Abstract

A Fourier analysis treatment of the wavelength dependences associated with modulo λr optical path control, treating the general case of a modulo λr optical path difference function OPD (x, y) mod λr in which the reset wavelength λr, is allowed to be an integer multiple of a nominal wavelength λ0, λr=Nλ0, is presented. Equations are derived describing the wavelength-dependent characteristics of the diffraction efficiency and the wavefront errors associated with all diffracted orders. The results are applied to the cases of diffraction of a planar wavefront and compensation of large aberrations and show that over an extended spectral bandwidth the output field consists of multiple diffracted orders with a range of fractional wavefront errors that diminishes with increasing reset multiple N, but does not reach the diffraction limit associated with conventional optics.

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    [CrossRef]
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  5. Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, and T. Hara, "High efficiency electrically-addressable phase-only spatial light modulator," Opt. Rev. 6, 339-344 (1999).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2005 (4)

M. T. Gruneisen, R. C. Dymale, J. R. Rotge, L. F. DeSandre, and D. L. Lubin, "Compensated telescope system with programmable diffractive optic," Opt. Eng. 44, 023201-1-023201-9 (2005).
[CrossRef]

R. Ryf, H. R. Stuart, and C. R. Giles, "MEMS tip/tilt and piston mirror arrays as diffractive optical elements," in Advanced Wavefront Control: Methods, Devices, and Applications III, M. T. Gruneisen, J. D. Gonglewski, M. K. Giles, eds., Proc. SPIE 5894, 113-123 (2005).

M. T. Gruneisen, R. C. Dymale, J. R. Rotge, L. F. DeSandre, and D. L. Lubin, "Wavelength-dependent characteristics of a telescope system with diffractive wavefront control," Opt. Eng. 44, 068002-1-068002-8 (2005).
[CrossRef]

P. McManamon, J. Shi, and P. J. Bos, "Broadband optical phased array beam steering," Opt. Eng. 44, 128004-1-128004-5 (2005).
[CrossRef]

2004 (2)

H. Zhu, P. Bierden, S. Cornelissen, T. Bifano, and J. Kim, "Design and fabrication of reflective spatial light modulators for high-dynamic-range wavefront control," in Advanced Wavefront Control: Methods, Devices, and Applications II, J. D. Gonglewski, M. T. Gruneisen, and M. K. Giles, eds., Proc. SPIE 5553, 39-45 (2004).
[CrossRef]

M. T. Gruneisen, L. F. DeSandre, J. R. Rotge, R. C. Dymale, and D. L. Lubin, "Programmable diffractive optics for wide-dynamic-range wavefront control using liquid-crystal spatial light modulators," Opt. Eng. 43, 1387-1393 (2004).
[CrossRef]

2003 (1)

X. Wang, B. Wang, J. Pouch, F. Miranda, M. Fisch, J. E. Anderson, V. Sergan, and P. Bos, "Liquid crystal on silicon (LCOS) wavefront corrector and beam steerer," in Advanced Wavefront Control: Methods, Devices, and Applications, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 5162, 139-146 (2003).
[CrossRef]

2002 (2)

K. Bauchert, S. Serati, and A. Furman, "Advances in liquid crystal spatial light modulators," in Optical Pattern Recognition XIII, D. P. Casasent and T. H. Chao, eds., Proc. SPIE 4734, 35-43 (2002).
[CrossRef]

J. Rha and M. K. Giles, "Implementation of an adaptive Shack-Hartmann sensor using a phase-modulated liquid crystal spatial light modulator," in High-Resolution Wavefront Control: Methods, Devices, and Applications, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 4493, 80-87 (2002).
[CrossRef]

2000 (1)

D. Guthals, D. Sox, M. Joswick, and P. J. Rodney, "Real-time holographic compensation of large optics for deployment in space," in High-Resolution Wavefront Control: Methods, Devices, and Applications II, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 4124, 245-256 (2000).
[CrossRef]

1999 (1)

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, and T. Hara, "High efficiency electrically-addressable phase-only spatial light modulator," Opt. Rev. 6, 339-344 (1999).
[CrossRef]

1996 (1)

P. F. McManamon, T. A. Dorschner, D. C. Corkum, L. J. Friedman, D. S. Hobbs, M. K. O. Holz, S. Liberman, H. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

1995 (2)

R. Dou and M. K. Giles, "Programmable phase grating and beam steerer by operating a LCTV," in Advanced Imaging Technologies and Commercial Applications, N. Clark and J. D. Gonglewski, eds., Proc. SPIE 2566, 26-34 (1995).
[CrossRef]

D. Faklis and G. M. Morris, "Spectral properties of multiorder diffractive lenses," Appl. Opt. 34, 2462-2468 (1995).
[CrossRef] [PubMed]

1994 (1)

A. Kirk, T. Tabata, M. Ishikawa, and H. Toyoda, "Reconfigurable computer generated holograms," Opt. Commun. 105, 302-308 (1994).
[CrossRef]

1993 (1)

P. F. McManamon, E. A. Watson, T. A. Dorschner, and L. J. Barnes, "Applications look at the use of liquid crystal writable gratings for steering passive radiation," Opt. Eng. 32, 2657-2664 (1993).
[CrossRef]

1989 (1)

Anderson, J. E.

X. Wang, B. Wang, J. Pouch, F. Miranda, M. Fisch, J. E. Anderson, V. Sergan, and P. Bos, "Liquid crystal on silicon (LCOS) wavefront corrector and beam steerer," in Advanced Wavefront Control: Methods, Devices, and Applications, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 5162, 139-146 (2003).
[CrossRef]

Barnes, L. J.

P. F. McManamon, E. A. Watson, T. A. Dorschner, and L. J. Barnes, "Applications look at the use of liquid crystal writable gratings for steering passive radiation," Opt. Eng. 32, 2657-2664 (1993).
[CrossRef]

Bauchert, K.

K. Bauchert, S. Serati, and A. Furman, "Advances in liquid crystal spatial light modulators," in Optical Pattern Recognition XIII, D. P. Casasent and T. H. Chao, eds., Proc. SPIE 4734, 35-43 (2002).
[CrossRef]

Bierden, P.

H. Zhu, P. Bierden, S. Cornelissen, T. Bifano, and J. Kim, "Design and fabrication of reflective spatial light modulators for high-dynamic-range wavefront control," in Advanced Wavefront Control: Methods, Devices, and Applications II, J. D. Gonglewski, M. T. Gruneisen, and M. K. Giles, eds., Proc. SPIE 5553, 39-45 (2004).
[CrossRef]

Bifano, T.

H. Zhu, P. Bierden, S. Cornelissen, T. Bifano, and J. Kim, "Design and fabrication of reflective spatial light modulators for high-dynamic-range wavefront control," in Advanced Wavefront Control: Methods, Devices, and Applications II, J. D. Gonglewski, M. T. Gruneisen, and M. K. Giles, eds., Proc. SPIE 5553, 39-45 (2004).
[CrossRef]

Bos, P.

X. Wang, B. Wang, J. Pouch, F. Miranda, M. Fisch, J. E. Anderson, V. Sergan, and P. Bos, "Liquid crystal on silicon (LCOS) wavefront corrector and beam steerer," in Advanced Wavefront Control: Methods, Devices, and Applications, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 5162, 139-146 (2003).
[CrossRef]

Bos, P. J.

P. McManamon, J. Shi, and P. J. Bos, "Broadband optical phased array beam steering," Opt. Eng. 44, 128004-1-128004-5 (2005).
[CrossRef]

Buralli, D. A.

Corkum, D. C.

P. F. McManamon, T. A. Dorschner, D. C. Corkum, L. J. Friedman, D. S. Hobbs, M. K. O. Holz, S. Liberman, H. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Cornelissen, S.

H. Zhu, P. Bierden, S. Cornelissen, T. Bifano, and J. Kim, "Design and fabrication of reflective spatial light modulators for high-dynamic-range wavefront control," in Advanced Wavefront Control: Methods, Devices, and Applications II, J. D. Gonglewski, M. T. Gruneisen, and M. K. Giles, eds., Proc. SPIE 5553, 39-45 (2004).
[CrossRef]

DeSandre, L. F.

M. T. Gruneisen, R. C. Dymale, J. R. Rotge, L. F. DeSandre, and D. L. Lubin, "Compensated telescope system with programmable diffractive optic," Opt. Eng. 44, 023201-1-023201-9 (2005).
[CrossRef]

M. T. Gruneisen, R. C. Dymale, J. R. Rotge, L. F. DeSandre, and D. L. Lubin, "Wavelength-dependent characteristics of a telescope system with diffractive wavefront control," Opt. Eng. 44, 068002-1-068002-8 (2005).
[CrossRef]

M. T. Gruneisen, L. F. DeSandre, J. R. Rotge, R. C. Dymale, and D. L. Lubin, "Programmable diffractive optics for wide-dynamic-range wavefront control using liquid-crystal spatial light modulators," Opt. Eng. 43, 1387-1393 (2004).
[CrossRef]

Dorschner, T. A.

P. F. McManamon, T. A. Dorschner, D. C. Corkum, L. J. Friedman, D. S. Hobbs, M. K. O. Holz, S. Liberman, H. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

P. F. McManamon, E. A. Watson, T. A. Dorschner, and L. J. Barnes, "Applications look at the use of liquid crystal writable gratings for steering passive radiation," Opt. Eng. 32, 2657-2664 (1993).
[CrossRef]

Dou, R.

R. Dou and M. K. Giles, "Programmable phase grating and beam steerer by operating a LCTV," in Advanced Imaging Technologies and Commercial Applications, N. Clark and J. D. Gonglewski, eds., Proc. SPIE 2566, 26-34 (1995).
[CrossRef]

Dymale, R. C.

M. T. Gruneisen, R. C. Dymale, J. R. Rotge, L. F. DeSandre, and D. L. Lubin, "Compensated telescope system with programmable diffractive optic," Opt. Eng. 44, 023201-1-023201-9 (2005).
[CrossRef]

M. T. Gruneisen, R. C. Dymale, J. R. Rotge, L. F. DeSandre, and D. L. Lubin, "Wavelength-dependent characteristics of a telescope system with diffractive wavefront control," Opt. Eng. 44, 068002-1-068002-8 (2005).
[CrossRef]

M. T. Gruneisen, L. F. DeSandre, J. R. Rotge, R. C. Dymale, and D. L. Lubin, "Programmable diffractive optics for wide-dynamic-range wavefront control using liquid-crystal spatial light modulators," Opt. Eng. 43, 1387-1393 (2004).
[CrossRef]

Faklis, D.

Fisch, M.

X. Wang, B. Wang, J. Pouch, F. Miranda, M. Fisch, J. E. Anderson, V. Sergan, and P. Bos, "Liquid crystal on silicon (LCOS) wavefront corrector and beam steerer," in Advanced Wavefront Control: Methods, Devices, and Applications, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 5162, 139-146 (2003).
[CrossRef]

Friedman, L. J.

P. F. McManamon, T. A. Dorschner, D. C. Corkum, L. J. Friedman, D. S. Hobbs, M. K. O. Holz, S. Liberman, H. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Furman, A.

K. Bauchert, S. Serati, and A. Furman, "Advances in liquid crystal spatial light modulators," in Optical Pattern Recognition XIII, D. P. Casasent and T. H. Chao, eds., Proc. SPIE 4734, 35-43 (2002).
[CrossRef]

Giles, C. R.

R. Ryf, H. R. Stuart, and C. R. Giles, "MEMS tip/tilt and piston mirror arrays as diffractive optical elements," in Advanced Wavefront Control: Methods, Devices, and Applications III, M. T. Gruneisen, J. D. Gonglewski, M. K. Giles, eds., Proc. SPIE 5894, 113-123 (2005).

Giles, M. K.

J. Rha and M. K. Giles, "Implementation of an adaptive Shack-Hartmann sensor using a phase-modulated liquid crystal spatial light modulator," in High-Resolution Wavefront Control: Methods, Devices, and Applications, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 4493, 80-87 (2002).
[CrossRef]

R. Dou and M. K. Giles, "Programmable phase grating and beam steerer by operating a LCTV," in Advanced Imaging Technologies and Commercial Applications, N. Clark and J. D. Gonglewski, eds., Proc. SPIE 2566, 26-34 (1995).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

Gruneisen, M. T.

M. T. Gruneisen, R. C. Dymale, J. R. Rotge, L. F. DeSandre, and D. L. Lubin, "Compensated telescope system with programmable diffractive optic," Opt. Eng. 44, 023201-1-023201-9 (2005).
[CrossRef]

M. T. Gruneisen, R. C. Dymale, J. R. Rotge, L. F. DeSandre, and D. L. Lubin, "Wavelength-dependent characteristics of a telescope system with diffractive wavefront control," Opt. Eng. 44, 068002-1-068002-8 (2005).
[CrossRef]

M. T. Gruneisen, L. F. DeSandre, J. R. Rotge, R. C. Dymale, and D. L. Lubin, "Programmable diffractive optics for wide-dynamic-range wavefront control using liquid-crystal spatial light modulators," Opt. Eng. 43, 1387-1393 (2004).
[CrossRef]

Guthals, D.

D. Guthals, D. Sox, M. Joswick, and P. J. Rodney, "Real-time holographic compensation of large optics for deployment in space," in High-Resolution Wavefront Control: Methods, Devices, and Applications II, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 4124, 245-256 (2000).
[CrossRef]

Hara, T.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, and T. Hara, "High efficiency electrically-addressable phase-only spatial light modulator," Opt. Rev. 6, 339-344 (1999).
[CrossRef]

H. Toyoda, Y. Kobayashi, N. Yoshida, Y. Igasaki, T. Hara, M. Ishikawa, and M. H. Wu, "High efficient electrically addressable spatial light modulator for reconfigurable optical connection," in OSA Snowmass Meeting, Spatial Light Modulators, OSA Technical Digest Series (Optical Society of America, 1999), SMB3, pp. 14-16.

Hobbs, D. S.

P. F. McManamon, T. A. Dorschner, D. C. Corkum, L. J. Friedman, D. S. Hobbs, M. K. O. Holz, S. Liberman, H. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Holz, M. K. O.

P. F. McManamon, T. A. Dorschner, D. C. Corkum, L. J. Friedman, D. S. Hobbs, M. K. O. Holz, S. Liberman, H. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Igasaki, Y.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, and T. Hara, "High efficiency electrically-addressable phase-only spatial light modulator," Opt. Rev. 6, 339-344 (1999).
[CrossRef]

H. Toyoda, Y. Kobayashi, N. Yoshida, Y. Igasaki, T. Hara, M. Ishikawa, and M. H. Wu, "High efficient electrically addressable spatial light modulator for reconfigurable optical connection," in OSA Snowmass Meeting, Spatial Light Modulators, OSA Technical Digest Series (Optical Society of America, 1999), SMB3, pp. 14-16.

Inoue, T.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, and T. Hara, "High efficiency electrically-addressable phase-only spatial light modulator," Opt. Rev. 6, 339-344 (1999).
[CrossRef]

Ishikawa, M.

A. Kirk, T. Tabata, M. Ishikawa, and H. Toyoda, "Reconfigurable computer generated holograms," Opt. Commun. 105, 302-308 (1994).
[CrossRef]

H. Toyoda, Y. Kobayashi, N. Yoshida, Y. Igasaki, T. Hara, M. Ishikawa, and M. H. Wu, "High efficient electrically addressable spatial light modulator for reconfigurable optical connection," in OSA Snowmass Meeting, Spatial Light Modulators, OSA Technical Digest Series (Optical Society of America, 1999), SMB3, pp. 14-16.

Joswick, M.

D. Guthals, D. Sox, M. Joswick, and P. J. Rodney, "Real-time holographic compensation of large optics for deployment in space," in High-Resolution Wavefront Control: Methods, Devices, and Applications II, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 4124, 245-256 (2000).
[CrossRef]

Kim, J.

H. Zhu, P. Bierden, S. Cornelissen, T. Bifano, and J. Kim, "Design and fabrication of reflective spatial light modulators for high-dynamic-range wavefront control," in Advanced Wavefront Control: Methods, Devices, and Applications II, J. D. Gonglewski, M. T. Gruneisen, and M. K. Giles, eds., Proc. SPIE 5553, 39-45 (2004).
[CrossRef]

Kirk, A.

A. Kirk, T. Tabata, M. Ishikawa, and H. Toyoda, "Reconfigurable computer generated holograms," Opt. Commun. 105, 302-308 (1994).
[CrossRef]

Kobayashi, Y.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, and T. Hara, "High efficiency electrically-addressable phase-only spatial light modulator," Opt. Rev. 6, 339-344 (1999).
[CrossRef]

H. Toyoda, Y. Kobayashi, N. Yoshida, Y. Igasaki, T. Hara, M. Ishikawa, and M. H. Wu, "High efficient electrically addressable spatial light modulator for reconfigurable optical connection," in OSA Snowmass Meeting, Spatial Light Modulators, OSA Technical Digest Series (Optical Society of America, 1999), SMB3, pp. 14-16.

Li, F.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, and T. Hara, "High efficiency electrically-addressable phase-only spatial light modulator," Opt. Rev. 6, 339-344 (1999).
[CrossRef]

Liberman, S.

P. F. McManamon, T. A. Dorschner, D. C. Corkum, L. J. Friedman, D. S. Hobbs, M. K. O. Holz, S. Liberman, H. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Lubin, D. L.

M. T. Gruneisen, R. C. Dymale, J. R. Rotge, L. F. DeSandre, and D. L. Lubin, "Compensated telescope system with programmable diffractive optic," Opt. Eng. 44, 023201-1-023201-9 (2005).
[CrossRef]

M. T. Gruneisen, R. C. Dymale, J. R. Rotge, L. F. DeSandre, and D. L. Lubin, "Wavelength-dependent characteristics of a telescope system with diffractive wavefront control," Opt. Eng. 44, 068002-1-068002-8 (2005).
[CrossRef]

M. T. Gruneisen, L. F. DeSandre, J. R. Rotge, R. C. Dymale, and D. L. Lubin, "Programmable diffractive optics for wide-dynamic-range wavefront control using liquid-crystal spatial light modulators," Opt. Eng. 43, 1387-1393 (2004).
[CrossRef]

McManamon, P.

P. McManamon, J. Shi, and P. J. Bos, "Broadband optical phased array beam steering," Opt. Eng. 44, 128004-1-128004-5 (2005).
[CrossRef]

McManamon, P. F.

P. F. McManamon, T. A. Dorschner, D. C. Corkum, L. J. Friedman, D. S. Hobbs, M. K. O. Holz, S. Liberman, H. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

P. F. McManamon, E. A. Watson, T. A. Dorschner, and L. J. Barnes, "Applications look at the use of liquid crystal writable gratings for steering passive radiation," Opt. Eng. 32, 2657-2664 (1993).
[CrossRef]

Miranda, F.

X. Wang, B. Wang, J. Pouch, F. Miranda, M. Fisch, J. E. Anderson, V. Sergan, and P. Bos, "Liquid crystal on silicon (LCOS) wavefront corrector and beam steerer," in Advanced Wavefront Control: Methods, Devices, and Applications, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 5162, 139-146 (2003).
[CrossRef]

Morris, G. M.

Mukohzaka, N.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, and T. Hara, "High efficiency electrically-addressable phase-only spatial light modulator," Opt. Rev. 6, 339-344 (1999).
[CrossRef]

Nguyen, H.

P. F. McManamon, T. A. Dorschner, D. C. Corkum, L. J. Friedman, D. S. Hobbs, M. K. O. Holz, S. Liberman, H. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Pouch, J.

X. Wang, B. Wang, J. Pouch, F. Miranda, M. Fisch, J. E. Anderson, V. Sergan, and P. Bos, "Liquid crystal on silicon (LCOS) wavefront corrector and beam steerer," in Advanced Wavefront Control: Methods, Devices, and Applications, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 5162, 139-146 (2003).
[CrossRef]

Resler, D. P.

P. F. McManamon, T. A. Dorschner, D. C. Corkum, L. J. Friedman, D. S. Hobbs, M. K. O. Holz, S. Liberman, H. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Rha, J.

J. Rha and M. K. Giles, "Implementation of an adaptive Shack-Hartmann sensor using a phase-modulated liquid crystal spatial light modulator," in High-Resolution Wavefront Control: Methods, Devices, and Applications, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 4493, 80-87 (2002).
[CrossRef]

Rodney, P. J.

D. Guthals, D. Sox, M. Joswick, and P. J. Rodney, "Real-time holographic compensation of large optics for deployment in space," in High-Resolution Wavefront Control: Methods, Devices, and Applications II, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 4124, 245-256 (2000).
[CrossRef]

Rogers, J. R.

Rotge, J. R.

M. T. Gruneisen, R. C. Dymale, J. R. Rotge, L. F. DeSandre, and D. L. Lubin, "Wavelength-dependent characteristics of a telescope system with diffractive wavefront control," Opt. Eng. 44, 068002-1-068002-8 (2005).
[CrossRef]

M. T. Gruneisen, R. C. Dymale, J. R. Rotge, L. F. DeSandre, and D. L. Lubin, "Compensated telescope system with programmable diffractive optic," Opt. Eng. 44, 023201-1-023201-9 (2005).
[CrossRef]

M. T. Gruneisen, L. F. DeSandre, J. R. Rotge, R. C. Dymale, and D. L. Lubin, "Programmable diffractive optics for wide-dynamic-range wavefront control using liquid-crystal spatial light modulators," Opt. Eng. 43, 1387-1393 (2004).
[CrossRef]

Ryf, R.

R. Ryf, H. R. Stuart, and C. R. Giles, "MEMS tip/tilt and piston mirror arrays as diffractive optical elements," in Advanced Wavefront Control: Methods, Devices, and Applications III, M. T. Gruneisen, J. D. Gonglewski, M. K. Giles, eds., Proc. SPIE 5894, 113-123 (2005).

Serati, S.

K. Bauchert, S. Serati, and A. Furman, "Advances in liquid crystal spatial light modulators," in Optical Pattern Recognition XIII, D. P. Casasent and T. H. Chao, eds., Proc. SPIE 4734, 35-43 (2002).
[CrossRef]

Sergan, V.

X. Wang, B. Wang, J. Pouch, F. Miranda, M. Fisch, J. E. Anderson, V. Sergan, and P. Bos, "Liquid crystal on silicon (LCOS) wavefront corrector and beam steerer," in Advanced Wavefront Control: Methods, Devices, and Applications, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 5162, 139-146 (2003).
[CrossRef]

Sharp, R. C.

P. F. McManamon, T. A. Dorschner, D. C. Corkum, L. J. Friedman, D. S. Hobbs, M. K. O. Holz, S. Liberman, H. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Shi, J.

P. McManamon, J. Shi, and P. J. Bos, "Broadband optical phased array beam steering," Opt. Eng. 44, 128004-1-128004-5 (2005).
[CrossRef]

Smith, W. J.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, 1966).

Sox, D.

D. Guthals, D. Sox, M. Joswick, and P. J. Rodney, "Real-time holographic compensation of large optics for deployment in space," in High-Resolution Wavefront Control: Methods, Devices, and Applications II, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 4124, 245-256 (2000).
[CrossRef]

Stuart, H. R.

R. Ryf, H. R. Stuart, and C. R. Giles, "MEMS tip/tilt and piston mirror arrays as diffractive optical elements," in Advanced Wavefront Control: Methods, Devices, and Applications III, M. T. Gruneisen, J. D. Gonglewski, M. K. Giles, eds., Proc. SPIE 5894, 113-123 (2005).

Swanson, G. J.

G. J. Swanson, "Binary optics technology: the theory and design of multi-level diffractive optical elements," MIT Lincoln Laboratory Tech. Rep. No. 854, pp. 1-47 (MIT, Cambridge, Mass., 1989).

Tabata, T.

A. Kirk, T. Tabata, M. Ishikawa, and H. Toyoda, "Reconfigurable computer generated holograms," Opt. Commun. 105, 302-308 (1994).
[CrossRef]

Toyoda, H.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, and T. Hara, "High efficiency electrically-addressable phase-only spatial light modulator," Opt. Rev. 6, 339-344 (1999).
[CrossRef]

A. Kirk, T. Tabata, M. Ishikawa, and H. Toyoda, "Reconfigurable computer generated holograms," Opt. Commun. 105, 302-308 (1994).
[CrossRef]

H. Toyoda, Y. Kobayashi, N. Yoshida, Y. Igasaki, T. Hara, M. Ishikawa, and M. H. Wu, "High efficient electrically addressable spatial light modulator for reconfigurable optical connection," in OSA Snowmass Meeting, Spatial Light Modulators, OSA Technical Digest Series (Optical Society of America, 1999), SMB3, pp. 14-16.

Tyson, R.

R. Tyson, Principles of Adaptive Optics (Academic, 1991).

Wang, B.

X. Wang, B. Wang, J. Pouch, F. Miranda, M. Fisch, J. E. Anderson, V. Sergan, and P. Bos, "Liquid crystal on silicon (LCOS) wavefront corrector and beam steerer," in Advanced Wavefront Control: Methods, Devices, and Applications, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 5162, 139-146 (2003).
[CrossRef]

Wang, X.

X. Wang, B. Wang, J. Pouch, F. Miranda, M. Fisch, J. E. Anderson, V. Sergan, and P. Bos, "Liquid crystal on silicon (LCOS) wavefront corrector and beam steerer," in Advanced Wavefront Control: Methods, Devices, and Applications, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 5162, 139-146 (2003).
[CrossRef]

Watson, E. A.

P. F. McManamon, T. A. Dorschner, D. C. Corkum, L. J. Friedman, D. S. Hobbs, M. K. O. Holz, S. Liberman, H. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

P. F. McManamon, E. A. Watson, T. A. Dorschner, and L. J. Barnes, "Applications look at the use of liquid crystal writable gratings for steering passive radiation," Opt. Eng. 32, 2657-2664 (1993).
[CrossRef]

Wu, M. H.

H. Toyoda, Y. Kobayashi, N. Yoshida, Y. Igasaki, T. Hara, M. Ishikawa, and M. H. Wu, "High efficient electrically addressable spatial light modulator for reconfigurable optical connection," in OSA Snowmass Meeting, Spatial Light Modulators, OSA Technical Digest Series (Optical Society of America, 1999), SMB3, pp. 14-16.

Yoshida, N.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, and T. Hara, "High efficiency electrically-addressable phase-only spatial light modulator," Opt. Rev. 6, 339-344 (1999).
[CrossRef]

H. Toyoda, Y. Kobayashi, N. Yoshida, Y. Igasaki, T. Hara, M. Ishikawa, and M. H. Wu, "High efficient electrically addressable spatial light modulator for reconfigurable optical connection," in OSA Snowmass Meeting, Spatial Light Modulators, OSA Technical Digest Series (Optical Society of America, 1999), SMB3, pp. 14-16.

Zhu, H.

H. Zhu, P. Bierden, S. Cornelissen, T. Bifano, and J. Kim, "Design and fabrication of reflective spatial light modulators for high-dynamic-range wavefront control," in Advanced Wavefront Control: Methods, Devices, and Applications II, J. D. Gonglewski, M. T. Gruneisen, and M. K. Giles, eds., Proc. SPIE 5553, 39-45 (2004).
[CrossRef]

Appl. Opt. (2)

Opt. Commun. (1)

A. Kirk, T. Tabata, M. Ishikawa, and H. Toyoda, "Reconfigurable computer generated holograms," Opt. Commun. 105, 302-308 (1994).
[CrossRef]

Opt. Eng. (5)

P. F. McManamon, E. A. Watson, T. A. Dorschner, and L. J. Barnes, "Applications look at the use of liquid crystal writable gratings for steering passive radiation," Opt. Eng. 32, 2657-2664 (1993).
[CrossRef]

M. T. Gruneisen, R. C. Dymale, J. R. Rotge, L. F. DeSandre, and D. L. Lubin, "Wavelength-dependent characteristics of a telescope system with diffractive wavefront control," Opt. Eng. 44, 068002-1-068002-8 (2005).
[CrossRef]

P. McManamon, J. Shi, and P. J. Bos, "Broadband optical phased array beam steering," Opt. Eng. 44, 128004-1-128004-5 (2005).
[CrossRef]

M. T. Gruneisen, L. F. DeSandre, J. R. Rotge, R. C. Dymale, and D. L. Lubin, "Programmable diffractive optics for wide-dynamic-range wavefront control using liquid-crystal spatial light modulators," Opt. Eng. 43, 1387-1393 (2004).
[CrossRef]

M. T. Gruneisen, R. C. Dymale, J. R. Rotge, L. F. DeSandre, and D. L. Lubin, "Compensated telescope system with programmable diffractive optic," Opt. Eng. 44, 023201-1-023201-9 (2005).
[CrossRef]

Opt. Rev. (1)

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, and T. Hara, "High efficiency electrically-addressable phase-only spatial light modulator," Opt. Rev. 6, 339-344 (1999).
[CrossRef]

Proc. IEEE (1)

P. F. McManamon, T. A. Dorschner, D. C. Corkum, L. J. Friedman, D. S. Hobbs, M. K. O. Holz, S. Liberman, H. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Proc. SPIE (7)

D. Guthals, D. Sox, M. Joswick, and P. J. Rodney, "Real-time holographic compensation of large optics for deployment in space," in High-Resolution Wavefront Control: Methods, Devices, and Applications II, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 4124, 245-256 (2000).
[CrossRef]

K. Bauchert, S. Serati, and A. Furman, "Advances in liquid crystal spatial light modulators," in Optical Pattern Recognition XIII, D. P. Casasent and T. H. Chao, eds., Proc. SPIE 4734, 35-43 (2002).
[CrossRef]

X. Wang, B. Wang, J. Pouch, F. Miranda, M. Fisch, J. E. Anderson, V. Sergan, and P. Bos, "Liquid crystal on silicon (LCOS) wavefront corrector and beam steerer," in Advanced Wavefront Control: Methods, Devices, and Applications, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 5162, 139-146 (2003).
[CrossRef]

R. Dou and M. K. Giles, "Programmable phase grating and beam steerer by operating a LCTV," in Advanced Imaging Technologies and Commercial Applications, N. Clark and J. D. Gonglewski, eds., Proc. SPIE 2566, 26-34 (1995).
[CrossRef]

J. Rha and M. K. Giles, "Implementation of an adaptive Shack-Hartmann sensor using a phase-modulated liquid crystal spatial light modulator," in High-Resolution Wavefront Control: Methods, Devices, and Applications, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 4493, 80-87 (2002).
[CrossRef]

H. Zhu, P. Bierden, S. Cornelissen, T. Bifano, and J. Kim, "Design and fabrication of reflective spatial light modulators for high-dynamic-range wavefront control," in Advanced Wavefront Control: Methods, Devices, and Applications II, J. D. Gonglewski, M. T. Gruneisen, and M. K. Giles, eds., Proc. SPIE 5553, 39-45 (2004).
[CrossRef]

R. Ryf, H. R. Stuart, and C. R. Giles, "MEMS tip/tilt and piston mirror arrays as diffractive optical elements," in Advanced Wavefront Control: Methods, Devices, and Applications III, M. T. Gruneisen, J. D. Gonglewski, M. K. Giles, eds., Proc. SPIE 5894, 113-123 (2005).

Other (5)

H. Toyoda, Y. Kobayashi, N. Yoshida, Y. Igasaki, T. Hara, M. Ishikawa, and M. H. Wu, "High efficient electrically addressable spatial light modulator for reconfigurable optical connection," in OSA Snowmass Meeting, Spatial Light Modulators, OSA Technical Digest Series (Optical Society of America, 1999), SMB3, pp. 14-16.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

R. Tyson, Principles of Adaptive Optics (Academic, 1991).

W. J. Smith, Modern Optical Engineering (McGraw-Hill, 1966).

G. J. Swanson, "Binary optics technology: the theory and design of multi-level diffractive optical elements," MIT Lincoln Laboratory Tech. Rep. No. 854, pp. 1-47 (MIT, Cambridge, Mass., 1989).

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Figures (7)

Fig. 1
Fig. 1

Graphical representation of a discrete-element step approximation to an optical path function modulo λ r as a function of spatial coordinate x. The solid curve shows an optical path function, the dashed curve shows the same function modulo λ r , and the dotted curve shows a discrete-element approximation to the modulo λ r function including a nonunity fill factor.

Fig. 2
Fig. 2

Graphical representation of modulo Nλ 0 optical path modulation. The solid curve shows a linear tilt function modulo λ 0 , the dashed curve shows the same function modulo 2λ 0 , and the dotted curve shows same function modulo 3λ 0 .

Fig. 3
Fig. 3

Gray-scale representation of the mth-order diffraction efficiency η m (Nλ 0 ∕λ) as a function of the grating order m and the parameter Nλ 0 ∕λ, where Nλ 0 is the reset distance, λ 0 is the nominal wavelength, and λ is the operating wavelength. The gray-scale legend is shown to the right.

Fig. 4
Fig. 4

Plots of the mth-order diffraction efficiency η m (Nλ 0 ∕λ) as a function of the parameter Nλ 0 ∕λ for diffraction orders given by m = 1, 2, and 3.

Fig. 5
Fig. 5

Gray-scale representation of the mth-order diffraction efficiency η m (Nλ 0 ∕λ) as a function of the grating order m and the reset multiple N for values of the ratio of the nominal wavelength λ 0 to the operating wavelength λ given by (a) λ 0 ∕λ = 1.0, (b) λ 0 ∕λ = 0.9, and (c) λ 0 ∕λ = 1.1. The diffraction efficiency is represented in gray scale according to the legend in Fig. 3.

Fig. 6
Fig. 6

Logarithmic plot of the order-dependent diffraction efficiency as a function of the grating order m for several values of the reset multiple N for the case where the ratio of the nominal wavelength λ 0 to the operating wavelength λ is given by λ 0 ∕λ = 0.9.

Fig. 7
Fig. 7

Plot of the mth-order fractional wavefront error as a function of operating wavelength λ for the specific case of a nominal wavelength λ 0 = 600 nm and values of the reset multiple given by N = (a) 1, (b) 5, (c) 10, and (d) 20. The diffraction efficiency is represented in gray scale according to the legend in Fig. 3 with the dashed curves representing the location of the first zeros of the sinc 2 diffraction efficiency function.

Equations (35)

Equations on this page are rendered with MathJax. Learn more.

T ( x , y , λ ) = exp [ i 2 π λ  OPD ( x , y ) ] ,
T ( x , y , N λ 0 , λ ) = exp [ i 2 π λ  OPD ( x , y ) mod N λ 0 ] ,
T ( x , y , N λ 0 , λ ) = m = sinc ( N λ 0 λ m ) × exp [ i m N 2 π λ 0  OPD ( x , y ) ] ,
η m ( N λ 0 λ ) = sinc 2 ( N λ 0 λ m )
T m ( x , y , N λ 0 ) = exp [ i m 2 π N λ 0  OPD ( x , y ) ] .
λ r = N λ 0 = m λ .
N λ 0 λ 1 < m < N λ 0 λ + 1.
W c ( x , y ) = OPD ( x , y ) ,
E in ( x , y , λ ) = 1.
E out ( x , y , N λ 0 , λ ) = E in ( x , y , λ ) T ( x , y , N λ 0 , λ ) .
E out ( x , y , N λ 0 , λ ) = m = η m 1 / 2 ( N λ 0 λ ) × exp [ i 2 π λ W m ( x , y , N λ 0 ) ] .
W m ( x , y , N λ 0 , m λ ) = m N λ λ 0  OPD ( x , y ) .
Δ W m ( x , y , N λ 0 , m λ ) = β m ( N λ 0 , m λ ) OPD ( x , y ) ,
β m ( N λ 0 , m λ ) = ( 1 m N λ λ 0 ) .
E in ( x , y , λ ) = exp [ i 2 π λ W ( x , y ) ] .
E out ( x , y , λ r , λ ) = m = η m 1 / 2 ( N λ 0 λ ) × exp [ i 2 π λ Δ W m ( x , y ) ] .
Δ W m ( x , y , N λ 0 , m λ ) = β m ( N λ 0 , m λ ) W ( x , y ) ,
η m ( N λ 0 λ ) = sinc 2 ( N λ 0 λ m ) ,
β m ( N λ 0 , m λ ) = ( 1 m N λ λ 0 ) .
η N ( λ = λ 0 ) = 1 ,
β N ( λ = λ 0 ) = 0.
λ m = N λ 0 m ,
η m ( λ m = N λ 0 m ) = 1 ,
β m ( λ m = N λ 0 m ) = 0.
β N ( λ 0 , λ ) = 1 λ λ 0 ,
d β N ( λ 0 , λ ) d λ = 1 λ 0 ,
β max ( λ ) = ± λ N λ 0 ,
d β max ( λ ) d λ = ± 1 N λ 0 ,
OPD ( x ) = α x ,
| β max ( λ ) | OPD ( x ) = λ α N λ 0 x .
Δ θ λ α N λ 0 .
Δ θ DL = λ D .
Δ θ < Δ θ DL .
N λ 0 > α D ,
γ N = Δ θ Δ θ DL = α D N λ 0 .

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