Effects of primary aberrations on the fluorescence depletion patterns of STED microscopy

Suhui Deng; Li Liu; Ya Cheng; Ruxin Li; Zhizhan Xu

doi:10.1364/OE.18.001657

Effects of primary aberrations on the fluorescence depletion patterns of STED microscopy

Suhui Deng, Li Liu, Ya Cheng, Ruxin Li, and Zhizhan Xu

Optics Express
Vol. 18,
Issue 2,
pp. 1657-1666
(2010)
•https://doi.org/10.1364/OE.18.001657

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Suhui Deng, Li Liu, Ya Cheng, Ruxin Li, and Zhizhan Xu, "Effects of primary aberrations on the fluorescence depletion patterns of STED microscopy," Opt. Express 18, 1657-1666 (2010)

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Related Topics
Table of Contents Category
- Microscopy
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Diffraction theory (050.1960)
- Microscopy (180.0180)
- Resolution (350.5730)

About this Article
History
- Original Manuscript: November 12, 2009
- Revised Manuscript: December 29, 2009
- Manuscript Accepted: December 30, 2009
- Published: January 14, 2010
Virtual Issues
Virtual Journal for Biomedical Optics Vol. 5, Iss. 3

Accessible

Open Access

Abstract

Effects of primary aberrations including spherical aberration, coma and astigmatism on the three fluorescence depletion patterns mainly used in stimulated emission of depletion (STED) microscopy are investigated by using vectorial integral. The three depletion patterns are created by inserting a vortex phase plate, a central half-wavelength plate or a semi-circular half-wavelength mask within Gaussian beam respectively. Attention is given to the modification of the shape, peak intensity, the central intensity of the dark hole and the hole size of these depletion patterns in the presence of primary aberrations.

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References

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|
Year
|
Author
|
Publication

S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19(11), 780–782 (1994).
[Crossref] [PubMed]
S. W. Hell, “Far-Field Optical Nanoscopy,” Science 316(5828), 1153–1158 (2007).
[Crossref] [PubMed]
S. W. Hell, “Microscopy and its focal switch,” Nat. Methods 6(1), 24–32 (2009).
[Crossref] [PubMed]
T. A. Klar, E. Engel, and S. W. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(6), 066613 (2001).
[Crossref] [PubMed]
T. Watanabe, M. Fujii, Y. Watanabe, N. Toyama, and Y. Iketaki, “Generation of a doughnut-shaped beam using a spiral phase plate,” Rev. Sci. Instrum. 75(12), 5131–5135 (2004).
[Crossref]
J. Keller, A. Schönle, and S. W. Hell, “Efficient fluorescence inhibition patterns for RESOLFT microscopy,” Opt. Express 15(6), 3361–3371 (2007).
[Crossref] [PubMed]
K. I. Willig, J. Keller, M. Bossi, and S. W. Hell, “STED microscopy resolves nanoparticle assemblies,” N. J. Phys. 8(6), 106 (2006).
[Crossref]
P. Török and P. R. T. Munro, “The use of Gauss-Laguerre vector beams in STED microscopy,” Opt. Express 12(15), 3605–3617 (2004).
[Crossref] [PubMed]
D. P. Biss and T. G. Brown, “Primary aberrations in focused radially polarized vortex beams,” Opt. Express 12(3), 384–393 (2004).
[Crossref] [PubMed]
B. R. Boruah and M. A. A. Neil, “Susceptibility to and correction of azimuthal aberrations in singular light beams,” Opt. Express 14(22), 10377–10385 (2006).
[Crossref] [PubMed]
B. R. Boruah and M. A. A. Neil, “Far field computation of an arbitrarily polarized beam using fast Fourier thrnsforms,” Opt. Commun. 282(24), 4660–4667 (2009).
[Crossref]
M. Born, and E. Wolf, Principles of Optics, (Cambridge University Press, Cambridge, UK, 1999).
R. Kant, “An analytical solution of vector diffraction for focusing optical systems with Seidel aberrations I. Spherical aberration, curvature of field, and distortion,” J. Mod. Opt. 40(11), 2293–2310 (1993).
[Crossref]
R. Kant, “An analytical method of vector diffraction for focusing optical systems with Seidel aberrations II: Astigmatism and coma,” J. Mod. Opt. 42(2), 299–320 (1995).
[Crossref]
R. K. Singh, P. Senthilkumaran, and K. Singh, “Effect of primary spherical aberration on high-numericalaperture focusing of a Laguerre-Gaussian beam,” J. Opt. Soc. Am. A 25(6), 1307–1318 (2008).
[Crossref]
R. K. Singh, P. Senthilkumaran, and K. Singh, “Focusing of a vortex carrying beam with Gaussian background by an apertured system in presence of coma,” Opt. Commun. 281(5), 923–934 (2008).
[Crossref]
R. K. Singh, P. Senthilkumaran, and K. Singh, “Focusing of linearly-, and circularly polarized Gaussian background vortex beams by a high numerical aperture system afflicted with third-order astigmatism,” Opt. Commun. 281(24), 5939–5948 (2008).
[Crossref]
S. H. Deng, L. Liu, Y. Cheng, R. X. Li, and Z. 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]
Y. Roichman, A. Waldron, E. Gardel, and D. G. Grier, “Optical traps with geometric aberrations,” Appl. Opt. 45(15), 3425–3429 (2006).
[Crossref] [PubMed]
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 Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]
V. Westphal and S. W. Hell, “Nanoscale resolution in the focal plane of an optical microscope,” Phys. Rev. Lett. 94(14), 143903 (2005).
[Crossref] [PubMed]
P. Dedecker, B. Muls, J. Hofkens, J. Enderlein, and J. Hotta, “Orientational effects in the excitation and de-excitation of single molecules interacting with donut-mode laser beams,” Opt. Express 15(6), 3372–3383 (2007).
[Crossref] [PubMed]
N. Bokor, Y. Iketaki, T. Watanabe, K. Daigoku, N. Davidson, and M. Fujii, “On polarization effects in fluorescence depletion microscopy,” Opt. Commun. 272(1), 263–268 (2007).
[Crossref]

2009 (3)

S. W. Hell, “Microscopy and its focal switch,” Nat. Methods 6(1), 24–32 (2009).
[Crossref] [PubMed]

B. R. Boruah and M. A. A. Neil, “Far field computation of an arbitrarily polarized beam using fast Fourier thrnsforms,” Opt. Commun. 282(24), 4660–4667 (2009).
[Crossref]

S. H. Deng, L. Liu, Y. Cheng, R. X. Li, and Z. 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]

2008 (3)

R. K. Singh, P. Senthilkumaran, and K. Singh, “Effect of primary spherical aberration on high-numericalaperture focusing of a Laguerre-Gaussian beam,” J. Opt. Soc. Am. A 25(6), 1307–1318 (2008).
[Crossref]

R. K. Singh, P. Senthilkumaran, and K. Singh, “Focusing of a vortex carrying beam with Gaussian background by an apertured system in presence of coma,” Opt. Commun. 281(5), 923–934 (2008).
[Crossref]

R. K. Singh, P. Senthilkumaran, and K. Singh, “Focusing of linearly-, and circularly polarized Gaussian background vortex beams by a high numerical aperture system afflicted with third-order astigmatism,” Opt. Commun. 281(24), 5939–5948 (2008).
[Crossref]

2007 (4)

S. W. Hell, “Far-Field Optical Nanoscopy,” Science 316(5828), 1153–1158 (2007).
[Crossref] [PubMed]

J. Keller, A. Schönle, and S. W. Hell, “Efficient fluorescence inhibition patterns for RESOLFT microscopy,” Opt. Express 15(6), 3361–3371 (2007).
[Crossref] [PubMed]

P. Dedecker, B. Muls, J. Hofkens, J. Enderlein, and J. Hotta, “Orientational effects in the excitation and de-excitation of single molecules interacting with donut-mode laser beams,” Opt. Express 15(6), 3372–3383 (2007).
[Crossref] [PubMed]

N. Bokor, Y. Iketaki, T. Watanabe, K. Daigoku, N. Davidson, and M. Fujii, “On polarization effects in fluorescence depletion microscopy,” Opt. Commun. 272(1), 263–268 (2007).
[Crossref]

2006 (3)

K. I. Willig, J. Keller, M. Bossi, and S. W. Hell, “STED microscopy resolves nanoparticle assemblies,” N. J. Phys. 8(6), 106 (2006).
[Crossref]

Y. Roichman, A. Waldron, E. Gardel, and D. G. Grier, “Optical traps with geometric aberrations,” Appl. Opt. 45(15), 3425–3429 (2006).
[Crossref] [PubMed]

B. R. Boruah and M. A. A. Neil, “Susceptibility to and correction of azimuthal aberrations in singular light beams,” Opt. Express 14(22), 10377–10385 (2006).
[Crossref] [PubMed]

2005 (1)

V. Westphal and S. W. Hell, “Nanoscale resolution in the focal plane of an optical microscope,” Phys. Rev. Lett. 94(14), 143903 (2005).
[Crossref] [PubMed]

2004 (3)

T. Watanabe, M. Fujii, Y. Watanabe, N. Toyama, and Y. Iketaki, “Generation of a doughnut-shaped beam using a spiral phase plate,” Rev. Sci. Instrum. 75(12), 5131–5135 (2004).
[Crossref]

P. Török and P. R. T. Munro, “The use of Gauss-Laguerre vector beams in STED microscopy,” Opt. Express 12(15), 3605–3617 (2004).
[Crossref] [PubMed]

D. P. Biss and T. G. Brown, “Primary aberrations in focused radially polarized vortex beams,” Opt. Express 12(3), 384–393 (2004).
[Crossref] [PubMed]

2001 (1)

T. A. Klar, E. Engel, and S. W. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(6), 066613 (2001).
[Crossref] [PubMed]

1995 (1)

R. Kant, “An analytical method of vector diffraction for focusing optical systems with Seidel aberrations II: Astigmatism and coma,” J. Mod. Opt. 42(2), 299–320 (1995).
[Crossref]

1994 (1)

S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19(11), 780–782 (1994).
[Crossref] [PubMed]

1993 (1)

R. Kant, “An analytical solution of vector diffraction for focusing optical systems with Seidel aberrations I. Spherical aberration, curvature of field, and distortion,” J. Mod. Opt. 40(11), 2293–2310 (1993).
[Crossref]

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 Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Biss, D. P.

D. P. Biss and T. G. Brown, “Primary aberrations in focused radially polarized vortex beams,” Opt. Express 12(3), 384–393 (2004).
[Crossref] [PubMed]

Bokor, N.

N. Bokor, Y. Iketaki, T. Watanabe, K. Daigoku, N. Davidson, and M. Fujii, “On polarization effects in fluorescence depletion microscopy,” Opt. Commun. 272(1), 263–268 (2007).
[Crossref]

Boruah, B. R.

B. R. Boruah and M. A. A. Neil, “Far field computation of an arbitrarily polarized beam using fast Fourier thrnsforms,” Opt. Commun. 282(24), 4660–4667 (2009).
[Crossref]

B. R. Boruah and M. A. A. Neil, “Susceptibility to and correction of azimuthal aberrations in singular light beams,” Opt. Express 14(22), 10377–10385 (2006).
[Crossref] [PubMed]

Bossi, M.

K. I. Willig, J. Keller, M. Bossi, and S. W. Hell, “STED microscopy resolves nanoparticle assemblies,” N. J. Phys. 8(6), 106 (2006).
[Crossref]

Brown, T. G.

D. P. Biss and T. G. Brown, “Primary aberrations in focused radially polarized vortex beams,” Opt. Express 12(3), 384–393 (2004).
[Crossref] [PubMed]

Cheng, Y.

Daigoku, K.

N. Bokor, Y. Iketaki, T. Watanabe, K. Daigoku, N. Davidson, and M. Fujii, “On polarization effects in fluorescence depletion microscopy,” Opt. Commun. 272(1), 263–268 (2007).
[Crossref]

Davidson, N.

N. Bokor, Y. Iketaki, T. Watanabe, K. Daigoku, N. Davidson, and M. Fujii, “On polarization effects in fluorescence depletion microscopy,” Opt. Commun. 272(1), 263–268 (2007).
[Crossref]

Dedecker, P.

Deng, S. H.

Enderlein, J.

Engel, E.

Fujii, M.

N. Bokor, Y. Iketaki, T. Watanabe, K. Daigoku, N. Davidson, and M. Fujii, “On polarization effects in fluorescence depletion microscopy,” Opt. Commun. 272(1), 263–268 (2007).
[Crossref]

T. Watanabe, M. Fujii, Y. Watanabe, N. Toyama, and Y. Iketaki, “Generation of a doughnut-shaped beam using a spiral phase plate,” Rev. Sci. Instrum. 75(12), 5131–5135 (2004).
[Crossref]

Gardel, E.

Y. Roichman, A. Waldron, E. Gardel, and D. G. Grier, “Optical traps with geometric aberrations,” Appl. Opt. 45(15), 3425–3429 (2006).
[Crossref] [PubMed]

Grier, D. G.

Y. Roichman, A. Waldron, E. Gardel, and D. G. Grier, “Optical traps with geometric aberrations,” Appl. Opt. 45(15), 3425–3429 (2006).
[Crossref] [PubMed]

Hell, S. W.

S. W. Hell, “Microscopy and its focal switch,” Nat. Methods 6(1), 24–32 (2009).
[Crossref] [PubMed]

J. Keller, A. Schönle, and S. W. Hell, “Efficient fluorescence inhibition patterns for RESOLFT microscopy,” Opt. Express 15(6), 3361–3371 (2007).
[Crossref] [PubMed]

S. W. Hell, “Far-Field Optical Nanoscopy,” Science 316(5828), 1153–1158 (2007).
[Crossref] [PubMed]

K. I. Willig, J. Keller, M. Bossi, and S. W. Hell, “STED microscopy resolves nanoparticle assemblies,” N. J. Phys. 8(6), 106 (2006).
[Crossref]

V. Westphal and S. W. Hell, “Nanoscale resolution in the focal plane of an optical microscope,” Phys. Rev. Lett. 94(14), 143903 (2005).
[Crossref] [PubMed]

Hofkens, J.

Hotta, J.

Iketaki, Y.

N. Bokor, Y. Iketaki, T. Watanabe, K. Daigoku, N. Davidson, and M. Fujii, “On polarization effects in fluorescence depletion microscopy,” Opt. Commun. 272(1), 263–268 (2007).
[Crossref]

T. Watanabe, M. Fujii, Y. Watanabe, N. Toyama, and Y. Iketaki, “Generation of a doughnut-shaped beam using a spiral phase plate,” Rev. Sci. Instrum. 75(12), 5131–5135 (2004).
[Crossref]

Kant, R.

R. Kant, “An analytical method of vector diffraction for focusing optical systems with Seidel aberrations II: Astigmatism and coma,” J. Mod. Opt. 42(2), 299–320 (1995).
[Crossref]

Keller, J.

J. Keller, A. Schönle, and S. W. Hell, “Efficient fluorescence inhibition patterns for RESOLFT microscopy,” Opt. Express 15(6), 3361–3371 (2007).
[Crossref] [PubMed]

K. I. Willig, J. Keller, M. Bossi, and S. W. Hell, “STED microscopy resolves nanoparticle assemblies,” N. J. Phys. 8(6), 106 (2006).
[Crossref]

Klar, T. A.

Li, R. X.

Liu, L.

Muls, B.

Munro, P. R. T.

P. Török and P. R. T. Munro, “The use of Gauss-Laguerre vector beams in STED microscopy,” Opt. Express 12(15), 3605–3617 (2004).
[Crossref] [PubMed]

Neil, M. A. A.

B. R. Boruah and M. A. A. Neil, “Far field computation of an arbitrarily polarized beam using fast Fourier thrnsforms,” Opt. Commun. 282(24), 4660–4667 (2009).
[Crossref]

B. R. Boruah and M. A. A. Neil, “Susceptibility to and correction of azimuthal aberrations in singular light beams,” Opt. Express 14(22), 10377–10385 (2006).
[Crossref] [PubMed]

Richards, B.

Roichman, Y.

Y. Roichman, A. Waldron, E. Gardel, and D. G. Grier, “Optical traps with geometric aberrations,” Appl. Opt. 45(15), 3425–3429 (2006).
[Crossref] [PubMed]

Schönle, A.

J. Keller, A. Schönle, and S. W. Hell, “Efficient fluorescence inhibition patterns for RESOLFT microscopy,” Opt. Express 15(6), 3361–3371 (2007).
[Crossref] [PubMed]

Senthilkumaran, P.

Singh, K.

Singh, R. K.

Török, P.

P. Török and P. R. T. Munro, “The use of Gauss-Laguerre vector beams in STED microscopy,” Opt. Express 12(15), 3605–3617 (2004).
[Crossref] [PubMed]

Toyama, N.

T. Watanabe, M. Fujii, Y. Watanabe, N. Toyama, and Y. Iketaki, “Generation of a doughnut-shaped beam using a spiral phase plate,” Rev. Sci. Instrum. 75(12), 5131–5135 (2004).
[Crossref]

Waldron, A.

Y. Roichman, A. Waldron, E. Gardel, and D. G. Grier, “Optical traps with geometric aberrations,” Appl. Opt. 45(15), 3425–3429 (2006).
[Crossref] [PubMed]

Watanabe, T.

N. Bokor, Y. Iketaki, T. Watanabe, K. Daigoku, N. Davidson, and M. Fujii, “On polarization effects in fluorescence depletion microscopy,” Opt. Commun. 272(1), 263–268 (2007).
[Crossref]

T. Watanabe, M. Fujii, Y. Watanabe, N. Toyama, and Y. Iketaki, “Generation of a doughnut-shaped beam using a spiral phase plate,” Rev. Sci. Instrum. 75(12), 5131–5135 (2004).
[Crossref]

Watanabe, Y.

T. Watanabe, M. Fujii, Y. Watanabe, N. Toyama, and Y. Iketaki, “Generation of a doughnut-shaped beam using a spiral phase plate,” Rev. Sci. Instrum. 75(12), 5131–5135 (2004).
[Crossref]

Westphal, V.

V. Westphal and S. W. Hell, “Nanoscale resolution in the focal plane of an optical microscope,” Phys. Rev. Lett. 94(14), 143903 (2005).
[Crossref] [PubMed]

Wichmann, J.

Willig, K. I.

K. I. Willig, J. Keller, M. Bossi, and S. W. Hell, “STED microscopy resolves nanoparticle assemblies,” N. J. Phys. 8(6), 106 (2006).
[Crossref]

Wolf, E.

Xu, Z. Z.

Appl. Opt. (1)

Y. Roichman, A. Waldron, E. Gardel, and D. G. Grier, “Optical traps with geometric aberrations,” Appl. Opt. 45(15), 3425–3429 (2006).
[Crossref] [PubMed]

J. Mod. Opt. (2)

R. Kant, “An analytical method of vector diffraction for focusing optical systems with Seidel aberrations II: Astigmatism and coma,” J. Mod. Opt. 42(2), 299–320 (1995).
[Crossref]

J. Opt. Soc. Am. A (1)

N. J. Phys. (1)

K. I. Willig, J. Keller, M. Bossi, and S. W. Hell, “STED microscopy resolves nanoparticle assemblies,” N. J. Phys. 8(6), 106 (2006).
[Crossref]

Nat. Methods (1)

S. W. Hell, “Microscopy and its focal switch,” Nat. Methods 6(1), 24–32 (2009).
[Crossref] [PubMed]

Opt. Commun. (4)

B. R. Boruah and M. A. A. Neil, “Far field computation of an arbitrarily polarized beam using fast Fourier thrnsforms,” Opt. Commun. 282(24), 4660–4667 (2009).
[Crossref]

N. Bokor, Y. Iketaki, T. Watanabe, K. Daigoku, N. Davidson, and M. Fujii, “On polarization effects in fluorescence depletion microscopy,” Opt. Commun. 272(1), 263–268 (2007).
[Crossref]

Opt. Express (6)

J. Keller, A. Schönle, and S. W. Hell, “Efficient fluorescence inhibition patterns for RESOLFT microscopy,” Opt. Express 15(6), 3361–3371 (2007).
[Crossref] [PubMed]

P. Török and P. R. T. Munro, “The use of Gauss-Laguerre vector beams in STED microscopy,” Opt. Express 12(15), 3605–3617 (2004).
[Crossref] [PubMed]

D. P. Biss and T. G. Brown, “Primary aberrations in focused radially polarized vortex beams,” Opt. Express 12(3), 384–393 (2004).
[Crossref] [PubMed]

B. R. Boruah and M. A. A. Neil, “Susceptibility to and correction of azimuthal aberrations in singular light beams,” Opt. Express 14(22), 10377–10385 (2006).
[Crossref] [PubMed]

Opt. Lett. (1)

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

Phys. Rev. Lett. (1)

V. Westphal and S. W. Hell, “Nanoscale resolution in the focal plane of an optical microscope,” Phys. Rev. Lett. 94(14), 143903 (2005).
[Crossref] [PubMed]

Proc. R. Soc. Lond. A Math. Phys. Sci. (1)

Rev. Sci. Instrum. (1)

T. Watanabe, M. Fujii, Y. Watanabe, N. Toyama, and Y. Iketaki, “Generation of a doughnut-shaped beam using a spiral phase plate,” Rev. Sci. Instrum. 75(12), 5131–5135 (2004).
[Crossref]

Science (1)

S. W. Hell, “Far-Field Optical Nanoscopy,” Science 316(5828), 1153–1158 (2007).
[Crossref] [PubMed]

Other (1)

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

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Fig. 1

Calculated intensity distribution on the focal plane and through the focus of a LC polarized Gaussian beam inserted with the vortex mask for different spherical aberration: (a) without aberration, (b) $A_{s} = 0.5$ , (c) $A_{s} = 2$ .

Download Full Size | PPT Slide | PDF

Fig. 2

Calculated intensity distribution on the focal plane and through the focus of a linearly polarized Gaussian beam inserted with the semi-circular $λ / 2$ phase mask for different spherical aberration: (a) without aberration, (b) $A_{s} = 0.5$ , (c) $A_{s} = 2$ .

Download Full Size | PPT Slide | PDF

Fig. 3

Calculated intensity distribution on the $x z$ plane of a LC polarized Gaussian beam inserted with the central $λ / 2$ phase mask for different spherical aberration: (a) without aberration, (b) $A_{s} = 0.5$ , (c) $A_{s} = 2$ . Figure (d) is normalized intensity profiles through central zero intensity of this pattern for different spherical aberrations.

Download Full Size | PPT Slide | PDF

Fig. 4

Calculated intensity distribution on the focal plane and through the focus of a LC polarized Gaussian beam inserted with the vortex mask for different coma: (a) $A_{c} = 0.15$ , (b) $A_{c} = 0.5$ , (c) $A_{c} = 1$ .

Download Full Size | PPT Slide | PDF

Fig. 5

Calculated intensity distribution through the focus and on the focal plane of a LC polarized Gaussian beam inserted with the central $λ / 2$ phase mask for different coma: (a) $A_{c} = 0.15$ , (b) $A_{c} = 0.5$ , (c) $A_{c} = 1$ .

Download Full Size | PPT Slide | PDF

Fig. 6

Calculated intensity distribution on the focal plane and through the focus of a linearly polarized Gaussian beam inserted with the semi-circular $λ / 2$ phase mask for different coma: (a) $A_{c} = 0.15$ , (b) $A_{c} = 0.5$ , (c) $A_{c} = 1$ . Figure (d) is normalized intensity profiles through central zero intensity of this pattern for different coma.

Download Full Size | PPT Slide | PDF

Fig. 7

Calculated intensity distribution on the focal plane and through the focus of a LC polarized Gaussian beam inserted with the vortex mask for different astigmatism: (a) $A_{a} = 0.15$ , (b) $A_{a} = 0.5$ , (c) $A_{a} = 1$ .

Download Full Size | PPT Slide | PDF

Fig. 8

Calculated intensity distribution on the $x z$ plane of a LC polarized Gaussian beam inserted with the central $λ / 2$ phase mask for different astigmatism: (a) $A_{a} = 0.15$ , (b) $A_{a} = 0.5$ , (c) $A_{a} = 1$ .

Download Full Size | PPT Slide | PDF

Fig. 9

Calculated intensity distribution on the focal plane and through the focus of a linearly polarized Gaussian beam inserted with the semi-circular $λ / 2$ phase mask for different astigmatism: (a) $A_{a} = 0.15$ , (b) $A_{a} = 0.5$ , (c) $A_{a} = 1$ . Figure (d) is normalized intensity profiles through central zero intensity of this pattern for different astigmatism.

Download Full Size | PPT Slide | PDF

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

E_{0} (γ, θ) = A_{0} \exp (- γ^{2} \frac{\sin^{2} θ}{\sin^{2} α})

\begin{array}{l} E (p) = (\begin{matrix} E_{x} \\ E_{y} \\ E_{z} \end{matrix}) = - \frac{i f}{λ} \int_{0}^{α} \int_{0}^{2 π} E_{0} \sqrt{\cos θ} A_{1} (θ, ϕ) \exp [i k (x \sin θ \cos ϕ + y \sin θ \sin ϕ + z \cos θ)] \\ \times φ_{s} (θ, ϕ) [\begin{array}{l} \cos θ \cos^{2} ϕ + \sin^{2} ϕ \\ \cos ϕ \sin ϕ (\cos θ - 1) \\ - \sin θ \cos θ \end{array}] \sin θ d θ d ϕ \end{array}

A_{1} (θ, ϕ) = \exp [i k A_{s} {(\frac{\sin θ}{\sin α})}^{4}]

A_{1} (θ, ϕ) = \exp [i k A_{c} {(\frac{\sin θ}{\sin α})}^{3} \cos ϕ]

A_{1} (θ, ϕ) = \exp [i k A_{a} {(\frac{\sin θ}{\sin α})}^{2} \cos^{2} ϕ]

\begin{array}{l} E (p) = (\begin{matrix} E_{x} \\ E_{y} \\ E_{z} \end{matrix}) = - \frac{i f}{λ} \int_{0}^{α} \int_{0}^{2 π} E_{0} \sqrt{\cos θ} A_{1} (θ, ϕ) \exp [i k (x \sin θ \cos ϕ + y \sin θ \sin ϕ + z \cos θ)] \\ \times φ_{s} (θ, ϕ) [\begin{array}{l} \cos θ \cos^{2} ϕ + \sin^{2} ϕ + i \sin ϕ \cos ϕ (\cos θ - 1) \\ \cos ϕ \sin ϕ (\cos θ - 1) + i (\cos θ \sin^{2} ϕ + \cos^{2} ϕ) \\ - \sin θ (\cos θ + i \sin ϕ) \end{array}] \sin θ d θ d ϕ \end{array}

d \approx λ / (2 N A \sqrt{1 + I_{S T E D}^{\max} / I_{s}})

Abstract

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