Abstract

A technique is proposed theoretically and verified experimentally to eliminate a zero-order beam caused by a pixelated phase-only spatial light modulator (SLM) for holographic projection. The formulas for determination of the optical field in the Fourier plane are deduced, and the influence of the pixelated structure of a SLM on the intensity of the zero-order beam is numerically investigated. Two currently existing techniques are studied and a new one is presented. These three techniques are used separately to eliminate the zero-order interruption, and the optical performances of the reconstructed patterns are compared. The new technique results in higher reconstruction quality and diffraction efficiency. A short animated movie is illuminated for holographic projection display. The experimental results show that the zero-order beam can be efficiently eliminated by the new technique. It is believed that this technique can be used in various optical systems that are based on pixelated phase-only SLMs, such as holographic optical tweezers and optical testing systems.

© 2009 Optical Society of America

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References

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  1. H. Dammann and K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312-315 (1971).
    [CrossRef]
  2. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 35, 237-246 (1972).
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    [CrossRef] [PubMed]
  4. B. Gu, G. Yang, and B. Dong, “General theory for performing an optical transform,” Appl. Opt. 25, 3197-3206 (1986).
    [CrossRef] [PubMed]
  5. S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671-680(1983).
    [CrossRef] [PubMed]
  6. A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A Pure Appl. Opt. 10, 035302 (2008).
    [CrossRef]
  7. A. Georgiou, J. Christmas, J. Moore, A. Jeziorska-Chapman, A. Davey, N. Collings, and W. A. Crossland, “Liquid crystal over silicon device characteristics for holographic projection of high-definition television images,” Appl. Opt. 47, 4793-4803 (2008).
    [CrossRef] [PubMed]
  8. H. Melville, G. Milne, G. Spalding, W. Sibbett, K. Dholakia, and D. McGloin, “Optical trapping of three-dimensional structures using dynamic holograms,” Opt. Express 11, 3562-3567 (2003).
    [CrossRef] [PubMed]
  9. Z. Cao, L. Xuan, L. Hu, Y. Liu, Q. Mu, and D. Li, “Investigation of optical testing with a phase-only liquid crystal spatial light modulator,” Opt. Express 13, 1059-1065 (2005).
    [CrossRef] [PubMed]
  10. A. Michalkiewicz, M. Kujawinska, J. Kretzel, L. Salbut, X. Wang, and P. J. Bos, “Phase manipulation and optoelectronic reconstruction of digital holograms by means of LCOS spatial light modulator,” Proc. SPIE 5776, 144-152 (2005).
    [CrossRef]
  11. C. Kohler, X. Schwab, and W. Osten, “Optimally tuned spatial light modulators for digital holography,” Appl. Opt. 45, 960-967 (2006).
    [CrossRef] [PubMed]
  12. J. Joseph and D. A. Waldman, “Homogenized Fourier transform holographic data storage using phase spatial light modulators and methods for recovery of data from the phase image,” Appl. Opt. 45, 6374-6380 (2006).
    [CrossRef] [PubMed]
  13. X. Xun and R. W. Cohn, “Phase calibration of spatially nonuniform spatial light modulators,” Appl. Opt. 43, 6400-6406(2004).
    [CrossRef] [PubMed]
  14. J. Otón, P. Ambs, M. S. Millán, and E. Pérez-Cabré, “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]
  15. V. Arrizon, E. Carreon, and M. Testorf, “Implementation of Fourier array illuminators using pixelated SLM: efficiency limitations,” Opt. Commun. 160, 207-213 (1999).
    [CrossRef]
  16. D. Palima and V. R. Daria, “Effect of spurious diffraction orders in arbitrary multifoci patterns produced via phase-only holograms,” Appl. Opt. 45, 6689-6693 (2006).
    [CrossRef] [PubMed]
  17. D. Palima and V. R. Daria, “Holographic projection of arbitrary light patterns with a suppressed zero-order beam,” Appl. Opt. 46, 4197-4201 (2007).
    [CrossRef] [PubMed]
  18. 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]
  19. M. Gruneisen, L. DeSandre, J. Rotge, R. Dymale, and D. Lubin, “Programmable diffractive optics for wide-dynamic-range wavefront control using liquid-crystal spatial light modulators,” Opt. Eng. 43, 1387-1393 (2004).
    [CrossRef]
  20. J. Christmas, N. Collings, A. Georgiou, “Blocking zero-order in phase shift hologram generation,” UK patent GB2438458 (28 November 2007).

2008 (2)

2007 (3)

2006 (3)

2005 (2)

Z. Cao, L. Xuan, L. Hu, Y. Liu, Q. Mu, and D. Li, “Investigation of optical testing with a phase-only liquid crystal spatial light modulator,” Opt. Express 13, 1059-1065 (2005).
[CrossRef] [PubMed]

A. Michalkiewicz, M. Kujawinska, J. Kretzel, L. Salbut, X. Wang, and P. J. Bos, “Phase manipulation and optoelectronic reconstruction of digital holograms by means of LCOS spatial light modulator,” Proc. SPIE 5776, 144-152 (2005).
[CrossRef]

2004 (2)

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

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

2003 (1)

1999 (1)

V. Arrizon, E. Carreon, and M. Testorf, “Implementation of Fourier array illuminators using pixelated SLM: efficiency limitations,” Opt. Commun. 160, 207-213 (1999).
[CrossRef]

1986 (1)

1983 (1)

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671-680(1983).
[CrossRef] [PubMed]

1978 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 35, 237-246 (1972).

1971 (1)

H. Dammann and K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312-315 (1971).
[CrossRef]

Ambs, P.

Arrizon, V.

V. Arrizon, E. Carreon, and M. Testorf, “Implementation of Fourier array illuminators using pixelated SLM: efficiency limitations,” Opt. Commun. 160, 207-213 (1999).
[CrossRef]

Bengtsson, J.

Bos, P. J.

A. Michalkiewicz, M. Kujawinska, J. Kretzel, L. Salbut, X. Wang, and P. J. Bos, “Phase manipulation and optoelectronic reconstruction of digital holograms by means of LCOS spatial light modulator,” Proc. SPIE 5776, 144-152 (2005).
[CrossRef]

Cao, Z.

Carreon, E.

V. Arrizon, E. Carreon, and M. Testorf, “Implementation of Fourier array illuminators using pixelated SLM: efficiency limitations,” Opt. Commun. 160, 207-213 (1999).
[CrossRef]

Christmas, J.

A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A Pure Appl. Opt. 10, 035302 (2008).
[CrossRef]

A. Georgiou, J. Christmas, J. Moore, A. Jeziorska-Chapman, A. Davey, N. Collings, and W. A. Crossland, “Liquid crystal over silicon device characteristics for holographic projection of high-definition television images,” Appl. Opt. 47, 4793-4803 (2008).
[CrossRef] [PubMed]

J. Christmas, N. Collings, A. Georgiou, “Blocking zero-order in phase shift hologram generation,” UK patent GB2438458 (28 November 2007).

Cohn, R. W.

Collings, N.

A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A Pure Appl. Opt. 10, 035302 (2008).
[CrossRef]

A. Georgiou, J. Christmas, J. Moore, A. Jeziorska-Chapman, A. Davey, N. Collings, and W. A. Crossland, “Liquid crystal over silicon device characteristics for holographic projection of high-definition television images,” Appl. Opt. 47, 4793-4803 (2008).
[CrossRef] [PubMed]

J. Christmas, N. Collings, A. Georgiou, “Blocking zero-order in phase shift hologram generation,” UK patent GB2438458 (28 November 2007).

Crossland, W. A.

Dammann, H.

H. Dammann and K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312-315 (1971).
[CrossRef]

Daria, V. R.

Davey, A.

DeSandre, L.

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

Dholakia, K.

Dong, B.

Dymale, R.

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

Engström, D.

Fienup, J. R.

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671-680(1983).
[CrossRef] [PubMed]

Georgiou, A.

A. Georgiou, J. Christmas, J. Moore, A. Jeziorska-Chapman, A. Davey, N. Collings, and W. A. Crossland, “Liquid crystal over silicon device characteristics for holographic projection of high-definition television images,” Appl. Opt. 47, 4793-4803 (2008).
[CrossRef] [PubMed]

A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A Pure Appl. Opt. 10, 035302 (2008).
[CrossRef]

J. Christmas, N. Collings, A. Georgiou, “Blocking zero-order in phase shift hologram generation,” UK patent GB2438458 (28 November 2007).

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 35, 237-246 (1972).

Gortler, K.

H. Dammann and K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312-315 (1971).
[CrossRef]

Gruneisen, M.

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

Gu, B.

Hu, L.

Jeziorska-Chapman, A.

Joseph, J.

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671-680(1983).
[CrossRef] [PubMed]

Kohler, C.

Kretzel, J.

A. Michalkiewicz, M. Kujawinska, J. Kretzel, L. Salbut, X. Wang, and P. J. Bos, “Phase manipulation and optoelectronic reconstruction of digital holograms by means of LCOS spatial light modulator,” Proc. SPIE 5776, 144-152 (2005).
[CrossRef]

Kujawinska, M.

A. Michalkiewicz, M. Kujawinska, J. Kretzel, L. Salbut, X. Wang, and P. J. Bos, “Phase manipulation and optoelectronic reconstruction of digital holograms by means of LCOS spatial light modulator,” Proc. SPIE 5776, 144-152 (2005).
[CrossRef]

Li, D.

Liu, Y.

Lubin, D.

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

McGloin, D.

Melville, H.

Michalkiewicz, A.

A. Michalkiewicz, M. Kujawinska, J. Kretzel, L. Salbut, X. Wang, and P. J. Bos, “Phase manipulation and optoelectronic reconstruction of digital holograms by means of LCOS spatial light modulator,” Proc. SPIE 5776, 144-152 (2005).
[CrossRef]

Milewski, G.

Millán, M. S.

Milne, G.

Moore, J.

Mu, Q.

Osten, W.

Otón, J.

Palima, D.

Pérez-Cabré, E.

Rotge, J.

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

Salbut, L.

A. Michalkiewicz, M. Kujawinska, J. Kretzel, L. Salbut, X. Wang, and P. J. Bos, “Phase manipulation and optoelectronic reconstruction of digital holograms by means of LCOS spatial light modulator,” Proc. SPIE 5776, 144-152 (2005).
[CrossRef]

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 35, 237-246 (1972).

Schwab, X.

Sibbett, W.

Spalding, G.

Testorf, M.

V. Arrizon, E. Carreon, and M. Testorf, “Implementation of Fourier array illuminators using pixelated SLM: efficiency limitations,” Opt. Commun. 160, 207-213 (1999).
[CrossRef]

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671-680(1983).
[CrossRef] [PubMed]

Waldman, D. A.

Wang, X.

A. Michalkiewicz, M. Kujawinska, J. Kretzel, L. Salbut, X. Wang, and P. J. Bos, “Phase manipulation and optoelectronic reconstruction of digital holograms by means of LCOS spatial light modulator,” Proc. SPIE 5776, 144-152 (2005).
[CrossRef]

Xuan, L.

Xun, X.

Yang, G.

Appl. Opt. (9)

B. Gu, G. Yang, and B. Dong, “General theory for performing an optical transform,” Appl. Opt. 25, 3197-3206 (1986).
[CrossRef] [PubMed]

A. Georgiou, J. Christmas, J. Moore, A. Jeziorska-Chapman, A. Davey, N. Collings, and W. A. Crossland, “Liquid crystal over silicon device characteristics for holographic projection of high-definition television images,” Appl. Opt. 47, 4793-4803 (2008).
[CrossRef] [PubMed]

C. Kohler, X. Schwab, and W. Osten, “Optimally tuned spatial light modulators for digital holography,” Appl. Opt. 45, 960-967 (2006).
[CrossRef] [PubMed]

J. Joseph and D. A. Waldman, “Homogenized Fourier transform holographic data storage using phase spatial light modulators and methods for recovery of data from the phase image,” Appl. Opt. 45, 6374-6380 (2006).
[CrossRef] [PubMed]

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

J. Otón, P. Ambs, M. S. Millán, and E. Pérez-Cabré, “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]

D. Palima and V. R. Daria, “Effect of spurious diffraction orders in arbitrary multifoci patterns produced via phase-only holograms,” Appl. Opt. 45, 6689-6693 (2006).
[CrossRef] [PubMed]

D. Palima and V. R. Daria, “Holographic projection of arbitrary light patterns with a suppressed zero-order beam,” Appl. Opt. 46, 4197-4201 (2007).
[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]

J. Opt. A Pure Appl. Opt. (1)

A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A Pure Appl. Opt. 10, 035302 (2008).
[CrossRef]

Opt. Commun. (2)

V. Arrizon, E. Carreon, and M. Testorf, “Implementation of Fourier array illuminators using pixelated SLM: efficiency limitations,” Opt. Commun. 160, 207-213 (1999).
[CrossRef]

H. Dammann and K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312-315 (1971).
[CrossRef]

Opt. Eng. (1)

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

Opt. Express (2)

Opt. Lett. (1)

Optik (Jena) (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 35, 237-246 (1972).

Proc. SPIE (1)

A. Michalkiewicz, M. Kujawinska, J. Kretzel, L. Salbut, X. Wang, and P. J. Bos, “Phase manipulation and optoelectronic reconstruction of digital holograms by means of LCOS spatial light modulator,” Proc. SPIE 5776, 144-152 (2005).
[CrossRef]

Science (1)

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671-680(1983).
[CrossRef] [PubMed]

Other (1)

J. Christmas, N. Collings, A. Georgiou, “Blocking zero-order in phase shift hologram generation,” UK patent GB2438458 (28 November 2007).

Supplementary Material (1)

» Media 1: MOV (2519 KB)     

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Figures (8)

Fig. 1
Fig. 1

Basic optical arrangement of the holographic projection system; f is the focal length of the Fourier lens.

Fig. 2
Fig. 2

Geometry of the pixelated phase-only SLM. L x and L y represent the width and the length of the SLM, respectively; a i ( i = x , y ) and d i ( i = x , y ) denote the pixel size and the period, respectively.

Fig. 3
Fig. 3

(a) Relative zero-order intensity as a function of amplitude modulation of the dead space areas. Numerically reconstructed patterns with (b)  A ds = 1 , μ = 83 % and (c)  A ds = 0 , μ = 83 % .

Fig. 4
Fig. 4

Optical arrangement for separating the zero-order illumination from the reconstructed pattern by the optimized phase with additional (a) spherically loaded phase, (b) linearly loaded phase, and (c) spherically and linearly loaded phase. Δ d is the distance between the reconstruction plane and the focal plane of the Fourier lens. Δ l is the distance between the center of the reconstructed pattern and the focus of the Fourier lens.

Fig. 5
Fig. 5

Output light intensities experimentally detected by a CCD camera for optimized phase (a) without additional loaded phase, (b) with additional spherically loaded phase, (c) with additional linearly loaded phase, (d) with additional spherically and linearly loaded phase. (The intersections of the dashed lines indicate the optical axis).

Fig. 6
Fig. 6

Single-frame excerpts from the video produced by holographic projection (Media 1).

Fig. 7
Fig. 7

Spatial frequency spectrum on the ξ axis in the image plane.

Fig. 8
Fig. 8

Spatial frequency with a 40 dB bandwidth as a function of (a) θ of the linearly loaded phase when r = and r = 750 mm , (b) r of the spherically loaded phase when θ = 0 ° , θ = 0.66 ° , and θ = 1.21 ° .

Equations (20)

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

t ( x , y ) = rect ( x L x , y L y ) [ t ac ( x , y ) + t ds ( x , y ) ] ,
t ac ( x , y ) = rect ( x a x , y a y ) { 1 d x d y comb ( x d x , y d y ) exp [ i ϕ ac ( x , y ) ] } ;
t ds ( x , y ) = { [ rect ( x d x , y d y ) rect ( x a x , y a y ) ] 1 d x d y comb ( x d x , y d y ) } A ds ( x , y ) exp [ i ϕ ds ( x , y ) ] ,
μ = a x a y / d x d y .
T ( f x , f y ) = L x L y sinc ( f x L x , f y L y ) [ T ac ( f x , f y ) + T ds ( f x , f y ) ] ,
T ac ( f x , f y ) = a x a y sinc ( f x a x , f y a y ) [ comb ( f x d x , f y d y ) E ( f x , f y ) ] , T ds ( f x , f y ) = { [ d x d y sinc ( f x d x , f y d y ) a x a y sinc ( f x a x , f y a y ) ] comb ( f x d x , f y d y ) } F ( f x , f y ) ,
E ( f x , f y ) = I { exp [ i ϕ ac ( x , y ) ] } , F ( f x , f y ) = I { A ds ( x , y ) exp [ i ϕ ds ( x , y ) ] } .
T ( 0 , 0 ) = a x a y d x d y E ( 0 , 0 ) + d x d y a x a y d x d y F ( 0 , 0 ) = μ E ( 0 , 0 ) + ( 1 μ ) F ( 0 , 0 ) ,
ϕ ds ( l ) = ϕ ac ( n ) + l ϕ ac ( n + 1 ) ϕ ac ( n ) Δ D , l ( 0 , Δ D ) ,
ε = I 0 / I ¯ ,
ϕ SLM = ϕ ac + ϕ s ,
ϕ s ( x , y ) = ± k 2 r ( x 2 + y 2 ) ,
Δ d = r f r f ,
ϕ SLM = ϕ ac + ϕ l ,
ϕ l ( x , y ) = ( x sin β + y cos β ) tan θ ,
β = arcsin ( x x 2 + y 2 ) .
Δ l = f tan θ .
ϕ SLM = ϕ ac + ϕ sl ,
ϕ sl = ϕ s + ϕ l .
SNR = { i = 1 M j = 1 N [ O ( i , j ) ] 2 i = 1 M j = 1 N [ O ( i , j ) R ( i , j ) ] 2 } 1 / 2 ,

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