Abstract

We present an implementation method for noiseless holographic projection of precalculated light fields with a spatial light modulator. In the reconstructed image, both the spatial amplitude and phase distributions can be programmed independently. This is achieved by diffracting the light from two successive phase holograms that are located in conjugate Fourier planes. The light path is folded such that the two corresponding phase masks can be displayed side by side at a single phase-only spatial light modulator. Such a device has relevant applications in holographic displayor projection systems, and for optical micromanipulation in laser tweezers.

© 2008 Optical Society of America

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References

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  1. P. Hariharan, Optical Holography: Principles, Techniques, and Applications (Cambridge University Press, 1996).
  2. B. Kress and P. Meyrueis, Digital diffractive optics (Wiley, 2000).
  3. H. Kim, K. Choi, and B. Lee, "Diffractive Optic Synthesis and Analysis of Light Fields and Recent Applications," Jpn. J. Appl. Phys. 45, 6555-6575 (2006).
    [CrossRef]
  4. M.-L. Hsieh, M.-L. Chen, and C.-J. Cheng, "Improvement of the complex modulated characteristic of cascaded liquid crystal spatial light modulators by using a novel amplitude compensated technique," Opt. Eng. 46, 07501 (2007).
    [CrossRef]
  5. J. P. Kirk and A. L. Jones, "Phase-Only Complex-Valued Spatial Filter," J. Opt. Soc. Am. 61, 1023-1028 (1971).
    [CrossRef]
  6. C. Maurer, A. Jesacher, S. F¨urhapter, S. Bernet, and M. Ritsch-Marte, "Tailoring of arbitrary optical vector beams," N. J. Phys. 9, 78 (2007).
    [CrossRef]
  7. H. Bartelt, "Computer-generated holographic component with optimum light efficiency," Appl. Opt. 23, 1499-1502 (1984).
    [CrossRef] [PubMed]
  8. H. O. Bartelt, "Applications of the tandem component: an element with optimum light efficiency," Appl. Opt. 24, 3811-3816 (1985).
    [CrossRef] [PubMed]
  9. Y. Roichman and D. G. Grier, "Projecting extended optical traps with shape-phase holography," Opt. Lett. 31, 1675-1677 (2006).
    [CrossRef] [PubMed]
  10. G. O. Reynolds, J. B. Develis, and B. J. Thompson, The New Physical Optics Notebook: Tutorials in Fourier Optics (SPIE, 1989).
    [CrossRef]
  11. R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik 35, 237-246 (1972).
  12. S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, "Experimental observation of optically trapped atoms," Phys. Rev. Lett. 57, 314-317 (1986).
    [CrossRef] [PubMed]
  13. 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).
    [CrossRef] [PubMed]
  14. J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, "Multi-functional optical tweezers using computergenerated holograms," Opt. Commun. 185, 77-82 (2000).
    [CrossRef]
  15. A. Jesacher, C. Maurer, S. F¨urhapter, A. Schwaighofer, S. Bernet, and M. Ritsch-Marte, "Optical tweezers of programmable shape with transverse scattering forces," Opt. Commun. (to be published).

2007 (2)

C. Maurer, A. Jesacher, S. F¨urhapter, S. Bernet, and M. Ritsch-Marte, "Tailoring of arbitrary optical vector beams," N. J. Phys. 9, 78 (2007).
[CrossRef]

M.-L. Hsieh, M.-L. Chen, and C.-J. Cheng, "Improvement of the complex modulated characteristic of cascaded liquid crystal spatial light modulators by using a novel amplitude compensated technique," Opt. Eng. 46, 07501 (2007).
[CrossRef]

2006 (2)

H. Kim, K. Choi, and B. Lee, "Diffractive Optic Synthesis and Analysis of Light Fields and Recent Applications," Jpn. J. Appl. Phys. 45, 6555-6575 (2006).
[CrossRef]

Y. Roichman and D. G. Grier, "Projecting extended optical traps with shape-phase holography," Opt. Lett. 31, 1675-1677 (2006).
[CrossRef] [PubMed]

2003 (1)

2000 (1)

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

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] [PubMed]

1985 (1)

1984 (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 35, 237-246 (1972).

1971 (1)

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] [PubMed]

Bartelt, H.

Bartelt, H. O.

Bernet, S.

C. Maurer, A. Jesacher, S. F¨urhapter, S. Bernet, and M. Ritsch-Marte, "Tailoring of arbitrary optical vector beams," N. J. Phys. 9, 78 (2007).
[CrossRef]

A. Jesacher, C. Maurer, S. F¨urhapter, A. Schwaighofer, S. Bernet, and M. Ritsch-Marte, "Optical tweezers of programmable shape with transverse scattering forces," Opt. Commun. (to be published).

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] [PubMed]

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] [PubMed]

Chen, M.-L.

M.-L. Hsieh, M.-L. Chen, and C.-J. Cheng, "Improvement of the complex modulated characteristic of cascaded liquid crystal spatial light modulators by using a novel amplitude compensated technique," Opt. Eng. 46, 07501 (2007).
[CrossRef]

Cheng, C.-J.

M.-L. Hsieh, M.-L. Chen, and C.-J. Cheng, "Improvement of the complex modulated characteristic of cascaded liquid crystal spatial light modulators by using a novel amplitude compensated technique," Opt. Eng. 46, 07501 (2007).
[CrossRef]

Choi, K.

H. Kim, K. Choi, and B. Lee, "Diffractive Optic Synthesis and Analysis of Light Fields and Recent Applications," Jpn. J. Appl. Phys. 45, 6555-6575 (2006).
[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] [PubMed]

Dholakia, K.

F¨urhapter, S.

C. Maurer, A. Jesacher, S. F¨urhapter, S. Bernet, and M. Ritsch-Marte, "Tailoring of arbitrary optical vector beams," N. J. Phys. 9, 78 (2007).
[CrossRef]

A. Jesacher, C. Maurer, S. F¨urhapter, A. Schwaighofer, S. Bernet, and M. Ritsch-Marte, "Optical tweezers of programmable shape with transverse scattering forces," Opt. Commun. (to be published).

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 35, 237-246 (1972).

Grier, D. G.

Haist, T.

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

Hsieh, M.-L.

M.-L. Hsieh, M.-L. Chen, and C.-J. Cheng, "Improvement of the complex modulated characteristic of cascaded liquid crystal spatial light modulators by using a novel amplitude compensated technique," Opt. Eng. 46, 07501 (2007).
[CrossRef]

Jesacher, A.

C. Maurer, A. Jesacher, S. F¨urhapter, S. Bernet, and M. Ritsch-Marte, "Tailoring of arbitrary optical vector beams," N. J. Phys. 9, 78 (2007).
[CrossRef]

A. Jesacher, C. Maurer, S. F¨urhapter, A. Schwaighofer, S. Bernet, and M. Ritsch-Marte, "Optical tweezers of programmable shape with transverse scattering forces," Opt. Commun. (to be published).

Jones, A. L.

Kim, H.

H. Kim, K. Choi, and B. Lee, "Diffractive Optic Synthesis and Analysis of Light Fields and Recent Applications," Jpn. J. Appl. Phys. 45, 6555-6575 (2006).
[CrossRef]

Kirk, J. P.

Lee, B.

H. Kim, K. Choi, and B. Lee, "Diffractive Optic Synthesis and Analysis of Light Fields and Recent Applications," Jpn. J. Appl. Phys. 45, 6555-6575 (2006).
[CrossRef]

Liesener, J.

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

Maurer, C.

C. Maurer, A. Jesacher, S. F¨urhapter, S. Bernet, and M. Ritsch-Marte, "Tailoring of arbitrary optical vector beams," N. J. Phys. 9, 78 (2007).
[CrossRef]

A. Jesacher, C. Maurer, S. F¨urhapter, A. Schwaighofer, S. Bernet, and M. Ritsch-Marte, "Optical tweezers of programmable shape with transverse scattering forces," Opt. Commun. (to be published).

McGloin, D.

Melville, H.

Reicherter, M.

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

Ritsch-Marte, M.

C. Maurer, A. Jesacher, S. F¨urhapter, S. Bernet, and M. Ritsch-Marte, "Tailoring of arbitrary optical vector beams," N. J. Phys. 9, 78 (2007).
[CrossRef]

A. Jesacher, C. Maurer, S. F¨urhapter, A. Schwaighofer, S. Bernet, and M. Ritsch-Marte, "Optical tweezers of programmable shape with transverse scattering forces," Opt. Commun. (to be published).

Roichman, Y.

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 35, 237-246 (1972).

Schwaighofer, A.

A. Jesacher, C. Maurer, S. F¨urhapter, A. Schwaighofer, S. Bernet, and M. Ritsch-Marte, "Optical tweezers of programmable shape with transverse scattering forces," Opt. Commun. (to be published).

Sibbett, W.

Spalding, G.

Tiziani, H. J.

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

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

Jpn. J. Appl. Phys. (1)

H. Kim, K. Choi, and B. Lee, "Diffractive Optic Synthesis and Analysis of Light Fields and Recent Applications," Jpn. J. Appl. Phys. 45, 6555-6575 (2006).
[CrossRef]

N. J. Phys. (1)

C. Maurer, A. Jesacher, S. F¨urhapter, S. Bernet, and M. Ritsch-Marte, "Tailoring of arbitrary optical vector beams," N. J. Phys. 9, 78 (2007).
[CrossRef]

Opt. Commun. (2)

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

A. Jesacher, C. Maurer, S. F¨urhapter, A. Schwaighofer, S. Bernet, and M. Ritsch-Marte, "Optical tweezers of programmable shape with transverse scattering forces," Opt. Commun. (to be published).

Opt. Eng. (1)

M.-L. Hsieh, M.-L. Chen, and C.-J. Cheng, "Improvement of the complex modulated characteristic of cascaded liquid crystal spatial light modulators by using a novel amplitude compensated technique," Opt. Eng. 46, 07501 (2007).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Optik (1)

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik 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] [PubMed]

Other (3)

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

P. Hariharan, Optical Holography: Principles, Techniques, and Applications (Cambridge University Press, 1996).

B. Kress and P. Meyrueis, Digital diffractive optics (Wiley, 2000).

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Figures (4)

Fig. 1.
Fig. 1.

Principle of the method. A specific complex light field in the object plane (right plane) is created by two phase-diffractive patterns (P1 and P2 – gray shades in the figure correspond to phase values from 0 to 2π), which are placed in two conjugate planes (plane 1 and the Fourier plane). P1 is iteratively optimized to create the amplitude |A| in the Fourier plane. There, the desired phase function Φ is shaped from the “noisy” phase Θ by pattern P2.

Fig. 2.
Fig. 2.

Sketch of the experimental setup. The phase patterns P1 and P2 are displayed side by side at the phase modulator panel. The light diffracted from P1 is reflected back onto P2 by a slightly tilted concave mirror, which additionally performs the optical Fourier transform. P2 rearranges the light phase and creates the desired phase function.

Fig. 3.
Fig. 3.

Holographical reconstructions of a gray-scale image. (a) represents the original. (b) and (c) have been created with the presented method, using 256 or 2 distinct phase levels for displaying the phase patterns, respectively. (d) shows the experimental reconstruction of the image from a single optimized phase DOE (256 phase levels) for comparison. Clearly visible are the “noisy” texture and the zero diffraction order, which is represented by the intense spot in the image center. The plots below the images show the individual intensities along a definite cross section (indicated by the yellow dashed line in (a))

Fig. 4.
Fig. 4.

Left: Images of a rabbit and an eagle are reconstructed in a common axial plane. Thus both animals appear sharply. Middle and right image: The rabbit and the eagle emerge in two distinct axial planes. Different focus settings allow to see only one animal sharply at a time, while the other one appears blurred.

Equations (2)

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A ( u , v ) = 1 λ f x y a ( x , y ) exp [ i 2 π λ f ( u x + y v ) ] d x d y .
P 2 = mod 2 π { Φ Θ } ,

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