Abstract

The spatial resolution characteristics in confocal laser scanning microscopy (LSM) and two-photon LSM utilizing a higher-order radially polarized Laguerre–Gaussian (RP-LG) beam are numerically analyzed. The size of the point spread function (PSF) and its dependence on the confocal pinhole size are compared with practical LSM using a circularly polarized Gaussian beam on the basis of vector diffraction theory. The spatial frequency response in terms of the optical transfer function (OTF) is also evaluated for LSM using the RP-LG beam. The smaller focal spot characteristics of higher-order RP-LG beams contribute to a dramatic enhancement of the lateral spatial resolution in confocal LSM and two-photon LSM.

© 2015 Optical Society of America

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  2. C. J. R. Sheppard and A. Choudhury, “Annular pupils, radial polarization, and superresolution,” Appl. Opt. 43(22), 4322–4327 (2004).
    [Crossref] [PubMed]
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  4. G. M. Lerman and U. Levy, “Effect of radial polarization and apodization on spot size under tight focusing conditions,” Opt. Express 16(7), 4567–4581 (2008).
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  23. Y. Kozawa and S. Sato, “Focusing property of a double-ring-shaped radially polarized beam,” Opt. Lett. 31(6), 820–822 (2006).
    [Crossref] [PubMed]
  24. 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]
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    [Crossref]
  28. P. Török, P. D. Higdon, and T. Wilson, “Theory for confocal and conventional microscopes imaging small dielectric scatterers,” J. Mod. Opt. 45(8), 1681–1698 (1998).
    [Crossref]
  29. P. D. Higdon, P. Török, and T. Wilson, “Imaging properties of high aperture multiphoton fluorescence scanning optical microscopes,” J. Microsc. 193(2), 127–141 (1999).
    [Crossref]
  30. M. R. Foreman and P. Török, “Computational methods in vectorial imaging,” J. Mod. Opt. 58(5–6), 339–364 (2011).
    [Crossref]
  31. C. J. R. Sheppard and M. Gu, “Image formation in two-photon fluorescence microscopy,” Optik (Stuttg.) 86(3), 104–106 (1990).

2014 (2)

S. Ipponjima, T. Hibi, Y. Kozawa, H. Horanai, H. Yokoyama, S. Sato, and T. Nemoto, “Improvement of lateral resolution and extension of depth of field in two-photon microscopy by a higher-order radially polarized beam,” Microscopy (Oxford) 63(1), 23–32 (2014).
[Crossref] [PubMed]

G. Thériault, M. Cottet, A. Castonguay, N. McCarthy, and Y. De Koninck, “Extended two-photon microscopy in live samples with Bessel beams: steadier focus, faster volume scans, and simpler stereoscopic imaging,” Front. Cell Neurosci. 8, 139 (2014).
[PubMed]

2012 (3)

2011 (2)

2010 (2)

2009 (2)

H. Dehez, M. Piché, and Y. De Koninck, “Enhanced resolution in two-photon imaging using a TM01 laser beam at a dielectric interface,” Opt. Lett. 34(23), 3601–3603 (2009).
[Crossref] [PubMed]

J. Kim, D. C. Kim, and S. H. Back, “Demonstration of high lateral resolution in laser confocal microscopy using annular and radially polarized light,” Microsc. Res. Tech. 72(6), 441–446 (2009).
[Crossref] [PubMed]

2008 (2)

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

G. M. Lerman and U. Levy, “Effect of radial polarization and apodization on spot size under tight focusing conditions,” Opt. Express 16(7), 4567–4581 (2008).
[Crossref] [PubMed]

2007 (2)

2006 (1)

2004 (1)

2003 (1)

2001 (1)

L. E. Helseth, “Roles of polarization, phase and amplitude in solid immersion lens systems,” Opt. Commun. 191(3–6), 161–172 (2001).
[Crossref]

2000 (2)

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179(1–6), 1–7 (2000).
[Crossref]

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000).
[Crossref] [PubMed]

1999 (1)

P. D. Higdon, P. Török, and T. Wilson, “Imaging properties of high aperture multiphoton fluorescence scanning optical microscopes,” J. Microsc. 193(2), 127–141 (1999).
[Crossref]

1998 (2)

A. A. Tovar, “Production and propagation of cylindrically polarized Laguerre–Gaussian laser beams,” J. Opt. Soc. Am. A 15(10), 2705–2711 (1998).
[Crossref]

P. Török, P. D. Higdon, and T. Wilson, “Theory for confocal and conventional microscopes imaging small dielectric scatterers,” J. Mod. Opt. 45(8), 1681–1698 (1998).
[Crossref]

1997 (1)

C. J. R. Sheppard and P. Török, “An electromagnetic theory of imaging in fluorescence microscopy, and imaging in polarization fluorescence microscopy,” Bioimaging 5(4), 205–218 (1997).
[Crossref]

1990 (1)

C. J. R. Sheppard and M. Gu, “Image formation in two-photon fluorescence microscopy,” Optik (Stuttg.) 86(3), 104–106 (1990).

1987 (1)

1977 (1)

C. J. R. Sheppard and A. Choudhury, “Image formation in the scanning microscope,” Opt. Acta (Lond.) 24(10), 1051–1073 (1977).
[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]

April, A.

Back, S. H.

J. Kim, D. C. Kim, and S. H. Back, “Demonstration of high lateral resolution in laser confocal microscopy using annular and radially polarized light,” Microsc. Res. Tech. 72(6), 441–446 (2009).
[Crossref] [PubMed]

Brown, T. G.

Carlini, A. R.

Castonguay, A.

G. Thériault, M. Cottet, A. Castonguay, N. McCarthy, and Y. De Koninck, “Extended two-photon microscopy in live samples with Bessel beams: steadier focus, faster volume scans, and simpler stereoscopic imaging,” Front. Cell Neurosci. 8, 139 (2014).
[PubMed]

Chong, C. T.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Choudhury, A.

C. J. R. Sheppard and A. Choudhury, “Annular pupils, radial polarization, and superresolution,” Appl. Opt. 43(22), 4322–4327 (2004).
[Crossref] [PubMed]

C. J. R. Sheppard and A. Choudhury, “Image formation in the scanning microscope,” Opt. Acta (Lond.) 24(10), 1051–1073 (1977).
[Crossref]

Cottet, M.

G. Thériault, M. Cottet, A. Castonguay, N. McCarthy, and Y. De Koninck, “Extended two-photon microscopy in live samples with Bessel beams: steadier focus, faster volume scans, and simpler stereoscopic imaging,” Front. Cell Neurosci. 8, 139 (2014).
[PubMed]

Courjon, D.

T. Grosjean and D. Courjon, “Smallest focal spots,” Opt. Commun. 272(2), 314–319 (2007).
[Crossref]

De Koninck, Y.

G. Thériault, M. Cottet, A. Castonguay, N. McCarthy, and Y. De Koninck, “Extended two-photon microscopy in live samples with Bessel beams: steadier focus, faster volume scans, and simpler stereoscopic imaging,” Front. Cell Neurosci. 8, 139 (2014).
[PubMed]

H. Dehez, M. Piché, and Y. De Koninck, “Enhanced resolution in two-photon imaging using a TM01 laser beam at a dielectric interface,” Opt. Lett. 34(23), 3601–3603 (2009).
[Crossref] [PubMed]

Dehez, H.

Dorn, R.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179(1–6), 1–7 (2000).
[Crossref]

Eberler, M.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179(1–6), 1–7 (2000).
[Crossref]

Foreman, M. R.

M. R. Foreman and P. Török, “Computational methods in vectorial imaging,” J. Mod. Opt. 58(5–6), 339–364 (2011).
[Crossref]

Glöckl, O.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179(1–6), 1–7 (2000).
[Crossref]

Grosjean, T.

T. Grosjean and D. Courjon, “Smallest focal spots,” Opt. Commun. 272(2), 314–319 (2007).
[Crossref]

Gu, M.

C. J. R. Sheppard and M. Gu, “Image formation in two-photon fluorescence microscopy,” Optik (Stuttg.) 86(3), 104–106 (1990).

Hashimoto, N.

Helseth, L. E.

L. E. Helseth, “Roles of polarization, phase and amplitude in solid immersion lens systems,” Opt. Commun. 191(3–6), 161–172 (2001).
[Crossref]

Hibi, T.

S. Ipponjima, T. Hibi, Y. Kozawa, H. Horanai, H. Yokoyama, S. Sato, and T. Nemoto, “Improvement of lateral resolution and extension of depth of field in two-photon microscopy by a higher-order radially polarized beam,” Microscopy (Oxford) 63(1), 23–32 (2014).
[Crossref] [PubMed]

Y. Kozawa, T. Hibi, A. Sato, H. Horanai, M. Kurihara, N. Hashimoto, H. Yokoyama, T. Nemoto, and S. Sato, “Lateral resolution enhancement of laser scanning microscopy by a higher-order radially polarized mode beam,” Opt. Express 19(17), 15947–15954 (2011).
[Crossref] [PubMed]

Higdon, P. D.

P. D. Higdon, P. Török, and T. Wilson, “Imaging properties of high aperture multiphoton fluorescence scanning optical microscopes,” J. Microsc. 193(2), 127–141 (1999).
[Crossref]

P. Török, P. D. Higdon, and T. Wilson, “Theory for confocal and conventional microscopes imaging small dielectric scatterers,” J. Mod. Opt. 45(8), 1681–1698 (1998).
[Crossref]

Horanai, H.

S. Ipponjima, T. Hibi, Y. Kozawa, H. Horanai, H. Yokoyama, S. Sato, and T. Nemoto, “Improvement of lateral resolution and extension of depth of field in two-photon microscopy by a higher-order radially polarized beam,” Microscopy (Oxford) 63(1), 23–32 (2014).
[Crossref] [PubMed]

Y. Kozawa, T. Hibi, A. Sato, H. Horanai, M. Kurihara, N. Hashimoto, H. Yokoyama, T. Nemoto, and S. Sato, “Lateral resolution enhancement of laser scanning microscopy by a higher-order radially polarized mode beam,” Opt. Express 19(17), 15947–15954 (2011).
[Crossref] [PubMed]

Ipponjima, S.

S. Ipponjima, T. Hibi, Y. Kozawa, H. Horanai, H. Yokoyama, S. Sato, and T. Nemoto, “Improvement of lateral resolution and extension of depth of field in two-photon microscopy by a higher-order radially polarized beam,” Microscopy (Oxford) 63(1), 23–32 (2014).
[Crossref] [PubMed]

Kano, H.

Kim, D. C.

J. Kim, D. C. Kim, and S. H. Back, “Demonstration of high lateral resolution in laser confocal microscopy using annular and radially polarized light,” Microsc. Res. Tech. 72(6), 441–446 (2009).
[Crossref] [PubMed]

Kim, J.

J. Kim, D. C. Kim, and S. H. Back, “Demonstration of high lateral resolution in laser confocal microscopy using annular and radially polarized light,” Microsc. Res. Tech. 72(6), 441–446 (2009).
[Crossref] [PubMed]

Kitamura, K.

Kozawa, Y.

Kurihara, M.

Lerman, G. M.

Leuchs, G.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179(1–6), 1–7 (2000).
[Crossref]

Levy, U.

Liu, C.-K.

Lukyanchuk, B.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

McCarthy, N.

G. Thériault, M. Cottet, A. Castonguay, N. McCarthy, and Y. De Koninck, “Extended two-photon microscopy in live samples with Bessel beams: steadier focus, faster volume scans, and simpler stereoscopic imaging,” Front. Cell Neurosci. 8, 139 (2014).
[PubMed]

Mehta, S.

Morigaki, K.

Nemoto, T.

S. Ipponjima, T. Hibi, Y. Kozawa, H. Horanai, H. Yokoyama, S. Sato, and T. Nemoto, “Improvement of lateral resolution and extension of depth of field in two-photon microscopy by a higher-order radially polarized beam,” Microscopy (Oxford) 63(1), 23–32 (2014).
[Crossref] [PubMed]

Y. Kozawa, T. Hibi, A. Sato, H. Horanai, M. Kurihara, N. Hashimoto, H. Yokoyama, T. Nemoto, and S. Sato, “Lateral resolution enhancement of laser scanning microscopy by a higher-order radially polarized mode beam,” Opt. Express 19(17), 15947–15954 (2011).
[Crossref] [PubMed]

Noda, S.

Okazaki, T.

Piché, M.

Quabis, S.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179(1–6), 1–7 (2000).
[Crossref]

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

Ryosuke, M.

Sakai, K.

Sato, A.

Sato, S.

Sheppard, C.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Sheppard, C. J. R.

C. J. R. Sheppard and S. Mehta, “Three-level filter for increased depth of focus and Bessel beam generation,” Opt. Express 20(25), 27212–27221 (2012).
[Crossref] [PubMed]

C. J. R. Sheppard and A. Choudhury, “Annular pupils, radial polarization, and superresolution,” Appl. Opt. 43(22), 4322–4327 (2004).
[Crossref] [PubMed]

C. J. R. Sheppard and P. Török, “An electromagnetic theory of imaging in fluorescence microscopy, and imaging in polarization fluorescence microscopy,” Bioimaging 5(4), 205–218 (1997).
[Crossref]

C. J. R. Sheppard and M. Gu, “Image formation in two-photon fluorescence microscopy,” Optik (Stuttg.) 86(3), 104–106 (1990).

C. J. R. Sheppard and A. Choudhury, “Image formation in the scanning microscope,” Opt. Acta (Lond.) 24(10), 1051–1073 (1977).
[Crossref]

Shi, L.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Sun, C.-C.

Terakado, G.

Thériault, G.

G. Thériault, M. Cottet, A. Castonguay, N. McCarthy, and Y. De Koninck, “Extended two-photon microscopy in live samples with Bessel beams: steadier focus, faster volume scans, and simpler stereoscopic imaging,” Front. Cell Neurosci. 8, 139 (2014).
[PubMed]

Török, P.

M. R. Foreman and P. Török, “Computational methods in vectorial imaging,” J. Mod. Opt. 58(5–6), 339–364 (2011).
[Crossref]

P. D. Higdon, P. Török, and T. Wilson, “Imaging properties of high aperture multiphoton fluorescence scanning optical microscopes,” J. Microsc. 193(2), 127–141 (1999).
[Crossref]

P. Török, P. D. Higdon, and T. Wilson, “Theory for confocal and conventional microscopes imaging small dielectric scatterers,” J. Mod. Opt. 45(8), 1681–1698 (1998).
[Crossref]

C. J. R. Sheppard and P. Török, “An electromagnetic theory of imaging in fluorescence microscopy, and imaging in polarization fluorescence microscopy,” Bioimaging 5(4), 205–218 (1997).
[Crossref]

Tovar, A. A.

Wang, H.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Watanabe, K.

Wilson, T.

P. D. Higdon, P. Török, and T. Wilson, “Imaging properties of high aperture multiphoton fluorescence scanning optical microscopes,” J. Microsc. 193(2), 127–141 (1999).
[Crossref]

P. Török, P. D. Higdon, and T. Wilson, “Theory for confocal and conventional microscopes imaging small dielectric scatterers,” J. Mod. Opt. 45(8), 1681–1698 (1998).
[Crossref]

T. Wilson and A. R. Carlini, “Size of the detector in confocal imaging systems,” Opt. Lett. 12(4), 227–229 (1987).
[Crossref] [PubMed]

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

Yokoyama, H.

S. Ipponjima, T. Hibi, Y. Kozawa, H. Horanai, H. Yokoyama, S. Sato, and T. Nemoto, “Improvement of lateral resolution and extension of depth of field in two-photon microscopy by a higher-order radially polarized beam,” Microscopy (Oxford) 63(1), 23–32 (2014).
[Crossref] [PubMed]

Y. Kozawa, T. Hibi, A. Sato, H. Horanai, M. Kurihara, N. Hashimoto, H. Yokoyama, T. Nemoto, and S. Sato, “Lateral resolution enhancement of laser scanning microscopy by a higher-order radially polarized mode beam,” Opt. Express 19(17), 15947–15954 (2011).
[Crossref] [PubMed]

Youngworth, K. S.

Appl. Opt. (2)

Bioimaging (1)

C. J. R. Sheppard and P. Török, “An electromagnetic theory of imaging in fluorescence microscopy, and imaging in polarization fluorescence microscopy,” Bioimaging 5(4), 205–218 (1997).
[Crossref]

Front. Cell Neurosci. (1)

G. Thériault, M. Cottet, A. Castonguay, N. McCarthy, and Y. De Koninck, “Extended two-photon microscopy in live samples with Bessel beams: steadier focus, faster volume scans, and simpler stereoscopic imaging,” Front. Cell Neurosci. 8, 139 (2014).
[PubMed]

J. Microsc. (1)

P. D. Higdon, P. Török, and T. Wilson, “Imaging properties of high aperture multiphoton fluorescence scanning optical microscopes,” J. Microsc. 193(2), 127–141 (1999).
[Crossref]

J. Mod. Opt. (2)

M. R. Foreman and P. Török, “Computational methods in vectorial imaging,” J. Mod. Opt. 58(5–6), 339–364 (2011).
[Crossref]

P. Török, P. D. Higdon, and T. Wilson, “Theory for confocal and conventional microscopes imaging small dielectric scatterers,” J. Mod. Opt. 45(8), 1681–1698 (1998).
[Crossref]

J. Opt. Soc. Am. A (3)

Microsc. Res. Tech. (1)

J. Kim, D. C. Kim, and S. H. Back, “Demonstration of high lateral resolution in laser confocal microscopy using annular and radially polarized light,” Microsc. Res. Tech. 72(6), 441–446 (2009).
[Crossref] [PubMed]

Microscopy (Oxford) (1)

S. Ipponjima, T. Hibi, Y. Kozawa, H. Horanai, H. Yokoyama, S. Sato, and T. Nemoto, “Improvement of lateral resolution and extension of depth of field in two-photon microscopy by a higher-order radially polarized beam,” Microscopy (Oxford) 63(1), 23–32 (2014).
[Crossref] [PubMed]

Nat. Photonics (1)

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Opt. Acta (Lond.) (1)

C. J. R. Sheppard and A. Choudhury, “Image formation in the scanning microscope,” Opt. Acta (Lond.) 24(10), 1051–1073 (1977).
[Crossref]

Opt. Commun. (3)

T. Grosjean and D. Courjon, “Smallest focal spots,” Opt. Commun. 272(2), 314–319 (2007).
[Crossref]

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[Crossref]

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Figures (6)

Fig. 1
Fig. 1 Simplified model of confocal microscopy using a higher-order RP-LG beam (shown in cross-section at the bottom of the figure).

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Fig. 2
Fig. 2 (a)–(d) Intensity distributions at the pupil (top), focal plane (middle), and xz-plane (bottom) for the focusing of a CP- Gaussian beam and higher-order RP-LGp,1 beams with p = 1, 5, and 10. The pupil diameter of the objective lens is depicted by a dashed circle in each top figure. (e) FWHM values of the focal spot size formed by the total intensity (black filled circles) and the longitudinal component only (blue open squares) for the higher-order RP-LG beams.

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Fig. 3
Fig. 3 Intensity distributions of the lateral PSFconf using an RP-LG5,1 beam without a confocal pinhole (a) and with pinholes of 4 AU (b), 1 AU (c), and 0.5 AU (d). The lateral profiles of PSFconf for several pinhole diameters D are shown in (e).

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Fig. 4
Fig. 4 Lateral (a) and axial (b) sizes of PSFconf using RP-LG5,1 and CP-Gaussian beams as a function of the pinhole diameter.

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Fig. 5
Fig. 5 Lateral optical transfer functions calculated for pinhole diameters of 4.0 AU (a), 1.0 AU (b), 0.5 AU (c), and 0 AU (d).

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Fig. 6
Fig. 6 PSFs corresponding to two-photon excitation microscopy using a CP-Gaussian beam (a) and an RP-LG5,1 beam (b). The lateral profiles of PSFs shown in (a) and (b) as well as the two-photon PSF calculated by scalar theory and the two-photon PSF of a J0-Bessel beam as a limiting case of an RP-beam with an infinitely narrow ring are shown in (c). The lateral OTF profiles obtained by the Fourier transform of (c) are shown in (d). A circular window with a radius of 100λ was considered for the computation of the Fourier transform of the PSF. The inset in (d) displays a magnified view of the OTF profiles in the spatial frequency between 2 NA/λ and 4 NA/λ.

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Equations (1)

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E p,1 (ρ)∝ ρ w 0 exp( − ρ 2 w 0 2 ) L p 1 ( 2 ρ 2 w 0 2 ),

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