Abstract

It is well known that vectorial analysis is essential to the study of high numerical aperture (NA) bright field scanning microscopes. We have constructed a high NA, vectorial model of a scanned Differential Interference Contrast (DIC) microscope which demonstrates that vectorial analysis is even more important to the study of this device. Our model is valid for coherent illumination and is able to model arbitrary scattering objects through the application of rigorous numerical methods for calculating electromagnetic scattering. We use our model to demonstrate how parameters such as sheer and bias affect imaging properties of both confocal and conventional scanning type DIC microscopes.

© 2005 Optical Society of America

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References

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    [Crossref]
  2. W. Galbraith, “The image of a point of light in differential interference contrast microscopy: Computer simulation,” Microsc. Acta 85, 233–254 (1982).
  3. T. Holmes and W. Levy, “Signal-processing characteristics of differential interference-contrast microscopy.” Appl. Opt. 26, 3929–3939 (1987).
    [Crossref] [PubMed]
  4. C. J. Cogswell and C. Sheppard, “Confocal differential interference contrast (DIC) microscopy: including a theoretical analysis of conventional and confocal DIC imaging,” J. Microsc. 165, 81–101 (1992).
    [Crossref]
  5. C. Preza, D. Snyder, and J. Conchello, “Theoretical development and experimental evaluation of imaging models for differential-interference-contrast microscopy,” J. Opt. Soc. Am. A 16, 2185–2199 (1999).
    [Crossref]
  6. C. Preza, “Rotational-diversity phase estimation from differential-interference-contrast microscopy images.” J. Opt. Soc. Am. A 17, 415–424 (2000).
    [Crossref]
  7. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. (London) A 253, 358–379 (1959).
    [Crossref]
  8. M. Born and E. Wolf, Principles of Optics, seventh ed. (Cambridge University Press, Cambridge, 1999).
  9. P. Török, P. Higdon, and T. Wilson, “Theory for confocal and conventional microscopes imaging small dielectric scatterers,” J. Mod. Opt. 45, 1681–1698 (1998).
    [Crossref]
  10. P. Munro and P. Török, “Vectorial, high-numerical-aperture study of phase-contrast microscopes,” J. Opt. Soc. Am. A 21, 1714–1723 (2004).
    [Crossref]
  11. P. Török, P. Higdon, and T. Wilson, “On the general properties of polarising conventional and confocal microscopes,” Opt. Commun. 148(4–6), 300–315 (1998).
    [Crossref]
  12. A. Taflove and S. Hagness, Computational electrodynamics, second edition (Artech House, 2000).
  13. K. Yee, “Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14(3), 302–307 (1966).
    [Crossref]
  14. P. Török, P. Higdon, R. Juškaitis, and T. Wilson, “Optimising the image contrast of conventional and confocal optical microscopes imaging finite sized spherical gold scatterers,” Opt. Commun. 155(4–6), 335–341 (1998).
    [Crossref]
  15. C. Bohren and D. Huffman, Absorption and scattering of light by small particles (Wiley Interscience, 1983).
  16. G. Arfken, Mathematical Methods for Physicists, 3rd ed. (Academic Press, Boston, 1985).
  17. P. Török and C. Sheppard, High numerical aperture focusing and imaging (Adam Hilger, (to pe published)).
  18. P. Munro and P. Török, “Effect of detector size on optical resolution in phase contrast microscopes,” Opt. Lett. 29, 623–625 (2004).
    [Crossref] [PubMed]

2004 (2)

2000 (1)

1999 (1)

1998 (3)

P. Török, P. Higdon, and T. Wilson, “Theory for confocal and conventional microscopes imaging small dielectric scatterers,” J. Mod. Opt. 45, 1681–1698 (1998).
[Crossref]

P. Török, P. Higdon, R. Juškaitis, and T. Wilson, “Optimising the image contrast of conventional and confocal optical microscopes imaging finite sized spherical gold scatterers,” Opt. Commun. 155(4–6), 335–341 (1998).
[Crossref]

P. Török, P. Higdon, and T. Wilson, “On the general properties of polarising conventional and confocal microscopes,” Opt. Commun. 148(4–6), 300–315 (1998).
[Crossref]

1992 (1)

C. J. Cogswell and C. Sheppard, “Confocal differential interference contrast (DIC) microscopy: including a theoretical analysis of conventional and confocal DIC imaging,” J. Microsc. 165, 81–101 (1992).
[Crossref]

1987 (1)

1982 (1)

W. Galbraith, “The image of a point of light in differential interference contrast microscopy: Computer simulation,” Microsc. Acta 85, 233–254 (1982).

1979 (1)

1966 (1)

K. Yee, “Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14(3), 302–307 (1966).
[Crossref]

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. (London) A 253, 358–379 (1959).
[Crossref]

Arfken, G.

G. Arfken, Mathematical Methods for Physicists, 3rd ed. (Academic Press, Boston, 1985).

Bohren, C.

C. Bohren and D. Huffman, Absorption and scattering of light by small particles (Wiley Interscience, 1983).

Born, M.

M. Born and E. Wolf, Principles of Optics, seventh ed. (Cambridge University Press, Cambridge, 1999).

Cogswell, C. J.

C. J. Cogswell and C. Sheppard, “Confocal differential interference contrast (DIC) microscopy: including a theoretical analysis of conventional and confocal DIC imaging,” J. Microsc. 165, 81–101 (1992).
[Crossref]

Conchello, J.

Galbraith, W.

W. Galbraith, “The image of a point of light in differential interference contrast microscopy: Computer simulation,” Microsc. Acta 85, 233–254 (1982).

Gordon, R.

Hagness, S.

A. Taflove and S. Hagness, Computational electrodynamics, second edition (Artech House, 2000).

Hartman, J.

Higdon, P.

P. Török, P. Higdon, and T. Wilson, “On the general properties of polarising conventional and confocal microscopes,” Opt. Commun. 148(4–6), 300–315 (1998).
[Crossref]

P. Török, P. Higdon, and T. Wilson, “Theory for confocal and conventional microscopes imaging small dielectric scatterers,” J. Mod. Opt. 45, 1681–1698 (1998).
[Crossref]

P. Török, P. Higdon, R. Juškaitis, and T. Wilson, “Optimising the image contrast of conventional and confocal optical microscopes imaging finite sized spherical gold scatterers,” Opt. Commun. 155(4–6), 335–341 (1998).
[Crossref]

Holmes, T.

Huffman, D.

C. Bohren and D. Huffman, Absorption and scattering of light by small particles (Wiley Interscience, 1983).

Juškaitis, R.

P. Török, P. Higdon, R. Juškaitis, and T. Wilson, “Optimising the image contrast of conventional and confocal optical microscopes imaging finite sized spherical gold scatterers,” Opt. Commun. 155(4–6), 335–341 (1998).
[Crossref]

Lessor, D.

Levy, W.

Munro, P.

Preza, C.

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. (London) A 253, 358–379 (1959).
[Crossref]

Sheppard, C.

C. J. Cogswell and C. Sheppard, “Confocal differential interference contrast (DIC) microscopy: including a theoretical analysis of conventional and confocal DIC imaging,” J. Microsc. 165, 81–101 (1992).
[Crossref]

P. Török and C. Sheppard, High numerical aperture focusing and imaging (Adam Hilger, (to pe published)).

Snyder, D.

Taflove, A.

A. Taflove and S. Hagness, Computational electrodynamics, second edition (Artech House, 2000).

Török, P.

P. Munro and P. Török, “Vectorial, high-numerical-aperture study of phase-contrast microscopes,” J. Opt. Soc. Am. A 21, 1714–1723 (2004).
[Crossref]

P. Munro and P. Török, “Effect of detector size on optical resolution in phase contrast microscopes,” Opt. Lett. 29, 623–625 (2004).
[Crossref] [PubMed]

P. Török, P. Higdon, and T. Wilson, “On the general properties of polarising conventional and confocal microscopes,” Opt. Commun. 148(4–6), 300–315 (1998).
[Crossref]

P. Török, P. Higdon, R. Juškaitis, and T. Wilson, “Optimising the image contrast of conventional and confocal optical microscopes imaging finite sized spherical gold scatterers,” Opt. Commun. 155(4–6), 335–341 (1998).
[Crossref]

P. Török, P. Higdon, and T. Wilson, “Theory for confocal and conventional microscopes imaging small dielectric scatterers,” J. Mod. Opt. 45, 1681–1698 (1998).
[Crossref]

P. Török and C. Sheppard, High numerical aperture focusing and imaging (Adam Hilger, (to pe published)).

Wilson, T.

P. Török, P. Higdon, R. Juškaitis, and T. Wilson, “Optimising the image contrast of conventional and confocal optical microscopes imaging finite sized spherical gold scatterers,” Opt. Commun. 155(4–6), 335–341 (1998).
[Crossref]

P. Török, P. Higdon, and T. Wilson, “Theory for confocal and conventional microscopes imaging small dielectric scatterers,” J. Mod. Opt. 45, 1681–1698 (1998).
[Crossref]

P. Török, P. Higdon, and T. Wilson, “On the general properties of polarising conventional and confocal microscopes,” Opt. Commun. 148(4–6), 300–315 (1998).
[Crossref]

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. (London) A 253, 358–379 (1959).
[Crossref]

M. Born and E. Wolf, Principles of Optics, seventh ed. (Cambridge University Press, Cambridge, 1999).

Yee, K.

K. Yee, “Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14(3), 302–307 (1966).
[Crossref]

Appl. Opt. (1)

IEEE Trans. Antennas Propag. (1)

K. Yee, “Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14(3), 302–307 (1966).
[Crossref]

J. Microsc. (1)

C. J. Cogswell and C. Sheppard, “Confocal differential interference contrast (DIC) microscopy: including a theoretical analysis of conventional and confocal DIC imaging,” J. Microsc. 165, 81–101 (1992).
[Crossref]

J. Mod. Opt. (1)

P. Török, P. Higdon, and T. Wilson, “Theory for confocal and conventional microscopes imaging small dielectric scatterers,” J. Mod. Opt. 45, 1681–1698 (1998).
[Crossref]

J. Opt. Soc. Am. (1)

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

Microsc. Acta (1)

W. Galbraith, “The image of a point of light in differential interference contrast microscopy: Computer simulation,” Microsc. Acta 85, 233–254 (1982).

Opt. Commun. (2)

P. Török, P. Higdon, and T. Wilson, “On the general properties of polarising conventional and confocal microscopes,” Opt. Commun. 148(4–6), 300–315 (1998).
[Crossref]

P. Török, P. Higdon, R. Juškaitis, and T. Wilson, “Optimising the image contrast of conventional and confocal optical microscopes imaging finite sized spherical gold scatterers,” Opt. Commun. 155(4–6), 335–341 (1998).
[Crossref]

Opt. Lett. (1)

Proc. Roy. Soc. (London) A (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. (London) A 253, 358–379 (1959).
[Crossref]

Other (5)

M. Born and E. Wolf, Principles of Optics, seventh ed. (Cambridge University Press, Cambridge, 1999).

A. Taflove and S. Hagness, Computational electrodynamics, second edition (Artech House, 2000).

C. Bohren and D. Huffman, Absorption and scattering of light by small particles (Wiley Interscience, 1983).

G. Arfken, Mathematical Methods for Physicists, 3rd ed. (Academic Press, Boston, 1985).

P. Török and C. Sheppard, High numerical aperture focusing and imaging (Adam Hilger, (to pe published)).

Supplementary Material (2)

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Figures (15)

Fig. 1.
Fig. 1.

Schematic diagram of a scanning type DIC microscope.

Fig. 2.
Fig. 2.

Diagram showing how a Wollaston prism modifies the phase front of the x and y-components of the incident field leading to two mutually shifted focused spots.

Fig. 3.
Fig. 3.

Diagram of a typical ray propagating through a Wollaston prism. The center of the prism, where both wedges have equal thickness is positioned at η = η c

Fig. 4.
Fig. 4.

Diagrams of (a) The detector field due to an arbitrary dipole moment p with a Wollaston prism in place and (b) without a Wollaston prism in place.

Fig. 5.
Fig. 5.

Components of electric field in the focus due to the x and y polarised beams. The top row correspond to the focused x-polarised beam and second the y polarised beam. The bottom row corresponds to the total field components. Each distribution is 2 μm wide and the origin is represented by a blue cross. Each component has been normalised by the peak | E x x | value.

Fig. 6.
Fig. 6.

Plots of the intensity of the electric and magnetic fields as well as the electromagnetic energy density.

Fig. 7.
Fig. 7.

Lateral point spread function of a confocal DIC microscope in reflection for ϕ b = 0 and ϕ b = π/2.

Fig. 8.
Fig. 8.

Animation showing the field scattered by the dielectric sphere (blue circle) as well as the field at the detector for the case of ϕ b = 0. [Media 1]

Fig. 9.
Fig. 9.

Animation showing the confocal DIC image, along the xz and yz planes, of a dielectric sphere situated in focus, on axis for ϕ b , ranging from 0 to π/2. [Media 2]

Fig. 10.
Fig. 10.

Line scans of dielectric sphere using confocal (point detector) and conventional (100 μm radius detector) detection.

Fig. 11.
Fig. 11.

Plot showing the components of detector signal obtained when a dielectric sphere is scanned along the x-axis of a conventional and confocal scanning DIC microscope. Corresponds to the case ϕ b = π/2 and sphere refractive index 1.

Fig. 12.
Fig. 12.

Animation showing the scattered field (top left) and detector fields for various values of ϕ b . The detector has side of 200μm. The ridge is constructed from perfectly conducting material with width λ/2 and height Δ = λ/4. A wavelength of λ = 632.8nm was used with a 0.85 NA, 100× objective.

Fig. 13.
Fig. 13.

Plot of confocal and conventional (detector radius 100μm) detector signals for a perfectly conducting ridge of height Δ = λ/4. The top of the ridge was in the geometrical focus. The scan position of the ridge relative to the detector signal is indicated in the plots. Bias values of (a) π/2, (b) π/4 and (c) 0 were used. A wavelength of λ=632.8 nm was employed, the ridge had width of λ/2 and a 0.85, 100 × objective was used.

Fig. 14.
Fig. 14.

Plots showing the confocal detector signal for a perfectly conducting step of various heights Δ, for bias values of (a) π/2, (b) 3π/10 and (c) 0. Note that the x-axis of the plot gives the position of step itself and that for x < 0 the optical axis intercepted the step surface at z = 0 and for x > 0 the optical axis intercepted the step surface at z = Δ. A shear of 0.5 was employed with wavelength λ=632.8 nm and a 0.85 NA (dry), 100× objective.

Fig. 15.
Fig. 15.

Plot showing how confocal detector signal varies as the shear is varied from 0.1 to 0.5 for bias values of (a) π/2, (b) 3π/10 and (c) 0. The wavelength was λ=632.8 nm and a 0.85 NA, 100 × objective was used. The step had height Δ = λ/4.

Equations (32)

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ϕ η = k ( T n + η c n _ tan θ w + ηn _ tan θ w )
ϕ ξ = k ( T n + + η c n _ tan θ w ηn _ tan θ w )
E ( r ) = ιf λ Ω ε 0 ( s ̂ ) s z exp ( ιk s ̂ r ) d s x d s y
ε 0 = exp ( ι ϕ η ) ε 0 x + exp ( ι ϕ ξ ) ε 0 y
E x ( r ) = ιf λ Ω ε 0 x ( s ̂ ) s z exp ( ιk s ̂ r ) exp ( ιk ( η c n _ tan θ w + ηn _ tan θ w ) ) d s x d s y
= ιf λ exp ( ι k η c n _ tan θ w ) Ω ε 0 x ( s ̂ ) s z exp ( ιk s ̂ ( x f n tan θ w , y , z ) d s x d s y
E x ( r ) = exp ( ι ϕ b 2 ) E 0 x ( x x s 2 , y , z )
E y ( r ) = exp ( ι ϕ b 2 ) E 0 y ( x + x s 2 , y , z )
E 0 , x x = I 0 + I 2 cos ( 2 ϕ ) E 0 , x y = I 2 sin ( 2 ϕ ) E 0 , y x = I 2 sin ( 2 ϕ ) E 0 , y x = I 0 I 2 cos ( 2 ϕ ) E 0 , z x = 2 ιI 1 cos ϕ E 0 , z y = 2 ι I 1 sin ϕ
I 0 = 0 α cos θ sin θ ( 1 + cos θ ) J 0 ( ρ ) exp ( ι Θ )
I 1 = 0 α cos θ sin 2 θ J 1 ( ρ ) exp ( ι Θ )
I 2 = 0 α cos θ sin θ ( 1 cos θ ) J 2 ( ρ ) exp ( ι Θ )
E x , p det = p x ( I 0 A + I 2 A cos 2 ϕ ) + p y I 2 A sin 2 ϕ 2 ι p z I 1 A cos ϕ
E y , p det = p y ( I 0 A + I 2 A cos 2 ϕ ) + p x I 2 A sin 2 ϕ 2 ι p z I 1 A sin ϕ
E z , p det = 2 ι ( p x cos ϕ + p y sin ϕ ) I 1 B 2 p z I 0 B
I 0 A = 0 α 2 cos θ 2 cos θ 1 sin θ 2 ( 1 + cos θ 1 cos θ 2 ) J 0 ( ρ ) exp ( ι Θ ) d θ 2
I 0 B = 0 α 2 cos θ 2 cos θ 1 sin 2 θ 2 sin θ 1 J 0 ( ρ ) exp ( ι Θ ) 2
I 1 A = 0 α 2 cos θ 2 cos θ 1 sin θ 2 cos θ 2 sin θ 1 J 1 ( ρ ) exp ( ι Θ ) d θ 2
I 1 B = 0 α 2 cos θ 2 cos θ 1 sin 2 θ 2 cos θ 1 J 1 ( ρ ) exp ( ι Θ ) d θ 2
I 2 A = 0 α 2 cos θ 2 cos θ 1 sin θ 2 ( 1 cos θ 1 cos θ 2 ) J 2 ( ρ ) exp ( ι Θ ) d θ 2
E x det = E x , p det ( x + β ( x d x s 2 ) , y + β y d , z ) exp ( ι ϕ b 2 )
E y det = E y , p det ( x + β ( x d + x s 2 ) , y + β y d , z ) exp ( - ι ϕ b 2 )
E p det = 0
I det = E det 2 DdS
E x t = 1 [ H z y H y z σ E x ]
E x i , j + 1 / 2 , k + 1 / 2 n + 1 / 2 = α i , j + 1 / 2 , k + 1 / 2 E x i , j + 1 / 2 , k + 1 / 2 n 1 / 2 + β i , j + 1 / 2 , k + 1 / 2 ( H z i , j + 1 , k + 1 / 2 n H z i , j , k + 1 / 2 n Δ y
H y i , j + 1 / 2 , k + 1 n H y i , j + 1 / 2 , k n Δ z )
E s ̂ r = ι f λ ε 0 ( s ̂ ) s z exp ( ι k s ̂ r )
T x = R z ( ϕ ) R y ( θ ) R z ( ϕ )
T y = R z ( π 2 ϕ ) R y ( θ ) R z ( ϕ )
R z ( ϕ ) = [ cos ϕ sin ϕ 0 sin ϕ cos ϕ 0 0 0 1 ] R y ( θ ) = [ cos θ 0 sin θ 0 1 0 sin θ 0 cos θ ]
I det = 2 S ( E sc 2 + E d 2 + 2 { E sc * E d } ) DdS = I sc + I d + I int

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