Abstract

Polarization control is of vital importance in two-axis Lloyd’s mirror interference lithography to achieve the preferred interference fringes. In this work, we first establish a three-dimensional polarization ray-tracing model to trace the evolution of polarization states of incident beams through the corner-cube-like interferometer unit of an orthogonal two-axis Lloyd’s mirror interferometer. With the established model, we then derive the optimal combination of initial polarization directions of the incident beams according to the orthogonality of polarization states and the contrast of interference fringes. The comparison between the simulated and experimental interference fringes obtained under different combinations of initial polarization states of incident beams verify the feasibility of the established model and the achieved optimal polarization modulation.

© 2017 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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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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2016 (2)

2015 (2)

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann.-. Manuf. Technol. 64(2), 773–796 (2015).
[Crossref]

H. L. Hsieh and S. W. Pan, “Development of a grating-based interferometer for six-degree-of-freedom displacement and angle measurements,” Opt. Express 23(3), 2451–2465 (2015).
[Crossref] [PubMed]

2014 (2)

X. Li, W. Gao, Y. Shimizu, and S. Ito, “A two-axis Lloyd’s mirror interferometer for fabrication of two-dimensional diffraction gratings,” CIRP Ann.-. Manuf. Technol. 63(1), 461–464 (2014).
[Crossref]

M. Vala and J. Homola, “Flexible method based on four-beam interference lithography for fabrication of large areas of perfectly periodic plasmonic arrays,” Opt. Express 22(15), 18778–18789 (2014).
[Crossref] [PubMed]

2013 (1)

X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng. 37(3), 771–781 (2013).
[Crossref]

2012 (1)

A. Kimura, W. Gao, W. J. Kim, K. Hosono, Y. Shimizu, L. Shi, and L. J. Zeng, “Sub-nanometric three-axis surface encoder with short-period planar gratings for stage motion measurement,” Precis. Eng. 36(4), 576–585 (2012).
[Crossref]

2011 (2)

2010 (1)

C. Lu and R. H. Lipson, “Interference lithography: a powerful tool for fabricating periodic structures,” Laser Photonics Rev. 4(4), 568–580 (2010).
[Crossref]

2009 (1)

2003 (1)

W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka, “Precision nano-fabrication and evaluation of a large area sinusoidal grid surface for a surface encoder,” Precis. Eng. 27(3), 289–298 (2003).
[Crossref]

2002 (1)

R. F. Pease, “Semiconductor technology: imprints offer Moore,” Nature 417(6891), 802–803 (2002).
[Crossref] [PubMed]

1997 (1)

J. A. Rogers, K. E. Paul, R. J. Jackman, and G. M. Whitesides, “Using an elastomeric phase mask for sub-100 nm photolithography in the optical near field,” Appl. Phys. Lett. 70(20), 2658–2660 (1997).
[Crossref]

1991 (1)

W. S. Blackley and R. O. Scattergood, “Ductile-regime machining model for diamond turning of brittle materials,” Precis. Eng. 13(2), 95–103 (1991).
[Crossref]

1949 (1)

1941 (1)

Aihara, R.

Araki, T.

W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka, “Precision nano-fabrication and evaluation of a large area sinusoidal grid surface for a surface encoder,” Precis. Eng. 27(3), 289–298 (2003).
[Crossref]

Azzam, R. M. A.

Blackley, W. S.

W. S. Blackley and R. O. Scattergood, “Ductile-regime machining model for diamond turning of brittle materials,” Precis. Eng. 13(2), 95–103 (1991).
[Crossref]

Bosse, H.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann.-. Manuf. Technol. 64(2), 773–796 (2015).
[Crossref]

Chen, Y. L.

Y. Shimizu, R. Aihara, Z. Ren, Y. L. Chen, S. Ito, and W. Gao, “Influences of misalignment errors of optical components in an orthogonal two-axis Lloyd’s mirror interferometer,” Opt. Express 24(24), 27521–27535 (2016).
[Crossref] [PubMed]

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann.-. Manuf. Technol. 64(2), 773–796 (2015).
[Crossref]

Chipman, R. A.

Crabtree, K.

de Boor, J.

Dian, S.

X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng. 37(3), 771–781 (2013).
[Crossref]

Estler, W. T.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann.-. Manuf. Technol. 64(2), 773–796 (2015).
[Crossref]

Gao, W.

Y. Shimizu, R. Aihara, Z. Ren, Y. L. Chen, S. Ito, and W. Gao, “Influences of misalignment errors of optical components in an orthogonal two-axis Lloyd’s mirror interferometer,” Opt. Express 24(24), 27521–27535 (2016).
[Crossref] [PubMed]

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann.-. Manuf. Technol. 64(2), 773–796 (2015).
[Crossref]

X. Li, W. Gao, Y. Shimizu, and S. Ito, “A two-axis Lloyd’s mirror interferometer for fabrication of two-dimensional diffraction gratings,” CIRP Ann.-. Manuf. Technol. 63(1), 461–464 (2014).
[Crossref]

X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng. 37(3), 771–781 (2013).
[Crossref]

A. Kimura, W. Gao, W. J. Kim, K. Hosono, Y. Shimizu, L. Shi, and L. J. Zeng, “Sub-nanometric three-axis surface encoder with short-period planar gratings for stage motion measurement,” Precis. Eng. 36(4), 576–585 (2012).
[Crossref]

W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka, “Precision nano-fabrication and evaluation of a large area sinusoidal grid surface for a surface encoder,” Precis. Eng. 27(3), 289–298 (2003).
[Crossref]

Geyer, N.

Gösele, U.

Haitjema, H.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann.-. Manuf. Technol. 64(2), 773–796 (2015).
[Crossref]

Harrison, G. R.

Homola, J.

Hosono, K.

A. Kimura, W. Gao, W. J. Kim, K. Hosono, Y. Shimizu, L. Shi, and L. J. Zeng, “Sub-nanometric three-axis surface encoder with short-period planar gratings for stage motion measurement,” Precis. Eng. 36(4), 576–585 (2012).
[Crossref]

Hsieh, H. L.

Ito, S.

Y. Shimizu, R. Aihara, Z. Ren, Y. L. Chen, S. Ito, and W. Gao, “Influences of misalignment errors of optical components in an orthogonal two-axis Lloyd’s mirror interferometer,” Opt. Express 24(24), 27521–27535 (2016).
[Crossref] [PubMed]

X. Li, W. Gao, Y. Shimizu, and S. Ito, “A two-axis Lloyd’s mirror interferometer for fabrication of two-dimensional diffraction gratings,” CIRP Ann.-. Manuf. Technol. 63(1), 461–464 (2014).
[Crossref]

X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng. 37(3), 771–781 (2013).
[Crossref]

Jackman, R. J.

J. A. Rogers, K. E. Paul, R. J. Jackman, and G. M. Whitesides, “Using an elastomeric phase mask for sub-100 nm photolithography in the optical near field,” Appl. Phys. Lett. 70(20), 2658–2660 (1997).
[Crossref]

Jones, R. C.

Kim, S. W.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann.-. Manuf. Technol. 64(2), 773–796 (2015).
[Crossref]

Kim, W. J.

A. Kimura, W. Gao, W. J. Kim, K. Hosono, Y. Shimizu, L. Shi, and L. J. Zeng, “Sub-nanometric three-axis surface encoder with short-period planar gratings for stage motion measurement,” Precis. Eng. 36(4), 576–585 (2012).
[Crossref]

Kimura, A.

A. Kimura, W. Gao, W. J. Kim, K. Hosono, Y. Shimizu, L. Shi, and L. J. Zeng, “Sub-nanometric three-axis surface encoder with short-period planar gratings for stage motion measurement,” Precis. Eng. 36(4), 576–585 (2012).
[Crossref]

Kiyono, S.

W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka, “Precision nano-fabrication and evaluation of a large area sinusoidal grid surface for a surface encoder,” Precis. Eng. 27(3), 289–298 (2003).
[Crossref]

Knapp, W.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann.-. Manuf. Technol. 64(2), 773–796 (2015).
[Crossref]

Kunzmann, H.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann.-. Manuf. Technol. 64(2), 773–796 (2015).
[Crossref]

Li, X.

X. Li, W. Gao, Y. Shimizu, and S. Ito, “A two-axis Lloyd’s mirror interferometer for fabrication of two-dimensional diffraction gratings,” CIRP Ann.-. Manuf. Technol. 63(1), 461–464 (2014).
[Crossref]

X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng. 37(3), 771–781 (2013).
[Crossref]

Lipson, R. H.

C. Lu and R. H. Lipson, “Interference lithography: a powerful tool for fabricating periodic structures,” Laser Photonics Rev. 4(4), 568–580 (2010).
[Crossref]

Lu, C.

C. Lu and R. H. Lipson, “Interference lithography: a powerful tool for fabricating periodic structures,” Laser Photonics Rev. 4(4), 568–580 (2010).
[Crossref]

Lu, X. D.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann.-. Manuf. Technol. 64(2), 773–796 (2015).
[Crossref]

Muto, H.

X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng. 37(3), 771–781 (2013).
[Crossref]

Okazaki, Y.

W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka, “Precision nano-fabrication and evaluation of a large area sinusoidal grid surface for a surface encoder,” Precis. Eng. 27(3), 289–298 (2003).
[Crossref]

Pan, S. W.

Paul, K. E.

J. A. Rogers, K. E. Paul, R. J. Jackman, and G. M. Whitesides, “Using an elastomeric phase mask for sub-100 nm photolithography in the optical near field,” Appl. Phys. Lett. 70(20), 2658–2660 (1997).
[Crossref]

Pease, R. F.

R. F. Pease, “Semiconductor technology: imprints offer Moore,” Nature 417(6891), 802–803 (2002).
[Crossref] [PubMed]

Ren, Z.

Rogers, J. A.

J. A. Rogers, K. E. Paul, R. J. Jackman, and G. M. Whitesides, “Using an elastomeric phase mask for sub-100 nm photolithography in the optical near field,” Appl. Phys. Lett. 70(20), 2658–2660 (1997).
[Crossref]

Scattergood, R. O.

W. S. Blackley and R. O. Scattergood, “Ductile-regime machining model for diamond turning of brittle materials,” Precis. Eng. 13(2), 95–103 (1991).
[Crossref]

Schmidt, V.

Shi, L.

A. Kimura, W. Gao, W. J. Kim, K. Hosono, Y. Shimizu, L. Shi, and L. J. Zeng, “Sub-nanometric three-axis surface encoder with short-period planar gratings for stage motion measurement,” Precis. Eng. 36(4), 576–585 (2012).
[Crossref]

Shimizu, Y.

Y. Shimizu, R. Aihara, Z. Ren, Y. L. Chen, S. Ito, and W. Gao, “Influences of misalignment errors of optical components in an orthogonal two-axis Lloyd’s mirror interferometer,” Opt. Express 24(24), 27521–27535 (2016).
[Crossref] [PubMed]

X. Li, W. Gao, Y. Shimizu, and S. Ito, “A two-axis Lloyd’s mirror interferometer for fabrication of two-dimensional diffraction gratings,” CIRP Ann.-. Manuf. Technol. 63(1), 461–464 (2014).
[Crossref]

X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng. 37(3), 771–781 (2013).
[Crossref]

A. Kimura, W. Gao, W. J. Kim, K. Hosono, Y. Shimizu, L. Shi, and L. J. Zeng, “Sub-nanometric three-axis surface encoder with short-period planar gratings for stage motion measurement,” Precis. Eng. 36(4), 576–585 (2012).
[Crossref]

Vala, M.

Weckenmann, A.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann.-. Manuf. Technol. 64(2), 773–796 (2015).
[Crossref]

Whitesides, G. M.

J. A. Rogers, K. E. Paul, R. J. Jackman, and G. M. Whitesides, “Using an elastomeric phase mask for sub-100 nm photolithography in the optical near field,” Appl. Phys. Lett. 70(20), 2658–2660 (1997).
[Crossref]

Yamanaka, M.

W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka, “Precision nano-fabrication and evaluation of a large area sinusoidal grid surface for a surface encoder,” Precis. Eng. 27(3), 289–298 (2003).
[Crossref]

Yun, G.

Zeng, L.

H. Zhou and L. Zeng, “Method to fabricate orthogonal crossed gratings based on a dual Lloyd’s mirror interferometer,” Opt. Commun. 360, 68–72 (2016).
[Crossref]

Zeng, L. J.

A. Kimura, W. Gao, W. J. Kim, K. Hosono, Y. Shimizu, L. Shi, and L. J. Zeng, “Sub-nanometric three-axis surface encoder with short-period planar gratings for stage motion measurement,” Precis. Eng. 36(4), 576–585 (2012).
[Crossref]

Zhou, H.

H. Zhou and L. Zeng, “Method to fabricate orthogonal crossed gratings based on a dual Lloyd’s mirror interferometer,” Opt. Commun. 360, 68–72 (2016).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

J. A. Rogers, K. E. Paul, R. J. Jackman, and G. M. Whitesides, “Using an elastomeric phase mask for sub-100 nm photolithography in the optical near field,” Appl. Phys. Lett. 70(20), 2658–2660 (1997).
[Crossref]

CIRP Ann.-. Manuf. Technol. (2)

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann.-. Manuf. Technol. 64(2), 773–796 (2015).
[Crossref]

X. Li, W. Gao, Y. Shimizu, and S. Ito, “A two-axis Lloyd’s mirror interferometer for fabrication of two-dimensional diffraction gratings,” CIRP Ann.-. Manuf. Technol. 63(1), 461–464 (2014).
[Crossref]

J. Opt. Soc. Am. (2)

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

Laser Photonics Rev. (1)

C. Lu and R. H. Lipson, “Interference lithography: a powerful tool for fabricating periodic structures,” Laser Photonics Rev. 4(4), 568–580 (2010).
[Crossref]

Nature (1)

R. F. Pease, “Semiconductor technology: imprints offer Moore,” Nature 417(6891), 802–803 (2002).
[Crossref] [PubMed]

Opt. Commun. (1)

H. Zhou and L. Zeng, “Method to fabricate orthogonal crossed gratings based on a dual Lloyd’s mirror interferometer,” Opt. Commun. 360, 68–72 (2016).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Precis. Eng. (4)

W. S. Blackley and R. O. Scattergood, “Ductile-regime machining model for diamond turning of brittle materials,” Precis. Eng. 13(2), 95–103 (1991).
[Crossref]

W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka, “Precision nano-fabrication and evaluation of a large area sinusoidal grid surface for a surface encoder,” Precis. Eng. 27(3), 289–298 (2003).
[Crossref]

A. Kimura, W. Gao, W. J. Kim, K. Hosono, Y. Shimizu, L. Shi, and L. J. Zeng, “Sub-nanometric three-axis surface encoder with short-period planar gratings for stage motion measurement,” Precis. Eng. 36(4), 576–585 (2012).
[Crossref]

X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng. 37(3), 771–781 (2013).
[Crossref]

Other (2)

KGM series Catalogue, Heidenhain GmbH.

E. Hecht, Optics (Addison-Wesley, 2002).

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Figures (7)

Fig. 1
Fig. 1 (a) Schematic and (b) photograph of the constructed orthogonal two-axis Lloyd’s mirror interferometer; (c) photograph of the interferometer unit [15].
Fig. 2
Fig. 2 Schematic of the propagation of polarized light in a sequence of optical interfaces.
Fig. 3
Fig. 3 (a) Optical configuration for the interferometer unit of the orthogonal two-axis Lloyd’s mirror interferometer and (b) definition of the global coordinate system { x ^ , y ^ , z ^ } , θ and ϕ in this paper, where θ is the angle between the direction of the incident beam and the XY-plane (substrate surface), and ϕ is the azimuthal angle between the X-axis and the plane of incidence associated with the beam (beam 1) incident upon the substrate [15].
Fig. 4
Fig. 4 The mapping of the DoO of beams 2 and 3 (γ23) for (a) Mirror 1 and (b) Mirror 2 under different combinations of initial orientation angles α2 and α3; (c) The variation of γ23 with respect to the initial orientation angle α3 of beam 3 for Mirror 1 and Mirror 2, where α2 = –α3.
Fig. 5
Fig. 5 The simulated interference fringes under the optimal combination of initial polarization states of (s, –33.5°, 33.5°) for (a) Mirror 1 and of (s, –62.2°, 62.2°) for (b) Mirror 2. The corresponding AFM images of the experimental interference fringes obtained under the optimal combination of initial polarization states for (c) Mirror 1 and (d) Mirror 2.
Fig. 6
Fig. 6 Representation of polarization states of beams 1, 2 and 3 ( E 1, E 2 and E 3) after their interaction with the Lloyd’s mirror interferometer under the associated optimal combination of initial polarization states in the global coordinate system for (a) Mirror 1 and (b) Mirror 2, where the sphere has a radius of 1.
Fig. 7
Fig. 7 (a) The variation of γ23 with respect to α3 for a virtual mirror similar to Mirror 1 but with a thickness of 2 nm for the oxide (Al2O3) layer (α2 = –α3), (b) The simulated interference fringe for the mirror under the optimal combination of initial polarization states of (s, 14.7°, –14.7°).

Tables (2)

Tables Icon

Table 1 Interference fringe patterns generated by each pair of beams

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Table 2 Comparison between the simulated and experimental interference fringes generated by beams 1, 2 and 3 under different combinations of initial polarization states of the three beams

Equations (44)

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E i = P i E i 1 .
P i = T o u t , i J i T i n , i 1 ,
T i n , i = [ p ^ i s ^ i k ^ i 1 ] ,
T o u t , i = [ p ^ i s ^ i k ^ i ] ,
J i = [ r p p , i r p s , i 0 r s p , i r s s , i 0 0 0 1 ] ,
s ^ i = s ^ i = k ^ i 1 × k ^ i | k ^ i 1 × k ^ i | ,
p ^ i = s ^ i × k ^ i ,
p ^ i = s ^ i × k ^ i 1 .
E N = P T o t a l E 1 ,
E l E m = E m E l = 0 ,
e ( r ) = i = 1 5 E i exp ( j k k ^ i r ) .
k ^ 1 = [ cos θ cos ϕ cos θ sin ϕ sin θ ] .
E 1 = T o u t , 1 E 01 ,
T o u t , 1 = [ p ^ 1 s ^ 1 k ^ 1 ] = [ sin θ cos ϕ sin ϕ cos θ cos ϕ sin θ sin ϕ cos ϕ cos θ sin ϕ cos θ 0 sin θ ] .
k ^ 2 = 2 ( n ^ X k ^ 1 ) n ^ X + k ^ 1 | 2 ( n ^ X k ^ 1 ) n ^ X + k ^ 1 | ,
n ^ X = R Y ( δ X Y ) R Z ( δ X Z ) x ^ = [ cos δ X Y 0 sin δ X Y 0 1 0 sin δ X Y 0 cos δ X Y ] [ cos δ X Z sin δ X Z 0 sin δ X Z cos δ X Z 0 0 0 1 ] [ 1 0 0 ] ,
n ^ X = R Z ( δ X Z ) R Y ( δ X Y ) x ^ = [ cos δ X Z sin δ X Z 0 sin δ X Z cos δ X Z 0 0 0 1 ] [ cos δ X Y 0 sin δ X Y 0 1 0 sin δ X Y 0 cos δ X Y ] [ 1 0 0 ] ,
E 2 = P 2 T o u t , 1 E 02 = T o u t , 2 J X T i n , 2 1 T o u t , 1 E 02 ,
T i n , 2 = [ p ^ 2 s ^ 2 k ^ 1 ] ,
T o u t , 2 = [ p ^ 2 s ^ 2 k ^ 2 ] ,
k ^ 3 = 2 ( n ^ Y k ^ 1 ) n ^ Y + k ^ 1 | 2 ( n ^ Y k ^ 1 ) n ^ Y + k ^ 1 | ,
E 3 = P 3 T o u t , 1 E 03 = T o u t , 3 J Y T i n , 3 1 T o u t , 1 E 03 ,
T i n , 3 = [ p ^ 3 s ^ 3 k ^ 1 ] ,
T o u t , 3 = [ p ^ 3 s ^ 3 k ^ 3 ] ,
k ^ 4 = 2 ( n ^ Y k ^ 2 ) n ^ Y + k ^ 2 | 2 ( n ^ Y k ^ 2 ) n ^ Y + k ^ 2 | .
E 4 = P 4 P 2 T o u t , 1 E 04 = T o u t , 4 J Y T i n , 4 1 P 2 T o u t , 1 E 04 ,
T i n , 4 = [ p ^ 4 s ^ 4 k ^ 2 ] ,
T o u t , 4 = [ p ^ 4 s ^ 4 k ^ 4 ] .
k ^ 5 = 2 ( n ^ X k ^ 3 ) n ^ X + k ^ 3 | 2 ( n ^ X k ^ 3 ) n ^ X + k ^ 3 | .
E 5 = P 5 P 3 T o u t , 1 E 05 = T o u t , 5 J X T i n , 5 1 P 3 T o u t , 1 E 05 ,
T i n , 5 = [ p ^ 5 s ^ 5 k ^ 3 ] ,
T o u t , 5 = [ p ^ 5 s ^ 5 k ^ 5 ] .
I ( r ) = [ e ( r ) ] e ( r ) = l = 1 5 | E l | 2 + 2 l = 2 5 m < l Re { E m E l exp [ j k ( k ^ m k ^ l ) r ] } ,
g l m = 2 π k | k ^ l k ^ m | .
E 2 E 3 = E 3 E 2 = 0.
γ l m = | E l E m | .
I l m = | E l | 2 + | E m | 2 + 2 γ l m cos [ k ( k ^ m k ^ l ) r + φ l m ] ,
C l m = max ( I l m ) m i n ( I l m ) max ( I l m ) + m i n ( I l m ) = 2 γ l m | E l | 2 + | E m | 2 ,
C 12 = C 13 .
α 2 = α 3
a 11 cos α 2 cos α 3 + a 12 cos α 2 sin α 3 + a 21 sin α 2 cos α 3 + a 22 sin α 2 sin α 3 = 0 ,
A = [ a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 ] = T o u t , 1 T P 2 P 3 T o u t , 1 .
α 2 = α 3 = arc tan a 21 a 12 ± ( a 12 a 21 ) 2 + 4 a 11 a 22 2 a 22 .
( α ^ 2 , α ^ 3 ) = arg min α 2 , α 3 Θ γ 23 ,

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