Abstract

A novel moving corner-cube mirror interferometer (MCCMI) is presented. It has neither tilt nor shearing problems. It consists of one moving corner-cube mirror (MCCM), one fixed double-sided mirror (FDSM), one fixed plane mirror, and one beam splitter. The FDSM is a plane-parallel glass plate with both faces coated with high-reflectivity films. The effect of a FDSM tilt is analyzed. The optical path difference (OPD) is created by the straight reciprocating motion of the MCCM, and the OPD value is four times the displacement of the MCCM. The reflection characteristic of the corner-cube mirror (CCM) is analyzed by means of the vector expression, and the formulas of deviation angle of a CCM are derived. The effect of a MCCM deviation angle is analyzed. The new MCCMI is very suitable for high-resolution Fourier- transform infrared spectrometers used for atmospheric sounding.

© 2010 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  8. Q. Yang, B. Zhao, and R. Zhou, “Novel moving cat’s-eye-pair interferometer,” J. Mod. Opt. 56, 1283–1287(2009).
    [CrossRef]
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    [CrossRef]
  14. J. Kauppinen and V.-M. Horneman, “Large aperture cube corner interferometer with a resolution of 0.001 cm−1,” Appl. Opt. 30, 2575–2578 (1991).
    [CrossRef] [PubMed]
  15. J. Kauppinen and P. Saarinen, “Line-shape distortions in misaligned cube corner interferometers,” Appl. Opt. 31, 69–74(1992).
    [CrossRef] [PubMed]
  16. P. Haschberger and V. Tank, “Optimization of a Michelson interferometer with a rotating retroreflector in optical design, spectral resolution, and optical throughput,” J. Opt. Soc. Am. A. 10, 2338–2345 (1993).
    [CrossRef]
  17. Q. Yang, R. Zhou, and B. Zhao, “Novel moving-corner-cube-pair interferometer,” J. Opt. A: Pure Appl. Opt. 11, 015505 (2009).
    [CrossRef]
  18. R. Beer and D. Marjaniemi, “Wavefronts and construction tolerances for a cat’s-eye retroreflector,” Appl. Opt. 5, 1191–1197(1966).
    [CrossRef] [PubMed]
  19. J. J. Snyder, “Paraxial ray analysis of a cat’s-eye retroreflector,” Appl. Opt. 14, 1825–1828 (1975).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  23. Bomem, Incorporated, interferometers such as Models DA3-002, DA3-01, and DA3-02.
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  27. H. R. Chandrasekhar, L. Genzel, and J. Kuhl, “Double-beam Fourier spectroscopy with interferometric background compensation,” Opt. Commun. 17, 106–110(1976).
    [CrossRef]
  28. L. Genzel and J. Kuhl, “A new version of a Michelson interferometer for Fourier transform infrared spectroscopy,” Infrared Phys. 18, 113–120 (1978).
    [CrossRef]
  29. L. Genzel and J. Kuhl, “Tilt-compensated Michelson interferometer for Fourier transform spectroscopy,” Appl. Opt. 17, 3304–3308 (1978).
    [CrossRef] [PubMed]
  30. W. H. Steel, “Interferometers for Fourier spectroscopy,” in Aspen International Conference on Fourier Spectroscopy (Air Force Cambridge Research Laboratories, 1970), p. 43.
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    [CrossRef]

2009 (2)

Q. Yang, B. Zhao, and R. Zhou, “Novel moving cat’s-eye-pair interferometer,” J. Mod. Opt. 56, 1283–1287(2009).
[CrossRef]

Q. Yang, R. Zhou, and B. Zhao, “Novel moving-corner-cube-pair interferometer,” J. Opt. A: Pure Appl. Opt. 11, 015505 (2009).
[CrossRef]

2004 (1)

J. Kauppinen, J. Heinonen, and I. Kauppinen, “Interferometers based on the rotational motion,” Appl. Spectrosc. Rev. 39, 99–129 (2004).
[CrossRef]

2002 (1)

1995 (2)

1993 (1)

P. Haschberger and V. Tank, “Optimization of a Michelson interferometer with a rotating retroreflector in optical design, spectral resolution, and optical throughput,” J. Opt. Soc. Am. A. 10, 2338–2345 (1993).
[CrossRef]

1992 (1)

1991 (1)

1986 (1)

1985 (2)

1978 (3)

1977 (2)

1976 (2)

R. Beer, “Paraxial ray analysis of a cat’s-eye retroreflector: comments,” Appl. Opt. 15, 856–857 (1976).
[CrossRef] [PubMed]

H. R. Chandrasekhar, L. Genzel, and J. Kuhl, “Double-beam Fourier spectroscopy with interferometric background compensation,” Opt. Commun. 17, 106–110(1976).
[CrossRef]

1975 (2)

1966 (2)

1964 (1)

W. H. Steel, “On Möbius-band interferometers,” J. Mod. Opt. 11, 211–217 (1964).
[CrossRef]

1960 (1)

1957 (1)

1953 (1)

1948 (1)

Beer, R.

Brault, J. W.

Chandrasekhar, H. R.

H. R. Chandrasekhar, L. Genzel, and J. Kuhl, “Double-beam Fourier spectroscopy with interferometric background compensation,” Opt. Commun. 17, 106–110(1976).
[CrossRef]

Connes, J.

Connes, P.

de Haseth, J. A.

P. R. Griffiths and J. A. de Haseth, Fourier Transform Infrared Spectrometry (Wiley-Interscience, 2007).
[CrossRef]

Durry, G.

Genzel, L.

L. Genzel and J. Kuhl, “Tilt-compensated Michelson interferometer for Fourier transform spectroscopy,” Appl. Opt. 17, 3304–3308 (1978).
[CrossRef] [PubMed]

L. Genzel and J. Kuhl, “A new version of a Michelson interferometer for Fourier transform infrared spectroscopy,” Infrared Phys. 18, 113–120 (1978).
[CrossRef]

H. R. Chandrasekhar, L. Genzel, and J. Kuhl, “Double-beam Fourier spectroscopy with interferometric background compensation,” Opt. Commun. 17, 106–110(1976).
[CrossRef]

Griffiths, P. R.

Guelachvili, G.

Haschberger, P.

P. Haschberger and V. Tank, “Optimization of a Michelson interferometer with a rotating retroreflector in optical design, spectral resolution, and optical throughput,” J. Opt. Soc. Am. A. 10, 2338–2345 (1993).
[CrossRef]

Heinonen, J.

J. Kauppinen, J. Heinonen, and I. Kauppinen, “Interferometers based on the rotational motion,” Appl. Spectrosc. Rev. 39, 99–129 (2004).
[CrossRef]

Horneman, V.-M.

Hubbard, R.

Jennings, D. E.

Kauppinen, I.

J. Kauppinen, J. Heinonen, and I. Kauppinen, “Interferometers based on the rotational motion,” Appl. Spectrosc. Rev. 39, 99–129 (2004).
[CrossRef]

Kauppinen, J.

Kauppinen, J. K.

Kuhl, J.

L. Genzel and J. Kuhl, “A new version of a Michelson interferometer for Fourier transform infrared spectroscopy,” Infrared Phys. 18, 113–120 (1978).
[CrossRef]

L. Genzel and J. Kuhl, “Tilt-compensated Michelson interferometer for Fourier transform spectroscopy,” Appl. Opt. 17, 3304–3308 (1978).
[CrossRef] [PubMed]

H. R. Chandrasekhar, L. Genzel, and J. Kuhl, “Double-beam Fourier spectroscopy with interferometric background compensation,” Opt. Commun. 17, 106–110(1976).
[CrossRef]

Marjaniemi, D.

Murty, M. V. R. K.

Obetz, S. W.

Partanen, J. O.

Peck, E. R.

Richardson, R. L.

Saarinen, P.

Salomaa, I. K.

Snyder, J. J.

Steel, W. H.

W. H. Steel, “On Möbius-band interferometers,” J. Mod. Opt. 11, 211–217 (1964).
[CrossRef]

W. H. Steel, “Interferometers for Fourier spectroscopy,” in Aspen International Conference on Fourier Spectroscopy (Air Force Cambridge Research Laboratories, 1970), p. 43.

Stroke, G. W.

Tank, V.

P. Haschberger and V. Tank, “Optimization of a Michelson interferometer with a rotating retroreflector in optical design, spectral resolution, and optical throughput,” J. Opt. Soc. Am. A. 10, 2338–2345 (1993).
[CrossRef]

Thomas, D. A.

White, R. L.

Wyant, J. C.

Yang, Q.

Q. Yang, B. Zhao, and R. Zhou, “Novel moving cat’s-eye-pair interferometer,” J. Mod. Opt. 56, 1283–1287(2009).
[CrossRef]

Q. Yang, R. Zhou, and B. Zhao, “Novel moving-corner-cube-pair interferometer,” J. Opt. A: Pure Appl. Opt. 11, 015505 (2009).
[CrossRef]

Zhao, B.

Q. Yang, R. Zhou, and B. Zhao, “Novel moving-corner-cube-pair interferometer,” J. Opt. A: Pure Appl. Opt. 11, 015505 (2009).
[CrossRef]

Q. Yang, B. Zhao, and R. Zhou, “Novel moving cat’s-eye-pair interferometer,” J. Mod. Opt. 56, 1283–1287(2009).
[CrossRef]

Zhou, R.

Q. Yang, B. Zhao, and R. Zhou, “Novel moving cat’s-eye-pair interferometer,” J. Mod. Opt. 56, 1283–1287(2009).
[CrossRef]

Q. Yang, R. Zhou, and B. Zhao, “Novel moving-corner-cube-pair interferometer,” J. Opt. A: Pure Appl. Opt. 11, 015505 (2009).
[CrossRef]

Appl. Opt. (14)

R. Beer and D. Marjaniemi, “Wavefronts and construction tolerances for a cat’s-eye retroreflector,” Appl. Opt. 5, 1191–1197(1966).
[CrossRef] [PubMed]

J. J. Snyder, “Paraxial ray analysis of a cat’s-eye retroreflector,” Appl. Opt. 14, 1825–1828 (1975).
[CrossRef] [PubMed]

J. Kauppinen, “Double-beam high resolution Fourier spectrometer for the far infrared,” Appl. Opt. 14, 1987–1992(1975).
[CrossRef] [PubMed]

G. Guelachvili, “Near infrared wide-band spectroscopy with 27 MHz resolution,” Appl. Opt. 16, 2097–2101 (1977).
[CrossRef] [PubMed]

G. Guelachvili, “High-accuracy Doppler-limited 106 samples Fourier transform spectroscopy,” Appl. Opt. 17, 1322–1326(1978).
[CrossRef] [PubMed]

L. Genzel and J. Kuhl, “Tilt-compensated Michelson interferometer for Fourier transform spectroscopy,” Appl. Opt. 17, 3304–3308 (1978).
[CrossRef] [PubMed]

G. Guelachvili, “Distortion free interferograms in Fourier transform spectroscopy with nonlinear detectors,” Appl. Opt. 25, 4644–4648 (1986).
[CrossRef] [PubMed]

J. Kauppinen and V.-M. Horneman, “Large aperture cube corner interferometer with a resolution of 0.001 cm−1,” Appl. Opt. 30, 2575–2578 (1991).
[CrossRef] [PubMed]

J. Kauppinen and P. Saarinen, “Line-shape distortions in misaligned cube corner interferometers,” Appl. Opt. 31, 69–74(1992).
[CrossRef] [PubMed]

G. Durry and G. Guelachvili, “High-information time-resolved step-scan Fourier interferometer,” Appl. Opt. 34, 1971–1981(1995).
[CrossRef] [PubMed]

J. K. Kauppinen, I. K. Salomaa, and J. O. Partanen, “Carousel interferometer,” Appl. Opt. 34, 6081–6085 (1995).
[CrossRef] [PubMed]

R. L. Richardson and P. R. Griffiths, “Design and performance considerations of cat’s-eye retroreflectors for use in open-path Fourier-transform-infrared spectrometry,” Appl. Opt. 41, 6332–6340 (2002).
[CrossRef] [PubMed]

D. E. Jennings, R. Hubbard, and J. W. Brault, “Double passing the Kitt Peak 1 m Fourier transform spectrometer,” Appl. Opt. 24, 3438–3440 (1985).
[CrossRef] [PubMed]

R. Beer, “Paraxial ray analysis of a cat’s-eye retroreflector: comments,” Appl. Opt. 15, 856–857 (1976).
[CrossRef] [PubMed]

Appl. Spectrosc. (1)

Appl. Spectrosc. Rev. (1)

J. Kauppinen, J. Heinonen, and I. Kauppinen, “Interferometers based on the rotational motion,” Appl. Spectrosc. Rev. 39, 99–129 (2004).
[CrossRef]

Infrared Phys. (1)

L. Genzel and J. Kuhl, “A new version of a Michelson interferometer for Fourier transform infrared spectroscopy,” Infrared Phys. 18, 113–120 (1978).
[CrossRef]

J. Mod. Opt. (2)

Q. Yang, B. Zhao, and R. Zhou, “Novel moving cat’s-eye-pair interferometer,” J. Mod. Opt. 56, 1283–1287(2009).
[CrossRef]

W. H. Steel, “On Möbius-band interferometers,” J. Mod. Opt. 11, 211–217 (1964).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

Q. Yang, R. Zhou, and B. Zhao, “Novel moving-corner-cube-pair interferometer,” J. Opt. A: Pure Appl. Opt. 11, 015505 (2009).
[CrossRef]

J. Opt. Soc. Am. (6)

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

P. Haschberger and V. Tank, “Optimization of a Michelson interferometer with a rotating retroreflector in optical design, spectral resolution, and optical throughput,” J. Opt. Soc. Am. A. 10, 2338–2345 (1993).
[CrossRef]

Opt. Commun. (1)

H. R. Chandrasekhar, L. Genzel, and J. Kuhl, “Double-beam Fourier spectroscopy with interferometric background compensation,” Opt. Commun. 17, 106–110(1976).
[CrossRef]

Other (3)

W. H. Steel, “Interferometers for Fourier spectroscopy,” in Aspen International Conference on Fourier Spectroscopy (Air Force Cambridge Research Laboratories, 1970), p. 43.

P. R. Griffiths and J. A. de Haseth, Fourier Transform Infrared Spectrometry (Wiley-Interscience, 2007).
[CrossRef]

Bomem, Incorporated, interferometers such as Models DA3-002, DA3-01, and DA3-02.

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Figures (7)

Fig. 1
Fig. 1

Optical layout of the novel MCCMI.

Fig. 2
Fig. 2

Ray tracing of an ideal CCM.

Fig. 3
Fig. 3

Two orthogonal plane surfaces with a right-angle error: S 1 and S 2 , plane surfaces; N 1 and N 2 , unit normal vectors of surfaces S 1 and S 2 ; and δ, right-angle error between orthogonal plane surfaces S 1 and S 2 .

Fig. 4
Fig. 4

Actual CCM with right-angle errors: N 1 , N 2 , and N 3 , unit normal vectors of the plane mirrors I, II, and III; ϕ 12 , right-angle error between mirrors I and II; ϕ 23 , right-angle error between mirrors II and III; and ϕ 13 , right-angle error between mirrors I and III.

Fig. 5
Fig. 5

Equivalent sketch map of the light path with a MCCM deviation angle: L, length of the light path from the FDSM to the detector for the moving arm of the interferometer; β, deviation angle of the MCCM; and d 0 , distance from the corner point of the MCCM to the center of the incident beam.

Fig. 6
Fig. 6

Sketch of the integral of the interference intensity for a square aperture.

Fig. 7
Fig. 7

Equivalent sketch map of the light path with a FDSM tilt: L 1 and L 2 , length of the light path from surfaces 1 and 2 of the FDSM to the detector; and θ, tilt angle of the FDSM.

Equations (49)

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x = 4 l ,
I ( x ) = B ( σ ) [ 1 + cos ( 2 π σ x ) ] ,
A = A 2 ( A · N ) N ,
R 2 = R 1 2 ( R 1 · N 1 ) N 1 = a i b j c k ,
R 3 = R 2 2 ( R 2 · N 2 ) N 2 = a i + b j c k ,
R 4 = R 3 2 ( R 3 · N 3 ) N 3 = a i + b j + c k = R 1 .
N 1 · N 2 = cos ( 90 ° δ ) = sin δ .
N 1 x · N 2 x + N 1 y · N 2 y + N 1 z · N 2 z = sin δ .
N 1 = i ,
N 2 = ϕ 12 i j ,
N 3 = ϕ 13 i ϕ 23 j k .
R 2 = R 1 2 ( R 1 · N 1 ) N 1 = a i b j c k ,
R 3 = R 2 2 ( R 2 · N 2 ) N 2 = ( a + 2 b ϕ 12 2 a ϕ 12 2 ) i + ( b 2 a ϕ 12 ) j c k .
R 3 = ( a + 2 b ϕ 12 ) i + ( b 2 a ϕ 12 ) j c k .
R 4 = R 3 2 ( R 3 · N 3 ) N 3 = ( a + 2 b ϕ 12 2 a ϕ 13 2 4 b ϕ 12 ϕ 13 2 2 b ϕ 13 ϕ 23 + 4 a ϕ 12 ϕ 23 ϕ 13 + 2 c ϕ 13 ) i + ( b 2 a ϕ 12 2 a ϕ 13 ϕ 23 4 b ϕ 12 ϕ 23 ϕ 13 2 b ϕ 23 2 + 4 a ϕ 12 ϕ 23 2 + 2 c ϕ 23 ) j + ( c 2 a ϕ 13 4 b ϕ 12 ϕ 13 2 b ϕ 23 + 4 a ϕ 12 ϕ 23 ) k .
R 4 = ( a + 2 b ϕ 12 + 2 c ϕ 13 ) i + ( b 2 a ϕ 12 + 2 c ϕ 23 ) j + ( c 2 a ϕ 13 2 b ϕ 23 ) k .
cos β = R 1 · R 4 | R 1 | · | R 4 | = a 2 + b 2 + c 2 ( a + 2 b ϕ 12 + 2 c ϕ 13 ) 2 + ( b 2 a ϕ 12 + 2 c ϕ 23 ) 2 + ( c 2 a ϕ 13 2 b ϕ 23 ) 2 .
a = b = c = 1 3 .
( a + 2 b ϕ 12 + 2 c ϕ 13 ) 2 + ( b 2 a ϕ 12 + 2 c ϕ 23 ) 2 + ( c 2 a ϕ 13 2 b ϕ 23 ) 2 = a 2 + b 2 + c 2 + 4 ( a 2 + b 2 ) ϕ 12 2 + 4 ( b 2 + c 2 ) ϕ 23 2 + 4 ( a 2 + c 2 ) ϕ 13 2 + 8 b c ϕ 12 ϕ 13 + 8 a b ϕ 13 ϕ 23 8 a c ϕ 12 ϕ 23 .
cos β = 1 1 + 8 3 ( ϕ 12 2 + ϕ 23 2 + ϕ 13 2 + ϕ 12 ϕ 13 + ϕ 13 ϕ 23 ϕ 12 ϕ 23 ) .
sin β = 1 cos 2 β = 8 3 ( ϕ 12 2 + ϕ 23 2 + ϕ 13 2 + ϕ 12 ϕ 13 + ϕ 13 ϕ 23 ϕ 12 ϕ 23 ) 1 + 8 3 ( ϕ 12 2 + ϕ 23 2 + ϕ 13 2 + ϕ 12 ϕ 13 + ϕ 13 ϕ 23 ϕ 12 ϕ 23 ) .
sin β 8 3 ( ϕ 12 2 + ϕ 23 2 + ϕ 13 2 + ϕ 12 ϕ 13 + ϕ 13 ϕ 23 ϕ 12 ϕ 23 ) .
β = sin β = 8 3 ( ϕ 12 2 + ϕ 23 2 + ϕ 13 2 + ϕ 12 ϕ 13 + ϕ 13 ϕ 23 ϕ 12 ϕ 23 ) .
β 123 = β 321 = 8 3 ( ϕ 12 2 + ϕ 23 2 + ϕ 13 2 + ϕ 12 ϕ 13 + ϕ 13 ϕ 23 ϕ 12 ϕ 23 ) ,
β 132 = β 231 = 8 3 ( ϕ 12 2 + ϕ 23 2 + ϕ 13 2 + ϕ 12 ϕ 13 + ϕ 12 ϕ 23 ϕ 13 ϕ 23 ) ,
β 213 = β 312 = 8 3 ( ϕ 12 2 + ϕ 23 2 + ϕ 13 2 + ϕ 13 ϕ 23 + ϕ 12 ϕ 23 ϕ 12 ϕ 13 ) .
x c = L cos 2 β L = 2 L sin 2 β cos 2 β ,
δ x = ( ξ + d 0 ) tan β + ( ξ + d 0 ) tan β cos 2 β = ( ξ + d 0 ) tan 2 β ,
m = L tan 2 β .
x = x + x c + δ x = x + 2 L sin 2 β cos 2 β + ( ξ + d 0 ) tan 2 β ,
S = S 1 + S 2 = D 2 .
I ( x ) = 1 S S 1 B ( σ ) [ 1 + cos ( 2 π σ x ) ] d S 1 + 1 S S 2 B ( σ ) d S 2 = B ( σ ) + 1 S S 1 B ( σ ) cos ( 2 π σ x ) d S 1 .
I ( x ) = B ( σ ) { 1 + sin [ π σ ( D L tan 2 β ) tan 2 β ] π σ D tan 2 β · cos { 2 π σ [ x + 2 L sin 2 β cos 2 β + ( L tan 2 β 2 + d 0 ) tan 2 β ] } } .
M ( D , L , β ) = sin [ π σ ( D L tan 2 β ) tan 2 β ] π σ D tan 2 β .
tan 2 β = 9 L 2 + 0.6 π 2 σ 2 D 4 3 L π 2 σ 2 D 3 .
β = 9 L 2 + 0.6 π 2 σ 2 D 4 3 L 2 π 2 σ 2 D 3 .
β max = 9 L max 2 + 0.6 π 2 σ 2 D 4 3 L max 2 π 2 σ 2 D 3 ,
φ ( L , d 0 , β ) = 2 π σ [ 2 L sin 2 β cos 2 β + ( L tan 2 β 2 + d 0 ) tan 2 β ] .
| Δ x k | = | x θ k x k | λ SNR ,
{ 2 π σ x k = ( 2 k + 1 2 ) π 2 π σ [ x θ k + 2 L sin 2 β cos 2 β + ( L tan 2 β 2 + d 0 ) tan 2 β ] = ( 2 k + 1 2 ) π { x k = 4 k + 1 4 λ x θ k = 4 k + 1 4 λ 2 L sin 2 β cos 2 β ( L tan 2 β 2 + d 0 ) tan 2 β ,
| 2 L sin 2 β cos 2 β + ( L tan 2 β 2 + d 0 ) tan 2 β | λ SNR .
β d 0 2 + 4 λ L SNR d 0 4 L .
β max = d 0 2 + 4 λ L max SNR d 0 4 L max ,
x = x + L 2 L 1 cos 2 θ ( L 2 L 1 ) = x + 2 ( L 2 L 1 ) sin 2 θ cos 2 θ ,
I ( x ) = B ( σ ) { 1 + D L 2 tan 2 θ D L 1 tan 2 θ cos [ 2 π σ ( x + 2 ( L 2 L 1 ) sin 2 θ cos 2 θ ) ] } .
M ( D , L 1 , L 2 , θ ) = D L 2 tan 2 θ D L 1 tan 2 θ ,
φ ( L 1 , L 2 , θ ) = 2 π σ · 2 ( L 2 L 1 ) sin 2 θ cos 2 θ .
θ max = 1 2 arctan D 10 ( L 2 max 0.9 L 1 min ) ,
θ max = arcsin λ 2 λ + 2 ( L 2 max L 1 min ) · SNR ,

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