Abstract

Subtraction microscopy has recently been promoted for its compactness and simplicity of enhancing spatial resolution. However, until now, the subtraction factors used in such microscopes to process raw images have been chosen experientially, and it has been impossible to determine whether the resolved structures after subtraction are appropriate or over-processed. Based on vector diffraction theory and two-dimensional convolution, this paper presents numerical investigations of the parameters that may offer the selection criterion of subtraction factors used in subtraction microscopy. It proposes two essential parameters for appropriately evaluating the subtraction factor: the fluorescence peak intensity after subtraction and resolution derivative.

© 2014 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref]
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  20. http://en.wikipedia.org/wiki/Circular_polarization .

2014 (3)

2013 (1)

2012 (1)

2009 (2)

S. Deng, L. Liu, Y. Cheng, R. Li, and Z. Xu, “Investigation of the influence of the aberration induced by a plane interface on STED microscopy,” Opt. Express 17(3), 1714–1725 (2009).
[Crossref] [PubMed]

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” P. Natl. Acad. Sci. USA 106(52), 22287–22292 (2009).
[Crossref]

2008 (1)

2006 (3)

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. L. Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref] [PubMed]

M. J. Rust, M. Bates, and X. W. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Meth. 3, 793–796 (2006).
[Crossref]

A. Sharonov and R. M. Hochstrasser, “Wide-field sub-diffraction imaging by accumulated binding of diffusing probes,” Proc. Natl. Acad. Sci. USA 103(50), 18911–18916 (2006).
[Crossref] [PubMed]

2004 (1)

M. P. Gordon, T. Ha, and P. R. Selvin, “Single-molecule high-resolution imaging with photobleaching,” P. Natl. Acad. Sci. USA 101(17), 6462–6465 (2004).
[Crossref]

2003 (2)

2000 (1)

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microscopy 198, 82–87 (2000).
[Crossref]

1994 (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. Lond. A 253, 358–379 (1959).
[Crossref]

Bates, M.

M. J. Rust, M. Bates, and X. W. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Meth. 3, 793–796 (2006).
[Crossref]

Betzig, E.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. L. Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref] [PubMed]

Bonifacino, J. S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. L. Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref] [PubMed]

Cheng, Y.

Colyer, R.

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” P. Natl. Acad. Sci. USA 106(52), 22287–22292 (2009).
[Crossref]

Davidson, M. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. L. Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref] [PubMed]

Dehez, H.

Deng, S.

Dertinger, T.

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” P. Natl. Acad. Sci. USA 106(52), 22287–22292 (2009).
[Crossref]

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[Crossref] [PubMed]

Enderlein, J.

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” P. Natl. Acad. Sci. USA 106(52), 22287–22292 (2009).
[Crossref]

Gan, X.

Ganic, D.

Ge, J. H.

C. F. Kuang, S. Li, W. Liu, X. Hao, Z. T. Gu, Y. F. Wang, J. H. Ge, H. F. Li, and X. Liu, “Breaking the diffraction barrier using fluorescence emission difference microscopy,” Sci. Rep.3(1441) (2013).
[Crossref]

Gordon, M. P.

M. P. Gordon, T. Ha, and P. R. Selvin, “Single-molecule high-resolution imaging with photobleaching,” P. Natl. Acad. Sci. USA 101(17), 6462–6465 (2004).
[Crossref]

Gu, M.

Gu, Z.

Gu, Z. T.

C. F. Kuang, S. Li, W. Liu, X. Hao, Z. T. Gu, Y. F. Wang, J. H. Ge, H. F. Li, and X. Liu, “Breaking the diffraction barrier using fluorescence emission difference microscopy,” Sci. Rep.3(1441) (2013).
[Crossref]

Gustafsson, M. G. L.

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microscopy 198, 82–87 (2000).
[Crossref]

Ha, T.

M. P. Gordon, T. Ha, and P. R. Selvin, “Single-molecule high-resolution imaging with photobleaching,” P. Natl. Acad. Sci. USA 101(17), 6462–6465 (2004).
[Crossref]

Hao, X.

C. F. Kuang, S. Li, W. Liu, X. Hao, Z. T. Gu, Y. F. Wang, J. H. Ge, H. F. Li, and X. Liu, “Breaking the diffraction barrier using fluorescence emission difference microscopy,” Sci. Rep.3(1441) (2013).
[Crossref]

X. Hao, C. Kuang, T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscope,” J. Opt.12(115707) (2010).
[Crossref]

Hayashi-Takagi, A.

Hell, S. W.

Hess, H. F.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. L. Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref] [PubMed]

Hochstrasser, R. M.

A. Sharonov and R. M. Hochstrasser, “Wide-field sub-diffraction imaging by accumulated binding of diffusing probes,” Proc. Natl. Acad. Sci. USA 103(50), 18911–18916 (2006).
[Crossref] [PubMed]

Iyer, G.

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” P. Natl. Acad. Sci. USA 106(52), 22287–22292 (2009).
[Crossref]

Kasai, H.

Kawasumi, K.

Kobayashi, T.

Koninck, Y. D.

Kozawa, Y.

Kuang, C.

Y. Xue, C. Kuang, S. Li, Z. Gu, and X. Liu, “Sharper fluorescent super-resolution spot generated by azimuthally polarized beam in STED microscopy,” Opt. Express 20(16), 17653–17666 (2012).
[Crossref] [PubMed]

X. Hao, C. Kuang, T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscope,” J. Opt.12(115707) (2010).
[Crossref]

Kuang, C. F.

C. F. Kuang, S. Li, W. Liu, X. Hao, Z. T. Gu, Y. F. Wang, J. H. Ge, H. F. Li, and X. Liu, “Breaking the diffraction barrier using fluorescence emission difference microscopy,” Sci. Rep.3(1441) (2013).
[Crossref]

Lerman, G. M.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[Crossref] [PubMed]

Levy, U.

Li, H. F.

C. F. Kuang, S. Li, W. Liu, X. Hao, Z. T. Gu, Y. F. Wang, J. H. Ge, H. F. Li, and X. Liu, “Breaking the diffraction barrier using fluorescence emission difference microscopy,” Sci. Rep.3(1441) (2013).
[Crossref]

Li, R.

Li, S.

Y. Xue, C. Kuang, S. Li, Z. Gu, and X. Liu, “Sharper fluorescent super-resolution spot generated by azimuthally polarized beam in STED microscopy,” Opt. Express 20(16), 17653–17666 (2012).
[Crossref] [PubMed]

C. F. Kuang, S. Li, W. Liu, X. Hao, Z. T. Gu, Y. F. Wang, J. H. Ge, H. F. Li, and X. Liu, “Breaking the diffraction barrier using fluorescence emission difference microscopy,” Sci. Rep.3(1441) (2013).
[Crossref]

Lindwasser, O. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. L. Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref] [PubMed]

Liu, L.

Liu, W.

C. F. Kuang, S. Li, W. Liu, X. Hao, Z. T. Gu, Y. F. Wang, J. H. Ge, H. F. Li, and X. Liu, “Breaking the diffraction barrier using fluorescence emission difference microscopy,” Sci. Rep.3(1441) (2013).
[Crossref]

Liu, X.

Y. Xue, C. Kuang, S. Li, Z. Gu, and X. Liu, “Sharper fluorescent super-resolution spot generated by azimuthally polarized beam in STED microscopy,” Opt. Express 20(16), 17653–17666 (2012).
[Crossref] [PubMed]

X. Hao, C. Kuang, T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscope,” J. Opt.12(115707) (2010).
[Crossref]

C. F. Kuang, S. Li, W. Liu, X. Hao, Z. T. Gu, Y. F. Wang, J. H. Ge, H. F. Li, and X. Liu, “Breaking the diffraction barrier using fluorescence emission difference microscopy,” Sci. Rep.3(1441) (2013).
[Crossref]

Miyazaki, J.

Olenych, S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. L. Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref] [PubMed]

Patterson, G. H.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. L. Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref] [PubMed]

Piche, M.

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[Crossref] [PubMed]

Richards, B.

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

Rust, M. J.

M. J. Rust, M. Bates, and X. W. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Meth. 3, 793–796 (2006).
[Crossref]

Sato, S.

Schwartz, J. L.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. L. Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref] [PubMed]

Segawa, S.

Selvin, P. R.

M. P. Gordon, T. Ha, and P. R. Selvin, “Single-molecule high-resolution imaging with photobleaching,” P. Natl. Acad. Sci. USA 101(17), 6462–6465 (2004).
[Crossref]

Sharonov, A.

A. Sharonov and R. M. Hochstrasser, “Wide-field sub-diffraction imaging by accumulated binding of diffusing probes,” Proc. Natl. Acad. Sci. USA 103(50), 18911–18916 (2006).
[Crossref] [PubMed]

Sougrat, R.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. L. Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref] [PubMed]

Tsurui, H.

Wang, T.

X. Hao, C. Kuang, T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscope,” J. Opt.12(115707) (2010).
[Crossref]

Wang, Y. F.

C. F. Kuang, S. Li, W. Liu, X. Hao, Z. T. Gu, Y. F. Wang, J. H. Ge, H. F. Li, and X. Liu, “Breaking the diffraction barrier using fluorescence emission difference microscopy,” Sci. Rep.3(1441) (2013).
[Crossref]

Weiss, S.

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” P. Natl. Acad. Sci. USA 106(52), 22287–22292 (2009).
[Crossref]

Wichmann, J.

Wolf, E.

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

Xu, Z.

Xue, Y.

Zhuang, X. W.

M. J. Rust, M. Bates, and X. W. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Meth. 3, 793–796 (2006).
[Crossref]

J. Microscopy (1)

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microscopy 198, 82–87 (2000).
[Crossref]

Nat. Meth. (1)

M. J. Rust, M. Bates, and X. W. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Meth. 3, 793–796 (2006).
[Crossref]

Opt. Express (6)

Opt. Lett. (3)

P. Natl. Acad. Sci. USA (2)

M. P. Gordon, T. Ha, and P. R. Selvin, “Single-molecule high-resolution imaging with photobleaching,” P. Natl. Acad. Sci. USA 101(17), 6462–6465 (2004).
[Crossref]

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” P. Natl. Acad. Sci. USA 106(52), 22287–22292 (2009).
[Crossref]

Phys. Rev. Lett. (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. USA (1)

A. Sharonov and R. M. Hochstrasser, “Wide-field sub-diffraction imaging by accumulated binding of diffusing probes,” Proc. Natl. Acad. Sci. USA 103(50), 18911–18916 (2006).
[Crossref] [PubMed]

Proc. R. Soc. Lond. 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. Lond. A 253, 358–379 (1959).
[Crossref]

Science (1)

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. L. Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref] [PubMed]

Other (3)

C. F. Kuang, S. Li, W. Liu, X. Hao, Z. T. Gu, Y. F. Wang, J. H. Ge, H. F. Li, and X. Liu, “Breaking the diffraction barrier using fluorescence emission difference microscopy,” Sci. Rep.3(1441) (2013).
[Crossref]

http://en.wikipedia.org/wiki/Circular_polarization .

X. Hao, C. Kuang, T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscope,” J. Opt.12(115707) (2010).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 Schematic of subtraction microscope.
Fig. 2
Fig. 2 (a) Convoluted images with sample sizes r=0, 0.2λ, 0.3λ. (b) The sample illustraction of Gaussian shape. The cross sections of the convoluted (c) Gaussian, (d) donut distributions, subtracted images with (e) r=0.2λ and (f) r=0.3λ while γ=0, 0.3 and 1.0, and subtracted images with (g) γ=0.3 and (h) γ=1.0 while r=0, 0.2λ, 0.3λ. (i) FWHM resolutions of the sample versus the subtraction factor with r=0, 0.2λ, 0.3λ.
Fig. 3
Fig. 3 The (a), (d)–(g) and (l) are simulated with sample r=0.15λ, while (b), (h)–(k) and (m) with sample r=0.25λ. The (a) and (b) are convoluted images of PSFs of Gaussian and donut shape with sample shapes of “Circ”, “Rect” and “Gauss”. (c) The sample illustration of semicircular shape (Circ) and rectangular shape (Rect). The cross sections of (d) and (h) Gaussian-PSF convolutions, (e) and (i) Donut-PSF convolutions, (f) and (j) subtracted images with γ=0.3, (g) and (k) subtracted images with γ=1.0. The FWHM resolutions versus (l) and (m) sample r, versus (n) and (o) γ with three sample shapes.
Fig. 4
Fig. 4 (a)–(c) FWHM(r, γ) with sample shape of “Gauss”, “Circ” and “Rect”. (d) Value of subtraction factors on the line of FWHM=r in (a). (e) FWHM(γ, r) with shape of “Gauss”. (f) Derivative of FWHM resolution to the subtraction factor. (g)Peak intensity after subtraction versus subtraction factor and object radius. (h)PSF intensity when r=0.3λ, γ=0.5.
Fig. 5
Fig. 5 (a) Gaussian and (b) donut spot convoluted images with (c) sample. (Laser wavelength: 488 nm; NA=1.4). (d) ΔFWHMγ. (e) Normalized peak intensity of four beads versus the subtraction factor. (f)–(j) Subtracted images with γ=0.2, 0.4, 0.6, 0.8 and 1.0.
Fig. 6
Fig. 6 Simulated results with NA=0.9. (a)–(c) FWHM(r, γ) with sample shape of “Gauss”, “Circ” and “Rect”. (d) Value of subtraction factors on the line of FWHM=r in (a). (e) FWHM(γ, r) with shape of “Gauss”. (f) Derivative of FWHM resolution to the subtraction factor. (g) Peak intensity after subtraction versus subtraction factor and object radius. (h)Fluorescence intensity when r=0.3λ, γ=0.5.
Fig. 7
Fig. 7 Simulated results with radial and azimuthal polarizations for excitation. (a) focal PSFs and (b) cut lines of PSFs and subtractions with factor γ=0,0.3,1.0. (c)–(e) FWHM(r, γ) with sample shape of “Gauss”, “Circ” and “Rect”. (f) Value of subtraction factors on the line of FWHM=r in (c). (g) FWHM(γ, r) with shape of “Gauss”. (h) Peak intensity after subtraction versus subtraction factor and object radius. (i) PSF intensity when r=0.3λ, γ=0.5.

Tables (3)

Tables Icon

Table 1 Setting values of IG and ID.

Tables Icon

Table 2 Polarization unit vector matrix.

Tables Icon

Table 3 Numerical models for the sample in Equation (1).

Equations (4)

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I RAW ( x , y ) = I G ( x , y ) * Ob ( x , y ) γ I D ( x , y ) * Ob ( x , y ) I ( x , y ) = { I RAW ( x , y ) I RAW ( x , y ) 0 0 I RAW ( x , y ) < 0
I G , D ( x , y , 0 ) = | E x | 2 + | E y | 2 + | E z | 2
E x , y , z ( x , y , 0 ) = i C λ 0 2 π 0 arcsin ( NA / n ) A AMP A Phase A L ( P x P y P z ) sin θ e i k n x 2 + y 2 sin θ cos ( φ arctan ( y / x ) ) d θ d φ
A L = cos θ ( 1 + ( cos θ 1 ) 2 cos 2 φ ( cos θ 1 ) cos φ sin φ sin θ cos φ ( cos θ 1 ) cos φ sin φ 1 + ( cos θ 1 ) sin 2 φ sin θ sin ϕ sin θ cos φ sin θ sin φ cos θ )

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