Abstract

We investigated the design, optimization, and evaluation method of an infrared (IR)/microwave (MW) multilayered dielectric plate type of beam combiner. The MW multilayered dielectrics design theory and IR film design theory were unified using transmission line theory. The principles in designing the initial structure of a beam combiner were presented. An objective function was presented in optimizing the beam combiner. Six evaluation indices were constructed to evaluate the performance of the beam combiner. To verify the feasibility of the proposed method an example was given. The results showed that the method could meet the joint design, optimization, and evaluation requirements of a beam combiner’s IR and MW characteristics. Finally, the design, optimization, and evaluation procedure was summarized.

© 2013 Optical Society of America

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References

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  1. Y. P. Zhang, S. X. Wang, and Y. H. Xu, “Dual-mode MMW/IR simulation of beam combiner,” Optik 121, 1003–1008(2010).
    [CrossRef]
  2. J. P. Gareri, G. H. Ballard, J. W. Morris, D. Bunfield, and D. Saylor, “Application of scene projection technologies at the AMRDEC SSDD HWIL facilities,” Proc. SPIE 8356, 83560L (2012).
    [CrossRef]
  3. S. A. Gearhart, T. J. Harris, C. J. Kardian, D. T. Prendergast, and D. T. Winters, “A hardware-in-the-loop test facility for dual-mode infrared and radar guidance systems,” Proc. SPIE 2469, 170–180 (1995).
    [CrossRef]
  4. T. E. O’Bannon and S. A. Gearhart, “Dual-mode infrared and radar hardware-in-the-loop test assets at The Johns Hopkins University Applied Physics Laboratory,” Proc. SPIE 2741, 332–346 (1996).
    [CrossRef]
  5. S. Mobley, “U. S. Army Missile Command dual-mode millimeter wave/infrared simulator development,” Proc. SPIE 2223, 100–111 (1994).
    [CrossRef]
  6. S. Mobley, V. Vanderford, J. Cooper, and B. Thomas, “U. S. Army Missile Command dual-mode millimeter wave/infrared simulator development,” Proc. SPIE 2469, 15–19 (1995).
    [CrossRef]
  7. L. Sadovnik, A. Manasson, V. Manasson, and V. Yepishin, “Infrared/Millimeter wave beam combiner utilizing holographic optical element,” Proc. SPIE 3464, 155–163 (1998).
    [CrossRef]
  8. R. R. Xu, Z. Y. Zong, W. Wu, and Y. P. Xu, “Dichroic beam combiner using fractal FSS,” Infrared Laser Eng. 37, 1058–1061 (2008).
  9. S. Mobley, J. Cole, J. Cooper, and J. Jarem, “U. S. Army Missile Command dual-mode millimeter wave/infrared simulator development,” Proc. SPIE 2741, 316–331 (1996).
  10. R. Shi and Z. Li, “Approach on IR/RF dichroic beam combiner,” Infrared Laser Eng. 35, 780–783 (2006).
  11. P. Li, Z. Lia, Y. Liu, Y. H. Li, L. X. Qian, and Z. S. Wang, “Design and implementation of a dichroic beam combiner based on the theory of photonic crystals,” Proc. SPIE 7847, 78470R (2010).
    [CrossRef]
  12. H. P. Ip and Y. R. Samii, “Analysis and characterization of multilayered reflector antennas: rain/snow accumulation and deployable membrane,” IEEE Trans. Antennas Propag. 46, 1593–1605 (1998).
    [CrossRef]
  13. J. D. Rancourt, Optical Thin Films: User Handbook (SPIE, 1996).
  14. M. A. A. Moneum, Z. Shen, J. L. Volakis, and O. Graham, “Hybrid PO-MoM analysis of large axi-symmetric radomes,” IEEE Trans. Antennas Propag. 49, 1657–1666 (2001).
    [CrossRef]
  15. D. T. Paris, “Computer-aided radome analysis,” IEEE Trans. Antennas Propag. AP-18, 7–15 (1970).
    [CrossRef]
  16. S. J. Orfanidis, Electromagnetic Waves and Antennas(Rutgers, 2002).
  17. S. B. Mobley and J. Gareri, “Hardware-in-the-loop simulation (HWIL) facility for development, test, and evaluation of multi-spectral missile systems—update,” Proc. SPIE 4027, 11–21 (2000).
    [CrossRef]

2012 (1)

J. P. Gareri, G. H. Ballard, J. W. Morris, D. Bunfield, and D. Saylor, “Application of scene projection technologies at the AMRDEC SSDD HWIL facilities,” Proc. SPIE 8356, 83560L (2012).
[CrossRef]

2010 (2)

Y. P. Zhang, S. X. Wang, and Y. H. Xu, “Dual-mode MMW/IR simulation of beam combiner,” Optik 121, 1003–1008(2010).
[CrossRef]

P. Li, Z. Lia, Y. Liu, Y. H. Li, L. X. Qian, and Z. S. Wang, “Design and implementation of a dichroic beam combiner based on the theory of photonic crystals,” Proc. SPIE 7847, 78470R (2010).
[CrossRef]

2008 (1)

R. R. Xu, Z. Y. Zong, W. Wu, and Y. P. Xu, “Dichroic beam combiner using fractal FSS,” Infrared Laser Eng. 37, 1058–1061 (2008).

2006 (1)

R. Shi and Z. Li, “Approach on IR/RF dichroic beam combiner,” Infrared Laser Eng. 35, 780–783 (2006).

2001 (1)

M. A. A. Moneum, Z. Shen, J. L. Volakis, and O. Graham, “Hybrid PO-MoM analysis of large axi-symmetric radomes,” IEEE Trans. Antennas Propag. 49, 1657–1666 (2001).
[CrossRef]

2000 (1)

S. B. Mobley and J. Gareri, “Hardware-in-the-loop simulation (HWIL) facility for development, test, and evaluation of multi-spectral missile systems—update,” Proc. SPIE 4027, 11–21 (2000).
[CrossRef]

1998 (2)

L. Sadovnik, A. Manasson, V. Manasson, and V. Yepishin, “Infrared/Millimeter wave beam combiner utilizing holographic optical element,” Proc. SPIE 3464, 155–163 (1998).
[CrossRef]

H. P. Ip and Y. R. Samii, “Analysis and characterization of multilayered reflector antennas: rain/snow accumulation and deployable membrane,” IEEE Trans. Antennas Propag. 46, 1593–1605 (1998).
[CrossRef]

1996 (2)

S. Mobley, J. Cole, J. Cooper, and J. Jarem, “U. S. Army Missile Command dual-mode millimeter wave/infrared simulator development,” Proc. SPIE 2741, 316–331 (1996).

T. E. O’Bannon and S. A. Gearhart, “Dual-mode infrared and radar hardware-in-the-loop test assets at The Johns Hopkins University Applied Physics Laboratory,” Proc. SPIE 2741, 332–346 (1996).
[CrossRef]

1995 (2)

S. A. Gearhart, T. J. Harris, C. J. Kardian, D. T. Prendergast, and D. T. Winters, “A hardware-in-the-loop test facility for dual-mode infrared and radar guidance systems,” Proc. SPIE 2469, 170–180 (1995).
[CrossRef]

S. Mobley, V. Vanderford, J. Cooper, and B. Thomas, “U. S. Army Missile Command dual-mode millimeter wave/infrared simulator development,” Proc. SPIE 2469, 15–19 (1995).
[CrossRef]

1994 (1)

S. Mobley, “U. S. Army Missile Command dual-mode millimeter wave/infrared simulator development,” Proc. SPIE 2223, 100–111 (1994).
[CrossRef]

1970 (1)

D. T. Paris, “Computer-aided radome analysis,” IEEE Trans. Antennas Propag. AP-18, 7–15 (1970).
[CrossRef]

Ballard, G. H.

J. P. Gareri, G. H. Ballard, J. W. Morris, D. Bunfield, and D. Saylor, “Application of scene projection technologies at the AMRDEC SSDD HWIL facilities,” Proc. SPIE 8356, 83560L (2012).
[CrossRef]

Bunfield, D.

J. P. Gareri, G. H. Ballard, J. W. Morris, D. Bunfield, and D. Saylor, “Application of scene projection technologies at the AMRDEC SSDD HWIL facilities,” Proc. SPIE 8356, 83560L (2012).
[CrossRef]

Cole, J.

S. Mobley, J. Cole, J. Cooper, and J. Jarem, “U. S. Army Missile Command dual-mode millimeter wave/infrared simulator development,” Proc. SPIE 2741, 316–331 (1996).

Cooper, J.

S. Mobley, J. Cole, J. Cooper, and J. Jarem, “U. S. Army Missile Command dual-mode millimeter wave/infrared simulator development,” Proc. SPIE 2741, 316–331 (1996).

S. Mobley, V. Vanderford, J. Cooper, and B. Thomas, “U. S. Army Missile Command dual-mode millimeter wave/infrared simulator development,” Proc. SPIE 2469, 15–19 (1995).
[CrossRef]

Gareri, J.

S. B. Mobley and J. Gareri, “Hardware-in-the-loop simulation (HWIL) facility for development, test, and evaluation of multi-spectral missile systems—update,” Proc. SPIE 4027, 11–21 (2000).
[CrossRef]

Gareri, J. P.

J. P. Gareri, G. H. Ballard, J. W. Morris, D. Bunfield, and D. Saylor, “Application of scene projection technologies at the AMRDEC SSDD HWIL facilities,” Proc. SPIE 8356, 83560L (2012).
[CrossRef]

Gearhart, S. A.

T. E. O’Bannon and S. A. Gearhart, “Dual-mode infrared and radar hardware-in-the-loop test assets at The Johns Hopkins University Applied Physics Laboratory,” Proc. SPIE 2741, 332–346 (1996).
[CrossRef]

S. A. Gearhart, T. J. Harris, C. J. Kardian, D. T. Prendergast, and D. T. Winters, “A hardware-in-the-loop test facility for dual-mode infrared and radar guidance systems,” Proc. SPIE 2469, 170–180 (1995).
[CrossRef]

Graham, O.

M. A. A. Moneum, Z. Shen, J. L. Volakis, and O. Graham, “Hybrid PO-MoM analysis of large axi-symmetric radomes,” IEEE Trans. Antennas Propag. 49, 1657–1666 (2001).
[CrossRef]

Harris, T. J.

S. A. Gearhart, T. J. Harris, C. J. Kardian, D. T. Prendergast, and D. T. Winters, “A hardware-in-the-loop test facility for dual-mode infrared and radar guidance systems,” Proc. SPIE 2469, 170–180 (1995).
[CrossRef]

Ip, H. P.

H. P. Ip and Y. R. Samii, “Analysis and characterization of multilayered reflector antennas: rain/snow accumulation and deployable membrane,” IEEE Trans. Antennas Propag. 46, 1593–1605 (1998).
[CrossRef]

Jarem, J.

S. Mobley, J. Cole, J. Cooper, and J. Jarem, “U. S. Army Missile Command dual-mode millimeter wave/infrared simulator development,” Proc. SPIE 2741, 316–331 (1996).

Kardian, C. J.

S. A. Gearhart, T. J. Harris, C. J. Kardian, D. T. Prendergast, and D. T. Winters, “A hardware-in-the-loop test facility for dual-mode infrared and radar guidance systems,” Proc. SPIE 2469, 170–180 (1995).
[CrossRef]

Li, P.

P. Li, Z. Lia, Y. Liu, Y. H. Li, L. X. Qian, and Z. S. Wang, “Design and implementation of a dichroic beam combiner based on the theory of photonic crystals,” Proc. SPIE 7847, 78470R (2010).
[CrossRef]

Li, Y. H.

P. Li, Z. Lia, Y. Liu, Y. H. Li, L. X. Qian, and Z. S. Wang, “Design and implementation of a dichroic beam combiner based on the theory of photonic crystals,” Proc. SPIE 7847, 78470R (2010).
[CrossRef]

Li, Z.

R. Shi and Z. Li, “Approach on IR/RF dichroic beam combiner,” Infrared Laser Eng. 35, 780–783 (2006).

Lia, Z.

P. Li, Z. Lia, Y. Liu, Y. H. Li, L. X. Qian, and Z. S. Wang, “Design and implementation of a dichroic beam combiner based on the theory of photonic crystals,” Proc. SPIE 7847, 78470R (2010).
[CrossRef]

Liu, Y.

P. Li, Z. Lia, Y. Liu, Y. H. Li, L. X. Qian, and Z. S. Wang, “Design and implementation of a dichroic beam combiner based on the theory of photonic crystals,” Proc. SPIE 7847, 78470R (2010).
[CrossRef]

Manasson, A.

L. Sadovnik, A. Manasson, V. Manasson, and V. Yepishin, “Infrared/Millimeter wave beam combiner utilizing holographic optical element,” Proc. SPIE 3464, 155–163 (1998).
[CrossRef]

Manasson, V.

L. Sadovnik, A. Manasson, V. Manasson, and V. Yepishin, “Infrared/Millimeter wave beam combiner utilizing holographic optical element,” Proc. SPIE 3464, 155–163 (1998).
[CrossRef]

Mobley, S.

S. Mobley, J. Cole, J. Cooper, and J. Jarem, “U. S. Army Missile Command dual-mode millimeter wave/infrared simulator development,” Proc. SPIE 2741, 316–331 (1996).

S. Mobley, V. Vanderford, J. Cooper, and B. Thomas, “U. S. Army Missile Command dual-mode millimeter wave/infrared simulator development,” Proc. SPIE 2469, 15–19 (1995).
[CrossRef]

S. Mobley, “U. S. Army Missile Command dual-mode millimeter wave/infrared simulator development,” Proc. SPIE 2223, 100–111 (1994).
[CrossRef]

Mobley, S. B.

S. B. Mobley and J. Gareri, “Hardware-in-the-loop simulation (HWIL) facility for development, test, and evaluation of multi-spectral missile systems—update,” Proc. SPIE 4027, 11–21 (2000).
[CrossRef]

Moneum, M. A. A.

M. A. A. Moneum, Z. Shen, J. L. Volakis, and O. Graham, “Hybrid PO-MoM analysis of large axi-symmetric radomes,” IEEE Trans. Antennas Propag. 49, 1657–1666 (2001).
[CrossRef]

Morris, J. W.

J. P. Gareri, G. H. Ballard, J. W. Morris, D. Bunfield, and D. Saylor, “Application of scene projection technologies at the AMRDEC SSDD HWIL facilities,” Proc. SPIE 8356, 83560L (2012).
[CrossRef]

O’Bannon, T. E.

T. E. O’Bannon and S. A. Gearhart, “Dual-mode infrared and radar hardware-in-the-loop test assets at The Johns Hopkins University Applied Physics Laboratory,” Proc. SPIE 2741, 332–346 (1996).
[CrossRef]

Orfanidis, S. J.

S. J. Orfanidis, Electromagnetic Waves and Antennas(Rutgers, 2002).

Paris, D. T.

D. T. Paris, “Computer-aided radome analysis,” IEEE Trans. Antennas Propag. AP-18, 7–15 (1970).
[CrossRef]

Prendergast, D. T.

S. A. Gearhart, T. J. Harris, C. J. Kardian, D. T. Prendergast, and D. T. Winters, “A hardware-in-the-loop test facility for dual-mode infrared and radar guidance systems,” Proc. SPIE 2469, 170–180 (1995).
[CrossRef]

Qian, L. X.

P. Li, Z. Lia, Y. Liu, Y. H. Li, L. X. Qian, and Z. S. Wang, “Design and implementation of a dichroic beam combiner based on the theory of photonic crystals,” Proc. SPIE 7847, 78470R (2010).
[CrossRef]

Rancourt, J. D.

J. D. Rancourt, Optical Thin Films: User Handbook (SPIE, 1996).

Sadovnik, L.

L. Sadovnik, A. Manasson, V. Manasson, and V. Yepishin, “Infrared/Millimeter wave beam combiner utilizing holographic optical element,” Proc. SPIE 3464, 155–163 (1998).
[CrossRef]

Samii, Y. R.

H. P. Ip and Y. R. Samii, “Analysis and characterization of multilayered reflector antennas: rain/snow accumulation and deployable membrane,” IEEE Trans. Antennas Propag. 46, 1593–1605 (1998).
[CrossRef]

Saylor, D.

J. P. Gareri, G. H. Ballard, J. W. Morris, D. Bunfield, and D. Saylor, “Application of scene projection technologies at the AMRDEC SSDD HWIL facilities,” Proc. SPIE 8356, 83560L (2012).
[CrossRef]

Shen, Z.

M. A. A. Moneum, Z. Shen, J. L. Volakis, and O. Graham, “Hybrid PO-MoM analysis of large axi-symmetric radomes,” IEEE Trans. Antennas Propag. 49, 1657–1666 (2001).
[CrossRef]

Shi, R.

R. Shi and Z. Li, “Approach on IR/RF dichroic beam combiner,” Infrared Laser Eng. 35, 780–783 (2006).

Thomas, B.

S. Mobley, V. Vanderford, J. Cooper, and B. Thomas, “U. S. Army Missile Command dual-mode millimeter wave/infrared simulator development,” Proc. SPIE 2469, 15–19 (1995).
[CrossRef]

Vanderford, V.

S. Mobley, V. Vanderford, J. Cooper, and B. Thomas, “U. S. Army Missile Command dual-mode millimeter wave/infrared simulator development,” Proc. SPIE 2469, 15–19 (1995).
[CrossRef]

Volakis, J. L.

M. A. A. Moneum, Z. Shen, J. L. Volakis, and O. Graham, “Hybrid PO-MoM analysis of large axi-symmetric radomes,” IEEE Trans. Antennas Propag. 49, 1657–1666 (2001).
[CrossRef]

Wang, S. X.

Y. P. Zhang, S. X. Wang, and Y. H. Xu, “Dual-mode MMW/IR simulation of beam combiner,” Optik 121, 1003–1008(2010).
[CrossRef]

Wang, Z. S.

P. Li, Z. Lia, Y. Liu, Y. H. Li, L. X. Qian, and Z. S. Wang, “Design and implementation of a dichroic beam combiner based on the theory of photonic crystals,” Proc. SPIE 7847, 78470R (2010).
[CrossRef]

Winters, D. T.

S. A. Gearhart, T. J. Harris, C. J. Kardian, D. T. Prendergast, and D. T. Winters, “A hardware-in-the-loop test facility for dual-mode infrared and radar guidance systems,” Proc. SPIE 2469, 170–180 (1995).
[CrossRef]

Wu, W.

R. R. Xu, Z. Y. Zong, W. Wu, and Y. P. Xu, “Dichroic beam combiner using fractal FSS,” Infrared Laser Eng. 37, 1058–1061 (2008).

Xu, R. R.

R. R. Xu, Z. Y. Zong, W. Wu, and Y. P. Xu, “Dichroic beam combiner using fractal FSS,” Infrared Laser Eng. 37, 1058–1061 (2008).

Xu, Y. H.

Y. P. Zhang, S. X. Wang, and Y. H. Xu, “Dual-mode MMW/IR simulation of beam combiner,” Optik 121, 1003–1008(2010).
[CrossRef]

Xu, Y. P.

R. R. Xu, Z. Y. Zong, W. Wu, and Y. P. Xu, “Dichroic beam combiner using fractal FSS,” Infrared Laser Eng. 37, 1058–1061 (2008).

Yepishin, V.

L. Sadovnik, A. Manasson, V. Manasson, and V. Yepishin, “Infrared/Millimeter wave beam combiner utilizing holographic optical element,” Proc. SPIE 3464, 155–163 (1998).
[CrossRef]

Zhang, Y. P.

Y. P. Zhang, S. X. Wang, and Y. H. Xu, “Dual-mode MMW/IR simulation of beam combiner,” Optik 121, 1003–1008(2010).
[CrossRef]

Zong, Z. Y.

R. R. Xu, Z. Y. Zong, W. Wu, and Y. P. Xu, “Dichroic beam combiner using fractal FSS,” Infrared Laser Eng. 37, 1058–1061 (2008).

IEEE Trans. Antennas Propag. (3)

H. P. Ip and Y. R. Samii, “Analysis and characterization of multilayered reflector antennas: rain/snow accumulation and deployable membrane,” IEEE Trans. Antennas Propag. 46, 1593–1605 (1998).
[CrossRef]

M. A. A. Moneum, Z. Shen, J. L. Volakis, and O. Graham, “Hybrid PO-MoM analysis of large axi-symmetric radomes,” IEEE Trans. Antennas Propag. 49, 1657–1666 (2001).
[CrossRef]

D. T. Paris, “Computer-aided radome analysis,” IEEE Trans. Antennas Propag. AP-18, 7–15 (1970).
[CrossRef]

Infrared Laser Eng. (2)

R. R. Xu, Z. Y. Zong, W. Wu, and Y. P. Xu, “Dichroic beam combiner using fractal FSS,” Infrared Laser Eng. 37, 1058–1061 (2008).

R. Shi and Z. Li, “Approach on IR/RF dichroic beam combiner,” Infrared Laser Eng. 35, 780–783 (2006).

Optik (1)

Y. P. Zhang, S. X. Wang, and Y. H. Xu, “Dual-mode MMW/IR simulation of beam combiner,” Optik 121, 1003–1008(2010).
[CrossRef]

Proc. SPIE (9)

J. P. Gareri, G. H. Ballard, J. W. Morris, D. Bunfield, and D. Saylor, “Application of scene projection technologies at the AMRDEC SSDD HWIL facilities,” Proc. SPIE 8356, 83560L (2012).
[CrossRef]

S. A. Gearhart, T. J. Harris, C. J. Kardian, D. T. Prendergast, and D. T. Winters, “A hardware-in-the-loop test facility for dual-mode infrared and radar guidance systems,” Proc. SPIE 2469, 170–180 (1995).
[CrossRef]

T. E. O’Bannon and S. A. Gearhart, “Dual-mode infrared and radar hardware-in-the-loop test assets at The Johns Hopkins University Applied Physics Laboratory,” Proc. SPIE 2741, 332–346 (1996).
[CrossRef]

S. Mobley, “U. S. Army Missile Command dual-mode millimeter wave/infrared simulator development,” Proc. SPIE 2223, 100–111 (1994).
[CrossRef]

S. Mobley, V. Vanderford, J. Cooper, and B. Thomas, “U. S. Army Missile Command dual-mode millimeter wave/infrared simulator development,” Proc. SPIE 2469, 15–19 (1995).
[CrossRef]

L. Sadovnik, A. Manasson, V. Manasson, and V. Yepishin, “Infrared/Millimeter wave beam combiner utilizing holographic optical element,” Proc. SPIE 3464, 155–163 (1998).
[CrossRef]

P. Li, Z. Lia, Y. Liu, Y. H. Li, L. X. Qian, and Z. S. Wang, “Design and implementation of a dichroic beam combiner based on the theory of photonic crystals,” Proc. SPIE 7847, 78470R (2010).
[CrossRef]

S. Mobley, J. Cole, J. Cooper, and J. Jarem, “U. S. Army Missile Command dual-mode millimeter wave/infrared simulator development,” Proc. SPIE 2741, 316–331 (1996).

S. B. Mobley and J. Gareri, “Hardware-in-the-loop simulation (HWIL) facility for development, test, and evaluation of multi-spectral missile systems—update,” Proc. SPIE 4027, 11–21 (2000).
[CrossRef]

Other (2)

S. J. Orfanidis, Electromagnetic Waves and Antennas(Rutgers, 2002).

J. D. Rancourt, Optical Thin Films: User Handbook (SPIE, 1996).

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Figures (4)

Fig. 1.
Fig. 1.

Structure of multilayered dielectric plate beam combiner.

Fig. 2.
Fig. 2.

IR power reflection rate (a,b), MW power transmission rate (c,d), and IPD (e,f) before optimization.

Fig. 3.
Fig. 3.

IR power reflection rate (a,b), MW power transmission rate (c,d), and IPD (e,f) after optimization.

Fig. 4.
Fig. 4.

Relative IR power reflection rate (a,b), relative MW power transmission rate (c,d), and IPD (e,f) before and after optimization.

Tables (3)

Tables Icon

Table 1. Initial Structure of Dielectrics

Tables Icon

Table 2. Structure of Dielectrics after Optimization

Tables Icon

Table 3. Evaluation Indices

Equations (37)

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

εnr=εn0r(1tanδn),
nIR=εnr.
tanδn=σnλ2πcεn0rμ0/ε0,
kn=2πλ.
[AnBnCnDn],
An=Dn=coshjkndn,
Bn=Znsinhjkndn,
Cn=sinhjkndn/Zn,
dn=dnεnrsin2θi,
Zn=1εnrεnrsin2θi,
Zn=1εnrsin2θi.
[ABCD]=[A1B1C1D1][AnBnCnDn][ANBNCNDN].
r=(A+B/Z0)(CZ0+D)A+B/Z0+CZ0+D=|r|ejφr=rN1jrN2,
t=2A+B/Z0+CZ0+D=|t|ejφt=tN1jtN2.
η=φt2πdλ0cosθi,
d=n=1Ndn,
φt=atan(tN2tN1).
R=|r|2,
T=|t|2.
|R(f)|2=h2TM2(x)1+h2TM2(x),
TM(x)=cos(Marccos(x)),
x=cosθP,
θ=2πdnλ.
(1|T|2)max=1+h2.
λ2=2πdnarccos(P).
λ1=2πdnπarccos(P).
λ0=2λ1λ2λ1+λ2=4dn.
Δff0=2(λ1λ2)λ1+λ2=24πarccos(P).
1|T|2=1+h2TN2(cosθP).
T¯MW=f1MWf2MWθ1θ2TMW(fMW,θ)dfMWdθf1MWf2MWθ1θ2dfMWdθ.
σMW=(f1MWf2MWθ1θ2(TMW(f,θ)T¯MW)2dfMWdθf1MWf2MWθ1θ2dfMWdθ)0.5.
TMW=min(TMW).
R¯IR=f1IRf2IRθ1θ2RIR(fIR,θ)dfIRdθf1IRf2IRθ1θ2dfIRdθ.
σIR=(f1IRf2IRθ1θ2(RIR(fIR,θ)R¯IR)2dfIRdθf1f2θ1θ2dfIRdθ)0.5,
RIR=min(RIR).
F=W[T¯MWT¯MWrσMWσMWrTMWTMWrR¯IRR¯IRrσIRσIRrRIRRIRr],
W=[w1w2w3w4w5w6].

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