Abstract

Spectral self-interference microscopy (SSM) relies on the balanced collection of light traveling two different paths from the sample to the detector, one direct and the other indirect from a reflecting substrate. The resulting spectral interference effects allow nanometer-scale axial localization of isolated emitters. To produce spectral fringes the difference between the two optical paths must be significant. Consequently, to ensure that both contributions are in focus, a low-numerical-aperture objective lens must be used, giving poor lateral resolution. Here this limitation is overcome using a 4Pi apparatus to produce the requisite two paths to the detector. The resulting instrument generalizes both SSM and 4Pi microscopy and allows a quantification of SSM resolution (rather than localization precision). Specifically, SSM is shown to be subject to the same resolution constraints as 4Pi microscopy.

© 2007 Optical Society of America

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References

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2007 (3)

2006 (6)

A. Bilenca, A. Ozcan, B. Bouma, and G. Tearney, "Fluorescence coherence tomography," Opt. Express 14, 7134-7143 (2006).
[CrossRef] [PubMed]

D. Baddeley, C. Carl, and C. Cremer, "4Pi microscopy deconvolution with a variable point-spread function," Appl. Opt. 45, 7056-7064 (2006).
[CrossRef] [PubMed]

S. Ram, E. S. Ward, and R. J. Ober, "Beyond Rayleigh's criterion: A resolution measure with application to single-molecule microscopy," Proc. Natl. Acad. Sci. U.S.A. 103, 4457-4462 (2006).
[CrossRef] [PubMed]

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, "STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis," Nature (London) 440, 935-939 (2006).
[CrossRef]

S. Ram, E. S. Ward, and R. J. Ober, "A stochastic analysis of performance limits for optical microscopes," Multidimens. Syst. Signal Process. 17, 27-57 (2006).
[CrossRef]

L. Moiseev, M. S. Ünlü, A. K. Swan, B. B. Goldberg, and C. R. Cantor, "DNA conformation on surfaces measured by fluorescence self-interference," Proc. Natl. Acad. Sci. U.S.A. 103, 2623-2628 (2006).
[CrossRef] [PubMed]

2005 (1)

M. G. L. Gustafsson, "Nonlinear structured-illumination microscopy: Wide-field fluorescence imaging with theoretically unlimited resolution," Proc. Natl. Acad. Sci. U.S.A. 102, 13081-13086 (2005).
[CrossRef] [PubMed]

2004 (4)

2003 (2)

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, "Myosin V walks hand-over-hand: Single fluorophore imaging with 1.5-nm localization," Science 300, 2061-2065 (2003).
[CrossRef] [PubMed]

A. K. Swan, L. A. Moiseev, C. R. Cantor, B. J. Davis, S. B. Ippolito, W. C. Karl, B. B. Goldberg, and M. S. Ünlü, "Toward nanometer-scale resolution in fluorescence microscopy using spectral self-interference," IEEE J. Sel. Top. Quantum Electron. 9, 294-300 (2003).
[CrossRef]

2002 (4)

H. Kano, S. Jakobs, M. Nagorni, and S. W. Hell, "Dual-color 4Pi-confocal microscopy with 3D-resolution in the 100nm range," Ultramicroscopy 90, 207-213 (2002).
[CrossRef] [PubMed]

M. R. Arnison and C. J. R. Sheppard, "A 3D vectorial optical transfer function suitable for arbitrary pupil functions," Opt. Commun. 211, 53-63 (2002).
[CrossRef]

C. W. McCutchen, "Generalized aperture and the three-dimensional diffraction image: Erratum," J. Opt. Soc. Am. A 19, 1781 (2002).
[CrossRef]

R. Heintzmann and T. M. Jovin, "Saturated patterned excitation microscopy--a concept for optical resolution improvement," J. Opt. Soc. Am. A 19, 1599-1609 (2002).
[CrossRef]

2001 (2)

2000 (1)

M. Schmidt, M. Nagorni, and S. W. Hell, "Subresolution axial distance measurements in far-field fluorescence microscopy with precision of 1 nanometer," Rev. Sci. Instrum. 71, 2742-2745 (2000).
[CrossRef]

1999 (3)

P. J. Verveer, M. J. Gemkow, and T. M. Jovin, "A comparison of image restoration approaches applied to three-dimensional confocal and wide-field fluorescence microscopy," J. Microsc. 193, 50-61 (1999).
[CrossRef]

M. G. L. Gustafsson, "Extended resolution fluorescence microscopy," Curr. Opin. Struct. Biol. 9, 627-634 (1999).
[CrossRef] [PubMed]

T. A. Klar and S. W. Hell, "Subdiffraction resolution in far-field fluorescence microscopy," Opt. Lett. 24, 954-956 (1999).
[CrossRef]

1998 (5)

S. W. Hell and M. Nagorni, "4Pi confocal microscopy with alternate interference," Opt. Lett. 23, 1567-1569 (1998).
[CrossRef]

M. Schrader, K. Bahlmann, G. Giese, and S. W. Hell, "4Pi-confocal imaging in fixed biological specimens," Biophys. J. 75, 1659-1668 (1998).
[CrossRef] [PubMed]

A. Egner, M. Schrader, and S. W. Hell, "Refractive index mismatch induced intensity and phase variations in fluorescence confocal, multiphoton and 4Pi-microscopy," Opt. Commun. 153, 211-217 (1998).
[CrossRef]

E. H. K. Stelzer, "Contrast, resolution, pixelation, dynamic range and signal-to-noise ratio: Fundamental limits to resolution in fluorescence light microscopy," J. Microsc. 189, 15-24 (1998).
[CrossRef]

M. Schrader, S. W. Hell, and H. T. M. van der Voort, "Three-dimensional super-resolution with a 4Pi-confocal microscope using image restoration," J. Appl. Phys. 84, 4033-4042 (1998).
[CrossRef]

1994 (2)

1992 (1)

1986 (3)

I. J. Cox and C. J. R. Sheppard, "Information capacity and resolution in an optical system," J. Opt. Soc. Am. A 3, 1152-1158 (1986).
[CrossRef]

C. J. R. Sheppard, "The spatial frequency cut-off in three-dimensional imaging," Optik (Stuttgart) 72, 131-133 (1986).

C. J. R. Sheppard, "The spatial frequency cut-off in three-dimensional imaging II," Optik (Stuttgart) 74, 128-129 (1986).

1964 (1)

1959 (1)

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system," Proc. R. Soc. London, Ser. A 253, 358-379 (1959).
[CrossRef]

1873 (1)

E. Abbe, "Beiträge zur Theorie des Mikroskops und der Mikroskopischen Wahrnehmung," Arch. Mikrosc. Anat. Entwicklungsmech. 9, 413-468 (1873).
[CrossRef]

Appl. Opt. (1)

Arch. Mikrosc. Anat. Entwicklungsmech. (1)

E. Abbe, "Beiträge zur Theorie des Mikroskops und der Mikroskopischen Wahrnehmung," Arch. Mikrosc. Anat. Entwicklungsmech. 9, 413-468 (1873).
[CrossRef]

Biophys. J. (2)

R. J. Ober, S. Ram, and E. S. Ward, "Localization accuracy in single-molecule microscopy," Biophys. J. 86, 1185-1200 (2004).
[CrossRef] [PubMed]

M. Schrader, K. Bahlmann, G. Giese, and S. W. Hell, "4Pi-confocal imaging in fixed biological specimens," Biophys. J. 75, 1659-1668 (1998).
[CrossRef] [PubMed]

Curr. Opin. Struct. Biol. (1)

M. G. L. Gustafsson, "Extended resolution fluorescence microscopy," Curr. Opin. Struct. Biol. 9, 627-634 (1999).
[CrossRef] [PubMed]

IEEE J. Sel. Top. Quantum Electron. (1)

A. K. Swan, L. A. Moiseev, C. R. Cantor, B. J. Davis, S. B. Ippolito, W. C. Karl, B. B. Goldberg, and M. S. Ünlü, "Toward nanometer-scale resolution in fluorescence microscopy using spectral self-interference," IEEE J. Sel. Top. Quantum Electron. 9, 294-300 (2003).
[CrossRef]

J. Appl. Phys. (2)

L. Moiseev, C. R. Cantor, M. I. Aksun, M. Dogan, B. B. Goldberg, A. K. Swan, and M. S. Ünlü, "Spectral self-interference fluorescence microscopy," J. Appl. Phys. 96, 5311-5315 (2004).
[CrossRef]

M. Schrader, S. W. Hell, and H. T. M. van der Voort, "Three-dimensional super-resolution with a 4Pi-confocal microscope using image restoration," J. Appl. Phys. 84, 4033-4042 (1998).
[CrossRef]

J. Microsc. (2)

P. J. Verveer, M. J. Gemkow, and T. M. Jovin, "A comparison of image restoration approaches applied to three-dimensional confocal and wide-field fluorescence microscopy," J. Microsc. 193, 50-61 (1999).
[CrossRef]

E. H. K. Stelzer, "Contrast, resolution, pixelation, dynamic range and signal-to-noise ratio: Fundamental limits to resolution in fluorescence light microscopy," J. Microsc. 189, 15-24 (1998).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (9)

B. J. Davis, A. K. Swan, M. S. Ünlü, W. C. Karl, B. B. Goldberg, J. C. Schotland, and P. S. Carney, "Spectral self-interference microscopy for low-signal nanoscale axial imaging," J. Opt. Soc. Am. A 24, 3587-3599 (2007).
[CrossRef]

C. W. McCutchen, "Generalized aperture and the three-dimensional diffraction image: Erratum," J. Opt. Soc. Am. A 19, 1781 (2002).
[CrossRef]

C. J. R. Sheppard and M. Gu, "Three-dimensional transfer functions for high-aperture systems," J. Opt. Soc. Am. A 11, 593-598 (1994).
[CrossRef]

M. Gu and C. J. R. Sheppard, "Three-dimensional transfer functions in 4Pi confocal microscopes," J. Opt. Soc. Am. A 11, 1619-1627 (1994).
[CrossRef]

I. J. Cox and C. J. R. Sheppard, "Information capacity and resolution in an optical system," J. Opt. Soc. Am. A 3, 1152-1158 (1986).
[CrossRef]

M. Nagorni and S. W. Hell, "Coherent use of opposing lenses for axial resolution increase. II. Power and limitation of nonlinear image restoration," J. Opt. Soc. Am. A 18, 49-54 (2001).
[CrossRef]

M. Nagorni and S. W. Hell, "Coherent use of opposing lenses for axial resolution increase in fluorescence microscopy. I. Comparative study of concepts," J. Opt. Soc. Am. A 18, 36-48 (2001).
[CrossRef]

S. Hell and E. H. K. Stelzer, "Properties of a 4Pi confocal fluorescence microscope," J. Opt. Soc. Am. A 9, 2159-2166 (1992).
[CrossRef]

R. Heintzmann and T. M. Jovin, "Saturated patterned excitation microscopy--a concept for optical resolution improvement," J. Opt. Soc. Am. A 19, 1599-1609 (2002).
[CrossRef]

Multidimens. Syst. Signal Process. (1)

S. Ram, E. S. Ward, and R. J. Ober, "A stochastic analysis of performance limits for optical microscopes," Multidimens. Syst. Signal Process. 17, 27-57 (2006).
[CrossRef]

Nature (London) (1)

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, "STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis," Nature (London) 440, 935-939 (2006).
[CrossRef]

Opt. Commun. (2)

M. R. Arnison and C. J. R. Sheppard, "A 3D vectorial optical transfer function suitable for arbitrary pupil functions," Opt. Commun. 211, 53-63 (2002).
[CrossRef]

A. Egner, M. Schrader, and S. W. Hell, "Refractive index mismatch induced intensity and phase variations in fluorescence confocal, multiphoton and 4Pi-microscopy," Opt. Commun. 153, 211-217 (1998).
[CrossRef]

Opt. Express (4)

Opt. Lett. (3)

Optik (Stuttgart) (2)

C. J. R. Sheppard, "The spatial frequency cut-off in three-dimensional imaging," Optik (Stuttgart) 72, 131-133 (1986).

C. J. R. Sheppard, "The spatial frequency cut-off in three-dimensional imaging II," Optik (Stuttgart) 74, 128-129 (1986).

Proc. Natl. Acad. Sci. U.S.A. (3)

M. G. L. Gustafsson, "Nonlinear structured-illumination microscopy: Wide-field fluorescence imaging with theoretically unlimited resolution," Proc. Natl. Acad. Sci. U.S.A. 102, 13081-13086 (2005).
[CrossRef] [PubMed]

L. Moiseev, M. S. Ünlü, A. K. Swan, B. B. Goldberg, and C. R. Cantor, "DNA conformation on surfaces measured by fluorescence self-interference," Proc. Natl. Acad. Sci. U.S.A. 103, 2623-2628 (2006).
[CrossRef] [PubMed]

S. Ram, E. S. Ward, and R. J. Ober, "Beyond Rayleigh's criterion: A resolution measure with application to single-molecule microscopy," Proc. Natl. Acad. Sci. U.S.A. 103, 4457-4462 (2006).
[CrossRef] [PubMed]

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

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system," Proc. R. Soc. London, Ser. A 253, 358-379 (1959).
[CrossRef]

Rev. Sci. Instrum. (1)

M. Schmidt, M. Nagorni, and S. W. Hell, "Subresolution axial distance measurements in far-field fluorescence microscopy with precision of 1 nanometer," Rev. Sci. Instrum. 71, 2742-2745 (2000).
[CrossRef]

Science (1)

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, "Myosin V walks hand-over-hand: Single fluorophore imaging with 1.5-nm localization," Science 300, 2061-2065 (2003).
[CrossRef] [PubMed]

Ultramicroscopy (1)

H. Kano, S. Jakobs, M. Nagorni, and S. W. Hell, "Dual-color 4Pi-confocal microscopy with 3D-resolution in the 100nm range," Ultramicroscopy 90, 207-213 (2002).
[CrossRef] [PubMed]

Other (4)

T.Basché, W.E.Moerner, M.Orrit, and U.P.Wild, eds., Single-Molecule Optical Detection, Imaging and Spectroscopy (VCH, 1997).

T. Wilson and C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).

S. W. Hell, "Double-scanning microscope," European patent 0491289, 18 December 1990.

M. Dogan, B. B. Goldberg, A. K. Swan, and M. S. Ünlü, "4Pi spectral self-interference fluorescence microscopy," presented at OSA Frontiers in Optics 2006/Laser Science XXII, Rochester, New York, October 8-12, 2006.

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Figures (9)

Fig. 1
Fig. 1

Basic illustration of one implementation of fluorescence spectral self-interference microscopy. Note that the light from the excitation source has been shown as focused while a ray illustration has been used for the emission. This is solely to provide a clear distinction between the two—both excitation and emission light undergo focusing effects.

Fig. 2
Fig. 2

Ray illustration of the difference in focusing between the direct and reflected paths in SSM. The two contributions converge to different points which cannot be simultaneously at the focal point of the objective lens.

Fig. 3
Fig. 3

Simplified schematic of a 4Pi Type C microscope. Excitation and detection are both through twin opposing objective lenses.

Fig. 4
Fig. 4

Example point spread functions for a 4Pi–SSM system. These plots are two-dimensional slices (the x z plane) of three-dimensional functions. Instrument parameters that are constant for all plots include NA = 1.4 , n = 1.518 , λ e = 488 nm , and the excitation polarization state, before focusing, which is in the x direction. In (a)–(f), λ d = 510 nm and r o = 0 , while ( ϕ e , ϕ d ) is ( 0 , 0 ) , ( 0 , π 2 ) , ( 0 , π ) , ( π , 0 ) , ( π 2 , π 2 ) , and ( π , π ) , respectively. In (g)–(i), λ d = 590 nm and r o = 0 , while ( ϕ e , ϕ d ) is ( 0 , 0 ) , ( 0 , π 2 ) , and ( 0 , π ) , respectively. In (j)–(l), λ d = 510 nm , and ( ϕ e , ϕ d ) = ( 0 , 0 ) , while r o is ( 0 , 0 , 200 ) nm , ( 0 , 0 , 400 ) nm , and ( 0 , 0 , 600 ) nm , respectively. A nonlinear display scale is used so that low-level detail is visible.

Fig. 5
Fig. 5

Magnitudes of the OTFs corresponding to the PSFs of Fig. 4. The k x - k z plane is shown for each, and the plots have all been scaled by the same constant so that the largest value seen is 1. A nonlinear display scale is used so that low-level detail is visible.

Fig. 6
Fig. 6

OTF supports for microscopes with λ e = 488 nm , λ d = 510 nm , n = 1.518 . Only the k x - k z plane is shown but the support is rotationally symmetric about the k z axis. The OTF support for a wide-field microscope with a NA of 1.4 is shown in (a). The OTF supports for 4Pi microscopes with NA = 1.4 and NA = 1 are shown in (b) and (c), respectively.

Fig. 7
Fig. 7

Diagram representing the experimental 4Pi–SSM system used. Beam paths are overlaid on a photograph of the triangular 4Pi microscope unit. The excitation and detection instrumentation are represented schematically, and the polarization of the excitation laser is indicated by E. Note that the photograph contains some optical elements not relevant to the discussion presented here—specifically, the mirror with mount behind the text “Moveable Mirror” and the filter cube behind the text “Moveable Objective.”

Fig. 8
Fig. 8

x z slice of the data collected by the 4Pi–SSM instrument operating in 4Pi mode from (a) a fluorescent bead, (b) the theoretically predicted data with no background, and (c) the data predicted when the background is modeled. The background model consists of a three-dimensional Gaussian with a standard deviation of 80 nm laterally and 180 nm axially. Axial cross sections of the data, the predicted data (with background included), and the background are given in (d). The spectral envelope s ( λ d ) used in the model was assumed to be Gaussian and centered around λ d = 550 nm with a standard deviation of 25 nm .

Fig. 9
Fig. 9

(a) Predicted and (b) measured axial-spectral data from a 4Pi–SSM system when imaging a thin lateral fluorescent layer. The data model is defined by the parameters D = 29.2 μ m , ϕ d , 0 = 0.94 π and ϕ e = 0.25 π . The background term b ( z ) is Gaussian with an amplitude of 0.06 and a standard deviation of 250 nm . Spectral profiles at z = 0 and the estimated spectral envelope s ( λ d ) are shown in (c), as is a spatial profile at λ d = 527 nm in (d).

Equations (8)

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h 4 Pi ( r ) = a 1 ( r ; λ e ) + a 2 ( r ; λ e ) 2 a 1 ( r ; λ d ) + a 2 ( r ; λ d ) 2 ,
ϕ d ( λ d ) = 2 π D λ d .
a 2 ( r ; λ ) e i ϕ ( λ ) a 2 ( r r o ; λ ) .
h 4 Pi SSM ( r ; λ d ) = a 1 ( r ; λ e ) + e i ϕ e a 2 ( r r o ; λ e ) 2 a 1 ( r ; λ d ) + e i ϕ d ( λ d ) a 2 ( r r o ; λ d ) 2 .
H 4 Pi ( k ) = { [ A 1 ( k ; λ e ) + A 2 ( k ; λ e ) ] [ A 1 ( k ; λ e ) + A 2 ( k ; λ e ) ] } { [ A 1 ( k ; λ d ) + A 2 ( k ; λ d ) ] [ A 1 ( k ; λ d ) + A 2 ( k ; λ d ) ] } .
A 2 ( k ; λ ) e i [ k r o ϕ ( λ ) ] A 2 ( k ; λ ) .
f ( r ) = s ( λ d ) [ h 4 Pi SSM ( r ; λ d ) o ( r ) ] d λ d + b ( r ) ,
f ( z , λ d ) = s ( λ d ) [ h 4 Pi SSM ( x , y , z ; λ d ) d x d y + b ( z ) ] .

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