Abstract

SR-POEM, the sounding rocket principle of equivalence measurement, uses a set of six tracking-frequency laser gauges operating in Fabry–Perot cavities to determine the relative acceleration of two test masses (TMs) that are chemically different. One end of each cavity is a flat mirror on a TM; the other end is a concave coupling mirror mounted to a common reference plate. The tracking-frequency laser gauges work by locking a variable frequency laser to the cavity by the method of Pound, Drever, and Hall. Because the TMs are unconstrained, they are expected to rotate slightly during measurement. Although the distance measurements are intended to be based on the TEM00 cavity mode, any misalignment will couple into higher-order transverse modes, particularly the TEM10 and TEM01. Light thus coupled will contribute a spurious signal to the cavity locking servo that causes a bias (i.e., a systematic error) in the length determination. The spurious signal proportional to the misalignment has an antisymmetric distribution at the detector and thus has a zero average, but causes a distance bias because of the inhomogeneity of the detector responsivity. To prevent such bias, SR-POEM includes a servo to keep the incoming laser beam aligned with the cavity. The required performance of that alignment servo is less stringent than has already been achieved by other projects. There is also a spurious signal proportional to the square of the misalignment that produces a symmetric distribution at the detector. This signal is also made unimportant by the operation of an alignment servo, even when operating well above the shot noise limit. We also look at the locking of a laser to a high finesse cavity and conclude that the alignment quality sets a bound on the ratio of measurement accuracy to cavity linewidth.

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  1. R. D. Reasenberg, B. R. Patla, J. D. Phillips, and R. Thapa, “Design and characteristics of a WEP test in a sounding-rocket payload,” Class. Quantum Grav. 29, 184013 (2012).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  5. T. A. Wagner, S. Schlamminger, J. H. Gundlachand, and E. G. Adelberger, “Torsion-balance tests of the weak equivalence principle,” Class. Quantum Grav. 29, 184002 (2012).
    [CrossRef]
  6. N. A. Robertson, J. R. Blackwood, S. Buchman, R. L. Byer, J. Camp, D. Gill, J. Hanson, S. Williams, and P. Zhou, “Kelvin probe measurements: investigations of the patch effect with applications to ST-7 and LISA,” Class. Quantum Grav. 23, 2665–2680 (2006).
    [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]
  13. R. D. Reasenberg, “Aligning a reflection cavity by Anderson’s method,” Appl. Opt. 51, 3132–3136 (2012).
    [CrossRef]

2012

R. D. Reasenberg, B. R. Patla, J. D. Phillips, and R. Thapa, “Design and characteristics of a WEP test in a sounding-rocket payload,” Class. Quantum Grav. 29, 184013 (2012).
[CrossRef]

T. A. Wagner, S. Schlamminger, J. H. Gundlachand, and E. G. Adelberger, “Torsion-balance tests of the weak equivalence principle,” Class. Quantum Grav. 29, 184002 (2012).
[CrossRef]

R. D. Reasenberg, “Aligning a reflection cavity by Anderson’s method,” Appl. Opt. 51, 3132–3136 (2012).
[CrossRef]

2011

2009

J. D. Phillips and R. D. Reasenberg, “Semiconductor laser tracking frequency distance gauge,” Proc. SPIE 7436, 74360T (2009).
[CrossRef]

2008

S. Schlamminger, K.-Y. Choi, T. A. Wagner, J. H. Gundlach, and E. G. Adelberger, “Test of the equivalence principle using a rotating torsion balance,” Phys. Rev. Lett. 100, 041101 (2008).
[CrossRef]

2006

N. A. Robertson, J. R. Blackwood, S. Buchman, R. L. Byer, J. Camp, D. Gill, J. Hanson, S. Williams, and P. Zhou, “Kelvin probe measurements: investigations of the patch effect with applications to ST-7 and LISA,” Class. Quantum Grav. 23, 2665–2680 (2006).
[CrossRef]

1998

T. C. Larason and S. S. Bruce, “Spatial uniformity of responsivity for silicon, gallium nitride, germanium, and indium gallium arsenide photodiodes,” Metrologia 35, 491–496 (1998).
[CrossRef]

1997

D. Babusci, H. Fang, G. Giordano, G. Matone, L. Matone, and V. Sannibale, “Alignment procedure for the VIRGO interferometer: experimental results from the Frascati prototype,” Phys. Lett. A 226, 31–40 (1997).
[CrossRef]

1990

1984

1983

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase, and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Adelberger, E. G.

T. A. Wagner, S. Schlamminger, J. H. Gundlachand, and E. G. Adelberger, “Torsion-balance tests of the weak equivalence principle,” Class. Quantum Grav. 29, 184002 (2012).
[CrossRef]

S. Schlamminger, K.-Y. Choi, T. A. Wagner, J. H. Gundlach, and E. G. Adelberger, “Test of the equivalence principle using a rotating torsion balance,” Phys. Rev. Lett. 100, 041101 (2008).
[CrossRef]

Anderson, D. Z.

Babusci, D.

D. Babusci, H. Fang, G. Giordano, G. Matone, L. Matone, and V. Sannibale, “Alignment procedure for the VIRGO interferometer: experimental results from the Frascati prototype,” Phys. Lett. A 226, 31–40 (1997).
[CrossRef]

Blackwood, J. R.

N. A. Robertson, J. R. Blackwood, S. Buchman, R. L. Byer, J. Camp, D. Gill, J. Hanson, S. Williams, and P. Zhou, “Kelvin probe measurements: investigations of the patch effect with applications to ST-7 and LISA,” Class. Quantum Grav. 23, 2665–2680 (2006).
[CrossRef]

Bruce, S. S.

T. C. Larason and S. S. Bruce, “Spatial uniformity of responsivity for silicon, gallium nitride, germanium, and indium gallium arsenide photodiodes,” Metrologia 35, 491–496 (1998).
[CrossRef]

Buchman, S.

N. A. Robertson, J. R. Blackwood, S. Buchman, R. L. Byer, J. Camp, D. Gill, J. Hanson, S. Williams, and P. Zhou, “Kelvin probe measurements: investigations of the patch effect with applications to ST-7 and LISA,” Class. Quantum Grav. 23, 2665–2680 (2006).
[CrossRef]

Byer, R. L.

N. A. Robertson, J. R. Blackwood, S. Buchman, R. L. Byer, J. Camp, D. Gill, J. Hanson, S. Williams, and P. Zhou, “Kelvin probe measurements: investigations of the patch effect with applications to ST-7 and LISA,” Class. Quantum Grav. 23, 2665–2680 (2006).
[CrossRef]

Camp, J.

N. A. Robertson, J. R. Blackwood, S. Buchman, R. L. Byer, J. Camp, D. Gill, J. Hanson, S. Williams, and P. Zhou, “Kelvin probe measurements: investigations of the patch effect with applications to ST-7 and LISA,” Class. Quantum Grav. 23, 2665–2680 (2006).
[CrossRef]

Choi, K.-Y.

S. Schlamminger, K.-Y. Choi, T. A. Wagner, J. H. Gundlach, and E. G. Adelberger, “Test of the equivalence principle using a rotating torsion balance,” Phys. Rev. Lett. 100, 041101 (2008).
[CrossRef]

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase, and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Fang, H.

D. Babusci, H. Fang, G. Giordano, G. Matone, L. Matone, and V. Sannibale, “Alignment procedure for the VIRGO interferometer: experimental results from the Frascati prototype,” Phys. Lett. A 226, 31–40 (1997).
[CrossRef]

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase, and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Gill, D.

N. A. Robertson, J. R. Blackwood, S. Buchman, R. L. Byer, J. Camp, D. Gill, J. Hanson, S. Williams, and P. Zhou, “Kelvin probe measurements: investigations of the patch effect with applications to ST-7 and LISA,” Class. Quantum Grav. 23, 2665–2680 (2006).
[CrossRef]

Giordano, G.

D. Babusci, H. Fang, G. Giordano, G. Matone, L. Matone, and V. Sannibale, “Alignment procedure for the VIRGO interferometer: experimental results from the Frascati prototype,” Phys. Lett. A 226, 31–40 (1997).
[CrossRef]

Gundlach, J. H.

S. Schlamminger, K.-Y. Choi, T. A. Wagner, J. H. Gundlach, and E. G. Adelberger, “Test of the equivalence principle using a rotating torsion balance,” Phys. Rev. Lett. 100, 041101 (2008).
[CrossRef]

Gundlachand, J. H.

T. A. Wagner, S. Schlamminger, J. H. Gundlachand, and E. G. Adelberger, “Torsion-balance tests of the weak equivalence principle,” Class. Quantum Grav. 29, 184002 (2012).
[CrossRef]

Hall, J. L.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase, and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Hanson, J.

N. A. Robertson, J. R. Blackwood, S. Buchman, R. L. Byer, J. Camp, D. Gill, J. Hanson, S. Williams, and P. Zhou, “Kelvin probe measurements: investigations of the patch effect with applications to ST-7 and LISA,” Class. Quantum Grav. 23, 2665–2680 (2006).
[CrossRef]

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase, and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase, and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Larason, T. C.

T. C. Larason and S. S. Bruce, “Spatial uniformity of responsivity for silicon, gallium nitride, germanium, and indium gallium arsenide photodiodes,” Metrologia 35, 491–496 (1998).
[CrossRef]

Matone, G.

D. Babusci, H. Fang, G. Giordano, G. Matone, L. Matone, and V. Sannibale, “Alignment procedure for the VIRGO interferometer: experimental results from the Frascati prototype,” Phys. Lett. A 226, 31–40 (1997).
[CrossRef]

Matone, L.

D. Babusci, H. Fang, G. Giordano, G. Matone, L. Matone, and V. Sannibale, “Alignment procedure for the VIRGO interferometer: experimental results from the Frascati prototype,” Phys. Lett. A 226, 31–40 (1997).
[CrossRef]

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase, and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Patla, B. R.

R. D. Reasenberg, B. R. Patla, J. D. Phillips, and R. Thapa, “Design and characteristics of a WEP test in a sounding-rocket payload,” Class. Quantum Grav. 29, 184013 (2012).
[CrossRef]

Phillips, J. D.

R. D. Reasenberg, B. R. Patla, J. D. Phillips, and R. Thapa, “Design and characteristics of a WEP test in a sounding-rocket payload,” Class. Quantum Grav. 29, 184013 (2012).
[CrossRef]

R. Thapa, J. D. Phillips, E. Rocco, and R. D. Reasenberg, “Subpicometer length measurement using semiconductor laser tracking frequency gauge,” Opt. Lett. 36, 3759–3761 (2011).
[CrossRef]

J. D. Phillips and R. D. Reasenberg, “Semiconductor laser tracking frequency distance gauge,” Proc. SPIE 7436, 74360T (2009).
[CrossRef]

Reasenberg, R. D.

R. D. Reasenberg, B. R. Patla, J. D. Phillips, and R. Thapa, “Design and characteristics of a WEP test in a sounding-rocket payload,” Class. Quantum Grav. 29, 184013 (2012).
[CrossRef]

R. D. Reasenberg, “Aligning a reflection cavity by Anderson’s method,” Appl. Opt. 51, 3132–3136 (2012).
[CrossRef]

R. Thapa, J. D. Phillips, E. Rocco, and R. D. Reasenberg, “Subpicometer length measurement using semiconductor laser tracking frequency gauge,” Opt. Lett. 36, 3759–3761 (2011).
[CrossRef]

J. D. Phillips and R. D. Reasenberg, “Semiconductor laser tracking frequency distance gauge,” Proc. SPIE 7436, 74360T (2009).
[CrossRef]

Robertson, N. A.

N. A. Robertson, J. R. Blackwood, S. Buchman, R. L. Byer, J. Camp, D. Gill, J. Hanson, S. Williams, and P. Zhou, “Kelvin probe measurements: investigations of the patch effect with applications to ST-7 and LISA,” Class. Quantum Grav. 23, 2665–2680 (2006).
[CrossRef]

Rocco, E.

Sampasand, N. M.

Sannibale, V.

D. Babusci, H. Fang, G. Giordano, G. Matone, L. Matone, and V. Sannibale, “Alignment procedure for the VIRGO interferometer: experimental results from the Frascati prototype,” Phys. Lett. A 226, 31–40 (1997).
[CrossRef]

Schlamminger, S.

T. A. Wagner, S. Schlamminger, J. H. Gundlachand, and E. G. Adelberger, “Torsion-balance tests of the weak equivalence principle,” Class. Quantum Grav. 29, 184002 (2012).
[CrossRef]

S. Schlamminger, K.-Y. Choi, T. A. Wagner, J. H. Gundlach, and E. G. Adelberger, “Test of the equivalence principle using a rotating torsion balance,” Phys. Rev. Lett. 100, 041101 (2008).
[CrossRef]

Thapa, R.

R. D. Reasenberg, B. R. Patla, J. D. Phillips, and R. Thapa, “Design and characteristics of a WEP test in a sounding-rocket payload,” Class. Quantum Grav. 29, 184013 (2012).
[CrossRef]

R. Thapa, J. D. Phillips, E. Rocco, and R. D. Reasenberg, “Subpicometer length measurement using semiconductor laser tracking frequency gauge,” Opt. Lett. 36, 3759–3761 (2011).
[CrossRef]

Wagner, T. A.

T. A. Wagner, S. Schlamminger, J. H. Gundlachand, and E. G. Adelberger, “Torsion-balance tests of the weak equivalence principle,” Class. Quantum Grav. 29, 184002 (2012).
[CrossRef]

S. Schlamminger, K.-Y. Choi, T. A. Wagner, J. H. Gundlach, and E. G. Adelberger, “Test of the equivalence principle using a rotating torsion balance,” Phys. Rev. Lett. 100, 041101 (2008).
[CrossRef]

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase, and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Williams, S.

N. A. Robertson, J. R. Blackwood, S. Buchman, R. L. Byer, J. Camp, D. Gill, J. Hanson, S. Williams, and P. Zhou, “Kelvin probe measurements: investigations of the patch effect with applications to ST-7 and LISA,” Class. Quantum Grav. 23, 2665–2680 (2006).
[CrossRef]

Yariv, A.

A. Yariv, Introduction to Optical Electronics (Holt, Rinehart and Winston, 1976).

Zhou, P.

N. A. Robertson, J. R. Blackwood, S. Buchman, R. L. Byer, J. Camp, D. Gill, J. Hanson, S. Williams, and P. Zhou, “Kelvin probe measurements: investigations of the patch effect with applications to ST-7 and LISA,” Class. Quantum Grav. 23, 2665–2680 (2006).
[CrossRef]

Appl. Opt.

Appl. Phys. B

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase, and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Class. Quantum Grav.

R. D. Reasenberg, B. R. Patla, J. D. Phillips, and R. Thapa, “Design and characteristics of a WEP test in a sounding-rocket payload,” Class. Quantum Grav. 29, 184013 (2012).
[CrossRef]

T. A. Wagner, S. Schlamminger, J. H. Gundlachand, and E. G. Adelberger, “Torsion-balance tests of the weak equivalence principle,” Class. Quantum Grav. 29, 184002 (2012).
[CrossRef]

N. A. Robertson, J. R. Blackwood, S. Buchman, R. L. Byer, J. Camp, D. Gill, J. Hanson, S. Williams, and P. Zhou, “Kelvin probe measurements: investigations of the patch effect with applications to ST-7 and LISA,” Class. Quantum Grav. 23, 2665–2680 (2006).
[CrossRef]

Metrologia

T. C. Larason and S. S. Bruce, “Spatial uniformity of responsivity for silicon, gallium nitride, germanium, and indium gallium arsenide photodiodes,” Metrologia 35, 491–496 (1998).
[CrossRef]

Opt. Lett.

Phys. Lett. A

D. Babusci, H. Fang, G. Giordano, G. Matone, L. Matone, and V. Sannibale, “Alignment procedure for the VIRGO interferometer: experimental results from the Frascati prototype,” Phys. Lett. A 226, 31–40 (1997).
[CrossRef]

Phys. Rev. Lett.

S. Schlamminger, K.-Y. Choi, T. A. Wagner, J. H. Gundlach, and E. G. Adelberger, “Test of the equivalence principle using a rotating torsion balance,” Phys. Rev. Lett. 100, 041101 (2008).
[CrossRef]

Proc. SPIE

J. D. Phillips and R. D. Reasenberg, “Semiconductor laser tracking frequency distance gauge,” Proc. SPIE 7436, 74360T (2009).
[CrossRef]

Other

A. Yariv, Introduction to Optical Electronics (Holt, Rinehart and Winston, 1976).

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Figures (1)

Fig. 1.
Fig. 1.

Cavity response for a finesse of 30: TEM00 mode, solid line; TEM01 mode, dashed line (shifted down for clarity). Spectrum at top shows laser line and first sidebands. Phases shown (e.g., δ1) are for light of the indicated frequency after a single round trip referenced to the light before the round trip.

Equations (46)

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

Ω=υΦ2F,
Um,n=Vm(x)Vn(y),
V0(x)=(2πwx2)14e(xwx)2eix2πλR,V1(x)=(2πwx2)142xwxe(xwx)2eix2πλR.
ViVj*dx=δi,j,
U0=U0,0,U1=U1,0.
Ψin=E0eiωt×(C0U0(J0(m)+J1(m)(eiΩteiΩt))+(p+iq)U1(J0(m)+J1(m)(eiΩteiΩt))),
ΓR=(1eiδ)Rc1Rceiδ,
δ1=2π(f00f10Φ+12),
Ψout=E0eiωtψout,
ψout=(C0U0[J0G0(δ0)+J1(Gm(δ0)eiΩtGm(δ0)eiΩt)]+(p+iq)U1[J0G1(δ1)+J1(G1(δ1+β)eiΩtG1(δ1β)eiΩt)]).
Pout=(Re[Ψout])2ω=E022ψoutψout*,
δ0U0U0=Δ=Δ1U0U1+Δ2U1U1+,
Δ1=21Rc1+Rcq+δ1(1Rc1+Rc)2p,Δ2=(1Rc)4(1+Rc22Rccos(β))(1+Rc)6×δ1csc2(β)(p2+q2)β2.
Δ2=2(1Rc)2(1+Rc22Rccos(2β))(1+Rc)4×δ1csc(2β)(p2+q2)β.
δ0=D(Δ)D(U0U0),
D(UαUβ)=G(x,y)UαUβ*dA.
δ0=ζΔ1+ξΔ2γ.
ϕ=atan(1+Rc1Rctan(β/2)).
ΩΦ2FRc21+Rc,
ζ=(1+ϵ1x)V1V0dx=ϵ1wx2.
U˜0,0=2π1wre(rwr)2eir2πλRU˜2,0=2π1wr(12(rwr)2)e(rwr)2eir2πλR,
U˜m,0U˜n,0*rdrdθ=δm,n,
Ψin=E0eiωt×(C0U˜0,0(J0+J1(eiΩteiΩt))+(τ+iκ)U˜2,0(J0+J1(eiΩteiΩt))),
δ2=2π(f00f20Φ+12),
Ψout=E0eiωtψout,
ψout=(C0U˜0,0(J0G0(δ0)+J1(Gm(δ0)eiΩtGm(δ0)eiΩt)+(τ+iκ)U˜2,0(J0G1(δ2)+J1(G1(δ2+β)eiΩtG1(δ2β)eiΩt)),
δ˜0U˜0,0U˜0,0=Δ˜=Δ˜1U˜0,0U˜2,0+Δ˜2U˜2,0U˜2,0+Δ˜1=21Rc1+Rcτ+δ2(1Rc1+Rc)2κΔ˜2=(1Rc)4(1+Rc22Rccos(β))(1+Rc)6×δ2csc2(β)(τ2+κ2)β2/4,
Δ˜2=(1Rc)2(1+Rc22Rccos(β))(1+Rc)4×δ2csc(β)(τ2+κ2)β.
δ˜0=D(Δ˜)D(U˜0,0U˜0,0),
δ˜0=ζ˜Δ˜1+ξ˜Δ˜2γ˜.
q=q0sin(2πtP),
q¨=q03.32×103s2.
ϵ0=λζ2π(1Rc)(1+Rc)q,
ϵ¨0λζ4F2(1+Rc)q03.32×103s2.
δ0=πF(ζq+ζ˜τ),
fb=Φ2F(ζq+ζ˜τ).
ρ(T)νσ(f,T),
ρ(T)<2αζq+ζ˜τ.
σ(f,T)=σ(f,1)T,
ρ(T)=ρ(1)T,
ΓR=(1eiδ)Rc1Rceiδ=(1+Rc)Rc(1cos(δ))1+Rc22Rccos(δ)i(1Rc)Rcsin(δ)1+Rc22Rccos(δ).
G0(δ0)=0iRc1Rcδ0,
G±m(δ0)=(1+Rc)Rc(1cos(β))1+Rc22Rccos(β)i(1Rc)Rcsin(±β)1+Rc22Rccos(β)+((1+Rc)(1Rc)2Rcsin(±β)(1+Rc22Rccos(β))2i(1Rc)Rc(cos(β)1+Rc22Rccos(β)2Rcsin(β)2(1+Rc22Rccos(β))2))δ0,
G±m(δ0)=iRcβ(1Rc)+(±(1+Rc)Rcβ(1Rc)2iRc(1Rc))δ0.
G1(δ1)=2Rc1+Rc+i(1Rc)Rc(1+Rc)2δ1,
G1(δ1±β)=G1(δ1)+i(1Rc)Rc(1+Rc)2(±β).

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