Abstract

An optical tomography system is developed for generating three-dimensional reconstructions of thick objects from projections. The system is useful for studying transparent structures that are 1–10 mm in diameter. Evaluation of the reconstruction system with a test object demonstrates 98% geometric accuracy, 90% accuracy in the detection of boundaries, and 90% accuracy in the measurement of absorbance. Reconstructions are computed from 96 parallel projections spaced evenly within 180°. Accurate alignment of the projections is achieved with a cross-correlation method following data acquisition. Application of the optical tomography reconstruction technique to an intact cochlea permits measurement of internal structures with 16-μm pixels and a diffraction-limited resolution of 24 μm.

© 1992 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. N. Hounsfield, “Computerized transverse axial scanning (tomography): part I. Description of system,” Brit. J. Radiol. 46, 1016–1022 (1973).
    [CrossRef] [PubMed]
  2. B. A. Bohne, “Location of small cochlear lesions by phase contrast microscopy prior to thin sectioning,” Laryngoscope 82, 1–16 (1972).
    [PubMed]
  3. S. R. Ray, H. G. Semerjian, “Laser tomography for simultaneous concentration and temperature measurement in reacting flows,” Prog. Astronaut. Aeronaut. 92, 300–324 (1983).
  4. S. Kawata, O. Nakamura, S. Minami, “Optical microscope tomography. I. support constraint,” J. Opt. Soc. Am. A 4, 292–297 (1987).
    [CrossRef]
  5. O. Nakamura, S. Kawata, S. Minami, “Optical microscope tomography. II. Nonnegative constraint by a gradient-projection method,” J. Opt. Soc. Am. A 5, 554–561 (1988).
    [CrossRef]
  6. S. Kawata, O. Nakamura, T. Noda, H. Ooki, K. Ogino, Y. Kuroiwa, S. Minami, “Laser computed-tomography microscope,” Appl. Opt. 29, 3805–3809 (1990).
    [CrossRef] [PubMed]
  7. K. E. Bennett, G. W. Faris, R. L. Byer, “Experimental optical fan beam tomography,” Appl. Opt. 23, 2678–2685 (1984).
    [CrossRef] [PubMed]
  8. G. W. Faris, R. L. Byer, “Quantitative optical tomographic imaging of a supersonic jet,” Opt. Lett. 11, 413–415 (1986).
    [CrossRef] [PubMed]
  9. D. J. DeRosier, A. Klug, “Reconstruction of three dimensional structures from electron micrographs,” Nature (London) 217, 130–134 (1968).
    [CrossRef]
  10. R. N. Bracewell, A. C. Riddle, “Inversion of fan-beam scans in radio astronomy,” Astrophys. J. 150, 427–434 (1967).
    [CrossRef]
  11. G. N. Ramachandran, A. V. Lakshminarayanan, “Three-dimensional reconstruction from radiographs and electron micrographs: application of convolutions instead of Fourier transforms,” Proc. Natl. Acad. Sci. USA 68, 2236–2240 (1971).
    [CrossRef] [PubMed]
  12. R. Gordon, R. Bender, G. T. Herman, “Algebraic reconstruction technique (ART) for three dimensional electron microscopy and x-ray photography,” J. Theor. Biol. 29, 471–481 (1970).
    [CrossRef] [PubMed]
  13. L. Hesselink, “Optical tomography,” in Handbook of Flow Visualization, W.-J. Yang, ed. (Hemisphere, New York, 1989), Chap. 20.
  14. N. Streibl, “Three-dimensional imaging by a microscope,” J. Opt. Soc. Am. A 2, 121–127 (1985).
    [CrossRef]
  15. R. Snyder, L. Hesselink, “Optical tomography for flow visualization of the density field around a revolving helicopter blade,” Appl. Opt. 23, 3650–3656 (1984).
    [CrossRef] [PubMed]
  16. R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965), pp. 194–198.
  17. N. Haq, “Application and evaluation of an imaging technique for 3-dimensional cochlear reconstruction,” M.S. thesis (University of Washington, Seattle, Wash., 1988).

1990 (1)

1988 (1)

1987 (1)

1986 (1)

1985 (1)

1984 (2)

1983 (1)

S. R. Ray, H. G. Semerjian, “Laser tomography for simultaneous concentration and temperature measurement in reacting flows,” Prog. Astronaut. Aeronaut. 92, 300–324 (1983).

1973 (1)

G. N. Hounsfield, “Computerized transverse axial scanning (tomography): part I. Description of system,” Brit. J. Radiol. 46, 1016–1022 (1973).
[CrossRef] [PubMed]

1972 (1)

B. A. Bohne, “Location of small cochlear lesions by phase contrast microscopy prior to thin sectioning,” Laryngoscope 82, 1–16 (1972).
[PubMed]

1971 (1)

G. N. Ramachandran, A. V. Lakshminarayanan, “Three-dimensional reconstruction from radiographs and electron micrographs: application of convolutions instead of Fourier transforms,” Proc. Natl. Acad. Sci. USA 68, 2236–2240 (1971).
[CrossRef] [PubMed]

1970 (1)

R. Gordon, R. Bender, G. T. Herman, “Algebraic reconstruction technique (ART) for three dimensional electron microscopy and x-ray photography,” J. Theor. Biol. 29, 471–481 (1970).
[CrossRef] [PubMed]

1968 (1)

D. J. DeRosier, A. Klug, “Reconstruction of three dimensional structures from electron micrographs,” Nature (London) 217, 130–134 (1968).
[CrossRef]

1967 (1)

R. N. Bracewell, A. C. Riddle, “Inversion of fan-beam scans in radio astronomy,” Astrophys. J. 150, 427–434 (1967).
[CrossRef]

Bender, R.

R. Gordon, R. Bender, G. T. Herman, “Algebraic reconstruction technique (ART) for three dimensional electron microscopy and x-ray photography,” J. Theor. Biol. 29, 471–481 (1970).
[CrossRef] [PubMed]

Bennett, K. E.

Bohne, B. A.

B. A. Bohne, “Location of small cochlear lesions by phase contrast microscopy prior to thin sectioning,” Laryngoscope 82, 1–16 (1972).
[PubMed]

Bracewell, R. N.

R. N. Bracewell, A. C. Riddle, “Inversion of fan-beam scans in radio astronomy,” Astrophys. J. 150, 427–434 (1967).
[CrossRef]

R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965), pp. 194–198.

Byer, R. L.

DeRosier, D. J.

D. J. DeRosier, A. Klug, “Reconstruction of three dimensional structures from electron micrographs,” Nature (London) 217, 130–134 (1968).
[CrossRef]

Faris, G. W.

Gordon, R.

R. Gordon, R. Bender, G. T. Herman, “Algebraic reconstruction technique (ART) for three dimensional electron microscopy and x-ray photography,” J. Theor. Biol. 29, 471–481 (1970).
[CrossRef] [PubMed]

Haq, N.

N. Haq, “Application and evaluation of an imaging technique for 3-dimensional cochlear reconstruction,” M.S. thesis (University of Washington, Seattle, Wash., 1988).

Herman, G. T.

R. Gordon, R. Bender, G. T. Herman, “Algebraic reconstruction technique (ART) for three dimensional electron microscopy and x-ray photography,” J. Theor. Biol. 29, 471–481 (1970).
[CrossRef] [PubMed]

Hesselink, L.

R. Snyder, L. Hesselink, “Optical tomography for flow visualization of the density field around a revolving helicopter blade,” Appl. Opt. 23, 3650–3656 (1984).
[CrossRef] [PubMed]

L. Hesselink, “Optical tomography,” in Handbook of Flow Visualization, W.-J. Yang, ed. (Hemisphere, New York, 1989), Chap. 20.

Hounsfield, G. N.

G. N. Hounsfield, “Computerized transverse axial scanning (tomography): part I. Description of system,” Brit. J. Radiol. 46, 1016–1022 (1973).
[CrossRef] [PubMed]

Kawata, S.

Klug, A.

D. J. DeRosier, A. Klug, “Reconstruction of three dimensional structures from electron micrographs,” Nature (London) 217, 130–134 (1968).
[CrossRef]

Kuroiwa, Y.

Lakshminarayanan, A. V.

G. N. Ramachandran, A. V. Lakshminarayanan, “Three-dimensional reconstruction from radiographs and electron micrographs: application of convolutions instead of Fourier transforms,” Proc. Natl. Acad. Sci. USA 68, 2236–2240 (1971).
[CrossRef] [PubMed]

Minami, S.

Nakamura, O.

Noda, T.

Ogino, K.

Ooki, H.

Ramachandran, G. N.

G. N. Ramachandran, A. V. Lakshminarayanan, “Three-dimensional reconstruction from radiographs and electron micrographs: application of convolutions instead of Fourier transforms,” Proc. Natl. Acad. Sci. USA 68, 2236–2240 (1971).
[CrossRef] [PubMed]

Ray, S. R.

S. R. Ray, H. G. Semerjian, “Laser tomography for simultaneous concentration and temperature measurement in reacting flows,” Prog. Astronaut. Aeronaut. 92, 300–324 (1983).

Riddle, A. C.

R. N. Bracewell, A. C. Riddle, “Inversion of fan-beam scans in radio astronomy,” Astrophys. J. 150, 427–434 (1967).
[CrossRef]

Semerjian, H. G.

S. R. Ray, H. G. Semerjian, “Laser tomography for simultaneous concentration and temperature measurement in reacting flows,” Prog. Astronaut. Aeronaut. 92, 300–324 (1983).

Snyder, R.

Streibl, N.

Appl. Opt. (3)

Astrophys. J. (1)

R. N. Bracewell, A. C. Riddle, “Inversion of fan-beam scans in radio astronomy,” Astrophys. J. 150, 427–434 (1967).
[CrossRef]

Brit. J. Radiol. (1)

G. N. Hounsfield, “Computerized transverse axial scanning (tomography): part I. Description of system,” Brit. J. Radiol. 46, 1016–1022 (1973).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (3)

J. Theor. Biol. (1)

R. Gordon, R. Bender, G. T. Herman, “Algebraic reconstruction technique (ART) for three dimensional electron microscopy and x-ray photography,” J. Theor. Biol. 29, 471–481 (1970).
[CrossRef] [PubMed]

Laryngoscope (1)

B. A. Bohne, “Location of small cochlear lesions by phase contrast microscopy prior to thin sectioning,” Laryngoscope 82, 1–16 (1972).
[PubMed]

Nature (London) (1)

D. J. DeRosier, A. Klug, “Reconstruction of three dimensional structures from electron micrographs,” Nature (London) 217, 130–134 (1968).
[CrossRef]

Opt. Lett. (1)

Proc. Natl. Acad. Sci. USA (1)

G. N. Ramachandran, A. V. Lakshminarayanan, “Three-dimensional reconstruction from radiographs and electron micrographs: application of convolutions instead of Fourier transforms,” Proc. Natl. Acad. Sci. USA 68, 2236–2240 (1971).
[CrossRef] [PubMed]

Prog. Astronaut. Aeronaut. (1)

S. R. Ray, H. G. Semerjian, “Laser tomography for simultaneous concentration and temperature measurement in reacting flows,” Prog. Astronaut. Aeronaut. 92, 300–324 (1983).

Other (3)

L. Hesselink, “Optical tomography,” in Handbook of Flow Visualization, W.-J. Yang, ed. (Hemisphere, New York, 1989), Chap. 20.

R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965), pp. 194–198.

N. Haq, “Application and evaluation of an imaging technique for 3-dimensional cochlear reconstruction,” M.S. thesis (University of Washington, Seattle, Wash., 1988).

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 (9)

Fig. 1
Fig. 1

Tilt stage and immersion chamber. The θ tilt axis is parallel to the z and z′ axes. Angle α is fixed at 25°.

Fig. 2
Fig. 2

Computed optical tomography system.

Fig. 3
Fig. 3

Projection optics: (a) divergence of rays through the reconstruction volume, (b) defocus of rays away from the object plane. σ, cone angle between optical axis and principal ray; p, amount of defocus.

Fig. 4
Fig. 4

Photographs of test object results: (a) OD density projection of the test object at θ = 0°, (b) transaxial cross section of the reconstruction at z = 0. OD’s are represented with a gray scale from 0 (black) to 127 (white).

Fig. 5
Fig. 5

Distributions of (a) projected OD, (b) reconstructed OD.

Fig. 6
Fig. 6

Projected boundary points of pipet 1. The best-fit circle, centered on the cross hairs, is plotted through the points.

Fig. 7
Fig. 7

OD profiles: (a) Reconstructed OD of pipet 1 plotted as a function of the distance from the pipet’s centroid and spatial frequency wc in cycles/per millimeter, (b) projected OD profile of pipet 1. The expected curves are those for a uniform disk with 289-μm radius. In the case of the projection profiles, the expected curve represents the chord length across a pipet cross section.

Fig. 8
Fig. 8

Cochlea images: (a) OD projection of the cochlea, (b) transaxial section of the reconstruction at z = −80 μm with a horizontal line drawn at y = 0, (c) axial section of the reconstruction at y = 0 with a horizontal line drawn at z = −80 μm. The added lines are drawn at the intersections of the transaxial (b) and the axial (c) sections. The arrows in (b) and (c) point to the tectorial membrane, a brightly stained region of the cochlea.

Fig. 9
Fig. 9

3-D representation of the central point of the tectorial membrane.

Tables (1)

Tables Icon

Table 1 Integrated Optical Density (OD) of the Expected, Projected, and Reconstructed Test Objecta

Equations (3)

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

OD θ ( x , z ) = - μ ( x , y , z ) d y = log [ I 0 ( x , z ) / I ( x , z ) ] ,
Δ r max = R max 2 d 2 ,
p ( y ) = a y d 2 .

Metrics