Abstract

A new microscope imaging system, modulation contrast, has been devised that reveals phase gradients; the image intensity is proportional to the first derivative of the optical density in the object. The modulator, a special filter, is placed in the Fourier plane, a plane conjugate with a slit aperture. The image of the slit aperture is registered within a gray region of the modulator; on one side of the gray region is a region of low transmittance and on the other side, a region of maximum transmittance. The modulator processes opposite gradients to produce opposite intensities, creating an optical shadowing effect. The dark region may be outside the optical system when the gray region is offset to the edge of the Fourier plane, to achieve maximum resolution. Modulation contrast is directional and capable of optical sectioning, revealing details without obscuring effects of structures above and below the plane of focus. The imaging theory of microscope optics has been extended to include effects of phase gradients. Phase gradients distribute the zero order across the Fourier plane. Intensity of the gradient's image is controlled by the zero order of the gradient diffraction pattern.

© 1975 Optical Society of America

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References

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  1. E. Abbe, Arch. Mikr. Anat. 9, 413, (1873).
    [CrossRef]
  2. G. Lipson, H. S. Lipson, Optical Physics (Cambridge U. P., Cambridge, 1969), p. 271.
  3. B. J. Thompson, in Optical Transforms, H. S. Lipson, Ed. (Academic, New York, 1972), p. 54.
  4. F. Zernike, Physica 9, 686, 674 (1942).
    [CrossRef]
  5. A. Wilska, Nature 171, 353 (1953).
    [CrossRef] [PubMed]
  6. A. G. Oettlé, J. R. Microsc. Soc. 70, 232 (1950).
    [CrossRef]
  7. M. Pluta, Microscope 16, 211 (1968).
  8. R. Hoffman, L. Gross, J. Microsc. 91, 3 (1970).
    [CrossRef]
  9. R. Hoffman, L. Gross, Nature 212, 929 (1966).
    [CrossRef]
  10. R. J. North, British A.R.C. 15099 (1952).
  11. D. W. Holder, R. J. North, Agardograph 23, NATO (November1956).
  12. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1964), p‥ 425.
  13. L. C. Martin, The Theory of the Microscope (Blackie & Son, London, 1966), Chap. 7.
  14. R. Barer, Nature 171, 697 (1953).
    [CrossRef] [PubMed]
  15. A. Bennett, H. Osterberg, H. Jupnik, O. W. Richards, Phase Microscopy (Wiley, New York, 1951).
  16. S. Delrus, M. Françon, C. P. Grover, M. May, M. L. Roblin, Appl. Opt. 11, 853 (1972).
    [CrossRef]
  17. J. G. Dodd, Modern Microscopy (McCrone Microscope, Chicago, (in press)).

1972 (1)

1970 (1)

R. Hoffman, L. Gross, J. Microsc. 91, 3 (1970).
[CrossRef]

1968 (1)

M. Pluta, Microscope 16, 211 (1968).

1966 (1)

R. Hoffman, L. Gross, Nature 212, 929 (1966).
[CrossRef]

1953 (2)

R. Barer, Nature 171, 697 (1953).
[CrossRef] [PubMed]

A. Wilska, Nature 171, 353 (1953).
[CrossRef] [PubMed]

1950 (1)

A. G. Oettlé, J. R. Microsc. Soc. 70, 232 (1950).
[CrossRef]

1942 (1)

F. Zernike, Physica 9, 686, 674 (1942).
[CrossRef]

1873 (1)

E. Abbe, Arch. Mikr. Anat. 9, 413, (1873).
[CrossRef]

Abbe, E.

E. Abbe, Arch. Mikr. Anat. 9, 413, (1873).
[CrossRef]

Barer, R.

R. Barer, Nature 171, 697 (1953).
[CrossRef] [PubMed]

Bennett, A.

A. Bennett, H. Osterberg, H. Jupnik, O. W. Richards, Phase Microscopy (Wiley, New York, 1951).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1964), p‥ 425.

Delrus, S.

Dodd, J. G.

J. G. Dodd, Modern Microscopy (McCrone Microscope, Chicago, (in press)).

Françon, M.

Gross, L.

R. Hoffman, L. Gross, J. Microsc. 91, 3 (1970).
[CrossRef]

R. Hoffman, L. Gross, Nature 212, 929 (1966).
[CrossRef]

Grover, C. P.

Hoffman, R.

R. Hoffman, L. Gross, J. Microsc. 91, 3 (1970).
[CrossRef]

R. Hoffman, L. Gross, Nature 212, 929 (1966).
[CrossRef]

Holder, D. W.

D. W. Holder, R. J. North, Agardograph 23, NATO (November1956).

Jupnik, H.

A. Bennett, H. Osterberg, H. Jupnik, O. W. Richards, Phase Microscopy (Wiley, New York, 1951).

Lipson, G.

G. Lipson, H. S. Lipson, Optical Physics (Cambridge U. P., Cambridge, 1969), p. 271.

Lipson, H. S.

G. Lipson, H. S. Lipson, Optical Physics (Cambridge U. P., Cambridge, 1969), p. 271.

Martin, L. C.

L. C. Martin, The Theory of the Microscope (Blackie & Son, London, 1966), Chap. 7.

May, M.

North, R. J.

D. W. Holder, R. J. North, Agardograph 23, NATO (November1956).

R. J. North, British A.R.C. 15099 (1952).

Oettlé, A. G.

A. G. Oettlé, J. R. Microsc. Soc. 70, 232 (1950).
[CrossRef]

Osterberg, H.

A. Bennett, H. Osterberg, H. Jupnik, O. W. Richards, Phase Microscopy (Wiley, New York, 1951).

Pluta, M.

M. Pluta, Microscope 16, 211 (1968).

Richards, O. W.

A. Bennett, H. Osterberg, H. Jupnik, O. W. Richards, Phase Microscopy (Wiley, New York, 1951).

Roblin, M. L.

Thompson, B. J.

B. J. Thompson, in Optical Transforms, H. S. Lipson, Ed. (Academic, New York, 1972), p. 54.

Wilska, A.

A. Wilska, Nature 171, 353 (1953).
[CrossRef] [PubMed]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1964), p‥ 425.

Zernike, F.

F. Zernike, Physica 9, 686, 674 (1942).
[CrossRef]

Appl. Opt. (1)

Arch. Mikr. Anat. (1)

E. Abbe, Arch. Mikr. Anat. 9, 413, (1873).
[CrossRef]

J. Microsc. (1)

R. Hoffman, L. Gross, J. Microsc. 91, 3 (1970).
[CrossRef]

J. R. Microsc. Soc. (1)

A. G. Oettlé, J. R. Microsc. Soc. 70, 232 (1950).
[CrossRef]

Microscope (1)

M. Pluta, Microscope 16, 211 (1968).

Nature (3)

R. Barer, Nature 171, 697 (1953).
[CrossRef] [PubMed]

R. Hoffman, L. Gross, Nature 212, 929 (1966).
[CrossRef]

A. Wilska, Nature 171, 353 (1953).
[CrossRef] [PubMed]

Physica (1)

F. Zernike, Physica 9, 686, 674 (1942).
[CrossRef]

Other (8)

G. Lipson, H. S. Lipson, Optical Physics (Cambridge U. P., Cambridge, 1969), p. 271.

B. J. Thompson, in Optical Transforms, H. S. Lipson, Ed. (Academic, New York, 1972), p. 54.

R. J. North, British A.R.C. 15099 (1952).

D. W. Holder, R. J. North, Agardograph 23, NATO (November1956).

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1964), p‥ 425.

L. C. Martin, The Theory of the Microscope (Blackie & Son, London, 1966), Chap. 7.

A. Bennett, H. Osterberg, H. Jupnik, O. W. Richards, Phase Microscopy (Wiley, New York, 1951).

J. G. Dodd, Modern Microscopy (McCrone Microscope, Chicago, (in press)).

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Figures (10)

Fig. 1
Fig. 1

Modulation contrast microscope schematic compared with brightfield microscope.

Fig. 2
Fig. 2

Human epithelial cheek cells seen with 40× objective under (a) phase contrast microscope; (b) differential interference microscope; (c) modulation contrast microscope; (d) modulation contrast microscope at level of cell surface, without obscuring by lower structures, demonstrating optical sectioning.

Fig. 3
Fig. 3

Tibia muscle of cockroach (Periplaneta americana) in two views illustrating directionality (a) showing nodules on muscle fibers, (b) rotated 45° to (a).

Fig. 4
Fig. 4

Elementary modulator design with three transmittance regions within exit pupil: (a) with centered gray region axial illumination, (b) with offset gray region to maximize resolution; oblique illumination. β = direction of gradient.

Fig. 5
Fig. 5

Schematic diagram indicating the regions of the modulator that process light from the phase gradients in the object to form an image of contrast. No phase changes are introduced by the modulator.

Fig. 6
Fig. 6

Phase gradient transforms.

Fig. 7
Fig. 7

Object function representing phase gradients in Fourier integral.

Fig. 8
Fig. 8

Description of object plane.

Fig. 9
Fig. 9

Modulation contrast sensitivity, based on image displacement of source in Fourier plane, w = width of gray region and Δw = image displacement due to gradient.

Fig. 10
Fig. 10

Metallurgical surface contours of a roughly polished and etched gold alloy casting.

Equations (20)

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T B > T G > T D
U ( θ ) exp ( i ϕ X ) exp ( i θ X ) d X ,
U ( θ ) ~ sin ( θ + ϕ ) / ( θ + ϕ ) .
U ( X ) = P A ( X ) + P a ( X ) F ( X ) P a ( X ) .
U ( X ) = P A ( X ) P a ( X ) .
F T [ U ( X ) ] = U ( θ ) = F T [ P A ( X ) ] F T [ P a ( X ) ]
~ 2 A sin A θ / A θ 2 a sin a θ / a θ ,
U ( X ) = F T [ U ( θ ) ] = P A ( X ) P a ( X ) .
U ( X ) = P A ( X ) + P a ( X ) exp ( i ϕ X ) P a ( X )
U ( θ ) = F T [ P A ( X ) ] + F T [ P a ( X ) exp ( i ϕ X ) ] F T [ P a ( X ) ]
= 2 A sin A θ / A θ + 2 a sin a ( θ + ϕ ) / a ( θ + ϕ ) 2 a sin a θ / a θ .
U ( θ ) = ( T G ) 1 / 2 { F T [ P A ( X ) ] } + ( T B ) 1 / 2 { F T [ P a ( X ) exp ( i ϕ X ) ] } ( T G ) 1 / 2 { F T [ P a ( X ) ] } .
U ( X ) = F T [ U ( θ ) ] = ( T G ) 1 / 2 P A ( X ) + ( T B ) 1 / 2 P a ( X ) exp ( i ϕ X ) ( T G ) 1 / 2 P a ( X ) .
I ( X ) = U * ( X ) U ( X ) .
I ( X ) = T G [ P A ( X ) ] 2 + T B [ P a ( X ) ] 2 + T G [ P a ( X ) ] 2 2 T G P A ( X ) P a ( X ) + 2 ( T G T B ) 1 / 2 P A ( X ) P a ( X ) cos ϕ X 2 ( T G T B ) 1 / 2 [ P a ( X ) ] 2 cos ϕ X .
Δ I * = ( I image I background ) cos β = I 0 [ T B Δ w / w + T G ( w Δ w ) / w T G ] cos β , Δ I * = I 0 f Δ ϕ ( T B T G ) cos β / w .
Δ I = I 0 f Δ ϕ ( T G T D ) cos β / w ,
c = ( I image I background ) / I background = Δ I / I G = Δ I / I 0 T G .
Δ I = 0.02 T G I 0 .
Δ ϕ = 0.02 T G w / f ( T B T G ) cos β .

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