Abstract

We report a technique for measuring the three-dimensional variation of refractive indices in a microscopic sample. The technique is an adaptation of optical computed tomography and is effective in measuring the three-dimensional refractive-index distribution of a nonabsorbing microscopic sample. Our report also includes a discussion of the conditions for the unambiguous application of the technique as well as results of experiments conducted with Aspergillus oryzae (commonly known as green mold) as the sample.

© 1992 Optical Society of America

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References

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  1. W. Lang, Nomarski Differential Interference-Contrast Microscopy, Zeiss reprint (Carl Zeiss, 7082 Oberkochen, Germany).
  2. S. Inoue, Video Microscopy (Plenum, New York, 1986), pp. 410–412.
  3. C. A. Burrus, R. D. Standley, “Viewing refractive-index profiles and small-scale inhomogeneities in glass optical fibers: some techniques,” Appl. Opt. 13, 2365–2369 (1974).
    [Crossref] [PubMed]
  4. F. Zernike, “Das Phasenkontrastverfahren bei der mikroskopischen Beobachtung,” Z. Tech. Phys. 16, 454–457 (1935).
  5. B. Kachar, “Asymmetric illumination contrast: a method of image formation for video light microscopy,” Science 227, 766–68 (1985).
    [Crossref] [PubMed]
  6. R. Hoffman, “The modulation contrast microscope: principles and performance,” J. Microsc. 110, 205–222 (1977).
    [Crossref]
  7. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 7.
  8. 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]
  9. S. Kawata, O. Nakamura, S. Minami, “Optical microscope tomography. I. Support constraint,” J. Opt. Soc. Am. A 4, 292–297 (1987).
    [Crossref]
  10. 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]
  11. T. Noda, S. Kawata, S. Minami, “Three-dimensional phase contrast imaging by an annular illumination microscope,” Appl. Opt. 29, 3810–3815 (1990).
    [Crossref] [PubMed]
  12. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
  13. N. Streibl, “Three-dimensional imaging by a microscope,” J. Opt. Soc. Am. A 2, 121–127 (1985).
    [Crossref]

1990 (2)

1988 (1)

1987 (1)

1985 (2)

B. Kachar, “Asymmetric illumination contrast: a method of image formation for video light microscopy,” Science 227, 766–68 (1985).
[Crossref] [PubMed]

N. Streibl, “Three-dimensional imaging by a microscope,” J. Opt. Soc. Am. A 2, 121–127 (1985).
[Crossref]

1977 (1)

R. Hoffman, “The modulation contrast microscope: principles and performance,” J. Microsc. 110, 205–222 (1977).
[Crossref]

1974 (1)

1935 (1)

F. Zernike, “Das Phasenkontrastverfahren bei der mikroskopischen Beobachtung,” Z. Tech. Phys. 16, 454–457 (1935).

Burrus, C. A.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 7.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

Hoffman, R.

R. Hoffman, “The modulation contrast microscope: principles and performance,” J. Microsc. 110, 205–222 (1977).
[Crossref]

Inoue, S.

S. Inoue, Video Microscopy (Plenum, New York, 1986), pp. 410–412.

Kachar, B.

B. Kachar, “Asymmetric illumination contrast: a method of image formation for video light microscopy,” Science 227, 766–68 (1985).
[Crossref] [PubMed]

Kawata, S.

Kuroiwa, Y.

Lang, W.

W. Lang, Nomarski Differential Interference-Contrast Microscopy, Zeiss reprint (Carl Zeiss, 7082 Oberkochen, Germany).

Minami, S.

Nakamura, O.

Noda, T.

Ogino, K.

Ooki, H.

Standley, R. D.

Streibl, N.

Zernike, F.

F. Zernike, “Das Phasenkontrastverfahren bei der mikroskopischen Beobachtung,” Z. Tech. Phys. 16, 454–457 (1935).

Appl. Opt. (3)

J. Microsc. (1)

R. Hoffman, “The modulation contrast microscope: principles and performance,” J. Microsc. 110, 205–222 (1977).
[Crossref]

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

Science (1)

B. Kachar, “Asymmetric illumination contrast: a method of image formation for video light microscopy,” Science 227, 766–68 (1985).
[Crossref] [PubMed]

Z. Tech. Phys. (1)

F. Zernike, “Das Phasenkontrastverfahren bei der mikroskopischen Beobachtung,” Z. Tech. Phys. 16, 454–457 (1935).

Other (4)

W. Lang, Nomarski Differential Interference-Contrast Microscopy, Zeiss reprint (Carl Zeiss, 7082 Oberkochen, Germany).

S. Inoue, Video Microscopy (Plenum, New York, 1986), pp. 410–412.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 7.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

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Figures (6)

Fig. 1
Fig. 1

Equivalent optical system of the laser CT microscope for phase measurement. Distance ρs of the point source from the optical axis equals the pupil size ρp

Fig. 2
Fig. 2

Computer plots of 3-D PTF’s under three types of coherent illumination. The value of the PTF is positive on the surface of one of the shells and negative for the other shell. The insides of the shells are hollow: (a) on-axis, (b) partially oblique, (c) critical angle of obliqueness.

Fig. 3
Fig. 3

Observable area with the phase CT microscope in the spatial domain.

Fig. 4
Fig. 4

Optical diagram of the laser CT microscope

Fig. 5
Fig. 5

Four representations of seventy-two projections of green mold by a laser CT microscope at λ = 632.8 nm.

Fig. 6
Fig. 6

Three major cross-sectional images of the reconstruction. Image brightness corresponds to the refractive indices. Each cross section is separated with 7 μm: (a) is the top, (b) is the middle, and (c) is the bottom.

Equations (3)

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E IMG ( ξ , η , ζ ) = B δ ( ξ , η , ζ ) + T P ( ξ , η , ζ ) P ( ξ , η , ζ ) ,
T P ( ξ, η, ζ ) = j λ 4 π p * ( ρ s cos ϕ ξ , ρ s sin ϕ η ) × δ { ζ ( λ 2 ρ s ) 1 / 2 + [ λ 2 ( ρ s cos ϕ ξ ) 2 ( ρ s sin ϕ η ) 2 ] 1 / 2 } j λ 4 π p ( ρ s cos ϕ + ξ, ρ s sin ϕ + η ) × δ { ζ + ( λ 2 ρ s 2 ) 1 / 2 [ λ 2 ( ρ s cos ϕ + ξ ) 2 ( ρ s sin ϕ + η ) 2 ] 1 / 2 } ,
p ( ξ, η ) = p ( ρ ) = { 1 if ρ ρ p , 0 if ρ > ρ p

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