Abstract

We discuss the quantitative location of objects from holographic images when the reconstruction wavelength differs from the recording wavelength. The holographic image equations are interpreted in a way that clarifies the meaning of stereo pairs of holographic images and indicates how backprojection methods can be used in holography to locate objects. Alternative methods involving the production of distortion-free regions in the holographic image field during reconstruction, the use of self-calibrating objects in the object field during recording, and triangulation can be used to locate objects.

© 1998 Optical Society of America

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References

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  1. R. W. Meier, “Magnification and third-order aberrations in holography,” J. Opt. Soc. Am. 55, 987–992 (1965).
  2. R. J. Collier, C. B. Burkhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).
  3. R. R. A. Syms, Practical Volume Holography (Clarendon, Oxford, 1990).
  4. P. Hariharan, Optical Holography, 2nd ed. (Cambridge U. Press, New York, 1996).
  5. A. K. Jain, Fundamentals of Digital Image Processing (Prentice Hall, Englewood Cliffs, N.J., 1989), Chap. 10.
  6. A. C. Kak, “Image reconstruction from projections,” in Digital Image Processing Techniques, M. P. Ekstrom, ed. (Academic, New York, 1984), pp. 111–171.
  7. S. W. Rowland, “Computer implementation of image reconstruction formulas,” in Image Reconstruction from Projections, Vol. 32 of Topics in Applied Physics (Springer-Verlag, New York, 1979), pp. 9–79.
    [CrossRef]
  8. G. T. Herman, Image Reconstruction From Projections: The Fundamentals of Computerized Tomography (Academic Press, New York, 1980).
  9. C. Anderson, J. Gordon, D. Watts, J. Marsh, “Measurement of behind-armor debris using cylindrical holograms,” Practical Holography IX, A. Benton, ed., Proc. SPIE2406, 132–146 (1995).
    [CrossRef]
  10. C. Anderson, J. Gordon, D. Watts, J. Marsh, “Measurement of behind-arm or debris using cylindrical holograms,” Opt. Eng. 36, 40–46 (1997).
    [CrossRef]
  11. E. B. Champagne, “Nonparaxial imaging, magnification, and aberration properties in holography,” J. Opt. Soc. Am. 57, 51–55 (1967).
    [CrossRef]
  12. J. M. Rebordao, “General form for aberration coefficients in holography,” J. Opt. Soc. Am. A 1, 788–790 (1984).
    [CrossRef]
  13. K.-O. Peng, H. J. Frankena, “Nonparaxial theory of curved holograms,” Appl. Opt. 25, 1319–1326 (1986).
    [CrossRef] [PubMed]
  14. G. H. Spencer, M. V. R. K. Murty, “General ray-tracing procedure,” J. Opt. Soc. Am. 52, 672–678 (1962).
    [CrossRef]
  15. A. Offner, “Ray tracing through a holographic system,” J. Opt. Soc. Am. 56, 1509–1512 (1966).
    [CrossRef]
  16. I. A. Abramowitz, “Evaluation of hologram imaging by ray-tracing,” Appl. Opt. 8, 403–410 (1969).
    [CrossRef] [PubMed]

1997 (1)

C. Anderson, J. Gordon, D. Watts, J. Marsh, “Measurement of behind-arm or debris using cylindrical holograms,” Opt. Eng. 36, 40–46 (1997).
[CrossRef]

1986 (1)

1984 (1)

1969 (1)

1967 (1)

1966 (1)

1965 (1)

1962 (1)

Abramowitz, I. A.

Anderson, C.

C. Anderson, J. Gordon, D. Watts, J. Marsh, “Measurement of behind-arm or debris using cylindrical holograms,” Opt. Eng. 36, 40–46 (1997).
[CrossRef]

C. Anderson, J. Gordon, D. Watts, J. Marsh, “Measurement of behind-armor debris using cylindrical holograms,” Practical Holography IX, A. Benton, ed., Proc. SPIE2406, 132–146 (1995).
[CrossRef]

Burkhardt, C. B.

R. J. Collier, C. B. Burkhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

Champagne, E. B.

Collier, R. J.

R. J. Collier, C. B. Burkhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

Frankena, H. J.

Gordon, J.

C. Anderson, J. Gordon, D. Watts, J. Marsh, “Measurement of behind-arm or debris using cylindrical holograms,” Opt. Eng. 36, 40–46 (1997).
[CrossRef]

C. Anderson, J. Gordon, D. Watts, J. Marsh, “Measurement of behind-armor debris using cylindrical holograms,” Practical Holography IX, A. Benton, ed., Proc. SPIE2406, 132–146 (1995).
[CrossRef]

Hariharan, P.

P. Hariharan, Optical Holography, 2nd ed. (Cambridge U. Press, New York, 1996).

Herman, G. T.

G. T. Herman, Image Reconstruction From Projections: The Fundamentals of Computerized Tomography (Academic Press, New York, 1980).

Jain, A. K.

A. K. Jain, Fundamentals of Digital Image Processing (Prentice Hall, Englewood Cliffs, N.J., 1989), Chap. 10.

Kak, A. C.

A. C. Kak, “Image reconstruction from projections,” in Digital Image Processing Techniques, M. P. Ekstrom, ed. (Academic, New York, 1984), pp. 111–171.

Lin, L. H.

R. J. Collier, C. B. Burkhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

Marsh, J.

C. Anderson, J. Gordon, D. Watts, J. Marsh, “Measurement of behind-arm or debris using cylindrical holograms,” Opt. Eng. 36, 40–46 (1997).
[CrossRef]

C. Anderson, J. Gordon, D. Watts, J. Marsh, “Measurement of behind-armor debris using cylindrical holograms,” Practical Holography IX, A. Benton, ed., Proc. SPIE2406, 132–146 (1995).
[CrossRef]

Meier, R. W.

Murty, M. V. R. K.

Offner, A.

Peng, K.-O.

Rebordao, J. M.

Rowland, S. W.

S. W. Rowland, “Computer implementation of image reconstruction formulas,” in Image Reconstruction from Projections, Vol. 32 of Topics in Applied Physics (Springer-Verlag, New York, 1979), pp. 9–79.
[CrossRef]

Spencer, G. H.

Syms, R. R. A.

R. R. A. Syms, Practical Volume Holography (Clarendon, Oxford, 1990).

Watts, D.

C. Anderson, J. Gordon, D. Watts, J. Marsh, “Measurement of behind-arm or debris using cylindrical holograms,” Opt. Eng. 36, 40–46 (1997).
[CrossRef]

C. Anderson, J. Gordon, D. Watts, J. Marsh, “Measurement of behind-armor debris using cylindrical holograms,” Practical Holography IX, A. Benton, ed., Proc. SPIE2406, 132–146 (1995).
[CrossRef]

Appl. Opt. (2)

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (1)

Opt. Eng. (1)

C. Anderson, J. Gordon, D. Watts, J. Marsh, “Measurement of behind-arm or debris using cylindrical holograms,” Opt. Eng. 36, 40–46 (1997).
[CrossRef]

Other (8)

R. J. Collier, C. B. Burkhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

R. R. A. Syms, Practical Volume Holography (Clarendon, Oxford, 1990).

P. Hariharan, Optical Holography, 2nd ed. (Cambridge U. Press, New York, 1996).

A. K. Jain, Fundamentals of Digital Image Processing (Prentice Hall, Englewood Cliffs, N.J., 1989), Chap. 10.

A. C. Kak, “Image reconstruction from projections,” in Digital Image Processing Techniques, M. P. Ekstrom, ed. (Academic, New York, 1984), pp. 111–171.

S. W. Rowland, “Computer implementation of image reconstruction formulas,” in Image Reconstruction from Projections, Vol. 32 of Topics in Applied Physics (Springer-Verlag, New York, 1979), pp. 9–79.
[CrossRef]

G. T. Herman, Image Reconstruction From Projections: The Fundamentals of Computerized Tomography (Academic Press, New York, 1980).

C. Anderson, J. Gordon, D. Watts, J. Marsh, “Measurement of behind-armor debris using cylindrical holograms,” Practical Holography IX, A. Benton, ed., Proc. SPIE2406, 132–146 (1995).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Vectors pointing from the hologram pupil to the image point R i , the object point R o , the origin of the reference beam R r , and the origin of the reconstruction beam R c . ρ points to positions in the pupil (cf. Appendix A).

Fig. 2
Fig. 2

Illustration of the object location from stereo views of an image point. Rays from two views of an image point emerge from the cylindrical hologram going toward a′ and b′. These rays are bent at the surface of the hologram and come from the common point P inside the holographic volume. This is the location of the object point. A similar construction applies to backprojections. The image rays emerging from the hologram have been bent at the holographic surface.

Fig. 3
Fig. 3

Illustration of a nearly distortion-free region of a cylindrical hologram as viewed from the top. The nearly distortion-free region is, roughly, the slab between the dotted lines.

Fig. 4
Fig. 4

Illustration of a self-calibrating object in two dimensions. By lining up the images of point pairs ab, ac, and ad and noting the locations of the pupils, one can determine the actual positions of object points a, b, c, and d without knowing the positions of the reference and reconstruction beams.

Fig. 5
Fig. 5

Illustration of triangulation: If image point c is lined up with images of fiducial points a and b, and the pupil locations noted, one can locate object point c without knowing where the reference and the reconstruction beams are.

Equations (9)

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

1 R i = 1 R c + μ 1 R o - 1 R r ,
u i = u c + μ u o - u r   | .
1 R i = μ R o + Δ ,
u i = μ u o + ν   | ,
Δ = 1 R c - μ R r ,
ν = u c - μ u r .
r j = R j 2 - 2 ρ · R j + ρ 2 1 / 2 R j - ρ · u j + ρ 2 / 2 R j ,
- ρ · u c + μ u o - u r + 1 2   ρ 2 1 R c + μ 1 R o - 1 R r = - ρ · u i + 1 2   ρ 2 1 R i .
n ˆ × u i - u c = μ n ˆ × u o - u r ,

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