Abstract

A numerical reconstruction method believed to be new is proposed for hybrid holographic microscopy in which the hologram of a microscopic object is recorded by an image sensor and is then reconstructed by a computer. Because the Fresnel–Kirchhoff integral must be used for numerical reconstruction to achieve high resolution, we propose an approximation technique for reducing the calculation time. This approximation technique is suitable for microscopic application. The numerical reconstruction of 1-µm-sized objects was demonstrated with a He–Ne laser (λ = 0.6328 µm).

© 1999 Optical Society of America

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References

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    [CrossRef]
  3. E. Leith, J. Upatnieks, “Hologram microscopy and lens aberration compensation by the use of holograms,” J. Opt. Soc. Am. 55, 595 (1965).
  4. J. C. Solem, G. C. Baldwin, “Microholography of living organisms,” Science 218, 229–235 (1982).
    [CrossRef] [PubMed]
  5. J. C. Solem, G. F. Chapline, “X-ray biomicroholography,” Opt. Eng. 23, 193–203 (1984).
    [CrossRef]
  6. L. P. Yaroslavskii, N. S. Merzlyakov, Methods of Digital Holography (Consultants Bureau, New York, 1980).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  13. T.-C. Poon, M. H. Wu, K. Shinoda, Y. Suzuki, “Optical scanning holography,” Proc. IEEE 84, 753–764 (1996).
    [CrossRef]
  14. B. W. Schilling, T.-C. Poon, G. Indebetouw, B. Storrie, K. Shinoda, Y. Suzuki, M. H. Wu, “Three-dimensional holographic fluorescence microscopy,” Opt. Lett. 22, 1506–1508 (1997).
    [CrossRef]
  15. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
  16. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, New York, 1995).
    [CrossRef]

1997

1996

T.-C. Poon, M. H. Wu, K. Shinoda, Y. Suzuki, “Optical scanning holography,” Proc. IEEE 84, 753–764 (1996).
[CrossRef]

1995

J. Pomarico, U. Schnars, H.-J. Hartmann, W. Jüptner, “Digital recording and numerical reconstruction of holograms: a new method of displaying light in flight,” Appl. Opt. 34, 8095–8099 (1995).
[CrossRef] [PubMed]

T.-C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

1994

1992

1984

J. C. Solem, G. F. Chapline, “X-ray biomicroholography,” Opt. Eng. 23, 193–203 (1984).
[CrossRef]

1982

J. C. Solem, G. C. Baldwin, “Microholography of living organisms,” Science 218, 229–235 (1982).
[CrossRef] [PubMed]

1965

E. Leith, J. Upatnieks, “Hologram microscopy and lens aberration compensation by the use of holograms,” J. Opt. Soc. Am. 55, 595 (1965).

E. Leith, J. Upatnieks, “Microscopy by wavefront reconstruction,” J. Opt. Soc. Am. 55, 569–570 (1965).
[CrossRef]

1948

D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948); Proc. R. Soc. London Ser. A 197, 454–487 (1949).

Baldwin, G. C.

J. C. Solem, G. C. Baldwin, “Microholography of living organisms,” Science 218, 229–235 (1982).
[CrossRef] [PubMed]

Boyer, K.

Chapline, G. F.

J. C. Solem, G. F. Chapline, “X-ray biomicroholography,” Opt. Eng. 23, 193–203 (1984).
[CrossRef]

Cullen, D.

Doh, K. B.

T.-C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Gabor, D.

D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948); Proc. R. Soc. London Ser. A 197, 454–487 (1949).

Goodman, J. W.

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

Haddad, W. S.

Hartmann, H.-J.

Indebetouw, G.

Jüptner, W.

Jüptner, W. P. O.

Leith, E.

E. Leith, J. Upatnieks, “Hologram microscopy and lens aberration compensation by the use of holograms,” J. Opt. Soc. Am. 55, 595 (1965).

E. Leith, J. Upatnieks, “Microscopy by wavefront reconstruction,” J. Opt. Soc. Am. 55, 569–570 (1965).
[CrossRef]

Longworth, J. W.

Mandel, L.

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, New York, 1995).
[CrossRef]

McPherson, A.

Merzlyakov, N. S.

L. P. Yaroslavskii, N. S. Merzlyakov, Methods of Digital Holography (Consultants Bureau, New York, 1980).
[CrossRef]

Pomarico, J.

Poon, T.-C.

B. W. Schilling, T.-C. Poon, G. Indebetouw, B. Storrie, K. Shinoda, Y. Suzuki, M. H. Wu, “Three-dimensional holographic fluorescence microscopy,” Opt. Lett. 22, 1506–1508 (1997).
[CrossRef]

T.-C. Poon, M. H. Wu, K. Shinoda, Y. Suzuki, “Optical scanning holography,” Proc. IEEE 84, 753–764 (1996).
[CrossRef]

T.-C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Rhodes, C. K.

Schilling, B. W.

B. W. Schilling, T.-C. Poon, G. Indebetouw, B. Storrie, K. Shinoda, Y. Suzuki, M. H. Wu, “Three-dimensional holographic fluorescence microscopy,” Opt. Lett. 22, 1506–1508 (1997).
[CrossRef]

T.-C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Schnars, U.

Shinoda, K.

B. W. Schilling, T.-C. Poon, G. Indebetouw, B. Storrie, K. Shinoda, Y. Suzuki, M. H. Wu, “Three-dimensional holographic fluorescence microscopy,” Opt. Lett. 22, 1506–1508 (1997).
[CrossRef]

T.-C. Poon, M. H. Wu, K. Shinoda, Y. Suzuki, “Optical scanning holography,” Proc. IEEE 84, 753–764 (1996).
[CrossRef]

T.-C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Solem, J. C.

W. S. Haddad, D. Cullen, J. C. Solem, J. W. Longworth, A. McPherson, K. Boyer, C. K. Rhodes, “Fourier-transform holographic microscope,” Appl. Opt. 31, 4973–4978 (1992).
[CrossRef] [PubMed]

J. C. Solem, G. F. Chapline, “X-ray biomicroholography,” Opt. Eng. 23, 193–203 (1984).
[CrossRef]

J. C. Solem, G. C. Baldwin, “Microholography of living organisms,” Science 218, 229–235 (1982).
[CrossRef] [PubMed]

Storrie, B.

Suzuki, Y.

B. W. Schilling, T.-C. Poon, G. Indebetouw, B. Storrie, K. Shinoda, Y. Suzuki, M. H. Wu, “Three-dimensional holographic fluorescence microscopy,” Opt. Lett. 22, 1506–1508 (1997).
[CrossRef]

T.-C. Poon, M. H. Wu, K. Shinoda, Y. Suzuki, “Optical scanning holography,” Proc. IEEE 84, 753–764 (1996).
[CrossRef]

T.-C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Upatnieks, J.

E. Leith, J. Upatnieks, “Microscopy by wavefront reconstruction,” J. Opt. Soc. Am. 55, 569–570 (1965).
[CrossRef]

E. Leith, J. Upatnieks, “Hologram microscopy and lens aberration compensation by the use of holograms,” J. Opt. Soc. Am. 55, 595 (1965).

Wolf, E.

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, New York, 1995).
[CrossRef]

Wu, M. H.

B. W. Schilling, T.-C. Poon, G. Indebetouw, B. Storrie, K. Shinoda, Y. Suzuki, M. H. Wu, “Three-dimensional holographic fluorescence microscopy,” Opt. Lett. 22, 1506–1508 (1997).
[CrossRef]

T.-C. Poon, M. H. Wu, K. Shinoda, Y. Suzuki, “Optical scanning holography,” Proc. IEEE 84, 753–764 (1996).
[CrossRef]

T.-C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Yaroslavskii, L. P.

L. P. Yaroslavskii, N. S. Merzlyakov, Methods of Digital Holography (Consultants Bureau, New York, 1980).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am.

E. Leith, J. Upatnieks, “Microscopy by wavefront reconstruction,” J. Opt. Soc. Am. 55, 569–570 (1965).
[CrossRef]

E. Leith, J. Upatnieks, “Hologram microscopy and lens aberration compensation by the use of holograms,” J. Opt. Soc. Am. 55, 595 (1965).

J. Opt. Soc. Am. A

Nature

D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948); Proc. R. Soc. London Ser. A 197, 454–487 (1949).

Opt. Eng.

T.-C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

J. C. Solem, G. F. Chapline, “X-ray biomicroholography,” Opt. Eng. 23, 193–203 (1984).
[CrossRef]

Opt. Lett.

Proc. IEEE

T.-C. Poon, M. H. Wu, K. Shinoda, Y. Suzuki, “Optical scanning holography,” Proc. IEEE 84, 753–764 (1996).
[CrossRef]

Science

J. C. Solem, G. C. Baldwin, “Microholography of living organisms,” Science 218, 229–235 (1982).
[CrossRef] [PubMed]

Other

L. P. Yaroslavskii, N. S. Merzlyakov, Methods of Digital Holography (Consultants Bureau, New York, 1980).
[CrossRef]

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

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, New York, 1995).
[CrossRef]

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Figures (15)

Fig. 1
Fig. 1

Hybrid holographic microscope.

Fig. 2
Fig. 2

Recording geometry of holographic microscopy.

Fig. 3
Fig. 3

Coordinate transformation scheme from the hologram plane to the spatial-frequency plane.

Fig. 4
Fig. 4

Test targets used for experiments: (a) 3-µm-wide lines, (b) 1-µm-wide lines.

Fig. 5
Fig. 5

Experimental results for a 3-µm-wide line target reconstructed by the approximated Fresnel–Kirchhoff integral [Eq. (8)]: (a) recorded hologram pattern, (b) reconstructed image.

Fig. 6
Fig. 6

Magnified real images of a 3-µm-wide line target: (a) by the approximated Fresnel–Kirchhoff integral [Eq. (8)]; (b) by the Fresnel–Kirchhoff integral [Eq. (1)], (c) by the Fresnel approximation.

Fig. 7
Fig. 7

Experimental results for a 1-µm-wide line target reconstructed by the approximated Fresnel–Kirchhoff integral [Eq. (8)]: (a) recorded hologram pattern, (b) coordinate transformed hologram pattern, (c) reconstructed image.

Fig. 8
Fig. 8

Magnified real images of a 1-µm-wide line target: (a) by the approximated Fresnel–Kirchhoff integral [Eq. (8)]; (b) by the Fresnel–Kirchhoff integral [Eq. (1)], (c) by the Fresnel approximation.

Fig. 9
Fig. 9

Two-beam interferometer-type recording system: (a) recording system, (b) object wave and reference wave on the focal plane of the objective lens.

Fig. 10
Fig. 10

Experimental results of a 3-µm-diameter polystyrene latex particle reconstructed by the approximated Fresnel–Kirchhoff integral [Eq. (8)]: (a) recorded hologram pattern, (b) coordinate transformed hologram pattern, (c) reconstructed image.

Fig. 11
Fig. 11

Magnified real images reconstructed by the approximated Fresnel–Kirchhoff integral [Eq. (8)]: (a) 3-µm-diameter particle, (b) 2-µm-diameter particles, (c) 1-µm-diameter particles.

Fig. 12
Fig. 12

Magnified real images reconstructed by the Fresnel approximation: (a) 3-µm-diameter particle, (b) 2-µm-diameter particles, (c) 1-µm-diameter particles.

Fig. 13
Fig. 13

Revised coordinate transformation scheme from the hologram plane to the spatial-frequency plane.

Fig. 14
Fig. 14

Magnified real images reconstructed by use of the revised coordinate transformation scheme: (a) 3-µm-diameter particle, (b) 2-µm-diameter particles, (c) 1-µm-diameter particles.

Fig. 15
Fig. 15

Magnified real images reconstructed at different depths: (a) δz = 0 µm, (b) δz = -10 µm.

Equations (24)

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Ox, y=i/λ  ux, yexpikr/r×1+z/r/2dxdy,r=z2+x-x2+y-y21/2,
Rx, y=i/λCexpikr/r1+z/r/2,r=z2+x2+y21/2,
z3>x-x2+y-y22/4λ.
H<2λz1/4.
δxF=λz/H.
δxF>λ3z1/4/2.
kr=kz2+x2+y2-2xx-2yy+x2+y21/2kz2+x2+y2-2xx-2yy1/2kz2+x2+y21/21-xx+yy/z2+x2+y2.
Ox, y=i/2λ1+z/z2+x2+y21/2expi2πz2+x2+y21/2/λ/z2+x2+y21/2×Uνx, νy,
νx=x/λz2+x2+y21/2,νy=y/λz2+x2+y21/2.
Rx, y=i/2λ1+z/z2+x2+y21/2C expi2πz2+x2+y21/2/λ/z2+x2+y21/2.
4λ2z2+x2+y21+z/z2+x2+y21/2-2Ix, y=C*Uνx, νy+CU*νx, νy+|Uνx, νy|2+|C|2,
νmax=1/λ2+4z/H21/2.
δxFK=λ1/2+z/H21/2.
kr=kz2+x2+y2-2xx-2yy1/21+x2+y2/2z2+x2+y2-2xx-2yy+kz2+x2+y2-2xx-2yy1/2.
x2+y2<λz2+x2+y2-2xx-2yy1/2.
x2+y2<λz.
z2+x2+y23/2>xx+yy2/λ.
x2+y2<λz2+x2+y23/2/x2+y2.
x2+y2<27/41/2λz.
wo=2λz.
xmn=mλz/N2δxFK2-λ2m2+n21/2,ymn=nλz/N2δxFK2-λ2m2+n21/2.
z/H=δxFK/λ2-1/21/2.
Ox, y=i/2λ1+z+δz/z+δz2+x2+y21/2/z+δz2+x2+y21/2×expi2πz+δz2+x2+y21/2/λUνx, νy,
Ox, y=1/λ2- Uα/λ, β/λexpi2π1-α2-β21/2z/λ×expi2παx+βydαdβ.

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