Abstract

A novel method to obtain the three-dimensional mathematical model of a transparent object from its hologram is presented. The proposed method can numerically extract the object information from the fringe pattern of the hologram. Then an iterative algorithm is used to imitate an imaging system by focusing on different layers of the object; and by operating in both the spatial domain and the frequency domain, the algorithm produces a series of two-dimensional layer images. The object is finally reconstructed layer by layer. A constraint condition should be satisfied, and the noise distribution can be rearranged in different reconstruction cycles so as to get better reconstruction quality. Numerical simulations have proved the effectiveness of the proposed method.

© 2001 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. A. Kronrod, L. P. Yaroslavskii, N. S. Merzlyakov, “Computer synthesis of transparency holograms,” Sov. Phys. Tech. Phys. 17, 329–332 (1972).
  2. M. A. Kronrod, N. S. Merzlyakov, L. P. Yaroslavskii, “Reconstruction of holograms with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).
  3. L. Onural, P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
    [CrossRef]
  4. G. Liu, P. D. Scott, “Hologram phase retrieval and twin-image elimination for in-line Fresnel holograms,” J. Opt. Soc. Am. A 4, 159 (1987).
    [CrossRef]
  5. I. Kodama, M. Yamaguchi, N. Ohyama, T. Honda, K. Shinohara, A. Ito, T. Matsumura, K. Kinoshita, K. Yada, “Image reconstruction from an in-line x-ray hologram with intensity distribution constraint,” Opt. Commun. 125, 36–42 (1996).
    [CrossRef]
  6. U. Schnars, W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
    [CrossRef] [PubMed]
  7. J. Pomarico, U. Schnars, H.-J. Hartmann, W. Jüptner, “Digital recording and numerical reconstruction of holo-grams: a new method for displaying light in flight,” Appl. Opt. 34, 8095–8099 (1995).
    [CrossRef] [PubMed]
  8. Y. Kajiki, N. Ueda, “Three-dimensional shape measurement using images reconstructed by the computer from a hologram,” in Practical Holography VIII, S. Benton, ed., Proc. SPIE2176, 272–282 (1994).
    [CrossRef]
  9. B. Nilsson, T. E. Carlsson, “Direct three-dimensional shape measurement by digital light-in-flight holography,” Appl. Opt. 37, 7954–7959 (1998).
    [CrossRef]
  10. U. Schnars, “Direct phase determination in hologram interferometry with use of digitally recorded holograms,” J. Opt. Soc. Am. A 11, 2011–2015 (1994).
    [CrossRef]
  11. E. Cuche, F. Bevilacqua, C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. 24, 291–293 (1999).
    [CrossRef]
  12. E. Cuche, P. Marquet, 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]
  13. F. Dubois, L. Joannes, J. Legros, “Improved three-dimensional imaging with a digital holography microscope with a source of partial spatial coherence,” Appl. Opt. 38, 7085–7094 (1999).
    [CrossRef]
  14. I. Yamaguchi, T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
    [CrossRef] [PubMed]
  15. T. Zhang, I. Yamaguchi, “Three-dimensional microscopy with phase-shifting digital holography,” Opt. Lett. 23, 1221–1223 (1998).
    [CrossRef]
  16. D. A. Agard, “Optical sectioning microscopy: cellular architecture in three dimensions,” Annu. Rev. Biophys. Bioeng. 13, 191–219 (1984).
    [CrossRef] [PubMed]
  17. P. Hariharan, Optical Holography, Principles, Techniques, and Applications, 2nd ed. (Cambridge U. Press, New York, 1996), Chap. 2.2, pp. 13–18.
  18. R. J. Collier, C. B. Bruckhardt, L. H. Lin, Optical Holography (Academic, San Diego, Calif., 1971), Chap. 5.2, pp. 101.
  19. A. K. Jain, Fundamentals of Digital Image Processing (Prentice–Hall, Englewood Cliffs, NJ, 1989), Chap. 9.4, pp. 347–357.
  20. M. Heuckel, “An operator which locates edges in digitized pictures,” J. Assoc. Comput. Mach. 18(1), 113–125.
  21. P. Das, Lasers and Optical Engineering (Springer–Verlag, New York, 1991), Chap. 2.4, pp. 81.
  22. L. P. Yaroslavskii, N. S. Merzlyakov, Methods of Digital Holography (Consultants Bureau, New York, 1980), Chap. 1, pp. 9–15.

1999

1998

1997

1996

I. Kodama, M. Yamaguchi, N. Ohyama, T. Honda, K. Shinohara, A. Ito, T. Matsumura, K. Kinoshita, K. Yada, “Image reconstruction from an in-line x-ray hologram with intensity distribution constraint,” Opt. Commun. 125, 36–42 (1996).
[CrossRef]

1995

1994

1987

1984

D. A. Agard, “Optical sectioning microscopy: cellular architecture in three dimensions,” Annu. Rev. Biophys. Bioeng. 13, 191–219 (1984).
[CrossRef] [PubMed]

1972

M. A. Kronrod, L. P. Yaroslavskii, N. S. Merzlyakov, “Computer synthesis of transparency holograms,” Sov. Phys. Tech. Phys. 17, 329–332 (1972).

M. A. Kronrod, N. S. Merzlyakov, L. P. Yaroslavskii, “Reconstruction of holograms with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

Agard, D. A.

D. A. Agard, “Optical sectioning microscopy: cellular architecture in three dimensions,” Annu. Rev. Biophys. Bioeng. 13, 191–219 (1984).
[CrossRef] [PubMed]

Bevilacqua, F.

Bruckhardt, C. B.

R. J. Collier, C. B. Bruckhardt, L. H. Lin, Optical Holography (Academic, San Diego, Calif., 1971), Chap. 5.2, pp. 101.

Carlsson, T. E.

Collier, R. J.

R. J. Collier, C. B. Bruckhardt, L. H. Lin, Optical Holography (Academic, San Diego, Calif., 1971), Chap. 5.2, pp. 101.

Cuche, E.

Das, P.

P. Das, Lasers and Optical Engineering (Springer–Verlag, New York, 1991), Chap. 2.4, pp. 81.

Depeursinge, C.

Dubois, F.

Hariharan, P.

P. Hariharan, Optical Holography, Principles, Techniques, and Applications, 2nd ed. (Cambridge U. Press, New York, 1996), Chap. 2.2, pp. 13–18.

Hartmann, H.-J.

Heuckel, M.

M. Heuckel, “An operator which locates edges in digitized pictures,” J. Assoc. Comput. Mach. 18(1), 113–125.

Honda, T.

I. Kodama, M. Yamaguchi, N. Ohyama, T. Honda, K. Shinohara, A. Ito, T. Matsumura, K. Kinoshita, K. Yada, “Image reconstruction from an in-line x-ray hologram with intensity distribution constraint,” Opt. Commun. 125, 36–42 (1996).
[CrossRef]

Ito, A.

I. Kodama, M. Yamaguchi, N. Ohyama, T. Honda, K. Shinohara, A. Ito, T. Matsumura, K. Kinoshita, K. Yada, “Image reconstruction from an in-line x-ray hologram with intensity distribution constraint,” Opt. Commun. 125, 36–42 (1996).
[CrossRef]

Jain, A. K.

A. K. Jain, Fundamentals of Digital Image Processing (Prentice–Hall, Englewood Cliffs, NJ, 1989), Chap. 9.4, pp. 347–357.

Joannes, L.

Jüptner, W.

Kajiki, Y.

Y. Kajiki, N. Ueda, “Three-dimensional shape measurement using images reconstructed by the computer from a hologram,” in Practical Holography VIII, S. Benton, ed., Proc. SPIE2176, 272–282 (1994).
[CrossRef]

Kinoshita, K.

I. Kodama, M. Yamaguchi, N. Ohyama, T. Honda, K. Shinohara, A. Ito, T. Matsumura, K. Kinoshita, K. Yada, “Image reconstruction from an in-line x-ray hologram with intensity distribution constraint,” Opt. Commun. 125, 36–42 (1996).
[CrossRef]

Kodama, I.

I. Kodama, M. Yamaguchi, N. Ohyama, T. Honda, K. Shinohara, A. Ito, T. Matsumura, K. Kinoshita, K. Yada, “Image reconstruction from an in-line x-ray hologram with intensity distribution constraint,” Opt. Commun. 125, 36–42 (1996).
[CrossRef]

Kronrod, M. A.

M. A. Kronrod, L. P. Yaroslavskii, N. S. Merzlyakov, “Computer synthesis of transparency holograms,” Sov. Phys. Tech. Phys. 17, 329–332 (1972).

M. A. Kronrod, N. S. Merzlyakov, L. P. Yaroslavskii, “Reconstruction of holograms with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

Legros, J.

Lin, L. H.

R. J. Collier, C. B. Bruckhardt, L. H. Lin, Optical Holography (Academic, San Diego, Calif., 1971), Chap. 5.2, pp. 101.

Liu, G.

Marquet, P.

Matsumura, T.

I. Kodama, M. Yamaguchi, N. Ohyama, T. Honda, K. Shinohara, A. Ito, T. Matsumura, K. Kinoshita, K. Yada, “Image reconstruction from an in-line x-ray hologram with intensity distribution constraint,” Opt. Commun. 125, 36–42 (1996).
[CrossRef]

Merzlyakov, N. S.

M. A. Kronrod, L. P. Yaroslavskii, N. S. Merzlyakov, “Computer synthesis of transparency holograms,” Sov. Phys. Tech. Phys. 17, 329–332 (1972).

M. A. Kronrod, N. S. Merzlyakov, L. P. Yaroslavskii, “Reconstruction of holograms with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

L. P. Yaroslavskii, N. S. Merzlyakov, Methods of Digital Holography (Consultants Bureau, New York, 1980), Chap. 1, pp. 9–15.

Nilsson, B.

Ohyama, N.

I. Kodama, M. Yamaguchi, N. Ohyama, T. Honda, K. Shinohara, A. Ito, T. Matsumura, K. Kinoshita, K. Yada, “Image reconstruction from an in-line x-ray hologram with intensity distribution constraint,” Opt. Commun. 125, 36–42 (1996).
[CrossRef]

Onural, L.

L. Onural, P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
[CrossRef]

Pomarico, J.

Schnars, U.

Scott, P. D.

Shinohara, K.

I. Kodama, M. Yamaguchi, N. Ohyama, T. Honda, K. Shinohara, A. Ito, T. Matsumura, K. Kinoshita, K. Yada, “Image reconstruction from an in-line x-ray hologram with intensity distribution constraint,” Opt. Commun. 125, 36–42 (1996).
[CrossRef]

Ueda, N.

Y. Kajiki, N. Ueda, “Three-dimensional shape measurement using images reconstructed by the computer from a hologram,” in Practical Holography VIII, S. Benton, ed., Proc. SPIE2176, 272–282 (1994).
[CrossRef]

Yada, K.

I. Kodama, M. Yamaguchi, N. Ohyama, T. Honda, K. Shinohara, A. Ito, T. Matsumura, K. Kinoshita, K. Yada, “Image reconstruction from an in-line x-ray hologram with intensity distribution constraint,” Opt. Commun. 125, 36–42 (1996).
[CrossRef]

Yamaguchi, I.

Yamaguchi, M.

I. Kodama, M. Yamaguchi, N. Ohyama, T. Honda, K. Shinohara, A. Ito, T. Matsumura, K. Kinoshita, K. Yada, “Image reconstruction from an in-line x-ray hologram with intensity distribution constraint,” Opt. Commun. 125, 36–42 (1996).
[CrossRef]

Yaroslavskii, L. P.

M. A. Kronrod, N. S. Merzlyakov, L. P. Yaroslavskii, “Reconstruction of holograms with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

M. A. Kronrod, L. P. Yaroslavskii, N. S. Merzlyakov, “Computer synthesis of transparency holograms,” Sov. Phys. Tech. Phys. 17, 329–332 (1972).

L. P. Yaroslavskii, N. S. Merzlyakov, Methods of Digital Holography (Consultants Bureau, New York, 1980), Chap. 1, pp. 9–15.

Zhang, T.

Annu. Rev. Biophys. Bioeng.

D. A. Agard, “Optical sectioning microscopy: cellular architecture in three dimensions,” Annu. Rev. Biophys. Bioeng. 13, 191–219 (1984).
[CrossRef] [PubMed]

Appl. Opt.

J. Assoc. Comput. Mach.

M. Heuckel, “An operator which locates edges in digitized pictures,” J. Assoc. Comput. Mach. 18(1), 113–125.

J. Opt. Soc. Am. A

Opt. Commun.

I. Kodama, M. Yamaguchi, N. Ohyama, T. Honda, K. Shinohara, A. Ito, T. Matsumura, K. Kinoshita, K. Yada, “Image reconstruction from an in-line x-ray hologram with intensity distribution constraint,” Opt. Commun. 125, 36–42 (1996).
[CrossRef]

Opt. Eng.

L. Onural, P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
[CrossRef]

Opt. Lett.

Sov. Phys. Tech. Phys.

M. A. Kronrod, L. P. Yaroslavskii, N. S. Merzlyakov, “Computer synthesis of transparency holograms,” Sov. Phys. Tech. Phys. 17, 329–332 (1972).

M. A. Kronrod, N. S. Merzlyakov, L. P. Yaroslavskii, “Reconstruction of holograms with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

Other

Y. Kajiki, N. Ueda, “Three-dimensional shape measurement using images reconstructed by the computer from a hologram,” in Practical Holography VIII, S. Benton, ed., Proc. SPIE2176, 272–282 (1994).
[CrossRef]

P. Hariharan, Optical Holography, Principles, Techniques, and Applications, 2nd ed. (Cambridge U. Press, New York, 1996), Chap. 2.2, pp. 13–18.

R. J. Collier, C. B. Bruckhardt, L. H. Lin, Optical Holography (Academic, San Diego, Calif., 1971), Chap. 5.2, pp. 101.

A. K. Jain, Fundamentals of Digital Image Processing (Prentice–Hall, Englewood Cliffs, NJ, 1989), Chap. 9.4, pp. 347–357.

P. Das, Lasers and Optical Engineering (Springer–Verlag, New York, 1991), Chap. 2.4, pp. 81.

L. P. Yaroslavskii, N. S. Merzlyakov, Methods of Digital Holography (Consultants Bureau, New York, 1980), Chap. 1, pp. 9–15.

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 (25)

Fig. 1
Fig. 1

3-D object expressed as many sectioning images.

Fig. 2
Fig. 2

3-D object in the light path of an optical arrangement.

Fig. 3
Fig. 3

Hologram recording with an off-axis reference beam.

Fig. 4
Fig. 4

Spatial frequency of (a) a hologram recorded with an off-axis reference beam, (b) the object beam.

Fig. 5
Fig. 5

Texture of the two layers.

Fig. 6
Fig. 6

(a) Object with two layers, (b) arrangement for forming an off-axis hologram.

Fig. 7
Fig. 7

Hologram.

Fig. 8
Fig. 8

Reconstructed images with Fresnel transformation method.

Fig. 9
Fig. 9

Spectrum of the hologram.

Fig. 10
Fig. 10

Object spectrum.

Fig. 11
Fig. 11

Sectioning images of layer 1 and layer 2.

Fig. 12
Fig. 12

Sectioning images (a) before layer 1, (b) between two layers, (c) after layer 2.

Fig. 13
Fig. 13

PLI’s after our algorithm when dl=0.2 m.

Fig. 14
Fig. 14

Sectioning images after our algorithm when dl=0.1 m.

Fig. 15
Fig. 15

Sectioning images after our algorithm when dl=0.05 m.

Fig. 16
Fig. 16

Sectioning images of the two-layer object with textures along the same axis.

Fig. 17
Fig. 17

Results of the first reconstruction cycle: (a) PLI of layer 1, (b) sectioning image of layer 2, (c) PLI of layer 2.

Fig. 18
Fig. 18

Results of the second reconstruction cycle: (a) PLI of layer 2, (b) sectioning image of layer 1, (c) PLI of layer 1.

Fig. 19
Fig. 19

Averaged PLI of the two layers.

Fig. 20
Fig. 20

Three-layer object’s (a) textures, (b) arrangement.

Fig. 21
Fig. 21

Sectioning images of the three-layer object.

Fig. 22
Fig. 22

First reconstruction cycle: PLI of (a) layer 1, (b) layer 2, (c) layer 3.

Fig. 23
Fig. 23

Second reconstruction cycle: PLI of (a) layer 2, (b) layer 3, and (c) layer 1.

Fig. 24
Fig. 24

Third reconstruction cycle: PLI of (a) layer 3, (b) layer 1, and (c) layer 2.

Fig. 25
Fig. 25

PLI’s after average: (a) layer 1, (b) layer 2, and (c) layer 3.

Tables (1)

Tables Icon

Table 1 Comparison of Time Used for Different Algorithms

Equations (37)

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

o(x, y)=i=1nli(x, y),
O(ξ, η)=i=1nLi(ξ, η),
ei(x, y)=li(x, y)-li(x, y),
Ei(ξ, η)=Li(ξ, η)-Li(ξ, η).
i=1nLi(ξ, η)=O(ξ, η)=constant.
i=1nEi(ξ, η)=0.
Ei(ξ, η)=Re[Ei(ξ, η)]+i Im[Ei(ξ, η)]
i=1n Re[Ei(ξ, η)]=0,
i=1n Im[Ei(ξ, η)]=0.
o(x, y)=|o(x, y)|exp[-iϕ(x, y)].
I(x, y)=|r(x, y)+o(x, y)|2=r2+|o(x, y)|2+r|o(x, y)|exp[-iϕ(x, y)]exp(-i2πξr)+r|o(x, y)|exp[iϕ(x, y)]exp(i22πξr).
U1(ξ, η)=F{r2}=r2δ(ξ, η),
U2(ξ, η)=F{|o(x, y)|2}=O(ξ, η)*O(ξ, η),
U3(ξ, η)=F{r|o(x, y)|exp[-iϕ(x, y)]×exp(-i2πξr)}=rO(ξ, η)δ(ξ-ξr, η),
U4(ξ, η)=F{r|o(x, y)|exp[iϕ(x, y)]exp(i2πξr)}=rO*(ξ, η)δ(ξ+ξr, η),
a(x, y)z=di
=a(x, y)z=dk×expi2π(di-dk)λ(1-λ2ξ2-λ2η2)1/2
=a(x, y)z=dk exp[i2π(di-dk)×(1/λ2-ξ2-η2)1/2],
A(ξ, η)z=di=A(ξ, η)z=dk×exp[i2π(di-dk)(1/λ2-ξ2-η2)1/2],
A(ξ, η)z=0=O(ξ, η).
A(ξ, η)z=di=A(ξ, η)z=0 exp[i2πdi(1/λ2-ξ2-η2)1/2]=O(ξ, η)exp[i2πdi(1/λ2-ξ2-η2)1/2],
a(x, y)z=di=F-1{A(ξ, η)z=di}=A(ξ, η)z=di exp[i2π(ξx+ηy)]dξdη,
aPLI(x, y)z=di=ET{[a(x, y)z=di]}(fori=1, , n).
a(x, y)z=di=aPLI(x, y)z=di+aOFI(x, y)z=di.
a(x, y)z=di=F-1{N(ξ, η)-M(ξ, η)},(i=1, 2, 3, , n)
N(ξ, η)=O(ξ, η)exp[i2πdi(1/λ2-ξ2-η2)1/2],
M(ξ, η)=k=1i-1APLI(ξ, η)z=dk exp[i2π(di-dk)(1/λ2-ξ2-η2)1/2](i=2, 3, , n)0(i=1),
A(ξ, η)z=dn=O(ξ, η)exp[i2πdn(1/λ2-ξ2-η2)1/2]-k=1n-1APLI(ξ, η)z=dk exp[i2π(dn-dk)×(1/λ2-ξ2-η2)1/2].
O(ξ, η)=k=1n-1APLI(ξ, η)z=dk×exp[-i2πdk(1/λ2-ξ2-η2)1/2]+A(ξ, η)z=dn exp[-i2πdn×(1/λ2-ξ2-η2)1/2].
AOFI(ξ, η)z=dn=0,
A(ξ, η)z=dn=APLI(ξ, η)z=dn.
O(ξ, η)=k=1nAPLI(ξ, η)z=dk×exp[-i2πdk(1/λ2-ξ2-η2)1/2],
Ak(ξ, η)=APLI(ξ, η)z=dk×exp[-i2πdk(1/λ2-ξ2-η2)1/2].
k=1nAk(ξ, η)=O(ξ, η)=const.
a¯PLI(x, y)z=di=1/Ll=1LaPLIl(x, y)z=di(i=1, 2,, n,l=1, 2,.., L)
a¯PLI(x, y)z=di=ET[1/Ll=1Lal(x, y)z=di](i=1, 2, , n,l=1, 2,, L),
ET{[a(x, y)z=di]}=a(x, y)z=diwhena(x, y)z=di0.5*MAX[a(x, y)z=di]0whena(x, y)z=di<0.5*MAX[a(x, y)z=di],

Metrics