Abstract

Phase compression is used to suppress the on-axis zero-order diffracted (ZOD) beam from a pixelated phase-only spatial light modulator (SLM) by a simple modification to the computer generated hologram (CGH) loaded onto the SLM. After CGH design, the phase of each SLM element is identically compressed by multiplying by a constant scale factor and rotated on the complex unit-circle to produce a cancellation beam that destructively interferes with the ZOD beam. Experiments achieved a factor of 3 reduction of the ZOD beam using two different liquid-crystal SLMs. Numerical simulation analyzed the reconstructed image quality and diffraction efficiency versus degree of phase compression and showed that phase compression resulted in little image degradation or power loss.

© 2012 Optical Society of America

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    [CrossRef]
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  7. A. Moya, D. Mendlovic, J. Garcia, and C. Ferreira, “Projection-invariant pattern recognition with a phase-only logarithmic-harmonic-derived filter,” Appl. Opt. 35, 3862–3862 (1996).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2010

J. Carpenter and T. D. Wilkinson, “Graphics processing unit–accelerated holography by simulated annealing,” Opt. Eng. 49, 095801 (2010).
[CrossRef]

S. Zwick, T. Haist, M. Warber, and W. Osten, “Dynamic holography using pixelated light modulators,” Appl. Opt. 49, F47–F58 (2010).
[CrossRef]

2009

2008

2007

2005

S.-H. Lee and D. Grier, “Robustness of holographic optical traps against phase scaling errors,” Opt. Express 13, 7458–7465 (2005).
[CrossRef]

M. J. Thomson and M. R. Taghizadeh, “Design and fabrication of Fourier plane diffractive optical elements for high-power fibre-coupling applications,” Opt. Lasers Eng. 43, 671–681 (2005).
[CrossRef]

2004

V. Kettunen, K. Jefimovs, J. Simonen, O. Ripoll, M. Kuittinen, and H. P. Herzig, “Diffractive elements designed to suppress unwanted zeroth order due to surface depth error,” J. Mod. Opt. 51, 2111–2123 (2004).
[CrossRef]

G. Sinclair, J. Leach, P. Jordan, G. Gibson, E. Yao, Z. Laczik, M. Padgett, and J. Courtial, “Interactive application in holographic optical tweezers of a multi-plane Gerchberg-Saxton algorithm for three-dimensional light shaping,” Opt. Express 12, 1665–1670 (2004).
[CrossRef]

O. Ripoll, V. Kettunen, and H. P. Herzig, “Review of iterative Fourier-transform algorithms for beam shaping applications,” Opt. Eng. 43, 2549–2556 (2004).
[CrossRef]

2003

2002

2000

1996

1972

R. W. Gerchberg and W. O. Saxton, “Practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–250 (1972).

1967

Bengtsson, J.

Braun, M.

Caley, A. J.

Carpenter, J.

J. Carpenter and T. D. Wilkinson, “Graphics processing unit–accelerated holography by simulated annealing,” Opt. Eng. 49, 095801 (2010).
[CrossRef]

Chen, G.

Cohn, R. W.

Courtial, J.

Daria, V. R.

Duelli, M.

Engström, D.

Ferreira, C.

Garcia, J.

Ge, L.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “Practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–250 (1972).

Gibson, G.

Gillet, J.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts & Co., 2005), pp 82–84.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts & Co., 2005), pp. 103–108.

Grier, D.

Haist, T.

Herzig, H. P.

O. Ripoll, V. Kettunen, and H. P. Herzig, “Review of iterative Fourier-transform algorithms for beam shaping applications,” Opt. Eng. 43, 2549–2556 (2004).
[CrossRef]

V. Kettunen, K. Jefimovs, J. Simonen, O. Ripoll, M. Kuittinen, and H. P. Herzig, “Diffractive elements designed to suppress unwanted zeroth order due to surface depth error,” J. Mod. Opt. 51, 2111–2123 (2004).
[CrossRef]

Jefimovs, K.

V. Kettunen, K. Jefimovs, J. Simonen, O. Ripoll, M. Kuittinen, and H. P. Herzig, “Diffractive elements designed to suppress unwanted zeroth order due to surface depth error,” J. Mod. Opt. 51, 2111–2123 (2004).
[CrossRef]

Jordan, P.

Kettunen, V.

V. Kettunen, K. Jefimovs, J. Simonen, O. Ripoll, M. Kuittinen, and H. P. Herzig, “Diffractive elements designed to suppress unwanted zeroth order due to surface depth error,” J. Mod. Opt. 51, 2111–2123 (2004).
[CrossRef]

O. Ripoll, V. Kettunen, and H. P. Herzig, “Review of iterative Fourier-transform algorithms for beam shaping applications,” Opt. Eng. 43, 2549–2556 (2004).
[CrossRef]

Kuittinen, M.

V. Kettunen, K. Jefimovs, J. Simonen, O. Ripoll, M. Kuittinen, and H. P. Herzig, “Diffractive elements designed to suppress unwanted zeroth order due to surface depth error,” J. Mod. Opt. 51, 2111–2123 (2004).
[CrossRef]

Laczik, Z.

Leach, J.

Lee, S.-H.

Liu, J.

Liu, J. S.

Lohmann, A. W.

Mendlovic, D.

Milewski, G.

Moya, A.

Osten, W.

Padgett, M.

Palima, D.

Paris, D. P.

Ripoll, O.

V. Kettunen, K. Jefimovs, J. Simonen, O. Ripoll, M. Kuittinen, and H. P. Herzig, “Diffractive elements designed to suppress unwanted zeroth order due to surface depth error,” J. Mod. Opt. 51, 2111–2123 (2004).
[CrossRef]

O. Ripoll, V. Kettunen, and H. P. Herzig, “Review of iterative Fourier-transform algorithms for beam shaping applications,” Opt. Eng. 43, 2549–2556 (2004).
[CrossRef]

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “Practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–250 (1972).

Sheng, Y.

Simonen, J.

V. Kettunen, K. Jefimovs, J. Simonen, O. Ripoll, M. Kuittinen, and H. P. Herzig, “Diffractive elements designed to suppress unwanted zeroth order due to surface depth error,” J. Mod. Opt. 51, 2111–2123 (2004).
[CrossRef]

Sinclair, G.

Taghizadeh, M. R.

Thomson, M. J.

M. J. Thomson and M. R. Taghizadeh, “Design and fabrication of Fourier plane diffractive optical elements for high-power fibre-coupling applications,” Opt. Lasers Eng. 43, 671–681 (2005).
[CrossRef]

Waddie, A. J.

Wang, Y.

Warber, M.

Wilkinson, T. D.

J. Carpenter and T. D. Wilkinson, “Graphics processing unit–accelerated holography by simulated annealing,” Opt. Eng. 49, 095801 (2010).
[CrossRef]

Wong, D. W. K.

Xie, J.

Yao, E.

Zhang, H.

Zwick, S.

Appl. Opt.

A. W. Lohmann and D. P. Paris, “Binary Frauhofer holograms, generated by computer,” Appl. Opt. 6, 1739–1748 (1967).
[CrossRef]

A. Moya, D. Mendlovic, J. Garcia, and C. Ferreira, “Projection-invariant pattern recognition with a phase-only logarithmic-harmonic-derived filter,” Appl. Opt. 35, 3862–3862 (1996).
[CrossRef]

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]

A. J. Caley, M. Braun, A. J. Waddie, and M. R. Taghizadeh, “Analysis of multimask fabrication errors for diffractive optical elements,” Appl. Opt. 46, 2180–2188 (2007).
[CrossRef]

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]

D. W. K. Wong and G. Chen, “Redistribution of the zero order by the use of a phase checkerboard pattern in computer generated holograms,” Appl. Opt. 47, 602–610 (2008).
[CrossRef]

H. Zhang, J. Xie, J. Liu, and Y. Wang, “Elimination of a zero-order beam induced by a pixelated spatial light modulator for holographic projection,” Appl. Opt. 48, 5834–5841 (2009).
[CrossRef]

S. Zwick, T. Haist, M. Warber, and W. Osten, “Dynamic holography using pixelated light modulators,” Appl. Opt. 49, F47–F58 (2010).
[CrossRef]

J. Gillet and Y. Sheng, “Multiplexed computer-generated holograms with polygonal-aperture layouts optimized by genetic algorithm,” Appl. Opt. 42, 4156–4165 (2003).
[CrossRef]

J. Mod. Opt.

V. Kettunen, K. Jefimovs, J. Simonen, O. Ripoll, M. Kuittinen, and H. P. Herzig, “Diffractive elements designed to suppress unwanted zeroth order due to surface depth error,” J. Mod. Opt. 51, 2111–2123 (2004).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

O. Ripoll, V. Kettunen, and H. P. Herzig, “Review of iterative Fourier-transform algorithms for beam shaping applications,” Opt. Eng. 43, 2549–2556 (2004).
[CrossRef]

J. Carpenter and T. D. Wilkinson, “Graphics processing unit–accelerated holography by simulated annealing,” Opt. Eng. 49, 095801 (2010).
[CrossRef]

Opt. Express

Opt. Lasers Eng.

M. J. Thomson and M. R. Taghizadeh, “Design and fabrication of Fourier plane diffractive optical elements for high-power fibre-coupling applications,” Opt. Lasers Eng. 43, 671–681 (2005).
[CrossRef]

Opt. Lett.

Optik

R. W. Gerchberg and W. O. Saxton, “Practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–250 (1972).

Other

J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts & Co., 2005), pp. 103–108.

Boulder Nonlinear Systems, “100% fill factor,” http://bnonlinear.com/papers/new/100%20Fill%20Factor%20White%20Paper.pdf .

J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts & Co., 2005), pp 82–84.

Boulder Nonlinear Systems, “XY format spatial light modulator date sheet,” http://www.bnonlinear.com/products/xyslm/XYSeriesDS0909.pdf .

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Figures (9)

Fig. 1.
Fig. 1.

Optical layout of the phase compression experiment. Pixelated SLM is in the ξ η coordinate system, and the holographic image is reconstructed at the x - y coordinate plane.

Fig. 2.
Fig. 2.

Representation of the phase compression technique: (a) uniformly distributed phase angle histogram of the CGH after the IFT algorithm; (b) phase compression redistributes the phase angle of the CGH pixels, P h ( ξ , η ) × c , as shown; (c) phase distribution, same as (b), on the complex unit-circle after phase compression; complex vectors sum up to create the ZOD cancellation vector at zero phase; (d) rotation angle, θ = π + ϕ zod , determines the phase of the resulting corrective vector.

Fig. 3.
Fig. 3.

Experimental setup for phase compression tests with lens focused to place the focal plane at the CCD surface.

Fig. 4.
Fig. 4.

ZOD suppression measurement using the BNS P512–0785. Normalized diffracted power of the ZOD beam versus (a) phase compression factor with experimental images of the ZOD beam evolution (inset above) and reconstructed image (inset middle), and (b) rotation angle with c = 0.8 . The data is normalized by the ZOD intensity for c = 1.0 and θ = 180 ° .

Fig. 5.
Fig. 5.

Diffraction power of the reconstructed image versus (a) phase compression factor c and (b) phase rotation angle θ .

Fig. 6.
Fig. 6.

ZOD suppression measurement using the BNS P512–1064. Diffracted power of ZOD beam versus (a) phase compression factor with c = 0.95 and (b) rotation angle with θ = 10 ° . The extracted region of letter “A” from reconstructed images for (i)  c = 1.0 and (ii)  c = 0.79 are inset into (b). The data is normalized by the ZOD intensity for c = 1.0 and θ = 10 ° .

Fig. 7.
Fig. 7.

Flowchart of the phase compression technique using the IFT algorithm (IFTA) and the quality comparisons of the reconstructed images.

Fig. 8.
Fig. 8.

Degradation of signal-to-noise ratio (SNR) versus phase compression factor for (a) different target images, and (b) GS and AA algorithms for the binary letter “A” image.

Fig. 9.
Fig. 9.

Simulated diffracted power versus phase compression factor.

Tables (1)

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Table 1. Summary of the Properties of the Four Test Images

Equations (12)

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U zod ( f x , f y ) = { [ A zod exp ( j ϕ zod ) ] δ ( f x , f y ) } M ( f x , f y ) ,
p c ( ξ , η ) = [ c p h ( ξ , η ) + ( π + ϕ zod ) ] ± 2 π m ,
u ( ξ , η ) = u a ( ξ , η ) [ b ( ξ , η ) exp ( j p SLM ( ξ , η ) ) ] ,
u a ( ξ , η ) = { exp [ j p h ( ξ , η ) ] comb ( ξ d , η d ) } rect ( ξ a , η a ) ,
rect ( ξ a , η a ) = { 1 , ( a / 2 < ξ , η < a / 2 ) 0 , otherwise , comb ( ξ d , η d ) = m = n = δ ( ξ m d , η n d ) .
U ( f x , f y ) = U a ( f x , f y ) M ( f x , f y ) ,
U a ( f x , f y ) = f f [ P h ( f x , f y ) + m , n 0 P h ( f x m d , f y n d ) ] sinc ( a f x , a f y )
U 0 ( f x , f y ) = { A zod exp ( j ϕ zod ) δ ( f x , f y ) + f f [ P h ( f x , f y ) + m , n 0 P h ( f x - m d , f y - n d ) ] sinc ( a f x , a f y ) } M ( f x , f y ) .
U 0 C ( f x , f y ) = { ( A zod A c ) exp ( j ϕ zod ) δ ( f x , f y ) + f f [ P i ( f x , f y ) + m , n 0 P h ( f x m d , f y n d ) ] sinc ( a f x , a f y ) } M ( f x , f y ) .
A c = A i f f - π c π c ρ ( θ ) c o s θ d θ = N f f s i n ( π c ) π c .
sinc ( c ) = A zod N f f ( 0 < c 1 ) .
SNR dB = 10 log 10 ( ( | A t ( f x , f y ) | 2 ) 2 ( | A o ( f x , f y ) | 2 | A t ( f x , f y ) | 2 ) 2 ) ,

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