Abstract

A method to remove undesired diffraction orders of computer-generated binary phase holograms is demonstrated. Normally, the reconstruction of binary Fourier holograms, made from just two phase levels, results in an undesired inverted image from the minus first diffraction order, which is superposed with the desired one. This can be avoided by reconstructing the hologram with a diffuse light field with a pseudorandom, but known, phase distribution, which is taken into account for the hologram computation. As a consequence, only the desired image is reconstructed, whereas all residual light is dispersed, propagating as a diffuse background wave. The method may be advantageous to employ ferroelectric spatial light modulators as holographic display devices, which can display only binary phase holograms, but which have the advantage of fast switching rates.

© 2008 Optical Society of America

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References

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  1. B. Kress and P. Meyrueis, Digital Diffractive Optics (Wiley, 2000).
  2. G. O. Reynolds, J. B. Develis, and B. J. Thompson, The New Physical Optics Notebook: Tutorials in Fourier Optics (SPIE Press, 1989).
  3. T. H. Barnes, T. Eiju, K. Matsuda, H. Ichikawa, M. R. Taghizadeh, and J. Turunen, “Reconfigurable free-space optical interconnections with a phase-only liquid-crystal spatial light modulator,” Appl. Opt. 31, 5527-5535 (1992).
  4. J. Gourlay, S. Samus, P. McOwan, D. G. Vass, I. Underwood, and M. Worboys, “Real-time binary phase holograms on a reflective ferroelectric liquid-crystal spatial light modulator,” Appl. Opt. 33, 8251-8254 (1994).
  5. W. Hossack, E. Theofanidou, J. Crain, K. Heggarty, and M. Birch, “High-speed holographic optical tweezers using a ferroelectric liquid crystal microdisplay,” Opt. Express 17, 2053-2059 (2003).
  6. K. M. Johnson, M. A. Handschy, and L. A. Pagano-Stauffer, “Optical computing and image processing with ferroelectric liquid crystals,” Opt. Eng. 26, 385-391 (1987).
  7. C. J. Henderson, D. G. Leyva, and T. D. Wilkinson, “Free space adaptive optical interconnect at 1.25 Gb/s, with beam steering using a ferroelectric liquid-crystal SLM,” J. Lightwave Technol. 24, 1989-1997 (2006).
    [CrossRef]
  8. A. Lafong, W. J. Hossack, J. Arlt, T. J. Nowakowski, and N. D. Read, “Time-multiplexed Laguerre-Gaussian holographic optical tweezers for biological applications,” Opt. Express 14, 3065-3072 (2006).
    [CrossRef]
  9. J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77-82 (2000).
    [CrossRef]
  10. 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).
  11. K. Dholakia, G. Spalding, and M. MacDonald, “Optical tweezers: the next generation,” Phys. World 15, 31-35 (2002).
  12. V. Bingelyte, J. Leach, J. Courtial, and M. J. Padgett, “Optically controlled three-dimensional rotation of microscopic objects,” Appl. Phys. Lett. 82, 829-831 (2003).
    [CrossRef]
  13. G. Gibson, L. Barron, F. Beck, G. Whyte, and M. Padgett, “Optically controlled grippers for manipulating micron-sized particles,” New J. Phys. 9, 14 (2007), doi: 10.1088/1367-2630/9/1/014.
    [CrossRef]
  14. H. Melville, G. F. Milne, G. C. Spalding, W. Sibbett, K. Dholakia, and D. McGloin, “Optical trapping of three-dimensional structures using dynamic hologram,” Opt. Express 11, 3562-3567 (2003).
  15. A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Diffractive optical tweezers in the Fresnel regime,” Opt. Express 12, 2243-2250 (2004).
  16. S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314-317 (1986).
    [CrossRef]
  17. D. McGloin, G. Spalding, H. Melville, W. Sibbett, and K. Dholakia, “Applications of spatial light modulators in atom optics,” Opt. Express 11, 158-166 (2003).
  18. E. Cuche, P. Marquet, and C. Depeursinge, “Spatial filtering for zero-order and twin-image elimination in digital off-axis holography,” Appl. Opt. 39, 4070-4075 (2000).
    [CrossRef]
  19. J. A. Davis, D. M. Cottrell, J. E. Davis, and R. A. Lilly, “Fresnel lens-encoded binary phase-only filters for optical pattern recognition,” Opt. Lett. 14, 659-661 (1989).
  20. M. A. A. Neil and E. G. S. Paige, “Breaking of inversion symmetry in 2-level binary, Fourier holograms,” in Fourth International Conference on Holographic Systems, Components and Applications (IEEE, 1993), pp. 85-90.
  21. V. Arrizón and M. Testorf, “Efficiency limit of spatially quantized Fourier array illuminators,” Opt. Lett. 15, 197-199(1997).
  22. The undistorted zero-order efficiency of a wave field transmitted through a phase mask is given by ?0=|(x2?x1)?1?x1x2T(x)dx|2, where T(x) is the complex transmission function. In the case of a random, uniformly distributed phase grating (in an interval between 0 and ?), this becomes ?0=|??1?0?exp?(i?)d?|2=0.405.
  23. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237-246 (1972).
  24. A. Jesacher, C. Maurer, A. Schwaighofer, S. Bernet, and M. Ritsch-Marte, “Near-perfect hologram reconstruction with a spatial light modulator,” Opt. Express 16, 2597-2603 (2008).

2008 (1)

2007 (1)

G. Gibson, L. Barron, F. Beck, G. Whyte, and M. Padgett, “Optically controlled grippers for manipulating micron-sized particles,” New J. Phys. 9, 14 (2007), doi: 10.1088/1367-2630/9/1/014.
[CrossRef]

2006 (2)

2004 (1)

2003 (4)

D. McGloin, G. Spalding, H. Melville, W. Sibbett, and K. Dholakia, “Applications of spatial light modulators in atom optics,” Opt. Express 11, 158-166 (2003).

H. Melville, G. F. Milne, G. C. Spalding, W. Sibbett, K. Dholakia, and D. McGloin, “Optical trapping of three-dimensional structures using dynamic hologram,” Opt. Express 11, 3562-3567 (2003).

W. Hossack, E. Theofanidou, J. Crain, K. Heggarty, and M. Birch, “High-speed holographic optical tweezers using a ferroelectric liquid crystal microdisplay,” Opt. Express 17, 2053-2059 (2003).

V. Bingelyte, J. Leach, J. Courtial, and M. J. Padgett, “Optically controlled three-dimensional rotation of microscopic objects,” Appl. Phys. Lett. 82, 829-831 (2003).
[CrossRef]

2002 (1)

K. Dholakia, G. Spalding, and M. MacDonald, “Optical tweezers: the next generation,” Phys. World 15, 31-35 (2002).

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).

2000 (3)

E. Cuche, P. Marquet, and C. Depeursinge, “Spatial filtering for zero-order and twin-image elimination in digital off-axis holography,” Appl. Opt. 39, 4070-4075 (2000).
[CrossRef]

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77-82 (2000).
[CrossRef]

B. Kress and P. Meyrueis, Digital Diffractive Optics (Wiley, 2000).

1997 (1)

V. Arrizón and M. Testorf, “Efficiency limit of spatially quantized Fourier array illuminators,” Opt. Lett. 15, 197-199(1997).

1994 (1)

1993 (1)

M. A. A. Neil and E. G. S. Paige, “Breaking of inversion symmetry in 2-level binary, Fourier holograms,” in Fourth International Conference on Holographic Systems, Components and Applications (IEEE, 1993), pp. 85-90.

1992 (1)

1989 (2)

G. O. Reynolds, J. B. Develis, and B. J. Thompson, The New Physical Optics Notebook: Tutorials in Fourier Optics (SPIE Press, 1989).

J. A. Davis, D. M. Cottrell, J. E. Davis, and R. A. Lilly, “Fresnel lens-encoded binary phase-only filters for optical pattern recognition,” Opt. Lett. 14, 659-661 (1989).

1987 (1)

K. M. Johnson, M. A. Handschy, and L. A. Pagano-Stauffer, “Optical computing and image processing with ferroelectric liquid crystals,” Opt. Eng. 26, 385-391 (1987).

1986 (1)

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314-317 (1986).
[CrossRef]

1972 (1)

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

Arlt, J.

Arrizón, V.

V. Arrizón and M. Testorf, “Efficiency limit of spatially quantized Fourier array illuminators,” Opt. Lett. 15, 197-199(1997).

Ashkin, A.

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314-317 (1986).
[CrossRef]

Barnes, T. H.

Barron, L.

G. Gibson, L. Barron, F. Beck, G. Whyte, and M. Padgett, “Optically controlled grippers for manipulating micron-sized particles,” New J. Phys. 9, 14 (2007), doi: 10.1088/1367-2630/9/1/014.
[CrossRef]

Beck, F.

G. Gibson, L. Barron, F. Beck, G. Whyte, and M. Padgett, “Optically controlled grippers for manipulating micron-sized particles,” New J. Phys. 9, 14 (2007), doi: 10.1088/1367-2630/9/1/014.
[CrossRef]

Bernet, S.

Bingelyte, V.

V. Bingelyte, J. Leach, J. Courtial, and M. J. Padgett, “Optically controlled three-dimensional rotation of microscopic objects,” Appl. Phys. Lett. 82, 829-831 (2003).
[CrossRef]

Birch, M.

W. Hossack, E. Theofanidou, J. Crain, K. Heggarty, and M. Birch, “High-speed holographic optical tweezers using a ferroelectric liquid crystal microdisplay,” Opt. Express 17, 2053-2059 (2003).

Bjorkholm, J. E.

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314-317 (1986).
[CrossRef]

Cable, A.

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314-317 (1986).
[CrossRef]

Chu, S.

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314-317 (1986).
[CrossRef]

Cottrell, D. M.

Courtial, J.

V. Bingelyte, J. Leach, J. Courtial, and M. J. Padgett, “Optically controlled three-dimensional rotation of microscopic objects,” Appl. Phys. Lett. 82, 829-831 (2003).
[CrossRef]

Crain, J.

W. Hossack, E. Theofanidou, J. Crain, K. Heggarty, and M. Birch, “High-speed holographic optical tweezers using a ferroelectric liquid crystal microdisplay,” Opt. Express 17, 2053-2059 (2003).

Cuche, E.

Davis, J. A.

Davis, J. E.

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).

Depeursinge, C.

Develis, J. B.

G. O. Reynolds, J. B. Develis, and B. J. Thompson, The New Physical Optics Notebook: Tutorials in Fourier Optics (SPIE Press, 1989).

Dholakia, K.

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).

Eiju, T.

Fürhapter, S.

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 (Stuttgart) 35, 237-246 (1972).

Gibson, G.

G. Gibson, L. Barron, F. Beck, G. Whyte, and M. Padgett, “Optically controlled grippers for manipulating micron-sized particles,” New J. Phys. 9, 14 (2007), doi: 10.1088/1367-2630/9/1/014.
[CrossRef]

Gourlay, J.

Grier, D. G.

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).

Haist, T.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77-82 (2000).
[CrossRef]

Handschy, M. A.

K. M. Johnson, M. A. Handschy, and L. A. Pagano-Stauffer, “Optical computing and image processing with ferroelectric liquid crystals,” Opt. Eng. 26, 385-391 (1987).

Heggarty, K.

W. Hossack, E. Theofanidou, J. Crain, K. Heggarty, and M. Birch, “High-speed holographic optical tweezers using a ferroelectric liquid crystal microdisplay,” Opt. Express 17, 2053-2059 (2003).

Henderson, C. J.

Hossack, W.

W. Hossack, E. Theofanidou, J. Crain, K. Heggarty, and M. Birch, “High-speed holographic optical tweezers using a ferroelectric liquid crystal microdisplay,” Opt. Express 17, 2053-2059 (2003).

Hossack, W. J.

Ichikawa, H.

Jesacher, A.

Johnson, K. M.

K. M. Johnson, M. A. Handschy, and L. A. Pagano-Stauffer, “Optical computing and image processing with ferroelectric liquid crystals,” Opt. Eng. 26, 385-391 (1987).

Kress, B.

B. Kress and P. Meyrueis, Digital Diffractive Optics (Wiley, 2000).

Lafong, A.

Leach, J.

V. Bingelyte, J. Leach, J. Courtial, and M. J. Padgett, “Optically controlled three-dimensional rotation of microscopic objects,” Appl. Phys. Lett. 82, 829-831 (2003).
[CrossRef]

Leyva, D. G.

Liesener, J.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77-82 (2000).
[CrossRef]

Lilly, R. A.

MacDonald, M.

K. Dholakia, G. Spalding, and M. MacDonald, “Optical tweezers: the next generation,” Phys. World 15, 31-35 (2002).

Marquet, P.

Matsuda, K.

Maurer, C.

McGloin, D.

McOwan, P.

Melville, H.

Meyrueis, P.

B. Kress and P. Meyrueis, Digital Diffractive Optics (Wiley, 2000).

Milne, G. F.

Neil, M. A. A.

M. A. A. Neil and E. G. S. Paige, “Breaking of inversion symmetry in 2-level binary, Fourier holograms,” in Fourth International Conference on Holographic Systems, Components and Applications (IEEE, 1993), pp. 85-90.

Nowakowski, T. J.

Padgett, M.

G. Gibson, L. Barron, F. Beck, G. Whyte, and M. Padgett, “Optically controlled grippers for manipulating micron-sized particles,” New J. Phys. 9, 14 (2007), doi: 10.1088/1367-2630/9/1/014.
[CrossRef]

Padgett, M. J.

V. Bingelyte, J. Leach, J. Courtial, and M. J. Padgett, “Optically controlled three-dimensional rotation of microscopic objects,” Appl. Phys. Lett. 82, 829-831 (2003).
[CrossRef]

Pagano-Stauffer, L. A.

K. M. Johnson, M. A. Handschy, and L. A. Pagano-Stauffer, “Optical computing and image processing with ferroelectric liquid crystals,” Opt. Eng. 26, 385-391 (1987).

Paige, E. G. S.

M. A. A. Neil and E. G. S. Paige, “Breaking of inversion symmetry in 2-level binary, Fourier holograms,” in Fourth International Conference on Holographic Systems, Components and Applications (IEEE, 1993), pp. 85-90.

Read, N. D.

Reicherter, M.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77-82 (2000).
[CrossRef]

Reynolds, G. O.

G. O. Reynolds, J. B. Develis, and B. J. Thompson, The New Physical Optics Notebook: Tutorials in Fourier Optics (SPIE Press, 1989).

Ritsch-Marte, M.

Samus, S.

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 (Stuttgart) 35, 237-246 (1972).

Schwaighofer, A.

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).

Sibbett, W.

Spalding, G.

D. McGloin, G. Spalding, H. Melville, W. Sibbett, and K. Dholakia, “Applications of spatial light modulators in atom optics,” Opt. Express 11, 158-166 (2003).

K. Dholakia, G. Spalding, and M. MacDonald, “Optical tweezers: the next generation,” Phys. World 15, 31-35 (2002).

Spalding, G. C.

H. Melville, G. F. Milne, G. C. Spalding, W. Sibbett, K. Dholakia, and D. McGloin, “Optical trapping of three-dimensional structures using dynamic hologram,” Opt. Express 11, 3562-3567 (2003).

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).

Taghizadeh, M. R.

Testorf, M.

V. Arrizón and M. Testorf, “Efficiency limit of spatially quantized Fourier array illuminators,” Opt. Lett. 15, 197-199(1997).

Theofanidou, E.

W. Hossack, E. Theofanidou, J. Crain, K. Heggarty, and M. Birch, “High-speed holographic optical tweezers using a ferroelectric liquid crystal microdisplay,” Opt. Express 17, 2053-2059 (2003).

Thompson, B. J.

G. O. Reynolds, J. B. Develis, and B. J. Thompson, The New Physical Optics Notebook: Tutorials in Fourier Optics (SPIE Press, 1989).

Tiziani, H. J.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77-82 (2000).
[CrossRef]

Turunen, J.

Underwood, I.

Vass, D. G.

Whyte, G.

G. Gibson, L. Barron, F. Beck, G. Whyte, and M. Padgett, “Optically controlled grippers for manipulating micron-sized particles,” New J. Phys. 9, 14 (2007), doi: 10.1088/1367-2630/9/1/014.
[CrossRef]

Wilkinson, T. D.

Worboys, M.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

V. Bingelyte, J. Leach, J. Courtial, and M. J. Padgett, “Optically controlled three-dimensional rotation of microscopic objects,” Appl. Phys. Lett. 82, 829-831 (2003).
[CrossRef]

J. Lightwave Technol. (1)

New J. Phys. (1)

G. Gibson, L. Barron, F. Beck, G. Whyte, and M. Padgett, “Optically controlled grippers for manipulating micron-sized particles,” New J. Phys. 9, 14 (2007), doi: 10.1088/1367-2630/9/1/014.
[CrossRef]

Opt. Commun. (1)

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77-82 (2000).
[CrossRef]

Opt. Eng. (1)

K. M. Johnson, M. A. Handschy, and L. A. Pagano-Stauffer, “Optical computing and image processing with ferroelectric liquid crystals,” Opt. Eng. 26, 385-391 (1987).

Opt. Express (6)

Opt. Lett. (2)

V. Arrizón and M. Testorf, “Efficiency limit of spatially quantized Fourier array illuminators,” Opt. Lett. 15, 197-199(1997).

J. A. Davis, D. M. Cottrell, J. E. Davis, and R. A. Lilly, “Fresnel lens-encoded binary phase-only filters for optical pattern recognition,” Opt. Lett. 14, 659-661 (1989).

Optik (Stuttgart) (1)

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

Phys. Rev. Lett. (1)

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314-317 (1986).
[CrossRef]

Phys. World (1)

K. Dholakia, G. Spalding, and M. MacDonald, “Optical tweezers: the next generation,” Phys. World 15, 31-35 (2002).

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).

Other (4)

B. Kress and P. Meyrueis, Digital Diffractive Optics (Wiley, 2000).

G. O. Reynolds, J. B. Develis, and B. J. Thompson, The New Physical Optics Notebook: Tutorials in Fourier Optics (SPIE Press, 1989).

M. A. A. Neil and E. G. S. Paige, “Breaking of inversion symmetry in 2-level binary, Fourier holograms,” in Fourth International Conference on Holographic Systems, Components and Applications (IEEE, 1993), pp. 85-90.

The undistorted zero-order efficiency of a wave field transmitted through a phase mask is given by ?0=|(x2?x1)?1?x1x2T(x)dx|2, where T(x) is the complex transmission function. In the case of a random, uniformly distributed phase grating (in an interval between 0 and ?), this becomes ?0=|??1?0?exp?(i?)d?|2=0.405.

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Figures (4)

Fig. 1
Fig. 1

Reconstructed computer-generated on-axis Fourier holograms using a spatial light modulator as a phase display. (a) and (c) were displayed using 256 phase levels in the interval between 0 and 2 π , whereas (b) and (d) are the corresponding binary holograms using only the phase levels 0 and π.

Fig. 2
Fig. 2

Explanation for the diffraction properties of different grating types. Details are explained in the text.

Fig. 3
Fig. 3

Experimental setup. The expanded beam of a He–Ne laser illuminates one-half of a high-resolution SLM with a size of 1920 pixels × 1080 pixels , acting as a diffuser by displaying a continuous pseudorandom phase pattern. From there, the light is reflected and sharply imaged (by a set of two lenses) at the other half of the SLM display. There a binary CGH is displayed, which takes the pseudorandom illumination into account. The hologram is reconstructed in its Fourier plane, using a Fourier-transforming lens in front of a CCD camera. In another configuration (not displayed), the Fourier transform of the light reflected from the first SLM pattern is projected at the second one, using only one Fourier-transforming lens arranged in the middle of the optical path between the two SLM displays.

Fig. 4
Fig. 4

Reconstructed holograms (upper line) in different reconstruction geometries (below). (a) shows a classic binary CGH with plane wave illumination. In (b) the pseudorandom phase mask H 1 is sharply imaged onto the corrected binary CGH H 2 . In (c) the pseudorandom phase mask H 1 acts as a diffuse illumination source by locating it in the Fourier plane of the binary CGH H 2 .

Equations (1)

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η = [ n π sin π n ] 2 .

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