Abstract

We report a higher precision measurement of the refractive index of carbon dioxide using a frequency comb as the light source in a Mach–Zehnder interferometer setup. The experimental sensitivity can reach the level of 8.8×109. Taking into account the measurement accuracy of temperature and pressure, the experimental accuracy has a value of 1.2×108. The measurement result has a deviation from the commonly quoted result [Old et al., J. Opt. Soc. Am. 61, 89 (1971) ] by 6.4×107 at 800nm.

© 2007 Optical Society of America

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  1. P. Falkowski, R. J. Scholes, E. Boyle, J. Canadell, D. Canfield, J. Elser, N. Gruber, K. Hibbard, P. Högberg, S. Linder, F. T. Mackenzie, B. Moore III, T. Pedersen, Y. Rosenthal, S. Seitzinger, V. Smetacek, and W. Steffen, Science 290, 291 (2000).
    [CrossRef] [PubMed]
  2. B. Edlén, Metrologia 2, 71 (1966).
    [CrossRef]
  3. K. P. Birch and M. J. Downs, Metrologia 30, 155 (1993).
    [CrossRef]
  4. K. P. Birch and M. J. Downs, Metrologia 31, 315 (1994).
    [CrossRef]
  5. G. Bönsch and E. Potulski, Metrologia 35, 133 (1998).
    [CrossRef]
  6. J. Zhang, Z. H. Lu, and L. J. Wang, Opt. Lett. 30, 3314 (2005).
    [CrossRef]
  7. J. Zhang, Z. H. Lu, B. Menegozzi, and L. J. Wang, Rev. Sci. Instrum. 77, 083104 (2006).
    [CrossRef]
  8. J. G. Old, K. L. Gentili, and E. R. Peck, J. Opt. Soc. Am. 61, 89 (1971).
    [CrossRef]
  9. K. P. Birch, M. J. Downs, and D. H. Ferriss, J. Phys. E 21, 690 (1988).
    [CrossRef]
  10. J. Hilsenrath, C. W. Beckett, W. S. Benedict, L. Fano, H. J. Hoge, J. F. Mosi, R. L. Nu Hall, Y. S. Touloukian, and H. W. Woolley, Natl. Bur. Stand. Circ. (U.S.) 564, 151 (1955).
  11. J. D. Wright, NIST Tech. Note (2004).
  12. C. Cuthbertson and M. Cuthbertson, Proc. R. Soc. London 97, 152 (1920).
    [CrossRef]
  13. A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, Opt. Commun. 9, 432 (1973).
    [CrossRef]
  14. A. C. Simmons, Opt. Commun. 25, 211 (1978).
    [CrossRef]
  15. J. M. St. Arnaud and T. K. Bose, J. Chem. Phys. 71, 4951 (1979).
    [CrossRef]
  16. M. E. Thomas and T. J. Tayag, Appl. Opt. 27, 3317 (1988).
    [CrossRef] [PubMed]
  17. K. P. Birch, J. Opt. Soc. Am. 8, 647 (1991).
    [CrossRef]
  18. H. J. Achtermann, G. Magnus, and T. K. Bose, J. Chem. Phys. 94, 5669 (1991).
    [CrossRef]
  19. R. C. Burns, C. Graham, and A. R. M. Weller, Mol. Phys. 59, 41 (1986).
    [CrossRef]

2006 (1)

J. Zhang, Z. H. Lu, B. Menegozzi, and L. J. Wang, Rev. Sci. Instrum. 77, 083104 (2006).
[CrossRef]

2005 (1)

2004 (1)

J. D. Wright, NIST Tech. Note (2004).

2000 (1)

P. Falkowski, R. J. Scholes, E. Boyle, J. Canadell, D. Canfield, J. Elser, N. Gruber, K. Hibbard, P. Högberg, S. Linder, F. T. Mackenzie, B. Moore III, T. Pedersen, Y. Rosenthal, S. Seitzinger, V. Smetacek, and W. Steffen, Science 290, 291 (2000).
[CrossRef] [PubMed]

1998 (1)

G. Bönsch and E. Potulski, Metrologia 35, 133 (1998).
[CrossRef]

1994 (1)

K. P. Birch and M. J. Downs, Metrologia 31, 315 (1994).
[CrossRef]

1993 (1)

K. P. Birch and M. J. Downs, Metrologia 30, 155 (1993).
[CrossRef]

1991 (2)

H. J. Achtermann, G. Magnus, and T. K. Bose, J. Chem. Phys. 94, 5669 (1991).
[CrossRef]

K. P. Birch, J. Opt. Soc. Am. 8, 647 (1991).
[CrossRef]

1988 (2)

M. E. Thomas and T. J. Tayag, Appl. Opt. 27, 3317 (1988).
[CrossRef] [PubMed]

K. P. Birch, M. J. Downs, and D. H. Ferriss, J. Phys. E 21, 690 (1988).
[CrossRef]

1986 (1)

R. C. Burns, C. Graham, and A. R. M. Weller, Mol. Phys. 59, 41 (1986).
[CrossRef]

1979 (1)

J. M. St. Arnaud and T. K. Bose, J. Chem. Phys. 71, 4951 (1979).
[CrossRef]

1978 (1)

A. C. Simmons, Opt. Commun. 25, 211 (1978).
[CrossRef]

1973 (1)

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, Opt. Commun. 9, 432 (1973).
[CrossRef]

1971 (1)

1966 (1)

B. Edlén, Metrologia 2, 71 (1966).
[CrossRef]

1955 (1)

J. Hilsenrath, C. W. Beckett, W. S. Benedict, L. Fano, H. J. Hoge, J. F. Mosi, R. L. Nu Hall, Y. S. Touloukian, and H. W. Woolley, Natl. Bur. Stand. Circ. (U.S.) 564, 151 (1955).

1920 (1)

C. Cuthbertson and M. Cuthbertson, Proc. R. Soc. London 97, 152 (1920).
[CrossRef]

Abjean, R.

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, Opt. Commun. 9, 432 (1973).
[CrossRef]

Achtermann, H. J.

H. J. Achtermann, G. Magnus, and T. K. Bose, J. Chem. Phys. 94, 5669 (1991).
[CrossRef]

Beckett, C. W.

J. Hilsenrath, C. W. Beckett, W. S. Benedict, L. Fano, H. J. Hoge, J. F. Mosi, R. L. Nu Hall, Y. S. Touloukian, and H. W. Woolley, Natl. Bur. Stand. Circ. (U.S.) 564, 151 (1955).

Benedict, W. S.

J. Hilsenrath, C. W. Beckett, W. S. Benedict, L. Fano, H. J. Hoge, J. F. Mosi, R. L. Nu Hall, Y. S. Touloukian, and H. W. Woolley, Natl. Bur. Stand. Circ. (U.S.) 564, 151 (1955).

Bideau-Mehu, A.

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, Opt. Commun. 9, 432 (1973).
[CrossRef]

Birch, K. P.

K. P. Birch and M. J. Downs, Metrologia 31, 315 (1994).
[CrossRef]

K. P. Birch and M. J. Downs, Metrologia 30, 155 (1993).
[CrossRef]

K. P. Birch, J. Opt. Soc. Am. 8, 647 (1991).
[CrossRef]

K. P. Birch, M. J. Downs, and D. H. Ferriss, J. Phys. E 21, 690 (1988).
[CrossRef]

Bönsch, G.

G. Bönsch and E. Potulski, Metrologia 35, 133 (1998).
[CrossRef]

Bose, T. K.

H. J. Achtermann, G. Magnus, and T. K. Bose, J. Chem. Phys. 94, 5669 (1991).
[CrossRef]

J. M. St. Arnaud and T. K. Bose, J. Chem. Phys. 71, 4951 (1979).
[CrossRef]

Boyle, E.

P. Falkowski, R. J. Scholes, E. Boyle, J. Canadell, D. Canfield, J. Elser, N. Gruber, K. Hibbard, P. Högberg, S. Linder, F. T. Mackenzie, B. Moore III, T. Pedersen, Y. Rosenthal, S. Seitzinger, V. Smetacek, and W. Steffen, Science 290, 291 (2000).
[CrossRef] [PubMed]

Burns, R. C.

R. C. Burns, C. Graham, and A. R. M. Weller, Mol. Phys. 59, 41 (1986).
[CrossRef]

Canadell, J.

P. Falkowski, R. J. Scholes, E. Boyle, J. Canadell, D. Canfield, J. Elser, N. Gruber, K. Hibbard, P. Högberg, S. Linder, F. T. Mackenzie, B. Moore III, T. Pedersen, Y. Rosenthal, S. Seitzinger, V. Smetacek, and W. Steffen, Science 290, 291 (2000).
[CrossRef] [PubMed]

Canfield, D.

P. Falkowski, R. J. Scholes, E. Boyle, J. Canadell, D. Canfield, J. Elser, N. Gruber, K. Hibbard, P. Högberg, S. Linder, F. T. Mackenzie, B. Moore III, T. Pedersen, Y. Rosenthal, S. Seitzinger, V. Smetacek, and W. Steffen, Science 290, 291 (2000).
[CrossRef] [PubMed]

Cuthbertson, C.

C. Cuthbertson and M. Cuthbertson, Proc. R. Soc. London 97, 152 (1920).
[CrossRef]

Cuthbertson, M.

C. Cuthbertson and M. Cuthbertson, Proc. R. Soc. London 97, 152 (1920).
[CrossRef]

Downs, M. J.

K. P. Birch and M. J. Downs, Metrologia 31, 315 (1994).
[CrossRef]

K. P. Birch and M. J. Downs, Metrologia 30, 155 (1993).
[CrossRef]

K. P. Birch, M. J. Downs, and D. H. Ferriss, J. Phys. E 21, 690 (1988).
[CrossRef]

Edlén, B.

B. Edlén, Metrologia 2, 71 (1966).
[CrossRef]

Elser, J.

P. Falkowski, R. J. Scholes, E. Boyle, J. Canadell, D. Canfield, J. Elser, N. Gruber, K. Hibbard, P. Högberg, S. Linder, F. T. Mackenzie, B. Moore III, T. Pedersen, Y. Rosenthal, S. Seitzinger, V. Smetacek, and W. Steffen, Science 290, 291 (2000).
[CrossRef] [PubMed]

Falkowski, P.

P. Falkowski, R. J. Scholes, E. Boyle, J. Canadell, D. Canfield, J. Elser, N. Gruber, K. Hibbard, P. Högberg, S. Linder, F. T. Mackenzie, B. Moore III, T. Pedersen, Y. Rosenthal, S. Seitzinger, V. Smetacek, and W. Steffen, Science 290, 291 (2000).
[CrossRef] [PubMed]

Fano, L.

J. Hilsenrath, C. W. Beckett, W. S. Benedict, L. Fano, H. J. Hoge, J. F. Mosi, R. L. Nu Hall, Y. S. Touloukian, and H. W. Woolley, Natl. Bur. Stand. Circ. (U.S.) 564, 151 (1955).

Ferriss, D. H.

K. P. Birch, M. J. Downs, and D. H. Ferriss, J. Phys. E 21, 690 (1988).
[CrossRef]

Gentili, K. L.

Graham, C.

R. C. Burns, C. Graham, and A. R. M. Weller, Mol. Phys. 59, 41 (1986).
[CrossRef]

Gruber, N.

P. Falkowski, R. J. Scholes, E. Boyle, J. Canadell, D. Canfield, J. Elser, N. Gruber, K. Hibbard, P. Högberg, S. Linder, F. T. Mackenzie, B. Moore III, T. Pedersen, Y. Rosenthal, S. Seitzinger, V. Smetacek, and W. Steffen, Science 290, 291 (2000).
[CrossRef] [PubMed]

Guern, Y.

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, Opt. Commun. 9, 432 (1973).
[CrossRef]

Hibbard, K.

P. Falkowski, R. J. Scholes, E. Boyle, J. Canadell, D. Canfield, J. Elser, N. Gruber, K. Hibbard, P. Högberg, S. Linder, F. T. Mackenzie, B. Moore III, T. Pedersen, Y. Rosenthal, S. Seitzinger, V. Smetacek, and W. Steffen, Science 290, 291 (2000).
[CrossRef] [PubMed]

Hilsenrath, J.

J. Hilsenrath, C. W. Beckett, W. S. Benedict, L. Fano, H. J. Hoge, J. F. Mosi, R. L. Nu Hall, Y. S. Touloukian, and H. W. Woolley, Natl. Bur. Stand. Circ. (U.S.) 564, 151 (1955).

Högberg, P.

P. Falkowski, R. J. Scholes, E. Boyle, J. Canadell, D. Canfield, J. Elser, N. Gruber, K. Hibbard, P. Högberg, S. Linder, F. T. Mackenzie, B. Moore III, T. Pedersen, Y. Rosenthal, S. Seitzinger, V. Smetacek, and W. Steffen, Science 290, 291 (2000).
[CrossRef] [PubMed]

Hoge, H. J.

J. Hilsenrath, C. W. Beckett, W. S. Benedict, L. Fano, H. J. Hoge, J. F. Mosi, R. L. Nu Hall, Y. S. Touloukian, and H. W. Woolley, Natl. Bur. Stand. Circ. (U.S.) 564, 151 (1955).

Johannin-Gilles, A.

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, Opt. Commun. 9, 432 (1973).
[CrossRef]

Linder, S.

P. Falkowski, R. J. Scholes, E. Boyle, J. Canadell, D. Canfield, J. Elser, N. Gruber, K. Hibbard, P. Högberg, S. Linder, F. T. Mackenzie, B. Moore III, T. Pedersen, Y. Rosenthal, S. Seitzinger, V. Smetacek, and W. Steffen, Science 290, 291 (2000).
[CrossRef] [PubMed]

Lu, Z. H.

J. Zhang, Z. H. Lu, B. Menegozzi, and L. J. Wang, Rev. Sci. Instrum. 77, 083104 (2006).
[CrossRef]

J. Zhang, Z. H. Lu, and L. J. Wang, Opt. Lett. 30, 3314 (2005).
[CrossRef]

Mackenzie, F. T.

P. Falkowski, R. J. Scholes, E. Boyle, J. Canadell, D. Canfield, J. Elser, N. Gruber, K. Hibbard, P. Högberg, S. Linder, F. T. Mackenzie, B. Moore III, T. Pedersen, Y. Rosenthal, S. Seitzinger, V. Smetacek, and W. Steffen, Science 290, 291 (2000).
[CrossRef] [PubMed]

Magnus, G.

H. J. Achtermann, G. Magnus, and T. K. Bose, J. Chem. Phys. 94, 5669 (1991).
[CrossRef]

Menegozzi, B.

J. Zhang, Z. H. Lu, B. Menegozzi, and L. J. Wang, Rev. Sci. Instrum. 77, 083104 (2006).
[CrossRef]

Moore, B.

P. Falkowski, R. J. Scholes, E. Boyle, J. Canadell, D. Canfield, J. Elser, N. Gruber, K. Hibbard, P. Högberg, S. Linder, F. T. Mackenzie, B. Moore III, T. Pedersen, Y. Rosenthal, S. Seitzinger, V. Smetacek, and W. Steffen, Science 290, 291 (2000).
[CrossRef] [PubMed]

Mosi, J. F.

J. Hilsenrath, C. W. Beckett, W. S. Benedict, L. Fano, H. J. Hoge, J. F. Mosi, R. L. Nu Hall, Y. S. Touloukian, and H. W. Woolley, Natl. Bur. Stand. Circ. (U.S.) 564, 151 (1955).

Nu Hall, R. L.

J. Hilsenrath, C. W. Beckett, W. S. Benedict, L. Fano, H. J. Hoge, J. F. Mosi, R. L. Nu Hall, Y. S. Touloukian, and H. W. Woolley, Natl. Bur. Stand. Circ. (U.S.) 564, 151 (1955).

Old, J. G.

Peck, E. R.

Pedersen, T.

P. Falkowski, R. J. Scholes, E. Boyle, J. Canadell, D. Canfield, J. Elser, N. Gruber, K. Hibbard, P. Högberg, S. Linder, F. T. Mackenzie, B. Moore III, T. Pedersen, Y. Rosenthal, S. Seitzinger, V. Smetacek, and W. Steffen, Science 290, 291 (2000).
[CrossRef] [PubMed]

Potulski, E.

G. Bönsch and E. Potulski, Metrologia 35, 133 (1998).
[CrossRef]

Rosenthal, Y.

P. Falkowski, R. J. Scholes, E. Boyle, J. Canadell, D. Canfield, J. Elser, N. Gruber, K. Hibbard, P. Högberg, S. Linder, F. T. Mackenzie, B. Moore III, T. Pedersen, Y. Rosenthal, S. Seitzinger, V. Smetacek, and W. Steffen, Science 290, 291 (2000).
[CrossRef] [PubMed]

Scholes, R. J.

P. Falkowski, R. J. Scholes, E. Boyle, J. Canadell, D. Canfield, J. Elser, N. Gruber, K. Hibbard, P. Högberg, S. Linder, F. T. Mackenzie, B. Moore III, T. Pedersen, Y. Rosenthal, S. Seitzinger, V. Smetacek, and W. Steffen, Science 290, 291 (2000).
[CrossRef] [PubMed]

Seitzinger, S.

P. Falkowski, R. J. Scholes, E. Boyle, J. Canadell, D. Canfield, J. Elser, N. Gruber, K. Hibbard, P. Högberg, S. Linder, F. T. Mackenzie, B. Moore III, T. Pedersen, Y. Rosenthal, S. Seitzinger, V. Smetacek, and W. Steffen, Science 290, 291 (2000).
[CrossRef] [PubMed]

Simmons, A. C.

A. C. Simmons, Opt. Commun. 25, 211 (1978).
[CrossRef]

Smetacek, V.

P. Falkowski, R. J. Scholes, E. Boyle, J. Canadell, D. Canfield, J. Elser, N. Gruber, K. Hibbard, P. Högberg, S. Linder, F. T. Mackenzie, B. Moore III, T. Pedersen, Y. Rosenthal, S. Seitzinger, V. Smetacek, and W. Steffen, Science 290, 291 (2000).
[CrossRef] [PubMed]

St. Arnaud, J. M.

J. M. St. Arnaud and T. K. Bose, J. Chem. Phys. 71, 4951 (1979).
[CrossRef]

Steffen, W.

P. Falkowski, R. J. Scholes, E. Boyle, J. Canadell, D. Canfield, J. Elser, N. Gruber, K. Hibbard, P. Högberg, S. Linder, F. T. Mackenzie, B. Moore III, T. Pedersen, Y. Rosenthal, S. Seitzinger, V. Smetacek, and W. Steffen, Science 290, 291 (2000).
[CrossRef] [PubMed]

Tayag, T. J.

Thomas, M. E.

Touloukian, Y. S.

J. Hilsenrath, C. W. Beckett, W. S. Benedict, L. Fano, H. J. Hoge, J. F. Mosi, R. L. Nu Hall, Y. S. Touloukian, and H. W. Woolley, Natl. Bur. Stand. Circ. (U.S.) 564, 151 (1955).

Wang, L. J.

J. Zhang, Z. H. Lu, B. Menegozzi, and L. J. Wang, Rev. Sci. Instrum. 77, 083104 (2006).
[CrossRef]

J. Zhang, Z. H. Lu, and L. J. Wang, Opt. Lett. 30, 3314 (2005).
[CrossRef]

Weller, A. R. M.

R. C. Burns, C. Graham, and A. R. M. Weller, Mol. Phys. 59, 41 (1986).
[CrossRef]

Woolley, H. W.

J. Hilsenrath, C. W. Beckett, W. S. Benedict, L. Fano, H. J. Hoge, J. F. Mosi, R. L. Nu Hall, Y. S. Touloukian, and H. W. Woolley, Natl. Bur. Stand. Circ. (U.S.) 564, 151 (1955).

Wright, J. D.

J. D. Wright, NIST Tech. Note (2004).

Zhang, J.

J. Zhang, Z. H. Lu, B. Menegozzi, and L. J. Wang, Rev. Sci. Instrum. 77, 083104 (2006).
[CrossRef]

J. Zhang, Z. H. Lu, and L. J. Wang, Opt. Lett. 30, 3314 (2005).
[CrossRef]

Appl. Opt. (1)

J. Chem. Phys. (2)

H. J. Achtermann, G. Magnus, and T. K. Bose, J. Chem. Phys. 94, 5669 (1991).
[CrossRef]

J. M. St. Arnaud and T. K. Bose, J. Chem. Phys. 71, 4951 (1979).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Phys. E (1)

K. P. Birch, M. J. Downs, and D. H. Ferriss, J. Phys. E 21, 690 (1988).
[CrossRef]

Metrologia (4)

B. Edlén, Metrologia 2, 71 (1966).
[CrossRef]

K. P. Birch and M. J. Downs, Metrologia 30, 155 (1993).
[CrossRef]

K. P. Birch and M. J. Downs, Metrologia 31, 315 (1994).
[CrossRef]

G. Bönsch and E. Potulski, Metrologia 35, 133 (1998).
[CrossRef]

Mol. Phys. (1)

R. C. Burns, C. Graham, and A. R. M. Weller, Mol. Phys. 59, 41 (1986).
[CrossRef]

Natl. Bur. Stand. Circ. (U.S.) (1)

J. Hilsenrath, C. W. Beckett, W. S. Benedict, L. Fano, H. J. Hoge, J. F. Mosi, R. L. Nu Hall, Y. S. Touloukian, and H. W. Woolley, Natl. Bur. Stand. Circ. (U.S.) 564, 151 (1955).

NIST Tech. Note (1)

J. D. Wright, NIST Tech. Note (2004).

Opt. Commun. (2)

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, Opt. Commun. 9, 432 (1973).
[CrossRef]

A. C. Simmons, Opt. Commun. 25, 211 (1978).
[CrossRef]

Opt. Lett. (1)

Proc. R. Soc. London (1)

C. Cuthbertson and M. Cuthbertson, Proc. R. Soc. London 97, 152 (1920).
[CrossRef]

Rev. Sci. Instrum. (1)

J. Zhang, Z. H. Lu, B. Menegozzi, and L. J. Wang, Rev. Sci. Instrum. 77, 083104 (2006).
[CrossRef]

Science (1)

P. Falkowski, R. J. Scholes, E. Boyle, J. Canadell, D. Canfield, J. Elser, N. Gruber, K. Hibbard, P. Högberg, S. Linder, F. T. Mackenzie, B. Moore III, T. Pedersen, Y. Rosenthal, S. Seitzinger, V. Smetacek, and W. Steffen, Science 290, 291 (2000).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Experimental setup. BS1, BS2, cube beam splitter; MPC, multipass cell; RR, retroreflector; L, lens; FC, fiber coupler; OSA, optical spectrum analyzer. The dashed line corresponds to the He Ne laser optical path.

Fig. 2
Fig. 2

Compressibility factor of carbon dioxide at 1 atm . Triangles, result from Old et al.; squares, result from the most recent NIST database; circles, result from the 1955 NBS table.

Fig. 3
Fig. 3

Refractive index of CO 2 . Dashed curve, Old and co-workers’ result; solid curve, our experimental result. Each data point represents an average of 45 measurements. A typical error bar is 7.8 × 10 8 .

Equations (6)

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

l cell = c τ g n g ( λ 0 ) 1 .
Δ Φ ( λ ) = Φ gas ( λ ) Φ vac ( λ ) = 2 π [ n ( λ ) 1 ] l cell λ 2 m π .
d Δ Φ ( λ ) d λ = 2 π l cell [ n ( λ ) λ d n ( λ ) d λ 1 ] λ 2 = 2 π l cell [ n g ( λ ) 1 ] λ 2 .
Z = 1 p ( 6.566770 0.076831 t + 0.0004205 t 2 ) × 10 8 .
D t p = p 1 + 10 8 ( 6.63996 0.077099 t + 0.0004205 t 2 ) p 1 + 0.0036610 t .
( n 1 ) × 10 8 = 7670.524 + 7466051 248.5560 1 λ 2 + 367244.7 57.75340 1 λ 2 .

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