Abstract

We present a method for converting the desired phase values of a hologram to the correct pixel addressing values of a spatial light modulator (SLM), taking into account detailed spatial variations in the phase response of the SLM. In addition to thickness variations in the liquid crystal layer of the SLM, we also show that these variations in phase response can be caused by a non-uniform electric drive scheme in the SLM or by local heating caused by the incident laser beam. We demonstrate that the use of a global look-up table (LUT), even in combination with a spatially varying scale factor, generally does not yield sufficiently accurate conversion for applications requiring highly controllable output fields, such as holographic optical trapping (HOT). We therefore propose a method where the pixel addressing values are given by a three-dimensional polynomial, with two of the variables being the (x, y)-positions of the pixels, and the third their desired phase values. The coefficients of the polynomial are determined by measuring the phase response in 8×8 sub-sections of the SLM surface; the degree of the polynomial is optimized so that the polynomial expression nearly replicates the measurement in the measurement points, while still showing a good interpolation behavior in between. The polynomial evaluation increases the total computation time for hologram generation by only a few percent. Compared to conventional phase conversion methods, for an SLM with varying phase response, we found that the proposed method increases the control of the trap intensities in HOT, and efficiently prevents the appearance of strong unwanted 0th order diffraction that commonly occurs in SLM systems.

© 2013 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. Marom and N. Konforti, “Dynamic optical interconnections,” Opt. Lett.12, 539–541 (1987).
    [CrossRef] [PubMed]
  2. P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holtz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. SPIE84, 268–298 (1996).
  3. 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 non-mechanical beam steering,” Opt.Eng.44, 045001 (2005).
    [CrossRef]
  4. 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, 608–610 (1999).
    [CrossRef]
  5. E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Instrum.72, 1810–1816 (2001).
    [CrossRef]
  6. M. A. Seldowitz, J. P. Allebach, and D. W. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt.26, 2788–2798 (1987).
    [CrossRef] [PubMed]
  7. B. K. Jennison, J. P. Allebach, and D. W. Sweeney, “Efficient design of direct-binary-search computer-generated holograms,” J. Opt. Soc. Am. A8, 652–660 (1991).
    [CrossRef]
  8. 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, 95–105 (2007).
    [CrossRef]
  9. R. W. Gerchberg and W. O. Saxton, “A Practical Algorithm for the Determination of Phase from Image and Diffraction Plane Pictures,” Optik35, 237–246 (1972).
  10. M. W. Farn, “New iterative algorithm for the design of phase-only gratings,” Proc. SPIE1555, 34–42 (1991).
    [CrossRef]
  11. J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun.207, 169–175 (2002).
    [CrossRef]
  12. D. Engström, A. Frank, J. Backsten, M. Goksör, and Jörgen Bengtsson, “Grid-free 3D multiple spot generation with an efficient single-plane FFT-based algorithm,” Opt. Express17, 9989–10000 (2009).
    [CrossRef] [PubMed]
  13. S. Bianchi and R. Di Leonardo, “Real-time optical micro-manipulation using optimized holograms generated on the GPU,” Comput. Phys. Commun.181, 1442–1446 (2010).
    [CrossRef]
  14. M. Persson, D. Engström, and M. Goksör, “Real-time generation of fully optimized holograms for optical trapping applications,” Proc. SPIE8097,80971H (2011).
    [CrossRef]
  15. X. D. Xun and R. W. Cohn, “Phase calibration of spatially nonuniform spatial light modulators,” Appl. Opt.43, 6400–6406 (2004).
    [CrossRef] [PubMed]
  16. J. Oton, P. Ambs, M. S. Millan, and E. Perez-Cabre, “Multipoint phase calibration for improved compensation of inherent wavefront distortion in parallel aligned liquid crystal on silicon displays,” Appl. Opt.46, 5667–5679 (2007).
    [CrossRef] [PubMed]
  17. D. Engström, M. Persson, and M. Goksör, “Spatial phase calibration used to improve holographic optical trapping,” in Biomedical Optics and 3-D Imaging, OSA Technical Digest (Optical Society of America, 2012), paper DSu2C.3.
    [CrossRef]
  18. G. Thalhammer, R. W. Bowman, G. D. Love, M. J. Padgett, and M. Ritsch-Marte, “Speeding up liquid crystal SLMs using overdrive with phase change reduction,” Opt. Express21, 1779–1797 (2013).
    [CrossRef] [PubMed]
  19. S. Reichelt, “Spatially resolved phase-response calibration of liquid-crystal-based spatial light modulators,” Appl. Opt.52, 2610–2618 (2013).
    [CrossRef] [PubMed]
  20. Z. Zhang, H. Yang, B. Robertson, M. Redmond, M. Pivnenko, N. Collings, W. A. Crossland, and D. Chu, “Diffraction based phase compensation method for phase-only liquid crystal on silicon devices in operation,” Appl. Opt.51, 3837–3846 (2012).
    [CrossRef] [PubMed]
  21. T. Cizmar, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics4, 388–394 (2010).
    [CrossRef]
  22. R. W. Bowman, A. J. Wright, and M. J. Padgett, “An SLM-based ShackHartmann wavefront sensor for aberration correction in optical tweezers,” J. Opt.12, 124004 (2010).
    [CrossRef]
  23. T. H. Barnes, K. Matsumoto, T. Eijo, K. Matsuda, and N. Ooyama, “Grating interferometer with extremely high stability, suitable for measuring small refractive index changes,” Appl. Opt.30, 745–751 (1991).
    [CrossRef] [PubMed]
  24. A. Bergeron, J. Gauvin, F. Gagnon, D. Gingras, H. H. Arsenault, and M. Doucet, “Phase calibration and applications of a liquid-crystal spatial light modulator,” Appl. Opt.34, 5133–5139 (1995).
    [CrossRef] [PubMed]
  25. Z. Zhang, G. Lu, and F. T. S. Yu, “Simple method for measuring phase modulation in liquid crystal televisions,” Opt. Eng.33, 3018–3022 (1994).
    [CrossRef]
  26. D. Engström, G. Milewski, J. Bengtsson, and S. Galt, “Diffraction-based determination of the phase modulation for general spatial light modulators,” Appl. Opt.45, 7195–7204 (2006).
    [CrossRef] [PubMed]
  27. A. Linnenberger, S. Serati, and J. Stockley, “Advances in Optical Phased Array Technology,” Proc. SPIE6304,63040T (2006).
  28. D. Preece, R. Bowman, A. Linnenberger, G. Gibson, S. Serati, and M. Padgett, “Increasing trap stiffness with position clamping in holographic optical tweezers,” Opt. Express17, 22718–22725 (2009).
    [CrossRef]
  29. M. Schadt and W. Helfrich, “Voltage-dependent optical activity of a twisted nematic liquid crystal,” Appl. Phys. Lett.18, 127–128 (1971).
    [CrossRef]
  30. A. Linnenberger and Teresa Ewing, Boulder Nonlinear Systems, 450 Courtney Way, #107 Lafayette, CO 80026, USA (personal communication, February 2013).
  31. Software available at http://www.physics.gu.se/forskning/komplexa-system/biophotonics/download/hotlab/
  32. M. Persson, D. Engström, and M. Goksör, “Reducing the effect of pixel crosstalk in phase only spatial light modulators,” Opt. Express20, 22334–22343 (2012).
    [CrossRef] [PubMed]
  33. C. Runge, “Über empirische Funktionen und die Interpolation zwischen äquidistanten Ordinaten,” inZeitschrift für Mathematik und Physik46,R. Mehmke and C. Runge, eds. (Druck und verlag von B. G. Teubner, Leipzig, 1901), 224–243.

2013 (2)

2012 (2)

2011 (1)

M. Persson, D. Engström, and M. Goksör, “Real-time generation of fully optimized holograms for optical trapping applications,” Proc. SPIE8097,80971H (2011).
[CrossRef]

2010 (3)

S. Bianchi and R. Di Leonardo, “Real-time optical micro-manipulation using optimized holograms generated on the GPU,” Comput. Phys. Commun.181, 1442–1446 (2010).
[CrossRef]

T. Cizmar, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics4, 388–394 (2010).
[CrossRef]

R. W. Bowman, A. J. Wright, and M. J. Padgett, “An SLM-based ShackHartmann wavefront sensor for aberration correction in optical tweezers,” J. Opt.12, 124004 (2010).
[CrossRef]

2009 (2)

2007 (2)

2006 (2)

2005 (1)

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 non-mechanical beam steering,” Opt.Eng.44, 045001 (2005).
[CrossRef]

2004 (1)

2002 (1)

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

2001 (1)

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Instrum.72, 1810–1816 (2001).
[CrossRef]

1999 (1)

1996 (1)

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holtz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. SPIE84, 268–298 (1996).

1995 (1)

1994 (1)

Z. Zhang, G. Lu, and F. T. S. Yu, “Simple method for measuring phase modulation in liquid crystal televisions,” Opt. Eng.33, 3018–3022 (1994).
[CrossRef]

1991 (3)

1987 (2)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A Practical Algorithm for the Determination of Phase from Image and Diffraction Plane Pictures,” Optik35, 237–246 (1972).

1971 (1)

M. Schadt and W. Helfrich, “Voltage-dependent optical activity of a twisted nematic liquid crystal,” Appl. Phys. Lett.18, 127–128 (1971).
[CrossRef]

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 non-mechanical beam steering,” Opt.Eng.44, 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 non-mechanical beam steering,” Opt.Eng.44, 045001 (2005).
[CrossRef]

Allebach, J. P.

Ambs, P.

Arsenault, H. H.

Backsten, J.

Barnes, T. H.

Bengtsson, J.

Bengtsson, Jörgen

Bergeron, A.

Bianchi, S.

S. Bianchi and R. Di Leonardo, “Real-time optical micro-manipulation using optimized holograms generated on the GPU,” Comput. Phys. Commun.181, 1442–1446 (2010).
[CrossRef]

Bowman, R.

Bowman, R. W.

G. Thalhammer, R. W. Bowman, G. D. Love, M. J. Padgett, and M. Ritsch-Marte, “Speeding up liquid crystal SLMs using overdrive with phase change reduction,” Opt. Express21, 1779–1797 (2013).
[CrossRef] [PubMed]

R. W. Bowman, A. J. Wright, and M. J. Padgett, “An SLM-based ShackHartmann wavefront sensor for aberration correction in optical tweezers,” J. Opt.12, 124004 (2010).
[CrossRef]

Chu, D.

Cizmar, T.

T. Cizmar, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics4, 388–394 (2010).
[CrossRef]

Cohn, R. W.

Collings, N.

Corkum, D. L.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holtz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. SPIE84, 268–298 (1996).

Crossland, W. A.

Curtis, J. E.

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

Dearing, M. T.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Instrum.72, 1810–1816 (2001).
[CrossRef]

Dholakia, K.

T. Cizmar, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics4, 388–394 (2010).
[CrossRef]

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, 1442–1446 (2010).
[CrossRef]

Dorschner, T. A.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holtz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. SPIE84, 268–298 (1996).

Doucet, M.

Dufresne, E. R.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Instrum.72, 1810–1816 (2001).
[CrossRef]

Eijo, T.

Engström, D.

M. Persson, D. Engström, and M. Goksör, “Reducing the effect of pixel crosstalk in phase only spatial light modulators,” Opt. Express20, 22334–22343 (2012).
[CrossRef] [PubMed]

M. Persson, D. Engström, and M. Goksör, “Real-time generation of fully optimized holograms for optical trapping applications,” Proc. SPIE8097,80971H (2011).
[CrossRef]

D. Engström, A. Frank, J. Backsten, M. Goksör, and Jörgen Bengtsson, “Grid-free 3D multiple spot generation with an efficient single-plane FFT-based algorithm,” Opt. Express17, 9989–10000 (2009).
[CrossRef] [PubMed]

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, 95–105 (2007).
[CrossRef]

D. Engström, G. Milewski, J. Bengtsson, and S. Galt, “Diffraction-based determination of the phase modulation for general spatial light modulators,” Appl. Opt.45, 7195–7204 (2006).
[CrossRef] [PubMed]

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 non-mechanical beam steering,” Opt.Eng.44, 045001 (2005).
[CrossRef]

D. Engström, M. Persson, and M. Goksör, “Spatial phase calibration used to improve holographic optical trapping,” in Biomedical Optics and 3-D Imaging, OSA Technical Digest (Optical Society of America, 2012), paper DSu2C.3.
[CrossRef]

Ewing, Teresa

A. Linnenberger and Teresa Ewing, Boulder Nonlinear Systems, 450 Courtney Way, #107 Lafayette, CO 80026, USA (personal communication, February 2013).

Farn, M. W.

M. W. Farn, “New iterative algorithm for the design of phase-only gratings,” Proc. SPIE1555, 34–42 (1991).
[CrossRef]

Frank, A.

Friedman, L. J.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holtz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. SPIE84, 268–298 (1996).

Gagnon, F.

Galt, S.

Gauvin, J.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A Practical Algorithm for the Determination of Phase from Image and Diffraction Plane Pictures,” Optik35, 237–246 (1972).

Gibson, G.

Gingras, D.

Goksör, M.

M. Persson, D. Engström, and M. Goksör, “Reducing the effect of pixel crosstalk in phase only spatial light modulators,” Opt. Express20, 22334–22343 (2012).
[CrossRef] [PubMed]

M. Persson, D. Engström, and M. Goksör, “Real-time generation of fully optimized holograms for optical trapping applications,” Proc. SPIE8097,80971H (2011).
[CrossRef]

D. Engström, A. Frank, J. Backsten, M. Goksör, and Jörgen Bengtsson, “Grid-free 3D multiple spot generation with an efficient single-plane FFT-based algorithm,” Opt. Express17, 9989–10000 (2009).
[CrossRef] [PubMed]

D. Engström, M. Persson, and M. Goksör, “Spatial phase calibration used to improve holographic optical trapping,” in Biomedical Optics and 3-D Imaging, OSA Technical Digest (Optical Society of America, 2012), paper DSu2C.3.
[CrossRef]

Grier, D. G.

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

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Instrum.72, 1810–1816 (2001).
[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 non-mechanical beam steering,” Opt.Eng.44, 045001 (2005).
[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 non-mechanical beam steering,” Opt.Eng.44, 045001 (2005).
[CrossRef]

Helfrich, W.

M. Schadt and W. Helfrich, “Voltage-dependent optical activity of a twisted nematic liquid crystal,” Appl. Phys. Lett.18, 127–128 (1971).
[CrossRef]

Hobbs, D. S.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holtz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. SPIE84, 268–298 (1996).

Holtz, M.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holtz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. SPIE84, 268–298 (1996).

Jennison, B. K.

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 non-mechanical beam steering,” Opt.Eng.44, 045001 (2005).
[CrossRef]

Konforti, N.

Koss, B. A.

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

Liberman, S.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holtz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. SPIE84, 268–298 (1996).

Linnenberger, A.

D. Preece, R. Bowman, A. Linnenberger, G. Gibson, S. Serati, and M. Padgett, “Increasing trap stiffness with position clamping in holographic optical tweezers,” Opt. Express17, 22718–22725 (2009).
[CrossRef]

A. Linnenberger, S. Serati, and J. Stockley, “Advances in Optical Phased Array Technology,” Proc. SPIE6304,63040T (2006).

A. Linnenberger and Teresa Ewing, Boulder Nonlinear Systems, 450 Courtney Way, #107 Lafayette, CO 80026, USA (personal communication, February 2013).

Love, G. D.

Lu, G.

Z. Zhang, G. Lu, and F. T. S. Yu, “Simple method for measuring phase modulation in liquid crystal televisions,” Opt. Eng.33, 3018–3022 (1994).
[CrossRef]

Marom, E.

Matsuda, K.

Matsumoto, K.

Mazilu, M.

T. Cizmar, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics4, 388–394 (2010).
[CrossRef]

McManamon, P. F.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holtz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. SPIE84, 268–298 (1996).

Milewski, G.

Millan, M. S.

Nguyen, H. Q.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holtz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. SPIE84, 268–298 (1996).

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 non-mechanical beam steering,” Opt.Eng.44, 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 non-mechanical beam steering,” Opt.Eng.44, 045001 (2005).
[CrossRef]

Ooyama, N.

Oton, J.

Padgett, M.

Padgett, M. J.

G. Thalhammer, R. W. Bowman, G. D. Love, M. J. Padgett, and M. Ritsch-Marte, “Speeding up liquid crystal SLMs using overdrive with phase change reduction,” Opt. Express21, 1779–1797 (2013).
[CrossRef] [PubMed]

R. W. Bowman, A. J. Wright, and M. J. Padgett, “An SLM-based ShackHartmann wavefront sensor for aberration correction in optical tweezers,” J. Opt.12, 124004 (2010).
[CrossRef]

Perez-Cabre, E.

Persson, M.

M. Persson, D. Engström, and M. Goksör, “Reducing the effect of pixel crosstalk in phase only spatial light modulators,” Opt. Express20, 22334–22343 (2012).
[CrossRef] [PubMed]

M. Persson, D. Engström, and M. Goksör, “Real-time generation of fully optimized holograms for optical trapping applications,” Proc. SPIE8097,80971H (2011).
[CrossRef]

D. Engström, M. Persson, and M. Goksör, “Spatial phase calibration used to improve holographic optical trapping,” in Biomedical Optics and 3-D Imaging, OSA Technical Digest (Optical Society of America, 2012), paper DSu2C.3.
[CrossRef]

Pivnenko, M.

Preece, D.

Redmond, M.

Reichelt, S.

Reicherter, M.

Resler, D. P.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holtz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. SPIE84, 268–298 (1996).

Ritsch-Marte, M.

Robertson, B.

Runge, C.

C. Runge, “Über empirische Funktionen und die Interpolation zwischen äquidistanten Ordinaten,” inZeitschrift für Mathematik und Physik46,R. Mehmke and C. Runge, eds. (Druck und verlag von B. G. Teubner, Leipzig, 1901), 224–243.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A Practical Algorithm for the Determination of Phase from Image and Diffraction Plane Pictures,” Optik35, 237–246 (1972).

Schadt, M.

M. Schadt and W. Helfrich, “Voltage-dependent optical activity of a twisted nematic liquid crystal,” Appl. Phys. Lett.18, 127–128 (1971).
[CrossRef]

Seldowitz, M. A.

Serati, S.

Sharp, R. C.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holtz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. SPIE84, 268–298 (1996).

Sheets, S. A.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Instrum.72, 1810–1816 (2001).
[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 non-mechanical beam steering,” Opt.Eng.44, 045001 (2005).
[CrossRef]

Spalding, G. C.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Instrum.72, 1810–1816 (2001).
[CrossRef]

Stockley, J.

A. Linnenberger, S. Serati, and J. Stockley, “Advances in Optical Phased Array Technology,” Proc. SPIE6304,63040T (2006).

Sweeney, D. W.

Thalhammer, G.

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 non-mechanical beam steering,” Opt.Eng.44, 045001 (2005).
[CrossRef]

Watson, E. A.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holtz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. SPIE84, 268–298 (1996).

Wright, A. J.

R. W. Bowman, A. J. Wright, and M. J. Padgett, “An SLM-based ShackHartmann wavefront sensor for aberration correction in optical tweezers,” J. Opt.12, 124004 (2010).
[CrossRef]

Xun, X. D.

Yang, H.

Yu, F. T. S.

Z. Zhang, G. Lu, and F. T. S. Yu, “Simple method for measuring phase modulation in liquid crystal televisions,” Opt. Eng.33, 3018–3022 (1994).
[CrossRef]

Zhang, Z.

Appl. Opt. (9)

M. A. Seldowitz, J. P. Allebach, and D. W. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt.26, 2788–2798 (1987).
[CrossRef] [PubMed]

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, 95–105 (2007).
[CrossRef]

X. D. Xun and R. W. Cohn, “Phase calibration of spatially nonuniform spatial light modulators,” Appl. Opt.43, 6400–6406 (2004).
[CrossRef] [PubMed]

J. Oton, P. Ambs, M. S. Millan, and E. Perez-Cabre, “Multipoint phase calibration for improved compensation of inherent wavefront distortion in parallel aligned liquid crystal on silicon displays,” Appl. Opt.46, 5667–5679 (2007).
[CrossRef] [PubMed]

S. Reichelt, “Spatially resolved phase-response calibration of liquid-crystal-based spatial light modulators,” Appl. Opt.52, 2610–2618 (2013).
[CrossRef] [PubMed]

Z. Zhang, H. Yang, B. Robertson, M. Redmond, M. Pivnenko, N. Collings, W. A. Crossland, and D. Chu, “Diffraction based phase compensation method for phase-only liquid crystal on silicon devices in operation,” Appl. Opt.51, 3837–3846 (2012).
[CrossRef] [PubMed]

T. H. Barnes, K. Matsumoto, T. Eijo, K. Matsuda, and N. Ooyama, “Grating interferometer with extremely high stability, suitable for measuring small refractive index changes,” Appl. Opt.30, 745–751 (1991).
[CrossRef] [PubMed]

A. Bergeron, J. Gauvin, F. Gagnon, D. Gingras, H. H. Arsenault, and M. Doucet, “Phase calibration and applications of a liquid-crystal spatial light modulator,” Appl. Opt.34, 5133–5139 (1995).
[CrossRef] [PubMed]

D. Engström, G. Milewski, J. Bengtsson, and S. Galt, “Diffraction-based determination of the phase modulation for general spatial light modulators,” Appl. Opt.45, 7195–7204 (2006).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

M. Schadt and W. Helfrich, “Voltage-dependent optical activity of a twisted nematic liquid crystal,” Appl. Phys. Lett.18, 127–128 (1971).
[CrossRef]

Comput. Phys. Commun. (1)

S. Bianchi and R. Di Leonardo, “Real-time optical micro-manipulation using optimized holograms generated on the GPU,” Comput. Phys. Commun.181, 1442–1446 (2010).
[CrossRef]

J. Opt. (1)

R. W. Bowman, A. J. Wright, and M. J. Padgett, “An SLM-based ShackHartmann wavefront sensor for aberration correction in optical tweezers,” J. Opt.12, 124004 (2010).
[CrossRef]

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

Nat. Photonics (1)

T. Cizmar, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics4, 388–394 (2010).
[CrossRef]

Opt. Commun. (1)

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

Opt. Eng. (1)

Z. Zhang, G. Lu, and F. T. S. Yu, “Simple method for measuring phase modulation in liquid crystal televisions,” Opt. Eng.33, 3018–3022 (1994).
[CrossRef]

Opt. Express (4)

Opt. Lett. (2)

Opt.Eng. (1)

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 non-mechanical beam steering,” Opt.Eng.44, 045001 (2005).
[CrossRef]

Optik (1)

R. W. Gerchberg and W. O. Saxton, “A Practical Algorithm for the Determination of Phase from Image and Diffraction Plane Pictures,” Optik35, 237–246 (1972).

Proc. SPIE (4)

M. W. Farn, “New iterative algorithm for the design of phase-only gratings,” Proc. SPIE1555, 34–42 (1991).
[CrossRef]

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holtz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. SPIE84, 268–298 (1996).

M. Persson, D. Engström, and M. Goksör, “Real-time generation of fully optimized holograms for optical trapping applications,” Proc. SPIE8097,80971H (2011).
[CrossRef]

A. Linnenberger, S. Serati, and J. Stockley, “Advances in Optical Phased Array Technology,” Proc. SPIE6304,63040T (2006).

Rev. Sci. Instrum. (1)

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Instrum.72, 1810–1816 (2001).
[CrossRef]

Other (4)

D. Engström, M. Persson, and M. Goksör, “Spatial phase calibration used to improve holographic optical trapping,” in Biomedical Optics and 3-D Imaging, OSA Technical Digest (Optical Society of America, 2012), paper DSu2C.3.
[CrossRef]

C. Runge, “Über empirische Funktionen und die Interpolation zwischen äquidistanten Ordinaten,” inZeitschrift für Mathematik und Physik46,R. Mehmke and C. Runge, eds. (Druck und verlag von B. G. Teubner, Leipzig, 1901), 224–243.

A. Linnenberger and Teresa Ewing, Boulder Nonlinear Systems, 450 Courtney Way, #107 Lafayette, CO 80026, USA (personal communication, February 2013).

Software available at http://www.physics.gu.se/forskning/komplexa-system/biophotonics/download/hotlab/

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1
Fig. 1

Simulated results. (a) Segment (64×64 pixels) of an optimized hologram generating 14 spots in a circle centered around the the optical axis; black and white corresponds to a phase of 0 and 2π, respectively. SLM imperfections: (b) static aberration (same color mapping as in (a)) and (c) spatially varying phase response; the phase response changes in the horizontal direction over the SLM. Inset shows which color corresponds to which area of the SLM. Simulated far-field patterns for (d) the ideal hologram in (a), (e) the ideal hologram with the static aberration in (b), and (f) the ideal hologram encoded with the spatially varying phase response in (c). (g–i) Similar as (d–f) but for a hologram optimized to produce 24 spots in a 5×5 grid centered on the optical axis; no spot is positioned on the optical axis. The uniformity u and P0, the fraction of the total power in the simulation window that falls into the unwanted zeroth order, are given for each case.

Fig. 2
Fig. 2

Measured phase response for 8×8 regions (each 64×64 pixels large) of an SLM (HSPDM512 1064-PCIe, Boulder Nonlinear Systems) as function of the addressed pixel value; the shape of φrealized as function of the pixel value varies over the SLM.

Fig. 3
Fig. 3

Pixel values yielding a specific pixel phase, φ, as determined from measurements with an incident power on the SLM (same device as in Fig. 2), of 50 mW (top row) and 1 W (bottom row). The color scaling shown in the bottom of each column is used both for 50 mW and 1 W. The results were obtained with the method described in Section 4.1.

Fig. 4
Fig. 4

Phase characterization method. (a) subregion i of the SLM is addressed with a binary grating. (b) Four binary gratings and their resulting diffraction patterns. The area in the measurement plane used to determine the power in the +1st order is indicated. (c) Normalized optical power in the +1st order as function of the pixel value. (d) Extracted phase modulation as function of the pixel value. In (c) and (d) the indicated numbers correspond to the four gratings shown in (b).

Fig. 5
Fig. 5

(a) The HOT setup is composed of a laser (λ =1070 nm), a polarizer (P), planoconvex lenses L1 (focal length 150 mm), L2 (120 mm), L3 (400 mm), and L4 (300 mm) with anti-reflection coating, an SLM, a microscope objective, and a camera. A halogen lamp, a condenser lens, and an IR blocking filter enable bright field imaging. (b) During characterization the SLM was locally addressed with binary gratings, the 0th order was blocked outside the microscope using a beam block (BB), bright field illumination was turned off, and the IR blocking filter was removed to allow detection of the laser light reflected off a cover glass or mirror. For PSLM ≥ 0.5 W, a reflective ND filter was also inserted outside the microscope to decrease the power reaching the camera.

Fig. 6
Fig. 6

Measured results for 52 regions (out of 8×8), all giving a strong enough optical signal through the microscope objective. The binary gratings had a period of 16 pixels. (a) Normalized measured power in the 1st diffraction order as function of the addressed PV and (b) desired PV as function of the desired phase for an incident power onto the SLM of 50 mW. (c) and (d) similar to (a) and (b) but for an incident power of 1 W. Inset shows which color corresponds to which area of the SLM.

Fig. 7
Fig. 7

Accuracy of the polynomial. (a) Difference in PV between the measured average and the values given by the fitted polynomial of 7th order for a desired phase of π/2, π, 3π/2, and 2π. (b) and (c) Largest maximal absolute error and largest mean absolute error in phase for the 52 and 32 most central SLM regions, respectively. An incident laser power of 50 mW was used.

Fig. 8
Fig. 8

Phase conversion comparison using gratings covering individual SLM subregions. (a–c) Measured power in the first diffraction order as a function of the desired phase for binary gratings converted using (a) a global LUT, (b) the scaling matrix method, and (c) a 3D polynomial. (d–f) Realized phase (derived from data shown in (a–c)) as a function of desired phase for binary gratings converted using (d) a global LUT, (e) the scaling matrix method, and (f) a 3D polynomial. The incident power on the SLM was 0.5 W.

Fig. 9
Fig. 9

Phase conversion comparison using gratings covering the full SLM. Measured power in the 0th (black dashed line) and ±1st (blue solid and red dotted lines) diffraction orders for binary gratings with a period of 16 pixels. Phase-to-PV-conversion was done using (a) a global LUT, (b) the scaling matrix method, and (c) a 3D polynomial. The incident power on the SLM was 1 W.

Fig. 10
Fig. 10

Measured spot patterns for optimized holograms producing (a–c) 14 traps in a circle centered on the optical axis and (d–f) 24 traps in a 5×5 grid (0th order omitted). Phase-to-PV conversion made using (a,d) a global LUT, (b,e) the scaling matrix method, and (c,f) a 3D polynomial. An incident power of 1 W onto the SLM was used.

Fig. 11
Fig. 11

Measured power spectral density for the Brownian motion of each of the 5 trapped beads and the corresponding Lorentzian curve fits. (a and b) Desired power in each trap equals 10% of the total power in the trapping plane. Hologram conversion using (a) a global LUT and (b) a 3D polynomial. (c and d) Same as (a and b) but with the desired power in each trap equalling 20% of the total power. (e) and (f) bright-field images of the trapped beads for a desired trap power of 2%; note that the middle bead looks different in (e) since it is captured by the 0th order spot 2.4 μm behind the traps. Hologram conversion using (e) a global LUT and (f) a 3D polynomial. An incident power of 1 W onto the SLM was used.

Tables (1)

Tables Icon

Table 1 Measured PVs that yield a phase of φ = π, 2π, and 3π. Data is given for an incident power of 50 mW and 1 W. The range of PVs for each phase and optical power is the minimum and maximum value among the measured 52 subregions.

Equations (7)

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

u = 1 max ( P spots ) min ( P spots ) max ( P spots ) + min ( P spots )
φ = 4 π λ Δ n d .
PV ( φ desired ( x , y ) , x , y ) = LUT ( φ desired ( x , y ) ) ,
PV ( φ desired ( x , y ) , x , y ) = LUT ( φ desired ( x , y ) ) × f ( x , y ) ,
φ i ( PV ) = { φ i wrapped ( PV ) , before first maximum 2 π φ i wrapped ( PV ) , before first maximum and first minimum
[ 1 x 1 y 1 φ 1 x 1 2 x 1 y 1 x 1 φ 1 y 1 φ 1 6 φ 1 7 1 x 1 y 1 φ K x 1 2 x 1 y 1 x 1 φ K y 1 φ K 6 φ K 7 1 x 2 y 2 φ 1 x 2 2 x 2 y 2 x 2 φ 1 y 2 φ 1 6 φ 1 7 1 x 2 y 2 φ K x 2 2 x 2 y 2 x 2 φ K y 2 φ K 6 φ K 7 1 x 3 y 3 φ 1 x 3 2 x 3 y 3 x 3 φ 1 y 3 φ 1 6 φ 1 7 1 x N y N φ 1 x N 2 x N y N x N φ 1 y N φ 1 6 φ 1 7 1 x N y N φ K x N 2 x N y N x N φ K y N φ K 6 φ K 7 ] c = [ PV ( φ 1 , x 1 , y 1 ) PV ( φ K , x 1 , y 1 ) PV ( φ 1 , x 2 , y 2 ) PV ( φ K , x 2 , y 2 ) PV ( φ 1 , x 3 , y 3 ) PV ( φ 1 , x N , y N ) PV ( φ K , x N , y N ) ] ,
PV ( φ desired ( x , y ) , x , y ) = f ( φ desired ( x , y ) , x , y ) .

Metrics