Abstract

We suggest a technique that allows reconstruction of three-dimensional objects with spatially incoherent broad-spectrum illuminating light sources. The reconstruction is obtained by the realization of a holographically recorded parallax-based stereo vision. Experimental results demonstrate the suggested technique.

© 2001 Optical Society of America

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References

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  1. D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
    [CrossRef] [PubMed]
  2. D. Gabor, “Microscopy by reconstructed wave fronts,” Proc. Roy. Soc. Biol. A 197, 454–487 (1949).
    [CrossRef]
  3. D. Gabor, “Microscopy by reconstructed wave fronts II,” Proc. Phys. Soc. London Sect. B 64, 449–469 (1951).
    [CrossRef]
  4. E. N. Leith, “Overview of the development of holography,” J. Imaging Sci. Technol. 41, 201–204 (1997).
  5. W. L. Bragg, “Microscopy by reconstructed wave fronts,” Nature 166, 399–400 (1950).
    [CrossRef] [PubMed]
  6. A. W. Lohmann, “Optische einseitenbandubertragung angewandt auf das Gabor–Mikroskop,” Opt. Acta 3, 97–100 (1956).
    [CrossRef]
  7. E. N. Leith, J. Upatnieks, “Wavefront reconstruction and communication theory,” J. Opt. Soc. Am. 52, 1123–1130 (1962).
    [CrossRef]
  8. J. D. Redman, “Novel approach to holography,” J. Sci. Instrum. 1, 821–822 (1968).
  9. S. A. Benton, “Hologram reconstructions with extended incoherent sources,” J. Opt. Soc. Am. 59, 1545–1546 (1969).
  10. R. V. Pole, “3-D imaging and holograms of objects illuminated in white light,” Appl. Phys. Lett. 10, 20–22 (1967).
    [CrossRef]
  11. Y. N. Denisyuk, “On the reproduction of the optical properties of an object by the wave fields of its scattered radiation,” Opt. Spectrosc. 15, 279–284 (1964).
  12. D. J. DeBotteto, “Holographic panoramic stereogram synthesis from white light recordings,” Appl. Opt. 8, 1740–1741 (1969).
    [CrossRef]
  13. J. T. McCrickerd, N. George, “Holographic stereogram from sequential components photographs,” Appl. Phys. Lett. 12, 10–12 (1968).
    [CrossRef]
  14. Z. Zalevsky, E. Leith, K. Mills, “Expanding system’s resolving abilities using spectral orthonormal coding multiplexing—Part I,” Opt. Commun. (to be published).
  15. A. R. Robertson, “The CIE 1976 color difference formula,” Color Res. Appl. 2, 7–11 (1977).

1997 (1)

E. N. Leith, “Overview of the development of holography,” J. Imaging Sci. Technol. 41, 201–204 (1997).

1977 (1)

A. R. Robertson, “The CIE 1976 color difference formula,” Color Res. Appl. 2, 7–11 (1977).

1969 (2)

S. A. Benton, “Hologram reconstructions with extended incoherent sources,” J. Opt. Soc. Am. 59, 1545–1546 (1969).

D. J. DeBotteto, “Holographic panoramic stereogram synthesis from white light recordings,” Appl. Opt. 8, 1740–1741 (1969).
[CrossRef]

1968 (2)

J. T. McCrickerd, N. George, “Holographic stereogram from sequential components photographs,” Appl. Phys. Lett. 12, 10–12 (1968).
[CrossRef]

J. D. Redman, “Novel approach to holography,” J. Sci. Instrum. 1, 821–822 (1968).

1967 (1)

R. V. Pole, “3-D imaging and holograms of objects illuminated in white light,” Appl. Phys. Lett. 10, 20–22 (1967).
[CrossRef]

1964 (1)

Y. N. Denisyuk, “On the reproduction of the optical properties of an object by the wave fields of its scattered radiation,” Opt. Spectrosc. 15, 279–284 (1964).

1962 (1)

1956 (1)

A. W. Lohmann, “Optische einseitenbandubertragung angewandt auf das Gabor–Mikroskop,” Opt. Acta 3, 97–100 (1956).
[CrossRef]

1951 (1)

D. Gabor, “Microscopy by reconstructed wave fronts II,” Proc. Phys. Soc. London Sect. B 64, 449–469 (1951).
[CrossRef]

1950 (1)

W. L. Bragg, “Microscopy by reconstructed wave fronts,” Nature 166, 399–400 (1950).
[CrossRef] [PubMed]

1949 (1)

D. Gabor, “Microscopy by reconstructed wave fronts,” Proc. Roy. Soc. Biol. A 197, 454–487 (1949).
[CrossRef]

1948 (1)

D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
[CrossRef] [PubMed]

Benton, S. A.

S. A. Benton, “Hologram reconstructions with extended incoherent sources,” J. Opt. Soc. Am. 59, 1545–1546 (1969).

Bragg, W. L.

W. L. Bragg, “Microscopy by reconstructed wave fronts,” Nature 166, 399–400 (1950).
[CrossRef] [PubMed]

DeBotteto, D. J.

Denisyuk, Y. N.

Y. N. Denisyuk, “On the reproduction of the optical properties of an object by the wave fields of its scattered radiation,” Opt. Spectrosc. 15, 279–284 (1964).

Gabor, D.

D. Gabor, “Microscopy by reconstructed wave fronts II,” Proc. Phys. Soc. London Sect. B 64, 449–469 (1951).
[CrossRef]

D. Gabor, “Microscopy by reconstructed wave fronts,” Proc. Roy. Soc. Biol. A 197, 454–487 (1949).
[CrossRef]

D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
[CrossRef] [PubMed]

George, N.

J. T. McCrickerd, N. George, “Holographic stereogram from sequential components photographs,” Appl. Phys. Lett. 12, 10–12 (1968).
[CrossRef]

Leith, E.

Z. Zalevsky, E. Leith, K. Mills, “Expanding system’s resolving abilities using spectral orthonormal coding multiplexing—Part I,” Opt. Commun. (to be published).

Leith, E. N.

E. N. Leith, “Overview of the development of holography,” J. Imaging Sci. Technol. 41, 201–204 (1997).

E. N. Leith, J. Upatnieks, “Wavefront reconstruction and communication theory,” J. Opt. Soc. Am. 52, 1123–1130 (1962).
[CrossRef]

Lohmann, A. W.

A. W. Lohmann, “Optische einseitenbandubertragung angewandt auf das Gabor–Mikroskop,” Opt. Acta 3, 97–100 (1956).
[CrossRef]

McCrickerd, J. T.

J. T. McCrickerd, N. George, “Holographic stereogram from sequential components photographs,” Appl. Phys. Lett. 12, 10–12 (1968).
[CrossRef]

Mills, K.

Z. Zalevsky, E. Leith, K. Mills, “Expanding system’s resolving abilities using spectral orthonormal coding multiplexing—Part I,” Opt. Commun. (to be published).

Pole, R. V.

R. V. Pole, “3-D imaging and holograms of objects illuminated in white light,” Appl. Phys. Lett. 10, 20–22 (1967).
[CrossRef]

Redman, J. D.

J. D. Redman, “Novel approach to holography,” J. Sci. Instrum. 1, 821–822 (1968).

Robertson, A. R.

A. R. Robertson, “The CIE 1976 color difference formula,” Color Res. Appl. 2, 7–11 (1977).

Upatnieks, J.

Zalevsky, Z.

Z. Zalevsky, E. Leith, K. Mills, “Expanding system’s resolving abilities using spectral orthonormal coding multiplexing—Part I,” Opt. Commun. (to be published).

Appl. Opt. (1)

Appl. Phys. Lett. (2)

J. T. McCrickerd, N. George, “Holographic stereogram from sequential components photographs,” Appl. Phys. Lett. 12, 10–12 (1968).
[CrossRef]

R. V. Pole, “3-D imaging and holograms of objects illuminated in white light,” Appl. Phys. Lett. 10, 20–22 (1967).
[CrossRef]

Color Res. Appl. (1)

A. R. Robertson, “The CIE 1976 color difference formula,” Color Res. Appl. 2, 7–11 (1977).

J. Imaging Sci. Technol. (1)

E. N. Leith, “Overview of the development of holography,” J. Imaging Sci. Technol. 41, 201–204 (1997).

J. Opt. Soc. Am. (2)

E. N. Leith, J. Upatnieks, “Wavefront reconstruction and communication theory,” J. Opt. Soc. Am. 52, 1123–1130 (1962).
[CrossRef]

S. A. Benton, “Hologram reconstructions with extended incoherent sources,” J. Opt. Soc. Am. 59, 1545–1546 (1969).

J. Sci. Instrum. (1)

J. D. Redman, “Novel approach to holography,” J. Sci. Instrum. 1, 821–822 (1968).

Nature (2)

W. L. Bragg, “Microscopy by reconstructed wave fronts,” Nature 166, 399–400 (1950).
[CrossRef] [PubMed]

D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
[CrossRef] [PubMed]

Opt. Acta (1)

A. W. Lohmann, “Optische einseitenbandubertragung angewandt auf das Gabor–Mikroskop,” Opt. Acta 3, 97–100 (1956).
[CrossRef]

Opt. Spectrosc. (1)

Y. N. Denisyuk, “On the reproduction of the optical properties of an object by the wave fields of its scattered radiation,” Opt. Spectrosc. 15, 279–284 (1964).

Proc. Phys. Soc. London Sect. B (1)

D. Gabor, “Microscopy by reconstructed wave fronts II,” Proc. Phys. Soc. London Sect. B 64, 449–469 (1951).
[CrossRef]

Proc. Roy. Soc. Biol. A (1)

D. Gabor, “Microscopy by reconstructed wave fronts,” Proc. Roy. Soc. Biol. A 197, 454–487 (1949).
[CrossRef]

Other (1)

Z. Zalevsky, E. Leith, K. Mills, “Expanding system’s resolving abilities using spectral orthonormal coding multiplexing—Part I,” Opt. Commun. (to be published).

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Figures (7)

Fig. 1
Fig. 1

Stereoscopic imaging configuration.

Fig. 2
Fig. 2

Grating interferometer.

Fig. 3
Fig. 3

Schematic sketch used for mathematical investigation.

Fig. 4
Fig. 4

Mach–Zhender interferometer used for the experimental recording.

Fig. 5
Fig. 5

Reconstruction configuration.

Fig. 6
Fig. 6

Experimental results. (a) The first stereoscopic reconstruction of target #1. (b) The second stereoscopic reconstruction of target #1. (c) The first stereoscopic reconstruction of target #2. (d) The second stereoscopic reconstruction of target #2.

Fig. 7
Fig. 7

Reconstruction of target #2 for a white-light illumination.

Equations (29)

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

Ix=|ux|2+|Rx|2+2 ReR*xux, texpiω0t,
Rx=exp-2πixν0  ux, t=uxut=uxexp-iΨt,
Ix=|ux|2+1+2uxγ cos2πν0x+ϕ,  γ expiϕ=utexpiω0t=1T0T exp-iψtexpiω0tdt,
γ=1,  ϕ=0,
γ=0,
0<γ<1.
x1=ΔX2-X0fR,  x2=-ΔX2+X0fR,
R=ΔXfx1-x2,
X0=x1+x2x2-x1ΔX2.
Ix=|u1x|2+|u2x|2+2+2γu1xcos2πν1x+ϕ1+u2xcos2πν2x+ϕ2,
λν1-ν2R=Δs,
Ix=n|unx|2+1+2γn unxcos2πν0x+ϕn.
Irecx=2γ n |unx|2
J12x1, x2=u2x1u2*x2= u1x¯1u1*x¯2hx1-x¯1×h*x2-x¯2dx¯1dx¯2,
u1x¯1u1*x¯2=Iinδx¯1-x¯2,  J12x1, x2= Iinδx¯1-x¯2hx1-x¯1×h*x2-x¯2dx¯1dx¯2,  =Iin  hx1-x¯1h*x2-x¯1dx¯1.
J12x1, x2=Gx1exp2πix1αG*x2×exp-2πix2αJ12x1, x2.
Gμ= gxexp-2πixμdx,
Ioμ= J12x1, x2exp-2πiμx1×exp2πiμx2dx1dx2,
Ioμ=Iin  exp2πiz1x¯1Hz1gμ-α-z1×exp-2πiz2x¯1H*z2×g*μ-α-z2dx¯1dz1dz2,
Hμ= hxexp-2πixμdx,
 exp-2πix1z2-z1dx¯1=δz2-z1,
Ioμ= |Hz|2|gμ-α-z|2dz.
J12x, x= ux0, texp-2πix0xdx0× ux0, texp-2πix0xdx0*,
ux0, tu*x0, t=rectx0/ΔxΔx2δx0-x0=rectx0/ΔxΔx2 δx0-x0,
J12x, x=sincΔxx-xΔx.
Ioμ= rectz/ΔxΔx2|gμ-α-z|2dz.
Δθ=Δs/R,
δx=2.44λf#=2.44λN.A.=2.440.5 μm4°π/180=18.3 μm.
λν2-ν1>8°180 π.

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