Abstract

We show that, by coherence-gate rejection of out-of-focus light, wave-front distortions can be measured in the presence of a scattering background that is dominant by several orders of magnitude. Applications are expected for multiphoton and confocal laser-scanning microscopy.

© 2004 Optical Society of America

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  1. F. Merkle, P. Kern, P. Lena, F. Rigaut, J. C. Fontanella, G. Rousset, C. Boyer, J. P. Gaffard, and P. Jagourel, ESO Messenger (58), 1 (1989).
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  3. R. Foy and A. Labeyrie, Astron. Astrophys. 152, L29 (1985).
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  7. J. Z. Liang, D. R. Williams, and D. T. Miller, J. Opt. Soc. Am. A 14, 2884 (1997).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  19. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
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2003 (2)

2002 (2)

L. Sherman, J. Y. Ye, O. Albert, and T. B. Norris, J. Microsc. 206, 65 (2002).
[CrossRef] [PubMed]

J. T. Trachtenberg, B. E. Chen, G. W. Knott, G. P. Feng, J. R. Sanes, E. Welker, and K. Svoboda, Nature 420, 788 (2002).
[CrossRef] [PubMed]

2001 (1)

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, J. Neurosci. Methods 111, 29 (2001).
[CrossRef] [PubMed]

2000 (2)

O. Albert, L. Sherman, G. Mourou, T. B. Norris, and G. Vdovin, Opt. Lett. 25, 52 (2000).
[CrossRef]

M. A. A. Neil, R. Juskaitis, M. J. Booth, T. Wilson, T. Tanaka, and S. Kawata, J. Microsc. 200, 105 (2000).
[CrossRef]

1999 (1)

D. Kleinfeld, P. P. Mitra, F. Helmchen, and W. Denk, Proc. Natl. Acad. Sci. USA 96, 8307 (1999).

1998 (1)

D. Kleinfeld, P. P. Mitra, F. Helmchen, and W. Denk, Proc. Natl. Acad. Sci. USA 95, 15741 (1998).
[CrossRef]

1997 (3)

W. Denk and K. Svoboda, Neuron 18, 351 (1997).
[CrossRef] [PubMed]

K. Svoboda, W. Denk, D. Kleinfeld, and D. W. Tank, Nature 385, 161 (1997).
[CrossRef] [PubMed]

J. Z. Liang, D. R. Williams, and D. T. Miller, J. Opt. Soc. Am. A 14, 2884 (1997).
[CrossRef]

1991 (2)

R. A. Humphreys, C. A. Primmerman, L. C. Bradley, and J. Herrmann, Opt. Lett. 16, 1367 (1991).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

1990 (1)

W. Denk, J. H. Strickler, and W. W. Webb, Science 248, 73 (1990).
[CrossRef] [PubMed]

1989 (2)

J. F. Bille, B. Grimm, J. Liang, and K. Mueller, Proc. SPIE 1161, 417 (1989).
[CrossRef]

F. Merkle, P. Kern, P. Lena, F. Rigaut, J. C. Fontanella, G. Rousset, C. Boyer, J. P. Gaffard, and P. Jagourel, ESO Messenger (58), 1 (1989).

1985 (1)

R. Foy and A. Labeyrie, Astron. Astrophys. 152, L29 (1985).

1979 (1)

1976 (1)

1971 (2)

R. V. Shack and B. C. Platt, Opt. Sci. Cent. Newsl. 5, 15 (1971).

M. A. Duguay and A. T. Mattick, Appl. Opt. 10, 2162 (1971).
[CrossRef] [PubMed]

1969 (1)

R. Crane, Appl. Opt. 8, 538 (1969).

1966 (1)

P. Carre, Metrologia 2, 13 (1966).
[CrossRef]

1934 (1)

F. Zernike, Physica 1, 689 (1934).
[CrossRef]

Albert, O.

L. Sherman, J. Y. Ye, O. Albert, and T. B. Norris, J. Microsc. 206, 65 (2002).
[CrossRef] [PubMed]

O. Albert, L. Sherman, G. Mourou, T. B. Norris, and G. Vdovin, Opt. Lett. 25, 52 (2000).
[CrossRef]

Beaurepaire, E.

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, J. Neurosci. Methods 111, 29 (2001).
[CrossRef] [PubMed]

Bille, J. F.

J. F. Bille, B. Grimm, J. Liang, and K. Mueller, Proc. SPIE 1161, 417 (1989).
[CrossRef]

Booth, M. J.

M. A. A. Neil, R. Juskaitis, M. J. Booth, T. Wilson, T. Tanaka, and S. Kawata, J. Microsc. 200, 105 (2000).
[CrossRef]

Boyer, C.

F. Merkle, P. Kern, P. Lena, F. Rigaut, J. C. Fontanella, G. Rousset, C. Boyer, J. P. Gaffard, and P. Jagourel, ESO Messenger (58), 1 (1989).

Bradley, L. C.

Burns, D.

Carre, P.

P. Carre, Metrologia 2, 13 (1966).
[CrossRef]

Chaigneau, E.

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, J. Neurosci. Methods 111, 29 (2001).
[CrossRef] [PubMed]

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Charpak, S.

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, J. Neurosci. Methods 111, 29 (2001).
[CrossRef] [PubMed]

Chen, B. E.

J. T. Trachtenberg, B. E. Chen, G. W. Knott, G. P. Feng, J. R. Sanes, E. Welker, and K. Svoboda, Nature 420, 788 (2002).
[CrossRef] [PubMed]

Crane, R.

R. Crane, Appl. Opt. 8, 538 (1969).

Cubalchini, R.

Denk, W.

P. Theer, M. T. Hasan, and W. Denk, Opt. Lett. 28, 1022 (2003).
[CrossRef] [PubMed]

D. Kleinfeld, P. P. Mitra, F. Helmchen, and W. Denk, Proc. Natl. Acad. Sci. USA 96, 8307 (1999).

D. Kleinfeld, P. P. Mitra, F. Helmchen, and W. Denk, Proc. Natl. Acad. Sci. USA 95, 15741 (1998).
[CrossRef]

K. Svoboda, W. Denk, D. Kleinfeld, and D. W. Tank, Nature 385, 161 (1997).
[CrossRef] [PubMed]

W. Denk and K. Svoboda, Neuron 18, 351 (1997).
[CrossRef] [PubMed]

W. Denk, J. H. Strickler, and W. W. Webb, Science 248, 73 (1990).
[CrossRef] [PubMed]

Duguay, M. A.

Feng, G. P.

J. T. Trachtenberg, B. E. Chen, G. W. Knott, G. P. Feng, J. R. Sanes, E. Welker, and K. Svoboda, Nature 420, 788 (2002).
[CrossRef] [PubMed]

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Fontanella, J. C.

F. Merkle, P. Kern, P. Lena, F. Rigaut, J. C. Fontanella, G. Rousset, C. Boyer, J. P. Gaffard, and P. Jagourel, ESO Messenger (58), 1 (1989).

Foy, R.

R. Foy and A. Labeyrie, Astron. Astrophys. 152, L29 (1985).

Fujimoto, J. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Gaffard, J. P.

F. Merkle, P. Kern, P. Lena, F. Rigaut, J. C. Fontanella, G. Rousset, C. Boyer, J. P. Gaffard, and P. Jagourel, ESO Messenger (58), 1 (1989).

Girkin, J. M.

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Grimm, B.

J. F. Bille, B. Grimm, J. Liang, and K. Mueller, Proc. SPIE 1161, 417 (1989).
[CrossRef]

Hasan, M. T.

Hee, M. R.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Helmchen, F.

D. Kleinfeld, P. P. Mitra, F. Helmchen, and W. Denk, Proc. Natl. Acad. Sci. USA 96, 8307 (1999).

D. Kleinfeld, P. P. Mitra, F. Helmchen, and W. Denk, Proc. Natl. Acad. Sci. USA 95, 15741 (1998).
[CrossRef]

Herrmann, J.

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Humphreys, R. A.

Jagourel, P.

F. Merkle, P. Kern, P. Lena, F. Rigaut, J. C. Fontanella, G. Rousset, C. Boyer, J. P. Gaffard, and P. Jagourel, ESO Messenger (58), 1 (1989).

Juskaitis, R.

M. A. A. Neil, R. Juskaitis, M. J. Booth, T. Wilson, T. Tanaka, and S. Kawata, J. Microsc. 200, 105 (2000).
[CrossRef]

Kawata, S.

M. A. A. Neil, R. Juskaitis, M. J. Booth, T. Wilson, T. Tanaka, and S. Kawata, J. Microsc. 200, 105 (2000).
[CrossRef]

Kern, P.

F. Merkle, P. Kern, P. Lena, F. Rigaut, J. C. Fontanella, G. Rousset, C. Boyer, J. P. Gaffard, and P. Jagourel, ESO Messenger (58), 1 (1989).

Kleinfeld, D.

D. Kleinfeld, P. P. Mitra, F. Helmchen, and W. Denk, Proc. Natl. Acad. Sci. USA 96, 8307 (1999).

D. Kleinfeld, P. P. Mitra, F. Helmchen, and W. Denk, Proc. Natl. Acad. Sci. USA 95, 15741 (1998).
[CrossRef]

K. Svoboda, W. Denk, D. Kleinfeld, and D. W. Tank, Nature 385, 161 (1997).
[CrossRef] [PubMed]

Knott, G. W.

J. T. Trachtenberg, B. E. Chen, G. W. Knott, G. P. Feng, J. R. Sanes, E. Welker, and K. Svoboda, Nature 420, 788 (2002).
[CrossRef] [PubMed]

Labeyrie, A.

R. Foy and A. Labeyrie, Astron. Astrophys. 152, L29 (1985).

Lena, P.

F. Merkle, P. Kern, P. Lena, F. Rigaut, J. C. Fontanella, G. Rousset, C. Boyer, J. P. Gaffard, and P. Jagourel, ESO Messenger (58), 1 (1989).

Liang, J.

J. F. Bille, B. Grimm, J. Liang, and K. Mueller, Proc. SPIE 1161, 417 (1989).
[CrossRef]

Liang, J. Z.

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Linnik, V. P.

V. P. Linnik, ESO Conference and Workshop Proceedings No. 48 (European Southern Observatory, Garching, Germany, 1993).

Malacara, D.

D. Malacara, Wiley Series in Pure and Applied Optics, 2nd ed. (Wiley, New York, 1992).

Marsh, P. N.

Mattick, A. T.

Merkle, F.

F. Merkle, P. Kern, P. Lena, F. Rigaut, J. C. Fontanella, G. Rousset, C. Boyer, J. P. Gaffard, and P. Jagourel, ESO Messenger (58), 1 (1989).

Mertz, J.

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, J. Neurosci. Methods 111, 29 (2001).
[CrossRef] [PubMed]

Miller, D. T.

Mitra, P. P.

D. Kleinfeld, P. P. Mitra, F. Helmchen, and W. Denk, Proc. Natl. Acad. Sci. USA 96, 8307 (1999).

D. Kleinfeld, P. P. Mitra, F. Helmchen, and W. Denk, Proc. Natl. Acad. Sci. USA 95, 15741 (1998).
[CrossRef]

Mourou, G.

Mueller, K.

J. F. Bille, B. Grimm, J. Liang, and K. Mueller, Proc. SPIE 1161, 417 (1989).
[CrossRef]

Neil, M. A. A.

M. A. A. Neil, R. Juskaitis, M. J. Booth, T. Wilson, T. Tanaka, and S. Kawata, J. Microsc. 200, 105 (2000).
[CrossRef]

Noll, R. J.

Norris, T. B.

L. Sherman, J. Y. Ye, O. Albert, and T. B. Norris, J. Microsc. 206, 65 (2002).
[CrossRef] [PubMed]

O. Albert, L. Sherman, G. Mourou, T. B. Norris, and G. Vdovin, Opt. Lett. 25, 52 (2000).
[CrossRef]

Oheim, M.

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, J. Neurosci. Methods 111, 29 (2001).
[CrossRef] [PubMed]

Platt, B. C.

R. V. Shack and B. C. Platt, Opt. Sci. Cent. Newsl. 5, 15 (1971).

Primmerman, C. A.

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Rigaut, F.

F. Merkle, P. Kern, P. Lena, F. Rigaut, J. C. Fontanella, G. Rousset, C. Boyer, J. P. Gaffard, and P. Jagourel, ESO Messenger (58), 1 (1989).

Rousset, G.

F. Merkle, P. Kern, P. Lena, F. Rigaut, J. C. Fontanella, G. Rousset, C. Boyer, J. P. Gaffard, and P. Jagourel, ESO Messenger (58), 1 (1989).

Sanes, J. R.

J. T. Trachtenberg, B. E. Chen, G. W. Knott, G. P. Feng, J. R. Sanes, E. Welker, and K. Svoboda, Nature 420, 788 (2002).
[CrossRef] [PubMed]

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Shack, R. V.

R. V. Shack and B. C. Platt, Opt. Sci. Cent. Newsl. 5, 15 (1971).

Sherman, L.

L. Sherman, J. Y. Ye, O. Albert, and T. B. Norris, J. Microsc. 206, 65 (2002).
[CrossRef] [PubMed]

O. Albert, L. Sherman, G. Mourou, T. B. Norris, and G. Vdovin, Opt. Lett. 25, 52 (2000).
[CrossRef]

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Strickler, J. H.

W. Denk, J. H. Strickler, and W. W. Webb, Science 248, 73 (1990).
[CrossRef] [PubMed]

Svoboda, K.

J. T. Trachtenberg, B. E. Chen, G. W. Knott, G. P. Feng, J. R. Sanes, E. Welker, and K. Svoboda, Nature 420, 788 (2002).
[CrossRef] [PubMed]

W. Denk and K. Svoboda, Neuron 18, 351 (1997).
[CrossRef] [PubMed]

K. Svoboda, W. Denk, D. Kleinfeld, and D. W. Tank, Nature 385, 161 (1997).
[CrossRef] [PubMed]

Swanson, E. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Tanaka, T.

M. A. A. Neil, R. Juskaitis, M. J. Booth, T. Wilson, T. Tanaka, and S. Kawata, J. Microsc. 200, 105 (2000).
[CrossRef]

Tank, D. W.

K. Svoboda, W. Denk, D. Kleinfeld, and D. W. Tank, Nature 385, 161 (1997).
[CrossRef] [PubMed]

Theer, P.

Trachtenberg, J. T.

J. T. Trachtenberg, B. E. Chen, G. W. Knott, G. P. Feng, J. R. Sanes, E. Welker, and K. Svoboda, Nature 420, 788 (2002).
[CrossRef] [PubMed]

Vdovin, G.

Webb, W. W.

W. Denk, J. H. Strickler, and W. W. Webb, Science 248, 73 (1990).
[CrossRef] [PubMed]

Welker, E.

J. T. Trachtenberg, B. E. Chen, G. W. Knott, G. P. Feng, J. R. Sanes, E. Welker, and K. Svoboda, Nature 420, 788 (2002).
[CrossRef] [PubMed]

Williams, D. R.

Wilson, T.

M. A. A. Neil, R. Juskaitis, M. J. Booth, T. Wilson, T. Tanaka, and S. Kawata, J. Microsc. 200, 105 (2000).
[CrossRef]

Ye, J. Y.

L. Sherman, J. Y. Ye, O. Albert, and T. B. Norris, J. Microsc. 206, 65 (2002).
[CrossRef] [PubMed]

Zernike, F.

F. Zernike, Physica 1, 689 (1934).
[CrossRef]

Appl. Opt. (2)

Astron. Astrophys. (1)

R. Foy and A. Labeyrie, Astron. Astrophys. 152, L29 (1985).

ESO Messenger (1)

F. Merkle, P. Kern, P. Lena, F. Rigaut, J. C. Fontanella, G. Rousset, C. Boyer, J. P. Gaffard, and P. Jagourel, ESO Messenger (58), 1 (1989).

J. Microsc. (2)

M. A. A. Neil, R. Juskaitis, M. J. Booth, T. Wilson, T. Tanaka, and S. Kawata, J. Microsc. 200, 105 (2000).
[CrossRef]

L. Sherman, J. Y. Ye, O. Albert, and T. B. Norris, J. Microsc. 206, 65 (2002).
[CrossRef] [PubMed]

J. Neurosci. Methods (1)

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, J. Neurosci. Methods 111, 29 (2001).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

Metrologia (1)

P. Carre, Metrologia 2, 13 (1966).
[CrossRef]

Nature (2)

K. Svoboda, W. Denk, D. Kleinfeld, and D. W. Tank, Nature 385, 161 (1997).
[CrossRef] [PubMed]

J. T. Trachtenberg, B. E. Chen, G. W. Knott, G. P. Feng, J. R. Sanes, E. Welker, and K. Svoboda, Nature 420, 788 (2002).
[CrossRef] [PubMed]

Neuron (1)

W. Denk and K. Svoboda, Neuron 18, 351 (1997).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (3)

Opt. Sci. Cent. Newsl. (1)

R. V. Shack and B. C. Platt, Opt. Sci. Cent. Newsl. 5, 15 (1971).

Physica (1)

F. Zernike, Physica 1, 689 (1934).
[CrossRef]

Proc. Natl. Acad. Sci. USA (2)

D. Kleinfeld, P. P. Mitra, F. Helmchen, and W. Denk, Proc. Natl. Acad. Sci. USA 95, 15741 (1998).
[CrossRef]

D. Kleinfeld, P. P. Mitra, F. Helmchen, and W. Denk, Proc. Natl. Acad. Sci. USA 96, 8307 (1999).

Proc. SPIE (1)

J. F. Bille, B. Grimm, J. Liang, and K. Mueller, Proc. SPIE 1161, 417 (1989).
[CrossRef]

Science (2)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

W. Denk, J. H. Strickler, and W. W. Webb, Science 248, 73 (1990).
[CrossRef] [PubMed]

Other (2)

D. Malacara, Wiley Series in Pure and Applied Optics, 2nd ed. (Wiley, New York, 1992).

V. P. Linnik, ESO Conference and Workshop Proceedings No. 48 (European Southern Observatory, Garching, Germany, 1993).

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Figures (3)

Fig. 1
Fig. 1

Experimental setup. Horizontally polarized light pulses from a Ti:sapphire laser (Coherent Mira, center wavelength of 915 nm) are split by 50/50 beam splitter cube BSC1 (nonpolarizing, BK7, Coherent) into reference and sample arms. In the sample arm the light falls by means of mirror M1 onto objective OBJ (Zeiss IR-Achroplan 63×, 0.90 W) into sample SMP (power at the sample <1 mW). Lenses L1 and L2 (LINOS near-infrared doublets, f=140 mm) image the back focal plane of the objective onto the CCD chip (Sony XC-77, pixel dimensions of 13 µm×13 µm). The reference light is reflected by mirror M2 mounted on a piezoactuator (PCL 100-40, LINOS), passes four dispersion-matching prisms DP (BK7, LINOS), a right angle prism RP (BK7, LINOS) for 180° deflection, and mirror M3, and is recombined with the sample light by means of a second beam splitter cube BSC2 (nonpolarizing, BK7, LINOS). M1–M3, protected silver mirrors (LINOS).

Fig. 2
Fig. 2

(a) Real part of the complex wave-front amplitude for 10µm defocus calculated with Eq. (1). (b) Virtual Shack–Hartmann spots generated by numerical propagation; the magnified view of a small subregion is shown. (c) Peak shifts calculated by fitting. (d) Wave-front reconstructed with a modal estimation algorithm.

Fig. 3
Fig. 3

(a) Zernike coefficients (Z4Z11) as a function of CG position. Negative positions are for the CG between focus and objective. The solid line shows the theoretical expectation for defocus. (b) Same as in (a) but with a tilted glass plate between sample and objective.

Equations (1)

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A=I1-I3+iI4-I2=4IrefIsample1/2cos Δϕ+i sin Δϕ,

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