Abstract

A general model of a subsurface microscopy system based on an aplanatic solid immersion lens (ASIL) is presented. This model is composed of three components: generation of incident light into the ASIL, interaction of the incident light with the sample, and imaging of the scattered light. Interaction of incident light with sample can be calculated numerically using electromagnetic scattering theory, while vector diffraction theory is used to treat the other two components. Examples of imaging small and extended scatterers are shown. For small scatterers, we show the differences between the actual resolution of the whole system and the resolution predicted by considering only one subsystem of the whole system. For extended scatterers, two types of illuminations—focusing light illumination and plane wave direct illumination—are used to image the scatterers, and observations are explained using interaction of the incident light with the sample.

© 2012 Optical Society of America

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2012 (2)

2011 (4)

2010 (1)

2009 (2)

F. H. Köklü, S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, “Subsurface microscopy of integrated circuits with angular spectrum and polarization control,” Opt. Lett. 34, 1261–1263 (2009).
[CrossRef]

S. H. Goh and C. J. R. Sheppard, “High aperture focusing through a spherical interface: application to refractive solid immersion lens (RSIL) for subsurface imaging,” Opt. Commun. 282, 1036–1041 (2009).
[CrossRef]

2008 (5)

2007 (3)

2006 (4)

2005 (3)

S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, “Theoretical analysis of numerical aperture increasing lens microscopy,” J. Appl. Phys. 97, 053105 (2005).
[CrossRef]

T. Chen, T. Milster, D. Nam, and S. H. Yang, “Experimental investigation of solid immersion lens lithography,” Proc. SPIE 5754, 254–261 (2005).

D. Nam, T. D. Milster, and T. Chen, “Potential of solid immersion lithography using I-line and KrF light source,” Proc. SPIE 5754, 1049–1055 (2005).

2004 (3)

T. Milster, T. Chen, D. Nam, and E. Schlesinger, “Maskless lithography with solid immersion lens nano probes,” Proc. SPIE 5567, 545–556 (2004).
[CrossRef]

A. Abubakar and P. M. van den Berg, “Iterative forward and inverse algorithms based on domain integral equations for three-dimensional electric and magnetic objects,” J. Comput. Phys. 195, 236–262 (2004).
[CrossRef]

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

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, “The focus of light-linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt. 50, 1917–1926 (2003).

2001 (4)

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

S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, “High spatial resolution subsurface microscopy,” Appl. Phys. Lett. 78, 4071–4073 (2001).
[CrossRef]

D. A. Fletcher, K. B. Crozier, K. W. Guarini, S. C. Minne, G. S. Kino, C. F. Quate, and K. E. Goodson, “Microfabricated silicon solid immersion lens,” J. Microelectromech. Syst. 10, 450–459 (2001).
[CrossRef]

T. D. Milster, “Near-field optical data storage: avenues for improved performance,” Opt. Eng. 40, 2255–2260 (2001).
[CrossRef]

2000 (3)

Q. Wu, L. P. Ghislain, and V. B. Elings, “Imaging with solid immersion lenses, spatial resolution, and applications,” Proc. IEEE 88, 1491–1498 (2000).
[CrossRef]

D. A. Fletcher, K. B. Crozier, C. F. Quate, G. S. Kino, K. E. Goodson, D. Simanovskii, and D. V. Palanker, “Near-field infrared imaging with a microfabricated solid immersion lens,” Appl. Phys. Lett. 77, 2109–2111 (2000).
[CrossRef]

J. Enderlein, “Theoretical study of detection of a dipole emitter through an objective with high numerical aperture,” Opt. Lett. 25, 634–636 (2000).
[CrossRef]

1999 (1)

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74, 501–503 (1999).
[CrossRef]

1998 (3)

L. P. Ghislain and V. B. Elings, “Near-field scanning solid immersion microscope,” Appl. Phys. Lett. 72, 2779–2781 (1998).
[CrossRef]

P. Török, P. D. Higdon, and T. Wilson, “On the general properties of polarised light conventional and confocal microscopes,” Opt. Commun. 148, 300–315 (1998).
[CrossRef]

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

1997 (1)

1996 (1)

B. D. Terris, H. J. Mamin, and D. Rugar, “Near-field optical data storage,” Appl. Phys. Lett. 68, 141–143 (1996).
[CrossRef]

1994 (1)

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical-data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388–390 (1994).
[CrossRef]

1990 (1)

S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57, 2615–2616 (1990).
[CrossRef]

1982 (1)

C. J. R. Sheppard and T. Wilson, “The image of a single point in microscopes of large numerical aperture,” Proc. R. Soc. A 379, 145–158 (1982).
[CrossRef]

1981 (1)

C. J. R. Sheppard and T. Wilson, “The theory of the direct-view confocal microscope,” J. Microsc. 124, 107–117 (1981).
[CrossRef]

1978 (1)

C. J. R. Sheppard and T. Wilson, “Image formation in scanning microscopes with partially coherent source and detector,” Opt. Acta 25, 315–325 (1978).
[CrossRef]

1977 (1)

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

1976 (1)

K. Yamamoto, Y. Ichioka, and T. Suzuki, “Influence of light coherence at exit pupil of condenser on image-formation,” Opt. Acta 23, 987–996 (1976).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

1959 (1)

E. Wolf, “Electromagnetic diffraction in optical systems. I. An integral representation of the image field,” Proc. R. Soc. Lond. A 253, 349–357 (1959).
[CrossRef]

1953 (1)

H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. A 217, 408–432 (1953).
[CrossRef]

Abubakar, A.

A. Abubakar and P. M. van den Berg, “Iterative forward and inverse algorithms based on domain integral equations for three-dimensional electric and magnetic objects,” J. Comput. Phys. 195, 236–262 (2004).
[CrossRef]

Agarwal, K.

Behringer, E. R.

A. N. Vamivakas, R. D. Younger, B. B. Goldberg, A. K. Swan, M. S. Ünlü, E. R. Behringer, and S. B. Ippolito, “A case study for optics: the solid immersion microscope,” Am. J. Phys. 76, 758–768 (2008).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 2001).

Chen, J. B.

Chen, R.

Chen, T.

D. Nam, T. D. Milster, and T. Chen, “Potential of solid immersion lithography using I-line and KrF light source,” Proc. SPIE 5754, 1049–1055 (2005).

T. Chen, T. Milster, D. Nam, and S. H. Yang, “Experimental investigation of solid immersion lens lithography,” Proc. SPIE 5754, 254–261 (2005).

T. Milster, T. Chen, D. Nam, and E. Schlesinger, “Maskless lithography with solid immersion lens nano probes,” Proc. SPIE 5567, 545–556 (2004).
[CrossRef]

Chen, X.

Choudhury, A.

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

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

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Crozier, K. B.

D. A. Fletcher, K. B. Crozier, K. W. Guarini, S. C. Minne, G. S. Kino, C. F. Quate, and K. E. Goodson, “Microfabricated silicon solid immersion lens,” J. Microelectromech. Syst. 10, 450–459 (2001).
[CrossRef]

D. A. Fletcher, K. B. Crozier, C. F. Quate, G. S. Kino, K. E. Goodson, D. Simanovskii, and D. V. Palanker, “Near-field infrared imaging with a microfabricated solid immersion lens,” Appl. Phys. Lett. 77, 2109–2111 (2000).
[CrossRef]

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74, 501–503 (1999).
[CrossRef]

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “The focus of light-linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt. 50, 1917–1926 (2003).

Elings, V. B.

Q. Wu, L. P. Ghislain, and V. B. Elings, “Imaging with solid immersion lenses, spatial resolution, and applications,” Proc. IEEE 88, 1491–1498 (2000).
[CrossRef]

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74, 501–503 (1999).
[CrossRef]

L. P. Ghislain and V. B. Elings, “Near-field scanning solid immersion microscope,” Appl. Phys. Lett. 72, 2779–2781 (1998).
[CrossRef]

Enderlein, J.

Fletcher, D. A.

D. A. Fletcher, K. B. Crozier, K. W. Guarini, S. C. Minne, G. S. Kino, C. F. Quate, and K. E. Goodson, “Microfabricated silicon solid immersion lens,” J. Microelectromech. Syst. 10, 450–459 (2001).
[CrossRef]

D. A. Fletcher, K. B. Crozier, C. F. Quate, G. S. Kino, K. E. Goodson, D. Simanovskii, and D. V. Palanker, “Near-field infrared imaging with a microfabricated solid immersion lens,” Appl. Phys. Lett. 77, 2109–2111 (2000).
[CrossRef]

Ghislain, L. P.

Q. Wu, L. P. Ghislain, and V. B. Elings, “Imaging with solid immersion lenses, spatial resolution, and applications,” Proc. IEEE 88, 1491–1498 (2000).
[CrossRef]

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74, 501–503 (1999).
[CrossRef]

L. P. Ghislain and V. B. Elings, “Near-field scanning solid immersion microscope,” Appl. Phys. Lett. 72, 2779–2781 (1998).
[CrossRef]

Goh, S. H.

S. H. Goh and C. J. R. Sheppard, “High aperture focusing through a spherical interface: application to refractive solid immersion lens (RSIL) for subsurface imaging,” Opt. Commun. 282, 1036–1041 (2009).
[CrossRef]

Goldberg, B. B.

F. H. Köklü, S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, “Subsurface microscopy of integrated circuits with angular spectrum and polarization control,” Opt. Lett. 34, 1261–1263 (2009).
[CrossRef]

F. H. Köklü, J. I. Quesnel, A. N. Vamivakas, S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, “Widefield subsurface microscopy of integrated circuits,” Opt. Express 16, 9501–9506 (2008).
[CrossRef]

A. N. Vamivakas, R. D. Younger, B. B. Goldberg, A. K. Swan, M. S. Ünlü, E. R. Behringer, and S. B. Ippolito, “A case study for optics: the solid immersion microscope,” Am. J. Phys. 76, 758–768 (2008).
[CrossRef]

S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, “Theoretical analysis of numerical aperture increasing lens microscopy,” J. Appl. Phys. 97, 053105 (2005).
[CrossRef]

S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, “High spatial resolution subsurface microscopy,” Appl. Phys. Lett. 78, 4071–4073 (2001).
[CrossRef]

Goodson, K. E.

D. A. Fletcher, K. B. Crozier, K. W. Guarini, S. C. Minne, G. S. Kino, C. F. Quate, and K. E. Goodson, “Microfabricated silicon solid immersion lens,” J. Microelectromech. Syst. 10, 450–459 (2001).
[CrossRef]

D. A. Fletcher, K. B. Crozier, C. F. Quate, G. S. Kino, K. E. Goodson, D. Simanovskii, and D. V. Palanker, “Near-field infrared imaging with a microfabricated solid immersion lens,” Appl. Phys. Lett. 77, 2109–2111 (2000).
[CrossRef]

Guarini, K. W.

D. A. Fletcher, K. B. Crozier, K. W. Guarini, S. C. Minne, G. S. Kino, C. F. Quate, and K. E. Goodson, “Microfabricated silicon solid immersion lens,” J. Microelectromech. Syst. 10, 450–459 (2001).
[CrossRef]

Guo, H. M.

Guo, S. W.

Hayashi, S.

Helseth, L. E.

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

Higdon, P. D.

P. Török, P. D. Higdon, and T. Wilson, “On the general properties of polarised light conventional and confocal microscopes,” Opt. Commun. 148, 300–315 (1998).
[CrossRef]

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

Hoang, T. X.

Hopkins, H. H.

H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. A 217, 408–432 (1953).
[CrossRef]

Hu, L.

Huat, G. S.

C. J. R. Sheppard and G. S. Huat, “Comment on ‘Theoretical analysis of numerical aperture increasing lens microscopy’ [J. Appl. Phys. 97, 053105 (2005)],” J. Appl. Phys. 100086106 (2006).
[CrossRef]

Ichimura, I.

Ichioka, Y.

K. Yamamoto, Y. Ichioka, and T. Suzuki, “Influence of light coherence at exit pupil of condenser on image-formation,” Opt. Acta 23, 987–996 (1976).
[CrossRef]

Ippolito, S. B.

F. H. Köklü, S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, “Subsurface microscopy of integrated circuits with angular spectrum and polarization control,” Opt. Lett. 34, 1261–1263 (2009).
[CrossRef]

A. N. Vamivakas, R. D. Younger, B. B. Goldberg, A. K. Swan, M. S. Ünlü, E. R. Behringer, and S. B. Ippolito, “A case study for optics: the solid immersion microscope,” Am. J. Phys. 76, 758–768 (2008).
[CrossRef]

F. H. Köklü, J. I. Quesnel, A. N. Vamivakas, S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, “Widefield subsurface microscopy of integrated circuits,” Opt. Express 16, 9501–9506 (2008).
[CrossRef]

S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, “Theoretical analysis of numerical aperture increasing lens microscopy,” J. Appl. Phys. 97, 053105 (2005).
[CrossRef]

S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, “High spatial resolution subsurface microscopy,” Appl. Phys. Lett. 78, 4071–4073 (2001).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Kim, J. H.

Kino, G. S.

D. A. Fletcher, K. B. Crozier, K. W. Guarini, S. C. Minne, G. S. Kino, C. F. Quate, and K. E. Goodson, “Microfabricated silicon solid immersion lens,” J. Microelectromech. Syst. 10, 450–459 (2001).
[CrossRef]

D. A. Fletcher, K. B. Crozier, C. F. Quate, G. S. Kino, K. E. Goodson, D. Simanovskii, and D. V. Palanker, “Near-field infrared imaging with a microfabricated solid immersion lens,” Appl. Phys. Lett. 77, 2109–2111 (2000).
[CrossRef]

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74, 501–503 (1999).
[CrossRef]

I. Ichimura, S. Hayashi, and G. S. Kino, “High-density optical recording using a solid immersion lens,” Appl. Opt. 36, 4339–4348 (1997).
[CrossRef]

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical-data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388–390 (1994).
[CrossRef]

S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57, 2615–2616 (1990).
[CrossRef]

Köklü, F. H.

Kriezis, E. E.

Lee, G. C. F.

Lee, J.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “The focus of light-linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt. 50, 1917–1926 (2003).

Liang, Z.

Liang, Z. C.

Lim, K. M.

Mamin, H. J.

B. D. Terris, H. J. Mamin, and D. Rugar, “Near-field optical data storage,” Appl. Phys. Lett. 68, 141–143 (1996).
[CrossRef]

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical-data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388–390 (1994).
[CrossRef]

Manalis, S. R.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74, 501–503 (1999).
[CrossRef]

Mansfield, S. M.

S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57, 2615–2616 (1990).
[CrossRef]

Milster, T.

T. Chen, T. Milster, D. Nam, and S. H. Yang, “Experimental investigation of solid immersion lens lithography,” Proc. SPIE 5754, 254–261 (2005).

T. Milster, T. Chen, D. Nam, and E. Schlesinger, “Maskless lithography with solid immersion lens nano probes,” Proc. SPIE 5567, 545–556 (2004).
[CrossRef]

Milster, T. D.

D. Nam, T. D. Milster, and T. Chen, “Potential of solid immersion lithography using I-line and KrF light source,” Proc. SPIE 5754, 1049–1055 (2005).

T. D. Milster, “Near-field optical data storage: avenues for improved performance,” Opt. Eng. 40, 2255–2260 (2001).
[CrossRef]

Minne, S. C.

D. A. Fletcher, K. B. Crozier, K. W. Guarini, S. C. Minne, G. S. Kino, C. F. Quate, and K. E. Goodson, “Microfabricated silicon solid immersion lens,” J. Microelectromech. Syst. 10, 450–459 (2001).
[CrossRef]

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74, 501–503 (1999).
[CrossRef]

Munro, P. R. T.

Nam, D.

D. Nam, T. D. Milster, and T. Chen, “Potential of solid immersion lithography using I-line and KrF light source,” Proc. SPIE 5754, 1049–1055 (2005).

T. Chen, T. Milster, D. Nam, and S. H. Yang, “Experimental investigation of solid immersion lens lithography,” Proc. SPIE 5754, 254–261 (2005).

T. Milster, T. Chen, D. Nam, and E. Schlesinger, “Maskless lithography with solid immersion lens nano probes,” Proc. SPIE 5567, 545–556 (2004).
[CrossRef]

Palanker, D. V.

D. A. Fletcher, K. B. Crozier, C. F. Quate, G. S. Kino, K. E. Goodson, D. Simanovskii, and D. V. Palanker, “Near-field infrared imaging with a microfabricated solid immersion lens,” Appl. Phys. Lett. 77, 2109–2111 (2000).
[CrossRef]

Phang, J. C. H.

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “The focus of light-linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt. 50, 1917–1926 (2003).

Quate, C. F.

D. A. Fletcher, K. B. Crozier, K. W. Guarini, S. C. Minne, G. S. Kino, C. F. Quate, and K. E. Goodson, “Microfabricated silicon solid immersion lens,” J. Microelectromech. Syst. 10, 450–459 (2001).
[CrossRef]

D. A. Fletcher, K. B. Crozier, C. F. Quate, G. S. Kino, K. E. Goodson, D. Simanovskii, and D. V. Palanker, “Near-field infrared imaging with a microfabricated solid immersion lens,” Appl. Phys. Lett. 77, 2109–2111 (2000).
[CrossRef]

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74, 501–503 (1999).
[CrossRef]

Quesnel, J. I.

Ramsay, E.

K. A. Serrels, E. Ramsay, R. J. Warburton, and D. T. Reid, “Nanoscale optical microscopy in the vectorial focusing regime,” Nat. Photonics 2, 311–314 (2008).
[CrossRef]

Reid, D. T.

K. A. Serrels, E. Ramsay, R. J. Warburton, and D. T. Reid, “Nanoscale optical microscopy in the vectorial focusing regime,” Nat. Photonics 2, 311–314 (2008).
[CrossRef]

Rugar, D.

B. D. Terris, H. J. Mamin, and D. Rugar, “Near-field optical data storage,” Appl. Phys. Lett. 68, 141–143 (1996).
[CrossRef]

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical-data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388–390 (1994).
[CrossRef]

Schlesinger, E.

T. Milster, T. Chen, D. Nam, and E. Schlesinger, “Maskless lithography with solid immersion lens nano probes,” Proc. SPIE 5567, 545–556 (2004).
[CrossRef]

Serrels, K. A.

K. A. Serrels, E. Ramsay, R. J. Warburton, and D. T. Reid, “Nanoscale optical microscopy in the vectorial focusing regime,” Nat. Photonics 2, 311–314 (2008).
[CrossRef]

Sheppard, C. J. R.

T. X. Hoang, X. Chen, and C. J. R. Sheppard, “Multipole theory for tight focusing of polarized light, including radially polarized and other special cases,” J. Opt. Soc. Am. A 29, 32–43 (2012).
[CrossRef]

R. Chen, K. Agarwal, C. J. R. Sheppard, J. C. H. Phang, and X. Chen, “Resolution of aplanatic solid immersion lens based microscopy,” J. Opt. Soc. Am. A 29, 1059–1070 (2012).
[CrossRef]

L. Hu, R. Chen, K. Agarwal, C. J. R. Sheppard, J. C. H. Phang, and X. Chen, “Dyadic Green’s function for aplanatic solid immersion lens based sub-surface microscopy,” Opt. Express 19, 19280–19295 (2011).
[CrossRef]

K. M. Lim, G. C. F. Lee, C. J. R. Sheppard, J. C. H. Phang, C. L. Wong, and X. Chen, “Effect of polarization on a solid immersion lens of arbitrary thickness,” J. Opt. Soc. Am. A 28, 903–911 (2011).
[CrossRef]

S. H. Goh and C. J. R. Sheppard, “High aperture focusing through a spherical interface: application to refractive solid immersion lens (RSIL) for subsurface imaging,” Opt. Commun. 282, 1036–1041 (2009).
[CrossRef]

C. J. R. Sheppard and G. S. Huat, “Comment on ‘Theoretical analysis of numerical aperture increasing lens microscopy’ [J. Appl. Phys. 97, 053105 (2005)],” J. Appl. Phys. 100086106 (2006).
[CrossRef]

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

C. J. R. Sheppard and T. Wilson, “The image of a single point in microscopes of large numerical aperture,” Proc. R. Soc. A 379, 145–158 (1982).
[CrossRef]

C. J. R. Sheppard and T. Wilson, “The theory of the direct-view confocal microscope,” J. Microsc. 124, 107–117 (1981).
[CrossRef]

C. J. R. Sheppard and T. Wilson, “Image formation in scanning microscopes with partially coherent source and detector,” Opt. Acta 25, 315–325 (1978).
[CrossRef]

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

Simanovskii, D.

D. A. Fletcher, K. B. Crozier, C. F. Quate, G. S. Kino, K. E. Goodson, D. Simanovskii, and D. V. Palanker, “Near-field infrared imaging with a microfabricated solid immersion lens,” Appl. Phys. Lett. 77, 2109–2111 (2000).
[CrossRef]

Studenmund, W. R.

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical-data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388–390 (1994).
[CrossRef]

Suzuki, T.

K. Yamamoto, Y. Ichioka, and T. Suzuki, “Influence of light coherence at exit pupil of condenser on image-formation,” Opt. Acta 23, 987–996 (1976).
[CrossRef]

Swan, A. K.

A. N. Vamivakas, R. D. Younger, B. B. Goldberg, A. K. Swan, M. S. Ünlü, E. R. Behringer, and S. B. Ippolito, “A case study for optics: the solid immersion microscope,” Am. J. Phys. 76, 758–768 (2008).
[CrossRef]

Terris, B. D.

B. D. Terris, H. J. Mamin, and D. Rugar, “Near-field optical data storage,” Appl. Phys. Lett. 68, 141–143 (1996).
[CrossRef]

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical-data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388–390 (1994).
[CrossRef]

Török, P.

P. Török, P. R. T. Munro, and E. E. Kriezis, “High numerical aperture vectorial imaging in coherent optical microscopes,” Opt. Express 16, 507–523 (2008).
[CrossRef]

P. R. T. Munro and P. Török, “Calculation of the image of an arbitrary vectorial electromagnetic field,” Opt. Express 15, 9293–9307 (2007).
[CrossRef]

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

P. Török, P. D. Higdon, and T. Wilson, “On the general properties of polarised light conventional and confocal microscopes,” Opt. Commun. 148, 300–315 (1998).
[CrossRef]

Ünlü, M. S.

F. H. Köklü and M. S. Ünlü, “Subsurface microscopy of interconnect layers of an integrated circuit,” Opt. Lett. 35, 184–186(2010).
[CrossRef]

F. H. Köklü, S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, “Subsurface microscopy of integrated circuits with angular spectrum and polarization control,” Opt. Lett. 34, 1261–1263 (2009).
[CrossRef]

F. H. Köklü, J. I. Quesnel, A. N. Vamivakas, S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, “Widefield subsurface microscopy of integrated circuits,” Opt. Express 16, 9501–9506 (2008).
[CrossRef]

A. N. Vamivakas, R. D. Younger, B. B. Goldberg, A. K. Swan, M. S. Ünlü, E. R. Behringer, and S. B. Ippolito, “A case study for optics: the solid immersion microscope,” Am. J. Phys. 76, 758–768 (2008).
[CrossRef]

S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, “Theoretical analysis of numerical aperture increasing lens microscopy,” J. Appl. Phys. 97, 053105 (2005).
[CrossRef]

S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, “High spatial resolution subsurface microscopy,” Appl. Phys. Lett. 78, 4071–4073 (2001).
[CrossRef]

Vamivakas, A. N.

A. N. Vamivakas, R. D. Younger, B. B. Goldberg, A. K. Swan, M. S. Ünlü, E. R. Behringer, and S. B. Ippolito, “A case study for optics: the solid immersion microscope,” Am. J. Phys. 76, 758–768 (2008).
[CrossRef]

F. H. Köklü, J. I. Quesnel, A. N. Vamivakas, S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, “Widefield subsurface microscopy of integrated circuits,” Opt. Express 16, 9501–9506 (2008).
[CrossRef]

van den Berg, P. M.

A. Abubakar and P. M. van den Berg, “Iterative forward and inverse algorithms based on domain integral equations for three-dimensional electric and magnetic objects,” J. Comput. Phys. 195, 236–262 (2004).
[CrossRef]

Warburton, R. J.

K. A. Serrels, E. Ramsay, R. J. Warburton, and D. T. Reid, “Nanoscale optical microscopy in the vectorial focusing regime,” Nat. Photonics 2, 311–314 (2008).
[CrossRef]

Wilder, K.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74, 501–503 (1999).
[CrossRef]

Wilson, T.

P. Török, P. D. Higdon, and T. Wilson, “On the general properties of polarised light conventional and confocal microscopes,” Opt. Commun. 148, 300–315 (1998).
[CrossRef]

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

C. J. R. Sheppard and T. Wilson, “The image of a single point in microscopes of large numerical aperture,” Proc. R. Soc. A 379, 145–158 (1982).
[CrossRef]

C. J. R. Sheppard and T. Wilson, “The theory of the direct-view confocal microscope,” J. Microsc. 124, 107–117 (1981).
[CrossRef]

C. J. R. Sheppard and T. Wilson, “Image formation in scanning microscopes with partially coherent source and detector,” Opt. Acta 25, 315–325 (1978).
[CrossRef]

Wolf, E.

E. Wolf, “Electromagnetic diffraction in optical systems. I. An integral representation of the image field,” Proc. R. Soc. Lond. A 253, 349–357 (1959).
[CrossRef]

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 2001).

Wong, C. L.

Wu, Q.

Q. Wu, L. P. Ghislain, and V. B. Elings, “Imaging with solid immersion lenses, spatial resolution, and applications,” Proc. IEEE 88, 1491–1498 (2000).
[CrossRef]

Yamamoto, K.

K. Yamamoto, Y. Ichioka, and T. Suzuki, “Influence of light coherence at exit pupil of condenser on image-formation,” Opt. Acta 23, 987–996 (1976).
[CrossRef]

Yang, S. H.

T. Chen, T. Milster, D. Nam, and S. H. Yang, “Experimental investigation of solid immersion lens lithography,” Proc. SPIE 5754, 254–261 (2005).

Yim, S. Y.

Younger, R. D.

A. N. Vamivakas, R. D. Younger, B. B. Goldberg, A. K. Swan, M. S. Ünlü, E. R. Behringer, and S. B. Ippolito, “A case study for optics: the solid immersion microscope,” Am. J. Phys. 76, 758–768 (2008).
[CrossRef]

Zhang, Y. J.

Zhong, Y.

Y. Zhong and X. Chen, “An FFT twofold subspace-based optimization method for solving electromagnetic inverse scattering problems,” IEEE Trans. Antennas Propag. 59, 914–927 (2011).
[CrossRef]

Y. Zhong and X. Chen, “MUSIC imaging and electromagnetic inverse scattering of multiple-scattering small anisotropic spheres,” IEEE Trans. Antennas Propag. 55, 3542–3549 (2007).
[CrossRef]

Zhuang, S. L.

Am. J. Phys. (1)

A. N. Vamivakas, R. D. Younger, B. B. Goldberg, A. K. Swan, M. S. Ünlü, E. R. Behringer, and S. B. Ippolito, “A case study for optics: the solid immersion microscope,” Am. J. Phys. 76, 758–768 (2008).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. Lett. (7)

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74, 501–503 (1999).
[CrossRef]

L. P. Ghislain and V. B. Elings, “Near-field scanning solid immersion microscope,” Appl. Phys. Lett. 72, 2779–2781 (1998).
[CrossRef]

D. A. Fletcher, K. B. Crozier, C. F. Quate, G. S. Kino, K. E. Goodson, D. Simanovskii, and D. V. Palanker, “Near-field infrared imaging with a microfabricated solid immersion lens,” Appl. Phys. Lett. 77, 2109–2111 (2000).
[CrossRef]

S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, “High spatial resolution subsurface microscopy,” Appl. Phys. Lett. 78, 4071–4073 (2001).
[CrossRef]

S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57, 2615–2616 (1990).
[CrossRef]

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical-data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388–390 (1994).
[CrossRef]

B. D. Terris, H. J. Mamin, and D. Rugar, “Near-field optical data storage,” Appl. Phys. Lett. 68, 141–143 (1996).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

Y. Zhong and X. Chen, “MUSIC imaging and electromagnetic inverse scattering of multiple-scattering small anisotropic spheres,” IEEE Trans. Antennas Propag. 55, 3542–3549 (2007).
[CrossRef]

Y. Zhong and X. Chen, “An FFT twofold subspace-based optimization method for solving electromagnetic inverse scattering problems,” IEEE Trans. Antennas Propag. 59, 914–927 (2011).
[CrossRef]

J. Appl. Phys. (2)

C. J. R. Sheppard and G. S. Huat, “Comment on ‘Theoretical analysis of numerical aperture increasing lens microscopy’ [J. Appl. Phys. 97, 053105 (2005)],” J. Appl. Phys. 100086106 (2006).
[CrossRef]

S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, “Theoretical analysis of numerical aperture increasing lens microscopy,” J. Appl. Phys. 97, 053105 (2005).
[CrossRef]

J. Comput. Phys. (1)

A. Abubakar and P. M. van den Berg, “Iterative forward and inverse algorithms based on domain integral equations for three-dimensional electric and magnetic objects,” J. Comput. Phys. 195, 236–262 (2004).
[CrossRef]

J. Microelectromech. Syst. (1)

D. A. Fletcher, K. B. Crozier, K. W. Guarini, S. C. Minne, G. S. Kino, C. F. Quate, and K. E. Goodson, “Microfabricated silicon solid immersion lens,” J. Microelectromech. Syst. 10, 450–459 (2001).
[CrossRef]

J. Microsc. (1)

C. J. R. Sheppard and T. Wilson, “The theory of the direct-view confocal microscope,” J. Microsc. 124, 107–117 (1981).
[CrossRef]

J. Mod. Opt. (2)

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

R. Dorn, S. Quabis, and G. Leuchs, “The focus of light-linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt. 50, 1917–1926 (2003).

J. Opt. Soc. Am. A (5)

J. Opt. Soc. Korea (1)

Nat. Photonics (1)

K. A. Serrels, E. Ramsay, R. J. Warburton, and D. T. Reid, “Nanoscale optical microscopy in the vectorial focusing regime,” Nat. Photonics 2, 311–314 (2008).
[CrossRef]

Opt. Acta (3)

K. Yamamoto, Y. Ichioka, and T. Suzuki, “Influence of light coherence at exit pupil of condenser on image-formation,” Opt. Acta 23, 987–996 (1976).
[CrossRef]

C. J. R. Sheppard and T. Wilson, “Image formation in scanning microscopes with partially coherent source and detector,” Opt. Acta 25, 315–325 (1978).
[CrossRef]

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

Opt. Commun. (3)

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

P. Török, P. D. Higdon, and T. Wilson, “On the general properties of polarised light conventional and confocal microscopes,” Opt. Commun. 148, 300–315 (1998).
[CrossRef]

S. H. Goh and C. J. R. Sheppard, “High aperture focusing through a spherical interface: application to refractive solid immersion lens (RSIL) for subsurface imaging,” Opt. Commun. 282, 1036–1041 (2009).
[CrossRef]

Opt. Eng. (1)

T. D. Milster, “Near-field optical data storage: avenues for improved performance,” Opt. Eng. 40, 2255–2260 (2001).
[CrossRef]

Opt. Express (5)

Opt. Lett. (4)

Phys. Rev. B (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Proc. IEEE (1)

Q. Wu, L. P. Ghislain, and V. B. Elings, “Imaging with solid immersion lenses, spatial resolution, and applications,” Proc. IEEE 88, 1491–1498 (2000).
[CrossRef]

Proc. R. Soc. A (2)

H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. A 217, 408–432 (1953).
[CrossRef]

C. J. R. Sheppard and T. Wilson, “The image of a single point in microscopes of large numerical aperture,” Proc. R. Soc. A 379, 145–158 (1982).
[CrossRef]

Proc. R. Soc. Lond. A (1)

E. Wolf, “Electromagnetic diffraction in optical systems. I. An integral representation of the image field,” Proc. R. Soc. Lond. A 253, 349–357 (1959).
[CrossRef]

Proc. SPIE (3)

T. Chen, T. Milster, D. Nam, and S. H. Yang, “Experimental investigation of solid immersion lens lithography,” Proc. SPIE 5754, 254–261 (2005).

T. Milster, T. Chen, D. Nam, and E. Schlesinger, “Maskless lithography with solid immersion lens nano probes,” Proc. SPIE 5567, 545–556 (2004).
[CrossRef]

D. Nam, T. D. Milster, and T. Chen, “Potential of solid immersion lithography using I-line and KrF light source,” Proc. SPIE 5754, 1049–1055 (2005).

Other (3)

Semicaps, “Optical fault localization system,” http://www.semicaps.com/innovations.htm .

Hamamatsu Photonics, K. K., “Solid immersion lens,” http://jp.hamamatsu.com/resources/products/sys/pdf/eng/e_phemos.pdf .

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 2001).

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Figures (15)

Fig. 1.
Fig. 1.

Diagrammatic description of ASIL microscopy system. The objective lens and the ASIL compose subsystem I (the path of the rays with red arrow). The ASIL, the objective lens, and the detector lens compose subsystem III (the path of the rays with green arrow). Subsystem II, interaction of the focusing light with the sample, links subsystems I and III of the ASIL microscopy system.

Fig. 2.
Fig. 2.

Equivalent representation of subsystem I. The rays corresponding to the incoming plane wave encounter a spherical references surface (GRS) and are subsequently focused to a point. The incident and refracted rays are in the meridional plane and obey the sine condition and the intensity law.

Fig. 3.
Fig. 3.

Equivalent representation of subsystem III, which shows various interfaces and path of a ray traveling through these interfaces. θobj and θccd are the semiaperture angles of the objective and the detector lens.

Fig. 4.
Fig. 4.

Intensity distribution when a small gold sphere is placed at the aplanatic point of ASIL for x- (the first row) and y- (the second row) polarized illumination. The horizontal and vertical coordinates are xccd/(Mlatλ) and yccd/(Mlatλ), respectively. Mlat is the lateral magnification of the ASIL microscopy system. (a)–(c) and (e)–(g) are the intensity distributions for three orthogonal field components. (d) and (h) are the total intensity distributions.

Fig. 5.
Fig. 5.

FWHM of the image along x-axis for the different orientation angles α of linearly polarized illumination. The scatterer is a single small gold sphere placed at the aplanatic point of ASIL.

Fig. 6.
Fig. 6.

Resolution of ASIL microscopy system for the different orientation angles α of linearly polarized illumination. The scatterers are two small gold spheres placed along the x-axis.

Fig. 7.
Fig. 7.

Image of two small gold spheres along x-axis, symmetric to the aplanatic point of ASIL, for x- (the first row) and y- (the second row) polarized illumination, when the distance between them is Δx=0.13λ. The horizontal and vertical coordinates are xccd/(Mlatλ) and yccd/(Mlatλ), respectively. Mlat is the lateral magnification of the ASIL microscopy system. (a)–(c) and (e)–(g) are the intensity distributions for three orthogonal field components. (d) and (h) are total intensity distributions.

Fig. 8.
Fig. 8.

Real (a) and imaginary (b) parts of the dominant electric field in the CCD region along the x-axis for the induced x^ dipoles only, the induced z^ dipoles only, and the sum of two types of induced dipoles, respectively, when Δx=0.13λ. The horizontal coordinate is xccd/(Mlatλ). Mlat is the lateral magnification of the ASIL microscopy system.

Fig. 9.
Fig. 9.

Refractive index distribution of cross section of (a) an annular ring and (b) three-bar pattern located on the aplanatic plane of the ASIL. In (a), R1 and R2 are the inner and outer radii of annular ring, respectively. In (b), the three-bar pattern consists of three lines separated by spaces of equal width, d. Each line is five times as long as it is wide.

Fig. 10.
Fig. 10.

Image of an annular ring in Fig. 9(a) using FLI with NAmax of subsystem I (the first column) and PWI (the second column). (a)–(b) are for x-polarized illumination while (c)–(d) y-polarized illumination, R1=0.125λ and R2=0.225λ. The horizontal and vertical coordinates are xccd/(Mlatλ) and yccd/(Mlatλ), respectively.

Fig. 11.
Fig. 11.

Magnitude distribution of induced currents on the annular ring in Fig. 9(a) using FLI with NAmax in subsystem I (the first two rows) and PWI (the last two rows). R1=0.125λ and R2=0.225λ. The horizontal and vertical coordinates are [0.3 0.3] and [0.3 0.3] for xsil/λ and ysil/λ, respectively. (a)–(c), (d)–(f), (g)–(i), and (j)–(l) are the induced current distributions for three orthogonal field components.

Fig. 12.
Fig. 12.

Intensity distribution of image (a) considering only induced x^ currents, and (b) considering only induced z^ currents, when using FLI of NAmax in subsystem I. The coordinates are the same as in Fig. 10.

Fig. 13.
Fig. 13.

Image of three-bar pattern in Fig. 9(b) using FLI with NAmax of subsystem I (the first column) and PWI (the second column). (a)–(b) are for x-polarized illumination while (c)–(d) are for y-polarized illumination, d=0.15λ. The horizontal and vertical coordinates are xccd/(Mlatλ) and yccd/(Mlatλ), respectively.

Fig. 14.
Fig. 14.

Magnitude distribution of induced currents on three-bar pattern in Fig. 9(b) using FLI with NAmax in subsystem I (the first two rows) and PWI (the last two rows). d=0.15λ. The horizontal and vertical coordinates are [0.60.6] and [0.60.6] for xsil/λ and ysil/λ, respectively. (a)–(c), (d)–(f), (g)–(i) and (j)–(l) are the induced current distributions for three orthogonal field components.

Fig. 15.
Fig. 15.

(a) Original pattern of letters “NUS,” (b) the image of letters “NUS” using x-polarized PWI. In (a), the linewidth of letters is 0.05λ and the distance between the lines of letters is 0.25λ. Other parameters are the same as for the annular ring in Fig. 9(a). In (a), the horizontal and vertical coordinates are xsil/λ and ysil/λ, respectively. In (b), the horizontal and vertical coordinates are xccd/(Mlatλ) and yccd/(Mlatλ), respectively.

Equations (21)

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ED(x,y,z)=i2πkx2+ky2k2reikrEei(kxx+kyykzz)1kzdkxdky,
ED=iksilfobjeikobjfobj2E0n0nobj[cosα(I0L+I2Lcos2ϕP)+sinαI2Lsin2ϕPcosαI2Lsin2ϕP+sinα(I0LI2Lcos2ϕP)2iI1L(cosαcosϕP+sinαsinϕP)],
ImL=0θmax(cosθ)3/2tanθJm(ksilρPsinθ)ΓmLeiksilzPcosθdθ,
θ=sin1(nsilsinθ/n1),
Γ0L=ts+tpcosθ,
Γ1L=tpsinθ,
Γ2L=tstpcosθ,
Il(rsil)=iωϵsil[ϵr(rsil)1]E(rsil),
[ϵr(rsil)1]ED(rsil)=Il(rsil)iωϵsil[ϵr(rsil)1]iωμ0(I¯¯+ksil2)·Dg(rsil,rsil)Il(rsil)drsil,
Eccd(rccd)=iωμG¯¯PSF(rccd,rsil)·Il(rsil).
G¯¯PSF(rccd,rsil)=Econst[I0cc+I2ccI2cs2iI1scI2csI0ccI2cc2iI1ss2iI1cc2iI1cs2I0ss],
Imcc,ss,cs,sc=0θmax(cosθobjcosθccd)1/2sinθobjΠmcc,ss,cs,scJm(ρ)eizdθobj,
Π0cc=ts+tpcosθccdcosθsil,Π0ss=tpsinθccdsinθsil,
Π1sc=tpcosθccdsinθsilcosψ,Π1ss=tpcosθccdsinθsilsinψ,
Π1cc=tpsinθccdcosθsilcosψ,Π1cs=tpsinθccdcosθsilsinψ,
Π2cc=(tstpcosθccdcosθsil)cos2ψ,Π2cs=(tstpcosθccdcosθsil)sin2ψ,
ρ=x2+y2;ψ=arctan(y/x),
x=(kccdxccdsinθccd+ksilxsilsinθsil),
y=(kccdyccdsinθccd+ksilysilsinθsil),
z=kccdzccdcosθccdksilzsilcosθsil.
nobjaλ1,nsilaλ1,

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