Abstract

We present a model describing the image formation in DIC (Differential Interference Contrast) mode microscopy, by including the actual refractive indexes and reflection coefficients of objects and substrates. We calculate the contrast of flat and level objects of nanometric thickness versus the bias retardation Γ and the numerical aperture NA. We show that high contrasts, of the edge and of the inner object, can be achieved in DIC mode with special anti-reflective substrates and large NA values. The calculations agree with contrast measurements on nanometric steps of silica and explain also the extreme ability to detect single molecules (stretched DNA molecules).

© 2008 Optical Society of America

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References

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  1. S. Hénon and J. Meunier, "Microscope at Brewster angle: direct observation of first order phase transitions in monolayers," Rev. Sci. Instrum. 62, 936-939 (1991).
    [CrossRef]
  2. D. Ausserré and M. -P. Valignat, "Wide-field optical imaging of surface nanostructures," Nano Lett. 6, 1384-1388 (2006).
    [CrossRef] [PubMed]
  3. D. Ausserré and M.-P. Valignat, "Surface enhanced ellipsometric contrast (SEEC) basic theory and λ/4 multilayered solutions," Opt. Express 15, 8329 (2007).
    [CrossRef] [PubMed]
  4. M. Pluta, Advanced Light Microscopy, (Elsevier, Amsterdam,1989) Vol. 2, Chap. 7.
  5. D. L. Lessor, J. S. Hartman, R. L. Gordon, " Quantitative surface topography determination by Nomarski reflection microscopy. I. Theory," J. Opt. Soc. Am. 69, 357-366 (1979).
    [CrossRef]
  6. W. Galbraith and G. B. David, "An aid to understanding differential interference contrast microscopy: computer simulation," J. Microsc. 108, 147-176 (1976).
    [CrossRef]
  7. C. J. Cogswell and C. J. R. Sheppard, "Confocal differential interference contrast (DIC) microscopy: including a theoretical analysis of conventional and confocal DIC imaging," J. Microsc. 165, 81-101 (1992).
    [CrossRef]
  8. C. Preza and D. L. Snyder, "Theoretical development and experimental evaluation of imaging models for differential-interference-contrast microscopy," J. Opt. Soc. Am. A 16, 2185-2199 (1999).
    [CrossRef]
  9. G. M. Holzwarth, D. B. Hill, and E. B. McLaughlin, "Polarization-modulated differential-interference contrast microscopy with a variable retarder," Appl. Opt. 39, 6288-6294 (2000).
    [CrossRef]
  10. P. R. T. Munro and P. Török, "Vectorial, high numerical aperture study of Nomarski's differential interference contrast microscope," Opt. Express 13, 6833 (2005).
    [CrossRef] [PubMed]
  11. R. M. A Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, New York, 1977).
  12. R. Oldenbourg and G. Mei, "New polarized light microscope with precision universal compensator," J. Microsc. 180, 140-147 (1995).
    [CrossRef] [PubMed]

2007

2006

D. Ausserré and M. -P. Valignat, "Wide-field optical imaging of surface nanostructures," Nano Lett. 6, 1384-1388 (2006).
[CrossRef] [PubMed]

2005

2000

1999

1995

R. Oldenbourg and G. Mei, "New polarized light microscope with precision universal compensator," J. Microsc. 180, 140-147 (1995).
[CrossRef] [PubMed]

1992

C. J. Cogswell and C. J. R. Sheppard, "Confocal differential interference contrast (DIC) microscopy: including a theoretical analysis of conventional and confocal DIC imaging," J. Microsc. 165, 81-101 (1992).
[CrossRef]

1991

S. Hénon and J. Meunier, "Microscope at Brewster angle: direct observation of first order phase transitions in monolayers," Rev. Sci. Instrum. 62, 936-939 (1991).
[CrossRef]

1979

1976

W. Galbraith and G. B. David, "An aid to understanding differential interference contrast microscopy: computer simulation," J. Microsc. 108, 147-176 (1976).
[CrossRef]

Ausserré, D.

Cogswell, C. J.

C. J. Cogswell and C. J. R. Sheppard, "Confocal differential interference contrast (DIC) microscopy: including a theoretical analysis of conventional and confocal DIC imaging," J. Microsc. 165, 81-101 (1992).
[CrossRef]

David, G. B.

W. Galbraith and G. B. David, "An aid to understanding differential interference contrast microscopy: computer simulation," J. Microsc. 108, 147-176 (1976).
[CrossRef]

Galbraith, W.

W. Galbraith and G. B. David, "An aid to understanding differential interference contrast microscopy: computer simulation," J. Microsc. 108, 147-176 (1976).
[CrossRef]

Gordon, R. L.

Hartman, J. S.

Hénon, S.

S. Hénon and J. Meunier, "Microscope at Brewster angle: direct observation of first order phase transitions in monolayers," Rev. Sci. Instrum. 62, 936-939 (1991).
[CrossRef]

Hill, D. B.

Holzwarth, G. M.

Lessor, D. L.

McLaughlin, E. B.

Mei, G.

R. Oldenbourg and G. Mei, "New polarized light microscope with precision universal compensator," J. Microsc. 180, 140-147 (1995).
[CrossRef] [PubMed]

Meunier, J.

S. Hénon and J. Meunier, "Microscope at Brewster angle: direct observation of first order phase transitions in monolayers," Rev. Sci. Instrum. 62, 936-939 (1991).
[CrossRef]

Munro, P. R. T.

Oldenbourg, R.

R. Oldenbourg and G. Mei, "New polarized light microscope with precision universal compensator," J. Microsc. 180, 140-147 (1995).
[CrossRef] [PubMed]

Preza, C.

Sheppard, C. J. R.

C. J. Cogswell and C. J. R. Sheppard, "Confocal differential interference contrast (DIC) microscopy: including a theoretical analysis of conventional and confocal DIC imaging," J. Microsc. 165, 81-101 (1992).
[CrossRef]

Snyder, D. L.

Török, P.

Valignat, M. -P.

D. Ausserré and M. -P. Valignat, "Wide-field optical imaging of surface nanostructures," Nano Lett. 6, 1384-1388 (2006).
[CrossRef] [PubMed]

Valignat, M.-P.

Appl. Opt.

J. Microsc.

W. Galbraith and G. B. David, "An aid to understanding differential interference contrast microscopy: computer simulation," J. Microsc. 108, 147-176 (1976).
[CrossRef]

C. J. Cogswell and C. J. R. Sheppard, "Confocal differential interference contrast (DIC) microscopy: including a theoretical analysis of conventional and confocal DIC imaging," J. Microsc. 165, 81-101 (1992).
[CrossRef]

R. Oldenbourg and G. Mei, "New polarized light microscope with precision universal compensator," J. Microsc. 180, 140-147 (1995).
[CrossRef] [PubMed]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Nano Lett.

D. Ausserré and M. -P. Valignat, "Wide-field optical imaging of surface nanostructures," Nano Lett. 6, 1384-1388 (2006).
[CrossRef] [PubMed]

Opt. Express

Rev. Sci. Instrum.

S. Hénon and J. Meunier, "Microscope at Brewster angle: direct observation of first order phase transitions in monolayers," Rev. Sci. Instrum. 62, 936-939 (1991).
[CrossRef]

Other

M. Pluta, Advanced Light Microscopy, (Elsevier, Amsterdam,1989) Vol. 2, Chap. 7.

R. M. A Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, New York, 1977).

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Figures (8)

Fig. 1.
Fig. 1.

Definition of the reflection coefficients for a sample made of a flat step with sharp edges. h is the step height and n and nS are the refractive index’s respectively of the step and of the substrate.

Fig. 2.
Fig. 2.

Illustration of the image intensity for a flat step object with sharp edges in (a) crossed polarizers mode, (b) DIC mode with Γ=0 and c) DIC mode with Γ≠0. In case A, the refractive index of the step and the substrate are identical (n=nS i.e. a rough substrate), and in case B they are different (n≠nS, i.e. object deposited on the substrate).

Fig. 3.
Fig. 3.

Calculation of edge contrasts CDIC-edge in normal incidence for a sharp silica step of thickness h=41 nm on a silicon substrate vs bias retardation Γ. Blue curve: assuming that the step refractive index is equal to the substrate refractive index, and that the reflection coefficient Rs, -Rp, R′s, and -R′p are all equal to one. Red curve: taking into account actual values of refractive index (nSi=4-0.02i, nSiO2=1.46) and reflection coefficients Rp, Rs, R′p, and R′s for the substrate and for the step.

Fig. 4.
Fig. 4.

(a). CDIC-edge and (b). CDIC-step calculated vs bias retardation Γ for a silica step on a silicon wafer, in the case of a step thickness of 4 nm (red) and 41 nm (blue) with NA 0 (thin solid line), 0.5 (circles) and 0.8 (solid bold line).

Fig. 5.
Fig. 5.

Contrast calculations for a silica step on a silicon wafer and on a Surf vs the step thickness h: CX (red), CDIC-edge (blue) and CDIC-step (green) on a silicon wafer (thin line) and on a surf (bold lines). All calculations correspond to λ=540 nm, NA=0.5 and Γ=5°.

Fig. 6.
Fig. 6.

Pictures with a magnification x5, a numerical aperture of 0.15 and white illumination of silica steps of heights 10, 18, 26, 32, 37 and 41 nm, (a) in crossed polarizers mode, and (b) in DIC mode with a bias retardation value set to Γ=5°.

Fig. 7.
Fig. 7.

Experimental (dots) and computed (solid line) contrast values versus bias retardation Γ for silica steps on Surf with a magnification x5 and a numerical aperture NA=0.15.(a) CDIC-edge for a step height of h=41 nm, and (b) CDIC-step for step heights h=41 nm (blue), h=32 nm (green), h=26 nm (orange), h=18 nm (red), and h=10 nm (black). The computed values take into account a background intensity of 0.05*I0.

Fig. 8.
Fig. 8.

Pictures with a magnification x50, a numerical aperture of 0.8, and monochromatic illumination at λ=540 nm of (a) resin steps (n=1.60) on a silicon wafer and (b) silica steps (n=1.46) on a Surf in crossed polarizers mode (top) and DIC mode (bottom) with a bias retardation value set to Γ=20°. (c) Calculated (solid line) and experimental (dots) contrasts for steps on a silicon wafer (thin lines and hollow dots) and on a Surf (bold lines and filled dots) in crossed polarizer mode CX (red) and DIC mode CDIC-step (green).

Equations (19)

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( E A ⁄⁄ E A ) = ( 1 0 0 0 ) ( cosA sinA sinA cosA ) ( R p 0 0 R s ) ( cosP sinP sinP cosP ) ( 2 2 0 ) A 0
[ - - - - - - - ANALYZER - - - - - ] [ SAMPLE ] [ - - POLARIZER - - ]
E A = A 0 2 2 [ ( R p + R s ) sin 2 φ ] u A
I = 0 2 π E ¯ A E A d φ = A 0 2 8 π R P + R S 2
I 0 = 2 π A 0 2
I NX = I I 0 = 1 16 R P + R s 2
( E A / / E A ) = ( 1 0 0 0 ) M 6 ( sin φ cos φ cos φ sin φ ) M 5 ( R p 0 0 R s ) M 4 ( 1 2 1 2 1 2 1 2 ) M 3 ( R p exp ( i ( Γ + 2 β 0 ) ) 0 0 R s exp ( i ( Γ + 2 β 0 ) ) ) M 4 , ( 1 2 1 2 1 2 1 2 ) M 3 , ( cos φ sin φ sin φ cos φ ) M 2 ( 2 2 0 ) M 1 A 0
[ - - - ANALYZER - - - ] [ - - - - - - - - - - - - SAMPLE & NOMARSKI - - - - - - - - - - ] [ - - - POLARIZER - - - ]
β 0 = 2 π hn 0 λ cos θ 0
E A = A i 2 [ ( cos φ + sin φ ) ( R P sin φ + R S cos φ ) + ( cos φ sin φ ) ( R P sin φ R S cos φ ) exp ( i ( Γ + 2 β 0 ) ) ] u A / /
I DIC edge = 1 16 [ R s 2 ( 1 + tan 2 Ψ + tan Ψ cos Δ ) + R s 2 ( 1 + tan 2 Ψ + tan Ψ cos Δ )
R s R s ( tan Ψ tan Ψ cos ( Δ Δ + Δ s Δ s + Γ + 2 β 0 ) + cos ( Δ s Δ s + Γ + 2 β 0 ) ) ]
I DIC edge * = 1 1 cos θ max 0 θ max I DIC edge sin θ d θ
I DIC flat = 1 16 [ R s + R p 2 + 2 ( R p 2 + R s 2 ) sin 2 Γ 2 ]
C X = I NX * ( step ) I NX * ( substrate ) I NX * ( step ) + I NX * ( substrate )
C DIC step = I DIC flat * ( step ) I DIC flat * ( substrate ) I DIC flat * ( step ) + I DIC flat * ( substrate )
C DIC edge = I DIC edge * I DIC flat * ( substrate ) I DIC edge * + I DIC flat * ( substrate )
I DIC edge = 1 4 sin 2 ( Γ + 2 β 0 2 )
C DIC edge = sin 2 ( Γ + 2 β 0 2 ) sin 2 ( Γ 2 ) sin 2 ( Γ + 2 β 0 2 ) + sin 2 ( Γ 2 )

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