Abstract

A tunable aberration compensation device for rectangular micro-optical systems is proposed and demonstrated. This device, which is based in nematic liquid crystal and a micro-electrode structure, forms gradients in the index of refraction as a function of voltage. We have developed a fringe skeletonizing application in order to extract the 3D wavefront from an interference pattern. This software tool obtains the optical aberrations using Chebyshev polynomials. By using phase shifted electrical signals the aberrations can be controlled independently. A complete independent control over the spherical and coma aberration has been demonstrated. Also, an independent control over the astigmatism aberration has been demonstrated in a broad range. This device has promising applications where aberration compensation is required. The independent compensation achieved for some coefficients, such as astigmatism for example, is more than 2.4 waves.

© 2015 Optical Society of America

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References

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2014 (2)

J. F. Algorri, V. Urruchi, N. Bennis, and J. M. Sánchez-Pena, “Using an Analytical Model to Design Liquid Crystal Microlenses,” IEEE Photon. Technol. Lett. 26(8), 793–796 (2014).
[Crossref]

J. F. Algorri, V. Urruchi, J. M. Sánchez-Pena, and J. M. Otón, “An Autostereoscopic Device for Mobile Applications Based on a Liquid Crystal Microlens Array and an OLED Display,” J. Disp. Technol. 10(9), 713–720 (2014).
[Crossref]

2013 (2)

2012 (3)

C. Bourgenot, C. D. Saunter, J. M. Taylor, J. M. Girkin, and G. D. Love, “3D adaptive optics in a light sheet microscope,” Opt. Express 20(12), 13252–13261 (2012).
[Crossref] [PubMed]

V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, N. Bennis, and J. M. Otón, “Electrooptic Characterization of Tunable Cylindrical Liquid Crystal Lenses,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 553(1), 211–219 (2012).
[Crossref]

V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, M. A. Geday, X. Quintana, and N. Bennis, “Lenticular Arrays Based on Liquid Crystals,” Opto-Electron. Rev. 20(3), 260–266 (2012).

2011 (3)

N. S. Holliman, N. A. Dodgson, G. E. Favalora, and L. Pockett, “Three-Dimensional Displays: A Review and Applications Analysis,” IEEE Trans. Broadcast 57(2), 362–371 (2011).
[Crossref]

F. Liu, B. M. Robinson, P. J. Reardon, and J. M. Geary, “Analyzing optics test data on rectangular apertures using 2-D Chebyshev polynomials,” Opt. Eng. 50(4), 043609(2011).
[Crossref]

G. Wang, Y. J. Li, and H. C. Zhou, “Application of the radial basis function interpolation to phase extraction from a single electronic speckle pattern interferometric fringe,” Appl. Opt. 50(19), 3110–3117 (2011).
[Crossref] [PubMed]

2010 (1)

Y. P. Huang, C. W. Chen, T. C. Shen, and J. F. Huang, “Autostereoscopic 3D display with scanning Multi-Electrode driven liquid crystal (MeD-LC) Lens,” J. 3D Res. 1(1), 39–42 (2010).
[Crossref]

2009 (1)

2008 (2)

G. M. Dai and V. N. Mahajan, “Orthonormal polynomials in wavefront analysis: error analysis,” Appl. Opt. 47(19), 3433–3445 (2008).
[Crossref] [PubMed]

A. Bich, J. Rieck, C. Dumouchel, S. Roth, K. J. Weible, M. Eisner, R. Voelkel, M. Zimmermann, M. Rank, M. Schmidt, R. Bitterli, N. Ramanan, P. Ruffieux, T. Scharf, W. Noell, H.-P. Herzig, and N. De Rooij, “Multifunctional micro-optical elements for laser beam homogenizing and beam shaping,” Proc. SPIE 6879, Photon Processing in Microelectronics and Photonics VII, 68790Q (2008).

2007 (3)

2006 (2)

2005 (3)

J. Knittel, H. Richter, M. Hain, S. Somalingam, and T. Tschudi, “Liquid crystal lens for spherical aberration compensation in a Blu-ray disc system,” IEE Proc. Sci. Meas. Technol. 152(1), 15–18 (2005).
[Crossref]

Q. Deng, C. Du, C. Wang, C. Zhou, X. Dong, Y. Liu, and T. Zhou, “Microlens array for stacked laser diode beam collimation,” Proc. SPIE 5636, 666–670 (2005).
[Crossref]

S. K. Ghorai, D. Kumar, and B. K. Hura, “Strain measurement in a Mach–Zehnder fiber interferometer using genetic algorithm,” Sens. Actuators A Phys. 122(2), 215–221 (2005).
[Crossref]

2004 (1)

M. Bray, “Orthogonal polynomials: a set for square areas,” Proc. SPIE 5252, 314–321 (2004).
[Crossref]

1999 (1)

1998 (1)

1997 (1)

1994 (1)

1982 (1)

Algorri, J. F.

J. F. Algorri, V. Urruchi, N. Bennis, and J. M. Sánchez-Pena, “Using an Analytical Model to Design Liquid Crystal Microlenses,” IEEE Photon. Technol. Lett. 26(8), 793–796 (2014).
[Crossref]

J. F. Algorri, V. Urruchi, J. M. Sánchez-Pena, and J. M. Otón, “An Autostereoscopic Device for Mobile Applications Based on a Liquid Crystal Microlens Array and an OLED Display,” J. Disp. Technol. 10(9), 713–720 (2014).
[Crossref]

J. F. Algorri, G. D. Love, and V. Urruchi, “Modal liquid crystal array of optical elements,” Opt. Express 21(21), 24809–24818 (2013).
[Crossref] [PubMed]

V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, N. Bennis, and J. M. Otón, “Electrooptic Characterization of Tunable Cylindrical Liquid Crystal Lenses,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 553(1), 211–219 (2012).
[Crossref]

V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, M. A. Geday, X. Quintana, and N. Bennis, “Lenticular Arrays Based on Liquid Crystals,” Opto-Electron. Rev. 20(3), 260–266 (2012).

Ares, M.

Bennis, N.

J. F. Algorri, V. Urruchi, N. Bennis, and J. M. Sánchez-Pena, “Using an Analytical Model to Design Liquid Crystal Microlenses,” IEEE Photon. Technol. Lett. 26(8), 793–796 (2014).
[Crossref]

V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, N. Bennis, and J. M. Otón, “Electrooptic Characterization of Tunable Cylindrical Liquid Crystal Lenses,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 553(1), 211–219 (2012).
[Crossref]

V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, M. A. Geday, X. Quintana, and N. Bennis, “Lenticular Arrays Based on Liquid Crystals,” Opto-Electron. Rev. 20(3), 260–266 (2012).

Bich, A.

A. Bich, J. Rieck, C. Dumouchel, S. Roth, K. J. Weible, M. Eisner, R. Voelkel, M. Zimmermann, M. Rank, M. Schmidt, R. Bitterli, N. Ramanan, P. Ruffieux, T. Scharf, W. Noell, H.-P. Herzig, and N. De Rooij, “Multifunctional micro-optical elements for laser beam homogenizing and beam shaping,” Proc. SPIE 6879, Photon Processing in Microelectronics and Photonics VII, 68790Q (2008).

Bitterli, R.

A. Bich, J. Rieck, C. Dumouchel, S. Roth, K. J. Weible, M. Eisner, R. Voelkel, M. Zimmermann, M. Rank, M. Schmidt, R. Bitterli, N. Ramanan, P. Ruffieux, T. Scharf, W. Noell, H.-P. Herzig, and N. De Rooij, “Multifunctional micro-optical elements for laser beam homogenizing and beam shaping,” Proc. SPIE 6879, Photon Processing in Microelectronics and Photonics VII, 68790Q (2008).

Bourgenot, C.

Bray, M.

M. Bray, “Orthogonal polynomials: a set for square areas,” Proc. SPIE 5252, 314–321 (2004).
[Crossref]

Burton, D. R.

Caum, J.

Chen, C. W.

Y. P. Huang, C. W. Chen, T. C. Shen, and J. F. Huang, “Autostereoscopic 3D display with scanning Multi-Electrode driven liquid crystal (MeD-LC) Lens,” J. 3D Res. 1(1), 39–42 (2010).
[Crossref]

Chen, C.-C.

C.-H. Chen, C.-C. Chen, and W.-C. Liang, “Light pipe line beam shaper,” Opt. Rev. 14(4), 231–235 (2007).
[Crossref]

Chen, C.-H.

C.-H. Chen, C.-C. Chen, and W.-C. Liang, “Light pipe line beam shaper,” Opt. Rev. 14(4), 231–235 (2007).
[Crossref]

Chen, M. F.

Chow, W. W.

Chung, C. W.

Dai, G. M.

De Rooij, N.

A. Bich, J. Rieck, C. Dumouchel, S. Roth, K. J. Weible, M. Eisner, R. Voelkel, M. Zimmermann, M. Rank, M. Schmidt, R. Bitterli, N. Ramanan, P. Ruffieux, T. Scharf, W. Noell, H.-P. Herzig, and N. De Rooij, “Multifunctional micro-optical elements for laser beam homogenizing and beam shaping,” Proc. SPIE 6879, Photon Processing in Microelectronics and Photonics VII, 68790Q (2008).

Deng, Q.

Q. Deng, C. Du, C. Wang, C. Zhou, X. Dong, Y. Liu, and T. Zhou, “Microlens array for stacked laser diode beam collimation,” Proc. SPIE 5636, 666–670 (2005).
[Crossref]

Dodgson, N. A.

N. S. Holliman, N. A. Dodgson, G. E. Favalora, and L. Pockett, “Three-Dimensional Displays: A Review and Applications Analysis,” IEEE Trans. Broadcast 57(2), 362–371 (2011).
[Crossref]

Dong, X.

Q. Deng, C. Du, C. Wang, C. Zhou, X. Dong, Y. Liu, and T. Zhou, “Microlens array for stacked laser diode beam collimation,” Proc. SPIE 5636, 666–670 (2005).
[Crossref]

Du, C.

Q. Deng, C. Du, C. Wang, C. Zhou, X. Dong, Y. Liu, and T. Zhou, “Microlens array for stacked laser diode beam collimation,” Proc. SPIE 5636, 666–670 (2005).
[Crossref]

Dumouchel, C.

A. Bich, J. Rieck, C. Dumouchel, S. Roth, K. J. Weible, M. Eisner, R. Voelkel, M. Zimmermann, M. Rank, M. Schmidt, R. Bitterli, N. Ramanan, P. Ruffieux, T. Scharf, W. Noell, H.-P. Herzig, and N. De Rooij, “Multifunctional micro-optical elements for laser beam homogenizing and beam shaping,” Proc. SPIE 6879, Photon Processing in Microelectronics and Photonics VII, 68790Q (2008).

Eisner, M.

A. Bich, J. Rieck, C. Dumouchel, S. Roth, K. J. Weible, M. Eisner, R. Voelkel, M. Zimmermann, M. Rank, M. Schmidt, R. Bitterli, N. Ramanan, P. Ruffieux, T. Scharf, W. Noell, H.-P. Herzig, and N. De Rooij, “Multifunctional micro-optical elements for laser beam homogenizing and beam shaping,” Proc. SPIE 6879, Photon Processing in Microelectronics and Photonics VII, 68790Q (2008).

Favalora, G. E.

N. S. Holliman, N. A. Dodgson, G. E. Favalora, and L. Pockett, “Three-Dimensional Displays: A Review and Applications Analysis,” IEEE Trans. Broadcast 57(2), 362–371 (2011).
[Crossref]

Gdeisat, M. A.

Geary, J. M.

F. Liu, B. M. Robinson, P. J. Reardon, and J. M. Geary, “Analyzing optics test data on rectangular apertures using 2-D Chebyshev polynomials,” Opt. Eng. 50(4), 043609(2011).
[Crossref]

Geday, M. A.

V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, M. A. Geday, X. Quintana, and N. Bennis, “Lenticular Arrays Based on Liquid Crystals,” Opto-Electron. Rev. 20(3), 260–266 (2012).

Ghorai, S. K.

S. K. Ghorai, D. Kumar, and B. K. Hura, “Strain measurement in a Mach–Zehnder fiber interferometer using genetic algorithm,” Sens. Actuators A Phys. 122(2), 215–221 (2005).
[Crossref]

Girkin, J. M.

Guralnik, I. R.

Hain, M.

J. Knittel, H. Richter, M. Hain, S. Somalingam, and T. Tschudi, “Liquid crystal lens for spherical aberration compensation in a Blu-ray disc system,” IEE Proc. Sci. Meas. Technol. 152(1), 15–18 (2005).
[Crossref]

Herzig, H.-P.

A. Bich, J. Rieck, C. Dumouchel, S. Roth, K. J. Weible, M. Eisner, R. Voelkel, M. Zimmermann, M. Rank, M. Schmidt, R. Bitterli, N. Ramanan, P. Ruffieux, T. Scharf, W. Noell, H.-P. Herzig, and N. De Rooij, “Multifunctional micro-optical elements for laser beam homogenizing and beam shaping,” Proc. SPIE 6879, Photon Processing in Microelectronics and Photonics VII, 68790Q (2008).

Holliman, N. S.

N. S. Holliman, N. A. Dodgson, G. E. Favalora, and L. Pockett, “Three-Dimensional Displays: A Review and Applications Analysis,” IEEE Trans. Broadcast 57(2), 362–371 (2011).
[Crossref]

Hsieh, C. T.

Hsu, Y. F.

Huang, C. Y.

Huang, J. F.

Y. P. Huang, C. W. Chen, T. C. Shen, and J. F. Huang, “Autostereoscopic 3D display with scanning Multi-Electrode driven liquid crystal (MeD-LC) Lens,” J. 3D Res. 1(1), 39–42 (2010).
[Crossref]

Huang, Y. P.

Y. P. Huang, C. W. Chen, T. C. Shen, and J. F. Huang, “Autostereoscopic 3D display with scanning Multi-Electrode driven liquid crystal (MeD-LC) Lens,” J. 3D Res. 1(1), 39–42 (2010).
[Crossref]

Hura, B. K.

S. K. Ghorai, D. Kumar, and B. K. Hura, “Strain measurement in a Mach–Zehnder fiber interferometer using genetic algorithm,” Sens. Actuators A Phys. 122(2), 215–221 (2005).
[Crossref]

Ina, H.

Kemao, Q.

Knittel, J.

J. Knittel, H. Richter, M. Hain, S. Somalingam, and T. Tschudi, “Liquid crystal lens for spherical aberration compensation in a Blu-ray disc system,” IEE Proc. Sci. Meas. Technol. 152(1), 15–18 (2005).
[Crossref]

Kobayashi, S.

Kumar, D.

S. K. Ghorai, D. Kumar, and B. K. Hura, “Strain measurement in a Mach–Zehnder fiber interferometer using genetic algorithm,” Sens. Actuators A Phys. 122(2), 215–221 (2005).
[Crossref]

Lalor, M. J.

Li, Y. J.

Liang, W.-C.

C.-H. Chen, C.-C. Chen, and W.-C. Liang, “Light pipe line beam shaper,” Opt. Rev. 14(4), 231–235 (2007).
[Crossref]

Liu, F.

F. Liu, B. M. Robinson, P. J. Reardon, and J. M. Geary, “Analyzing optics test data on rectangular apertures using 2-D Chebyshev polynomials,” Opt. Eng. 50(4), 043609(2011).
[Crossref]

Liu, Y.

Q. Deng, C. Du, C. Wang, C. Zhou, X. Dong, Y. Liu, and T. Zhou, “Microlens array for stacked laser diode beam collimation,” Proc. SPIE 5636, 666–670 (2005).
[Crossref]

Loktev, M. Y.

Love, G.

Love, G. D.

Mahajan, V. N.

Naumov, A.

Naumov, A. F.

Noell, W.

A. Bich, J. Rieck, C. Dumouchel, S. Roth, K. J. Weible, M. Eisner, R. Voelkel, M. Zimmermann, M. Rank, M. Schmidt, R. Bitterli, N. Ramanan, P. Ruffieux, T. Scharf, W. Noell, H.-P. Herzig, and N. De Rooij, “Multifunctional micro-optical elements for laser beam homogenizing and beam shaping,” Proc. SPIE 6879, Photon Processing in Microelectronics and Photonics VII, 68790Q (2008).

Otón, J. M.

J. F. Algorri, V. Urruchi, J. M. Sánchez-Pena, and J. M. Otón, “An Autostereoscopic Device for Mobile Applications Based on a Liquid Crystal Microlens Array and an OLED Display,” J. Disp. Technol. 10(9), 713–720 (2014).
[Crossref]

V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, N. Bennis, and J. M. Otón, “Electrooptic Characterization of Tunable Cylindrical Liquid Crystal Lenses,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 553(1), 211–219 (2012).
[Crossref]

Pockett, L.

N. S. Holliman, N. A. Dodgson, G. E. Favalora, and L. Pockett, “Three-Dimensional Displays: A Review and Applications Analysis,” IEEE Trans. Broadcast 57(2), 362–371 (2011).
[Crossref]

Quintana, X.

V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, M. A. Geday, X. Quintana, and N. Bennis, “Lenticular Arrays Based on Liquid Crystals,” Opto-Electron. Rev. 20(3), 260–266 (2012).

Ramanan, N.

A. Bich, J. Rieck, C. Dumouchel, S. Roth, K. J. Weible, M. Eisner, R. Voelkel, M. Zimmermann, M. Rank, M. Schmidt, R. Bitterli, N. Ramanan, P. Ruffieux, T. Scharf, W. Noell, H.-P. Herzig, and N. De Rooij, “Multifunctional micro-optical elements for laser beam homogenizing and beam shaping,” Proc. SPIE 6879, Photon Processing in Microelectronics and Photonics VII, 68790Q (2008).

Rank, M.

A. Bich, J. Rieck, C. Dumouchel, S. Roth, K. J. Weible, M. Eisner, R. Voelkel, M. Zimmermann, M. Rank, M. Schmidt, R. Bitterli, N. Ramanan, P. Ruffieux, T. Scharf, W. Noell, H.-P. Herzig, and N. De Rooij, “Multifunctional micro-optical elements for laser beam homogenizing and beam shaping,” Proc. SPIE 6879, Photon Processing in Microelectronics and Photonics VII, 68790Q (2008).

Reardon, P. J.

F. Liu, B. M. Robinson, P. J. Reardon, and J. M. Geary, “Analyzing optics test data on rectangular apertures using 2-D Chebyshev polynomials,” Opt. Eng. 50(4), 043609(2011).
[Crossref]

Richter, H.

J. Knittel, H. Richter, M. Hain, S. Somalingam, and T. Tschudi, “Liquid crystal lens for spherical aberration compensation in a Blu-ray disc system,” IEE Proc. Sci. Meas. Technol. 152(1), 15–18 (2005).
[Crossref]

Rieck, J.

A. Bich, J. Rieck, C. Dumouchel, S. Roth, K. J. Weible, M. Eisner, R. Voelkel, M. Zimmermann, M. Rank, M. Schmidt, R. Bitterli, N. Ramanan, P. Ruffieux, T. Scharf, W. Noell, H.-P. Herzig, and N. De Rooij, “Multifunctional micro-optical elements for laser beam homogenizing and beam shaping,” Proc. SPIE 6879, Photon Processing in Microelectronics and Photonics VII, 68790Q (2008).

Robinson, B. M.

F. Liu, B. M. Robinson, P. J. Reardon, and J. M. Geary, “Analyzing optics test data on rectangular apertures using 2-D Chebyshev polynomials,” Opt. Eng. 50(4), 043609(2011).
[Crossref]

Roth, S.

A. Bich, J. Rieck, C. Dumouchel, S. Roth, K. J. Weible, M. Eisner, R. Voelkel, M. Zimmermann, M. Rank, M. Schmidt, R. Bitterli, N. Ramanan, P. Ruffieux, T. Scharf, W. Noell, H.-P. Herzig, and N. De Rooij, “Multifunctional micro-optical elements for laser beam homogenizing and beam shaping,” Proc. SPIE 6879, Photon Processing in Microelectronics and Photonics VII, 68790Q (2008).

Royo, S.

Ruffieux, P.

A. Bich, J. Rieck, C. Dumouchel, S. Roth, K. J. Weible, M. Eisner, R. Voelkel, M. Zimmermann, M. Rank, M. Schmidt, R. Bitterli, N. Ramanan, P. Ruffieux, T. Scharf, W. Noell, H.-P. Herzig, and N. De Rooij, “Multifunctional micro-optical elements for laser beam homogenizing and beam shaping,” Proc. SPIE 6879, Photon Processing in Microelectronics and Photonics VII, 68790Q (2008).

Sánchez-Pena, J. M.

J. F. Algorri, V. Urruchi, N. Bennis, and J. M. Sánchez-Pena, “Using an Analytical Model to Design Liquid Crystal Microlenses,” IEEE Photon. Technol. Lett. 26(8), 793–796 (2014).
[Crossref]

J. F. Algorri, V. Urruchi, J. M. Sánchez-Pena, and J. M. Otón, “An Autostereoscopic Device for Mobile Applications Based on a Liquid Crystal Microlens Array and an OLED Display,” J. Disp. Technol. 10(9), 713–720 (2014).
[Crossref]

V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, N. Bennis, and J. M. Otón, “Electrooptic Characterization of Tunable Cylindrical Liquid Crystal Lenses,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 553(1), 211–219 (2012).
[Crossref]

V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, M. A. Geday, X. Quintana, and N. Bennis, “Lenticular Arrays Based on Liquid Crystals,” Opto-Electron. Rev. 20(3), 260–266 (2012).

Sato, S.

T. Takahashi, M. Ye, and S. Sato, “Aberrations of liquid crystal lens,” Electron. Lett. 42(25), 1476–1477 (2006).
[Crossref]

Saunter, C. D.

Scharf, T.

A. Bich, J. Rieck, C. Dumouchel, S. Roth, K. J. Weible, M. Eisner, R. Voelkel, M. Zimmermann, M. Rank, M. Schmidt, R. Bitterli, N. Ramanan, P. Ruffieux, T. Scharf, W. Noell, H.-P. Herzig, and N. De Rooij, “Multifunctional micro-optical elements for laser beam homogenizing and beam shaping,” Proc. SPIE 6879, Photon Processing in Microelectronics and Photonics VII, 68790Q (2008).

Schmidt, M.

A. Bich, J. Rieck, C. Dumouchel, S. Roth, K. J. Weible, M. Eisner, R. Voelkel, M. Zimmermann, M. Rank, M. Schmidt, R. Bitterli, N. Ramanan, P. Ruffieux, T. Scharf, W. Noell, H.-P. Herzig, and N. De Rooij, “Multifunctional micro-optical elements for laser beam homogenizing and beam shaping,” Proc. SPIE 6879, Photon Processing in Microelectronics and Photonics VII, 68790Q (2008).

Shen, T. C.

Y. P. Huang, C. W. Chen, T. C. Shen, and J. F. Huang, “Autostereoscopic 3D display with scanning Multi-Electrode driven liquid crystal (MeD-LC) Lens,” J. 3D Res. 1(1), 39–42 (2010).
[Crossref]

Somalingam, S.

J. Knittel, H. Richter, M. Hain, S. Somalingam, and T. Tschudi, “Liquid crystal lens for spherical aberration compensation in a Blu-ray disc system,” IEE Proc. Sci. Meas. Technol. 152(1), 15–18 (2005).
[Crossref]

Su, W. C.

Swantner, W.

Takahashi, T.

T. Takahashi, M. Ye, and S. Sato, “Aberrations of liquid crystal lens,” Electron. Lett. 42(25), 1476–1477 (2006).
[Crossref]

Takeda, M.

Taylor, J. M.

Tschudi, T.

J. Knittel, H. Richter, M. Hain, S. Somalingam, and T. Tschudi, “Liquid crystal lens for spherical aberration compensation in a Blu-ray disc system,” IEE Proc. Sci. Meas. Technol. 152(1), 15–18 (2005).
[Crossref]

Urruchi, V.

J. F. Algorri, V. Urruchi, N. Bennis, and J. M. Sánchez-Pena, “Using an Analytical Model to Design Liquid Crystal Microlenses,” IEEE Photon. Technol. Lett. 26(8), 793–796 (2014).
[Crossref]

J. F. Algorri, V. Urruchi, J. M. Sánchez-Pena, and J. M. Otón, “An Autostereoscopic Device for Mobile Applications Based on a Liquid Crystal Microlens Array and an OLED Display,” J. Disp. Technol. 10(9), 713–720 (2014).
[Crossref]

J. F. Algorri, G. D. Love, and V. Urruchi, “Modal liquid crystal array of optical elements,” Opt. Express 21(21), 24809–24818 (2013).
[Crossref] [PubMed]

V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, N. Bennis, and J. M. Otón, “Electrooptic Characterization of Tunable Cylindrical Liquid Crystal Lenses,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 553(1), 211–219 (2012).
[Crossref]

V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, M. A. Geday, X. Quintana, and N. Bennis, “Lenticular Arrays Based on Liquid Crystals,” Opto-Electron. Rev. 20(3), 260–266 (2012).

Vdovin, G.

Vladimirov, F.

Voelkel, R.

A. Bich, J. Rieck, C. Dumouchel, S. Roth, K. J. Weible, M. Eisner, R. Voelkel, M. Zimmermann, M. Rank, M. Schmidt, R. Bitterli, N. Ramanan, P. Ruffieux, T. Scharf, W. Noell, H.-P. Herzig, and N. De Rooij, “Multifunctional micro-optical elements for laser beam homogenizing and beam shaping,” Proc. SPIE 6879, Photon Processing in Microelectronics and Photonics VII, 68790Q (2008).

Wang, C.

Q. Deng, C. Du, C. Wang, C. Zhou, X. Dong, Y. Liu, and T. Zhou, “Microlens array for stacked laser diode beam collimation,” Proc. SPIE 5636, 666–670 (2005).
[Crossref]

Wang, G.

Wang, H.

Weible, K. J.

A. Bich, J. Rieck, C. Dumouchel, S. Roth, K. J. Weible, M. Eisner, R. Voelkel, M. Zimmermann, M. Rank, M. Schmidt, R. Bitterli, N. Ramanan, P. Ruffieux, T. Scharf, W. Noell, H.-P. Herzig, and N. De Rooij, “Multifunctional micro-optical elements for laser beam homogenizing and beam shaping,” Proc. SPIE 6879, Photon Processing in Microelectronics and Photonics VII, 68790Q (2008).

Ye, M.

T. Takahashi, M. Ye, and S. Sato, “Aberrations of liquid crystal lens,” Electron. Lett. 42(25), 1476–1477 (2006).
[Crossref]

Zhou, C.

Q. Deng, C. Du, C. Wang, C. Zhou, X. Dong, Y. Liu, and T. Zhou, “Microlens array for stacked laser diode beam collimation,” Proc. SPIE 5636, 666–670 (2005).
[Crossref]

Zhou, H. C.

Zhou, T.

Q. Deng, C. Du, C. Wang, C. Zhou, X. Dong, Y. Liu, and T. Zhou, “Microlens array for stacked laser diode beam collimation,” Proc. SPIE 5636, 666–670 (2005).
[Crossref]

Zimmermann, M.

A. Bich, J. Rieck, C. Dumouchel, S. Roth, K. J. Weible, M. Eisner, R. Voelkel, M. Zimmermann, M. Rank, M. Schmidt, R. Bitterli, N. Ramanan, P. Ruffieux, T. Scharf, W. Noell, H.-P. Herzig, and N. De Rooij, “Multifunctional micro-optical elements for laser beam homogenizing and beam shaping,” Proc. SPIE 6879, Photon Processing in Microelectronics and Photonics VII, 68790Q (2008).

Appl. Opt. (5)

Electron. Lett. (1)

T. Takahashi, M. Ye, and S. Sato, “Aberrations of liquid crystal lens,” Electron. Lett. 42(25), 1476–1477 (2006).
[Crossref]

IEE Proc. Sci. Meas. Technol. (1)

J. Knittel, H. Richter, M. Hain, S. Somalingam, and T. Tschudi, “Liquid crystal lens for spherical aberration compensation in a Blu-ray disc system,” IEE Proc. Sci. Meas. Technol. 152(1), 15–18 (2005).
[Crossref]

IEEE Photon. Technol. Lett. (1)

J. F. Algorri, V. Urruchi, N. Bennis, and J. M. Sánchez-Pena, “Using an Analytical Model to Design Liquid Crystal Microlenses,” IEEE Photon. Technol. Lett. 26(8), 793–796 (2014).
[Crossref]

IEEE Trans. Broadcast (1)

N. S. Holliman, N. A. Dodgson, G. E. Favalora, and L. Pockett, “Three-Dimensional Displays: A Review and Applications Analysis,” IEEE Trans. Broadcast 57(2), 362–371 (2011).
[Crossref]

J. 3D Res. (1)

Y. P. Huang, C. W. Chen, T. C. Shen, and J. F. Huang, “Autostereoscopic 3D display with scanning Multi-Electrode driven liquid crystal (MeD-LC) Lens,” J. 3D Res. 1(1), 39–42 (2010).
[Crossref]

J. Disp. Technol. (1)

J. F. Algorri, V. Urruchi, J. M. Sánchez-Pena, and J. M. Otón, “An Autostereoscopic Device for Mobile Applications Based on a Liquid Crystal Microlens Array and an OLED Display,” J. Disp. Technol. 10(9), 713–720 (2014).
[Crossref]

J. Opt. Soc. Am. (1)

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

Mol. Cryst. Liq. Cryst. (Phila. Pa.) (1)

V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, N. Bennis, and J. M. Otón, “Electrooptic Characterization of Tunable Cylindrical Liquid Crystal Lenses,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 553(1), 211–219 (2012).
[Crossref]

Opt. Eng. (1)

F. Liu, B. M. Robinson, P. J. Reardon, and J. M. Geary, “Analyzing optics test data on rectangular apertures using 2-D Chebyshev polynomials,” Opt. Eng. 50(4), 043609(2011).
[Crossref]

Opt. Express (5)

Opt. Lett. (2)

Opt. Rev. (1)

C.-H. Chen, C.-C. Chen, and W.-C. Liang, “Light pipe line beam shaper,” Opt. Rev. 14(4), 231–235 (2007).
[Crossref]

Opto-Electron. Rev. (1)

V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, M. A. Geday, X. Quintana, and N. Bennis, “Lenticular Arrays Based on Liquid Crystals,” Opto-Electron. Rev. 20(3), 260–266 (2012).

Proc. SPIE (2)

Q. Deng, C. Du, C. Wang, C. Zhou, X. Dong, Y. Liu, and T. Zhou, “Microlens array for stacked laser diode beam collimation,” Proc. SPIE 5636, 666–670 (2005).
[Crossref]

M. Bray, “Orthogonal polynomials: a set for square areas,” Proc. SPIE 5252, 314–321 (2004).
[Crossref]

Proc. SPIE 6879, Photon Processing in Microelectronics and Photonics (1)

A. Bich, J. Rieck, C. Dumouchel, S. Roth, K. J. Weible, M. Eisner, R. Voelkel, M. Zimmermann, M. Rank, M. Schmidt, R. Bitterli, N. Ramanan, P. Ruffieux, T. Scharf, W. Noell, H.-P. Herzig, and N. De Rooij, “Multifunctional micro-optical elements for laser beam homogenizing and beam shaping,” Proc. SPIE 6879, Photon Processing in Microelectronics and Photonics VII, 68790Q (2008).

Sens. Actuators A Phys. (1)

S. K. Ghorai, D. Kumar, and B. K. Hura, “Strain measurement in a Mach–Zehnder fiber interferometer using genetic algorithm,” Sens. Actuators A Phys. 122(2), 215–221 (2005).
[Crossref]

Other (4)

P. Yeh and C. Gu, Optics of Liquid Crystal Displays, 2nd ed. (John Wiley & Sons, 2008), New Jersey, NJ, USA.

Patent title “Patterned glass cylindrical lens arrays for concentrated photovoltaic systems, and/or methods of making the same,” Inventors: Alexey Krasnov, Willem den Boer. Pub. No.: US20140069143 A1 International Application No.: PCT/US2011/000644. Publication Date: 13.03.2014.

E. Otón, A. Carrasco, R. Vergaz, J. M. Otón, J. M. Sanchez-Pena, X. Quintana, and M. Geday, “2D tunable beam steering - lens device based on high birefringence liquid crystals,” International Conference on Space Optical Systems and Applications, ICSOS'11, art. no. 5783671, 218–219, (2011).
[Crossref]

M. Born and E. Wolf, Principles of Optics, 7th ed. (Oxford, 1999).

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Figures (16)

Fig. 1
Fig. 1 Tunable liquid crystal one dimensional array of cylindrical micro-optical elements for aberration compensation. (a) Designed mask, (b) zoom over three electrodes and (c) 3D representation.
Fig. 2
Fig. 2 2D Chebyshev polynomial set, Fj, related to classical aberrations [12].
Fig. 3
Fig. 3 The simplified scheme of the method for a 3D phase map extraction.
Fig. 4
Fig. 4 Experimental set-up for characterizing a tunable LC cylindrical micro-optical array for aberration compensation.
Fig. 5
Fig. 5 Interferograms obtained in the CCD (x10 objective) for (a) 100lpi and (b) 200lpi devices.
Fig. 6
Fig. 6 Fringe Skeletonizing technique (a) interference pattern and Skeletons (b) Skeletons taken the mean value of the peaks (c) comparison between captured skeletons and mean value.
Fig. 7
Fig. 7 Experimental wavefront for 100lpi device (normalized), W(x,y). (a) Interference fringes (b) 3D phase maps. (c) 2D (x,y) phase maps.
Fig. 8
Fig. 8 Amplitude of 36 Chebyshev aberration coefficients, Aj, for different voltages applied to the LC tunable micro-optical array of 100lpi.
Fig. 9
Fig. 9 Amplitude of spherical aberration coefficients as a function of voltage. (a) Primary spherical X (A10). (b) Secondary spherical X (A21).
Fig. 10
Fig. 10 Amplitude of coma aberration coefficients as a function of voltage. (a) Primary coma X (A6). (b) Secondary coma X (A15).
Fig. 11
Fig. 11 (a) Amplitude of astigmatism X aberration, A3 (b) focal distance as a function of voltage (FP from interference patterns and A3 from astigmatism coefficient), (c) RMS error.
Fig. 12
Fig. 12 Amplitude of (a) astigmatism X aberration and (b) spherical X and coma X.
Fig. 13
Fig. 13 Independent control of spherical aberration. Amplitude of (a) astigmatism X aberration and (b) spherical X and coma X.
Fig. 14
Fig. 14 Independent control of astigmatism aberration. Amplitude of (a) astigmatism X aberration and (b) spherical X and coma X.
Fig. 15
Fig. 15 Independent control of coma aberration. Amplitude of (a) astigmatism X aberration and (b) spherical X and coma X.
Fig. 16
Fig. 16 RMS FIT error in waves.

Tables (1)

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Table 1 2D Chebyshev polynomials set related to classical aberrations [12].

Equations (4)

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

W(x,y)= j A j F j (x,y),
A j = 1 1 1 1 W(x,y) F i (x,y) K 1 x 2 1 y 2 dx dy
W(x,y)=Δn(x,y)d= ΔΦ(x,y)λ 2π
RM S FITERROR = 1 N 1 M i=1 N j=1 M ( W(i,j)W'(i,j) ) 2

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