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

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    [CrossRef] [PubMed]
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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)

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]

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]

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.

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.

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.

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.

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

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