Abstract

The reconstruction quality of turbulence-induced phase distortions from Hartmann data is calculated for masks with different subpupil forms by means of computer simulations. Four subpupil forms are considered: the circle, the square, the hexagon, and the polar segment. We show that, for the case of a circular aperture, the mask with polar segment subpupils provides the best reconstruction quality.

© 2001 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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2000

1999

1998

D. Kouznetsov, V. V. Voitsekhovich, “Method of random wave vectors in the simulation of correlated random processes,” Meteorol. Z. N. F. 7, 230–236 (1998).

V. V. Voitsekhovich, S. Bara, S. Rios, E. Acosta, “Minimum-error phase reconstruction from Hartmann sensors with circular subpupils,” Opt. Commun. 148, 225–229 (1998).
[CrossRef]

1997

1996

V. V. Voitsekhovich, “Hartmann test in atmospheric research,” J. Opt. Soc. Am. A 8, 1749–1757 (1996).
[CrossRef]

1995

1994

D. R. Purdy, “Fabrication of complex micro-optics components using photo-sculpting through halftone transmission masks,” Pure Appl. Opt. 3, 167–175 (1994).
[CrossRef]

D. Colucci, M. Lloyd-Hart, D. Wittman, R. Angel, A. Ghez, B. McLeod, “A reflective Shack–Hartmann wave-front sensor for adaptive optics,” Publ. Astron. Soc. Pac. 106, 1104–1110 (1994).
[CrossRef]

P. A. Bakut, V. E. Kirakosyants, V. A. Loginov, C. J. Solomon, J. C. Dainty, “Optimal wave-front reconstruction from a Shack–Hartmann sensor by use of a Bayesian algorithm,” Opt. Commun. 109, 10–15 (1994).
[CrossRef]

B. L. Ellerbroek, “First-order performance evaluation of adaptive-optics systems for atmospheric-turbulence compensation in extended-field-of-view astronomical telescopes,” J. Opt. Soc. Am. A 11, 783–805 (1994).
[CrossRef]

1991

F. Rigaut, G. Rousset, P. Kern, J. C. Fontanella, J. P. Gaffard, F. Merkle, “Adaptive optics on a 3.6-m telescope: results and performance,” Astron. Astrosphys. 250, 280–290 (1991).

1990

1989

1988

V. V. Voitsekhovich, V. B. Gubin, A. V. Mikulich, “An estimation of the parameters of adaptive astronomical systems on the base of experimental data,” Opt. Atmosferi. 1, 66–70 (1988) (in Russian).

1983

1980

1976

Acosta, E.

V. V. Voitsekhovich, S. Bara, S. Rios, E. Acosta, “Minimum-error phase reconstruction from Hartmann sensors with circular subpupils,” Opt. Commun. 148, 225–229 (1998).
[CrossRef]

Angel, R.

D. Colucci, M. Lloyd-Hart, D. Wittman, R. Angel, A. Ghez, B. McLeod, “A reflective Shack–Hartmann wave-front sensor for adaptive optics,” Publ. Astron. Soc. Pac. 106, 1104–1110 (1994).
[CrossRef]

Bakut, P. A.

P. A. Bakut, V. E. Kirakosyants, V. A. Loginov, C. J. Solomon, J. C. Dainty, “Optimal wave-front reconstruction from a Shack–Hartmann sensor by use of a Bayesian algorithm,” Opt. Commun. 109, 10–15 (1994).
[CrossRef]

Balakhovskaya, T. I.

T. I. Balakhovskaya, V. I. Borisenko, E. A. Vitrichenko, K. L. Maslennikov, A. M. Prokhorov, P. Z. Sagdeyev, E. V. Trushin, L. S. Chesalin, “Fast Hartmann test for problems in astronomical adaptive optics,” Reports of Academy of Sciences USSR, Dokl. Acad. Nauk SSSR274, 257–260 (1984).

Bara, S.

R. Navarro, E. Moreno-Barriuso, S. Bara, T. Mancebo, “Phase plates for wave aberration compensation in the human eye,” Opt. Lett. 25, 236–238 (2000).
[CrossRef]

V. V. Voitsekhovich, S. Bara, S. Rios, E. Acosta, “Minimum-error phase reconstruction from Hartmann sensors with circular subpupils,” Opt. Commun. 148, 225–229 (1998).
[CrossRef]

Borisenko, V. I.

T. I. Balakhovskaya, V. I. Borisenko, E. A. Vitrichenko, K. L. Maslennikov, A. M. Prokhorov, P. Z. Sagdeyev, E. V. Trushin, L. S. Chesalin, “Fast Hartmann test for problems in astronomical adaptive optics,” Reports of Academy of Sciences USSR, Dokl. Acad. Nauk SSSR274, 257–260 (1984).

Cannon, R. C.

Chesalin, L. S.

T. I. Balakhovskaya, V. I. Borisenko, E. A. Vitrichenko, K. L. Maslennikov, A. M. Prokhorov, P. Z. Sagdeyev, E. V. Trushin, L. S. Chesalin, “Fast Hartmann test for problems in astronomical adaptive optics,” Reports of Academy of Sciences USSR, Dokl. Acad. Nauk SSSR274, 257–260 (1984).

Colucci, D.

D. Colucci, M. Lloyd-Hart, D. Wittman, R. Angel, A. Ghez, B. McLeod, “A reflective Shack–Hartmann wave-front sensor for adaptive optics,” Publ. Astron. Soc. Pac. 106, 1104–1110 (1994).
[CrossRef]

Cuevas, S.

Dainty, J. C.

C. J. Solomon, J. C. Dainty, N. J. Wooder, “Bayesian estimation of atmospherically distorted wave fronts using Shack–Hartmann sensors,” Opt. Rev. 2, 217–220 (1995).
[CrossRef]

P. A. Bakut, V. E. Kirakosyants, V. A. Loginov, C. J. Solomon, J. C. Dainty, “Optimal wave-front reconstruction from a Shack–Hartmann sensor by use of a Bayesian algorithm,” Opt. Commun. 109, 10–15 (1994).
[CrossRef]

Ellerbroek, B. L.

Fontanella, J. C.

F. Rigaut, G. Rousset, P. Kern, J. C. Fontanella, J. P. Gaffard, F. Merkle, “Adaptive optics on a 3.6-m telescope: results and performance,” Astron. Astrosphys. 250, 280–290 (1991).

J. Primot, G. Rousset, J. C. Fontanella, “Deconvolution from wave-front sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A 7, 1598–1608 (1990).
[CrossRef]

Gaffard, J. P.

F. Rigaut, G. Rousset, P. Kern, J. C. Fontanella, J. P. Gaffard, F. Merkle, “Adaptive optics on a 3.6-m telescope: results and performance,” Astron. Astrosphys. 250, 280–290 (1991).

Gardner, C. S.

Ghez, A.

D. Colucci, M. Lloyd-Hart, D. Wittman, R. Angel, A. Ghez, B. McLeod, “A reflective Shack–Hartmann wave-front sensor for adaptive optics,” Publ. Astron. Soc. Pac. 106, 1104–1110 (1994).
[CrossRef]

Guan, C.

W. Jiang, H. Li, C. Liu, X. Wu, S. Huang, H. Xian, Z. Rong, C. Wang, M. Li, N. Ling, C. Guan, “A 37-element adaptive optics system with H-S wavefront sensor,” in Proceedings of the ICO-16 Satellite Conference on Active and Adaptive Optics, F. Merkle, ed. (International Commission for Optics 16 Secretariat, Garching, Germany, 1993), pp. 127–135.

Gubin, V. B.

V. V. Voitsekhovich, V. B. Gubin, A. V. Mikulich, “An estimation of the parameters of adaptive astronomical systems on the base of experimental data,” Opt. Atmosferi. 1, 66–70 (1988) (in Russian).

Herrmann, J.

Huang, S.

W. Jiang, H. Li, C. Liu, X. Wu, S. Huang, H. Xian, Z. Rong, C. Wang, M. Li, N. Ling, C. Guan, “A 37-element adaptive optics system with H-S wavefront sensor,” in Proceedings of the ICO-16 Satellite Conference on Active and Adaptive Optics, F. Merkle, ed. (International Commission for Optics 16 Secretariat, Garching, Germany, 1993), pp. 127–135.

Jiang, W.

W. Jiang, H. Li, C. Liu, X. Wu, S. Huang, H. Xian, Z. Rong, C. Wang, M. Li, N. Ling, C. Guan, “A 37-element adaptive optics system with H-S wavefront sensor,” in Proceedings of the ICO-16 Satellite Conference on Active and Adaptive Optics, F. Merkle, ed. (International Commission for Optics 16 Secretariat, Garching, Germany, 1993), pp. 127–135.

H. Li, H. Xian, W. Jiang, “Atmospheric turbulence parameter measurement using Hartmann–Shack wave-front sensor,” in Proceedings of the ICO-16 Satellite Conference on Active and Adaptive Optics, F. Merkle, ed. (International Commission for Optics 16 Secretariat, Garching, Germany, 1993), pp. 21–25.

Kern, P.

F. Rigaut, G. Rousset, P. Kern, J. C. Fontanella, J. P. Gaffard, F. Merkle, “Adaptive optics on a 3.6-m telescope: results and performance,” Astron. Astrosphys. 250, 280–290 (1991).

Kirakosyants, V. E.

P. A. Bakut, V. E. Kirakosyants, V. A. Loginov, C. J. Solomon, J. C. Dainty, “Optimal wave-front reconstruction from a Shack–Hartmann sensor by use of a Bayesian algorithm,” Opt. Commun. 109, 10–15 (1994).
[CrossRef]

Kouznetsov, D.

V. V. Voitsekhovich, D. Kouznetsov, V. G. Orlov, S. Cuevas, “Method of random wave vectors in simulation of anisoplanatic effects,” Appl. Opt. 38, 3985–3992 (1999).
[CrossRef]

D. Kouznetsov, V. V. Voitsekhovich, “Method of random wave vectors in the simulation of correlated random processes,” Meteorol. Z. N. F. 7, 230–236 (1998).

D. Kouznetsov, V. V. Voitsekhovich, R. Ortega-Martinez, “Simulation of turbulence-induced phase and logamplitude distortions,” Appl. Opt. 36, 464–469 (1997).
[CrossRef] [PubMed]

V. V. Voitsekhovich, D. Kouznetsov, “Simulation of cross-correlated turbulence-induced phase fluctuations produced by many stars,” in Digest of ESO/OSA Topical Meeting on Astronomy with Adaptive Optics, D. Bonaccini, ed. (European Southern Observatory, Garching, Germany, 1998), pp. 721–728.

Li, H.

H. Li, H. Xian, W. Jiang, “Atmospheric turbulence parameter measurement using Hartmann–Shack wave-front sensor,” in Proceedings of the ICO-16 Satellite Conference on Active and Adaptive Optics, F. Merkle, ed. (International Commission for Optics 16 Secretariat, Garching, Germany, 1993), pp. 21–25.

W. Jiang, H. Li, C. Liu, X. Wu, S. Huang, H. Xian, Z. Rong, C. Wang, M. Li, N. Ling, C. Guan, “A 37-element adaptive optics system with H-S wavefront sensor,” in Proceedings of the ICO-16 Satellite Conference on Active and Adaptive Optics, F. Merkle, ed. (International Commission for Optics 16 Secretariat, Garching, Germany, 1993), pp. 127–135.

Li, M.

W. Jiang, H. Li, C. Liu, X. Wu, S. Huang, H. Xian, Z. Rong, C. Wang, M. Li, N. Ling, C. Guan, “A 37-element adaptive optics system with H-S wavefront sensor,” in Proceedings of the ICO-16 Satellite Conference on Active and Adaptive Optics, F. Merkle, ed. (International Commission for Optics 16 Secretariat, Garching, Germany, 1993), pp. 127–135.

Ling, N.

W. Jiang, H. Li, C. Liu, X. Wu, S. Huang, H. Xian, Z. Rong, C. Wang, M. Li, N. Ling, C. Guan, “A 37-element adaptive optics system with H-S wavefront sensor,” in Proceedings of the ICO-16 Satellite Conference on Active and Adaptive Optics, F. Merkle, ed. (International Commission for Optics 16 Secretariat, Garching, Germany, 1993), pp. 127–135.

Liu, C.

W. Jiang, H. Li, C. Liu, X. Wu, S. Huang, H. Xian, Z. Rong, C. Wang, M. Li, N. Ling, C. Guan, “A 37-element adaptive optics system with H-S wavefront sensor,” in Proceedings of the ICO-16 Satellite Conference on Active and Adaptive Optics, F. Merkle, ed. (International Commission for Optics 16 Secretariat, Garching, Germany, 1993), pp. 127–135.

Lloyd-Hart, M.

D. Colucci, M. Lloyd-Hart, D. Wittman, R. Angel, A. Ghez, B. McLeod, “A reflective Shack–Hartmann wave-front sensor for adaptive optics,” Publ. Astron. Soc. Pac. 106, 1104–1110 (1994).
[CrossRef]

Loginov, V. A.

P. A. Bakut, V. E. Kirakosyants, V. A. Loginov, C. J. Solomon, J. C. Dainty, “Optimal wave-front reconstruction from a Shack–Hartmann sensor by use of a Bayesian algorithm,” Opt. Commun. 109, 10–15 (1994).
[CrossRef]

Mancebo, T.

Maslennikov, K. L.

T. I. Balakhovskaya, V. I. Borisenko, E. A. Vitrichenko, K. L. Maslennikov, A. M. Prokhorov, P. Z. Sagdeyev, E. V. Trushin, L. S. Chesalin, “Fast Hartmann test for problems in astronomical adaptive optics,” Reports of Academy of Sciences USSR, Dokl. Acad. Nauk SSSR274, 257–260 (1984).

McLeod, B.

D. Colucci, M. Lloyd-Hart, D. Wittman, R. Angel, A. Ghez, B. McLeod, “A reflective Shack–Hartmann wave-front sensor for adaptive optics,” Publ. Astron. Soc. Pac. 106, 1104–1110 (1994).
[CrossRef]

Merkle, F.

F. Rigaut, G. Rousset, P. Kern, J. C. Fontanella, J. P. Gaffard, F. Merkle, “Adaptive optics on a 3.6-m telescope: results and performance,” Astron. Astrosphys. 250, 280–290 (1991).

Mikulich, A. V.

V. V. Voitsekhovich, V. B. Gubin, A. V. Mikulich, “An estimation of the parameters of adaptive astronomical systems on the base of experimental data,” Opt. Atmosferi. 1, 66–70 (1988) (in Russian).

Moreno-Barriuso, E.

Navarro, R.

Noll, R. J.

Northcott, M. J.

O’Shea, D. C.

Orlov, V. G.

Ortega-Martinez, R.

Primot, J.

Prokhorov, A. M.

T. I. Balakhovskaya, V. I. Borisenko, E. A. Vitrichenko, K. L. Maslennikov, A. M. Prokhorov, P. Z. Sagdeyev, E. V. Trushin, L. S. Chesalin, “Fast Hartmann test for problems in astronomical adaptive optics,” Reports of Academy of Sciences USSR, Dokl. Acad. Nauk SSSR274, 257–260 (1984).

Purdy, D. R.

D. R. Purdy, “Fabrication of complex micro-optics components using photo-sculpting through halftone transmission masks,” Pure Appl. Opt. 3, 167–175 (1994).
[CrossRef]

Rigaut, F.

F. Rigaut, B. L. Ellerbroek, M. J. Northcott, “Comparison of curvature-based and Shack–Hartmann-based adaptive optics for large astronomical telescopes,” Appl. Opt. 36, 2856–2868 (1997).
[CrossRef] [PubMed]

F. Rigaut, G. Rousset, P. Kern, J. C. Fontanella, J. P. Gaffard, F. Merkle, “Adaptive optics on a 3.6-m telescope: results and performance,” Astron. Astrosphys. 250, 280–290 (1991).

Rios, S.

V. V. Voitsekhovich, S. Bara, S. Rios, E. Acosta, “Minimum-error phase reconstruction from Hartmann sensors with circular subpupils,” Opt. Commun. 148, 225–229 (1998).
[CrossRef]

Rong, Z.

W. Jiang, H. Li, C. Liu, X. Wu, S. Huang, H. Xian, Z. Rong, C. Wang, M. Li, N. Ling, C. Guan, “A 37-element adaptive optics system with H-S wavefront sensor,” in Proceedings of the ICO-16 Satellite Conference on Active and Adaptive Optics, F. Merkle, ed. (International Commission for Optics 16 Secretariat, Garching, Germany, 1993), pp. 127–135.

Rousset, G.

F. Rigaut, G. Rousset, P. Kern, J. C. Fontanella, J. P. Gaffard, F. Merkle, “Adaptive optics on a 3.6-m telescope: results and performance,” Astron. Astrosphys. 250, 280–290 (1991).

J. Primot, G. Rousset, J. C. Fontanella, “Deconvolution from wave-front sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A 7, 1598–1608 (1990).
[CrossRef]

Sagdeyev, P. Z.

T. I. Balakhovskaya, V. I. Borisenko, E. A. Vitrichenko, K. L. Maslennikov, A. M. Prokhorov, P. Z. Sagdeyev, E. V. Trushin, L. S. Chesalin, “Fast Hartmann test for problems in astronomical adaptive optics,” Reports of Academy of Sciences USSR, Dokl. Acad. Nauk SSSR274, 257–260 (1984).

Solomon, C. J.

C. J. Solomon, J. C. Dainty, N. J. Wooder, “Bayesian estimation of atmospherically distorted wave fronts using Shack–Hartmann sensors,” Opt. Rev. 2, 217–220 (1995).
[CrossRef]

P. A. Bakut, V. E. Kirakosyants, V. A. Loginov, C. J. Solomon, J. C. Dainty, “Optimal wave-front reconstruction from a Shack–Hartmann sensor by use of a Bayesian algorithm,” Opt. Commun. 109, 10–15 (1994).
[CrossRef]

Suleski, T. J.

Trushin, E. V.

T. I. Balakhovskaya, V. I. Borisenko, E. A. Vitrichenko, K. L. Maslennikov, A. M. Prokhorov, P. Z. Sagdeyev, E. V. Trushin, L. S. Chesalin, “Fast Hartmann test for problems in astronomical adaptive optics,” Reports of Academy of Sciences USSR, Dokl. Acad. Nauk SSSR274, 257–260 (1984).

Vitrichenko, E. A.

T. I. Balakhovskaya, V. I. Borisenko, E. A. Vitrichenko, K. L. Maslennikov, A. M. Prokhorov, P. Z. Sagdeyev, E. V. Trushin, L. S. Chesalin, “Fast Hartmann test for problems in astronomical adaptive optics,” Reports of Academy of Sciences USSR, Dokl. Acad. Nauk SSSR274, 257–260 (1984).

Voitsekhovich, V. V.

V. V. Voitsekhovich, D. Kouznetsov, V. G. Orlov, S. Cuevas, “Method of random wave vectors in simulation of anisoplanatic effects,” Appl. Opt. 38, 3985–3992 (1999).
[CrossRef]

D. Kouznetsov, V. V. Voitsekhovich, “Method of random wave vectors in the simulation of correlated random processes,” Meteorol. Z. N. F. 7, 230–236 (1998).

V. V. Voitsekhovich, S. Bara, S. Rios, E. Acosta, “Minimum-error phase reconstruction from Hartmann sensors with circular subpupils,” Opt. Commun. 148, 225–229 (1998).
[CrossRef]

D. Kouznetsov, V. V. Voitsekhovich, R. Ortega-Martinez, “Simulation of turbulence-induced phase and logamplitude distortions,” Appl. Opt. 36, 464–469 (1997).
[CrossRef] [PubMed]

V. V. Voitsekhovich, “Hartmann test in atmospheric research,” J. Opt. Soc. Am. A 8, 1749–1757 (1996).
[CrossRef]

V. V. Voitsekhovich, V. B. Gubin, A. V. Mikulich, “An estimation of the parameters of adaptive astronomical systems on the base of experimental data,” Opt. Atmosferi. 1, 66–70 (1988) (in Russian).

V. V. Voitsekhovich, D. Kouznetsov, “Simulation of cross-correlated turbulence-induced phase fluctuations produced by many stars,” in Digest of ESO/OSA Topical Meeting on Astronomy with Adaptive Optics, D. Bonaccini, ed. (European Southern Observatory, Garching, Germany, 1998), pp. 721–728.

Wallner, E. P.

Wang, C.

W. Jiang, H. Li, C. Liu, X. Wu, S. Huang, H. Xian, Z. Rong, C. Wang, M. Li, N. Ling, C. Guan, “A 37-element adaptive optics system with H-S wavefront sensor,” in Proceedings of the ICO-16 Satellite Conference on Active and Adaptive Optics, F. Merkle, ed. (International Commission for Optics 16 Secretariat, Garching, Germany, 1993), pp. 127–135.

Welsh, B. M.

Wittman, D.

D. Colucci, M. Lloyd-Hart, D. Wittman, R. Angel, A. Ghez, B. McLeod, “A reflective Shack–Hartmann wave-front sensor for adaptive optics,” Publ. Astron. Soc. Pac. 106, 1104–1110 (1994).
[CrossRef]

Wooder, N. J.

C. J. Solomon, J. C. Dainty, N. J. Wooder, “Bayesian estimation of atmospherically distorted wave fronts using Shack–Hartmann sensors,” Opt. Rev. 2, 217–220 (1995).
[CrossRef]

Wu, X.

W. Jiang, H. Li, C. Liu, X. Wu, S. Huang, H. Xian, Z. Rong, C. Wang, M. Li, N. Ling, C. Guan, “A 37-element adaptive optics system with H-S wavefront sensor,” in Proceedings of the ICO-16 Satellite Conference on Active and Adaptive Optics, F. Merkle, ed. (International Commission for Optics 16 Secretariat, Garching, Germany, 1993), pp. 127–135.

Xian, H.

W. Jiang, H. Li, C. Liu, X. Wu, S. Huang, H. Xian, Z. Rong, C. Wang, M. Li, N. Ling, C. Guan, “A 37-element adaptive optics system with H-S wavefront sensor,” in Proceedings of the ICO-16 Satellite Conference on Active and Adaptive Optics, F. Merkle, ed. (International Commission for Optics 16 Secretariat, Garching, Germany, 1993), pp. 127–135.

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Figures (3)

Fig. 1
Fig. 1

Hartmann masks that were used for the simulations.

Fig. 2
Fig. 2

Relative statistical errors of tilt reconstruction versus outer scale.

Fig. 3
Fig. 3

Normalized total error versus relative noise. The normalization factor is equal to the absolute total error associated with mask (c) in noiseless conditions.

Tables (3)

Tables Icon

Table 1 Comparison of the Theoretical and the Simulated Statistical Errors for Mask (c) in Fig. 1

Tables Icon

Table 2 Statistical Errors Associated with Five Masks (Noiseless Case)a

Tables Icon

Table 3 Statistical Errors Associated with Five Masks (Noise, 20%)a

Equations (14)

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Hρs=1AsGsd2ρSρ,  s=1,  , N, Sρ=S/x, S/y,
Sρ=i=2 aiZiρ/R, ai=1πR2GRd2ρZiρ/RSρ,
aie=TH,
δi2=ai-aie2,  σi2=ai-aie2/ai2,
s=1Ni=2IaieZiρs/R-Hρs2=min,
ΦnK=K2+1/L02-11/6,
Sρ=l=1L Fl cospl·ρ+ϕl,
Flpl=WSplπLΩpl1/2, WSpl=3.088r0-5/3pl2+1/L02-11/6.
Ωpl=1Ω0pl2+1/L02,  Ω0=π lnK22+1/L02K12+1/L02,
Hρs=-1Asl=1L FlplGsd2 ρ sinpl·ρ+ϕl, s=1,  , N.
ai=2n+11/2l=1L Flcosπn2+ϕlJn+1plRplR×2 cosmθl, i is even, m02 sinmθl, i is odd, m01, m=0,
Σk=i=221 ai-aie2/Σmax,
Hρs=1AsGsd2ρSρ+νs,  s=1,  , N.
σν=σν2/H21/2, H2=1Ns=1NHx2ρs+Hy2ρs, Hρs=Hxρs, Hyρs.

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