Abstract

We propose a model for imaging point objects through a dielectric interface or stratified media. The model is applicable to conventional and confocal fluorescence microscopy, with single- or multiphoton excitation. An analytical solution is obtained in the form of readily computable functions. When large mismatches occur in the refractive indices of the media of the objective lens and specimen the illumination and detection point spread functions differ significantly, showing that currently used imaging models may fail to correctly predict imaging properties of optical microscopes.

© 2003 Optical Society of America

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References

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  1. F. Perrin, �??La fluorescence des solutions,�?? Ann. Phys. (Paris) 12, 169-275 (1929)
  2. P. Soleillet, �??Sur les paramètres caractérisant la polarization partielle de la lumière dans les phénomènes de fluorescence,�?? Ann. Phys. (Paris) 12, 23-86 (1929)
  3. D. Axelrod, �??Carbocyanine dye orientation in red cell membrane studied by microscopi fluorescence polarization,�?? Biophys. J. 26, 557-574 (1979)
    [CrossRef] [PubMed]
  4. I. Gryczynski, H. Malak and J.R. Lakowicz, �??Multiphoton excitation of the DNA stains DAPI and Hoechst,�?? Bioimaging 4, 138-148 (1996)
    [CrossRef]
  5. P. Török, P.D. Higdon, and T. Wilson, �??On the general properties of polarized light conventional and confocal microscopes,�?? Opt. Commun. 148, 300-315 (1998)
    [CrossRef]
  6. P.D. Higdon, P. Török, and T. Wilson, �??Imaging properties of high aperture multiphoton fluorescence scanning optical microscopes,�?? J. Microsc. (Oxford) 193, 127-141 (1999)
    [CrossRef]
  7. P. Török, P.D. Higdon and T. Wilson, �??Theory for confocal and conventional microscopes imaging small dielectric scatterers,�?? J. Mod. Opt. 45, 1681-1698 (1998)
    [CrossRef]
  8. C.J.R. Sheppard and P. Török, �??An electromagnetic theory of imaging in fluorescence microscopy, and imaging in polarization fluorescence microscopy,�?? Bioimaging 5, 205-218 (1997)
    [CrossRef]
  9. P. Török and P. Varga, �??Electromagnetic diffraction of light focused through a stratified medium,�?? Appl. Opt. 36, 2305-2312 (1997)
    [CrossRef] [PubMed]
  10. P. Török, �??Propagation of electromagnetic dipole waves through dielectric interfaces,�?? Opt. Lett. 25, 1463-1465 (2000)
    [CrossRef]
  11. Note that there was a typo in Eq. (6) and Eq. (14c) defining Ydet in Ref. 10
  12. D. Minsky, �??Memoir on Inventing the Confocal Scanning Microscope,�?? Scanning 10, 128-138 (1988)
    [CrossRef]
  13. S. Hell and E.H.K. Stelzer, �??Fundamental improvement of resolution with a 4-Pi-confocal microscope using two-photon excitation,�?? Opt. Comm. 93, 277-281 (1992)
    [CrossRef]
  14. E. H. K. Stelzer and S. Lindek, �??Fundamental reduction of the observation volume in far-field light microscopy by detection orthogonal to the illumination axis: confocal theta microscopy,�?? Opt. Commun. 111, 536-547 (1994)
    [CrossRef]
  15. O. Haeberlé et al., �??Multiple-objective microscopy with three-dimensional resolution near 100 nm and a long working distance,�?? Opt. Lett. 26, 1684-1686 (2001)
    [CrossRef]
  16. O. Haeberlé, �??Focusing of light through a stratified medium: a practical approach for computing microscope point spread functions. Part I: Conventional microscopy,�?? Opt. Commun. 216, 55-63 (2003)
    [CrossRef]

Ann. Phys. (Paris) (2)

F. Perrin, �??La fluorescence des solutions,�?? Ann. Phys. (Paris) 12, 169-275 (1929)

P. Soleillet, �??Sur les paramètres caractérisant la polarization partielle de la lumière dans les phénomènes de fluorescence,�?? Ann. Phys. (Paris) 12, 23-86 (1929)

Appl. Opt. (1)

Bioimaging (2)

I. Gryczynski, H. Malak and J.R. Lakowicz, �??Multiphoton excitation of the DNA stains DAPI and Hoechst,�?? Bioimaging 4, 138-148 (1996)
[CrossRef]

C.J.R. Sheppard and P. Török, �??An electromagnetic theory of imaging in fluorescence microscopy, and imaging in polarization fluorescence microscopy,�?? Bioimaging 5, 205-218 (1997)
[CrossRef]

Biophys. J. (1)

D. Axelrod, �??Carbocyanine dye orientation in red cell membrane studied by microscopi fluorescence polarization,�?? Biophys. J. 26, 557-574 (1979)
[CrossRef] [PubMed]

J. Microsc. (Oxford) (1)

P.D. Higdon, P. Török, and T. Wilson, �??Imaging properties of high aperture multiphoton fluorescence scanning optical microscopes,�?? J. Microsc. (Oxford) 193, 127-141 (1999)
[CrossRef]

J. Mod. Opt. (1)

P. Török, P.D. Higdon and T. Wilson, �??Theory for confocal and conventional microscopes imaging small dielectric scatterers,�?? J. Mod. Opt. 45, 1681-1698 (1998)
[CrossRef]

Opt. Comm. (1)

S. Hell and E.H.K. Stelzer, �??Fundamental improvement of resolution with a 4-Pi-confocal microscope using two-photon excitation,�?? Opt. Comm. 93, 277-281 (1992)
[CrossRef]

Opt. Commun. (3)

E. H. K. Stelzer and S. Lindek, �??Fundamental reduction of the observation volume in far-field light microscopy by detection orthogonal to the illumination axis: confocal theta microscopy,�?? Opt. Commun. 111, 536-547 (1994)
[CrossRef]

O. Haeberlé, �??Focusing of light through a stratified medium: a practical approach for computing microscope point spread functions. Part I: Conventional microscopy,�?? Opt. Commun. 216, 55-63 (2003)
[CrossRef]

P. Török, P.D. Higdon, and T. Wilson, �??On the general properties of polarized light conventional and confocal microscopes,�?? Opt. Commun. 148, 300-315 (1998)
[CrossRef]

Opt. Lett. (2)

Scanning (1)

D. Minsky, �??Memoir on Inventing the Confocal Scanning Microscope,�?? Scanning 10, 128-138 (1988)
[CrossRef]

Other (1)

Note that there was a typo in Eq. (6) and Eq. (14c) defining Ydet in Ref. 10

Supplementary Material (2)

» Media 1: MPG (2441 KB)     
» Media 2: MPG (2441 KB)     

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Figures (3)

Fig. 1.
Fig. 1.

(a) Focusing of an electromagnetic wave through a three-layer stratified medium. The origin O of the (x, y, z) reference frame is at the unaberrated Gaussian focal point. (b) Dipole radiation imaged through the same medium. The dipole is placed at the origin O of the (x’, y’, z’) reference frame. Superscripts 1, 2, 3, and d are for the three media and the detector region.

Fig. 2.
Fig. 2.

Illumination and detection PSF at λ=488 nm with a 40×, N.A.=0.9 dry objective, for a single fluorescent molecule located in a watery medium 50 µm below (a): a 120 µm thickness cover glass and (b): a 170 µm thickness cover glass. (a) and (b) are for a conventional microscope. (c) and (d): confocal PSFs computed with the usual model and our dipole model. Figures (c) and (d) correspond to the same conditions as (a) and (b), respectively.

Fig. 3.
Fig. 3.

(Movies 2.3 MB each) (a) Illumination and detection PSF for a single fluorescent molecule located in a watery medium 50 µm below a 170 µm thickness cover glass, using a 63× oil immersion objective lens (noil=1.515) with N.A.=1.2 with both detection and illumination wavelength at 633 nm. (b) Illumination and detection PSF at 46.5 µm into diamond (nspec=2.418). Both detection and illumination wavelengths are at 633 nm, using a 40× air immersion objective lens of N.A.=0.9. In the latter case the curves are very different, in contrast with the former case. Click panels to view movies of the PSFs as function of the observation depth. Figures hold for a conventional microscope. [Media 2]

Equations (29)

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E Nx = i ( I 0 ill + I 2 ill cos 2 ϕ )
E Ny = iI 2 ill sin 2 ϕ
E Nz = 2 I 1 ill cos ϕ
I 0 ill = 0 α 1 ( cos θ 1 ) 1 2 sin θ 1 J 0 ( k 1 ρ sin θ 1 ) ( T s + T p cos θ N ) exp ( i k 0 Ψ ill ) exp ( i k N z cos θ N ) d θ 1
I 1 ill = 0 α 1 ( cos θ 1 ) 1 2 sin θ 1 J 1 ( k 1 ρ sin θ 1 ) T p sin θ N exp ( i k 0 Ψ ill ) exp ( i k N z cos θ N ) d θ 1
I 2 ill = 0 α 1 ( cos θ 1 ) 1 2 sin θ 1 J 2 ( k 1 ρ sin θ 1 ) ( T s T p cos θ N ) exp ( i k 0 Ψ ill ) exp ( i k N z cos θ N ) d θ 1
Ψ ill = h N 1 n N cos θ N h 1 n 1 cos θ 1
E 1 x = 1 2 [ p ex * ( T s + T p cos θ N cos θ 1 ) 2 p ez * T p sin θ N cos θ 1 cos ϕ 1
( T s T p cos θ N cos θ 1 ) ( p ex * cos 2 ϕ 1 + p ey * sin 2 ϕ 1 ) ]
E 1 y = 1 2 [ p ey * ( T s + T p cos θ N cos θ 1 ) 2 p ez * T p sin θ N cos θ 1 sin ϕ 1
( T s T p cos θ N cos θ 1 ) ( p ex * sin 2 ϕ 1 p ey * cos 2 ϕ 1 ) ]
E 1 z = [ p ez * T p sin θ N sin θ 1 T p cos θ N sin θ 1 ( p ex * cos ϕ 1 + p ey * sin ϕ 1 ) ]
E = ( cos θ 1 ) 1 2 R 1 · L 1 · R · E 1
E x = cos 1 2 θ 1 { p ex * [ ( T s + T p cos θ N ) ( T s T p cos θ N ) cos 2 ϕ 1 ]
p ey * ( T s T p cos θ N ) sin 2 ϕ 1 2 p ez * T p sin θ N cos ϕ 1 }
E y = cos 1 2 θ 1 { p ex * ( T s T p cos θ N ) sin 2 ϕ 1
+ p ey * [ ( T s + T p cos θ N ) + ( T s T p cos θ N ) cos 2 ϕ 1 ] 2 p ez * T p sin θ N sin ϕ 1 }
E z = 0
E x = FT ( E x ) = p ex * ( I 0 det + I 2 det cos 2 ϕ d ) + p ey * ( I 2 det sin 2 ϕ d ) 2 i I 1 det p ez * cos ϕ d
E y = FT ( E y ) = p ex * I 2 det sin 2 ϕ d + p ey * ( I 0 det I 2 det cos 2 ϕ d ) 2 i I 1 det p ez * sin ϕ d
I 0 det = 0 α d ( cos θ 1 ) 1 2 sin 2 θ d J 0 ( k d ρ sin θ d ) ( T s + T p cos θ 3 )
× exp ( i k 0 Ψ det ) exp ( i k 1 z cos θ 1 ) d θ d
I 1 det = 0 α d ( cos θ 1 ) 1 2 sin 2 θ d J 1 ( k d ρ sin θ d ) T p sin θ 3
× exp ( i k 0 Ψ det ) exp ( i k 1 z cos θ 1 ) d θ d
I 2 det = 0 α d ( cos θ 1 ) 1 2 sin 2 θ d J 2 ( k d ρ sin θ d ) ( T s T p cos θ 3 )
× exp ( i k 0 Ψ det ) exp ( i k 1 z cos θ 1 ) d θ d
k 1 sin α 1 k d sin α d = k 1 sin θ 1 k d sin θ d = β
Ψ det = n 1 h 1 cos θ 1 n N h N 1 cos θ N
PSF det ( x , y , z ) = E x 2 + E y 2

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