Abstract

Evanescent field distribution in the focal region of the elliptical-mirror-based total-internal-reflection fluorescence (e-TIRF) microscopy is analyzed based on vectorial diffraction theory. The simulation demonstrates that the intensity of an evanescent field generated by elliptical mirror decreases exponentially with the penetration depth, and the polarization characteristic of the evanescent wave in various directions is given. We build up an e-TIRF microscope utilizing a focused hollow-cone illumination with all-direction and large range of incidence. The experiment shows the artifact effect can be well suppressed by using the azimuthal-direction illumination method. In addition, the penetration depth of the evanescent field can be controlled by adjusting the sizes of the aperture and obstruction with a large range.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (1)

2017 (4)

L. Jin, J. Wu, P. Xiu, J. Fan, M. Hu, C. Kuang, Y. Xu, X. Zheng, and X. Liu, “High-resolution 3D reconstruction of microtubule structures by quantitative multi-angle total internal reflection fluorescence microscopy,” Opt. Commun. 395, 16–23 (2017).
[Crossref]

P. P. Mondal and S. T. Hess, “Total internal reflection fluorescence based multiplane localization microscopy enables super-resolved volume imaging,” Appl. Phys. Lett. 110, 211102 (2017).
[Crossref]

J. Liu, Q. Li, M. Li, S. Gao, C. Liu, L. Zou, and J. Tan, “Elliptical mirror-based TIRF microscopy with shadowless illumination and adjustable penetration depth,” Opt. Lett. 42(13), 2587–2590 (2017).
[Crossref] [PubMed]

B. Schreiber, K. Elsayad, and K. G. Heinze, “Axicon-based Bessel beams for flat-field illumination in total internal reflection fluorescence microscopy,” Opt. Lett. 42(19), 3880–3883 (2017).
[Crossref] [PubMed]

2016 (3)

2015 (1)

K. L. Ellefsen, J. L. Dynes, and I. Parker, “Spinning-spot shadowless TIRF microscopy,” PLoS One 10(8), e0136055 (2015).
[Crossref] [PubMed]

2014 (4)

J. Boulanger, C. Gueudry, D. Münch, B. Cinquin, P. Paul-Gilloteaux, S. Bardin, C. Guérin, F. Senger, L. Blanchoin, and J. Salamero, “Fast high-resolution 3D total internal reflection fluorescence microscopy by incidence angle scanning and azimuthal averaging,” Proc. Natl. Acad. Sci. U.S.A. 111(48), 17164–17169 (2014).
[Crossref] [PubMed]

J. Chen, R. V. Dalal, A. N. Petrov, A. Tsai, S. E. O’Leary, K. Chapin, J. Cheng, M. Ewan, P. L. Hsiung, P. Lundquist, S. W. Turner, D. R. Hsu, and J. D. Puglisi, “High-throughput platform for real-time monitoring of biological processes by multicolor single-molecule fluorescence,” Proc. Natl. Acad. Sci. U.S.A. 111(2), 664–669 (2014).
[Crossref] [PubMed]

W. Zong, X. Huang, C. Zhang, T. Yuan, L. L. Zhu, M. Fan, and L. Chen, “Shadowless-illuminated variable-angle TIRF (siva-TIRF) microscopy for the observation of spatial-temporal dynamics in live cells,” Biomed. Opt. Express 5(5), 1530–1540 (2014).
[Crossref] [PubMed]

J. Liu, M. Ai, H. Zhang, and J. Tan, “Focusing properties of elliptical mirror with an aperture,” Opt. Eng. 53(6), 061606 (2014).
[Crossref]

2013 (1)

J. Lin and A. D. Hoppe, “Uniform total internal reflection fluorescence illumination enables live cell fluorescence resonance energy transfer microscopy,” Microsc. Microanal. 19(2), 350–359 (2013).
[Crossref] [PubMed]

2012 (2)

T. P. Burghardt, “Measuring incidence angle for through-the-objective total internal reflection fluorescence microscopy,” J. Biomed. Opt. 17(12), 126007 (2012).
[Crossref] [PubMed]

J. Liu, J. Tan, T. Wilson, and C. Zhong, “Rigorous theory on elliptical mirror focusing for point scanning microscopy,” Opt. Express 20(6), 6175–6184 (2012).
[Crossref] [PubMed]

2010 (3)

M. Lei and A. Zumbusch, “Total-internal-reflection fluorescence microscopy with W-shaped axicon mirrors,” Opt. Lett. 35(23), 4057–4059 (2010).
[Crossref] [PubMed]

S. J. Holden, S. Uphoff, J. Hohlbein, D. Yadin, L. Le Reste, O. J. Britton, and A. N. Kapanidis, “Defining the limits of single-molecule FRET resolution in TIRF microscopy,” Biophys. J. 99(9), 3102–3111 (2010).
[Crossref] [PubMed]

A. L. Mattheyses, S. M. Simon, and J. Z. Rappoport, “Imaging with total internal reflection fluorescence microscopy for the cell biologist,” J. Cell Sci. 123(21), 3621–3628 (2010).
[Crossref] [PubMed]

2008 (5)

M. Tokunaga, N. Imamoto, and K. Sakata-Sogawa, “Highly inclined thin illumination enables clear single-molecule imaging in cells,” Nat. Methods 5(2), 159–161 (2008).
[Crossref] [PubMed]

H. Shroff, C. G. Galbraith, J. A. Galbraith, and E. Betzig, “Live-cell photoactivated localization microscopy of nanoscale adhesion dynamics,” Nat. Methods 5(5), 417–423 (2008).
[Crossref] [PubMed]

R. Fiolka, M. Beck, and A. Stemmer, “Structured illumination in total internal reflection fluorescence microscopy using a spatial light modulator,” Opt. Lett. 33(14), 1629–1631 (2008).
[Crossref] [PubMed]

J. F. Beausang, H. W. Schroeder, P. C. Nelson, and Y. E. Goldman, “Twirling of actin by myosins II and V observed via polarized TIRF in a modified gliding assay,” Biophys. J. 95(12), 5820–5831 (2008).
[Crossref] [PubMed]

M. van ’t Hoff, V. de Sars, and M. Oheim, “A programmable light engine for quantitative single molecule TIRF and HILO imaging,” Opt. Express 16(22), 18495–18504 (2008).
[Crossref] [PubMed]

2007 (1)

2006 (3)

A. L. Mattheyses, K. Shaw, and D. Axelrod, “Effective elimination of laser interference fringing in fluorescence microscopy by spinning azimuthal incidence angle,” Microsc. Res. Tech. 69(8), 642–647 (2006).
[Crossref] [PubMed]

M. Ohara-Imaizumi and S. Nagamatsu, “Insulin exocytotic mechanism by imaging technique,” J. Biochem. 140(1), 1–5 (2006).
[Crossref] [PubMed]

J. Tschmelak, M. Kumpf, N. Käppel, G. Proll, and G. Gauglitz, “Total internal reflectance fluorescence (TIRF) biosensor for environmental monitoring of testosterone with commercially available immunochemistry: antibody characterization, assay development and real sample measurements,” Talanta 69(2), 343–350 (2006).
[Crossref] [PubMed]

2004 (1)

2003 (1)

K. Stock, R. Sailer, W. S. L. Strauss, M. Lyttek, R. Steiner, and H. Schneckenburger, “Variable-angle total internal reflection fluorescence microscopy (VA-TIRFM): realization and application of a compact illumination device,” J. Microsc. 211(1), 19–29 (2003).
[Crossref] [PubMed]

2001 (1)

D. Axelrod, “Total internal reflection fluorescence microscopy in cell biology,” Traffic 2(11), 764–774 (2001).
[Crossref] [PubMed]

1995 (1)

1981 (1)

D. Axelrod, “Cell-substrate contacts illuminated by total internal reflection fluorescence,” J. Cell Biol. 89(1), 141–145 (1981).
[Crossref] [PubMed]

Ai, M.

J. Liu, M. Ai, H. Zhang, and J. Tan, “Focusing properties of elliptical mirror with an aperture,” Opt. Eng. 53(6), 061606 (2014).
[Crossref]

Axelrod, D.

A. L. Mattheyses, K. Shaw, and D. Axelrod, “Effective elimination of laser interference fringing in fluorescence microscopy by spinning azimuthal incidence angle,” Microsc. Res. Tech. 69(8), 642–647 (2006).
[Crossref] [PubMed]

D. Axelrod, “Total internal reflection fluorescence microscopy in cell biology,” Traffic 2(11), 764–774 (2001).
[Crossref] [PubMed]

D. Axelrod, “Cell-substrate contacts illuminated by total internal reflection fluorescence,” J. Cell Biol. 89(1), 141–145 (1981).
[Crossref] [PubMed]

Bardin, S.

J. Boulanger, C. Gueudry, D. Münch, B. Cinquin, P. Paul-Gilloteaux, S. Bardin, C. Guérin, F. Senger, L. Blanchoin, and J. Salamero, “Fast high-resolution 3D total internal reflection fluorescence microscopy by incidence angle scanning and azimuthal averaging,” Proc. Natl. Acad. Sci. U.S.A. 111(48), 17164–17169 (2014).
[Crossref] [PubMed]

Beausang, J. F.

J. F. Beausang, H. W. Schroeder, P. C. Nelson, and Y. E. Goldman, “Twirling of actin by myosins II and V observed via polarized TIRF in a modified gliding assay,” Biophys. J. 95(12), 5820–5831 (2008).
[Crossref] [PubMed]

Beck, M.

Benda, A.

Betzig, E.

H. Shroff, C. G. Galbraith, J. A. Galbraith, and E. Betzig, “Live-cell photoactivated localization microscopy of nanoscale adhesion dynamics,” Nat. Methods 5(5), 417–423 (2008).
[Crossref] [PubMed]

Blanchoin, L.

J. Boulanger, C. Gueudry, D. Münch, B. Cinquin, P. Paul-Gilloteaux, S. Bardin, C. Guérin, F. Senger, L. Blanchoin, and J. Salamero, “Fast high-resolution 3D total internal reflection fluorescence microscopy by incidence angle scanning and azimuthal averaging,” Proc. Natl. Acad. Sci. U.S.A. 111(48), 17164–17169 (2014).
[Crossref] [PubMed]

Booker, G. R.

Boulanger, J.

J. Boulanger, C. Gueudry, D. Münch, B. Cinquin, P. Paul-Gilloteaux, S. Bardin, C. Guérin, F. Senger, L. Blanchoin, and J. Salamero, “Fast high-resolution 3D total internal reflection fluorescence microscopy by incidence angle scanning and azimuthal averaging,” Proc. Natl. Acad. Sci. U.S.A. 111(48), 17164–17169 (2014).
[Crossref] [PubMed]

Britton, O. J.

S. J. Holden, S. Uphoff, J. Hohlbein, D. Yadin, L. Le Reste, O. J. Britton, and A. N. Kapanidis, “Defining the limits of single-molecule FRET resolution in TIRF microscopy,” Biophys. J. 99(9), 3102–3111 (2010).
[Crossref] [PubMed]

Burghardt, T. P.

T. P. Burghardt, “Measuring incidence angle for through-the-objective total internal reflection fluorescence microscopy,” J. Biomed. Opt. 17(12), 126007 (2012).
[Crossref] [PubMed]

Chapin, K.

J. Chen, R. V. Dalal, A. N. Petrov, A. Tsai, S. E. O’Leary, K. Chapin, J. Cheng, M. Ewan, P. L. Hsiung, P. Lundquist, S. W. Turner, D. R. Hsu, and J. D. Puglisi, “High-throughput platform for real-time monitoring of biological processes by multicolor single-molecule fluorescence,” Proc. Natl. Acad. Sci. U.S.A. 111(2), 664–669 (2014).
[Crossref] [PubMed]

Chen, J.

J. Chen, R. V. Dalal, A. N. Petrov, A. Tsai, S. E. O’Leary, K. Chapin, J. Cheng, M. Ewan, P. L. Hsiung, P. Lundquist, S. W. Turner, D. R. Hsu, and J. D. Puglisi, “High-throughput platform for real-time monitoring of biological processes by multicolor single-molecule fluorescence,” Proc. Natl. Acad. Sci. U.S.A. 111(2), 664–669 (2014).
[Crossref] [PubMed]

Chen, L.

Chen, Y.

Cheng, J.

J. Chen, R. V. Dalal, A. N. Petrov, A. Tsai, S. E. O’Leary, K. Chapin, J. Cheng, M. Ewan, P. L. Hsiung, P. Lundquist, S. W. Turner, D. R. Hsu, and J. D. Puglisi, “High-throughput platform for real-time monitoring of biological processes by multicolor single-molecule fluorescence,” Proc. Natl. Acad. Sci. U.S.A. 111(2), 664–669 (2014).
[Crossref] [PubMed]

Chon, J. W. M.

Cinquin, B.

J. Boulanger, C. Gueudry, D. Münch, B. Cinquin, P. Paul-Gilloteaux, S. Bardin, C. Guérin, F. Senger, L. Blanchoin, and J. Salamero, “Fast high-resolution 3D total internal reflection fluorescence microscopy by incidence angle scanning and azimuthal averaging,” Proc. Natl. Acad. Sci. U.S.A. 111(48), 17164–17169 (2014).
[Crossref] [PubMed]

Dalal, R. V.

J. Chen, R. V. Dalal, A. N. Petrov, A. Tsai, S. E. O’Leary, K. Chapin, J. Cheng, M. Ewan, P. L. Hsiung, P. Lundquist, S. W. Turner, D. R. Hsu, and J. D. Puglisi, “High-throughput platform for real-time monitoring of biological processes by multicolor single-molecule fluorescence,” Proc. Natl. Acad. Sci. U.S.A. 111(2), 664–669 (2014).
[Crossref] [PubMed]

de Sars, V.

Dynes, J. L.

K. L. Ellefsen, J. L. Dynes, and I. Parker, “Spinning-spot shadowless TIRF microscopy,” PLoS One 10(8), e0136055 (2015).
[Crossref] [PubMed]

Ellefsen, K. L.

K. L. Ellefsen, J. L. Dynes, and I. Parker, “Spinning-spot shadowless TIRF microscopy,” PLoS One 10(8), e0136055 (2015).
[Crossref] [PubMed]

Elsayad, K.

Ewan, M.

J. Chen, R. V. Dalal, A. N. Petrov, A. Tsai, S. E. O’Leary, K. Chapin, J. Cheng, M. Ewan, P. L. Hsiung, P. Lundquist, S. W. Turner, D. R. Hsu, and J. D. Puglisi, “High-throughput platform for real-time monitoring of biological processes by multicolor single-molecule fluorescence,” Proc. Natl. Acad. Sci. U.S.A. 111(2), 664–669 (2014).
[Crossref] [PubMed]

Fan, J.

L. Jin, J. Wu, P. Xiu, J. Fan, M. Hu, C. Kuang, Y. Xu, X. Zheng, and X. Liu, “High-resolution 3D reconstruction of microtubule structures by quantitative multi-angle total internal reflection fluorescence microscopy,” Opt. Commun. 395, 16–23 (2017).
[Crossref]

Fan, M.

Fiolka, R.

Fu, Y.

Y. Fu, P. W. Winter, R. Rojas, V. Wang, M. McAuliffe, and G. H. Patterson, “Axial superresolution via multiangle TIRF microscopy with sequential imaging and photobleaching,” Proc. Natl. Acad. Sci. U.S.A. 113(16), 4368–4373 (2016).
[Crossref] [PubMed]

Galbraith, C. G.

H. Shroff, C. G. Galbraith, J. A. Galbraith, and E. Betzig, “Live-cell photoactivated localization microscopy of nanoscale adhesion dynamics,” Nat. Methods 5(5), 417–423 (2008).
[Crossref] [PubMed]

Galbraith, J. A.

H. Shroff, C. G. Galbraith, J. A. Galbraith, and E. Betzig, “Live-cell photoactivated localization microscopy of nanoscale adhesion dynamics,” Nat. Methods 5(5), 417–423 (2008).
[Crossref] [PubMed]

Gao, S.

Gauglitz, G.

J. Tschmelak, M. Kumpf, N. Käppel, G. Proll, and G. Gauglitz, “Total internal reflectance fluorescence (TIRF) biosensor for environmental monitoring of testosterone with commercially available immunochemistry: antibody characterization, assay development and real sample measurements,” Talanta 69(2), 343–350 (2006).
[Crossref] [PubMed]

Gaus, K.

Goldman, Y. E.

J. F. Beausang, H. W. Schroeder, P. C. Nelson, and Y. E. Goldman, “Twirling of actin by myosins II and V observed via polarized TIRF in a modified gliding assay,” Biophys. J. 95(12), 5820–5831 (2008).
[Crossref] [PubMed]

Gu, M.

Guérin, C.

J. Boulanger, C. Gueudry, D. Münch, B. Cinquin, P. Paul-Gilloteaux, S. Bardin, C. Guérin, F. Senger, L. Blanchoin, and J. Salamero, “Fast high-resolution 3D total internal reflection fluorescence microscopy by incidence angle scanning and azimuthal averaging,” Proc. Natl. Acad. Sci. U.S.A. 111(48), 17164–17169 (2014).
[Crossref] [PubMed]

Gueudry, C.

J. Boulanger, C. Gueudry, D. Münch, B. Cinquin, P. Paul-Gilloteaux, S. Bardin, C. Guérin, F. Senger, L. Blanchoin, and J. Salamero, “Fast high-resolution 3D total internal reflection fluorescence microscopy by incidence angle scanning and azimuthal averaging,” Proc. Natl. Acad. Sci. U.S.A. 111(48), 17164–17169 (2014).
[Crossref] [PubMed]

Heinze, K. G.

Hess, S. T.

P. P. Mondal and S. T. Hess, “Total internal reflection fluorescence based multiplane localization microscopy enables super-resolved volume imaging,” Appl. Phys. Lett. 110, 211102 (2017).
[Crossref]

Hohlbein, J.

S. J. Holden, S. Uphoff, J. Hohlbein, D. Yadin, L. Le Reste, O. J. Britton, and A. N. Kapanidis, “Defining the limits of single-molecule FRET resolution in TIRF microscopy,” Biophys. J. 99(9), 3102–3111 (2010).
[Crossref] [PubMed]

Holden, S. J.

S. J. Holden, S. Uphoff, J. Hohlbein, D. Yadin, L. Le Reste, O. J. Britton, and A. N. Kapanidis, “Defining the limits of single-molecule FRET resolution in TIRF microscopy,” Biophys. J. 99(9), 3102–3111 (2010).
[Crossref] [PubMed]

Hoppe, A. D.

J. Lin and A. D. Hoppe, “Uniform total internal reflection fluorescence illumination enables live cell fluorescence resonance energy transfer microscopy,” Microsc. Microanal. 19(2), 350–359 (2013).
[Crossref] [PubMed]

Horiguchi, N.

Hsiung, P. L.

J. Chen, R. V. Dalal, A. N. Petrov, A. Tsai, S. E. O’Leary, K. Chapin, J. Cheng, M. Ewan, P. L. Hsiung, P. Lundquist, S. W. Turner, D. R. Hsu, and J. D. Puglisi, “High-throughput platform for real-time monitoring of biological processes by multicolor single-molecule fluorescence,” Proc. Natl. Acad. Sci. U.S.A. 111(2), 664–669 (2014).
[Crossref] [PubMed]

Hsu, D. R.

J. Chen, R. V. Dalal, A. N. Petrov, A. Tsai, S. E. O’Leary, K. Chapin, J. Cheng, M. Ewan, P. L. Hsiung, P. Lundquist, S. W. Turner, D. R. Hsu, and J. D. Puglisi, “High-throughput platform for real-time monitoring of biological processes by multicolor single-molecule fluorescence,” Proc. Natl. Acad. Sci. U.S.A. 111(2), 664–669 (2014).
[Crossref] [PubMed]

Hu, M.

L. Jin, J. Wu, P. Xiu, J. Fan, M. Hu, C. Kuang, Y. Xu, X. Zheng, and X. Liu, “High-resolution 3D reconstruction of microtubule structures by quantitative multi-angle total internal reflection fluorescence microscopy,” Opt. Commun. 395, 16–23 (2017).
[Crossref]

Huang, X.

Imamoto, N.

M. Tokunaga, N. Imamoto, and K. Sakata-Sogawa, “Highly inclined thin illumination enables clear single-molecule imaging in cells,” Nat. Methods 5(2), 159–161 (2008).
[Crossref] [PubMed]

Jacob, Z.

Jin, L.

C. Zheng, G. Zhao, W. Liu, Y. Chen, Z. Zhang, L. Jin, Y. Xu, C. Kuang, and X. Liu, “Three-dimensional super-resolved live cell imaging through polarized multi-angle TIRF,” Opt. Lett. 43(7), 1423–1426 (2018).
[Crossref] [PubMed]

L. Jin, J. Wu, P. Xiu, J. Fan, M. Hu, C. Kuang, Y. Xu, X. Zheng, and X. Liu, “High-resolution 3D reconstruction of microtubule structures by quantitative multi-angle total internal reflection fluorescence microscopy,” Opt. Commun. 395, 16–23 (2017).
[Crossref]

Kano, H.

Kapanidis, A. N.

S. J. Holden, S. Uphoff, J. Hohlbein, D. Yadin, L. Le Reste, O. J. Britton, and A. N. Kapanidis, “Defining the limits of single-molecule FRET resolution in TIRF microscopy,” Biophys. J. 99(9), 3102–3111 (2010).
[Crossref] [PubMed]

Käppel, N.

J. Tschmelak, M. Kumpf, N. Käppel, G. Proll, and G. Gauglitz, “Total internal reflectance fluorescence (TIRF) biosensor for environmental monitoring of testosterone with commercially available immunochemistry: antibody characterization, assay development and real sample measurements,” Talanta 69(2), 343–350 (2006).
[Crossref] [PubMed]

Kuang, C.

C. Zheng, G. Zhao, W. Liu, Y. Chen, Z. Zhang, L. Jin, Y. Xu, C. Kuang, and X. Liu, “Three-dimensional super-resolved live cell imaging through polarized multi-angle TIRF,” Opt. Lett. 43(7), 1423–1426 (2018).
[Crossref] [PubMed]

L. Jin, J. Wu, P. Xiu, J. Fan, M. Hu, C. Kuang, Y. Xu, X. Zheng, and X. Liu, “High-resolution 3D reconstruction of microtubule structures by quantitative multi-angle total internal reflection fluorescence microscopy,” Opt. Commun. 395, 16–23 (2017).
[Crossref]

Kumpf, M.

J. Tschmelak, M. Kumpf, N. Käppel, G. Proll, and G. Gauglitz, “Total internal reflectance fluorescence (TIRF) biosensor for environmental monitoring of testosterone with commercially available immunochemistry: antibody characterization, assay development and real sample measurements,” Talanta 69(2), 343–350 (2006).
[Crossref] [PubMed]

Laczik, Z.

Le Reste, L.

S. J. Holden, S. Uphoff, J. Hohlbein, D. Yadin, L. Le Reste, O. J. Britton, and A. N. Kapanidis, “Defining the limits of single-molecule FRET resolution in TIRF microscopy,” Biophys. J. 99(9), 3102–3111 (2010).
[Crossref] [PubMed]

Lei, M.

Li, M.

Li, Q.

Lin, J.

J. Lin and A. D. Hoppe, “Uniform total internal reflection fluorescence illumination enables live cell fluorescence resonance energy transfer microscopy,” Microsc. Microanal. 19(2), 350–359 (2013).
[Crossref] [PubMed]

Liu, C.

Liu, J.

Liu, W.

Liu, X.

C. Zheng, G. Zhao, W. Liu, Y. Chen, Z. Zhang, L. Jin, Y. Xu, C. Kuang, and X. Liu, “Three-dimensional super-resolved live cell imaging through polarized multi-angle TIRF,” Opt. Lett. 43(7), 1423–1426 (2018).
[Crossref] [PubMed]

L. Jin, J. Wu, P. Xiu, J. Fan, M. Hu, C. Kuang, Y. Xu, X. Zheng, and X. Liu, “High-resolution 3D reconstruction of microtubule structures by quantitative multi-angle total internal reflection fluorescence microscopy,” Opt. Commun. 395, 16–23 (2017).
[Crossref]

Lundquist, P.

J. Chen, R. V. Dalal, A. N. Petrov, A. Tsai, S. E. O’Leary, K. Chapin, J. Cheng, M. Ewan, P. L. Hsiung, P. Lundquist, S. W. Turner, D. R. Hsu, and J. D. Puglisi, “High-throughput platform for real-time monitoring of biological processes by multicolor single-molecule fluorescence,” Proc. Natl. Acad. Sci. U.S.A. 111(2), 664–669 (2014).
[Crossref] [PubMed]

Lyttek, M.

K. Stock, R. Sailer, W. S. L. Strauss, M. Lyttek, R. Steiner, and H. Schneckenburger, “Variable-angle total internal reflection fluorescence microscopy (VA-TIRFM): realization and application of a compact illumination device,” J. Microsc. 211(1), 19–29 (2003).
[Crossref] [PubMed]

Ma, Y.

Mattheyses, A. L.

A. L. Mattheyses, S. M. Simon, and J. Z. Rappoport, “Imaging with total internal reflection fluorescence microscopy for the cell biologist,” J. Cell Sci. 123(21), 3621–3628 (2010).
[Crossref] [PubMed]

A. L. Mattheyses, K. Shaw, and D. Axelrod, “Effective elimination of laser interference fringing in fluorescence microscopy by spinning azimuthal incidence angle,” Microsc. Res. Tech. 69(8), 642–647 (2006).
[Crossref] [PubMed]

McAuliffe, M.

Y. Fu, P. W. Winter, R. Rojas, V. Wang, M. McAuliffe, and G. H. Patterson, “Axial superresolution via multiangle TIRF microscopy with sequential imaging and photobleaching,” Proc. Natl. Acad. Sci. U.S.A. 113(16), 4368–4373 (2016).
[Crossref] [PubMed]

Mondal, P. P.

P. P. Mondal and S. T. Hess, “Total internal reflection fluorescence based multiplane localization microscopy enables super-resolved volume imaging,” Appl. Phys. Lett. 110, 211102 (2017).
[Crossref]

Münch, D.

J. Boulanger, C. Gueudry, D. Münch, B. Cinquin, P. Paul-Gilloteaux, S. Bardin, C. Guérin, F. Senger, L. Blanchoin, and J. Salamero, “Fast high-resolution 3D total internal reflection fluorescence microscopy by incidence angle scanning and azimuthal averaging,” Proc. Natl. Acad. Sci. U.S.A. 111(48), 17164–17169 (2014).
[Crossref] [PubMed]

Nagamatsu, S.

M. Ohara-Imaizumi and S. Nagamatsu, “Insulin exocytotic mechanism by imaging technique,” J. Biochem. 140(1), 1–5 (2006).
[Crossref] [PubMed]

Nazemifard, N.

Nelson, P. C.

J. F. Beausang, H. W. Schroeder, P. C. Nelson, and Y. E. Goldman, “Twirling of actin by myosins II and V observed via polarized TIRF in a modified gliding assay,” Biophys. J. 95(12), 5820–5831 (2008).
[Crossref] [PubMed]

Newman, W.

Nicovich, P. R.

O’Leary, S. E.

J. Chen, R. V. Dalal, A. N. Petrov, A. Tsai, S. E. O’Leary, K. Chapin, J. Cheng, M. Ewan, P. L. Hsiung, P. Lundquist, S. W. Turner, D. R. Hsu, and J. D. Puglisi, “High-throughput platform for real-time monitoring of biological processes by multicolor single-molecule fluorescence,” Proc. Natl. Acad. Sci. U.S.A. 111(2), 664–669 (2014).
[Crossref] [PubMed]

Ogg, S.

Ohara-Imaizumi, M.

M. Ohara-Imaizumi and S. Nagamatsu, “Insulin exocytotic mechanism by imaging technique,” J. Biochem. 140(1), 1–5 (2006).
[Crossref] [PubMed]

Oheim, M.

Parker, I.

K. L. Ellefsen, J. L. Dynes, and I. Parker, “Spinning-spot shadowless TIRF microscopy,” PLoS One 10(8), e0136055 (2015).
[Crossref] [PubMed]

Patterson, G. H.

Y. Fu, P. W. Winter, R. Rojas, V. Wang, M. McAuliffe, and G. H. Patterson, “Axial superresolution via multiangle TIRF microscopy with sequential imaging and photobleaching,” Proc. Natl. Acad. Sci. U.S.A. 113(16), 4368–4373 (2016).
[Crossref] [PubMed]

Paul-Gilloteaux, P.

J. Boulanger, C. Gueudry, D. Münch, B. Cinquin, P. Paul-Gilloteaux, S. Bardin, C. Guérin, F. Senger, L. Blanchoin, and J. Salamero, “Fast high-resolution 3D total internal reflection fluorescence microscopy by incidence angle scanning and azimuthal averaging,” Proc. Natl. Acad. Sci. U.S.A. 111(48), 17164–17169 (2014).
[Crossref] [PubMed]

Pendharker, S.

Petrov, A. N.

J. Chen, R. V. Dalal, A. N. Petrov, A. Tsai, S. E. O’Leary, K. Chapin, J. Cheng, M. Ewan, P. L. Hsiung, P. Lundquist, S. W. Turner, D. R. Hsu, and J. D. Puglisi, “High-throughput platform for real-time monitoring of biological processes by multicolor single-molecule fluorescence,” Proc. Natl. Acad. Sci. U.S.A. 111(2), 664–669 (2014).
[Crossref] [PubMed]

Proll, G.

J. Tschmelak, M. Kumpf, N. Käppel, G. Proll, and G. Gauglitz, “Total internal reflectance fluorescence (TIRF) biosensor for environmental monitoring of testosterone with commercially available immunochemistry: antibody characterization, assay development and real sample measurements,” Talanta 69(2), 343–350 (2006).
[Crossref] [PubMed]

Puglisi, J. D.

J. Chen, R. V. Dalal, A. N. Petrov, A. Tsai, S. E. O’Leary, K. Chapin, J. Cheng, M. Ewan, P. L. Hsiung, P. Lundquist, S. W. Turner, D. R. Hsu, and J. D. Puglisi, “High-throughput platform for real-time monitoring of biological processes by multicolor single-molecule fluorescence,” Proc. Natl. Acad. Sci. U.S.A. 111(2), 664–669 (2014).
[Crossref] [PubMed]

Rappoport, J. Z.

A. L. Mattheyses, S. M. Simon, and J. Z. Rappoport, “Imaging with total internal reflection fluorescence microscopy for the cell biologist,” J. Cell Sci. 123(21), 3621–3628 (2010).
[Crossref] [PubMed]

Rojas, R.

Y. Fu, P. W. Winter, R. Rojas, V. Wang, M. McAuliffe, and G. H. Patterson, “Axial superresolution via multiangle TIRF microscopy with sequential imaging and photobleaching,” Proc. Natl. Acad. Sci. U.S.A. 113(16), 4368–4373 (2016).
[Crossref] [PubMed]

Sailer, R.

K. Stock, R. Sailer, W. S. L. Strauss, M. Lyttek, R. Steiner, and H. Schneckenburger, “Variable-angle total internal reflection fluorescence microscopy (VA-TIRFM): realization and application of a compact illumination device,” J. Microsc. 211(1), 19–29 (2003).
[Crossref] [PubMed]

Sakata-Sogawa, K.

M. Tokunaga, N. Imamoto, and K. Sakata-Sogawa, “Highly inclined thin illumination enables clear single-molecule imaging in cells,” Nat. Methods 5(2), 159–161 (2008).
[Crossref] [PubMed]

Salamero, J.

J. Boulanger, C. Gueudry, D. Münch, B. Cinquin, P. Paul-Gilloteaux, S. Bardin, C. Guérin, F. Senger, L. Blanchoin, and J. Salamero, “Fast high-resolution 3D total internal reflection fluorescence microscopy by incidence angle scanning and azimuthal averaging,” Proc. Natl. Acad. Sci. U.S.A. 111(48), 17164–17169 (2014).
[Crossref] [PubMed]

Schneckenburger, H.

K. Stock, R. Sailer, W. S. L. Strauss, M. Lyttek, R. Steiner, and H. Schneckenburger, “Variable-angle total internal reflection fluorescence microscopy (VA-TIRFM): realization and application of a compact illumination device,” J. Microsc. 211(1), 19–29 (2003).
[Crossref] [PubMed]

Schreiber, B.

Schroeder, H. W.

J. F. Beausang, H. W. Schroeder, P. C. Nelson, and Y. E. Goldman, “Twirling of actin by myosins II and V observed via polarized TIRF in a modified gliding assay,” Biophys. J. 95(12), 5820–5831 (2008).
[Crossref] [PubMed]

Senger, F.

J. Boulanger, C. Gueudry, D. Münch, B. Cinquin, P. Paul-Gilloteaux, S. Bardin, C. Guérin, F. Senger, L. Blanchoin, and J. Salamero, “Fast high-resolution 3D total internal reflection fluorescence microscopy by incidence angle scanning and azimuthal averaging,” Proc. Natl. Acad. Sci. U.S.A. 111(48), 17164–17169 (2014).
[Crossref] [PubMed]

Shaw, K.

A. L. Mattheyses, K. Shaw, and D. Axelrod, “Effective elimination of laser interference fringing in fluorescence microscopy by spinning azimuthal incidence angle,” Microsc. Res. Tech. 69(8), 642–647 (2006).
[Crossref] [PubMed]

Shende, S.

Shroff, H.

H. Shroff, C. G. Galbraith, J. A. Galbraith, and E. Betzig, “Live-cell photoactivated localization microscopy of nanoscale adhesion dynamics,” Nat. Methods 5(5), 417–423 (2008).
[Crossref] [PubMed]

Simon, S. M.

A. L. Mattheyses, S. M. Simon, and J. Z. Rappoport, “Imaging with total internal reflection fluorescence microscopy for the cell biologist,” J. Cell Sci. 123(21), 3621–3628 (2010).
[Crossref] [PubMed]

Steiner, R.

K. Stock, R. Sailer, W. S. L. Strauss, M. Lyttek, R. Steiner, and H. Schneckenburger, “Variable-angle total internal reflection fluorescence microscopy (VA-TIRFM): realization and application of a compact illumination device,” J. Microsc. 211(1), 19–29 (2003).
[Crossref] [PubMed]

Stemmer, A.

Stock, K.

K. Stock, R. Sailer, W. S. L. Strauss, M. Lyttek, R. Steiner, and H. Schneckenburger, “Variable-angle total internal reflection fluorescence microscopy (VA-TIRFM): realization and application of a compact illumination device,” J. Microsc. 211(1), 19–29 (2003).
[Crossref] [PubMed]

Strauss, W. S. L.

K. Stock, R. Sailer, W. S. L. Strauss, M. Lyttek, R. Steiner, and H. Schneckenburger, “Variable-angle total internal reflection fluorescence microscopy (VA-TIRFM): realization and application of a compact illumination device,” J. Microsc. 211(1), 19–29 (2003).
[Crossref] [PubMed]

Tan, J.

Tokunaga, M.

M. Tokunaga, N. Imamoto, and K. Sakata-Sogawa, “Highly inclined thin illumination enables clear single-molecule imaging in cells,” Nat. Methods 5(2), 159–161 (2008).
[Crossref] [PubMed]

Török, P.

Tsai, A.

J. Chen, R. V. Dalal, A. N. Petrov, A. Tsai, S. E. O’Leary, K. Chapin, J. Cheng, M. Ewan, P. L. Hsiung, P. Lundquist, S. W. Turner, D. R. Hsu, and J. D. Puglisi, “High-throughput platform for real-time monitoring of biological processes by multicolor single-molecule fluorescence,” Proc. Natl. Acad. Sci. U.S.A. 111(2), 664–669 (2014).
[Crossref] [PubMed]

Tschmelak, J.

J. Tschmelak, M. Kumpf, N. Käppel, G. Proll, and G. Gauglitz, “Total internal reflectance fluorescence (TIRF) biosensor for environmental monitoring of testosterone with commercially available immunochemistry: antibody characterization, assay development and real sample measurements,” Talanta 69(2), 343–350 (2006).
[Crossref] [PubMed]

Turner, S. W.

J. Chen, R. V. Dalal, A. N. Petrov, A. Tsai, S. E. O’Leary, K. Chapin, J. Cheng, M. Ewan, P. L. Hsiung, P. Lundquist, S. W. Turner, D. R. Hsu, and J. D. Puglisi, “High-throughput platform for real-time monitoring of biological processes by multicolor single-molecule fluorescence,” Proc. Natl. Acad. Sci. U.S.A. 111(2), 664–669 (2014).
[Crossref] [PubMed]

Uphoff, S.

S. J. Holden, S. Uphoff, J. Hohlbein, D. Yadin, L. Le Reste, O. J. Britton, and A. N. Kapanidis, “Defining the limits of single-molecule FRET resolution in TIRF microscopy,” Biophys. J. 99(9), 3102–3111 (2010).
[Crossref] [PubMed]

van ’t Hoff, M.

Varga, P.

Wang, V.

Y. Fu, P. W. Winter, R. Rojas, V. Wang, M. McAuliffe, and G. H. Patterson, “Axial superresolution via multiangle TIRF microscopy with sequential imaging and photobleaching,” Proc. Natl. Acad. Sci. U.S.A. 113(16), 4368–4373 (2016).
[Crossref] [PubMed]

Watanabe, K.

Wilson, T.

Winter, P. W.

Y. Fu, P. W. Winter, R. Rojas, V. Wang, M. McAuliffe, and G. H. Patterson, “Axial superresolution via multiangle TIRF microscopy with sequential imaging and photobleaching,” Proc. Natl. Acad. Sci. U.S.A. 113(16), 4368–4373 (2016).
[Crossref] [PubMed]

Wu, J.

L. Jin, J. Wu, P. Xiu, J. Fan, M. Hu, C. Kuang, Y. Xu, X. Zheng, and X. Liu, “High-resolution 3D reconstruction of microtubule structures by quantitative multi-angle total internal reflection fluorescence microscopy,” Opt. Commun. 395, 16–23 (2017).
[Crossref]

Xiu, P.

L. Jin, J. Wu, P. Xiu, J. Fan, M. Hu, C. Kuang, Y. Xu, X. Zheng, and X. Liu, “High-resolution 3D reconstruction of microtubule structures by quantitative multi-angle total internal reflection fluorescence microscopy,” Opt. Commun. 395, 16–23 (2017).
[Crossref]

Xu, Y.

C. Zheng, G. Zhao, W. Liu, Y. Chen, Z. Zhang, L. Jin, Y. Xu, C. Kuang, and X. Liu, “Three-dimensional super-resolved live cell imaging through polarized multi-angle TIRF,” Opt. Lett. 43(7), 1423–1426 (2018).
[Crossref] [PubMed]

L. Jin, J. Wu, P. Xiu, J. Fan, M. Hu, C. Kuang, Y. Xu, X. Zheng, and X. Liu, “High-resolution 3D reconstruction of microtubule structures by quantitative multi-angle total internal reflection fluorescence microscopy,” Opt. Commun. 395, 16–23 (2017).
[Crossref]

Yadin, D.

S. J. Holden, S. Uphoff, J. Hohlbein, D. Yadin, L. Le Reste, O. J. Britton, and A. N. Kapanidis, “Defining the limits of single-molecule FRET resolution in TIRF microscopy,” Biophys. J. 99(9), 3102–3111 (2010).
[Crossref] [PubMed]

Yuan, T.

Zhang, C.

Zhang, H.

J. Liu, M. Ai, H. Zhang, and J. Tan, “Focusing properties of elliptical mirror with an aperture,” Opt. Eng. 53(6), 061606 (2014).
[Crossref]

Zhang, Z.

Zhao, G.

Zheng, C.

Zheng, X.

L. Jin, J. Wu, P. Xiu, J. Fan, M. Hu, C. Kuang, Y. Xu, X. Zheng, and X. Liu, “High-resolution 3D reconstruction of microtubule structures by quantitative multi-angle total internal reflection fluorescence microscopy,” Opt. Commun. 395, 16–23 (2017).
[Crossref]

Zhong, C.

Zhu, L. L.

Zong, W.

Zou, L.

Zumbusch, A.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

P. P. Mondal and S. T. Hess, “Total internal reflection fluorescence based multiplane localization microscopy enables super-resolved volume imaging,” Appl. Phys. Lett. 110, 211102 (2017).
[Crossref]

Biomed. Opt. Express (2)

Biophys. J. (2)

J. F. Beausang, H. W. Schroeder, P. C. Nelson, and Y. E. Goldman, “Twirling of actin by myosins II and V observed via polarized TIRF in a modified gliding assay,” Biophys. J. 95(12), 5820–5831 (2008).
[Crossref] [PubMed]

S. J. Holden, S. Uphoff, J. Hohlbein, D. Yadin, L. Le Reste, O. J. Britton, and A. N. Kapanidis, “Defining the limits of single-molecule FRET resolution in TIRF microscopy,” Biophys. J. 99(9), 3102–3111 (2010).
[Crossref] [PubMed]

J. Biochem. (1)

M. Ohara-Imaizumi and S. Nagamatsu, “Insulin exocytotic mechanism by imaging technique,” J. Biochem. 140(1), 1–5 (2006).
[Crossref] [PubMed]

J. Biomed. Opt. (1)

T. P. Burghardt, “Measuring incidence angle for through-the-objective total internal reflection fluorescence microscopy,” J. Biomed. Opt. 17(12), 126007 (2012).
[Crossref] [PubMed]

J. Cell Biol. (1)

D. Axelrod, “Cell-substrate contacts illuminated by total internal reflection fluorescence,” J. Cell Biol. 89(1), 141–145 (1981).
[Crossref] [PubMed]

J. Cell Sci. (1)

A. L. Mattheyses, S. M. Simon, and J. Z. Rappoport, “Imaging with total internal reflection fluorescence microscopy for the cell biologist,” J. Cell Sci. 123(21), 3621–3628 (2010).
[Crossref] [PubMed]

J. Microsc. (1)

K. Stock, R. Sailer, W. S. L. Strauss, M. Lyttek, R. Steiner, and H. Schneckenburger, “Variable-angle total internal reflection fluorescence microscopy (VA-TIRFM): realization and application of a compact illumination device,” J. Microsc. 211(1), 19–29 (2003).
[Crossref] [PubMed]

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

Microsc. Microanal. (1)

J. Lin and A. D. Hoppe, “Uniform total internal reflection fluorescence illumination enables live cell fluorescence resonance energy transfer microscopy,” Microsc. Microanal. 19(2), 350–359 (2013).
[Crossref] [PubMed]

Microsc. Res. Tech. (1)

A. L. Mattheyses, K. Shaw, and D. Axelrod, “Effective elimination of laser interference fringing in fluorescence microscopy by spinning azimuthal incidence angle,” Microsc. Res. Tech. 69(8), 642–647 (2006).
[Crossref] [PubMed]

Nat. Methods (2)

M. Tokunaga, N. Imamoto, and K. Sakata-Sogawa, “Highly inclined thin illumination enables clear single-molecule imaging in cells,” Nat. Methods 5(2), 159–161 (2008).
[Crossref] [PubMed]

H. Shroff, C. G. Galbraith, J. A. Galbraith, and E. Betzig, “Live-cell photoactivated localization microscopy of nanoscale adhesion dynamics,” Nat. Methods 5(5), 417–423 (2008).
[Crossref] [PubMed]

Opt. Commun. (1)

L. Jin, J. Wu, P. Xiu, J. Fan, M. Hu, C. Kuang, Y. Xu, X. Zheng, and X. Liu, “High-resolution 3D reconstruction of microtubule structures by quantitative multi-angle total internal reflection fluorescence microscopy,” Opt. Commun. 395, 16–23 (2017).
[Crossref]

Opt. Eng. (1)

J. Liu, M. Ai, H. Zhang, and J. Tan, “Focusing properties of elliptical mirror with an aperture,” Opt. Eng. 53(6), 061606 (2014).
[Crossref]

Opt. Express (2)

Opt. Lett. (6)

PLoS One (1)

K. L. Ellefsen, J. L. Dynes, and I. Parker, “Spinning-spot shadowless TIRF microscopy,” PLoS One 10(8), e0136055 (2015).
[Crossref] [PubMed]

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

J. Chen, R. V. Dalal, A. N. Petrov, A. Tsai, S. E. O’Leary, K. Chapin, J. Cheng, M. Ewan, P. L. Hsiung, P. Lundquist, S. W. Turner, D. R. Hsu, and J. D. Puglisi, “High-throughput platform for real-time monitoring of biological processes by multicolor single-molecule fluorescence,” Proc. Natl. Acad. Sci. U.S.A. 111(2), 664–669 (2014).
[Crossref] [PubMed]

J. Boulanger, C. Gueudry, D. Münch, B. Cinquin, P. Paul-Gilloteaux, S. Bardin, C. Guérin, F. Senger, L. Blanchoin, and J. Salamero, “Fast high-resolution 3D total internal reflection fluorescence microscopy by incidence angle scanning and azimuthal averaging,” Proc. Natl. Acad. Sci. U.S.A. 111(48), 17164–17169 (2014).
[Crossref] [PubMed]

Y. Fu, P. W. Winter, R. Rojas, V. Wang, M. McAuliffe, and G. H. Patterson, “Axial superresolution via multiangle TIRF microscopy with sequential imaging and photobleaching,” Proc. Natl. Acad. Sci. U.S.A. 113(16), 4368–4373 (2016).
[Crossref] [PubMed]

Talanta (1)

J. Tschmelak, M. Kumpf, N. Käppel, G. Proll, and G. Gauglitz, “Total internal reflectance fluorescence (TIRF) biosensor for environmental monitoring of testosterone with commercially available immunochemistry: antibody characterization, assay development and real sample measurements,” Talanta 69(2), 343–350 (2006).
[Crossref] [PubMed]

Traffic (1)

D. Axelrod, “Total internal reflection fluorescence microscopy in cell biology,” Traffic 2(11), 764–774 (2001).
[Crossref] [PubMed]

Other (2)

D. Axelrod, Total Internal Reflection Fluorescence Microscopy Chap. 9 (elsevier,1989).

M. Gu, Advanced optical imaging theory Chap. 6 (Springer,1999).

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Figures (9)

Fig. 1
Fig. 1 Schematic of the illumination device involving (a) the high-NA objective, (b) the elliptical mirror.
Fig. 2
Fig. 2 Schematic of elliptical mirror system.
Fig. 3
Fig. 3 Contour plots of intensity within 2λ radius near the evanescent focus of the elliptical mirror illuminated by the beam linearly polarized in the x direction (a)|Ex|2,(b) |Ey|2,(c) |Ez|2,(d) |(E)|2.Peak intensities of |(E)|2 have been normalized to 100; critical angle corresponding to the interface K9 glass (n1 = 1.518) and water (n2 = 1.333) is 61.4°; incident angular range: 62°–89°; long axis: 2a = 100 mm, eccentricity e = 0.8.
Fig. 4
Fig. 4 Contour plots of intensity within 2λ radius near the evanescent focus of the elliptical mirror illuminated by the left-handed circularly polarized beam (a) |Ex|2,(b) |Ey|2,(c) |Ez|2,(d) |(E)|2. Peak intensities of |(E)|2 have been normalized to 100; critical angle corresponding to the interface K9 glass (n1 = 1.518) and water (n2 = 1.333) is 61.4°; incident angular range: 62°–89°; long axis: 2a = 100 mm, eccentricity e = 0.8.
Fig. 5
Fig. 5 Plots of (a) the peak intensity ratio |Ez|2/|Ex|2, (b)the focus separation Δ x and (c) the normalized dip depth η versus minimum incident angle ( θ m i n ). The red and blue lines correspond to the device of high-NA objective (NA = 1.49) and elliptical mirror, respectively. The solid and dashed lines correspond to the interfaces between immersion oil (n = 1.518) and air (n = 1), and between immersion oil (n = 1.518) and water (n = 1.333), respectively. The illuminated beam is polarized along the x direction.
Fig. 6
Fig. 6 Normalized intensity versus evanescent field depth of (a) elliptical mirror; (b) high-NA objective (NA = 1.49)
Fig. 7
Fig. 7 (a) The basic schematic of e-TIRF microscopy; (b) the photograph of the experimental setup.
Fig. 8
Fig. 8 (a) Fluorescence pollen particle image in the inclined illumination method. (b) Fluorescence pollen particle image in the prism-based TIRF method, (c) Fluorescence pollen particle image in the e-TIRF method.
Fig. 9
Fig. 9 Fluorescent microsphere images with different ranges of incident angles (a) 75–85° (b) 65–85°.

Equations (12)

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E ( ρ , φ s , z ) = π i λ { [ I 0 + cos ( 2 φ s ) I 2 ] e x + sin ( 2 φ s ) I 2 e y + 2 i cos φ s I 1 e z }
I 0 = θ min θ max P ( θ 1 ) sin θ 1 ( t s + t p cos θ 2 ) exp [ i k 0 Φ ( θ 1 ) ] J 0 ( k 1 ρ sin θ 1 ) exp ( i k 2 z cos θ 2 ) d θ 1
I 1 = θ min θ max P ( θ 1 ) sin θ 1 ( t p sin θ 2 ) exp [ i k 0 Φ ( θ 1 ) ] J 1 ( k 1 ρ sin θ 1 ) exp ( i k 2 z cos θ 2 ) d θ 1
I 2 = θ min θ max P ( θ 1 ) sin θ 1 ( t s t p sin θ 2 ) exp [ i k 0 Φ ( θ 1 ) ] J 2 ( k 1 ρ sin θ 1 ) exp ( i k 2 z cos θ 2 ) d θ 1
t s = 2 cos θ 1 sin θ 2 sin ( θ 1 + θ 2 )
t p = 2 n 1 cos θ 1 n 2 cos θ 1 + n 1 cos θ 2
Φ ( θ 1 ) = d ( n 1 cos θ 1 n 2 cos θ 2 )
p ( θ ) = 1 + e 1 e ( a e ( z + c ) ) ( a + e ( z + c ) )
P ( θ ) = p ( θ ) cos α = 1 + e 1 e a e ( z + c ) a + e ( z + c ) ( z + c ) + a e a + e ( z + c )
E x = i A 2 [ I 0 + I 2 cos ( 2 φ s ) + i I 2 sin ( 2 φ s ) ]
E y = i A 2 [ I 2 sin ( 2 φ s ) i I 2 cos ( 2 φ s ) + i I 0 ]
E z = 2 A [ I 1 cos ( φ s ) + i I 1 sin ( φ s ) ]

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