Abstract

Three methods for improving the image of phase-contrast microscopy are proposed. The first two methods subtract, from the ordinary phase-contrast image, the image obtained through an objective with different pupil functions from that of the ordinary objective. These methods can reduce the distortion due to nonlinearity to less than 1/10 of the ordinary phase-contrast image. The third method simply uses a brighter objective lens along with a television camera with offset adjustment. The brighter lens results in higher sensitivity and less distortion. Theory, computer simulation, and a few experimental results are presented.

© 1991 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. D. Allen, J. L. Travis, N. S. Allen, H. Yilmaz, “Video-enhanced contrast polarization (AVEC-POL) microscopy,” Cell Motil. 1, 275–289 (1981).
    [Crossref]
  2. N. Streibl, “Three-dimensional imaging by a microscope,” J. Opt. Soc. Am. A 2, 121–127 (1985).
    [Crossref]
  3. I. Nemoto, “Three-dimensional imaging in microscopy as an extension of the theory of two-dimensional imaging,” J. Opt. Soc. Am. A 5, 1848–1851 (1988).
    [Crossref]
  4. H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. R. Soc. London Ser. A 231, 91–103 (1957).
  5. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

1988 (1)

1985 (1)

1981 (1)

R. D. Allen, J. L. Travis, N. S. Allen, H. Yilmaz, “Video-enhanced contrast polarization (AVEC-POL) microscopy,” Cell Motil. 1, 275–289 (1981).
[Crossref]

1957 (1)

H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. R. Soc. London Ser. A 231, 91–103 (1957).

Allen, N. S.

R. D. Allen, J. L. Travis, N. S. Allen, H. Yilmaz, “Video-enhanced contrast polarization (AVEC-POL) microscopy,” Cell Motil. 1, 275–289 (1981).
[Crossref]

Allen, R. D.

R. D. Allen, J. L. Travis, N. S. Allen, H. Yilmaz, “Video-enhanced contrast polarization (AVEC-POL) microscopy,” Cell Motil. 1, 275–289 (1981).
[Crossref]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

Hopkins, H. H.

H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. R. Soc. London Ser. A 231, 91–103 (1957).

Nemoto, I.

Streibl, N.

Travis, J. L.

R. D. Allen, J. L. Travis, N. S. Allen, H. Yilmaz, “Video-enhanced contrast polarization (AVEC-POL) microscopy,” Cell Motil. 1, 275–289 (1981).
[Crossref]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

Yilmaz, H.

R. D. Allen, J. L. Travis, N. S. Allen, H. Yilmaz, “Video-enhanced contrast polarization (AVEC-POL) microscopy,” Cell Motil. 1, 275–289 (1981).
[Crossref]

Cell Motil. (1)

R. D. Allen, J. L. Travis, N. S. Allen, H. Yilmaz, “Video-enhanced contrast polarization (AVEC-POL) microscopy,” Cell Motil. 1, 275–289 (1981).
[Crossref]

J. Opt. Soc. Am. A (2)

Proc. R. Soc. London Ser. A (1)

H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. R. Soc. London Ser. A 231, 91–103 (1957).

Other (1)

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

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 (11)

Fig. 1
Fig. 1

Telecentric system.

Fig. 2
Fig. 2

Condenser and objective lens.

Fig. 3
Fig. 3

Optical transfer functions for the phase-contrast microscope [c ≃ 0.4, θ = π/2 in Eq. (5)]: logarithmic scale for (a) |TA|, (b) |TP|.

Fig. 4
Fig. 4

(a) |TA|, (b) |TP| when the phase plate has no phase component (c ≃ 0.4, θ = 0).

Fig. 5
Fig. 5

Power spectrum (top) of the phase-contrast image of a pseudorandom object (latex beads dispersed in water) and the transfer function TP (bottom).

Fig. 6
Fig. 6

Simulation results for the reverse-phase method: the phase object (top left), the reference phase-contrast image with a numerical aperture of 0.7 (bottom left), the image by the reverse-phase pupil (top right), and the image by the reverse-phase method (bottom right). ϕ = −π/4.

Fig. 7
Fig. 7

Result of the reverse-phase method and its application to solution of the inverse problem (simulation). The object is a pure phase object with the same dimensions as those of Fig. 6, and ϕ = π/6: the simulated phase-contrast image (top left), the image obtained by the reverse-phase method (bottom left), the inverse-filtered phase-contrast image (top right), and the inverse-filtered reverse-phase-method image (bottom right).

Fig. 8
Fig. 8

Phase-contrast microscope for the dark-pupil and reverse-phase methods.

Fig. 9
Fig. 9

Comparison of images taken with (a) an ordinary phase-contrast objective (c ≃ 0.4), (b) a bright (c = 1) objective. The numerical aperture is 0.7 for both. Peripheral part of a fibroblast cell.

Fig. 10
Fig. 10

Comparison of images taken with (a) an ordinary objective, (b) a bright objective. Hamster alveolar macrophages (arrow) with latex beads.

Fig. 11
Fig. 11

Distortion-rate characteristics of the conventional phase-contrast microscopy: dark-pupil (D.P.) method and the reverse-phase (R.P.) method. Both the amplitude a of the sinusoidal change of the phase retardation of the object and the transmission coefficient c assume two values as indicated in the figure: freq., frequency; N.A., numerical aperture.

Equations (44)

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

I ( μ , ζ ) = B δ ( μ , ζ ) + P ( μ , ζ ) T P ( μ , ζ ) + i A ( μ , ζ ) T A ( μ , ζ ) ,
B = S ( μ ) p ( μ ) 2 d μ ,
( T A T P ) = λ 4 π p ( μ + 1 2 μ ) [ S ( μ + 1 2 μ ) ± S ( μ - 1 2 μ ) ] × p * ( μ - 1 2 μ ) δ ( ζ + λ μ · μ ) d μ .
f ( x , z ) = γ ( x , z ) exp [ i ϕ ( x , z ) ] ,
f ( x , z ) = 1 + f A ( x , z ) + i f P ( x , z ) ,
1 + f A ( x , z ) = R [ f ( x , z ) ] , f P ( x , z ) = T [ f ( x , z ) ] .
f A ( x , z ) 1 , f P ( x , z ) ϕ ( x , z ) .
I ( μ , ζ ) = B δ ( μ , ζ ) + i F P ( μ , ζ ) T P F ( μ , ζ ) + F A ( μ , ζ ) T A F ( μ , ζ ) ,
T A F = 4 π λ T A , T P F = 4 π λ T P .
S ( μ ) = { 1 ( m ρ / λ μ n ρ / λ ) 0 ( otherwise ) ,
p ( μ ) = { c e i θ ( m ρ / λ μ n ρ / λ ) 1 ( otherwise ) ,
p ( μ ) = p P ( μ ) + p D ( μ ) ,
p P ( μ ) = c e i θ S ( μ ) = { c e i θ ( m ρ / λ μ n ρ / λ ) 0 ( otherwise )
p D ( μ ) = { 0 ( m ρ / λ μ n ρ / λ ) 1 ( otherwise ) .
( T A F T P F ) = p P ( μ + ) [ S ( μ + ) ± S ( μ - ) ] p P * ( μ - ) δ ( ζ + λ μ · μ ) d μ + p P ( μ + ) S ( μ + ) p D ( μ - ) δ ( ζ + λ μ · μ ) d μ ± p D ( μ + ) S ( μ - ) p P * ( μ - ) δ ( ζ + λ μ · μ ) d μ ,
μ + = μ + ½ μ
μ - = μ - ½ μ
T A F = 2 λ μ ( T a + T b ) ,             T P F = 2 λ μ ( T a - T b ) ,
T a = T 1 + T 2 + T 3 ,             T b = T 1 + T 4 + T 5 ,
T 1 = c 2 [ ( β 1 - Γ ) 1 / 2 - ( α 1 - Γ ) 1 / 2 ] ,
T k = c e i θ [ ( β k - Γ ) 1 / 2 - ( α k - Γ ) 1 / 2 ]             ( k = 2 , 3 , 4 , 5 )
α 1 = max { Γ , m 2 ρ 2 λ 2 + | ζ λ | } , α 2 = max { Γ , m 2 ρ 2 λ 2 + ζ λ } , α 3 = max { Γ , m 2 ρ 2 λ 2 + ζ λ , n 2 ρ 2 λ 2 - ζ λ } , α 4 = max { Γ , m 2 ρ 2 λ 2 - ζ λ } , α 5 = max { Γ , m 2 ρ 2 λ 2 - ζ λ , n 2 ρ 2 λ 2 - ζ λ } , β 1 = n 2 ρ 2 λ 2 - | ζ λ | , β 2 = min { n 2 ρ 2 λ 2 + ζ λ , m 2 ρ 2 λ 2 - ζ λ } , β 3 = min { n 2 ρ 2 λ 2 + ζ λ , ρ 2 - ζ λ } , β 4 = min { n 2 ρ 2 λ 2 - ζ λ , m 2 ρ 2 λ 2 + ζ λ } , β 5 = min { n 2 ρ 2 λ 2 - ζ λ , ρ 2 + ζ λ }
Γ = μ 2 4 - η 2 λ 2 μ 2 .
I ( μ , z ) = δ ( μ ) τ ( o , o , z ) + τ A ( μ , z ) F A ( μ , z ) + i τ P ( μ , z ) F P ( μ , z ) + R 2 τ ( μ + μ , μ , z ) F o ( μ + μ , z ) F o * ( μ , z ) d μ ,
τ A ( μ , z ) = τ ( o , - μ , z ) + τ ( μ , o , z ) , τ P ( μ , z ) = τ ( μ , o , z ) - τ ( o , - μ , z ) ,
τ ( μ 1 , μ 2 , z ) = R 2 S ( μ ) K ( μ 1 + μ , z ) K ( μ 2 + μ , z ) d μ .
K ( μ , z ) = exp ( i π λ μ 2 z n c ) p ( - μ ) ,
τ D ( μ 1 , μ 2 ) = S ( μ ) p D ( μ 1 + μ ) p D ( μ 2 + μ ) d μ .
τ ( μ 1 , μ 2 ) = S ( μ ) [ p P ( μ 1 + μ ) p P * ( μ 2 + μ ) + p P ( μ 1 + μ ) × p D ( μ 2 + μ ) + p D ( μ 1 + μ ) p P * ( μ 2 + μ ) ] d μ + S ( μ ) p D ( μ 1 + μ ) p D ( μ 2 + μ ) d μ .
I D ( μ ) = δ ( μ ) τ ( o , o ) + τ A ( μ ) F A ( μ ) + i τ P ( μ ) F P ( μ ) + [ τ ( μ + μ , μ ) - τ D ( μ + μ , μ ) ] × F o ( μ + μ ) F o * ( μ ) d μ .
p R ( μ ) = - p P ( μ ) = p P ( μ ) e i π .
τ R ( μ 1 , μ 2 ) = S ( μ ) [ p P ( μ 1 + μ ) p P * ( μ 2 + μ ) - p P ( μ 1 + μ ) × p D ( μ 2 + μ ) - p D ( μ 1 + μ ) p P * ( μ 2 + μ ) ] d μ + S ( μ ) p D ( μ 1 + μ ) p D ( μ 2 + μ ) d μ .
[ τ ( μ + μ , μ ) - τ R ( μ + μ , μ ) ] F o ( μ + μ ) F o * ( μ ) d μ ,
τ ( μ 1 , μ 2 ) - τ R ( μ 1 , μ 2 ) = 2 S ( μ ) [ p P ( μ 1 + μ ) p D ( μ 2 + μ ) + p D ( μ 1 + μ ) p P * ( μ 2 + μ ) ] d μ .
I R ( μ ) = τ R A ( μ ) F A ( μ ) + i τ R P ( μ ) F P ( μ ) + ( nonlinear terms ) ,
τ R A ( μ ) = 4 c cos θ S ( μ ) S ( μ + μ ) d μ
τ R P ( μ ) = 2 τ P ( μ ) .
f ( x ) = exp [ i ϕ ( x ) ] ,
ϕ ( x ) = { ϕ ( - 3.5 x , y 3.5 ) 0 ( otherwise ) .
f A ( x ) = cos ϕ ( x ) - 1
f P ( x ) = sin ϕ ( x ) .
I ( μ ) = i τ P ( μ ) F P ( μ ) .
f ( x , y ) = exp ( i a cos ω x ) .
r ( ω ) = ( k 1 n c k 2 ) 1 / 2 c 1 ,

Metrics