Abstract

In this paper, a simple and effective control system to monitor and suppress the beam jitter noise at the input of an optical system, called a beam pointing control (BPC) system, will be described, showing the theoretical principle and an experimental demonstration for the application of large-scale gravitational wave (GW) interferometers (ITFs), in particular for the Advanced Virgo detector. For this purpose, the requirements for the control accuracy and the sensing noise will be computed by taking into account the Advanced Virgo optical configuration, and the outcomes will be compared with the experimental measurement obtained in the laboratory. The system has shown unprecedented performance in terms of control accuracy and sensing noise. The BPC system has achieved a control accuracy of 108rad for the tilt and 107m for the shift and a sensing noise of less than 1 nrad/Hz, which is compliant with the Advanced Virgo GW ITF requirements.

© 2014 Optical Society of America

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References

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  1. T. Kanai, A. Suda, S. Bohman, M. Kaku, S. Yamaguchi, and K. Midorikawa, “Pointing stabilization of a high-repetition-rate high-power femtosecond laser for intense few-cycle pulse generation,” Appl. Phys. Lett. 92, 061106 (2008).
    [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]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  14. A. Freise, G. Heinzel, H. Luck, R. Schilling, B. Willke, and K. Danzmann, “Frequency-domain interferometer simulation with higher-order spatial modes,” Class. Quantum Grav. 21, S1067–S1074 (2004).
    [CrossRef]
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    [CrossRef]
  21. The Virgo Collaboration, “The Virgo 3  km interferometer for gravitational wave detection,” J. Opt. A 10, 064009 (2008).
    [CrossRef]
  22. M. Mantovani, “BeaKm pointing control system low frequency accuracy requirements evaluation,” (2013), https://tds.ego-gw.it/ql/?c=9959 .
  23. F. Cleva and J. P. Coulon, “Beam automatic alignment: procedure for optical setup sizing and tuning-application for the reference mass,” .
  24. http://www.eosystems.com/uploads/2/0/1/3/20135707/s-025-078-qd.pdf .
  25. http://www.physikinstrumente.com/en/products/prdetail.php?sortnr=300800 .
  26. A. Bertolini, “EIB-SAS status: improving workability on the bench,” .

2011 (3)

G. Genoud, F. Wojda, M. Burza, A. Persson, and C.-G. Wahlström, “Active control of the pointing of a multi-terawatt laser,” Rev. Sci. Instrum. 82, 033102 (2011).
[CrossRef]

The Virgo Collaboration, “Automatic alignment system during the second science run of the Virgo interferometer,” Astropart. Phys. 34, 327–332 (2011).
[CrossRef]

P. Groß, L. Kleinschmidt, S. Beer, and C. Fallnich, “Beam position stabilization for a confocal multiphoton microscope,” Appl. Opt. 50, 5361–5368 (2011).
[CrossRef]

2010 (2)

G. M. Harry, “Advanced LIGO: the next generation of gravitational wave detectors,” Class. Quantum Grav. 27, 084006 (2010).
[CrossRef]

The Virgo Collaboration, “Automatic alignment for the first science run of the Virgo interferometer,” Astroparticle Phys. 33, 131–139 (2010).

2008 (2)

The Virgo Collaboration, “The Virgo 3  km interferometer for gravitational wave detection,” J. Opt. A 10, 064009 (2008).
[CrossRef]

T. Kanai, A. Suda, S. Bohman, M. Kaku, S. Yamaguchi, and K. Midorikawa, “Pointing stabilization of a high-repetition-rate high-power femtosecond laser for intense few-cycle pulse generation,” Appl. Phys. Lett. 92, 061106 (2008).
[CrossRef]

2005 (1)

2004 (1)

A. Freise, G. Heinzel, H. Luck, R. Schilling, B. Willke, and K. Danzmann, “Frequency-domain interferometer simulation with higher-order spatial modes,” Class. Quantum Grav. 21, S1067–S1074 (2004).
[CrossRef]

2002 (1)

1998 (1)

1997 (1)

T. A. Savard, K. M. O. Hara, and J. E. Thomas, “Laser-noise-induced heating in far-off resonance optical traps,” Phys. Rev. A 56, R1095–R1098 (1997).
[CrossRef]

1996 (1)

F. Barone, E. Calloni, L. Di Fiore, A. Grado, P. Hello, L. Milano, and G. Russo, “Effects of misalignments and beam jitters in interferometric gravitational wave detectors,” Phys. Lett. A 217, 90–96 (1996).
[CrossRef]

1989 (1)

1966 (1)

Araki, K.

Bachar, J.

Barone, F.

F. Barone, E. Calloni, L. Di Fiore, A. Grado, P. Hello, L. Milano, and G. Russo, “Effects of misalignments and beam jitters in interferometric gravitational wave detectors,” Phys. Lett. A 217, 90–96 (1996).
[CrossRef]

Barsuglia, M.

M. Barsuglia, H. Heitmann, and N. Man, “Mode spectrum of a ring Fabry–Perot cavity,” (1998), https://tds.ego-gw.it/ql/?c=680 .

Beer, S.

Bertolini, A.

A. Bertolini, “EIB-SAS status: improving workability on the bench,” .

Bohman, S.

T. Kanai, A. Suda, S. Bohman, M. Kaku, S. Yamaguchi, and K. Midorikawa, “Pointing stabilization of a high-repetition-rate high-power femtosecond laser for intense few-cycle pulse generation,” Appl. Phys. Lett. 92, 061106 (2008).
[CrossRef]

Burza, M.

G. Genoud, F. Wojda, M. Burza, A. Persson, and C.-G. Wahlström, “Active control of the pointing of a multi-terawatt laser,” Rev. Sci. Instrum. 82, 033102 (2011).
[CrossRef]

Calloni, E.

F. Barone, E. Calloni, L. Di Fiore, A. Grado, P. Hello, L. Milano, and G. Russo, “Effects of misalignments and beam jitters in interferometric gravitational wave detectors,” Phys. Lett. A 217, 90–96 (1996).
[CrossRef]

Cleva, F.

F. Cleva and J. P. Coulon, “Beam automatic alignment: procedure for optical setup sizing and tuning-application for the reference mass,” .

Coulon, J. P.

F. Cleva and J. P. Coulon, “Beam automatic alignment: procedure for optical setup sizing and tuning-application for the reference mass,” .

Danzmann, K.

A. Freise, G. Heinzel, H. Luck, R. Schilling, B. Willke, and K. Danzmann, “Frequency-domain interferometer simulation with higher-order spatial modes,” Class. Quantum Grav. 21, S1067–S1074 (2004).
[CrossRef]

Di Fiore, L.

F. Barone, E. Calloni, L. Di Fiore, A. Grado, P. Hello, L. Milano, and G. Russo, “Effects of misalignments and beam jitters in interferometric gravitational wave detectors,” Phys. Lett. A 217, 90–96 (1996).
[CrossRef]

Fallnich, C.

Freise, A.

A. Freise, G. Heinzel, H. Luck, R. Schilling, B. Willke, and K. Danzmann, “Frequency-domain interferometer simulation with higher-order spatial modes,” Class. Quantum Grav. 21, S1067–S1074 (2004).
[CrossRef]

Fritschel, P.

Fujioka, T.

Genin, E.

J. Marque, E. Genin, and M. Parisi, “AdV INJ: Requirements for input beam jitter for SVC configuration,” (2011), https://tds.ego-gw.it/ql/?c=8386 .

Genoud, G.

G. Genoud, F. Wojda, M. Burza, A. Persson, and C.-G. Wahlström, “Active control of the pointing of a multi-terawatt laser,” Rev. Sci. Instrum. 82, 033102 (2011).
[CrossRef]

González, G.

Grado, A.

F. Barone, E. Calloni, L. Di Fiore, A. Grado, P. Hello, L. Milano, and G. Russo, “Effects of misalignments and beam jitters in interferometric gravitational wave detectors,” Phys. Lett. A 217, 90–96 (1996).
[CrossRef]

Groß, P.

Hara, K. M. O.

T. A. Savard, K. M. O. Hara, and J. E. Thomas, “Laser-noise-induced heating in far-off resonance optical traps,” Phys. Rev. A 56, R1095–R1098 (1997).
[CrossRef]

Harry, G. M.

G. M. Harry, “Advanced LIGO: the next generation of gravitational wave detectors,” Class. Quantum Grav. 27, 084006 (2010).
[CrossRef]

Heinzel, G.

A. Freise, G. Heinzel, H. Luck, R. Schilling, B. Willke, and K. Danzmann, “Frequency-domain interferometer simulation with higher-order spatial modes,” Class. Quantum Grav. 21, S1067–S1074 (2004).
[CrossRef]

Heitmann, H.

M. Barsuglia, H. Heitmann, and N. Man, “Mode spectrum of a ring Fabry–Perot cavity,” (1998), https://tds.ego-gw.it/ql/?c=680 .

Hello, P.

F. Barone, E. Calloni, L. Di Fiore, A. Grado, P. Hello, L. Milano, and G. Russo, “Effects of misalignments and beam jitters in interferometric gravitational wave detectors,” Phys. Lett. A 217, 90–96 (1996).
[CrossRef]

Kaku, M.

T. Kanai, A. Suda, S. Bohman, M. Kaku, S. Yamaguchi, and K. Midorikawa, “Pointing stabilization of a high-repetition-rate high-power femtosecond laser for intense few-cycle pulse generation,” Appl. Phys. Lett. 92, 061106 (2008).
[CrossRef]

Kanai, T.

T. Kanai, A. Suda, S. Bohman, M. Kaku, S. Yamaguchi, and K. Midorikawa, “Pointing stabilization of a high-repetition-rate high-power femtosecond laser for intense few-cycle pulse generation,” Appl. Phys. Lett. 92, 061106 (2008).
[CrossRef]

Kleinschmidt, L.

Kogelink, H.

Li, T.

Luck, H.

A. Freise, G. Heinzel, H. Luck, R. Schilling, B. Willke, and K. Danzmann, “Frequency-domain interferometer simulation with higher-order spatial modes,” Class. Quantum Grav. 21, S1067–S1074 (2004).
[CrossRef]

Man, N.

M. Barsuglia, H. Heitmann, and N. Man, “Mode spectrum of a ring Fabry–Perot cavity,” (1998), https://tds.ego-gw.it/ql/?c=680 .

Mantovani, M.

M. Mantovani, “Automatic alignment sensing and control scheme for Advanced Virgo MSRC configuration,” (2011), https://tds.ego-gw.it/ql/?c=8255 .

M. Mantovani, “BeaKm pointing control system low frequency accuracy requirements evaluation,” (2013), https://tds.ego-gw.it/ql/?c=9959 .

Marque, J.

J. Marque, E. Genin, and M. Parisi, “AdV INJ: Requirements for input beam jitter for SVC configuration,” (2011), https://tds.ego-gw.it/ql/?c=8386 .

Matsumi, Y.

Mavalvala, N.

Midorikawa, K.

T. Kanai, A. Suda, S. Bohman, M. Kaku, S. Yamaguchi, and K. Midorikawa, “Pointing stabilization of a high-repetition-rate high-power femtosecond laser for intense few-cycle pulse generation,” Appl. Phys. Lett. 92, 061106 (2008).
[CrossRef]

Milano, L.

F. Barone, E. Calloni, L. Di Fiore, A. Grado, P. Hello, L. Milano, and G. Russo, “Effects of misalignments and beam jitters in interferometric gravitational wave detectors,” Phys. Lett. A 217, 90–96 (1996).
[CrossRef]

Mueller, G.

G. Mueller, “Beam jitter coupling in advanced LIGO,” Opt. Express 13, 7118–7132 (2005).
[CrossRef]

G. Mueller, “Input optics subsystem design requirements document,” .

Obara, M.

Ohta, K.

Parisi, M.

J. Marque, E. Genin, and M. Parisi, “AdV INJ: Requirements for input beam jitter for SVC configuration,” (2011), https://tds.ego-gw.it/ql/?c=8386 .

Persson, A.

G. Genoud, F. Wojda, M. Burza, A. Persson, and C.-G. Wahlström, “Active control of the pointing of a multi-terawatt laser,” Rev. Sci. Instrum. 82, 033102 (2011).
[CrossRef]

Russo, G.

F. Barone, E. Calloni, L. Di Fiore, A. Grado, P. Hello, L. Milano, and G. Russo, “Effects of misalignments and beam jitters in interferometric gravitational wave detectors,” Phys. Lett. A 217, 90–96 (1996).
[CrossRef]

Saito, H.

Savard, T. A.

T. A. Savard, K. M. O. Hara, and J. E. Thomas, “Laser-noise-induced heating in far-off resonance optical traps,” Phys. Rev. A 56, R1095–R1098 (1997).
[CrossRef]

Schilling, R.

A. Freise, G. Heinzel, H. Luck, R. Schilling, B. Willke, and K. Danzmann, “Frequency-domain interferometer simulation with higher-order spatial modes,” Class. Quantum Grav. 21, S1067–S1074 (2004).
[CrossRef]

Shoemaker, D.

Sigg, D.

Suda, A.

T. Kanai, A. Suda, S. Bohman, M. Kaku, S. Yamaguchi, and K. Midorikawa, “Pointing stabilization of a high-repetition-rate high-power femtosecond laser for intense few-cycle pulse generation,” Appl. Phys. Lett. 92, 061106 (2008).
[CrossRef]

Suzuki, Y.

Thomas, J. E.

T. A. Savard, K. M. O. Hara, and J. E. Thomas, “Laser-noise-induced heating in far-off resonance optical traps,” Phys. Rev. A 56, R1095–R1098 (1997).
[CrossRef]

Toyoda, M.

Wahlström, C.-G.

G. Genoud, F. Wojda, M. Burza, A. Persson, and C.-G. Wahlström, “Active control of the pointing of a multi-terawatt laser,” Rev. Sci. Instrum. 82, 033102 (2011).
[CrossRef]

Willke, B.

A. Freise, G. Heinzel, H. Luck, R. Schilling, B. Willke, and K. Danzmann, “Frequency-domain interferometer simulation with higher-order spatial modes,” Class. Quantum Grav. 21, S1067–S1074 (2004).
[CrossRef]

Wojda, F.

G. Genoud, F. Wojda, M. Burza, A. Persson, and C.-G. Wahlström, “Active control of the pointing of a multi-terawatt laser,” Rev. Sci. Instrum. 82, 033102 (2011).
[CrossRef]

Yagi, T.

Yamaguchi, S.

T. Kanai, A. Suda, S. Bohman, M. Kaku, S. Yamaguchi, and K. Midorikawa, “Pointing stabilization of a high-repetition-rate high-power femtosecond laser for intense few-cycle pulse generation,” Appl. Phys. Lett. 92, 061106 (2008).
[CrossRef]

Zucker, M.

Appl. Opt. (5)

Appl. Phys. Lett. (1)

T. Kanai, A. Suda, S. Bohman, M. Kaku, S. Yamaguchi, and K. Midorikawa, “Pointing stabilization of a high-repetition-rate high-power femtosecond laser for intense few-cycle pulse generation,” Appl. Phys. Lett. 92, 061106 (2008).
[CrossRef]

Astropart. Phys. (1)

The Virgo Collaboration, “Automatic alignment system during the second science run of the Virgo interferometer,” Astropart. Phys. 34, 327–332 (2011).
[CrossRef]

Astroparticle Phys. (1)

The Virgo Collaboration, “Automatic alignment for the first science run of the Virgo interferometer,” Astroparticle Phys. 33, 131–139 (2010).

Class. Quantum Grav. (2)

G. M. Harry, “Advanced LIGO: the next generation of gravitational wave detectors,” Class. Quantum Grav. 27, 084006 (2010).
[CrossRef]

A. Freise, G. Heinzel, H. Luck, R. Schilling, B. Willke, and K. Danzmann, “Frequency-domain interferometer simulation with higher-order spatial modes,” Class. Quantum Grav. 21, S1067–S1074 (2004).
[CrossRef]

J. Opt. A (1)

The Virgo Collaboration, “The Virgo 3  km interferometer for gravitational wave detection,” J. Opt. A 10, 064009 (2008).
[CrossRef]

Opt. Express (1)

Phys. Lett. A (1)

F. Barone, E. Calloni, L. Di Fiore, A. Grado, P. Hello, L. Milano, and G. Russo, “Effects of misalignments and beam jitters in interferometric gravitational wave detectors,” Phys. Lett. A 217, 90–96 (1996).
[CrossRef]

Phys. Rev. A (1)

T. A. Savard, K. M. O. Hara, and J. E. Thomas, “Laser-noise-induced heating in far-off resonance optical traps,” Phys. Rev. A 56, R1095–R1098 (1997).
[CrossRef]

Rev. Sci. Instrum. (1)

G. Genoud, F. Wojda, M. Burza, A. Persson, and C.-G. Wahlström, “Active control of the pointing of a multi-terawatt laser,” Rev. Sci. Instrum. 82, 033102 (2011).
[CrossRef]

Other (11)

The Virgo Collaboration, “Advanced Virgo technical design report,” (2012), https://tds.ego-gw.it/ql/?c=8940 .

M. Mantovani, “Automatic alignment sensing and control scheme for Advanced Virgo MSRC configuration,” (2011), https://tds.ego-gw.it/ql/?c=8255 .

M. Evans, “Optickle, frequency domain MATLAB methods for doing interferometer simulation,” Optickle home-page: https://awiki.ligo-wa.caltech.edu/aLIGO/ISC_Modeling_Software .

J. Marque, E. Genin, and M. Parisi, “AdV INJ: Requirements for input beam jitter for SVC configuration,” (2011), https://tds.ego-gw.it/ql/?c=8386 .

M. Mantovani, “BeaKm pointing control system low frequency accuracy requirements evaluation,” (2013), https://tds.ego-gw.it/ql/?c=9959 .

F. Cleva and J. P. Coulon, “Beam automatic alignment: procedure for optical setup sizing and tuning-application for the reference mass,” .

http://www.eosystems.com/uploads/2/0/1/3/20135707/s-025-078-qd.pdf .

http://www.physikinstrumente.com/en/products/prdetail.php?sortnr=300800 .

A. Bertolini, “EIB-SAS status: improving workability on the bench,” .

G. Mueller, “Input optics subsystem design requirements document,” .

M. Barsuglia, H. Heitmann, and N. Man, “Mode spectrum of a ring Fabry–Perot cavity,” (1998), https://tds.ego-gw.it/ql/?c=680 .

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Figures (15)

Fig. 1.
Fig. 1.

Scheme of advanced laser ITF GW detectors.

Fig. 2.
Fig. 2.

Advanced Virgo jitter requirements at the input of the ITF (solid curves) for the tilt and shift degree of freedom. The dashed curves represent the jitter requirements in case the radiation pressure effects have not been taken into account in the modeling, showing requirements much more relaxed at low frequencies of about a factor 30 at 10 Hz.

Fig. 3.
Fig. 3.

Advanced Virgo Jitter requirements at the input of the IMC for the shift and tilt degrees of freedom, blue and black curves, respectively. The requirements for the horizontal and vertical directions are different due to the fact that the filtering of the IMC triangular cavity is different in the two directions.

Fig. 4.
Fig. 4.

Scheme of the effect of a input beam shift and tilt (x and θ) at the entrance of the IMC triangular cavity. The beam will pass through the IMC unperturbed, thanks to the IMC automatic alignment reaching the IMs tilted and shifted after passing through the shaping optics. The requirements of the input beam shift and tilt have been set in order to have a maximum displacement of the beam entering in the north cavity of 104m.

Fig. 5.
Fig. 5.

Principle of the BPC. The beam coming from the laser is shaped to the IMC input by using a telescope. The input beam jitter is then controlled by two piezo tip/tilt actuators and sensed by two quadrant split photodetectors.

Fig. 6.
Fig. 6.

S/αI0 behavior as a function of w for a detector gap of 2b=200μm and size a=3.9mm.

Fig. 7.
Fig. 7.

Top: BPC FF setup showing the beam and Gouy phase propagation. Bottom: BPC NF setup showing the beam and Gouy phase propagation.

Fig. 8.
Fig. 8.

Shift measurement: BPC FF quadrant outputs (top); BPC NF quadrant outputs (bottom).

Fig. 9.
Fig. 9.

Mirror mounted on the piezoelectric actuator PI S330 on the left. Mirror mounted on the piezoelectric actuator PI S340 on the right.

Fig. 10.
Fig. 10.

Transfer function of pitch and yaw direction for the PI S340 piezo actuator (Pzt2).

Fig. 11.
Fig. 11.

Sensing calibration procedure of the FF quadrant (top plot) and the NF quadrant (bottom plot).

Fig. 12.
Fig. 12.

Block scheme for the BPC system.

Fig. 13.
Fig. 13.

BPC open-loop transfer function on the top plot, closed-loop TF on the middle plot, and the phase on the bottom plot for the shift and tilt control filters (red and black curves, respectively). As shown in the transfer function, the unity gain frequency of the two loops is 20 Hz for the tilt direction and 1 Hz for the shift direction.

Fig. 14.
Fig. 14.

Beam shift and tilt spectra at the level of the input of the mode cleaner cavity in case of open and close loop (red and blue curve, respectively) for all the directions. The open loop spectra have been computed with a statistical approach, setting a confidence threshold of 95%, which means the beam displacement spectra will be below that curve for the 95% of the time. The control accuracy RMS (the blue dash curve) fulfill the requirement (the dashed black curve) for all the four degrees of freedom.

Fig. 15.
Fig. 15.

Beam jitter measurement and projection over the detection bandwidth.

Tables (2)

Tables Icon

Table 1. Angular Requirements for Advanced Virgo for the Arm Cavity Modesa

Tables Icon

Table 2. Control Matrix in [μm] for the x and y Directions and in [μrad] in the θx and θy Directions

Equations (36)

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

SJitter=hAdV10×TFW/hTFTEM01,
[ABCD]=[14.36171.050.22.46]
xIMC=|AxITF|2+|BθITF|2·γh,
yIMC=|AxITF|2+|BθITF|2·γv,
θyIMC=|CxITF|2+|DθITF|2·γh,
θxIMC=|CxITF|2+|DθITF|2·γv,
xIM=[1L]·[ABCD]·[1d01]·[xIMCθIMC]<104m,
xIMC<4.2μmθIMC<0.35μrad.
I(x,y)=2I0πw2e2(x+y)2w2.
S(xqd,yqd)=αI*(h1(xqd,yqd)+h2(xqd,yqd)h3(xqd,yqd)h4(xqd,yqd)),
h1(x,y)=Θ(ax)Θ(ay)Θ(xb)Θ(yb)h2(x,y)=Θ(ax)Θ(a+y)Θ(xb)Θ(by)h3(x,y)=Θ(a+x)Θ(a+y)Θ(bx)Θ(by)h4(x,y)=Θ(a+x)Θ(ay)Θ(bx)Θ(yb).
S(xqd,yqd)=αI04U+(xqd)U(yqd),
U±(xqd)=erf(2(axqd)w)erf(2(a+xqd)w)±erf(2(b+xqd)w)erf(2(bxqd)w).
S(xqd,0)=S(xqd)=αI04U+(xqd)U(0)
U(0)=2erf(2aw)2erf(2bw).
U+(xqd)42πw(e2a2w2e2b2w2)xqd
Sh(xqd)=Sxqd
S=αI02πwU(0)(e2a2w2e2b2w2).
SN=SαI022πw.
[xqdθqd]=[1d01][101f1][1d01][xinθin].
xqd=xin[1df]+θin[dd(1df)].
xqd=KNFxin,
KNF=fd+f.
SNF(xin)=22πKNFwNFxin,
w2(z)=λπzR[1+(zz0zR)2],
{z0=zR2(KNFd/f21/f)1/KNF2+zR2/f2zR=zR1/KNF2+zR2/f2,
wNF2=w2(KNFd)=λπzR[1+zR2f2(KNFdf1)2].
wNF2=λπKNF2zR=KNF2w02
SNF(xin)=22πxinw0.
[xqdθqd]=[1d01][101f21][1d1201][101f11][1d01][xinθin].
xqd=xin(df2d+d12(1df2)f1+1)+θin(d+d12(1df2)+d(df2d+d12(1df2)f1+1)).
xqd=KFFθin
KFF=f1f2f1+f2d12
SFF(θin)=22πKFFwFFθin,
wFF2=λπKFF21zR=(λπ)2KFF2w02
SFF(θin)=22πθinλ/(πw0).

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