Abstract

Holographic optical trapping uses forces exerted by computer-generated holograms to organize microscopic materials into three-dimensional structures. In a complementary manner, holographic video microscopy uses real-time recordings of in-line holograms to create time-resolved volumetric images of three-dimensional microstructures. The combination is exceptionally effective for organizing, inspecting and analyzing soft-matter systems.

© 2007 Optical Society of America

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References

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  1. E. R. Dufresne and D. G. Grier, "Optical tweezer arrays and optical substrates created with diffractive optical elements," Rev. Sci. Instrum. 69, 1974-1977 (1998).
    [CrossRef]
  2. D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
    [CrossRef] [PubMed]
  3. P. Jordan, H. Clare, L. Flendrig, J. Leach, J. Cooper, and M. Padgett, "Permanent 3D microstructures in a polymeric host created using holographic optical tweezers," J. Mod. Opt. 51, 627-632 (2004).
  4. Y. Roichman and D. G. Grier, "Holographic assembly of quasicrystalline photonic heterostructures," Opt. Express 13, 5434-5439 (2005).
    [CrossRef] [PubMed]
  5. R. Agarwal, K. Ladavac, Y. Roichman, G. Yu, C. M. Lieber, and D. G. Grier, "Manipulation and assembly of nanowires with holographic optical traps," Opt. Express 13, 8906-8912 (2005).
    [CrossRef] [PubMed]
  6. J. Sheng, E. Malkiel, and J. Katz, "Digital holographic microscope for measuring three-dimensional particle distributions and motions," Appl. Opt. 45, 3893-3901 (2006).
    [CrossRef] [PubMed]
  7. U. Schnars and W. Jüptner, "Direct recording of holograms by a CCD target and numerical reconstruction," Appl. Opt. 33, 179-181 (1994).
    [CrossRef] [PubMed]
  8. E. Cuche, P. Marquet, and C. Depeursinge, "Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms," Appl. Opt. 38, 6994-7001 (1999).
    [CrossRef]
  9. U. Schnars and W. P. O. Jüptner, "Digital recording and reconstruction of holograms," Meas. Sci. Technol. 13, R85-R101 (2002).
    [CrossRef]
  10. W. Xu, M. H. Jerico, I. A. Meinertzhagen, and H. J. Kreuzer, "Digital in-line holography of microspheres," Appl. Opt. 41, 5367-5375 (2002).
    [CrossRef] [PubMed]
  11. M. Polin, K. Ladavac, S.-H. Lee, Y. Roichman, and D. G. Grier, "Optimized holographic optical traps," Opt. Express 13, 5831-5845 (2005).
    [CrossRef] [PubMed]
  12. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, "Observation of a single-beam gradient force optical trap for dielectric particles," Opt. Lett. 11, 288-290 (1986).
    [CrossRef] [PubMed]
  13. M. Reicherter, T. Haist, E. U. Wagemann, and H. J. Tiziani, "Optical particle trapping with computer-generated holograms written on a liquid-crystal display," Opt. Lett. 24, 608-610 (1999).
    [CrossRef]
  14. 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]
  15. J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers." Opt. Commun. 207, 169-175 (2002).
    [CrossRef]
  16. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 2005), 3rd ed.
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    [CrossRef] [PubMed]
  18. Y. Roichman, A. S. Waldron, E. Gardel, and D. G. Grier, "Performance of optical traps with geometric aberrations," Appl. Opt. 45, 3425-3429 (2005).
    [CrossRef]
  19. M. S. Elliot and W. C. K. Poon, "Conventional optical microscopy of colloidal suspensions," Adv. Colloid Interface Sci. 92, 133-194 (2001).
    [CrossRef] [PubMed]
  20. J. C. Crocker and D. G. Grier, "Methods of digital video microscopy for colloidal studies," J. Colloid Interface Sci. 179, 298-310 (1996).
    [CrossRef]
  21. M. Wu, J. W. Roberts, and M. Buckley, "Three-dimensional fluorescent particle tracking at micron-scale using a single camera," Exp. Fluids 38, 461-465 (2005).
    [CrossRef]
  22. A. D. Dinsmore, E. R. Weeks, V. Prasad, A. C. Levitt, and D. A. Weitz, "Three-dimensional confocal microscopy of colloids," Appl. Opt. 40, 4152-4159 (2001).
    [CrossRef]
  23. S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, "Synthetic aperture Fourier holographic optical microscopy," Phys. Rev. Lett. 97, 68102 (2006).
    [CrossRef]
  24. Y. Roichman, I. Cholis, and D. G. Grier, "Volumetric imaging of holographic optical traps," Opt. Express 14, 10907-10912 (2006).
    [CrossRef] [PubMed]
  25. K. Dholakia, H. Little, C. T. A. Brown, B. Agate, D. McGloin, L. Paterson, and W. Sibbett, "Imaging in optical micromanipulation using two-photon excitation," New J. Phys. 6, 136 (2004).
    [CrossRef]
  26. T. Cizmar, E. Kollarova, Z. Bouchal, and P. Zemanek, "Sub-micron particle organization by self-imaging of non-diffracting beams," New J. Phys. 8, 43 (2006).
    [CrossRef]

2006 (4)

J. Sheng, E. Malkiel, and J. Katz, "Digital holographic microscope for measuring three-dimensional particle distributions and motions," Appl. Opt. 45, 3893-3901 (2006).
[CrossRef] [PubMed]

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, "Synthetic aperture Fourier holographic optical microscopy," Phys. Rev. Lett. 97, 68102 (2006).
[CrossRef]

Y. Roichman, I. Cholis, and D. G. Grier, "Volumetric imaging of holographic optical traps," Opt. Express 14, 10907-10912 (2006).
[CrossRef] [PubMed]

T. Cizmar, E. Kollarova, Z. Bouchal, and P. Zemanek, "Sub-micron particle organization by self-imaging of non-diffracting beams," New J. Phys. 8, 43 (2006).
[CrossRef]

2005 (5)

2004 (2)

P. Jordan, H. Clare, L. Flendrig, J. Leach, J. Cooper, and M. Padgett, "Permanent 3D microstructures in a polymeric host created using holographic optical tweezers," J. Mod. Opt. 51, 627-632 (2004).

K. Dholakia, H. Little, C. T. A. Brown, B. Agate, D. McGloin, L. Paterson, and W. Sibbett, "Imaging in optical micromanipulation using two-photon excitation," New J. Phys. 6, 136 (2004).
[CrossRef]

2003 (1)

D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
[CrossRef] [PubMed]

2002 (3)

U. Schnars and W. P. O. Jüptner, "Digital recording and reconstruction of holograms," Meas. Sci. Technol. 13, R85-R101 (2002).
[CrossRef]

W. Xu, M. H. Jerico, I. A. Meinertzhagen, and H. J. Kreuzer, "Digital in-line holography of microspheres," Appl. Opt. 41, 5367-5375 (2002).
[CrossRef] [PubMed]

J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers." Opt. Commun. 207, 169-175 (2002).
[CrossRef]

2001 (3)

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]

A. D. Dinsmore, E. R. Weeks, V. Prasad, A. C. Levitt, and D. A. Weitz, "Three-dimensional confocal microscopy of colloids," Appl. Opt. 40, 4152-4159 (2001).
[CrossRef]

M. S. Elliot and W. C. K. Poon, "Conventional optical microscopy of colloidal suspensions," Adv. Colloid Interface Sci. 92, 133-194 (2001).
[CrossRef] [PubMed]

1999 (2)

1998 (1)

E. R. Dufresne and D. G. Grier, "Optical tweezer arrays and optical substrates created with diffractive optical elements," Rev. Sci. Instrum. 69, 1974-1977 (1998).
[CrossRef]

1996 (1)

J. C. Crocker and D. G. Grier, "Methods of digital video microscopy for colloidal studies," J. Colloid Interface Sci. 179, 298-310 (1996).
[CrossRef]

1994 (1)

1986 (1)

1967 (1)

Agarwal, R.

Agate, B.

K. Dholakia, H. Little, C. T. A. Brown, B. Agate, D. McGloin, L. Paterson, and W. Sibbett, "Imaging in optical micromanipulation using two-photon excitation," New J. Phys. 6, 136 (2004).
[CrossRef]

Alexandrov, S. A.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, "Synthetic aperture Fourier holographic optical microscopy," Phys. Rev. Lett. 97, 68102 (2006).
[CrossRef]

Ashkin, A.

Bjorkholm, J. E.

Bouchal, Z.

T. Cizmar, E. Kollarova, Z. Bouchal, and P. Zemanek, "Sub-micron particle organization by self-imaging of non-diffracting beams," New J. Phys. 8, 43 (2006).
[CrossRef]

Brown, C. T. A.

K. Dholakia, H. Little, C. T. A. Brown, B. Agate, D. McGloin, L. Paterson, and W. Sibbett, "Imaging in optical micromanipulation using two-photon excitation," New J. Phys. 6, 136 (2004).
[CrossRef]

Buckley, M.

M. Wu, J. W. Roberts, and M. Buckley, "Three-dimensional fluorescent particle tracking at micron-scale using a single camera," Exp. Fluids 38, 461-465 (2005).
[CrossRef]

Cholis, I.

Chu, S.

Cizmar, T.

T. Cizmar, E. Kollarova, Z. Bouchal, and P. Zemanek, "Sub-micron particle organization by self-imaging of non-diffracting beams," New J. Phys. 8, 43 (2006).
[CrossRef]

Clare, H.

P. Jordan, H. Clare, L. Flendrig, J. Leach, J. Cooper, and M. Padgett, "Permanent 3D microstructures in a polymeric host created using holographic optical tweezers," J. Mod. Opt. 51, 627-632 (2004).

Cooper, J.

P. Jordan, H. Clare, L. Flendrig, J. Leach, J. Cooper, and M. Padgett, "Permanent 3D microstructures in a polymeric host created using holographic optical tweezers," J. Mod. Opt. 51, 627-632 (2004).

Crocker, J. C.

J. C. Crocker and D. G. Grier, "Methods of digital video microscopy for colloidal studies," J. Colloid Interface Sci. 179, 298-310 (1996).
[CrossRef]

Cuche, E.

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]

Depeursinge, C.

Dholakia, K.

K. Dholakia, H. Little, C. T. A. Brown, B. Agate, D. McGloin, L. Paterson, and W. Sibbett, "Imaging in optical micromanipulation using two-photon excitation," New J. Phys. 6, 136 (2004).
[CrossRef]

Dinsmore, A. D.

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]

E. R. Dufresne and D. G. Grier, "Optical tweezer arrays and optical substrates created with diffractive optical elements," Rev. Sci. Instrum. 69, 1974-1977 (1998).
[CrossRef]

Dziedzic, J. M.

Elliot, M. S.

M. S. Elliot and W. C. K. Poon, "Conventional optical microscopy of colloidal suspensions," Adv. Colloid Interface Sci. 92, 133-194 (2001).
[CrossRef] [PubMed]

Flendrig, L.

P. Jordan, H. Clare, L. Flendrig, J. Leach, J. Cooper, and M. Padgett, "Permanent 3D microstructures in a polymeric host created using holographic optical tweezers," J. Mod. Opt. 51, 627-632 (2004).

Gardel, E.

Grier, D. G.

Y. Roichman, I. Cholis, and D. G. Grier, "Volumetric imaging of holographic optical traps," Opt. Express 14, 10907-10912 (2006).
[CrossRef] [PubMed]

Y. Roichman, A. S. Waldron, E. Gardel, and D. G. Grier, "Performance of optical traps with geometric aberrations," Appl. Opt. 45, 3425-3429 (2005).
[CrossRef]

M. Polin, K. Ladavac, S.-H. Lee, Y. Roichman, and D. G. Grier, "Optimized holographic optical traps," Opt. Express 13, 5831-5845 (2005).
[CrossRef] [PubMed]

Y. Roichman and D. G. Grier, "Holographic assembly of quasicrystalline photonic heterostructures," Opt. Express 13, 5434-5439 (2005).
[CrossRef] [PubMed]

R. Agarwal, K. Ladavac, Y. Roichman, G. Yu, C. M. Lieber, and D. G. Grier, "Manipulation and assembly of nanowires with holographic optical traps," Opt. Express 13, 8906-8912 (2005).
[CrossRef] [PubMed]

D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
[CrossRef] [PubMed]

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]

E. R. Dufresne and D. G. Grier, "Optical tweezer arrays and optical substrates created with diffractive optical elements," Rev. Sci. Instrum. 69, 1974-1977 (1998).
[CrossRef]

J. C. Crocker and D. G. Grier, "Methods of digital video microscopy for colloidal studies," J. Colloid Interface Sci. 179, 298-310 (1996).
[CrossRef]

Gutzler, T.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, "Synthetic aperture Fourier holographic optical microscopy," Phys. Rev. Lett. 97, 68102 (2006).
[CrossRef]

Haist, T.

Hillman, T. R.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, "Synthetic aperture Fourier holographic optical microscopy," Phys. Rev. Lett. 97, 68102 (2006).
[CrossRef]

Jerico, M. H.

Jordan, P.

P. Jordan, H. Clare, L. Flendrig, J. Leach, J. Cooper, and M. Padgett, "Permanent 3D microstructures in a polymeric host created using holographic optical tweezers," J. Mod. Opt. 51, 627-632 (2004).

Jüptner, W.

Jüptner, W. P. O.

U. Schnars and W. P. O. Jüptner, "Digital recording and reconstruction of holograms," Meas. Sci. Technol. 13, R85-R101 (2002).
[CrossRef]

Katz, J.

Kollarova, E.

T. Cizmar, E. Kollarova, Z. Bouchal, and P. Zemanek, "Sub-micron particle organization by self-imaging of non-diffracting beams," New J. Phys. 8, 43 (2006).
[CrossRef]

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers." Opt. Commun. 207, 169-175 (2002).
[CrossRef]

Kreuzer, H. J.

Ladavac, K.

Leach, J.

P. Jordan, H. Clare, L. Flendrig, J. Leach, J. Cooper, and M. Padgett, "Permanent 3D microstructures in a polymeric host created using holographic optical tweezers," J. Mod. Opt. 51, 627-632 (2004).

Lee, S.-H.

Levitt, A. C.

Lieber, C. M.

Little, H.

K. Dholakia, H. Little, C. T. A. Brown, B. Agate, D. McGloin, L. Paterson, and W. Sibbett, "Imaging in optical micromanipulation using two-photon excitation," New J. Phys. 6, 136 (2004).
[CrossRef]

Malkiel, E.

Marquet, P.

McGloin, D.

K. Dholakia, H. Little, C. T. A. Brown, B. Agate, D. McGloin, L. Paterson, and W. Sibbett, "Imaging in optical micromanipulation using two-photon excitation," New J. Phys. 6, 136 (2004).
[CrossRef]

Meinertzhagen, I. A.

Padgett, M.

P. Jordan, H. Clare, L. Flendrig, J. Leach, J. Cooper, and M. Padgett, "Permanent 3D microstructures in a polymeric host created using holographic optical tweezers," J. Mod. Opt. 51, 627-632 (2004).

Paterson, L.

K. Dholakia, H. Little, C. T. A. Brown, B. Agate, D. McGloin, L. Paterson, and W. Sibbett, "Imaging in optical micromanipulation using two-photon excitation," New J. Phys. 6, 136 (2004).
[CrossRef]

Polin, M.

Poon, W. C. K.

M. S. Elliot and W. C. K. Poon, "Conventional optical microscopy of colloidal suspensions," Adv. Colloid Interface Sci. 92, 133-194 (2001).
[CrossRef] [PubMed]

Prasad, V.

Reicherter, M.

Roberts, J. W.

M. Wu, J. W. Roberts, and M. Buckley, "Three-dimensional fluorescent particle tracking at micron-scale using a single camera," Exp. Fluids 38, 461-465 (2005).
[CrossRef]

Roichman, Y.

Sampson, D. D.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, "Synthetic aperture Fourier holographic optical microscopy," Phys. Rev. Lett. 97, 68102 (2006).
[CrossRef]

Schnars, U.

U. Schnars and W. P. O. Jüptner, "Digital recording and reconstruction of holograms," Meas. Sci. Technol. 13, R85-R101 (2002).
[CrossRef]

U. Schnars and W. Jüptner, "Direct recording of holograms by a CCD target and numerical reconstruction," Appl. Opt. 33, 179-181 (1994).
[CrossRef] [PubMed]

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]

Sheng, J.

Sherman, G. C.

Sibbett, W.

K. Dholakia, H. Little, C. T. A. Brown, B. Agate, D. McGloin, L. Paterson, and W. Sibbett, "Imaging in optical micromanipulation using two-photon excitation," New J. Phys. 6, 136 (2004).
[CrossRef]

Spalding, G. C.

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]

Tiziani, H. J.

Wagemann, E. U.

Waldron, A. S.

Weeks, E. R.

Weitz, D. A.

Wu, M.

M. Wu, J. W. Roberts, and M. Buckley, "Three-dimensional fluorescent particle tracking at micron-scale using a single camera," Exp. Fluids 38, 461-465 (2005).
[CrossRef]

Xu, W.

Yu, G.

Zemanek, P.

T. Cizmar, E. Kollarova, Z. Bouchal, and P. Zemanek, "Sub-micron particle organization by self-imaging of non-diffracting beams," New J. Phys. 8, 43 (2006).
[CrossRef]

Adv. Colloid Interface Sci. (1)

M. S. Elliot and W. C. K. Poon, "Conventional optical microscopy of colloidal suspensions," Adv. Colloid Interface Sci. 92, 133-194 (2001).
[CrossRef] [PubMed]

Appl. Opt. (6)

Exp. Fluids (1)

M. Wu, J. W. Roberts, and M. Buckley, "Three-dimensional fluorescent particle tracking at micron-scale using a single camera," Exp. Fluids 38, 461-465 (2005).
[CrossRef]

J. Colloid Interface Sci. (1)

J. C. Crocker and D. G. Grier, "Methods of digital video microscopy for colloidal studies," J. Colloid Interface Sci. 179, 298-310 (1996).
[CrossRef]

J. Mod. Opt. (1)

P. Jordan, H. Clare, L. Flendrig, J. Leach, J. Cooper, and M. Padgett, "Permanent 3D microstructures in a polymeric host created using holographic optical tweezers," J. Mod. Opt. 51, 627-632 (2004).

J. Opt. Soc. Am. (1)

Meas. Sci. Technol. (1)

U. Schnars and W. P. O. Jüptner, "Digital recording and reconstruction of holograms," Meas. Sci. Technol. 13, R85-R101 (2002).
[CrossRef]

Nature (1)

D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
[CrossRef] [PubMed]

New J. Phys. (2)

K. Dholakia, H. Little, C. T. A. Brown, B. Agate, D. McGloin, L. Paterson, and W. Sibbett, "Imaging in optical micromanipulation using two-photon excitation," New J. Phys. 6, 136 (2004).
[CrossRef]

T. Cizmar, E. Kollarova, Z. Bouchal, and P. Zemanek, "Sub-micron particle organization by self-imaging of non-diffracting beams," New J. Phys. 8, 43 (2006).
[CrossRef]

Opt. Commun. (1)

J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers." Opt. Commun. 207, 169-175 (2002).
[CrossRef]

Opt. Express (4)

Opt. Lett. (2)

Phys. Rev. Lett. (1)

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, "Synthetic aperture Fourier holographic optical microscopy," Phys. Rev. Lett. 97, 68102 (2006).
[CrossRef]

Rev. Sci. Instrum. (2)

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]

E. R. Dufresne and D. G. Grier, "Optical tweezer arrays and optical substrates created with diffractive optical elements," Rev. Sci. Instrum. 69, 1974-1977 (1998).
[CrossRef]

Other (1)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 2005), 3rd ed.

Supplementary Material (1)

» Media 1: GIF (3004 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

Combined dynamic holographic optical trapping and holographic video microscopy system.

Fig. 2.
Fig. 2.

Holographic imaging of a three-dimensional configuration of holographically trapped colloidal spheres. (a) Conventional bright-field image of five colloidal spheres trapped in the xy plane. Scale bar indicates 5 μm. (b) The pattern is rotated around the y axis by 45°. (c) Bright-field image of the rotated pattern, as seen in the xy plane. (d) Coherent image of the same structure, as seen in the xy plane. (e) Holographic reconstruction of an xz slice through the tilted pattern. Circles denote the intended particle coordinates. [Media 1]

Fig. 3.
Fig. 3.

Axial structure of the light field scattered by a colloidal sphere. (a) Hologram recorded in the xy plane of a single sphere trapped at z = 17 μm above the focal plane.(b) Real part of the scattered field reconstructed from (a). (c) Hologram recorded with sphere at z = 0. (d) Axial section of the scattering field obtained by translating the particle past the focal plane in Δz = 0.122 μm steps. (e) Equivalent reconstruction using conventional illumination. Scale bar indicates 5 μm. (f) Axial intensity profiles from (b) and (d) demonstrating accuracy of the axial reconstruction.

Fig. 4.
Fig. 4.

Resolution limits for occluded objects. (a) Hologram of the holographically organized structure rotated to 90°, with 4 spheres arranged along the optical axis. Scale bar indicates 5 μm. (b) Holographic reconstruction of ∣v(r, z)∣ in the yz plane. (c) The same section through ∣ℑ{v(r, z)}∣2. (d) Axial traces through ∣ℑ{v(r, z)}∣2 showing positions of axially stacked spheres compared with individual sphere (filled red trace).

Equations (8)

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h z ( r ) = 1 2 π z e ikR R ,
I ( r ) = a ( r ) 2 + 2 { a * ( u h z ) } + u h z 2 .
b ( r ) = I ( r ) a ( r ) 2 a ( r ) 2 { a * ( u h z ) } a ( r ) 2 { u h z }
B ( q ) b ( r ) exp ( iq r ) d 2 r U ( q ) H z ( q ) + U * ( q ) H z * ( q ) ,
H z ( q ) = exp ( ikz [ 1 ( λq 2 πn ) 2 ] 1 2 )
B ( q ) H z ' ( q ) U ( q ) H z z ' ( q ) + U * ( q ) H z z ' ( q ) .
v ( r , z ) v ( r , z ) exp ( ( r , z ) )
= 1 4 π 2 B ( q ) H z ( q ) exp ( iq r ) d 2 q .

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