Abstract

Isotropic single-objective (ISO) microscopy is a recently proposed imaging technique that can theoretically exhibit the same axial and transverse resolutions as 4Pi microscopy while using a classical single-objective confocal microscope. This achievement is obtained by placing the sample on a mirror and shaping the illumination beam so that the interference of the incident and mirror-reflected fields yields a quasi-spherical spot. In this work, we model the image formation in the ISO fluorescence microscope and simulate its point spread function. Then, we describe the experimental implementation and discuss its practical difficulties.

© 2011 Optical Society of America

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  29. J.-J. Greffet and R. Carminati, “Image formation in near-field optics,” Prog. Surf. Sci. 56, 133–237 (1997).
    [CrossRef]
  30. M. Schrader, M. Kozubek, S. W. Hell, and T. Wilson, “Optical transfer functions of 4Pi confocal microscopes: theory and experiment,” Opt. Lett. 22, 436–438 (1997).
    [CrossRef] [PubMed]
  31. P. Torok and C. J. R. Sheppard, “The role of pinhole size in high-aperture two and three-photon microscopy,” in Confocal and Two-Photon Microscopy, A.Diaspro, ed. (Wiley-Liss, 2001).
  32. H. J. Matthews, D. K. Hamilton, and C. J. R. Sheppard, “Aberration measurement by confocal interferometry,” J. Mod. Opt. 36, 233–250 (1989).
    [CrossRef]
  33. M. Lang, T. Muller, J. Engelhardt, and S. W. Hell, “4Pi microscopy of type A with 1-photon excitation in biological fluorescence imaging,” Opt. Express 15, 2459–2467 (2007).
    [CrossRef] [PubMed]

2010

W. Chen and Q. Zhan, “Diffraction limited focusing with controllable arbitrary three-dimensional polarization,” J. Opt. 12, 045707 (2010).
[CrossRef]

E. Mudry, E. Le Moal, P. Ferrand, P. C. Chaumet, and A. Sentenac, “Isotropic diffraction-limited focusing using a single objective lens,” Phys. Rev. Lett. 105, 203903 (2010).
[CrossRef]

E. Mudry, P. C. Chaumet, K. Belkebir, G. Maire, and A. Sentenac, “Mirror-assisted optical diffraction tomography with isotropic resolution,” Opt. Lett. 35, 1857–1859 (2010).
[CrossRef] [PubMed]

2009

M. Martínez-Corral and G. Saavedra, “The resolution challenge in 3D optical microscopy,” Prog. Opt. 53, 1–67 (2009).
[CrossRef]

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

2008

C. Selhuber-Unkel, I. Zins, O. Schubert, C. Sonnichsen, and L. Oddershede, “Quantitative optical trapping of single gold nanorods,” Nano Lett. 8, 2998–3003 (2008).
[CrossRef] [PubMed]

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophotonics 2, 021875(2008).
[CrossRef]

2007

2006

J. Bewersdorf, B. T. Bennett, and K. L. Knight, “H2AX chromatin structures and their response to DNA damage revealed by 4Pi microscopy,” Proc. Natl. Acad. Sci. USA 103, 18137–18142(2006).
[CrossRef] [PubMed]

A. S. van de Nes, J. J. M. Braat, and S. F. Pereira, “High-density optical data storage,” Rep. Prog. Phys. 69, 2323–2363(2006).
[CrossRef]

J. Bewersdorf, R. Schmidt, and S. W. Hell, “Comparison of I5M and 4Pi-microscopy,” J. Microsc. 222, 105–117 (2006).
[CrossRef] [PubMed]

2005

L. Melton, “Imaging: the big picture,” Nature 437, 775–779(2005).
[CrossRef] [PubMed]

2004

H. Gugel, J. Bewersdorf, S. Jakobs, J. Engelhardt, R. Storz, and S. W. Hell, “Cooperative 4Pi excitation and detection yields sevenfold sharper optical sections in live cell microscopy,” Biophys. J. 87, 4146–4152 (2004).
[CrossRef] [PubMed]

B. J. Davis, W. C. Karl, A. K. Swan, M. S. Unlu, and B. B. Goldberg, “Capabilities and limitations of pupil-plane filters for superresolution and image enhancement,” Opt. Express 12, 4150–4156 (2004).
[CrossRef] [PubMed]

2003

2002

2001

1999

M. Martínez-Corral, P. Andrés, C. J. Zapata-Rodriguez, and M. Kowalczyk, “Three-dimensional superresolution by annular binary filters,” Opt. Commun. 165, 267–278 (1999).
[CrossRef]

1998

M. Nagorni and S. W. Hell, “4Pi-confocal microscopy provides three-dimensional images of the microtubule network with 100- to 150 nm resolution,” J. Struct. Biol. 123, 236–247 (1998).
[CrossRef]

1997

C. J. R. Sheppard and P. Torok, “Electromagnetic field in the focal region of an electric dipole wave,” Optik 104, 175–177(1997).

J.-J. Greffet and R. Carminati, “Image formation in near-field optics,” Prog. Surf. Sci. 56, 133–237 (1997).
[CrossRef]

M. Schrader, M. Kozubek, S. W. Hell, and T. Wilson, “Optical transfer functions of 4Pi confocal microscopes: theory and experiment,” Opt. Lett. 22, 436–438 (1997).
[CrossRef] [PubMed]

1995

1992

1989

H. J. Matthews, D. K. Hamilton, and C. J. R. Sheppard, “Aberration measurement by confocal interferometry,” J. Mod. Opt. 36, 233–250 (1989).
[CrossRef]

1988

Andrés, P.

M. Martínez-Corral, P. Andrés, C. J. Zapata-Rodriguez, and M. Kowalczyk, “Three-dimensional superresolution by annular binary filters,” Opt. Commun. 165, 267–278 (1999).
[CrossRef]

Belkebir, K.

Bennett, B. T.

J. Bewersdorf, B. T. Bennett, and K. L. Knight, “H2AX chromatin structures and their response to DNA damage revealed by 4Pi microscopy,” Proc. Natl. Acad. Sci. USA 103, 18137–18142(2006).
[CrossRef] [PubMed]

Bewersdorf, J.

J. Bewersdorf, B. T. Bennett, and K. L. Knight, “H2AX chromatin structures and their response to DNA damage revealed by 4Pi microscopy,” Proc. Natl. Acad. Sci. USA 103, 18137–18142(2006).
[CrossRef] [PubMed]

J. Bewersdorf, R. Schmidt, and S. W. Hell, “Comparison of I5M and 4Pi-microscopy,” J. Microsc. 222, 105–117 (2006).
[CrossRef] [PubMed]

H. Gugel, J. Bewersdorf, S. Jakobs, J. Engelhardt, R. Storz, and S. W. Hell, “Cooperative 4Pi excitation and detection yields sevenfold sharper optical sections in live cell microscopy,” Biophys. J. 87, 4146–4152 (2004).
[CrossRef] [PubMed]

Boyer, G.

Braat, J. J. M.

A. S. van de Nes, J. J. M. Braat, and S. F. Pereira, “High-density optical data storage,” Rep. Prog. Phys. 69, 2323–2363(2006).
[CrossRef]

Caballero, M. T.

Carminati, R.

Chaumet, P. C.

E. Mudry, E. Le Moal, P. Ferrand, P. C. Chaumet, and A. Sentenac, “Isotropic diffraction-limited focusing using a single objective lens,” Phys. Rev. Lett. 105, 203903 (2010).
[CrossRef]

E. Mudry, P. C. Chaumet, K. Belkebir, G. Maire, and A. Sentenac, “Mirror-assisted optical diffraction tomography with isotropic resolution,” Opt. Lett. 35, 1857–1859 (2010).
[CrossRef] [PubMed]

P. C. ChaumetB. Pouligny, R. Dimova, and N. Sojic, “Optical tweezers in interaction with an apertureless probe,” J. Appl. Phys. 102, 024915 (2007).
[CrossRef]

Chen, W.

W. Chen and Q. Zhan, “Diffraction limited focusing with controllable arbitrary three-dimensional polarization,” J. Opt. 12, 045707 (2010).
[CrossRef]

Coblentz, K.

Davis, B. J.

de Rosny, J.

Dholakia, K.

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophotonics 2, 021875(2008).
[CrossRef]

Dienerowitz, M.

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophotonics 2, 021875(2008).
[CrossRef]

Dimova, R.

P. C. ChaumetB. Pouligny, R. Dimova, and N. Sojic, “Optical tweezers in interaction with an apertureless probe,” J. Appl. Phys. 102, 024915 (2007).
[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]

Dvornikov, A.

Engelhardt, J.

M. Lang, T. Muller, J. Engelhardt, and S. W. Hell, “4Pi microscopy of type A with 1-photon excitation in biological fluorescence imaging,” Opt. Express 15, 2459–2467 (2007).
[CrossRef] [PubMed]

H. Gugel, J. Bewersdorf, S. Jakobs, J. Engelhardt, R. Storz, and S. W. Hell, “Cooperative 4Pi excitation and detection yields sevenfold sharper optical sections in live cell microscopy,” Biophys. J. 87, 4146–4152 (2004).
[CrossRef] [PubMed]

Esener, S.

Ferrand, P.

E. Mudry, E. Le Moal, P. Ferrand, P. C. Chaumet, and A. Sentenac, “Isotropic diffraction-limited focusing using a single objective lens,” Phys. Rev. Lett. 105, 203903 (2010).
[CrossRef]

Fink, M.

Goldberg, B. B.

Greffet, J.-J.

J.-J. Greffet and R. Carminati, “Image formation in near-field optics,” Prog. Surf. Sci. 56, 133–237 (1997).
[CrossRef]

Gugel, H.

H. Gugel, J. Bewersdorf, S. Jakobs, J. Engelhardt, R. Storz, and S. W. Hell, “Cooperative 4Pi excitation and detection yields sevenfold sharper optical sections in live cell microscopy,” Biophys. J. 87, 4146–4152 (2004).
[CrossRef] [PubMed]

Hamilton, D. K.

H. J. Matthews, D. K. Hamilton, and C. J. R. Sheppard, “Aberration measurement by confocal interferometry,” J. Mod. Opt. 36, 233–250 (1989).
[CrossRef]

Hegedus, Z. S.

Hell, S. W.

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

M. Lang, T. Muller, J. Engelhardt, and S. W. Hell, “4Pi microscopy of type A with 1-photon excitation in biological fluorescence imaging,” Opt. Express 15, 2459–2467 (2007).
[CrossRef] [PubMed]

J. Bewersdorf, R. Schmidt, and S. W. Hell, “Comparison of I5M and 4Pi-microscopy,” J. Microsc. 222, 105–117 (2006).
[CrossRef] [PubMed]

H. Gugel, J. Bewersdorf, S. Jakobs, J. Engelhardt, R. Storz, and S. W. Hell, “Cooperative 4Pi excitation and detection yields sevenfold sharper optical sections in live cell microscopy,” Biophys. J. 87, 4146–4152 (2004).
[CrossRef] [PubMed]

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]

M. Nagorni and S. W. Hell, “4Pi-confocal microscopy provides three-dimensional images of the microtubule network with 100- to 150 nm resolution,” J. Struct. Biol. 123, 236–247 (1998).
[CrossRef]

M. Schrader, M. Kozubek, S. W. Hell, and T. Wilson, “Optical transfer functions of 4Pi confocal microscopes: theory and experiment,” Opt. Lett. 22, 436–438 (1997).
[CrossRef] [PubMed]

S. W. Hell and E. Stelzer, “Properties of a 4Pi confocal fluorescence microscope,” J. Opt. Soc. Am. A 9, 2159–2166 (1992).
[CrossRef]

Ibanez-Lopez, C.

Jakobs, S.

H. Gugel, J. Bewersdorf, S. Jakobs, J. Engelhardt, R. Storz, and S. W. Hell, “Cooperative 4Pi excitation and detection yields sevenfold sharper optical sections in live cell microscopy,” Biophys. J. 87, 4146–4152 (2004).
[CrossRef] [PubMed]

Karl, W. C.

Knight, K. L.

J. Bewersdorf, B. T. Bennett, and K. L. Knight, “H2AX chromatin structures and their response to DNA damage revealed by 4Pi microscopy,” Proc. Natl. Acad. Sci. USA 103, 18137–18142(2006).
[CrossRef] [PubMed]

Kowalczyk, M.

M. Martínez-Corral, P. Andrés, C. J. Zapata-Rodriguez, and M. Kowalczyk, “Three-dimensional superresolution by annular binary filters,” Opt. Commun. 165, 267–278 (1999).
[CrossRef]

Kozubek, M.

Lang, M.

Larkin, K. J.

Le Moal, E.

E. Mudry, E. Le Moal, P. Ferrand, P. C. Chaumet, and A. Sentenac, “Isotropic diffraction-limited focusing using a single objective lens,” Phys. Rev. Lett. 105, 203903 (2010).
[CrossRef]

Leuchs, G.

Lindlein, N.

Maire, G.

Martínez-Corral, M.

M. Martínez-Corral and G. Saavedra, “The resolution challenge in 3D optical microscopy,” Prog. Opt. 53, 1–67 (2009).
[CrossRef]

M. Martínez-Corral, C. Ibanez-Lopez, G. Saavedra, and M. T. Caballero, “Axial gain in resolution in optical sectioning fluorescence microscopy by shaded-ring filters,” Opt. Express 11, 1740–1745 (2003).
[CrossRef] [PubMed]

M. Martínez-Corral, M. T. Caballero, E. H. K. Stelzer, and J. Swoger, “Tailoring the axial shape of the point spread function using the Toraldo concept,” Opt. Express 10, 98–103(2002).
[PubMed]

M. Martínez-Corral, P. Andrés, C. J. Zapata-Rodriguez, and M. Kowalczyk, “Three-dimensional superresolution by annular binary filters,” Opt. Commun. 165, 267–278 (1999).
[CrossRef]

Matthews, H. J.

H. J. Matthews, D. K. Hamilton, and C. J. R. Sheppard, “Aberration measurement by confocal interferometry,” J. Mod. Opt. 36, 233–250 (1989).
[CrossRef]

Mazilu, M.

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophotonics 2, 021875(2008).
[CrossRef]

Melton, L.

L. Melton, “Imaging: the big picture,” Nature 437, 775–779(2005).
[CrossRef] [PubMed]

Mudry, E.

E. Mudry, E. Le Moal, P. Ferrand, P. C. Chaumet, and A. Sentenac, “Isotropic diffraction-limited focusing using a single objective lens,” Phys. Rev. Lett. 105, 203903 (2010).
[CrossRef]

E. Mudry, P. C. Chaumet, K. Belkebir, G. Maire, and A. Sentenac, “Mirror-assisted optical diffraction tomography with isotropic resolution,” Opt. Lett. 35, 1857–1859 (2010).
[CrossRef] [PubMed]

Muller, T.

Nagorni, M.

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]

M. Nagorni and S. W. Hell, “4Pi-confocal microscopy provides three-dimensional images of the microtubule network with 100- to 150 nm resolution,” J. Struct. Biol. 123, 236–247 (1998).
[CrossRef]

Oddershede, L.

C. Selhuber-Unkel, I. Zins, O. Schubert, C. Sonnichsen, and L. Oddershede, “Quantitative optical trapping of single gold nanorods,” Nano Lett. 8, 2998–3003 (2008).
[CrossRef] [PubMed]

Pereira, S. F.

A. S. van de Nes, J. J. M. Braat, and S. F. Pereira, “High-density optical data storage,” Rep. Prog. Phys. 69, 2323–2363(2006).
[CrossRef]

Peschel, U.

Pierrat, R.

Pouligny, B.

P. C. ChaumetB. Pouligny, R. Dimova, and N. Sojic, “Optical tweezers in interaction with an apertureless probe,” J. Appl. Phys. 102, 024915 (2007).
[CrossRef]

Quabis, S.

Rentzepis, P.

Saavedra, G.

Schmidt, R.

J. Bewersdorf, R. Schmidt, and S. W. Hell, “Comparison of I5M and 4Pi-microscopy,” J. Microsc. 222, 105–117 (2006).
[CrossRef] [PubMed]

Schrader, M.

Schubert, O.

C. Selhuber-Unkel, I. Zins, O. Schubert, C. Sonnichsen, and L. Oddershede, “Quantitative optical trapping of single gold nanorods,” Nano Lett. 8, 2998–3003 (2008).
[CrossRef] [PubMed]

Selhuber-Unkel, C.

C. Selhuber-Unkel, I. Zins, O. Schubert, C. Sonnichsen, and L. Oddershede, “Quantitative optical trapping of single gold nanorods,” Nano Lett. 8, 2998–3003 (2008).
[CrossRef] [PubMed]

Sentenac, A.

E. Mudry, P. C. Chaumet, K. Belkebir, G. Maire, and A. Sentenac, “Mirror-assisted optical diffraction tomography with isotropic resolution,” Opt. Lett. 35, 1857–1859 (2010).
[CrossRef] [PubMed]

E. Mudry, E. Le Moal, P. Ferrand, P. C. Chaumet, and A. Sentenac, “Isotropic diffraction-limited focusing using a single objective lens,” Phys. Rev. Lett. 105, 203903 (2010).
[CrossRef]

Sheppard, C. J. R.

C. J. R. Sheppard and P. Torok, “Electromagnetic field in the focal region of an electric dipole wave,” Optik 104, 175–177(1997).

C. J. R. Sheppard and K. J. Larkin, “Effect of numerical aperture on interference fringe spacing interferometry,” Appl. Opt. 34, 4731–4734 (1995).
[CrossRef] [PubMed]

H. J. Matthews, D. K. Hamilton, and C. J. R. Sheppard, “Aberration measurement by confocal interferometry,” J. Mod. Opt. 36, 233–250 (1989).
[CrossRef]

C. J. R. Sheppard and Z. S. Hegedus, “Axial behavior of pupil-plane filters,” J. Opt. Soc. Am. A 5, 643–647 (1988).
[CrossRef]

P. Torok and C. J. R. Sheppard, “The role of pinhole size in high-aperture two and three-photon microscopy,” in Confocal and Two-Photon Microscopy, A.Diaspro, ed. (Wiley-Liss, 2001).

Sojic, N.

P. C. ChaumetB. Pouligny, R. Dimova, and N. Sojic, “Optical tweezers in interaction with an apertureless probe,” J. Appl. Phys. 102, 024915 (2007).
[CrossRef]

Sonnichsen, C.

C. Selhuber-Unkel, I. Zins, O. Schubert, C. Sonnichsen, and L. Oddershede, “Quantitative optical trapping of single gold nanorods,” Nano Lett. 8, 2998–3003 (2008).
[CrossRef] [PubMed]

Stelzer, E.

Stelzer, E. H. K.

Storz, R.

H. Gugel, J. Bewersdorf, S. Jakobs, J. Engelhardt, R. Storz, and S. W. Hell, “Cooperative 4Pi excitation and detection yields sevenfold sharper optical sections in live cell microscopy,” Biophys. J. 87, 4146–4152 (2004).
[CrossRef] [PubMed]

Swan, A. K.

Swoger, J.

Torok, P.

C. J. R. Sheppard and P. Torok, “Electromagnetic field in the focal region of an electric dipole wave,” Optik 104, 175–177(1997).

P. Torok and C. J. R. Sheppard, “The role of pinhole size in high-aperture two and three-photon microscopy,” in Confocal and Two-Photon Microscopy, A.Diaspro, ed. (Wiley-Liss, 2001).

Unlu, M. S.

van de Nes, A. S.

A. S. van de Nes, J. J. M. Braat, and S. F. Pereira, “High-density optical data storage,” Rep. Prog. Phys. 69, 2323–2363(2006).
[CrossRef]

Walker, E.

Wilson, T.

Zapata-Rodriguez, C. J.

M. Martínez-Corral, P. Andrés, C. J. Zapata-Rodriguez, and M. Kowalczyk, “Three-dimensional superresolution by annular binary filters,” Opt. Commun. 165, 267–278 (1999).
[CrossRef]

Zhan, Q.

W. Chen and Q. Zhan, “Diffraction limited focusing with controllable arbitrary three-dimensional polarization,” J. Opt. 12, 045707 (2010).
[CrossRef]

Zins, I.

C. Selhuber-Unkel, I. Zins, O. Schubert, C. Sonnichsen, and L. Oddershede, “Quantitative optical trapping of single gold nanorods,” Nano Lett. 8, 2998–3003 (2008).
[CrossRef] [PubMed]

Appl. Opt.

Biophys. J.

H. Gugel, J. Bewersdorf, S. Jakobs, J. Engelhardt, R. Storz, and S. W. Hell, “Cooperative 4Pi excitation and detection yields sevenfold sharper optical sections in live cell microscopy,” Biophys. J. 87, 4146–4152 (2004).
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J. Appl. Phys.

P. C. ChaumetB. Pouligny, R. Dimova, and N. Sojic, “Optical tweezers in interaction with an apertureless probe,” J. Appl. Phys. 102, 024915 (2007).
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J. Microsc.

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J. Mod. Opt.

H. J. Matthews, D. K. Hamilton, and C. J. R. Sheppard, “Aberration measurement by confocal interferometry,” J. Mod. Opt. 36, 233–250 (1989).
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J. Nanophotonics

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophotonics 2, 021875(2008).
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W. Chen and Q. Zhan, “Diffraction limited focusing with controllable arbitrary three-dimensional polarization,” J. Opt. 12, 045707 (2010).
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J. Struct. Biol.

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Nat. Methods

S. W. Hell, “Microscopy and its focal switch,” Nat. Methods 6, 24–32 (2009).
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Nature

L. Melton, “Imaging: the big picture,” Nature 437, 775–779(2005).
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Opt. Commun.

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Phys. Rev. Lett.

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Proc. Natl. Acad. Sci. USA

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Figures (11)

Fig. 1
Fig. 1

Illustration of the ISO focusing concept, based on the time-reversal theory. (a) The incident field is made of a sum of plane waves propagating along u with complex vector amplitude e i ( u ) . (b) The field radiated by a dipole placed at z 0 z ^ before the mirror can be decomposed as a sum of plane waves propagating along u with complex vector amplitude e p ( u ) . To focus at point z 0 z ^ , the time-reversal focusing theory states that e i ( u ) should ideally be equal to the conjugate of e p ( u ) .

Fig. 2
Fig. 2

Global PSF of an ISO microscope, simulated for two different objectives in air: (a) and (c) ideal objective with NA = sin θ max = 0.99 ; (b) and (d) realistic objective, NA = sin θ max = 0.80 . These images corresponds to slices taken in the (a), (b) transverse and (c), (d) axial planes.

Fig. 3
Fig. 3

Axial profiles taken from the PSF of an ISO microscope (solid curve) and a conventional confocal microscope (dashed curve), simulated for different NA in vacuum. (a)  NA = 0.99 . (b)  NA = 0.80 . For comparison purposes, the PSF of the conventional confocal microscope has been plotted after modulation by cos 2 [ β k 0 ( z z 0 ) ] (circles). The observed dissymetry stems from the phase mask discretization induced by the SLM.

Fig. 4
Fig. 4

Examples of phase masks for ISO focusing. For symmetry reasons, only the top right quarter of the masks are shown (bottom left corner is the center of symmetry). Mask designs are based on (a) and (d) the principle of time-reversal focusing and (b), (c), (e), and (f) combinations of Fresnel phase plates following (b), (e) a checkerboard of 50 × 50 pixel squares and (c), (f) a pie chart of 16 slices. These masks were generated for two different configurations in which the mirror is placed (a)–(c) in the genuine focal plane of the objective lens and (d)–(f) at d = 6 μm above it. In the latter case, the term k 0 d cos θ has been added to all the phase patterns given in the text.

Fig. 5
Fig. 5

Schematic of the microscope setup. APD, avalanche photodiode; HWP, half-wave plate; SLM, phase-only spatial light modulator; rfp, rear focal plane. Lenses are achromatic doublets. See details in text.

Fig. 6
Fig. 6

Profile intensity along the z axis of the images of isolated 100 nm fluorescent beads, measured by ISO microscopy. Vertical and horizontal slices of these images are shown in insets. Phase mask designs were based on (a) time-reversal and (b) combinations of Fresnel phase plates with respect to a pie chart of 16 slices; see Fig. 4. Note that the image of the bead was recorded by transverse scanning with the nanopositioning stage and axial scanning of the sample with the SLM.

Fig. 7
Fig. 7

Intensity profiles taken along the axial direction of 3D images of 100 nm fluorescent beads, measured by ISO microscopy using time-reversal phase masks. Bead-to-mirror distances are estimated, on the basis of the position of the brightest fringe in the interference patterns, to 2.1 μm (solid curve), 2.5 μm (dotted curve), and 4.3 μm (dashed curve).

Fig. 8
Fig. 8

Relative variation of the fluorescent signal as a function of the phase masks displayed on the SLM, measured by focusing light in a droplet of fluorescent dye solution (Rhodamine 6G). Fresnel-lens phase masks were used to focus light in a single spot 0 to 12 μm before the genuine focal plane of the objective lens. Spatial filtering at detection was performed with pinholes of diameter 30 μm (solid curve) and 50 μm (dashed curve). These curves reveal the dependence of the detection sensitivity on the SLM display.

Fig. 9
Fig. 9

Spot radii at 1 / e 2 , evaluated by fitting (with a Gaussian curve) axial and transverse profiles taken from fluorescence images of a 100 nm bead, measured while controlling the actual plane where light focuses using the SLM. Insert: axial slices of two of these images, measured while focusing (a) in the genuine focal plane of the lens and (b) in a plane located 12 μm before it.

Fig. 10
Fig. 10

Fluorescence images (axial slices) of a 100 nm bead, measured with time-reversal phase masks that yield pairs of spots separated by (a) 0, (b) 2, and (c)  4 μm along the optical axis in the absence of the mirror.

Fig. 11
Fig. 11

Three intensity profiles, taken in the axial direction from fluorescence images of a single 100 nm bead, for different positions of the mirror. In the middle and bottom profiles, the mirror position differs by 0.10 and 0.21 μm from that of the top profile, respectively. Top and bottom profiles are fitted with envelope curves (dashed curve) corresponding to (top) a Gaussian function of radius 0.65 μm at 1 / e 2 and (bottom) a sum of two identical Gaussian functions of same radius 0.65 μm but of different centers.

Equations (7)

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E inc ( r ) = 0 2 π d ϕ θ max θ max d θ sin θ e i ( u ) exp ( i k 0 u · r ) ,
E refl ( r ) = 0 2 π d ϕ θ max θ max d θ sin θ e r ( u ) e i k 0 [ u 2 ( u · z ^ ) z ^ ] · r ,
e i ideal ( u ) sin ( z 0 k 0 cos θ ) [ p ( p · u ) p ] ,
sin θ = ( sin θ max ) ρ / R ,
e i ( u ) = cos θ { [ E ( ρ , ψ ) · u ϕ ] u ψ [ E ( ρ , ψ ) · u ρ ] u θ } .
f ( ρ , ψ ) = π 2 sign [ sin ( z 0 k 0 cos θ ) ] ,
I ( r , r 0 ) PSF ill λ ( r r 0 ) PSF det λ ( r r 0 ) ,

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