Abstract

In sinusoidal phase-modulating laser diode interferometers, an injection current of a laser diode is sinusoidally modulated to scan the laser wavelength. However, the modulation of the injection current also involves an intensity modulation of the light, which increases the measurement error if a conventional signal processing is used. A novel signal processing for displacement measurement is proposed to eliminate the influence of the intensity modulation. Numerical simulation results and experimental results make it clear that an optimal depth of the sinusoidal phase modulation exists that can reduce the measurement error to a few nanometers.

© 2012 Optical Society of America

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References

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  1. O. Sasaki and K. Takahashi, “Sinusoidal phase modulating interferometer using optical fibers for displacement measurement,” Appl. Opt. 27, 4139–4142 (1988).
    [CrossRef]
  2. K. Wang, Z. Ding, Y. Zeng, J. Meng, and M. Chen, “Sinusoidal B-M method based spectral domain optical coherence tomography for the elimination of complex-conjugate artifact,” Opt. Express. 17, 16820–16833 (2009).
    [CrossRef]
  3. G. Heinzel, F. G. Cervantes, A. G. Marín, J. Kullmann, W. Feng, and K. Danzmann, “Deep phase modulation interferometry,” Opt. Express. 18, 19076–19086 (2010).
    [CrossRef]
  4. K. Falaggis, D. Towers, and C. Towers, “Phase measurement through sinusoidal excitation with application to multi-wavelength interferometry,” J. Opt. A 11, 054008(2009).
    [CrossRef]
  5. U. Minoni, E. Sardini, E. Gelmini, F. Docchio, and D. Marioli, “A high-frequency sinusoidal phase-modulation interferometer using an electro-optic modulator: Development and evaluation,” Rev. Sci. Instrum. 62, 2579–2583(1991).
    [CrossRef]
  6. T. Suzuki, M. Matsuda, O. Sasaki, and T. Maruyama, “Laserdiode interferometer with a photothermal modulation,” Appl. Opt. 38, 7069–7075 (1999).
    [CrossRef]
  7. X. Wang, X. Wang, F. Qian, G. Chen, G. Chen, and Z. Fang, “Photothermal modulation of laser diode wavelength: application to sinusoiadal phase-modulating interferometer for displacement measurements,” Opt. Laser Technol. 31, 559–564 (1999).
    [CrossRef]
  8. X. Wang, X. Wang, Y. Liu, C. Zhang, and D. Yu, “A sinusoidal phase-modulating fiber-optic interferometer insensitive to the intensity change of the light source,” Opt. Laser Technol. 35, 219–222 (2003).
    [CrossRef]
  9. Z. Li, X. Wang, Y. Liu, and Y. Bu, “All fiber-optic sinusoidal phase-modulating interferometer insensitive to intensity modulation of light source,” Chin. J. Lasers 34, 1267–1270 (2007).
  10. Z. Li, X. Wang, P. Bu, B. Huang, and D. Zhen, “Sinusoidal phase-modulating laser diode interferometer insensitive to the intensity modulation of light source,” Optik 120, 799–803(2009).
    [CrossRef]
  11. O. Sasaki, T. Suzuki, and K. Takahashi, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29, 1511–1515 (1990).
    [CrossRef]
  12. X. Wang, X. Wang, H. Lu, F. Qian, and Y. Bu, “Laser diode interferometer used to measure displacements within large range with a few nanometer accuracy,” Opt. Laser Techonol. 33, 219–223 (2001).
    [CrossRef]

2010 (1)

G. Heinzel, F. G. Cervantes, A. G. Marín, J. Kullmann, W. Feng, and K. Danzmann, “Deep phase modulation interferometry,” Opt. Express. 18, 19076–19086 (2010).
[CrossRef]

2009 (3)

K. Falaggis, D. Towers, and C. Towers, “Phase measurement through sinusoidal excitation with application to multi-wavelength interferometry,” J. Opt. A 11, 054008(2009).
[CrossRef]

K. Wang, Z. Ding, Y. Zeng, J. Meng, and M. Chen, “Sinusoidal B-M method based spectral domain optical coherence tomography for the elimination of complex-conjugate artifact,” Opt. Express. 17, 16820–16833 (2009).
[CrossRef]

Z. Li, X. Wang, P. Bu, B. Huang, and D. Zhen, “Sinusoidal phase-modulating laser diode interferometer insensitive to the intensity modulation of light source,” Optik 120, 799–803(2009).
[CrossRef]

2007 (1)

Z. Li, X. Wang, Y. Liu, and Y. Bu, “All fiber-optic sinusoidal phase-modulating interferometer insensitive to intensity modulation of light source,” Chin. J. Lasers 34, 1267–1270 (2007).

2003 (1)

X. Wang, X. Wang, Y. Liu, C. Zhang, and D. Yu, “A sinusoidal phase-modulating fiber-optic interferometer insensitive to the intensity change of the light source,” Opt. Laser Technol. 35, 219–222 (2003).
[CrossRef]

2001 (1)

X. Wang, X. Wang, H. Lu, F. Qian, and Y. Bu, “Laser diode interferometer used to measure displacements within large range with a few nanometer accuracy,” Opt. Laser Techonol. 33, 219–223 (2001).
[CrossRef]

1999 (2)

T. Suzuki, M. Matsuda, O. Sasaki, and T. Maruyama, “Laserdiode interferometer with a photothermal modulation,” Appl. Opt. 38, 7069–7075 (1999).
[CrossRef]

X. Wang, X. Wang, F. Qian, G. Chen, G. Chen, and Z. Fang, “Photothermal modulation of laser diode wavelength: application to sinusoiadal phase-modulating interferometer for displacement measurements,” Opt. Laser Technol. 31, 559–564 (1999).
[CrossRef]

1991 (1)

U. Minoni, E. Sardini, E. Gelmini, F. Docchio, and D. Marioli, “A high-frequency sinusoidal phase-modulation interferometer using an electro-optic modulator: Development and evaluation,” Rev. Sci. Instrum. 62, 2579–2583(1991).
[CrossRef]

1990 (1)

O. Sasaki, T. Suzuki, and K. Takahashi, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29, 1511–1515 (1990).
[CrossRef]

1988 (1)

Bu, P.

Z. Li, X. Wang, P. Bu, B. Huang, and D. Zhen, “Sinusoidal phase-modulating laser diode interferometer insensitive to the intensity modulation of light source,” Optik 120, 799–803(2009).
[CrossRef]

Bu, Y.

Z. Li, X. Wang, Y. Liu, and Y. Bu, “All fiber-optic sinusoidal phase-modulating interferometer insensitive to intensity modulation of light source,” Chin. J. Lasers 34, 1267–1270 (2007).

X. Wang, X. Wang, H. Lu, F. Qian, and Y. Bu, “Laser diode interferometer used to measure displacements within large range with a few nanometer accuracy,” Opt. Laser Techonol. 33, 219–223 (2001).
[CrossRef]

Cervantes, F. G.

G. Heinzel, F. G. Cervantes, A. G. Marín, J. Kullmann, W. Feng, and K. Danzmann, “Deep phase modulation interferometry,” Opt. Express. 18, 19076–19086 (2010).
[CrossRef]

Chen, G.

X. Wang, X. Wang, F. Qian, G. Chen, G. Chen, and Z. Fang, “Photothermal modulation of laser diode wavelength: application to sinusoiadal phase-modulating interferometer for displacement measurements,” Opt. Laser Technol. 31, 559–564 (1999).
[CrossRef]

X. Wang, X. Wang, F. Qian, G. Chen, G. Chen, and Z. Fang, “Photothermal modulation of laser diode wavelength: application to sinusoiadal phase-modulating interferometer for displacement measurements,” Opt. Laser Technol. 31, 559–564 (1999).
[CrossRef]

Chen, M.

K. Wang, Z. Ding, Y. Zeng, J. Meng, and M. Chen, “Sinusoidal B-M method based spectral domain optical coherence tomography for the elimination of complex-conjugate artifact,” Opt. Express. 17, 16820–16833 (2009).
[CrossRef]

Danzmann, K.

G. Heinzel, F. G. Cervantes, A. G. Marín, J. Kullmann, W. Feng, and K. Danzmann, “Deep phase modulation interferometry,” Opt. Express. 18, 19076–19086 (2010).
[CrossRef]

Ding, Z.

K. Wang, Z. Ding, Y. Zeng, J. Meng, and M. Chen, “Sinusoidal B-M method based spectral domain optical coherence tomography for the elimination of complex-conjugate artifact,” Opt. Express. 17, 16820–16833 (2009).
[CrossRef]

Docchio, F.

U. Minoni, E. Sardini, E. Gelmini, F. Docchio, and D. Marioli, “A high-frequency sinusoidal phase-modulation interferometer using an electro-optic modulator: Development and evaluation,” Rev. Sci. Instrum. 62, 2579–2583(1991).
[CrossRef]

Falaggis, K.

K. Falaggis, D. Towers, and C. Towers, “Phase measurement through sinusoidal excitation with application to multi-wavelength interferometry,” J. Opt. A 11, 054008(2009).
[CrossRef]

Fang, Z.

X. Wang, X. Wang, F. Qian, G. Chen, G. Chen, and Z. Fang, “Photothermal modulation of laser diode wavelength: application to sinusoiadal phase-modulating interferometer for displacement measurements,” Opt. Laser Technol. 31, 559–564 (1999).
[CrossRef]

Feng, W.

G. Heinzel, F. G. Cervantes, A. G. Marín, J. Kullmann, W. Feng, and K. Danzmann, “Deep phase modulation interferometry,” Opt. Express. 18, 19076–19086 (2010).
[CrossRef]

Gelmini, E.

U. Minoni, E. Sardini, E. Gelmini, F. Docchio, and D. Marioli, “A high-frequency sinusoidal phase-modulation interferometer using an electro-optic modulator: Development and evaluation,” Rev. Sci. Instrum. 62, 2579–2583(1991).
[CrossRef]

Heinzel, G.

G. Heinzel, F. G. Cervantes, A. G. Marín, J. Kullmann, W. Feng, and K. Danzmann, “Deep phase modulation interferometry,” Opt. Express. 18, 19076–19086 (2010).
[CrossRef]

Huang, B.

Z. Li, X. Wang, P. Bu, B. Huang, and D. Zhen, “Sinusoidal phase-modulating laser diode interferometer insensitive to the intensity modulation of light source,” Optik 120, 799–803(2009).
[CrossRef]

Kullmann, J.

G. Heinzel, F. G. Cervantes, A. G. Marín, J. Kullmann, W. Feng, and K. Danzmann, “Deep phase modulation interferometry,” Opt. Express. 18, 19076–19086 (2010).
[CrossRef]

Li, Z.

Z. Li, X. Wang, P. Bu, B. Huang, and D. Zhen, “Sinusoidal phase-modulating laser diode interferometer insensitive to the intensity modulation of light source,” Optik 120, 799–803(2009).
[CrossRef]

Z. Li, X. Wang, Y. Liu, and Y. Bu, “All fiber-optic sinusoidal phase-modulating interferometer insensitive to intensity modulation of light source,” Chin. J. Lasers 34, 1267–1270 (2007).

Liu, Y.

Z. Li, X. Wang, Y. Liu, and Y. Bu, “All fiber-optic sinusoidal phase-modulating interferometer insensitive to intensity modulation of light source,” Chin. J. Lasers 34, 1267–1270 (2007).

X. Wang, X. Wang, Y. Liu, C. Zhang, and D. Yu, “A sinusoidal phase-modulating fiber-optic interferometer insensitive to the intensity change of the light source,” Opt. Laser Technol. 35, 219–222 (2003).
[CrossRef]

Lu, H.

X. Wang, X. Wang, H. Lu, F. Qian, and Y. Bu, “Laser diode interferometer used to measure displacements within large range with a few nanometer accuracy,” Opt. Laser Techonol. 33, 219–223 (2001).
[CrossRef]

Marín, A. G.

G. Heinzel, F. G. Cervantes, A. G. Marín, J. Kullmann, W. Feng, and K. Danzmann, “Deep phase modulation interferometry,” Opt. Express. 18, 19076–19086 (2010).
[CrossRef]

Marioli, D.

U. Minoni, E. Sardini, E. Gelmini, F. Docchio, and D. Marioli, “A high-frequency sinusoidal phase-modulation interferometer using an electro-optic modulator: Development and evaluation,” Rev. Sci. Instrum. 62, 2579–2583(1991).
[CrossRef]

Maruyama, T.

Matsuda, M.

Meng, J.

K. Wang, Z. Ding, Y. Zeng, J. Meng, and M. Chen, “Sinusoidal B-M method based spectral domain optical coherence tomography for the elimination of complex-conjugate artifact,” Opt. Express. 17, 16820–16833 (2009).
[CrossRef]

Minoni, U.

U. Minoni, E. Sardini, E. Gelmini, F. Docchio, and D. Marioli, “A high-frequency sinusoidal phase-modulation interferometer using an electro-optic modulator: Development and evaluation,” Rev. Sci. Instrum. 62, 2579–2583(1991).
[CrossRef]

Qian, F.

X. Wang, X. Wang, H. Lu, F. Qian, and Y. Bu, “Laser diode interferometer used to measure displacements within large range with a few nanometer accuracy,” Opt. Laser Techonol. 33, 219–223 (2001).
[CrossRef]

X. Wang, X. Wang, F. Qian, G. Chen, G. Chen, and Z. Fang, “Photothermal modulation of laser diode wavelength: application to sinusoiadal phase-modulating interferometer for displacement measurements,” Opt. Laser Technol. 31, 559–564 (1999).
[CrossRef]

Sardini, E.

U. Minoni, E. Sardini, E. Gelmini, F. Docchio, and D. Marioli, “A high-frequency sinusoidal phase-modulation interferometer using an electro-optic modulator: Development and evaluation,” Rev. Sci. Instrum. 62, 2579–2583(1991).
[CrossRef]

Sasaki, O.

Suzuki, T.

T. Suzuki, M. Matsuda, O. Sasaki, and T. Maruyama, “Laserdiode interferometer with a photothermal modulation,” Appl. Opt. 38, 7069–7075 (1999).
[CrossRef]

O. Sasaki, T. Suzuki, and K. Takahashi, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29, 1511–1515 (1990).
[CrossRef]

Takahashi, K.

O. Sasaki, T. Suzuki, and K. Takahashi, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29, 1511–1515 (1990).
[CrossRef]

O. Sasaki and K. Takahashi, “Sinusoidal phase modulating interferometer using optical fibers for displacement measurement,” Appl. Opt. 27, 4139–4142 (1988).
[CrossRef]

Towers, C.

K. Falaggis, D. Towers, and C. Towers, “Phase measurement through sinusoidal excitation with application to multi-wavelength interferometry,” J. Opt. A 11, 054008(2009).
[CrossRef]

Towers, D.

K. Falaggis, D. Towers, and C. Towers, “Phase measurement through sinusoidal excitation with application to multi-wavelength interferometry,” J. Opt. A 11, 054008(2009).
[CrossRef]

Wang, K.

K. Wang, Z. Ding, Y. Zeng, J. Meng, and M. Chen, “Sinusoidal B-M method based spectral domain optical coherence tomography for the elimination of complex-conjugate artifact,” Opt. Express. 17, 16820–16833 (2009).
[CrossRef]

Wang, X.

Z. Li, X. Wang, P. Bu, B. Huang, and D. Zhen, “Sinusoidal phase-modulating laser diode interferometer insensitive to the intensity modulation of light source,” Optik 120, 799–803(2009).
[CrossRef]

Z. Li, X. Wang, Y. Liu, and Y. Bu, “All fiber-optic sinusoidal phase-modulating interferometer insensitive to intensity modulation of light source,” Chin. J. Lasers 34, 1267–1270 (2007).

X. Wang, X. Wang, Y. Liu, C. Zhang, and D. Yu, “A sinusoidal phase-modulating fiber-optic interferometer insensitive to the intensity change of the light source,” Opt. Laser Technol. 35, 219–222 (2003).
[CrossRef]

X. Wang, X. Wang, Y. Liu, C. Zhang, and D. Yu, “A sinusoidal phase-modulating fiber-optic interferometer insensitive to the intensity change of the light source,” Opt. Laser Technol. 35, 219–222 (2003).
[CrossRef]

X. Wang, X. Wang, H. Lu, F. Qian, and Y. Bu, “Laser diode interferometer used to measure displacements within large range with a few nanometer accuracy,” Opt. Laser Techonol. 33, 219–223 (2001).
[CrossRef]

X. Wang, X. Wang, H. Lu, F. Qian, and Y. Bu, “Laser diode interferometer used to measure displacements within large range with a few nanometer accuracy,” Opt. Laser Techonol. 33, 219–223 (2001).
[CrossRef]

X. Wang, X. Wang, F. Qian, G. Chen, G. Chen, and Z. Fang, “Photothermal modulation of laser diode wavelength: application to sinusoiadal phase-modulating interferometer for displacement measurements,” Opt. Laser Technol. 31, 559–564 (1999).
[CrossRef]

X. Wang, X. Wang, F. Qian, G. Chen, G. Chen, and Z. Fang, “Photothermal modulation of laser diode wavelength: application to sinusoiadal phase-modulating interferometer for displacement measurements,” Opt. Laser Technol. 31, 559–564 (1999).
[CrossRef]

Yu, D.

X. Wang, X. Wang, Y. Liu, C. Zhang, and D. Yu, “A sinusoidal phase-modulating fiber-optic interferometer insensitive to the intensity change of the light source,” Opt. Laser Technol. 35, 219–222 (2003).
[CrossRef]

Zeng, Y.

K. Wang, Z. Ding, Y. Zeng, J. Meng, and M. Chen, “Sinusoidal B-M method based spectral domain optical coherence tomography for the elimination of complex-conjugate artifact,” Opt. Express. 17, 16820–16833 (2009).
[CrossRef]

Zhang, C.

X. Wang, X. Wang, Y. Liu, C. Zhang, and D. Yu, “A sinusoidal phase-modulating fiber-optic interferometer insensitive to the intensity change of the light source,” Opt. Laser Technol. 35, 219–222 (2003).
[CrossRef]

Zhen, D.

Z. Li, X. Wang, P. Bu, B. Huang, and D. Zhen, “Sinusoidal phase-modulating laser diode interferometer insensitive to the intensity modulation of light source,” Optik 120, 799–803(2009).
[CrossRef]

Appl. Opt. (2)

Chin. J. Lasers (1)

Z. Li, X. Wang, Y. Liu, and Y. Bu, “All fiber-optic sinusoidal phase-modulating interferometer insensitive to intensity modulation of light source,” Chin. J. Lasers 34, 1267–1270 (2007).

J. Opt. A (1)

K. Falaggis, D. Towers, and C. Towers, “Phase measurement through sinusoidal excitation with application to multi-wavelength interferometry,” J. Opt. A 11, 054008(2009).
[CrossRef]

Opt. Eng. (1)

O. Sasaki, T. Suzuki, and K. Takahashi, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29, 1511–1515 (1990).
[CrossRef]

Opt. Express. (2)

K. Wang, Z. Ding, Y. Zeng, J. Meng, and M. Chen, “Sinusoidal B-M method based spectral domain optical coherence tomography for the elimination of complex-conjugate artifact,” Opt. Express. 17, 16820–16833 (2009).
[CrossRef]

G. Heinzel, F. G. Cervantes, A. G. Marín, J. Kullmann, W. Feng, and K. Danzmann, “Deep phase modulation interferometry,” Opt. Express. 18, 19076–19086 (2010).
[CrossRef]

Opt. Laser Technol. (2)

X. Wang, X. Wang, F. Qian, G. Chen, G. Chen, and Z. Fang, “Photothermal modulation of laser diode wavelength: application to sinusoiadal phase-modulating interferometer for displacement measurements,” Opt. Laser Technol. 31, 559–564 (1999).
[CrossRef]

X. Wang, X. Wang, Y. Liu, C. Zhang, and D. Yu, “A sinusoidal phase-modulating fiber-optic interferometer insensitive to the intensity change of the light source,” Opt. Laser Technol. 35, 219–222 (2003).
[CrossRef]

Opt. Laser Techonol. (1)

X. Wang, X. Wang, H. Lu, F. Qian, and Y. Bu, “Laser diode interferometer used to measure displacements within large range with a few nanometer accuracy,” Opt. Laser Techonol. 33, 219–223 (2001).
[CrossRef]

Optik (1)

Z. Li, X. Wang, P. Bu, B. Huang, and D. Zhen, “Sinusoidal phase-modulating laser diode interferometer insensitive to the intensity modulation of light source,” Optik 120, 799–803(2009).
[CrossRef]

Rev. Sci. Instrum. (1)

U. Minoni, E. Sardini, E. Gelmini, F. Docchio, and D. Marioli, “A high-frequency sinusoidal phase-modulation interferometer using an electro-optic modulator: Development and evaluation,” Rev. Sci. Instrum. 62, 2579–2583(1991).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Sinusoidal phase-modulating laser diode interferometer using optical fibers for displacement measurement.

Fig. 2.
Fig. 2.

Relationship between SPM depth z and Rm(z) in z(0.5,3.5).

Fig. 3.
Fig. 3.

Relation between a and determination ratio mb.

Fig. 4.
Fig. 4.

Absolute values of determination error Δz.

Fig. 5.
Fig. 5.

Measurement error εd versus Δmb/mb and Δa at SPM depth of (a) z=1rad, (b) z=2.37rad, and (c) z=3rad.

Fig. 6.
Fig. 6.

(a) Interference signal S(t), Amplitude distributions of (b) its Fourier transform F(ω), (c) F1(ωωc), and (d) F2(ω2ωc).

Fig. 7.
Fig. 7.

(a) Displacement dm(t) measured with modulation depth z=2.37rad. Difference Δd(t) at (b) z=1.01rad, (c) 2.37 rad and (d) 2.98 rad corresponding to amplitude of modulation current a=1.44mA, 3.42 mA, and 4.30 mA, respectively. (e) Measurement error obtained again with z=2.37rad after the measurement of (d).

Tables (1)

Tables Icon

Table 1. Error εd and THD of the Measured Displacement

Equations (19)

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λ(t)=λ0+βλIm(t),g(t)=βI[I0+Im(t)]=S(1+mbcosωct),
z=2πaβλL0/λ02,
S(t)=g(t){S0+S1cos[zcosωct+α(t)]}=βI[I0+Im(t)]{S0+S1cos[zcosωct+α(t)]}=S(1+mbcosωct){S0+S1cos[zcosωct+α(t)]},
S(t)=S(1+mbcosωct){S0+S1cos[zcosωct+α(t)]}=S(1+mbcosωct){S0+S1cosα(t)[J0(z)2J2(z)cos2ωct+]S1sinα(t)[2J1(z)cosωct2J3(z)cos3ωct+]},
I{cosα(t)}=0,I{sinα(t)}=0,|ω|ωc2,
F1(ωωc)=12βSS0+12βSS1[J0(z)J2(z)]I{cosα(t)}SS1J1(z)I{sinα(t)},
F2(ω2ωc)=12mbSS1[J1(z)J3(z)]I{sinα(t)}SS1J2(z)I{cosα(t)}.
{K1=12mb[J0(z)J2(z)]K2=J1(z)K3=J2(z)K4=12mb[J1(z)J3(z)].
P1(t)=12mbSS0+SS1K1cosα(t)+SS1K2sinα(t),
P2(t)=SS1K4sinα(t)+SS1K3cosα(t).
α(t)=arctan{sinα(t)cosα(t)}=arctan{K3[P1(t)12mbSS0]K1P2(t)K2P2(t)K4[P1(t)12mbSS0]}.
mb=ka,
P1(t)=12mbSS0+SS1K12+K22sin[α(t)+ϕ],
P2(t)=SS1K32+K42sin[α(t)+φ],
P1max=12mbSS0+SS1K12+K22,P1min=12mbSS0SS1K12+K22.
mbSS0=P1max+P1min.
P2max=SS1K32+K42,P2min=SS1K32+K42.
P1maxP1minP2maxP2min=K12+K22K32+K42=R(z)m.
|K1J1(z)|=|K4J2(z)|,

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