Abstract

A new method of designing soft X-ray transmission multilayer polarizer for use at a single wavelength using a merit function has been developed. A merit function of product of p-transmittance throughput and logarithm of transmittance polarization ratio was chosen. Characteristics of Mo/Si multilayer calculated using the merit function at 13.0 nm have been compared with those calculated using the traditional method by the present authors and those reported so far. The merit function has given the most optimal results of throughput of 30.0% and polarization ratio of 202. The polarizers of much higher polarization ratio or much larger p-transmittance can be designed by choosing the number of layers and optimizing the thickness of each layer to maximize the merit function. Using this method, the roughness effect has been studied on Mo/Si and La/B multilayer polarizers at 13.0 nm and 6.7 nm, respectively. It was found that the influence of roughness is crucial in shorter wavelength region.

©2009 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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  22. http://www-cxro.lbl.gov/, Jan 24, 2008

2007 (1)

J. T. Zhu, Z. S. Wang, H. C. Wang, Z. Zhang, F. L. Wang, S. J. Qin, L. Y. Chen, M. Q. Cui, Y. D. Zhao, L. J. Sun, H. J. Zhou, and T. L. Huo, “Broadband aperiodic Mo/ Si multilayer polarization elements for EUV region,” Opt. Precis. Eng. 15, 1886–1893 (2007).

2006 (1)

Z. S. Wang, H. C. Wang, J. T. Zhu, Y. Xu, S. M. Zhang, C. X. Li, F. L. Wang, Z. Zhang, Y. R. Wu, X. B. Cheng, L. Y. Chen, A. G. Michette, S. J. Pfauntsch, A. K. Powell, F. Schafers, A. Gaupp, and M. MacDonald, “Extreme ultraviolet broadband Mo/Y multilayer analyzers,” Appl. Phys. Lett. 89, 241120–241122 (2006).
[Crossref]

2005 (2)

Z. S. Wang, F. L. Wang, Z. Zhong, H. C. Wang, W. J. Wu, S. M. Zhang, Y. Xu, Z. X. Gu, X. B. Cheng, C. X. Li, Y. R. Wu, B. Wang, S. J. Qin, and L. Y. Chen, “Research of multilayers in EUV, soft X-ray and X-ray,” Opt. Precis. Eng. 13, 512–518 (2005).

S. S. Andreev, M. S. Bibishkin, N. I. Chkhalo, A. Ya. Lopatin, V. I. Luchin, A. E. Pestov, K. A. Prokhorov, and N. N. Salaschchenko, “Application of free-standing multilayer films as polarizers for x-ray radiation,” Nucl. Instrum, Methods A543, 340–345 (2005).

2004 (1)

1999 (1)

H. Grimmer, O. Zaharko, M. Horisberger, H. C. Mertins, F. Schaefers, and U. Staub, “Optical components for polarization analysis of soft x-ray radiation,” Proc. SPIE 3773, 224–235 (1999).
[Crossref]

1998 (3)

T. Haga, Y. Utsumi, and S. Itabashia, “Soft X-ray Ellipsometer using Transmissive Multilayer Polarizers,” Proc. SPIE 3443, 117–127(1998).
[Crossref]

H. W. Wende, J. Freeland, V. Chakarian, Y. U. Idzerda, L. Lemke, and K. Baberschke, “Probing local magnetic disorder by investigating spin dependent photoelectron scattering,” J. Appl. Phys. 83, 7028–7030 (1998).
[Crossref]

W. Hu, T. Hatano, M. Yamamoto, and M. Watanabe, “Transmission multilayer polarizers for use in the 55-90eV region,” J Synchrotron Rad. 5, 732–734 (1998).
[Crossref]

1996 (2)

P. Fischer, G. Schutz, G. Schmahl, P. Guttmann, and D. Raasch, “Imaging of magnetic domains with the X-ray microscope at BESSY using X-ray magnetic circular dichroism,” Z. Phys. B101, 313–316 (1996).
[Crossref]

W. Hu, M. Yamamoto, and M. Watanabe, “Development of EUV free-standing multilayer polarizers,” Proc. SPIE 2873, 74–77 (1996).

1995 (1)

J. B. Kortright, M. Rice, and R. Carr, “Soft-x-ray Faraday rotation at Fe L2,3 edges,” Phys. Rev. B51, 10240–10244 (1995).

1993 (1)

M. Yamamoto, “Polarimetry with use of soft x-ray multilayers,” Proc. SPIE 2010, 152–159 (1993).
[Crossref]

1992 (2)

H. Nomura, K. Mayama, T. Sasaki, M. Yamamoto, and M. Yanagihara, “Design, fabrication, and polarization of soft-x-ray transmission multilayers,” Proc. SPIE 1720, 395–401 (1992).
[Crossref]

D. G. Stearns, “X-ray scattering from interfacial roughness in multilayer structures,” J. Appl. Phys. 71, 4286–4296 (1992).
[Crossref]

1990 (1)

J. B. Kortright and J. H. Underwood, “Multilayer Optical Elements for Generation and Analysis of Circularly Polarized X-rays,” Nucl. Instrum. Methods A291, 272–277 (1990).

1989 (1)

D. G. Stearns, “The scattering of x rays from nonideal multiplayer structures,” J. Appl. Phys. 65, 491–506 (1989).
[Crossref]

1986 (1)

E. S. Gluskin, S. V. Gaponov, P. Dhez, P. P. Ilyinsky, N. N. Salashchenko, Yu. M. Shatunov, and E. M. Trakhtenberg, “A polarimeter for soft X-ray and VUV radiation,” Nucl. Instrum. Methods A246, 394–396 (1986).

1985 (2)

Andreev, S. S.

S. S. Andreev, M. S. Bibishkin, N. I. Chkhalo, A. Ya. Lopatin, V. I. Luchin, A. E. Pestov, K. A. Prokhorov, and N. N. Salaschchenko, “Application of free-standing multilayer films as polarizers for x-ray radiation,” Nucl. Instrum, Methods A543, 340–345 (2005).

Baberschke, K.

H. W. Wende, J. Freeland, V. Chakarian, Y. U. Idzerda, L. Lemke, and K. Baberschke, “Probing local magnetic disorder by investigating spin dependent photoelectron scattering,” J. Appl. Phys. 83, 7028–7030 (1998).
[Crossref]

Bajt, S.

Barbee, T. W.

Bibishkin, M. S.

S. S. Andreev, M. S. Bibishkin, N. I. Chkhalo, A. Ya. Lopatin, V. I. Luchin, A. E. Pestov, K. A. Prokhorov, and N. N. Salaschchenko, “Application of free-standing multilayer films as polarizers for x-ray radiation,” Nucl. Instrum, Methods A543, 340–345 (2005).

Carr, R.

J. B. Kortright, M. Rice, and R. Carr, “Soft-x-ray Faraday rotation at Fe L2,3 edges,” Phys. Rev. B51, 10240–10244 (1995).

Chakarian, V.

H. W. Wende, J. Freeland, V. Chakarian, Y. U. Idzerda, L. Lemke, and K. Baberschke, “Probing local magnetic disorder by investigating spin dependent photoelectron scattering,” J. Appl. Phys. 83, 7028–7030 (1998).
[Crossref]

Chen, L. Y.

J. T. Zhu, Z. S. Wang, H. C. Wang, Z. Zhang, F. L. Wang, S. J. Qin, L. Y. Chen, M. Q. Cui, Y. D. Zhao, L. J. Sun, H. J. Zhou, and T. L. Huo, “Broadband aperiodic Mo/ Si multilayer polarization elements for EUV region,” Opt. Precis. Eng. 15, 1886–1893 (2007).

Z. S. Wang, H. C. Wang, J. T. Zhu, Y. Xu, S. M. Zhang, C. X. Li, F. L. Wang, Z. Zhang, Y. R. Wu, X. B. Cheng, L. Y. Chen, A. G. Michette, S. J. Pfauntsch, A. K. Powell, F. Schafers, A. Gaupp, and M. MacDonald, “Extreme ultraviolet broadband Mo/Y multilayer analyzers,” Appl. Phys. Lett. 89, 241120–241122 (2006).
[Crossref]

Z. S. Wang, F. L. Wang, Z. Zhong, H. C. Wang, W. J. Wu, S. M. Zhang, Y. Xu, Z. X. Gu, X. B. Cheng, C. X. Li, Y. R. Wu, B. Wang, S. J. Qin, and L. Y. Chen, “Research of multilayers in EUV, soft X-ray and X-ray,” Opt. Precis. Eng. 13, 512–518 (2005).

Cheng, X. B.

Z. S. Wang, H. C. Wang, J. T. Zhu, Y. Xu, S. M. Zhang, C. X. Li, F. L. Wang, Z. Zhang, Y. R. Wu, X. B. Cheng, L. Y. Chen, A. G. Michette, S. J. Pfauntsch, A. K. Powell, F. Schafers, A. Gaupp, and M. MacDonald, “Extreme ultraviolet broadband Mo/Y multilayer analyzers,” Appl. Phys. Lett. 89, 241120–241122 (2006).
[Crossref]

Z. S. Wang, F. L. Wang, Z. Zhong, H. C. Wang, W. J. Wu, S. M. Zhang, Y. Xu, Z. X. Gu, X. B. Cheng, C. X. Li, Y. R. Wu, B. Wang, S. J. Qin, and L. Y. Chen, “Research of multilayers in EUV, soft X-ray and X-ray,” Opt. Precis. Eng. 13, 512–518 (2005).

Chkhalo, N. I.

S. S. Andreev, M. S. Bibishkin, N. I. Chkhalo, A. Ya. Lopatin, V. I. Luchin, A. E. Pestov, K. A. Prokhorov, and N. N. Salaschchenko, “Application of free-standing multilayer films as polarizers for x-ray radiation,” Nucl. Instrum, Methods A543, 340–345 (2005).

Cui, M. Q.

J. T. Zhu, Z. S. Wang, H. C. Wang, Z. Zhang, F. L. Wang, S. J. Qin, L. Y. Chen, M. Q. Cui, Y. D. Zhao, L. J. Sun, H. J. Zhou, and T. L. Huo, “Broadband aperiodic Mo/ Si multilayer polarization elements for EUV region,” Opt. Precis. Eng. 15, 1886–1893 (2007).

Dhez, P.

E. S. Gluskin, S. V. Gaponov, P. Dhez, P. P. Ilyinsky, N. N. Salashchenko, Yu. M. Shatunov, and E. M. Trakhtenberg, “A polarimeter for soft X-ray and VUV radiation,” Nucl. Instrum. Methods A246, 394–396 (1986).

A. Khandar and P. Dhez, “Multilayer X-ray polarizers,” Proc. SPIE 563, 158–163 (1985).

Fischer, P.

P. Fischer, G. Schutz, G. Schmahl, P. Guttmann, and D. Raasch, “Imaging of magnetic domains with the X-ray microscope at BESSY using X-ray magnetic circular dichroism,” Z. Phys. B101, 313–316 (1996).
[Crossref]

Freeland, J.

H. W. Wende, J. Freeland, V. Chakarian, Y. U. Idzerda, L. Lemke, and K. Baberschke, “Probing local magnetic disorder by investigating spin dependent photoelectron scattering,” J. Appl. Phys. 83, 7028–7030 (1998).
[Crossref]

Gaponov, S. V.

E. S. Gluskin, S. V. Gaponov, P. Dhez, P. P. Ilyinsky, N. N. Salashchenko, Yu. M. Shatunov, and E. M. Trakhtenberg, “A polarimeter for soft X-ray and VUV radiation,” Nucl. Instrum. Methods A246, 394–396 (1986).

Gaupp, A.

Z. S. Wang, H. C. Wang, J. T. Zhu, Y. Xu, S. M. Zhang, C. X. Li, F. L. Wang, Z. Zhang, Y. R. Wu, X. B. Cheng, L. Y. Chen, A. G. Michette, S. J. Pfauntsch, A. K. Powell, F. Schafers, A. Gaupp, and M. MacDonald, “Extreme ultraviolet broadband Mo/Y multilayer analyzers,” Appl. Phys. Lett. 89, 241120–241122 (2006).
[Crossref]

Gluskin, E. S.

E. S. Gluskin, S. V. Gaponov, P. Dhez, P. P. Ilyinsky, N. N. Salashchenko, Yu. M. Shatunov, and E. M. Trakhtenberg, “A polarimeter for soft X-ray and VUV radiation,” Nucl. Instrum. Methods A246, 394–396 (1986).

Grimmer, H.

H. Grimmer, O. Zaharko, M. Horisberger, H. C. Mertins, F. Schaefers, and U. Staub, “Optical components for polarization analysis of soft x-ray radiation,” Proc. SPIE 3773, 224–235 (1999).
[Crossref]

Gu, Z. X.

Z. S. Wang, F. L. Wang, Z. Zhong, H. C. Wang, W. J. Wu, S. M. Zhang, Y. Xu, Z. X. Gu, X. B. Cheng, C. X. Li, Y. R. Wu, B. Wang, S. J. Qin, and L. Y. Chen, “Research of multilayers in EUV, soft X-ray and X-ray,” Opt. Precis. Eng. 13, 512–518 (2005).

Guttmann, P.

P. Fischer, G. Schutz, G. Schmahl, P. Guttmann, and D. Raasch, “Imaging of magnetic domains with the X-ray microscope at BESSY using X-ray magnetic circular dichroism,” Z. Phys. B101, 313–316 (1996).
[Crossref]

Haga, T.

T. Haga, Y. Utsumi, and S. Itabashia, “Soft X-ray Ellipsometer using Transmissive Multilayer Polarizers,” Proc. SPIE 3443, 117–127(1998).
[Crossref]

Hatano, T.

W. Hu, T. Hatano, M. Yamamoto, and M. Watanabe, “Transmission multilayer polarizers for use in the 55-90eV region,” J Synchrotron Rad. 5, 732–734 (1998).
[Crossref]

Hettrick, M. C.

Horisberger, M.

H. Grimmer, O. Zaharko, M. Horisberger, H. C. Mertins, F. Schaefers, and U. Staub, “Optical components for polarization analysis of soft x-ray radiation,” Proc. SPIE 3773, 224–235 (1999).
[Crossref]

Hu, W.

W. Hu, T. Hatano, M. Yamamoto, and M. Watanabe, “Transmission multilayer polarizers for use in the 55-90eV region,” J Synchrotron Rad. 5, 732–734 (1998).
[Crossref]

W. Hu, M. Yamamoto, and M. Watanabe, “Development of EUV free-standing multilayer polarizers,” Proc. SPIE 2873, 74–77 (1996).

Huo, T. L.

J. T. Zhu, Z. S. Wang, H. C. Wang, Z. Zhang, F. L. Wang, S. J. Qin, L. Y. Chen, M. Q. Cui, Y. D. Zhao, L. J. Sun, H. J. Zhou, and T. L. Huo, “Broadband aperiodic Mo/ Si multilayer polarization elements for EUV region,” Opt. Precis. Eng. 15, 1886–1893 (2007).

Idzerda, Y. U.

H. W. Wende, J. Freeland, V. Chakarian, Y. U. Idzerda, L. Lemke, and K. Baberschke, “Probing local magnetic disorder by investigating spin dependent photoelectron scattering,” J. Appl. Phys. 83, 7028–7030 (1998).
[Crossref]

Ilyinsky, P. P.

E. S. Gluskin, S. V. Gaponov, P. Dhez, P. P. Ilyinsky, N. N. Salashchenko, Yu. M. Shatunov, and E. M. Trakhtenberg, “A polarimeter for soft X-ray and VUV radiation,” Nucl. Instrum. Methods A246, 394–396 (1986).

Itabashia, S.

T. Haga, Y. Utsumi, and S. Itabashia, “Soft X-ray Ellipsometer using Transmissive Multilayer Polarizers,” Proc. SPIE 3443, 117–127(1998).
[Crossref]

Khandar, A.

A. Khandar and P. Dhez, “Multilayer X-ray polarizers,” Proc. SPIE 563, 158–163 (1985).

Kjornrattanawanich, B.

Kortright, J. B.

J. B. Kortright, M. Rice, and R. Carr, “Soft-x-ray Faraday rotation at Fe L2,3 edges,” Phys. Rev. B51, 10240–10244 (1995).

J. B. Kortright and J. H. Underwood, “Multilayer Optical Elements for Generation and Analysis of Circularly Polarized X-rays,” Nucl. Instrum. Methods A291, 272–277 (1990).

Lemke, L.

H. W. Wende, J. Freeland, V. Chakarian, Y. U. Idzerda, L. Lemke, and K. Baberschke, “Probing local magnetic disorder by investigating spin dependent photoelectron scattering,” J. Appl. Phys. 83, 7028–7030 (1998).
[Crossref]

Li, C. X.

Z. S. Wang, H. C. Wang, J. T. Zhu, Y. Xu, S. M. Zhang, C. X. Li, F. L. Wang, Z. Zhang, Y. R. Wu, X. B. Cheng, L. Y. Chen, A. G. Michette, S. J. Pfauntsch, A. K. Powell, F. Schafers, A. Gaupp, and M. MacDonald, “Extreme ultraviolet broadband Mo/Y multilayer analyzers,” Appl. Phys. Lett. 89, 241120–241122 (2006).
[Crossref]

Z. S. Wang, F. L. Wang, Z. Zhong, H. C. Wang, W. J. Wu, S. M. Zhang, Y. Xu, Z. X. Gu, X. B. Cheng, C. X. Li, Y. R. Wu, B. Wang, S. J. Qin, and L. Y. Chen, “Research of multilayers in EUV, soft X-ray and X-ray,” Opt. Precis. Eng. 13, 512–518 (2005).

Lopatin, A. Ya.

S. S. Andreev, M. S. Bibishkin, N. I. Chkhalo, A. Ya. Lopatin, V. I. Luchin, A. E. Pestov, K. A. Prokhorov, and N. N. Salaschchenko, “Application of free-standing multilayer films as polarizers for x-ray radiation,” Nucl. Instrum, Methods A543, 340–345 (2005).

Luchin, V. I.

S. S. Andreev, M. S. Bibishkin, N. I. Chkhalo, A. Ya. Lopatin, V. I. Luchin, A. E. Pestov, K. A. Prokhorov, and N. N. Salaschchenko, “Application of free-standing multilayer films as polarizers for x-ray radiation,” Nucl. Instrum, Methods A543, 340–345 (2005).

MacDonald, M.

Z. S. Wang, H. C. Wang, J. T. Zhu, Y. Xu, S. M. Zhang, C. X. Li, F. L. Wang, Z. Zhang, Y. R. Wu, X. B. Cheng, L. Y. Chen, A. G. Michette, S. J. Pfauntsch, A. K. Powell, F. Schafers, A. Gaupp, and M. MacDonald, “Extreme ultraviolet broadband Mo/Y multilayer analyzers,” Appl. Phys. Lett. 89, 241120–241122 (2006).
[Crossref]

Mayama, K.

H. Nomura, K. Mayama, T. Sasaki, M. Yamamoto, and M. Yanagihara, “Design, fabrication, and polarization of soft-x-ray transmission multilayers,” Proc. SPIE 1720, 395–401 (1992).
[Crossref]

Mertins, H. C.

H. Grimmer, O. Zaharko, M. Horisberger, H. C. Mertins, F. Schaefers, and U. Staub, “Optical components for polarization analysis of soft x-ray radiation,” Proc. SPIE 3773, 224–235 (1999).
[Crossref]

Michette, A. G.

Z. S. Wang, H. C. Wang, J. T. Zhu, Y. Xu, S. M. Zhang, C. X. Li, F. L. Wang, Z. Zhang, Y. R. Wu, X. B. Cheng, L. Y. Chen, A. G. Michette, S. J. Pfauntsch, A. K. Powell, F. Schafers, A. Gaupp, and M. MacDonald, “Extreme ultraviolet broadband Mo/Y multilayer analyzers,” Appl. Phys. Lett. 89, 241120–241122 (2006).
[Crossref]

Mrowka, S.

Nomura, H.

H. Nomura, K. Mayama, T. Sasaki, M. Yamamoto, and M. Yanagihara, “Design, fabrication, and polarization of soft-x-ray transmission multilayers,” Proc. SPIE 1720, 395–401 (1992).
[Crossref]

Pestov, A. E.

S. S. Andreev, M. S. Bibishkin, N. I. Chkhalo, A. Ya. Lopatin, V. I. Luchin, A. E. Pestov, K. A. Prokhorov, and N. N. Salaschchenko, “Application of free-standing multilayer films as polarizers for x-ray radiation,” Nucl. Instrum, Methods A543, 340–345 (2005).

Pfauntsch, S. J.

Z. S. Wang, H. C. Wang, J. T. Zhu, Y. Xu, S. M. Zhang, C. X. Li, F. L. Wang, Z. Zhang, Y. R. Wu, X. B. Cheng, L. Y. Chen, A. G. Michette, S. J. Pfauntsch, A. K. Powell, F. Schafers, A. Gaupp, and M. MacDonald, “Extreme ultraviolet broadband Mo/Y multilayer analyzers,” Appl. Phys. Lett. 89, 241120–241122 (2006).
[Crossref]

Powell, A. K.

Z. S. Wang, H. C. Wang, J. T. Zhu, Y. Xu, S. M. Zhang, C. X. Li, F. L. Wang, Z. Zhang, Y. R. Wu, X. B. Cheng, L. Y. Chen, A. G. Michette, S. J. Pfauntsch, A. K. Powell, F. Schafers, A. Gaupp, and M. MacDonald, “Extreme ultraviolet broadband Mo/Y multilayer analyzers,” Appl. Phys. Lett. 89, 241120–241122 (2006).
[Crossref]

Prokhorov, K. A.

S. S. Andreev, M. S. Bibishkin, N. I. Chkhalo, A. Ya. Lopatin, V. I. Luchin, A. E. Pestov, K. A. Prokhorov, and N. N. Salaschchenko, “Application of free-standing multilayer films as polarizers for x-ray radiation,” Nucl. Instrum, Methods A543, 340–345 (2005).

Qin, S. J.

J. T. Zhu, Z. S. Wang, H. C. Wang, Z. Zhang, F. L. Wang, S. J. Qin, L. Y. Chen, M. Q. Cui, Y. D. Zhao, L. J. Sun, H. J. Zhou, and T. L. Huo, “Broadband aperiodic Mo/ Si multilayer polarization elements for EUV region,” Opt. Precis. Eng. 15, 1886–1893 (2007).

Z. S. Wang, F. L. Wang, Z. Zhong, H. C. Wang, W. J. Wu, S. M. Zhang, Y. Xu, Z. X. Gu, X. B. Cheng, C. X. Li, Y. R. Wu, B. Wang, S. J. Qin, and L. Y. Chen, “Research of multilayers in EUV, soft X-ray and X-ray,” Opt. Precis. Eng. 13, 512–518 (2005).

Raasch, D.

P. Fischer, G. Schutz, G. Schmahl, P. Guttmann, and D. Raasch, “Imaging of magnetic domains with the X-ray microscope at BESSY using X-ray magnetic circular dichroism,” Z. Phys. B101, 313–316 (1996).
[Crossref]

Rice, M.

J. B. Kortright, M. Rice, and R. Carr, “Soft-x-ray Faraday rotation at Fe L2,3 edges,” Phys. Rev. B51, 10240–10244 (1995).

Salaschchenko, N. N.

S. S. Andreev, M. S. Bibishkin, N. I. Chkhalo, A. Ya. Lopatin, V. I. Luchin, A. E. Pestov, K. A. Prokhorov, and N. N. Salaschchenko, “Application of free-standing multilayer films as polarizers for x-ray radiation,” Nucl. Instrum, Methods A543, 340–345 (2005).

Salashchenko, N. N.

E. S. Gluskin, S. V. Gaponov, P. Dhez, P. P. Ilyinsky, N. N. Salashchenko, Yu. M. Shatunov, and E. M. Trakhtenberg, “A polarimeter for soft X-ray and VUV radiation,” Nucl. Instrum. Methods A246, 394–396 (1986).

Sasaki, T.

H. Nomura, K. Mayama, T. Sasaki, M. Yamamoto, and M. Yanagihara, “Design, fabrication, and polarization of soft-x-ray transmission multilayers,” Proc. SPIE 1720, 395–401 (1992).
[Crossref]

Schaefers, F.

H. Grimmer, O. Zaharko, M. Horisberger, H. C. Mertins, F. Schaefers, and U. Staub, “Optical components for polarization analysis of soft x-ray radiation,” Proc. SPIE 3773, 224–235 (1999).
[Crossref]

Schafers, F.

Z. S. Wang, H. C. Wang, J. T. Zhu, Y. Xu, S. M. Zhang, C. X. Li, F. L. Wang, Z. Zhang, Y. R. Wu, X. B. Cheng, L. Y. Chen, A. G. Michette, S. J. Pfauntsch, A. K. Powell, F. Schafers, A. Gaupp, and M. MacDonald, “Extreme ultraviolet broadband Mo/Y multilayer analyzers,” Appl. Phys. Lett. 89, 241120–241122 (2006).
[Crossref]

Schmahl, G.

P. Fischer, G. Schutz, G. Schmahl, P. Guttmann, and D. Raasch, “Imaging of magnetic domains with the X-ray microscope at BESSY using X-ray magnetic circular dichroism,” Z. Phys. B101, 313–316 (1996).
[Crossref]

Schutz, G.

P. Fischer, G. Schutz, G. Schmahl, P. Guttmann, and D. Raasch, “Imaging of magnetic domains with the X-ray microscope at BESSY using X-ray magnetic circular dichroism,” Z. Phys. B101, 313–316 (1996).
[Crossref]

Seely, J. F.

Shatunov, Yu. M.

E. S. Gluskin, S. V. Gaponov, P. Dhez, P. P. Ilyinsky, N. N. Salashchenko, Yu. M. Shatunov, and E. M. Trakhtenberg, “A polarimeter for soft X-ray and VUV radiation,” Nucl. Instrum. Methods A246, 394–396 (1986).

Staub, U.

H. Grimmer, O. Zaharko, M. Horisberger, H. C. Mertins, F. Schaefers, and U. Staub, “Optical components for polarization analysis of soft x-ray radiation,” Proc. SPIE 3773, 224–235 (1999).
[Crossref]

Stearns, D. G.

D. G. Stearns, “X-ray scattering from interfacial roughness in multilayer structures,” J. Appl. Phys. 71, 4286–4296 (1992).
[Crossref]

D. G. Stearns, “The scattering of x rays from nonideal multiplayer structures,” J. Appl. Phys. 65, 491–506 (1989).
[Crossref]

Sun, L. J.

J. T. Zhu, Z. S. Wang, H. C. Wang, Z. Zhang, F. L. Wang, S. J. Qin, L. Y. Chen, M. Q. Cui, Y. D. Zhao, L. J. Sun, H. J. Zhou, and T. L. Huo, “Broadband aperiodic Mo/ Si multilayer polarization elements for EUV region,” Opt. Precis. Eng. 15, 1886–1893 (2007).

Tang, J. F.

J. F. Tang and Q. Zheng, Applied Thin Film Optics, (Shanghai Science and Technology Press; Shanghai1984: 57–60).

Trakhtenberg, E. M.

E. S. Gluskin, S. V. Gaponov, P. Dhez, P. P. Ilyinsky, N. N. Salashchenko, Yu. M. Shatunov, and E. M. Trakhtenberg, “A polarimeter for soft X-ray and VUV radiation,” Nucl. Instrum. Methods A246, 394–396 (1986).

Underwood, J. H.

J. B. Kortright and J. H. Underwood, “Multilayer Optical Elements for Generation and Analysis of Circularly Polarized X-rays,” Nucl. Instrum. Methods A291, 272–277 (1990).

Utsumi, Y.

T. Haga, Y. Utsumi, and S. Itabashia, “Soft X-ray Ellipsometer using Transmissive Multilayer Polarizers,” Proc. SPIE 3443, 117–127(1998).
[Crossref]

Wang, B.

Z. S. Wang, F. L. Wang, Z. Zhong, H. C. Wang, W. J. Wu, S. M. Zhang, Y. Xu, Z. X. Gu, X. B. Cheng, C. X. Li, Y. R. Wu, B. Wang, S. J. Qin, and L. Y. Chen, “Research of multilayers in EUV, soft X-ray and X-ray,” Opt. Precis. Eng. 13, 512–518 (2005).

Wang, F. L.

J. T. Zhu, Z. S. Wang, H. C. Wang, Z. Zhang, F. L. Wang, S. J. Qin, L. Y. Chen, M. Q. Cui, Y. D. Zhao, L. J. Sun, H. J. Zhou, and T. L. Huo, “Broadband aperiodic Mo/ Si multilayer polarization elements for EUV region,” Opt. Precis. Eng. 15, 1886–1893 (2007).

Z. S. Wang, H. C. Wang, J. T. Zhu, Y. Xu, S. M. Zhang, C. X. Li, F. L. Wang, Z. Zhang, Y. R. Wu, X. B. Cheng, L. Y. Chen, A. G. Michette, S. J. Pfauntsch, A. K. Powell, F. Schafers, A. Gaupp, and M. MacDonald, “Extreme ultraviolet broadband Mo/Y multilayer analyzers,” Appl. Phys. Lett. 89, 241120–241122 (2006).
[Crossref]

Z. S. Wang, F. L. Wang, Z. Zhong, H. C. Wang, W. J. Wu, S. M. Zhang, Y. Xu, Z. X. Gu, X. B. Cheng, C. X. Li, Y. R. Wu, B. Wang, S. J. Qin, and L. Y. Chen, “Research of multilayers in EUV, soft X-ray and X-ray,” Opt. Precis. Eng. 13, 512–518 (2005).

Wang, H. C.

J. T. Zhu, Z. S. Wang, H. C. Wang, Z. Zhang, F. L. Wang, S. J. Qin, L. Y. Chen, M. Q. Cui, Y. D. Zhao, L. J. Sun, H. J. Zhou, and T. L. Huo, “Broadband aperiodic Mo/ Si multilayer polarization elements for EUV region,” Opt. Precis. Eng. 15, 1886–1893 (2007).

Z. S. Wang, H. C. Wang, J. T. Zhu, Y. Xu, S. M. Zhang, C. X. Li, F. L. Wang, Z. Zhang, Y. R. Wu, X. B. Cheng, L. Y. Chen, A. G. Michette, S. J. Pfauntsch, A. K. Powell, F. Schafers, A. Gaupp, and M. MacDonald, “Extreme ultraviolet broadband Mo/Y multilayer analyzers,” Appl. Phys. Lett. 89, 241120–241122 (2006).
[Crossref]

Z. S. Wang, F. L. Wang, Z. Zhong, H. C. Wang, W. J. Wu, S. M. Zhang, Y. Xu, Z. X. Gu, X. B. Cheng, C. X. Li, Y. R. Wu, B. Wang, S. J. Qin, and L. Y. Chen, “Research of multilayers in EUV, soft X-ray and X-ray,” Opt. Precis. Eng. 13, 512–518 (2005).

Wang, Z. S.

J. T. Zhu, Z. S. Wang, H. C. Wang, Z. Zhang, F. L. Wang, S. J. Qin, L. Y. Chen, M. Q. Cui, Y. D. Zhao, L. J. Sun, H. J. Zhou, and T. L. Huo, “Broadband aperiodic Mo/ Si multilayer polarization elements for EUV region,” Opt. Precis. Eng. 15, 1886–1893 (2007).

Z. S. Wang, H. C. Wang, J. T. Zhu, Y. Xu, S. M. Zhang, C. X. Li, F. L. Wang, Z. Zhang, Y. R. Wu, X. B. Cheng, L. Y. Chen, A. G. Michette, S. J. Pfauntsch, A. K. Powell, F. Schafers, A. Gaupp, and M. MacDonald, “Extreme ultraviolet broadband Mo/Y multilayer analyzers,” Appl. Phys. Lett. 89, 241120–241122 (2006).
[Crossref]

Z. S. Wang, F. L. Wang, Z. Zhong, H. C. Wang, W. J. Wu, S. M. Zhang, Y. Xu, Z. X. Gu, X. B. Cheng, C. X. Li, Y. R. Wu, B. Wang, S. J. Qin, and L. Y. Chen, “Research of multilayers in EUV, soft X-ray and X-ray,” Opt. Precis. Eng. 13, 512–518 (2005).

Watanabe, M.

W. Hu, T. Hatano, M. Yamamoto, and M. Watanabe, “Transmission multilayer polarizers for use in the 55-90eV region,” J Synchrotron Rad. 5, 732–734 (1998).
[Crossref]

W. Hu, M. Yamamoto, and M. Watanabe, “Development of EUV free-standing multilayer polarizers,” Proc. SPIE 2873, 74–77 (1996).

Wende, H. W.

H. W. Wende, J. Freeland, V. Chakarian, Y. U. Idzerda, L. Lemke, and K. Baberschke, “Probing local magnetic disorder by investigating spin dependent photoelectron scattering,” J. Appl. Phys. 83, 7028–7030 (1998).
[Crossref]

Wu, W. J.

Z. S. Wang, F. L. Wang, Z. Zhong, H. C. Wang, W. J. Wu, S. M. Zhang, Y. Xu, Z. X. Gu, X. B. Cheng, C. X. Li, Y. R. Wu, B. Wang, S. J. Qin, and L. Y. Chen, “Research of multilayers in EUV, soft X-ray and X-ray,” Opt. Precis. Eng. 13, 512–518 (2005).

Wu, Y. R.

Z. S. Wang, H. C. Wang, J. T. Zhu, Y. Xu, S. M. Zhang, C. X. Li, F. L. Wang, Z. Zhang, Y. R. Wu, X. B. Cheng, L. Y. Chen, A. G. Michette, S. J. Pfauntsch, A. K. Powell, F. Schafers, A. Gaupp, and M. MacDonald, “Extreme ultraviolet broadband Mo/Y multilayer analyzers,” Appl. Phys. Lett. 89, 241120–241122 (2006).
[Crossref]

Z. S. Wang, F. L. Wang, Z. Zhong, H. C. Wang, W. J. Wu, S. M. Zhang, Y. Xu, Z. X. Gu, X. B. Cheng, C. X. Li, Y. R. Wu, B. Wang, S. J. Qin, and L. Y. Chen, “Research of multilayers in EUV, soft X-ray and X-ray,” Opt. Precis. Eng. 13, 512–518 (2005).

Xu, Y.

Z. S. Wang, H. C. Wang, J. T. Zhu, Y. Xu, S. M. Zhang, C. X. Li, F. L. Wang, Z. Zhang, Y. R. Wu, X. B. Cheng, L. Y. Chen, A. G. Michette, S. J. Pfauntsch, A. K. Powell, F. Schafers, A. Gaupp, and M. MacDonald, “Extreme ultraviolet broadband Mo/Y multilayer analyzers,” Appl. Phys. Lett. 89, 241120–241122 (2006).
[Crossref]

Z. S. Wang, F. L. Wang, Z. Zhong, H. C. Wang, W. J. Wu, S. M. Zhang, Y. Xu, Z. X. Gu, X. B. Cheng, C. X. Li, Y. R. Wu, B. Wang, S. J. Qin, and L. Y. Chen, “Research of multilayers in EUV, soft X-ray and X-ray,” Opt. Precis. Eng. 13, 512–518 (2005).

Yamamoto, M.

W. Hu, T. Hatano, M. Yamamoto, and M. Watanabe, “Transmission multilayer polarizers for use in the 55-90eV region,” J Synchrotron Rad. 5, 732–734 (1998).
[Crossref]

W. Hu, M. Yamamoto, and M. Watanabe, “Development of EUV free-standing multilayer polarizers,” Proc. SPIE 2873, 74–77 (1996).

M. Yamamoto, “Polarimetry with use of soft x-ray multilayers,” Proc. SPIE 2010, 152–159 (1993).
[Crossref]

H. Nomura, K. Mayama, T. Sasaki, M. Yamamoto, and M. Yanagihara, “Design, fabrication, and polarization of soft-x-ray transmission multilayers,” Proc. SPIE 1720, 395–401 (1992).
[Crossref]

Yanagihara, M.

H. Nomura, K. Mayama, T. Sasaki, M. Yamamoto, and M. Yanagihara, “Design, fabrication, and polarization of soft-x-ray transmission multilayers,” Proc. SPIE 1720, 395–401 (1992).
[Crossref]

Zaharko, O.

H. Grimmer, O. Zaharko, M. Horisberger, H. C. Mertins, F. Schaefers, and U. Staub, “Optical components for polarization analysis of soft x-ray radiation,” Proc. SPIE 3773, 224–235 (1999).
[Crossref]

Zhang, S. M.

Z. S. Wang, H. C. Wang, J. T. Zhu, Y. Xu, S. M. Zhang, C. X. Li, F. L. Wang, Z. Zhang, Y. R. Wu, X. B. Cheng, L. Y. Chen, A. G. Michette, S. J. Pfauntsch, A. K. Powell, F. Schafers, A. Gaupp, and M. MacDonald, “Extreme ultraviolet broadband Mo/Y multilayer analyzers,” Appl. Phys. Lett. 89, 241120–241122 (2006).
[Crossref]

Z. S. Wang, F. L. Wang, Z. Zhong, H. C. Wang, W. J. Wu, S. M. Zhang, Y. Xu, Z. X. Gu, X. B. Cheng, C. X. Li, Y. R. Wu, B. Wang, S. J. Qin, and L. Y. Chen, “Research of multilayers in EUV, soft X-ray and X-ray,” Opt. Precis. Eng. 13, 512–518 (2005).

Zhang, Z.

J. T. Zhu, Z. S. Wang, H. C. Wang, Z. Zhang, F. L. Wang, S. J. Qin, L. Y. Chen, M. Q. Cui, Y. D. Zhao, L. J. Sun, H. J. Zhou, and T. L. Huo, “Broadband aperiodic Mo/ Si multilayer polarization elements for EUV region,” Opt. Precis. Eng. 15, 1886–1893 (2007).

Z. S. Wang, H. C. Wang, J. T. Zhu, Y. Xu, S. M. Zhang, C. X. Li, F. L. Wang, Z. Zhang, Y. R. Wu, X. B. Cheng, L. Y. Chen, A. G. Michette, S. J. Pfauntsch, A. K. Powell, F. Schafers, A. Gaupp, and M. MacDonald, “Extreme ultraviolet broadband Mo/Y multilayer analyzers,” Appl. Phys. Lett. 89, 241120–241122 (2006).
[Crossref]

Zhao, Y. D.

J. T. Zhu, Z. S. Wang, H. C. Wang, Z. Zhang, F. L. Wang, S. J. Qin, L. Y. Chen, M. Q. Cui, Y. D. Zhao, L. J. Sun, H. J. Zhou, and T. L. Huo, “Broadband aperiodic Mo/ Si multilayer polarization elements for EUV region,” Opt. Precis. Eng. 15, 1886–1893 (2007).

Zheng, Q.

J. F. Tang and Q. Zheng, Applied Thin Film Optics, (Shanghai Science and Technology Press; Shanghai1984: 57–60).

Zhong, Z.

Z. S. Wang, F. L. Wang, Z. Zhong, H. C. Wang, W. J. Wu, S. M. Zhang, Y. Xu, Z. X. Gu, X. B. Cheng, C. X. Li, Y. R. Wu, B. Wang, S. J. Qin, and L. Y. Chen, “Research of multilayers in EUV, soft X-ray and X-ray,” Opt. Precis. Eng. 13, 512–518 (2005).

Zhou, H. J.

J. T. Zhu, Z. S. Wang, H. C. Wang, Z. Zhang, F. L. Wang, S. J. Qin, L. Y. Chen, M. Q. Cui, Y. D. Zhao, L. J. Sun, H. J. Zhou, and T. L. Huo, “Broadband aperiodic Mo/ Si multilayer polarization elements for EUV region,” Opt. Precis. Eng. 15, 1886–1893 (2007).

Zhu, J. T.

J. T. Zhu, Z. S. Wang, H. C. Wang, Z. Zhang, F. L. Wang, S. J. Qin, L. Y. Chen, M. Q. Cui, Y. D. Zhao, L. J. Sun, H. J. Zhou, and T. L. Huo, “Broadband aperiodic Mo/ Si multilayer polarization elements for EUV region,” Opt. Precis. Eng. 15, 1886–1893 (2007).

Z. S. Wang, H. C. Wang, J. T. Zhu, Y. Xu, S. M. Zhang, C. X. Li, F. L. Wang, Z. Zhang, Y. R. Wu, X. B. Cheng, L. Y. Chen, A. G. Michette, S. J. Pfauntsch, A. K. Powell, F. Schafers, A. Gaupp, and M. MacDonald, “Extreme ultraviolet broadband Mo/Y multilayer analyzers,” Appl. Phys. Lett. 89, 241120–241122 (2006).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

Z. S. Wang, H. C. Wang, J. T. Zhu, Y. Xu, S. M. Zhang, C. X. Li, F. L. Wang, Z. Zhang, Y. R. Wu, X. B. Cheng, L. Y. Chen, A. G. Michette, S. J. Pfauntsch, A. K. Powell, F. Schafers, A. Gaupp, and M. MacDonald, “Extreme ultraviolet broadband Mo/Y multilayer analyzers,” Appl. Phys. Lett. 89, 241120–241122 (2006).
[Crossref]

J Synchrotron Rad. (1)

W. Hu, T. Hatano, M. Yamamoto, and M. Watanabe, “Transmission multilayer polarizers for use in the 55-90eV region,” J Synchrotron Rad. 5, 732–734 (1998).
[Crossref]

J. Appl. Phys. (3)

D. G. Stearns, “The scattering of x rays from nonideal multiplayer structures,” J. Appl. Phys. 65, 491–506 (1989).
[Crossref]

D. G. Stearns, “X-ray scattering from interfacial roughness in multilayer structures,” J. Appl. Phys. 71, 4286–4296 (1992).
[Crossref]

H. W. Wende, J. Freeland, V. Chakarian, Y. U. Idzerda, L. Lemke, and K. Baberschke, “Probing local magnetic disorder by investigating spin dependent photoelectron scattering,” J. Appl. Phys. 83, 7028–7030 (1998).
[Crossref]

Nucl. Instrum, Methods (1)

S. S. Andreev, M. S. Bibishkin, N. I. Chkhalo, A. Ya. Lopatin, V. I. Luchin, A. E. Pestov, K. A. Prokhorov, and N. N. Salaschchenko, “Application of free-standing multilayer films as polarizers for x-ray radiation,” Nucl. Instrum, Methods A543, 340–345 (2005).

Nucl. Instrum. Methods (2)

E. S. Gluskin, S. V. Gaponov, P. Dhez, P. P. Ilyinsky, N. N. Salashchenko, Yu. M. Shatunov, and E. M. Trakhtenberg, “A polarimeter for soft X-ray and VUV radiation,” Nucl. Instrum. Methods A246, 394–396 (1986).

J. B. Kortright and J. H. Underwood, “Multilayer Optical Elements for Generation and Analysis of Circularly Polarized X-rays,” Nucl. Instrum. Methods A291, 272–277 (1990).

Opt. Precis. Eng. (2)

Z. S. Wang, F. L. Wang, Z. Zhong, H. C. Wang, W. J. Wu, S. M. Zhang, Y. Xu, Z. X. Gu, X. B. Cheng, C. X. Li, Y. R. Wu, B. Wang, S. J. Qin, and L. Y. Chen, “Research of multilayers in EUV, soft X-ray and X-ray,” Opt. Precis. Eng. 13, 512–518 (2005).

J. T. Zhu, Z. S. Wang, H. C. Wang, Z. Zhang, F. L. Wang, S. J. Qin, L. Y. Chen, M. Q. Cui, Y. D. Zhao, L. J. Sun, H. J. Zhou, and T. L. Huo, “Broadband aperiodic Mo/ Si multilayer polarization elements for EUV region,” Opt. Precis. Eng. 15, 1886–1893 (2007).

Phys. Rev. (1)

J. B. Kortright, M. Rice, and R. Carr, “Soft-x-ray Faraday rotation at Fe L2,3 edges,” Phys. Rev. B51, 10240–10244 (1995).

Proc. SPIE (6)

H. Nomura, K. Mayama, T. Sasaki, M. Yamamoto, and M. Yanagihara, “Design, fabrication, and polarization of soft-x-ray transmission multilayers,” Proc. SPIE 1720, 395–401 (1992).
[Crossref]

W. Hu, M. Yamamoto, and M. Watanabe, “Development of EUV free-standing multilayer polarizers,” Proc. SPIE 2873, 74–77 (1996).

T. Haga, Y. Utsumi, and S. Itabashia, “Soft X-ray Ellipsometer using Transmissive Multilayer Polarizers,” Proc. SPIE 3443, 117–127(1998).
[Crossref]

H. Grimmer, O. Zaharko, M. Horisberger, H. C. Mertins, F. Schaefers, and U. Staub, “Optical components for polarization analysis of soft x-ray radiation,” Proc. SPIE 3773, 224–235 (1999).
[Crossref]

A. Khandar and P. Dhez, “Multilayer X-ray polarizers,” Proc. SPIE 563, 158–163 (1985).

M. Yamamoto, “Polarimetry with use of soft x-ray multilayers,” Proc. SPIE 2010, 152–159 (1993).
[Crossref]

Z. Phys. (1)

P. Fischer, G. Schutz, G. Schmahl, P. Guttmann, and D. Raasch, “Imaging of magnetic domains with the X-ray microscope at BESSY using X-ray magnetic circular dichroism,” Z. Phys. B101, 313–316 (1996).
[Crossref]

Other (2)

J. F. Tang and Q. Zheng, Applied Thin Film Optics, (Shanghai Science and Technology Press; Shanghai1984: 57–60).

http://www-cxro.lbl.gov/, Jan 24, 2008

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Figures (15)

Fig. 1.
Fig. 1. Schematic of multilayer structure
Fig. 2.
Fig. 2. Incident angle dependence of p-transmittance Tp and polarization ratio Tp /Ts of Mo/Si multilayers at wavelength of 13.0 nm.
Fig. 3.
Fig. 3. Layer number dependence of p-transmittance Tp and polarization ratio Tp /Ts of Mo/Si multilayers at wavelength of 13.0 nm at incident angle of 43.0°.
Fig. 4.
Fig. 4. Incident angle dependence of merit function I Tp log10(Tp /Ts ) of Mo/Si multilayers with different layer numbers for use at wavelength of 13.0 nm.
Fig. 5.
Fig. 5. Layer number dependence of merit function I Tp log10(Tp /Ts ) of Mo/Si multilayers for use at wavelength of 13.0 nm at incident angle of 43.0°.
Fig. 6.
Fig. 6. Layer number dependence of p-transmittance Tp and polarization ratio Tp /Ts of Mo/Si multilayers at wavelength of 13.0 nm at incident angle of 43.0° using merit function I Tp log10(Tp /Ts ).
Fig. 7.
Fig. 7. Incident angle dependence of merit function II Rs ./Rp . with different layers of Mo/Si multilayers with different layer numbers for use at wavelength of 13.0 nm.
Fig. 8.
Fig. 8. Layer number dependence of merit function II Rs ./Rp . of Mo/Si multilayers for use at wavelength of 13.0 nm at incident angle of 43.0 °.
Fig. 9.
Fig. 9. Layer number dependence of p-transmittance Tp and polarization ratio Tp /Ts of Mo/Si multilayers at wavelength of 13.0 nm at incident angle of 43.0° using merit function II Rs /Rp .
Fig. 10.
Fig. 10. Layer number dependence of Rs of Mo/Si multilayers for use at wavelength of 13.0 nm at incident of 45.0°.
Fig. 11.
Fig. 11. Layer number dependence of p-transmittance Tp and polarization ratio Tp /Ts of Mo/Si multilayers at wavelength of 13.0 nm at incident angle of 45.0°.
Fig. 12.
Fig. 12. The s- and p-transmittance (Ts , Tp ) spectra of Mo/Si multilayers with different roughnesses σ for use at wavelength of 13.0 nm at incident angle of 43.0°.
Fig. 13.
Fig. 13. Polarization ratio Tp /Ts spectra of Mo/Si transmission multilayers with different roughnesses σ for use at wavelength of 13.0 nm at incident angle of 43.0°.
Fig. 14.
Fig. 14. The s- and p-transmittance Ts , Tp spectra of La/B multilayers with different roughnesses σ for use at wavelength of 6.7 nm at incident angle of 44.5 °.
Fig. 15.
Fig. 15. Polarization ratio (Tp /Ts ) spectra of La/B transmission multilayers with different roughnesses σ for use at wavelength of 6.7 nm at incident angle of 44.5°.

Tables (3)

Tables Icon

Table 1 Characteristics of multilayers for use at 13.0 nm calculated using merit functions

Tables Icon

Table 2 Characteristics of multilayers for use at 13.0 nm calculated using traditional method

Tables Icon

Table 3 Characteristics of multilayers for use at 12.8, 13.5 and 15.5 nm calculated using merit function I and designed in references

Equations (11)

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

r ' j p = n ˜ j 1 cos θ j n ˜ j cos θ j 1 n ˜ j 1 cos θ j + n ˜ j cos θ j 1
r ' j s = n ˜ j 1 cos θ j 1 n ˜ j cos θ j n ˜ j 1 cos θ j 1 + n ˜ j cos θ j
t ' j p = 2 n ˜ j 1 cos θ j 1 n ˜ j 1 cos θ j + n ˜ j cos θ j 1
t ' j s = 2 n ˜ j 1 cos θ j 1 n ˜ j 1 cos θ j 1 + n ˜ j cos θ j
r j = r j ' + r j + 1 exp ( 2 i δ j ) 1 + r j ' r j + 1 exp ( 2 i δ j )
t j = t j 1 t j ' exp ( i δ j 1 ) 1 + r j 1 ' r j exp ( 2 i δ j 1 )
R ( s , p ) = r 1 ( s , p ) · r 1 ( s , p ) *
T ( s , p ) = t m ( s , p ) · t m ( s , p ) *
D W j = exp [ 2 ( 2 π σ j cos θ j / λ ) 2 ]
F = T p × log 10 ( T p T s )
F = R s / R p

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