Abstract

A method for compensating for pixel crosstalk in liquid crystal based spatial light modulators is presented. By modifying a commonly used hologram generating algorithm to account for pixel crosstalk, the intensity errors in obtained diffraction spot intensities are significantly reduced. We also introduce a novel method for characterizing the pixel crosstalk in phase-only spatial light modulators, providing input for the hologram generating algorithm. The methods are experimentally evaluated and an improvement of the spot uniformity by more than 100% is demonstrated for an SLM with large pixel crosstalk.

© 2012 OSA

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References

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  1. P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84(2), 268–298 (1996).
    [CrossRef]
  2. E. Hällstig, J. Öhgren, L. Allard, L. Sjöqvist, D. Engström, S. Hård, D. Ågren, S. Junique, Q. Wang, and B. Noharet, “Retrocommunication utilizing electroabsorption modulators and nonmechanical beam steering,” Opt. Eng. 44(4), 045001 (2005).
    [CrossRef]
  3. M. Reicherter, T. Haist, E. U. Wagemann, and H. J. Tiziani, “Optical particle trapping with computer-generated holograms written on a liquid-crystal display,” Opt. Lett. 24(9), 608–610 (1999).
    [CrossRef] [PubMed]
  4. J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1-6), 169–175 (2002).
    [CrossRef]
  5. P. M. H. Hirsch, TX), Jordan Jr., James A. (Houston, TX), Lesem, Louis B. (Houston, TX), “Method of making an object dependent diffuser,” U.S. patent 3,619,022 (9 November 1971).
  6. N. C. Gallagher and B. Liu, “Method for computing kinoforms that reduces image reconstruction error,” Appl. Opt. 12(10), 2328–2335 (1973).
    [CrossRef] [PubMed]
  7. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21(15), 2758–2769 (1982).
    [CrossRef] [PubMed]
  8. M. W. Farn, “New iterative algorithm for the design of phase-only gratings,” Proc. SPIE 1555, 34–42 (1991).
    [CrossRef]
  9. J. Bengtsson, “Kinoform design with an optimal-rotation-angle method,” Appl. Opt. 33(29), 6879–6884 (1994).
    [CrossRef] [PubMed]
  10. V. V. Kotlyar, P. G. Seraphimovich, and V. A. Soifer, “An iterative weight-based method for calculating kinoforms,” Proc. SPIE 2363, 177–183 (1995).
    [CrossRef]
  11. R. Di Leonardo, F. Ianni, and G. Ruocco; “Computer generation of optimal holograms for optical trap arrays,” Opt. Express 15(4), 1913–1922 (2007).
    [CrossRef] [PubMed]
  12. D. Engström, A. Frank, J. Backsten, M. Goksör, and J. Bengtsson, “Grid-free 3D multiple spot generation with an efficient single-plane FFT-based algorithm,” Opt. Express 17(12), 9989–10000 (2009).
    [CrossRef] [PubMed]
  13. M. Polin, K. Ladavac, S.-H. Lee, Y. Roichman, and D. Grier, “Optimized holographic optical traps,” Opt. Express 13(15), 5831–5845 (2005).
    [CrossRef] [PubMed]
  14. E. Hällstig, J. Stigwall, T. Martin, L. Sjöqvist, and M. Lindgren, “Fringing fields in a liquid crystal spatial light modulator for beam steering,” J. Mod. Opt. 51(8), 1233–1247 (2004).
    [CrossRef]
  15. B. Apter, U. Efron, and E. Bahat-Treidel, “On the fringing-field effect in liquid-crystal beam-steering devices,” Appl. Opt. 43(1), 11–19 (2004).
    [CrossRef] [PubMed]
  16. R. James, F. A. Fernández, S. E. Day, M. Komarcević, and W. A. Crossland, “Modeling of the diffraction efficiency and polarization sensitivity for a liquid crystal 2D spatial light modulator for reconfigurable beam steering,” J. Opt. Soc. Am. A 24(8), 2464–2473 (2007).
    [CrossRef] [PubMed]
  17. A. Márquez, C. Iemmi, I. Moreno, J. Campos, and M. J. Yzuel, “Anamorphic and spatial frequency dependent phase modulation on liquid crystal displays. Optimization of the modulation diffraction efficiency,” Opt. Express 13(6), 2111–2119 (2005).
    [CrossRef] [PubMed]
  18. J. Bengtsson, “Direct inclusion of the proximity effect in the calculation of kinoforms,” Appl. Opt. 33(22), 4993–4996 (1994).
    [CrossRef] [PubMed]
  19. A. G. Georgiou, M. Komarcevic, T. D. Wilkinson, and W. A. Crossland, “Hologram optimisation using liquid crystal modelling,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 434(1), 183–198 (2005).
    [CrossRef]
  20. G. Milewski, D. Engström, and J. Bengtsson, “Diffractive optical elements designed for highly precise far-field generation in the presence of artifacts typical for pixelated spatial light modulators,” Appl. Opt. 46(1), 95–105 (2007).
    [CrossRef] [PubMed]
  21. M. Persson, D. Engström, and M. Goksör, “Real-time generation of fully optimized holograms for optical trapping applications,” Proc. SPIE 8097, 80971H, 80971H-9 (2011).
    [CrossRef]
  22. M. Persson, D. Engström, J. Bengtsson, and M. Goksör, “Realistic treatment of spatial light modulator pixelation in real-time design algorithms for holographic spot generation,” in OSA Technical Digest (CD) (Optical Society of America, 2011), paper DWC32.
  23. S. Bianchi and R. Di Leonardo, “Real-time optical micro-manipulation using optimized holograms generated on the GPU,” Comput. Phys. Commun. 181(8), 1444–1446 (2010).
    [CrossRef]
  24. M. Persson, D. Engström, A. Frank, J. Backsten, J. Bengtsson, and M. Goksör, “Minimizing intensity fluctuations in dynamic holographic optical tweezers by restricted phase change,” Opt. Express 18(11), 11250–11263 (2010).
    [CrossRef] [PubMed]
  25. M. Persson, Holographic Optical Trapping: Improvements and Applications (Department of Physics, University of Gothenburg, 2011).
  26. X. Xun and R. W. Cohn, “Phase calibration of spatially nonuniform spatial light modulators,” Appl. Opt. 43(35), 6400–6406 (2004).
    [CrossRef] [PubMed]
  27. A. Márquez, C. Iemmi, I. Moreno, J. Campos, and M. Yzuel, “Anamorphic and spatial frequency dependent phase modulation on liquid crystal displays. Optimization of the modulation diffraction efficiency,” Opt. Express 13(6), 2111–2119 (2005).
    [CrossRef] [PubMed]

2011

M. Persson, D. Engström, and M. Goksör, “Real-time generation of fully optimized holograms for optical trapping applications,” Proc. SPIE 8097, 80971H, 80971H-9 (2011).
[CrossRef]

2010

S. Bianchi and R. Di Leonardo, “Real-time optical micro-manipulation using optimized holograms generated on the GPU,” Comput. Phys. Commun. 181(8), 1444–1446 (2010).
[CrossRef]

M. Persson, D. Engström, A. Frank, J. Backsten, J. Bengtsson, and M. Goksör, “Minimizing intensity fluctuations in dynamic holographic optical tweezers by restricted phase change,” Opt. Express 18(11), 11250–11263 (2010).
[CrossRef] [PubMed]

2009

2007

2005

2004

2002

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1-6), 169–175 (2002).
[CrossRef]

1999

1996

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84(2), 268–298 (1996).
[CrossRef]

1995

V. V. Kotlyar, P. G. Seraphimovich, and V. A. Soifer, “An iterative weight-based method for calculating kinoforms,” Proc. SPIE 2363, 177–183 (1995).
[CrossRef]

1994

1991

M. W. Farn, “New iterative algorithm for the design of phase-only gratings,” Proc. SPIE 1555, 34–42 (1991).
[CrossRef]

1982

1973

Ågren, D.

E. Hällstig, J. Öhgren, L. Allard, L. Sjöqvist, D. Engström, S. Hård, D. Ågren, S. Junique, Q. Wang, and B. Noharet, “Retrocommunication utilizing electroabsorption modulators and nonmechanical beam steering,” Opt. Eng. 44(4), 045001 (2005).
[CrossRef]

Allard, L.

E. Hällstig, J. Öhgren, L. Allard, L. Sjöqvist, D. Engström, S. Hård, D. Ågren, S. Junique, Q. Wang, and B. Noharet, “Retrocommunication utilizing electroabsorption modulators and nonmechanical beam steering,” Opt. Eng. 44(4), 045001 (2005).
[CrossRef]

Apter, B.

Backsten, J.

Bahat-Treidel, E.

Bengtsson, J.

Bianchi, S.

S. Bianchi and R. Di Leonardo, “Real-time optical micro-manipulation using optimized holograms generated on the GPU,” Comput. Phys. Commun. 181(8), 1444–1446 (2010).
[CrossRef]

Campos, J.

Cohn, R. W.

Corkum, D. L.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84(2), 268–298 (1996).
[CrossRef]

Crossland, W. A.

Curtis, J. E.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1-6), 169–175 (2002).
[CrossRef]

Day, S. E.

Di Leonardo, R.

S. Bianchi and R. Di Leonardo, “Real-time optical micro-manipulation using optimized holograms generated on the GPU,” Comput. Phys. Commun. 181(8), 1444–1446 (2010).
[CrossRef]

R. Di Leonardo, F. Ianni, and G. Ruocco; “Computer generation of optimal holograms for optical trap arrays,” Opt. Express 15(4), 1913–1922 (2007).
[CrossRef] [PubMed]

Dorschner, T. A.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84(2), 268–298 (1996).
[CrossRef]

Efron, U.

Engström, D.

Farn, M. W.

M. W. Farn, “New iterative algorithm for the design of phase-only gratings,” Proc. SPIE 1555, 34–42 (1991).
[CrossRef]

Fernández, F. A.

Fienup, J. R.

Frank, A.

Friedman, L. J.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84(2), 268–298 (1996).
[CrossRef]

Gallagher, N. C.

Georgiou, A. G.

A. G. Georgiou, M. Komarcevic, T. D. Wilkinson, and W. A. Crossland, “Hologram optimisation using liquid crystal modelling,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 434(1), 183–198 (2005).
[CrossRef]

Goksör, M.

Grier, D.

Grier, D. G.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1-6), 169–175 (2002).
[CrossRef]

Haist, T.

Hällstig, E.

E. Hällstig, J. Öhgren, L. Allard, L. Sjöqvist, D. Engström, S. Hård, D. Ågren, S. Junique, Q. Wang, and B. Noharet, “Retrocommunication utilizing electroabsorption modulators and nonmechanical beam steering,” Opt. Eng. 44(4), 045001 (2005).
[CrossRef]

E. Hällstig, J. Stigwall, T. Martin, L. Sjöqvist, and M. Lindgren, “Fringing fields in a liquid crystal spatial light modulator for beam steering,” J. Mod. Opt. 51(8), 1233–1247 (2004).
[CrossRef]

Hård, S.

E. Hällstig, J. Öhgren, L. Allard, L. Sjöqvist, D. Engström, S. Hård, D. Ågren, S. Junique, Q. Wang, and B. Noharet, “Retrocommunication utilizing electroabsorption modulators and nonmechanical beam steering,” Opt. Eng. 44(4), 045001 (2005).
[CrossRef]

Hobbs, D. S.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84(2), 268–298 (1996).
[CrossRef]

Holz, M.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84(2), 268–298 (1996).
[CrossRef]

Ianni, F.

Iemmi, C.

James, R.

Junique, S.

E. Hällstig, J. Öhgren, L. Allard, L. Sjöqvist, D. Engström, S. Hård, D. Ågren, S. Junique, Q. Wang, and B. Noharet, “Retrocommunication utilizing electroabsorption modulators and nonmechanical beam steering,” Opt. Eng. 44(4), 045001 (2005).
[CrossRef]

Komarcevic, M.

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1-6), 169–175 (2002).
[CrossRef]

Kotlyar, V. V.

V. V. Kotlyar, P. G. Seraphimovich, and V. A. Soifer, “An iterative weight-based method for calculating kinoforms,” Proc. SPIE 2363, 177–183 (1995).
[CrossRef]

Ladavac, K.

Lee, S.-H.

Liberman, S.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84(2), 268–298 (1996).
[CrossRef]

Lindgren, M.

E. Hällstig, J. Stigwall, T. Martin, L. Sjöqvist, and M. Lindgren, “Fringing fields in a liquid crystal spatial light modulator for beam steering,” J. Mod. Opt. 51(8), 1233–1247 (2004).
[CrossRef]

Liu, B.

Márquez, A.

Martin, T.

E. Hällstig, J. Stigwall, T. Martin, L. Sjöqvist, and M. Lindgren, “Fringing fields in a liquid crystal spatial light modulator for beam steering,” J. Mod. Opt. 51(8), 1233–1247 (2004).
[CrossRef]

McManamon, P. F.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84(2), 268–298 (1996).
[CrossRef]

Milewski, G.

Moreno, I.

Nguyen, H. Q.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84(2), 268–298 (1996).
[CrossRef]

Noharet, B.

E. Hällstig, J. Öhgren, L. Allard, L. Sjöqvist, D. Engström, S. Hård, D. Ågren, S. Junique, Q. Wang, and B. Noharet, “Retrocommunication utilizing electroabsorption modulators and nonmechanical beam steering,” Opt. Eng. 44(4), 045001 (2005).
[CrossRef]

Öhgren, J.

E. Hällstig, J. Öhgren, L. Allard, L. Sjöqvist, D. Engström, S. Hård, D. Ågren, S. Junique, Q. Wang, and B. Noharet, “Retrocommunication utilizing electroabsorption modulators and nonmechanical beam steering,” Opt. Eng. 44(4), 045001 (2005).
[CrossRef]

Persson, M.

M. Persson, D. Engström, and M. Goksör, “Real-time generation of fully optimized holograms for optical trapping applications,” Proc. SPIE 8097, 80971H, 80971H-9 (2011).
[CrossRef]

M. Persson, D. Engström, A. Frank, J. Backsten, J. Bengtsson, and M. Goksör, “Minimizing intensity fluctuations in dynamic holographic optical tweezers by restricted phase change,” Opt. Express 18(11), 11250–11263 (2010).
[CrossRef] [PubMed]

Polin, M.

Reicherter, M.

Resler, D. P.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84(2), 268–298 (1996).
[CrossRef]

Roichman, Y.

Ruocco, G.

Seraphimovich, P. G.

V. V. Kotlyar, P. G. Seraphimovich, and V. A. Soifer, “An iterative weight-based method for calculating kinoforms,” Proc. SPIE 2363, 177–183 (1995).
[CrossRef]

Sharp, R. C.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84(2), 268–298 (1996).
[CrossRef]

Sjöqvist, L.

E. Hällstig, J. Öhgren, L. Allard, L. Sjöqvist, D. Engström, S. Hård, D. Ågren, S. Junique, Q. Wang, and B. Noharet, “Retrocommunication utilizing electroabsorption modulators and nonmechanical beam steering,” Opt. Eng. 44(4), 045001 (2005).
[CrossRef]

E. Hällstig, J. Stigwall, T. Martin, L. Sjöqvist, and M. Lindgren, “Fringing fields in a liquid crystal spatial light modulator for beam steering,” J. Mod. Opt. 51(8), 1233–1247 (2004).
[CrossRef]

Soifer, V. A.

V. V. Kotlyar, P. G. Seraphimovich, and V. A. Soifer, “An iterative weight-based method for calculating kinoforms,” Proc. SPIE 2363, 177–183 (1995).
[CrossRef]

Stigwall, J.

E. Hällstig, J. Stigwall, T. Martin, L. Sjöqvist, and M. Lindgren, “Fringing fields in a liquid crystal spatial light modulator for beam steering,” J. Mod. Opt. 51(8), 1233–1247 (2004).
[CrossRef]

Tiziani, H. J.

Wagemann, E. U.

Wang, Q.

E. Hällstig, J. Öhgren, L. Allard, L. Sjöqvist, D. Engström, S. Hård, D. Ågren, S. Junique, Q. Wang, and B. Noharet, “Retrocommunication utilizing electroabsorption modulators and nonmechanical beam steering,” Opt. Eng. 44(4), 045001 (2005).
[CrossRef]

Watson, E. A.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84(2), 268–298 (1996).
[CrossRef]

Wilkinson, T. D.

A. G. Georgiou, M. Komarcevic, T. D. Wilkinson, and W. A. Crossland, “Hologram optimisation using liquid crystal modelling,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 434(1), 183–198 (2005).
[CrossRef]

Xun, X.

Yzuel, M.

Yzuel, M. J.

Appl. Opt.

Comput. Phys. Commun.

S. Bianchi and R. Di Leonardo, “Real-time optical micro-manipulation using optimized holograms generated on the GPU,” Comput. Phys. Commun. 181(8), 1444–1446 (2010).
[CrossRef]

J. Mod. Opt.

E. Hällstig, J. Stigwall, T. Martin, L. Sjöqvist, and M. Lindgren, “Fringing fields in a liquid crystal spatial light modulator for beam steering,” J. Mod. Opt. 51(8), 1233–1247 (2004).
[CrossRef]

J. Opt. Soc. Am. A

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

A. G. Georgiou, M. Komarcevic, T. D. Wilkinson, and W. A. Crossland, “Hologram optimisation using liquid crystal modelling,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 434(1), 183–198 (2005).
[CrossRef]

Opt. Commun.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1-6), 169–175 (2002).
[CrossRef]

Opt. Eng.

E. Hällstig, J. Öhgren, L. Allard, L. Sjöqvist, D. Engström, S. Hård, D. Ågren, S. Junique, Q. Wang, and B. Noharet, “Retrocommunication utilizing electroabsorption modulators and nonmechanical beam steering,” Opt. Eng. 44(4), 045001 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. IEEE

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84(2), 268–298 (1996).
[CrossRef]

Proc. SPIE

M. W. Farn, “New iterative algorithm for the design of phase-only gratings,” Proc. SPIE 1555, 34–42 (1991).
[CrossRef]

V. V. Kotlyar, P. G. Seraphimovich, and V. A. Soifer, “An iterative weight-based method for calculating kinoforms,” Proc. SPIE 2363, 177–183 (1995).
[CrossRef]

M. Persson, D. Engström, and M. Goksör, “Real-time generation of fully optimized holograms for optical trapping applications,” Proc. SPIE 8097, 80971H, 80971H-9 (2011).
[CrossRef]

Other

M. Persson, D. Engström, J. Bengtsson, and M. Goksör, “Realistic treatment of spatial light modulator pixelation in real-time design algorithms for holographic spot generation,” in OSA Technical Digest (CD) (Optical Society of America, 2011), paper DWC32.

P. M. H. Hirsch, TX), Jordan Jr., James A. (Houston, TX), Lesem, Louis B. (Houston, TX), “Method of making an object dependent diffuser,” U.S. patent 3,619,022 (9 November 1971).

M. Persson, Holographic Optical Trapping: Improvements and Applications (Department of Physics, University of Gothenburg, 2011).

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Figures (5)

Fig. 1
Fig. 1

A detail from a typical two dimensional phase hologram (a) and its calculated far field diffraction spots (c). (b) and (d) shows the same hologram and resulting far field diffraction spots after convolution of the hologram with a Gaussian PSF with a radius 0.5 SLM pixels.

Fig. 2
Fig. 2

Flowchart of the modified algorithm for hologram generation. Added steps in the iteration cycle are marked with red boxes.

Fig. 3
Fig. 3

The effect of pixel crosstalk on binary gratings with long (a, c, e) and short (b, d, f) period. (a) and (b) show cross sections of the desired phase gratings and (c) and (d) show the gratings as realized by an SLM suffering from strong pixel crosstalk, simulated by convolution of the desired gratings with a Gaussian PSF with a radius of 0.5 SLM pixels. (e) and (f) show the simulated first diffraction order response curves for the desired (dashed line) and realized (solid line) gratings.

Fig. 4
Fig. 4

Measured first diffraction order response curves in the x (a) and y (b) direction. (c) shows the RMSE for measurements and simulations with the optimal rx and ry for each value of γ. (d) shows the optimal rx (black) and ry (red) for each value of γ. (e) and (f) show the simulated first diffraction order response curves for the values of rx, ry and γ minimizing the RMS error; same legend as for (a) and (b). 8 times oversampling was used for all simulations shown here.

Fig. 5
Fig. 5

Measured spot patterns for holograms without (a-f) and with (m-r) compensation for pixel crosstalk, and simulated spot patterns for holograms generated without compensation (g-l). The compensation was done without oversampling and using a PSF with the optimal radii and shape parameter shown in Table 1. The spots are separated by 36 (a, g, m, d, j, p), 48 (b, h, n, e, k, q) and 60 (c, i, o, f, l, r) spot sizes. The average measured uniformity and corresponding standard deviation is given in each image corresponding to holograms generated with crosstalk compensation.

Tables (2)

Tables Icon

Table 1 Optimized Values of rx, ry and γ for the Different Degrees of Oversampling

Tables Icon

Table 2 Obtained Average Uniformity for Optimized Holograms

Equations (6)

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

I( Δϕ )=0.405 sin 2 ( Δϕ 2 ),
a r x , r y ,γ (x,y)=exp( ( x 2 2 r x 2 + y 2 2 r y 2 ) γ ),
| FFT( exp( i( ϕ Λ,Δϕ ( x i , y i )a( x i , y i ) ) ) ) | 2 .
RMSE= Λ,Δϕ ( I Λ,Δϕ mx I Λ,Δϕ sx ) 2 + Λ,Δϕ ( I Λ,Δϕ my I Λ,Δϕ sy ) 2 N tot ,
ϕ( x i , y i )a( x i , y i )=FFT -1 ( FFT( ϕ( x i , y i ) )FFT( a( x i , y i ) ) ) .
u=1 I max I min I max + I min ,

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