Abstract

The three-dimensional (3-D) coherent transfer function for reflection confocal microscopy of high-numerical-aperture objectives is derived and calculated in the presence of refractive-index mismatch when a laser beam is focused into a medium of refractive index different from its immersion medium. This aberrated coherent transfer function is then used to estimate the readout efficiency of 3-D data bits recorded in a thick medium. It is shown that the readout efficiency of confocal microscopy for 3-D bit data storage is decreased with the focal depth of an objective in a recording medium. However, a high readout efficiency can be maintained if the tube length of a reading objective is linearly altered to compensate for the spherical aberration caused by the refractive-index mismatch.

© 2001 Optical Society of America

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References

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    [CrossRef] [PubMed]
  2. A. Toriumi, S. Kawata, M. Gu, “Reflection confocal microscope readout system in three-dimensional photochromic optical data storage,” Opt. Lett. 23, 1924–1926 (1998).
    [CrossRef]
  3. D. Day, M. Gu, A. Smallridge, “Use of two-photon excitation for erasable/rewritable three-dimensional bit optical data storage in a photorefractive polymer,” Opt. Lett. 24, 948–950 (1999).
    [CrossRef]
  4. Y. Kawata, H. Ishitobi, S. Kawata, “Use of two-photon absorption in a photorefractive crystal for three-dimensional optical memory,” Opt. Lett. 23, 756–758 (1998).
    [CrossRef]
  5. P. Cheng, J. Bhawalkar, S. Pan, J. Wiatakiewicz, J. Samarabandu, W. Liou, G. He, G. Ruland, N. Kumar, P. Prasad, “Two-photon generated three-dimensional photon bleached patterns in polymer matrix,” Scanning 18, 129–131 (1996).
  6. E. N. Glezer, E. Mazur, “Ultrafast-driven micro-explosions in transparent materials,” Appl. Phys. Lett. 71, 882–884 (1997).
    [CrossRef]
  7. D. Day, M. Gu, “Effects of refractive-index mismatch on three-dimensional optical data storage density in a two-photon bleaching polymer,” Appl. Opt. 37, 6299–6304 (1998).
    [CrossRef]
  8. D. Ganic, X. Gan, M. Gu, “Reduced effect of spherical aberration under two-photon excitation,” Appl. Opt. 39, 3943–3945 (2000).
    [CrossRef]
  9. M. Watanabe, S. Juodkazis, H. Sun, S. Matsuo, H. Misawa, “Two-photon readout in three-dimensional memory in silica,” Appl. Phys. Lett. 77, 13–15 (2000).
    [CrossRef]
  10. M. Gu, “Conditions for confocal readout of three-dimensional photorefractive data bits,” in Photorefractive Optics: Materials, Properties and Applications, F. T. S. Yu, ed. (Academic, London, 2000), pp. 307–331.
  11. C. J. R. Sheppard, “Scanning optical microscopy,” in Optical and Electronic Microscopy (Academic, London, 1987), pp. 1–98.
  12. M. Gu, Principles of Three-Dimensional Imaging in Confocal Microscopes (World Scientific, Singapore, 1996).
  13. P. Török, P. Verga, Z. Laczik, G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: an integral representation,” J. Opt. Soc. Am. A 12, 325–332 (1995).
    [CrossRef]
  14. P. Török, “Focusing of electromagnetic waves through dielectric interfaces—theory and correction of aberration,” Opt. Mem. Neural Networks 8, 9–24 (1999).
  15. C. J. R. Sheppard, P. Török, “Effects of specimen refractive index on confocal imaging,” J. Microsc. 185, 366–374 (1997).
    [CrossRef]
  16. B. Richard, E. Wolf, “Electromagnetic diffraction in optical systems II: structure of the image field in an aplanatic system,” Proc. R. Soc. London, Ser. A 253, 358–379 (1959).
    [CrossRef]
  17. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1980).
  18. M. Gu, Advanced Optical Imaging Theory (Springer–Verlag, Heidelberg, 1999).
  19. C. J. R. Sheppard, M. Gu, Y. Kawata, S. Kawata, “Three-dimensional transfer functions for high-aperture systems,” J. Opt. Soc. Am. A 11, 593–598 (1994).
    [CrossRef]
  20. M. Gu, C. J. R. Sheppard, “Effects of defocus and primary spherical aberration on three-dimensional coherent transfer functions in confocal microscopes,” Appl. Opt. 31, 2541–2549 (1992).
    [CrossRef] [PubMed]
  21. M. Neil, T. Wilson, R. Juškaitis, “A wavefront generator for complex pupil function synthesis and point spread function engineering,” J. Microsc. 197, 219–223 (2000).
    [CrossRef] [PubMed]
  22. C. J. R. Sheppard, M. Gu, “Imaging by a high aperture optical system,” J. Mod. Opt. 40, 1631–1651 (1993).
    [CrossRef]
  23. M. Ishikawa, Y. Kawata, C. Egami, O. Sugihara, N. Okamota, M. Tsuchimori, O. Watanabe, “Reflection-type confocal readout for multilayered optical memory,” Opt. Lett. 23, 1781–1783 (1998).
    [CrossRef]

2000

D. Ganic, X. Gan, M. Gu, “Reduced effect of spherical aberration under two-photon excitation,” Appl. Opt. 39, 3943–3945 (2000).
[CrossRef]

M. Watanabe, S. Juodkazis, H. Sun, S. Matsuo, H. Misawa, “Two-photon readout in three-dimensional memory in silica,” Appl. Phys. Lett. 77, 13–15 (2000).
[CrossRef]

M. Neil, T. Wilson, R. Juškaitis, “A wavefront generator for complex pupil function synthesis and point spread function engineering,” J. Microsc. 197, 219–223 (2000).
[CrossRef] [PubMed]

1999

P. Török, “Focusing of electromagnetic waves through dielectric interfaces—theory and correction of aberration,” Opt. Mem. Neural Networks 8, 9–24 (1999).

D. Day, M. Gu, A. Smallridge, “Use of two-photon excitation for erasable/rewritable three-dimensional bit optical data storage in a photorefractive polymer,” Opt. Lett. 24, 948–950 (1999).
[CrossRef]

1998

1997

C. J. R. Sheppard, P. Török, “Effects of specimen refractive index on confocal imaging,” J. Microsc. 185, 366–374 (1997).
[CrossRef]

E. N. Glezer, E. Mazur, “Ultrafast-driven micro-explosions in transparent materials,” Appl. Phys. Lett. 71, 882–884 (1997).
[CrossRef]

1996

P. Cheng, J. Bhawalkar, S. Pan, J. Wiatakiewicz, J. Samarabandu, W. Liou, G. He, G. Ruland, N. Kumar, P. Prasad, “Two-photon generated three-dimensional photon bleached patterns in polymer matrix,” Scanning 18, 129–131 (1996).

1995

1994

1993

C. J. R. Sheppard, M. Gu, “Imaging by a high aperture optical system,” J. Mod. Opt. 40, 1631–1651 (1993).
[CrossRef]

1992

1991

1959

B. Richard, E. Wolf, “Electromagnetic diffraction in optical systems II: structure of the image field in an aplanatic system,” Proc. R. Soc. London, Ser. A 253, 358–379 (1959).
[CrossRef]

Bhawalkar, J.

P. Cheng, J. Bhawalkar, S. Pan, J. Wiatakiewicz, J. Samarabandu, W. Liou, G. He, G. Ruland, N. Kumar, P. Prasad, “Two-photon generated three-dimensional photon bleached patterns in polymer matrix,” Scanning 18, 129–131 (1996).

Booker, G. R.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1980).

Cheng, P.

P. Cheng, J. Bhawalkar, S. Pan, J. Wiatakiewicz, J. Samarabandu, W. Liou, G. He, G. Ruland, N. Kumar, P. Prasad, “Two-photon generated three-dimensional photon bleached patterns in polymer matrix,” Scanning 18, 129–131 (1996).

Day, D.

Egami, C.

Gan, X.

D. Ganic, X. Gan, M. Gu, “Reduced effect of spherical aberration under two-photon excitation,” Appl. Opt. 39, 3943–3945 (2000).
[CrossRef]

Ganic, D.

D. Ganic, X. Gan, M. Gu, “Reduced effect of spherical aberration under two-photon excitation,” Appl. Opt. 39, 3943–3945 (2000).
[CrossRef]

Glezer, E. N.

E. N. Glezer, E. Mazur, “Ultrafast-driven micro-explosions in transparent materials,” Appl. Phys. Lett. 71, 882–884 (1997).
[CrossRef]

Gu, M.

D. Ganic, X. Gan, M. Gu, “Reduced effect of spherical aberration under two-photon excitation,” Appl. Opt. 39, 3943–3945 (2000).
[CrossRef]

D. Day, M. Gu, A. Smallridge, “Use of two-photon excitation for erasable/rewritable three-dimensional bit optical data storage in a photorefractive polymer,” Opt. Lett. 24, 948–950 (1999).
[CrossRef]

A. Toriumi, S. Kawata, M. Gu, “Reflection confocal microscope readout system in three-dimensional photochromic optical data storage,” Opt. Lett. 23, 1924–1926 (1998).
[CrossRef]

D. Day, M. Gu, “Effects of refractive-index mismatch on three-dimensional optical data storage density in a two-photon bleaching polymer,” Appl. Opt. 37, 6299–6304 (1998).
[CrossRef]

C. J. R. Sheppard, M. Gu, Y. Kawata, S. Kawata, “Three-dimensional transfer functions for high-aperture systems,” J. Opt. Soc. Am. A 11, 593–598 (1994).
[CrossRef]

C. J. R. Sheppard, M. Gu, “Imaging by a high aperture optical system,” J. Mod. Opt. 40, 1631–1651 (1993).
[CrossRef]

M. Gu, C. J. R. Sheppard, “Effects of defocus and primary spherical aberration on three-dimensional coherent transfer functions in confocal microscopes,” Appl. Opt. 31, 2541–2549 (1992).
[CrossRef] [PubMed]

M. Gu, Advanced Optical Imaging Theory (Springer–Verlag, Heidelberg, 1999).

M. Gu, Principles of Three-Dimensional Imaging in Confocal Microscopes (World Scientific, Singapore, 1996).

M. Gu, “Conditions for confocal readout of three-dimensional photorefractive data bits,” in Photorefractive Optics: Materials, Properties and Applications, F. T. S. Yu, ed. (Academic, London, 2000), pp. 307–331.

He, G.

P. Cheng, J. Bhawalkar, S. Pan, J. Wiatakiewicz, J. Samarabandu, W. Liou, G. He, G. Ruland, N. Kumar, P. Prasad, “Two-photon generated three-dimensional photon bleached patterns in polymer matrix,” Scanning 18, 129–131 (1996).

Ishikawa, M.

Ishitobi, H.

Juodkazis, S.

M. Watanabe, S. Juodkazis, H. Sun, S. Matsuo, H. Misawa, “Two-photon readout in three-dimensional memory in silica,” Appl. Phys. Lett. 77, 13–15 (2000).
[CrossRef]

Juškaitis, R.

M. Neil, T. Wilson, R. Juškaitis, “A wavefront generator for complex pupil function synthesis and point spread function engineering,” J. Microsc. 197, 219–223 (2000).
[CrossRef] [PubMed]

Kawata, S.

Kawata, Y.

Kumar, N.

P. Cheng, J. Bhawalkar, S. Pan, J. Wiatakiewicz, J. Samarabandu, W. Liou, G. He, G. Ruland, N. Kumar, P. Prasad, “Two-photon generated three-dimensional photon bleached patterns in polymer matrix,” Scanning 18, 129–131 (1996).

Laczik, Z.

Liou, W.

P. Cheng, J. Bhawalkar, S. Pan, J. Wiatakiewicz, J. Samarabandu, W. Liou, G. He, G. Ruland, N. Kumar, P. Prasad, “Two-photon generated three-dimensional photon bleached patterns in polymer matrix,” Scanning 18, 129–131 (1996).

Matsuo, S.

M. Watanabe, S. Juodkazis, H. Sun, S. Matsuo, H. Misawa, “Two-photon readout in three-dimensional memory in silica,” Appl. Phys. Lett. 77, 13–15 (2000).
[CrossRef]

Mazur, E.

E. N. Glezer, E. Mazur, “Ultrafast-driven micro-explosions in transparent materials,” Appl. Phys. Lett. 71, 882–884 (1997).
[CrossRef]

Misawa, H.

M. Watanabe, S. Juodkazis, H. Sun, S. Matsuo, H. Misawa, “Two-photon readout in three-dimensional memory in silica,” Appl. Phys. Lett. 77, 13–15 (2000).
[CrossRef]

Neil, M.

M. Neil, T. Wilson, R. Juškaitis, “A wavefront generator for complex pupil function synthesis and point spread function engineering,” J. Microsc. 197, 219–223 (2000).
[CrossRef] [PubMed]

Okamota, N.

Pan, S.

P. Cheng, J. Bhawalkar, S. Pan, J. Wiatakiewicz, J. Samarabandu, W. Liou, G. He, G. Ruland, N. Kumar, P. Prasad, “Two-photon generated three-dimensional photon bleached patterns in polymer matrix,” Scanning 18, 129–131 (1996).

Prasad, P.

P. Cheng, J. Bhawalkar, S. Pan, J. Wiatakiewicz, J. Samarabandu, W. Liou, G. He, G. Ruland, N. Kumar, P. Prasad, “Two-photon generated three-dimensional photon bleached patterns in polymer matrix,” Scanning 18, 129–131 (1996).

Richard, B.

B. Richard, E. Wolf, “Electromagnetic diffraction in optical systems II: structure of the image field in an aplanatic system,” Proc. R. Soc. London, Ser. A 253, 358–379 (1959).
[CrossRef]

Ruland, G.

P. Cheng, J. Bhawalkar, S. Pan, J. Wiatakiewicz, J. Samarabandu, W. Liou, G. He, G. Ruland, N. Kumar, P. Prasad, “Two-photon generated three-dimensional photon bleached patterns in polymer matrix,” Scanning 18, 129–131 (1996).

Samarabandu, J.

P. Cheng, J. Bhawalkar, S. Pan, J. Wiatakiewicz, J. Samarabandu, W. Liou, G. He, G. Ruland, N. Kumar, P. Prasad, “Two-photon generated three-dimensional photon bleached patterns in polymer matrix,” Scanning 18, 129–131 (1996).

Sheppard, C. J. R.

C. J. R. Sheppard, P. Török, “Effects of specimen refractive index on confocal imaging,” J. Microsc. 185, 366–374 (1997).
[CrossRef]

C. J. R. Sheppard, M. Gu, Y. Kawata, S. Kawata, “Three-dimensional transfer functions for high-aperture systems,” J. Opt. Soc. Am. A 11, 593–598 (1994).
[CrossRef]

C. J. R. Sheppard, M. Gu, “Imaging by a high aperture optical system,” J. Mod. Opt. 40, 1631–1651 (1993).
[CrossRef]

M. Gu, C. J. R. Sheppard, “Effects of defocus and primary spherical aberration on three-dimensional coherent transfer functions in confocal microscopes,” Appl. Opt. 31, 2541–2549 (1992).
[CrossRef] [PubMed]

C. J. R. Sheppard, “Scanning optical microscopy,” in Optical and Electronic Microscopy (Academic, London, 1987), pp. 1–98.

Smallridge, A.

Strickler, H.

Sugihara, O.

Sun, H.

M. Watanabe, S. Juodkazis, H. Sun, S. Matsuo, H. Misawa, “Two-photon readout in three-dimensional memory in silica,” Appl. Phys. Lett. 77, 13–15 (2000).
[CrossRef]

Toriumi, A.

Török, P.

P. Török, “Focusing of electromagnetic waves through dielectric interfaces—theory and correction of aberration,” Opt. Mem. Neural Networks 8, 9–24 (1999).

C. J. R. Sheppard, P. Török, “Effects of specimen refractive index on confocal imaging,” J. Microsc. 185, 366–374 (1997).
[CrossRef]

P. Török, P. Verga, Z. Laczik, G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: an integral representation,” J. Opt. Soc. Am. A 12, 325–332 (1995).
[CrossRef]

Tsuchimori, M.

Verga, P.

Watanabe, M.

M. Watanabe, S. Juodkazis, H. Sun, S. Matsuo, H. Misawa, “Two-photon readout in three-dimensional memory in silica,” Appl. Phys. Lett. 77, 13–15 (2000).
[CrossRef]

Watanabe, O.

Webb, W. W.

Wiatakiewicz, J.

P. Cheng, J. Bhawalkar, S. Pan, J. Wiatakiewicz, J. Samarabandu, W. Liou, G. He, G. Ruland, N. Kumar, P. Prasad, “Two-photon generated three-dimensional photon bleached patterns in polymer matrix,” Scanning 18, 129–131 (1996).

Wilson, T.

M. Neil, T. Wilson, R. Juškaitis, “A wavefront generator for complex pupil function synthesis and point spread function engineering,” J. Microsc. 197, 219–223 (2000).
[CrossRef] [PubMed]

Wolf, E.

B. Richard, E. Wolf, “Electromagnetic diffraction in optical systems II: structure of the image field in an aplanatic system,” Proc. R. Soc. London, Ser. A 253, 358–379 (1959).
[CrossRef]

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1980).

Appl. Opt.

Appl. Phys. Lett.

M. Watanabe, S. Juodkazis, H. Sun, S. Matsuo, H. Misawa, “Two-photon readout in three-dimensional memory in silica,” Appl. Phys. Lett. 77, 13–15 (2000).
[CrossRef]

E. N. Glezer, E. Mazur, “Ultrafast-driven micro-explosions in transparent materials,” Appl. Phys. Lett. 71, 882–884 (1997).
[CrossRef]

J. Microsc.

C. J. R. Sheppard, P. Török, “Effects of specimen refractive index on confocal imaging,” J. Microsc. 185, 366–374 (1997).
[CrossRef]

M. Neil, T. Wilson, R. Juškaitis, “A wavefront generator for complex pupil function synthesis and point spread function engineering,” J. Microsc. 197, 219–223 (2000).
[CrossRef] [PubMed]

J. Mod. Opt.

C. J. R. Sheppard, M. Gu, “Imaging by a high aperture optical system,” J. Mod. Opt. 40, 1631–1651 (1993).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Lett.

Opt. Mem. Neural Networks

P. Török, “Focusing of electromagnetic waves through dielectric interfaces—theory and correction of aberration,” Opt. Mem. Neural Networks 8, 9–24 (1999).

Proc. R. Soc. London, Ser. A

B. Richard, E. Wolf, “Electromagnetic diffraction in optical systems II: structure of the image field in an aplanatic system,” Proc. R. Soc. London, Ser. A 253, 358–379 (1959).
[CrossRef]

Scanning

P. Cheng, J. Bhawalkar, S. Pan, J. Wiatakiewicz, J. Samarabandu, W. Liou, G. He, G. Ruland, N. Kumar, P. Prasad, “Two-photon generated three-dimensional photon bleached patterns in polymer matrix,” Scanning 18, 129–131 (1996).

Other

M. Gu, “Conditions for confocal readout of three-dimensional photorefractive data bits,” in Photorefractive Optics: Materials, Properties and Applications, F. T. S. Yu, ed. (Academic, London, 2000), pp. 307–331.

C. J. R. Sheppard, “Scanning optical microscopy,” in Optical and Electronic Microscopy (Academic, London, 1987), pp. 1–98.

M. Gu, Principles of Three-Dimensional Imaging in Confocal Microscopes (World Scientific, Singapore, 1996).

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1980).

M. Gu, Advanced Optical Imaging Theory (Springer–Verlag, Heidelberg, 1999).

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Figures (6)

Fig. 1
Fig. 1

Dependence of the modulus of the 3-D coherent transfer function on the focal depth d when a plane wave at wavelength 800 nm is focused by an objective (NA=0.85) from air (n1=1) to a medium of refractive index 1.59: (a) d=0, (b) d=50 μm, (c) d=100 μm, (d) d=200 μm.

Fig. 2
Fig. 2

Dependence of the modulus of the 3-D coherent transfer function on the focal depth d when a plane wave at wavelength 800 nm is focused by an objective (NA=1.4) from immersion (n1=1.518) to a medium of refractive index 1.59: (a) d=0, (b) d=50 μm, (c) d=100 μm, (d) d=200 μm.

Fig. 3
Fig. 3

Dependence of the modulus of the 3-D coherent transfer function on the focal depth d when a plane wave at wavelength 800 nm is focused by an objective (NA=0.85) from air (n1=1) to a medium of refractive index 1.59 under the compensation condition of B=-1.5kd: (a) d=50, (b) d=100 μm, (c) d=200 μm, (d) d=400 μm.

Fig. 4
Fig. 4

Dependence of the modulus of the 2-D coherent transfer function for a dry objective of numerical aperture 0.85 on the focal depth (d=0, 20, 50, and 100 μm).

Fig. 5
Fig. 5

Dependence of the modulus of the 2-D coherent transfer function for an oil objective of numerical aperture 1.4 on the focal depth (d=0, 20, 50, and 100 μm).

Fig. 6
Fig. 6

Readout efficiency η of reflection confocal microscopy in 3-D data storage as a function of the focal depth d. The curve for NA=1.4 (compensated) is similar to that for NA=0.85 (compensated).

Equations (23)

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

h(r, z)=A0aP(θ1)(τs+τpcos θ2)J0(krn1sin θ1)×exp(iΦ+ikzn2cos θ2)sin θ1dθ1,
Φ=-kd(n1cos θ1-n2cos θ2),
c(l, s)=P(l)δ [s-(1-l2)1/2](1-l2)1/2,
P(l)=P(θ1) (τs+τpcos θ2)exp(iΦ)cos θ2cos θ1,
l=sin θ2.
cr(l, s)=4π(l2+s2)1/20π/2P(θ2+)P(θ2-)dβ,2(l sin α+|s| cos α)l2+s24π/2-β0π/2P(θ2+)P(θ2-)dβ,l2+s22(l sin θ+|s| cos α), |s| 2 cos α0,otherwise.
β0=sin-1|s|(l2+s2)1/22l1-l+s241/21-2 cos α|s|,
cos θ2±=|s|21cos β 2l|s|(l2+s2)1/21-l2+s241/2.
α=sin-1NAn2,
cr(l=0, s)=2 cos2 θ2|s| cos θ1 (τs+τpcos θ2)2exp(2iΦ),
Φ1=B sin4(θ1/2).
B-1.5kd.
l(x, y, z)=-c(m, n, s)O(m, n, s)×exp[i2π(mx+ny+sz)]dmdnds2,
I(x, y, z)-|c(m, n, s)O(m, n, s)|2dmdnds.
I(x, y, z)M-|c(m, n, s)|2dmdnds.
η(d)(1-0.35)exp(-d/30)+0.18,d>20 μm,
η(d)(1-0.35)exp(-d/39)+0.29,d>20 μm,
C(l, s)=4π(l2+s2)1/20β0P(θ2+)P*(θ2-)dβ,l2+s22(l sin α-|s| cos α)0,otherwise,
 β0=cos-1|s|(l2+s2)1/22l1-l2+s241/22 cos α|s|+1,
cos θ2±=|s|2cos β 2l|s|(l2+s2)1/21-l2+s241.
Φ=-k(L-d)(n1cos θ1-n2cos θ2).
c(l, s)=4π(l2+s2)1/20β0P(θ2+)P(θ2-)dβ,l2+s22(l sin α-|s| cos α)0,otherwise,
P(θ2)=P(θ1) (τs+τpcos θ2)exp(iΦ)cos θ2cos θ1.

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