-2533 (1992).
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[CrossRef] [PubMed]

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[CrossRef]

Appl. Opt. (12)

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[CrossRef]

Opt. Commun. (2)

T. D. Wilkinson, D. C. O'Brien, and R. J. Mears, "Dynamic asymmetric binary holograms using a ferroelectric liquid crystal spatial light modulator," Opt. Commun. 109, 222-226 (1994).
[CrossRef]

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[CrossRef]

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C. J. Henderson, B. Robertson, D. Gil-Leyva, T. D. Wilkinson, D. C. O'Brien, and G. Faulkner, "Control of a free space adaptive optical interconnect using a liquid crystal spatial light modulator for beam steering," Opt. Eng. 44, 075401 (2005).
[CrossRef]

Opt. Lett. (2)

M. A. A. Neil, M. J. Booth, and T. Wilson, "Dynamic wave-front generation for the characterization and testing of optical systems," Opt. Lett. 23, 1849-1851 (1998).
[CrossRef]

M. A. A. Neil, M. J. Booth, and T. Wilson, "Closed-loop aberration correction by use of a modal Zernike wave-front sensor," Opt. Lett. 25, 1083-1085 (2000).
[CrossRef]

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M. J. Booth, "Direct measurement of Zernike aberration modes with a modal wave-front sensor," in Advanced Wavefront Control: Methods, Devices, and Applications, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 5162, 79-90 (2003).
[CrossRef]

D. Gil-Leyva, B. Robertson, C. J. Henderson, T. D. Wilkinson, D. C. O'Brien, and G. Faulkner, "Free space optical interconnect using a FLC SLM for active beam steering and wave front correction," in Micro-Optics, VCSELs and Photonic Interconnects, H. Thienpont, K. D. Choquette, and M. R. Taghizadeh, eds., Proc. SPIE 5453, 62-71 (2004).
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R. K. Tyson, Principles of Adaptive Optics, 2nd ed. (Academic, 1991).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2000).

H. J. White, N. A. Brownjohn, C. Stace, G. M. Proudley, A. C. Walker, M. R. Taghizadeh, B. Robertson, C. P. Barrett, and M. J. Birch, "Practical demonstration of a free space optical crossbar switch," in Photonics in Switching, J.W.Goodman and R.C.Alferness, eds., Vol. 146 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1993), pp. 129-132.

www.crlopto.com.

www.ulm-photonics.de.

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Figures (15)

Fig. 1
Fig. 1

Unfolded F system used for a free-space optical interconnect.

Fig. 2
Fig. 2

Wavefront sensor response plotted against different magnitude ak of input aberrations for different magnitude bk of bias aberration of an arbitrary Zernike mode. The values for bk and ak are in waves.

Fig. 3
Fig. 3

(a) Holographic wavefront sensor that performs a spatially multiplexing operation to detect several Zernike modes. The pattern is created with a direct binary search with simulated annealing. (b) Amplitude of the simulated replay field imaged on a logarithmic scale [log(100 × amplitude + 1)]. The percentage of light in the signal window in (b) is 60%.

Fig. 4
Fig. 4

(a) Holographic wavefront sensor that performs a spatially multiplexing operation to detect several Zernike modes. The pattern is created with an EDA. (b) Simulated amplitude of the replay field imaged on a logarithmic scale [log(100 × amplitude + 1)]. The percentage of light in the signal window in (b) is 7.74%.

Fig. 5
Fig. 5

Optical setup.

Fig. 6
Fig. 6

Strehl ratio variation across the input field.

Fig. 7
Fig. 7

(a) CGH for fan-out operation only (no aberration biasing). (b) Experimental replay field. Note the presence of the zero order.

Fig. 8
Fig. 8

Experimental replay field for a hologram designed for a wavefront sensing operation. The modes with the associated spots are indicated.

Fig. 9
Fig. 9

Off-axis experimental replay field for a hologram designed for a wavefront sensing operation. The modes with the associated spots are indicated.

Fig. 10
Fig. 10

Experimental replay field of a hologram designed for adding the phase conjugate Ψ c to the wavefront obtained for an off-axis beam. As expected, the +1 order gets brighter whereas the −1 order is dimmer.

Fig. 11
Fig. 11

(a) Off-axis experimental replay field of a hologram designed for wavefront sensing plus a correction phase Ψ c. (b) Off-axis experimental replay field for a hologram designed for wavefront sensing plus a correction equal to −ψ c. The output of the overall wavefront sensor is calculated by using the conjugate spots, which are labeled on each figure.

Fig. 12
Fig. 12

(a) Grating structure for beam steering. (b) Grating structure with the added phase conjugation Ψ c obtained for the off-axis beam. (c) and (d) Experimental replay field for both modulation functions respectively. (e) Experimental replay of the corrective grating with an overexposure of the camera.

Fig. 13
Fig. 13

(a) Grating structure for beam steering. (b) Grating structure with the added phase conjugation Ψ c obtained for the on-axis beam (c) and (d) Experimental replay field for both modulation functions.

Fig. 14
Fig. 14

(a) Grating structure for beam steering plus a phase conjugation factor Ψ c designed to correct for the off-axis beam. (b) Experimental replay field of the on-axis beam. (c) Experimental replay field of the off-axis beam.

Fig. 15
Fig. 15

(a) Grating structure for beam steering plus a phase conjugation factor Ψ c designed to optimize the Strehl ratio for both the on and off-axis beam. (b) Experimental replay field of the on-axis beam. (c) Experimental replay field of the off-axis beam.

Tables (3)

Tables Icon

Table 1 Sensitivity Matrix Obtained for a Spatially Multiplexing Sensor Designed with Direct Binary Search with Simulated Annealing

Tables Icon

Table 2 Zernike Polynomials

Tables Icon

Table 3 Sensitivity Matrix Obtained With a Spatially Multiplexed Sensor Designed with an EDA

Equations (26)

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W = exp ( i Ψ ) = exp ( i j a j Z j ) .
f b ( x , y ) = 2 π n = 1 n sin ( π n 2 ) exp [ i n ( Φ ) ]
= 2 π { exp [ i ( Φ ) ] + exp [ i ( Φ ) ] 1 3 exp [ i 3 ( Φ ) ] 1 3 exp [ i 3 ( Φ ) ] + } .
I + 1 = | { W exp [ i b j Z j ] } | 2 = | { exp [ i a k Z k + i b j Z j ] } | 2 ,
I 1 = | { W exp [ i b j Z j ] } | 2 = | { exp [ i a k Z k i b j Z j ] } | 2 .
Δ I = S k a k ,
C k = Real [ { h } × 1 { i Z k × h * } ] .
h = exp [ i ( τ 1 + b 4 Z 4 ) ] + exp [ i ( τ 2 + b 5 Z 5 ) ] + exp [ i ( τ 3 + b 6 Z 6 ) ] + exp [ i ( τ 4 + b 7 Z 7 ) ] + exp [ i ( τ 5 + b 8 Z 8 ) ] + exp [ i ( τ 6 + b 9 Z 9 ) ] + exp [ i ( τ 7 + b 10 Z 10 ) ] + exp [ i ( τ 8 + b 11 Z 11 ) ] .
d = [ 0 1 7 / 16 3 / 16 5 / 16 1 / 16 ] .
Ψ c = j c j Z j .
w = ( A + B + ) ( A B ) B + + B .
h c = exp ( i Ψ c ) h ,
c n + 1 = c n + μ × w n .
W = exp ( i Ψ ) exp ( i Ψ c ) h
= { exp [ i ( Ψ + Ψ c + b j Z j + τ j ) ] + exp [ i ( Ψ + Ψ c b j Z j τ j ) ] } .
h = exp ( i Ψ c ) h
= { exp [ i ( Ψ c + b j Z j + τ j ) ] + exp [ i ( Ψ c b j Z j τ j ) ] } .
W = exp ( i Ψ ) h
= { exp [ i ( Ψ + Ψ c + b j Z j + τ j ) ] + exp [ i ( Ψ Ψ c b j Z j τ j ) ] } .
W = exp ( i Ψ ) h neg
= { exp [ i ( Ψ Ψ c + b j Z j + τ j ) ] + exp [ i ( Ψ + Ψ c b j Z j τ j ) ] } .
W = exp ( i Ψ ) h
= { exp [ i ( Ψ + Ψ c + b j Z j + τ j ) ] + exp [ i ( Ψ Ψ c b j Z j τ j ) ] } .
I 1 ( 2 π ) 2 j ( c j ) 2 ,
d n + 1 = d n + μ n   on-axis × w n   on-axis + μ n   off-axis × w n   off-axis ,
μ on∕off-axis = 1 I on/off-axis I on-axis + I off-axis .

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