Abstract

A two-dimensional coherent imaging equation is derived for confocal self-interference microscopy (CSIM), which uses a birefringent material to generate an interference pattern in the detection optics. This interference pattern, called a self-interference pattern, sharpens the point-spread function (PSF) along the lateral direction. To derive the imaging equation, an equation for the self-interference pattern is derived. Numerical simulation results based on the imaging equation are presented. One-point response results show a 42.8% reduction in the FWHM of the lateral PSF. Two-point response results show a nearly twofold improvement in two-point resolution.

© 2005 Optical Society of America

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References

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  1. C. J. R. Sheppard, D. M. Shotton, Confocal Laser Scanning Microscopy (BIOS Scientific, 1997).
  2. J. B. Pawley, Handbook of Biological Confocal Microscopy (Plenum, 1995).
  3. M. Nishitani-Gamo, T. Ando, K. Yamamoto, K. Watanabe, P. A. Dennig, Y. Sato, M. Sekita, “A nondiamond phase at the interface between oriented diamond and Si observed by confocal Raman spectroscopy,” Appl. Phys. Lett. 70, 1530–1532 (1997).
    [Crossref]
  4. M. Nishitani-Gamo, I. Sakaguchi, K. Ping Loh, H. Kanda, T. Andoa, “Confocal Raman spectroscopic observation of hexagonal diamond formation from dissolved carbon in nickel under chemical vapor deposition conditions,” Appl. Phys. Lett. 73, 765–767 (1998).
    [Crossref]
  5. S. Lee, Micro Nano System Technology R/D Laboratory, Mechatronics Center, Samsung Electronics Co, Ltd., 416, Maetan2-dong, Paldal-gu, Suwon, Gyonggi, Korea, 442–742 (personal communication, 2004).
  6. V. Westphal, C. M. Blanca, M. Dyba, L. Kastrup, S. W. Hell, “Laser-diode-stimulated emission depletion microscopy,” Appl. Phys. Lett. 82, 3125–3127 (2003).
    [Crossref]
  7. S. W. Hell, M. Cyba, S. Jakobs, “Concepts for nanoscale resolution in fluorescence microscopy,” Curr. Opin. Neurobiol. 14, 599–609 (2004).
    [Crossref] [PubMed]
  8. C. Lee, J. Wang, “Noninterferometric differential confocal microscopy with 2-nm depth resolution,” Opt. Commun. 135, 233–237 (1997).
    [Crossref]
  9. C. Lee, H. Chiang, H. Mong, “Sub-diffraction-limit imaging based on the topographic contrast of differential confocal microscopy,” Opt. Lett. 28, 1772–1774 (2003).
    [Crossref] [PubMed]
  10. M. Martinez-Corral, A. Pons, M. Caballero, “Axial apodization in 4Pi-confocal microscopy by annular binary filters,” J. Opt. Soc. Am. A 19, 1532–1536 (2002).
    [Crossref]
  11. M. A. A. Neil, T. Wilson, R. Juskaitis, “A wavefront generator for complex pupil function synthesis and point spread function engineering,” J. Microsc. 197, 219–223 (2000).
    [Crossref] [PubMed]
  12. M. A. A. Neil, R. Juskaitis, T. Wilson, Z. J. Laczik, “Optimized pupil-plane filters for confocal microscope point-spread function engineering,” Opt. Lett. 25, 245–247 (2000).
    [Crossref]
  13. D. Kang, D. Gweon, “Enhancement of lateral resolution in confocal self-interference microscopy,” Opt. Lett. 28, 2470–2472 (2003).
    [Crossref] [PubMed]
  14. M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
    [Crossref]
  15. D. Kang, H. Yoo, S. Lee, D. Gweon, “Lateral resolution enhancement in confocal self-interference microscopy with commercial calcite plate,” J. Opt. Soc. Korea 9, 32–35 (2005).
  16. A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, 2003).
  17. Min Gu, Principles of Three-Dimensional Imaging in Confocal Microscopes (World Scientific, 1996).
  18. T. Wilson, C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).

2004 (1)

S. W. Hell, M. Cyba, S. Jakobs, “Concepts for nanoscale resolution in fluorescence microscopy,” Curr. Opin. Neurobiol. 14, 599–609 (2004).
[Crossref] [PubMed]

2003 (3)

2002 (1)

2000 (2)

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

M. A. A. Neil, R. Juskaitis, T. Wilson, Z. J. Laczik, “Optimized pupil-plane filters for confocal microscope point-spread function engineering,” Opt. Lett. 25, 245–247 (2000).
[Crossref]

1998 (1)

M. Nishitani-Gamo, I. Sakaguchi, K. Ping Loh, H. Kanda, T. Andoa, “Confocal Raman spectroscopic observation of hexagonal diamond formation from dissolved carbon in nickel under chemical vapor deposition conditions,” Appl. Phys. Lett. 73, 765–767 (1998).
[Crossref]

1997 (2)

M. Nishitani-Gamo, T. Ando, K. Yamamoto, K. Watanabe, P. A. Dennig, Y. Sato, M. Sekita, “A nondiamond phase at the interface between oriented diamond and Si observed by confocal Raman spectroscopy,” Appl. Phys. Lett. 70, 1530–1532 (1997).
[Crossref]

C. Lee, J. Wang, “Noninterferometric differential confocal microscopy with 2-nm depth resolution,” Opt. Commun. 135, 233–237 (1997).
[Crossref]

Ando, T.

M. Nishitani-Gamo, T. Ando, K. Yamamoto, K. Watanabe, P. A. Dennig, Y. Sato, M. Sekita, “A nondiamond phase at the interface between oriented diamond and Si observed by confocal Raman spectroscopy,” Appl. Phys. Lett. 70, 1530–1532 (1997).
[Crossref]

Andoa, T.

M. Nishitani-Gamo, I. Sakaguchi, K. Ping Loh, H. Kanda, T. Andoa, “Confocal Raman spectroscopic observation of hexagonal diamond formation from dissolved carbon in nickel under chemical vapor deposition conditions,” Appl. Phys. Lett. 73, 765–767 (1998).
[Crossref]

Blanca, C. M.

V. Westphal, C. M. Blanca, M. Dyba, L. Kastrup, S. W. Hell, “Laser-diode-stimulated emission depletion microscopy,” Appl. Phys. Lett. 82, 3125–3127 (2003).
[Crossref]

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
[Crossref]

Caballero, M.

Chiang, H.

Cyba, M.

S. W. Hell, M. Cyba, S. Jakobs, “Concepts for nanoscale resolution in fluorescence microscopy,” Curr. Opin. Neurobiol. 14, 599–609 (2004).
[Crossref] [PubMed]

Dennig, P. A.

M. Nishitani-Gamo, T. Ando, K. Yamamoto, K. Watanabe, P. A. Dennig, Y. Sato, M. Sekita, “A nondiamond phase at the interface between oriented diamond and Si observed by confocal Raman spectroscopy,” Appl. Phys. Lett. 70, 1530–1532 (1997).
[Crossref]

Dyba, M.

V. Westphal, C. M. Blanca, M. Dyba, L. Kastrup, S. W. Hell, “Laser-diode-stimulated emission depletion microscopy,” Appl. Phys. Lett. 82, 3125–3127 (2003).
[Crossref]

Gu, Min

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

Gweon, D.

D. Kang, D. Gweon, “Enhancement of lateral resolution in confocal self-interference microscopy,” Opt. Lett. 28, 2470–2472 (2003).
[Crossref] [PubMed]

D. Kang, H. Yoo, S. Lee, D. Gweon, “Lateral resolution enhancement in confocal self-interference microscopy with commercial calcite plate,” J. Opt. Soc. Korea 9, 32–35 (2005).

Hell, S. W.

S. W. Hell, M. Cyba, S. Jakobs, “Concepts for nanoscale resolution in fluorescence microscopy,” Curr. Opin. Neurobiol. 14, 599–609 (2004).
[Crossref] [PubMed]

V. Westphal, C. M. Blanca, M. Dyba, L. Kastrup, S. W. Hell, “Laser-diode-stimulated emission depletion microscopy,” Appl. Phys. Lett. 82, 3125–3127 (2003).
[Crossref]

Jakobs, S.

S. W. Hell, M. Cyba, S. Jakobs, “Concepts for nanoscale resolution in fluorescence microscopy,” Curr. Opin. Neurobiol. 14, 599–609 (2004).
[Crossref] [PubMed]

Juskaitis, R.

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

M. A. A. Neil, R. Juskaitis, T. Wilson, Z. J. Laczik, “Optimized pupil-plane filters for confocal microscope point-spread function engineering,” Opt. Lett. 25, 245–247 (2000).
[Crossref]

Kanda, H.

M. Nishitani-Gamo, I. Sakaguchi, K. Ping Loh, H. Kanda, T. Andoa, “Confocal Raman spectroscopic observation of hexagonal diamond formation from dissolved carbon in nickel under chemical vapor deposition conditions,” Appl. Phys. Lett. 73, 765–767 (1998).
[Crossref]

Kang, D.

D. Kang, D. Gweon, “Enhancement of lateral resolution in confocal self-interference microscopy,” Opt. Lett. 28, 2470–2472 (2003).
[Crossref] [PubMed]

D. Kang, H. Yoo, S. Lee, D. Gweon, “Lateral resolution enhancement in confocal self-interference microscopy with commercial calcite plate,” J. Opt. Soc. Korea 9, 32–35 (2005).

Kastrup, L.

V. Westphal, C. M. Blanca, M. Dyba, L. Kastrup, S. W. Hell, “Laser-diode-stimulated emission depletion microscopy,” Appl. Phys. Lett. 82, 3125–3127 (2003).
[Crossref]

Laczik, Z. J.

Lee, C.

C. Lee, H. Chiang, H. Mong, “Sub-diffraction-limit imaging based on the topographic contrast of differential confocal microscopy,” Opt. Lett. 28, 1772–1774 (2003).
[Crossref] [PubMed]

C. Lee, J. Wang, “Noninterferometric differential confocal microscopy with 2-nm depth resolution,” Opt. Commun. 135, 233–237 (1997).
[Crossref]

Lee, S.

S. Lee, Micro Nano System Technology R/D Laboratory, Mechatronics Center, Samsung Electronics Co, Ltd., 416, Maetan2-dong, Paldal-gu, Suwon, Gyonggi, Korea, 442–742 (personal communication, 2004).

D. Kang, H. Yoo, S. Lee, D. Gweon, “Lateral resolution enhancement in confocal self-interference microscopy with commercial calcite plate,” J. Opt. Soc. Korea 9, 32–35 (2005).

Loh, K. Ping

M. Nishitani-Gamo, I. Sakaguchi, K. Ping Loh, H. Kanda, T. Andoa, “Confocal Raman spectroscopic observation of hexagonal diamond formation from dissolved carbon in nickel under chemical vapor deposition conditions,” Appl. Phys. Lett. 73, 765–767 (1998).
[Crossref]

Martinez-Corral, M.

Mong, H.

Neil, M. A. A.

M. A. A. Neil, R. Juskaitis, T. Wilson, Z. J. Laczik, “Optimized pupil-plane filters for confocal microscope point-spread function engineering,” Opt. Lett. 25, 245–247 (2000).
[Crossref]

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

Nishitani-Gamo, M.

M. Nishitani-Gamo, I. Sakaguchi, K. Ping Loh, H. Kanda, T. Andoa, “Confocal Raman spectroscopic observation of hexagonal diamond formation from dissolved carbon in nickel under chemical vapor deposition conditions,” Appl. Phys. Lett. 73, 765–767 (1998).
[Crossref]

M. Nishitani-Gamo, T. Ando, K. Yamamoto, K. Watanabe, P. A. Dennig, Y. Sato, M. Sekita, “A nondiamond phase at the interface between oriented diamond and Si observed by confocal Raman spectroscopy,” Appl. Phys. Lett. 70, 1530–1532 (1997).
[Crossref]

Pawley, J. B.

J. B. Pawley, Handbook of Biological Confocal Microscopy (Plenum, 1995).

Pons, A.

Sakaguchi, I.

M. Nishitani-Gamo, I. Sakaguchi, K. Ping Loh, H. Kanda, T. Andoa, “Confocal Raman spectroscopic observation of hexagonal diamond formation from dissolved carbon in nickel under chemical vapor deposition conditions,” Appl. Phys. Lett. 73, 765–767 (1998).
[Crossref]

Sato, Y.

M. Nishitani-Gamo, T. Ando, K. Yamamoto, K. Watanabe, P. A. Dennig, Y. Sato, M. Sekita, “A nondiamond phase at the interface between oriented diamond and Si observed by confocal Raman spectroscopy,” Appl. Phys. Lett. 70, 1530–1532 (1997).
[Crossref]

Sekita, M.

M. Nishitani-Gamo, T. Ando, K. Yamamoto, K. Watanabe, P. A. Dennig, Y. Sato, M. Sekita, “A nondiamond phase at the interface between oriented diamond and Si observed by confocal Raman spectroscopy,” Appl. Phys. Lett. 70, 1530–1532 (1997).
[Crossref]

Sheppard, C. J. R.

C. J. R. Sheppard, D. M. Shotton, Confocal Laser Scanning Microscopy (BIOS Scientific, 1997).

T. Wilson, C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).

Shotton, D. M.

C. J. R. Sheppard, D. M. Shotton, Confocal Laser Scanning Microscopy (BIOS Scientific, 1997).

Wang, J.

C. Lee, J. Wang, “Noninterferometric differential confocal microscopy with 2-nm depth resolution,” Opt. Commun. 135, 233–237 (1997).
[Crossref]

Watanabe, K.

M. Nishitani-Gamo, T. Ando, K. Yamamoto, K. Watanabe, P. A. Dennig, Y. Sato, M. Sekita, “A nondiamond phase at the interface between oriented diamond and Si observed by confocal Raman spectroscopy,” Appl. Phys. Lett. 70, 1530–1532 (1997).
[Crossref]

Westphal, V.

V. Westphal, C. M. Blanca, M. Dyba, L. Kastrup, S. W. Hell, “Laser-diode-stimulated emission depletion microscopy,” Appl. Phys. Lett. 82, 3125–3127 (2003).
[Crossref]

Wilson, T.

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

M. A. A. Neil, R. Juskaitis, T. Wilson, Z. J. Laczik, “Optimized pupil-plane filters for confocal microscope point-spread function engineering,” Opt. Lett. 25, 245–247 (2000).
[Crossref]

T. Wilson, C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
[Crossref]

Yamamoto, K.

M. Nishitani-Gamo, T. Ando, K. Yamamoto, K. Watanabe, P. A. Dennig, Y. Sato, M. Sekita, “A nondiamond phase at the interface between oriented diamond and Si observed by confocal Raman spectroscopy,” Appl. Phys. Lett. 70, 1530–1532 (1997).
[Crossref]

Yariv, A.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, 2003).

Yeh, P.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, 2003).

Yoo, H.

D. Kang, H. Yoo, S. Lee, D. Gweon, “Lateral resolution enhancement in confocal self-interference microscopy with commercial calcite plate,” J. Opt. Soc. Korea 9, 32–35 (2005).

Appl. Phys. Lett. (3)

M. Nishitani-Gamo, T. Ando, K. Yamamoto, K. Watanabe, P. A. Dennig, Y. Sato, M. Sekita, “A nondiamond phase at the interface between oriented diamond and Si observed by confocal Raman spectroscopy,” Appl. Phys. Lett. 70, 1530–1532 (1997).
[Crossref]

M. Nishitani-Gamo, I. Sakaguchi, K. Ping Loh, H. Kanda, T. Andoa, “Confocal Raman spectroscopic observation of hexagonal diamond formation from dissolved carbon in nickel under chemical vapor deposition conditions,” Appl. Phys. Lett. 73, 765–767 (1998).
[Crossref]

V. Westphal, C. M. Blanca, M. Dyba, L. Kastrup, S. W. Hell, “Laser-diode-stimulated emission depletion microscopy,” Appl. Phys. Lett. 82, 3125–3127 (2003).
[Crossref]

Curr. Opin. Neurobiol. (1)

S. W. Hell, M. Cyba, S. Jakobs, “Concepts for nanoscale resolution in fluorescence microscopy,” Curr. Opin. Neurobiol. 14, 599–609 (2004).
[Crossref] [PubMed]

J. Microsc. (1)

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

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

Opt. Commun. (1)

C. Lee, J. Wang, “Noninterferometric differential confocal microscopy with 2-nm depth resolution,” Opt. Commun. 135, 233–237 (1997).
[Crossref]

Opt. Lett. (3)

Other (8)

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
[Crossref]

D. Kang, H. Yoo, S. Lee, D. Gweon, “Lateral resolution enhancement in confocal self-interference microscopy with commercial calcite plate,” J. Opt. Soc. Korea 9, 32–35 (2005).

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, 2003).

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

T. Wilson, C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).

S. Lee, Micro Nano System Technology R/D Laboratory, Mechatronics Center, Samsung Electronics Co, Ltd., 416, Maetan2-dong, Paldal-gu, Suwon, Gyonggi, Korea, 442–742 (personal communication, 2004).

C. J. R. Sheppard, D. M. Shotton, Confocal Laser Scanning Microscopy (BIOS Scientific, 1997).

J. B. Pawley, Handbook of Biological Confocal Microscopy (Plenum, 1995).

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Figures (16)

Fig. 1
Fig. 1

Schematic diagram of CSIM.

Fig. 2
Fig. 2

Beam paths through the self-interference optics.

Fig. 3
Fig. 3

Phase difference as a function of the incidence angle.

Fig. 4
Fig. 4

Sensitivity of phase difference as a function of incidence angle.

Fig. 5
Fig. 5

Intensities of e and o rays after the calcite plate: solid curve, e ray; dashed curve, o ray.

Fig. 6
Fig. 6

Visibility of self-interference pattern.

Fig. 7
Fig. 7

Self-interference pattern.

Fig. 8
Fig. 8

Schematic diagram of the simplified version of CSIM.

Fig. 9
Fig. 9

One-point responses for various values of c si .

Fig. 10
Fig. 10

Summary of one-point response simulation results: (a) FWHM of the central lobe, (b) height of the first sidelobe.

Fig. 11
Fig. 11

Two-point responses when two points are separated by 1.2.

Fig. 12
Fig. 12

Summary of two-point response simulation results when two points are separated by 1.2: (a) center intensity graph, (b) sidelobe height graph.

Fig. 13
Fig. 13

Two-point responses when two points are separated by 2.0.

Fig. 14
Fig. 14

Summary of two-point response simulation results when two points are separated by 2.0: (a) center intensity graph, (b) sidelobe height graph.

Fig. 15
Fig. 15

Two-point responses for various two-point distances when c si is 0.5 π .

Fig. 16
Fig. 16

Summary of two-point response simulation results for various two-point distances when c si is 0.5 π : (a) center intensity graph, (b) sidelobe height graph.

Equations (24)

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ϕ si = 2 π λ [ ( n o cos θ o n e ( θ inc ) cos θ e ) + ( tan θ e tan θ o ) sin θ inc ] ,
1 n e 2 ( θ e , oa ) = cos 2 θ e , oa n o 2 + sin 2 θ e , oa n e 2 ,
sin θ inc n e ( θ e , oa ) = sin θ e = sin θ e , oa cos θ oa cos θ e , oa sin θ oa .
sin 2 θ e , oa ( cos 2 θ oa sin 2 θ inc n e 2 ) 2 sin θ e , oa cos θ e , oa sin θ oa cos θ oa + cos 2 θ e , oa ( sin 2 θ oa sin 2 θ inc n o 2 ) = 0 .
cos 2 θ e , oa [ cos 2 θ oa + sin 2 θ inc ( 1 n o 2 1 n e 2 ) ] + sin 2 θ e , oa sin 2 θ oa = 1 sin 2 θ inc ( 1 n e 2 + 1 n o 2 ) .
k sin ( 2 θ e , oa + φ ) = C ,
θ e , oa = 1 2 [ sin 1 ( C k ) φ ] .
I si = I e + I o + 2 I e I o cos ϕ si ,
V = 2 I e I o I e + I o .
E si = E 0 cos ( k r ω t ) + E 0 cos ( k r ω t + ϕ si ) ,
E si = E 0 T si ( ϕ si ) cos [ k r ω t + ψ si ( ϕ si ) ] ,
T si ( ϕ si ) = 2 cos ϕ si 2 ,
ψ si ( ϕ si ) = ϕ si 2 .
ϕ si = c cal θ inc .
T si ( x 1 ) = 2 cos ( c cal M to x 1 2 f ol ) ,
ψ si ( x 1 ) = c cal M to x 1 2 f ol .
U 1 ( r 1 , r s ) = [ δ ( r 0 ) h 1 ( r 0 + M 1 r 1 ) d r 0 ] o ( r s r 1 ) ,
U 1 ( r 1 , r s ) = [ δ ( r 0 ) h 1 ( r 0 + M 1 r 1 ) d r 0 ] T si ( x 1 ) exp [ i ψ si ( x 1 ) ] o ( r s r 1 ) .
U 2 ( r 2 , r s ) = [ δ ( r 0 ) h 1 ( r 0 + M 1 r 1 ) d r 0 ] T si ( x 1 ) exp [ i ψ si ( x 1 ) ] o ( r s r 1 ) h 2 ( r 1 + M 2 r 2 ) d r 1 ,
U 2 ( r 2 , r s ) = h csim ( r s ) 2 o ( r s ) ,
h csim ( r ) = h 1 ( M 1 r ) T si ( x ) exp [ i ψ si ( x ) ] h 2 ( r + M 2 r 2 ) .
I ( r s ) = U 2 ( r 2 , r s ) 2 D ( r 2 ) d r 2 ,
ϕ si = c cal M to x 1 f ol = c cal M to λ π f ol d ol 1 f ol v x = c cal M to λ π d ol v x = c si v x ,
h a ( v ) = [ J 1 ( v ) v ] { J 1 [ ( v x v 2 x ) 2 + ( v y v 2 y ) 2 ] ( v x v 2 x ) 2 + ( v y v 2 y ) 2 } cos ( c si v x 2 ) exp ( i c si v x 2 ) ,

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