Abstract

Volume holographic imaging utilizes Bragg selectivity to optically slice the object space of the imaging system and measure four- (three spatial and one spectral) dimensional object information. The N-ocular version of this method combines multiple-volume holographic sensors and digital postprocessing to yield high-resolution three-dimensional images for broadband objects located at long working distances. We discuss the physical properties of volume holography pertinent to imaging performance and describe two computational algorithms for image inversion based on filtered backprojection and least-squares optimization.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. Barbastathis, D. J. Brady, “Multidimensional tomographic imaging using volume holography,” Proc. IEEE 87, 2098–2120 (1999).
    [CrossRef]
  2. E. N. Leith, A. Kozma, J. Upatnieks, J. Marks, N. Massey, “Holographic data storage in three-dimensional media,” Appl. Opt. 5, 1303–1311 (1966).
    [CrossRef] [PubMed]
  3. P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).
  4. P. J. van Heerden, “Theory of optical information storage in solids,” Appl. Opt. 2, 393–400 (1963).
    [CrossRef]
  5. A. Sinha, W. Sun, T. Shih, G. Barbastathis, “Volume holographic imaging in the transmission geometry,” Appl. Opt. 43, 1–19 (2004).
  6. G. Barbastathis, M. Balberg, D. J. Brady, “Confocal microscopy with a volume holographic filter,” Opt. Lett. 24, 811–813 (1999).
    [CrossRef]
  7. W. Liu, D. Psaltis, G. Barbastathis, “Real time spectral imaging in three spatial dimensions,” Opt. Lett. 27, 854–856 (2002).
    [CrossRef]
  8. A. Sinha, G. Barbastathis, “Volume holographic telescope,” Opt. Lett. 27, 1690–1692 (2002).
    [CrossRef]
  9. A. Sinha, G. Barbastathis, “Volume holographic imaging for surface metrology at long working distances,” Opt. Express 11, 3202–3209 (2003), http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  10. A. Sinha, W. Sun, G. Barbastathis, “Broadband volume holographic imaging,” Appl. Opt. 43, 5214–5221 (2004).
    [CrossRef] [PubMed]
  11. M. Born, E. Wolf, Principles of Optics, 7th ed. (Pergamon, Cambridge, UK, 1998).
  12. O. Faugeras, Q.-T. Luong, The Geometry of Multiple Images (MIT Press, Cambridge, Mass., 2001).
  13. U. R. Dhond, J. K. Aggarwal, “Structure from stereo: a review,” IEEE Trans. Syst. Man. Cybern. 14, 1489–1510 (1989).
    [CrossRef]
  14. J. Aloimonos, I. Weiss, A. Bandyopadhyay, “Active vision,” in Proceedings of IEEE First International Conference on Computer Vision (Institute of Electrical and Electronics Engineers, New York, 1987), pp. 35–54.
  15. N. Ahuja, A. Abbott, “Active stereo: integrating disparity, vergence, focus, aperture, and calibration for surface estimation,” IEEE Trans. Pattern Anal. Mach. Intell. 15, 1007–1029 (1993).
    [CrossRef]
  16. D. Psaltis, F. Mok, H. Y.-S. Li, “Nonvolatile storage in photorefractive crystals,” Opt. Lett. 19, 210–212 (1994).
    [CrossRef] [PubMed]
  17. H. Martin, T. Kanade, “Incremental reconstruction of 3D scenes from multiple, complex images,” Artif. Intell. 30, 289–341 (1986).
    [CrossRef]
  18. M. V. Klein, T. E. Furtak, Optics (Wiley, New York, 1986).
  19. E. R. Dowski, W. T. Cathey, “Extended depth of field through wave-front coding,” Appl. Opt. 34, 1859–1866 (1994).
    [CrossRef]
  20. N. George, W. Chi, “Extended depth of field using a logarithmic asphere,” J. Opt. A Pure Appl. Opt. 5, S157–S163 (2003).
    [CrossRef]
  21. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
  22. M. Bertero, P. Boccacci, Introduction to Inverse Problems in Imaging (Institute of Physics, London, 1998).
    [CrossRef]
  23. G. Barbastathis, A. Sinha, “Information content of volume holographic imaging,” Trends Biotechnol. 19, 383–392 (2001).
    [CrossRef] [PubMed]
  24. A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1999).

2004 (2)

A. Sinha, W. Sun, T. Shih, G. Barbastathis, “Volume holographic imaging in the transmission geometry,” Appl. Opt. 43, 1–19 (2004).

A. Sinha, W. Sun, G. Barbastathis, “Broadband volume holographic imaging,” Appl. Opt. 43, 5214–5221 (2004).
[CrossRef] [PubMed]

2003 (2)

2002 (2)

2001 (1)

G. Barbastathis, A. Sinha, “Information content of volume holographic imaging,” Trends Biotechnol. 19, 383–392 (2001).
[CrossRef] [PubMed]

1999 (2)

G. Barbastathis, D. J. Brady, “Multidimensional tomographic imaging using volume holography,” Proc. IEEE 87, 2098–2120 (1999).
[CrossRef]

G. Barbastathis, M. Balberg, D. J. Brady, “Confocal microscopy with a volume holographic filter,” Opt. Lett. 24, 811–813 (1999).
[CrossRef]

1994 (2)

1993 (1)

N. Ahuja, A. Abbott, “Active stereo: integrating disparity, vergence, focus, aperture, and calibration for surface estimation,” IEEE Trans. Pattern Anal. Mach. Intell. 15, 1007–1029 (1993).
[CrossRef]

1989 (1)

U. R. Dhond, J. K. Aggarwal, “Structure from stereo: a review,” IEEE Trans. Syst. Man. Cybern. 14, 1489–1510 (1989).
[CrossRef]

1986 (1)

H. Martin, T. Kanade, “Incremental reconstruction of 3D scenes from multiple, complex images,” Artif. Intell. 30, 289–341 (1986).
[CrossRef]

1966 (1)

1963 (1)

Abbott, A.

N. Ahuja, A. Abbott, “Active stereo: integrating disparity, vergence, focus, aperture, and calibration for surface estimation,” IEEE Trans. Pattern Anal. Mach. Intell. 15, 1007–1029 (1993).
[CrossRef]

Aggarwal, J. K.

U. R. Dhond, J. K. Aggarwal, “Structure from stereo: a review,” IEEE Trans. Syst. Man. Cybern. 14, 1489–1510 (1989).
[CrossRef]

Ahuja, N.

N. Ahuja, A. Abbott, “Active stereo: integrating disparity, vergence, focus, aperture, and calibration for surface estimation,” IEEE Trans. Pattern Anal. Mach. Intell. 15, 1007–1029 (1993).
[CrossRef]

Aloimonos, J.

J. Aloimonos, I. Weiss, A. Bandyopadhyay, “Active vision,” in Proceedings of IEEE First International Conference on Computer Vision (Institute of Electrical and Electronics Engineers, New York, 1987), pp. 35–54.

Balberg, M.

Bandyopadhyay, A.

J. Aloimonos, I. Weiss, A. Bandyopadhyay, “Active vision,” in Proceedings of IEEE First International Conference on Computer Vision (Institute of Electrical and Electronics Engineers, New York, 1987), pp. 35–54.

Barbastathis, G.

Bertero, M.

M. Bertero, P. Boccacci, Introduction to Inverse Problems in Imaging (Institute of Physics, London, 1998).
[CrossRef]

Boccacci, P.

M. Bertero, P. Boccacci, Introduction to Inverse Problems in Imaging (Institute of Physics, London, 1998).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Pergamon, Cambridge, UK, 1998).

Brady, D. J.

G. Barbastathis, M. Balberg, D. J. Brady, “Confocal microscopy with a volume holographic filter,” Opt. Lett. 24, 811–813 (1999).
[CrossRef]

G. Barbastathis, D. J. Brady, “Multidimensional tomographic imaging using volume holography,” Proc. IEEE 87, 2098–2120 (1999).
[CrossRef]

Cathey, W. T.

Chi, W.

N. George, W. Chi, “Extended depth of field using a logarithmic asphere,” J. Opt. A Pure Appl. Opt. 5, S157–S163 (2003).
[CrossRef]

Dhond, U. R.

U. R. Dhond, J. K. Aggarwal, “Structure from stereo: a review,” IEEE Trans. Syst. Man. Cybern. 14, 1489–1510 (1989).
[CrossRef]

Dowski, E. R.

Faugeras, O.

O. Faugeras, Q.-T. Luong, The Geometry of Multiple Images (MIT Press, Cambridge, Mass., 2001).

Furtak, T. E.

M. V. Klein, T. E. Furtak, Optics (Wiley, New York, 1986).

George, N.

N. George, W. Chi, “Extended depth of field using a logarithmic asphere,” J. Opt. A Pure Appl. Opt. 5, S157–S163 (2003).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Kak, A. C.

A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1999).

Kanade, T.

H. Martin, T. Kanade, “Incremental reconstruction of 3D scenes from multiple, complex images,” Artif. Intell. 30, 289–341 (1986).
[CrossRef]

Klein, M. V.

M. V. Klein, T. E. Furtak, Optics (Wiley, New York, 1986).

Kozma, A.

Leith, E. N.

Li, H. Y.-S.

Liu, W.

Luong, Q.-T.

O. Faugeras, Q.-T. Luong, The Geometry of Multiple Images (MIT Press, Cambridge, Mass., 2001).

Marks, J.

Martin, H.

H. Martin, T. Kanade, “Incremental reconstruction of 3D scenes from multiple, complex images,” Artif. Intell. 30, 289–341 (1986).
[CrossRef]

Massey, N.

Mok, F.

Psaltis, D.

Shih, T.

A. Sinha, W. Sun, T. Shih, G. Barbastathis, “Volume holographic imaging in the transmission geometry,” Appl. Opt. 43, 1–19 (2004).

Sinha, A.

Slaney, M.

A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1999).

Sun, W.

A. Sinha, W. Sun, G. Barbastathis, “Broadband volume holographic imaging,” Appl. Opt. 43, 5214–5221 (2004).
[CrossRef] [PubMed]

A. Sinha, W. Sun, T. Shih, G. Barbastathis, “Volume holographic imaging in the transmission geometry,” Appl. Opt. 43, 1–19 (2004).

Upatnieks, J.

van Heerden, P. J.

Weiss, I.

J. Aloimonos, I. Weiss, A. Bandyopadhyay, “Active vision,” in Proceedings of IEEE First International Conference on Computer Vision (Institute of Electrical and Electronics Engineers, New York, 1987), pp. 35–54.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Pergamon, Cambridge, UK, 1998).

Yeh, P.

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).

Appl. Opt. (5)

Artif. Intell. (1)

H. Martin, T. Kanade, “Incremental reconstruction of 3D scenes from multiple, complex images,” Artif. Intell. 30, 289–341 (1986).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

N. Ahuja, A. Abbott, “Active stereo: integrating disparity, vergence, focus, aperture, and calibration for surface estimation,” IEEE Trans. Pattern Anal. Mach. Intell. 15, 1007–1029 (1993).
[CrossRef]

IEEE Trans. Syst. Man. Cybern. (1)

U. R. Dhond, J. K. Aggarwal, “Structure from stereo: a review,” IEEE Trans. Syst. Man. Cybern. 14, 1489–1510 (1989).
[CrossRef]

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

N. George, W. Chi, “Extended depth of field using a logarithmic asphere,” J. Opt. A Pure Appl. Opt. 5, S157–S163 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Proc. IEEE (1)

G. Barbastathis, D. J. Brady, “Multidimensional tomographic imaging using volume holography,” Proc. IEEE 87, 2098–2120 (1999).
[CrossRef]

Trends Biotechnol. (1)

G. Barbastathis, A. Sinha, “Information content of volume holographic imaging,” Trends Biotechnol. 19, 383–392 (2001).
[CrossRef] [PubMed]

Other (8)

A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1999).

J. Aloimonos, I. Weiss, A. Bandyopadhyay, “Active vision,” in Proceedings of IEEE First International Conference on Computer Vision (Institute of Electrical and Electronics Engineers, New York, 1987), pp. 35–54.

M. V. Klein, T. E. Furtak, Optics (Wiley, New York, 1986).

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).

M. Born, E. Wolf, Principles of Optics, 7th ed. (Pergamon, Cambridge, UK, 1998).

O. Faugeras, Q.-T. Luong, The Geometry of Multiple Images (MIT Press, Cambridge, Mass., 2001).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

M. Bertero, P. Boccacci, Introduction to Inverse Problems in Imaging (Institute of Physics, London, 1998).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (16)

Fig. 1
Fig. 1

Schematic for recording of volume holograms in PR VHI.

Fig. 2
Fig. 2

Imaging setup for PR VHI.

Fig. 3
Fig. 3

Use of the k-sphere formulation to explain the lateral mapping of several spectral components.

Fig. 4
Fig. 4

Diffraction pattern observed experimentally for a broadband fluorescent object emitting at λ p = 580 ± 20 nm. (a) Comparison of a Bragg-matched laser, λ p = 532 nm, and a fluorescent source. (b) The fluorescent source stays visible for a large lateral translation, Δx′ = 3 mm. (c) The Bragg slit at δ = 2 mm for the fluorescent source is wider than the laser’s Bragg slit. Source: Ref. 10.

Fig. 5
Fig. 5

Comparison of depth resolution for monochromatic and broadband illumination. The broadband PSF (dashed curve) is broader than the monochromatic PSF (solid curve).

Fig. 6
Fig. 6

Theoretical performance of imaging with multiple sensors. (i) PSF of a single sensor. (ii) PSFs of two sensors at ϕ = 90°. (iii) PSFs of three sensors at 45°. (iv) PSFs of four sensors at 30°.

Fig. 7
Fig. 7

Experimental PSFs for two individual sensors oriented at ϕ = 10° for point sources located at the following distances in front of the sensor: (a) 29 cm, (b) 45 cm, (c) 72 cm.

Fig. 8
Fig. 8

Schematic of an N-ocular VHI system. For illustration purposes we have depicted N = 3.

Fig. 9
Fig. 9

All voxels located along a line in the object space are mapped onto the same lateral location on the detector.

Fig. 10
Fig. 10

Several point sources that satisfy Eq. (12) are simultaneously imaged by the PR volume hologram according to Eq. (13).

Fig. 11
Fig. 11

Inversion scheme for reconstructing 3D object data from 2D VHI images.

Fig. 12
Fig. 12

Broadband PR VHI system measures the Radon transform of an object along a direction specified by the inclination of the sensor.

Fig. 13
Fig. 13

N-ocular PR VHI of broadband objects. (a) The object of interest consisted of two fluorescent beads of diameters 0.66 and 0.72 mm separated by an aluminum spacer of 2.91-mm length. (b), (c) VHI PR images of the object at inclination angles ϕ b = 0° and ϕ c = 45°, respectively.

Fig. 14
Fig. 14

3D image of the object shown in Fig. 13 obtained by the inverse Radon transform approach. (a) Five slices through the object. (b), (c), (d), (e), (f) The same slices at y = 0, 0.25, 0.5, 0.75, 1 mm, respectively. All dimensions are in millimeters. The separation between the centroids of the two reconstructed beads was calculated to be 3.60 ± 0.01 mm.

Fig. 15
Fig. 15

Least-squares inversion is able to recover the object shown in Fig. 13. (a) Five slices through the object. (b), (c), (d), (e), (f) The same slices at y = 0, 0.25, 0.5, 0.75, 1 mm, respectively. All dimensions are in millimeters.

Fig. 16
Fig. 16

Three-ocular PR VHI image of a broadband object. (a) The object was a 3D helical arrangement of fluorescent beads with helix radius 6.5 mm. (b) The reconstruction recovers the 3D object. Note that for simplicity just the centroids of the fluorescent beads are shown. All dimensions are in millimeters.

Equations (20)

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

Ix, y; δIθsF, 0; δ=circx-θsF2+y21/2Faδ/f2×sinc2LθsλfxF-θs.
Iδ= Ix, y; δdxdy.
ΔzFWHM= 5.34λfd2θsaL.
ΔxB= 2λfdθsL.
IBBx, y; δ= Ix, y; δ, μSμdμ.
Ix, y; δ, μIb=circ|r|Faδ/f2sinc2LθsλpxF- θs1+μ2,
r2=x-Fθs1+μ2- δθs1-μ2f2+y2
Iδ= IBBx, y; δdxdy,
x= fθs1-μ2
x= Fθs1+μ2.
x=fθs1- xFθs.
xc±Δx= fθs1-μc2± fθsΔμ2,
xc±Δx=Fθs1- xcfθs± FΔxf.
ζ1i=xi cos ϕ1-zi sin ϕ1.
x1i=Fθs1- ζ1ifθs.
Iˆ1i=I1x1i.
xji=Fθs1- xi cos ϕj-zi sin ϕjfθs,
Iˆji=Ijxji.
Iˆi=arg minjIˆ-Iˆji2.
xji=Fθs1- χ+xi cos ϕj-zi sin ϕjfθs.

Metrics