Abstract

Polarization-resolved second harmonic generation (PSHG) imaging microscopy allows one to provide information such as anisotropy parameters and molecule orientation. We analyze the precision of parameter estimation for samples with cylindrical symmetry and a Gaussian additive noise model. We introduce improvements of existing techniques that can be useful to get rapid acquisition and processing of PSHG images, and we discuss the influence of photon noise.

© 2011 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
  3. D. A. Dombeck, K. A. Kasischke, H. D. Vishwasrao, M. Ingelsson, B. T. Hyman, and W. W. Webb, Proc. Natl. Acad. Sci. USA 100, 7081 (2003).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  5. P. Stoller, B. M. Kim, A. M. Rubenchik, K. M. Reiser, and L. B. Da Silva, J. Biomed. Opt. 7, 205 (2002).
    [CrossRef] [PubMed]
  6. T. Yasui, K. Sasaki, Y. Tohno, and T. Araki, Opt. Quantum Electron. 37, 1397 (2005).
    [CrossRef]
  7. R. M. Williams, W. R. Zipfel, and W. W. Webb, Biophys. J. 88, 1377 (2005).
    [CrossRef]
  8. F. Tiaho, G. Recher, and D. Rouède, Opt. Express 15, 12286 (2007).
    [CrossRef] [PubMed]
  9. W.-L. Chen, T.-H. Li, P.-J. Su, C.-K. Chou, P. T. Fwu, S.-J. Lin, D. Kim, P. T. C. So, and C.-Y. Dong, Appl. Phys. Lett. 94, 183902 (2009).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2010 (3)

2009 (2)

W.-L. Chen, T.-H. Li, P.-J. Su, C.-K. Chou, P. T. Fwu, S.-J. Lin, D. Kim, P. T. C. So, and C.-Y. Dong, Appl. Phys. Lett. 94, 183902 (2009).
[CrossRef]

S. Psilodimitrakopoulos, S. I. C. O. Santos, I. Amat-Roldan, A. K. N. Thayil, D. Artigas, and P. Loza-Alvarez, J. Biomed. Opt. 14, 014001 (2009).
[CrossRef] [PubMed]

2008 (2)

M. Strupler, M. Hernest, C. Fligny, J. L. Martin, P.-L. Tharaux, and M. C. Schanne-Klein, J. Biomed. Opt. 13, 054041 (2008).
[CrossRef] [PubMed]

M. R. Foreman, C. M. Romero, and P. Török, Opt. Lett. 33, 1020 (2008).
[CrossRef] [PubMed]

2007 (1)

2005 (2)

T. Yasui, K. Sasaki, Y. Tohno, and T. Araki, Opt. Quantum Electron. 37, 1397 (2005).
[CrossRef]

R. M. Williams, W. R. Zipfel, and W. W. Webb, Biophys. J. 88, 1377 (2005).
[CrossRef]

2003 (1)

D. A. Dombeck, K. A. Kasischke, H. D. Vishwasrao, M. Ingelsson, B. T. Hyman, and W. W. Webb, Proc. Natl. Acad. Sci. USA 100, 7081 (2003).
[CrossRef] [PubMed]

2002 (2)

P. Stoller, B. M. Kim, A. M. Rubenchik, K. M. Reiser, and L. B. Da Silva, J. Biomed. Opt. 7, 205 (2002).
[CrossRef] [PubMed]

P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone, and W. A. Mohler, Biophys. J. 82, 493 (2002).
[CrossRef]

1986 (1)

I. Freund, M. Deutsch, and A. Sprecher, Biophys. J. 50, 693 (1986).
[CrossRef] [PubMed]

Aït-Belkacem, D.

Amat-Roldan, I.

I. Amat-Roldan, S. Psilodimitrakopoulos, P. Loza-Alvarez, and D. Artigas, Opt. Express 18, 17209 (2010).
[CrossRef] [PubMed]

S. Psilodimitrakopoulos, S. I. C. O. Santos, I. Amat-Roldan, A. K. N. Thayil, D. Artigas, and P. Loza-Alvarez, J. Biomed. Opt. 14, 014001 (2009).
[CrossRef] [PubMed]

Araki, T.

T. Yasui, K. Sasaki, Y. Tohno, and T. Araki, Opt. Quantum Electron. 37, 1397 (2005).
[CrossRef]

Artigas, D.

I. Amat-Roldan, S. Psilodimitrakopoulos, P. Loza-Alvarez, and D. Artigas, Opt. Express 18, 17209 (2010).
[CrossRef] [PubMed]

S. Psilodimitrakopoulos, S. I. C. O. Santos, I. Amat-Roldan, A. K. N. Thayil, D. Artigas, and P. Loza-Alvarez, J. Biomed. Opt. 14, 014001 (2009).
[CrossRef] [PubMed]

Brasselet, S.

Brustlein, S.

Campagnola, P. J.

P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone, and W. A. Mohler, Biophys. J. 82, 493 (2002).
[CrossRef]

Chen, W.-L.

W.-L. Chen, T.-H. Li, P.-J. Su, C.-K. Chou, P. T. Fwu, S.-J. Lin, D. Kim, P. T. C. So, and C.-Y. Dong, Appl. Phys. Lett. 94, 183902 (2009).
[CrossRef]

Chou, C.-K.

W.-L. Chen, T.-H. Li, P.-J. Su, C.-K. Chou, P. T. Fwu, S.-J. Lin, D. Kim, P. T. C. So, and C.-Y. Dong, Appl. Phys. Lett. 94, 183902 (2009).
[CrossRef]

Da Silva, L. B.

P. Stoller, B. M. Kim, A. M. Rubenchik, K. M. Reiser, and L. B. Da Silva, J. Biomed. Opt. 7, 205 (2002).
[CrossRef] [PubMed]

Deutsch, M.

I. Freund, M. Deutsch, and A. Sprecher, Biophys. J. 50, 693 (1986).
[CrossRef] [PubMed]

Dombeck, D. A.

D. A. Dombeck, K. A. Kasischke, H. D. Vishwasrao, M. Ingelsson, B. T. Hyman, and W. W. Webb, Proc. Natl. Acad. Sci. USA 100, 7081 (2003).
[CrossRef] [PubMed]

Dong, C.-Y.

W.-L. Chen, T.-H. Li, P.-J. Su, C.-K. Chou, P. T. Fwu, S.-J. Lin, D. Kim, P. T. C. So, and C.-Y. Dong, Appl. Phys. Lett. 94, 183902 (2009).
[CrossRef]

Fligny, C.

M. Strupler, M. Hernest, C. Fligny, J. L. Martin, P.-L. Tharaux, and M. C. Schanne-Klein, J. Biomed. Opt. 13, 054041 (2008).
[CrossRef] [PubMed]

Foreman, M. R.

Freund, I.

I. Freund, M. Deutsch, and A. Sprecher, Biophys. J. 50, 693 (1986).
[CrossRef] [PubMed]

Fwu, P. T.

W.-L. Chen, T.-H. Li, P.-J. Su, C.-K. Chou, P. T. Fwu, S.-J. Lin, D. Kim, P. T. C. So, and C.-Y. Dong, Appl. Phys. Lett. 94, 183902 (2009).
[CrossRef]

Gasecka, A.

Gusachenko, I.

Hernest, M.

M. Strupler, M. Hernest, C. Fligny, J. L. Martin, P.-L. Tharaux, and M. C. Schanne-Klein, J. Biomed. Opt. 13, 054041 (2008).
[CrossRef] [PubMed]

Hoppe, P. E.

P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone, and W. A. Mohler, Biophys. J. 82, 493 (2002).
[CrossRef]

Hyman, B. T.

D. A. Dombeck, K. A. Kasischke, H. D. Vishwasrao, M. Ingelsson, B. T. Hyman, and W. W. Webb, Proc. Natl. Acad. Sci. USA 100, 7081 (2003).
[CrossRef] [PubMed]

Ingelsson, M.

D. A. Dombeck, K. A. Kasischke, H. D. Vishwasrao, M. Ingelsson, B. T. Hyman, and W. W. Webb, Proc. Natl. Acad. Sci. USA 100, 7081 (2003).
[CrossRef] [PubMed]

Kasischke, K. A.

D. A. Dombeck, K. A. Kasischke, H. D. Vishwasrao, M. Ingelsson, B. T. Hyman, and W. W. Webb, Proc. Natl. Acad. Sci. USA 100, 7081 (2003).
[CrossRef] [PubMed]

Kim, B. M.

P. Stoller, B. M. Kim, A. M. Rubenchik, K. M. Reiser, and L. B. Da Silva, J. Biomed. Opt. 7, 205 (2002).
[CrossRef] [PubMed]

Kim, D.

W.-L. Chen, T.-H. Li, P.-J. Su, C.-K. Chou, P. T. Fwu, S.-J. Lin, D. Kim, P. T. C. So, and C.-Y. Dong, Appl. Phys. Lett. 94, 183902 (2009).
[CrossRef]

Latour, G.

Li, T.-H.

W.-L. Chen, T.-H. Li, P.-J. Su, C.-K. Chou, P. T. Fwu, S.-J. Lin, D. Kim, P. T. C. So, and C.-Y. Dong, Appl. Phys. Lett. 94, 183902 (2009).
[CrossRef]

Lin, S.-J.

W.-L. Chen, T.-H. Li, P.-J. Su, C.-K. Chou, P. T. Fwu, S.-J. Lin, D. Kim, P. T. C. So, and C.-Y. Dong, Appl. Phys. Lett. 94, 183902 (2009).
[CrossRef]

Loza-Alvarez, P.

I. Amat-Roldan, S. Psilodimitrakopoulos, P. Loza-Alvarez, and D. Artigas, Opt. Express 18, 17209 (2010).
[CrossRef] [PubMed]

S. Psilodimitrakopoulos, S. I. C. O. Santos, I. Amat-Roldan, A. K. N. Thayil, D. Artigas, and P. Loza-Alvarez, J. Biomed. Opt. 14, 014001 (2009).
[CrossRef] [PubMed]

Malone, C. J.

P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone, and W. A. Mohler, Biophys. J. 82, 493 (2002).
[CrossRef]

Martin, J. L.

M. Strupler, M. Hernest, C. Fligny, J. L. Martin, P.-L. Tharaux, and M. C. Schanne-Klein, J. Biomed. Opt. 13, 054041 (2008).
[CrossRef] [PubMed]

Millard, A. C.

P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone, and W. A. Mohler, Biophys. J. 82, 493 (2002).
[CrossRef]

Mohler, W. A.

P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone, and W. A. Mohler, Biophys. J. 82, 493 (2002).
[CrossRef]

Munhoz, F.

Poor, H. V.

H. V. Poor, An Introduction to Signal Detection and Estimation (Springer-Verlag, 1998).

Psilodimitrakopoulos, S.

I. Amat-Roldan, S. Psilodimitrakopoulos, P. Loza-Alvarez, and D. Artigas, Opt. Express 18, 17209 (2010).
[CrossRef] [PubMed]

S. Psilodimitrakopoulos, S. I. C. O. Santos, I. Amat-Roldan, A. K. N. Thayil, D. Artigas, and P. Loza-Alvarez, J. Biomed. Opt. 14, 014001 (2009).
[CrossRef] [PubMed]

Recher, G.

Reiser, K. M.

P. Stoller, B. M. Kim, A. M. Rubenchik, K. M. Reiser, and L. B. Da Silva, J. Biomed. Opt. 7, 205 (2002).
[CrossRef] [PubMed]

Romero, C. M.

Rouède, D.

Rubenchik, A. M.

P. Stoller, B. M. Kim, A. M. Rubenchik, K. M. Reiser, and L. B. Da Silva, J. Biomed. Opt. 7, 205 (2002).
[CrossRef] [PubMed]

Santos, S. I. C. O.

S. Psilodimitrakopoulos, S. I. C. O. Santos, I. Amat-Roldan, A. K. N. Thayil, D. Artigas, and P. Loza-Alvarez, J. Biomed. Opt. 14, 014001 (2009).
[CrossRef] [PubMed]

Sasaki, K.

T. Yasui, K. Sasaki, Y. Tohno, and T. Araki, Opt. Quantum Electron. 37, 1397 (2005).
[CrossRef]

Schanne-Klein, M. C.

M. Strupler, M. Hernest, C. Fligny, J. L. Martin, P.-L. Tharaux, and M. C. Schanne-Klein, J. Biomed. Opt. 13, 054041 (2008).
[CrossRef] [PubMed]

Schanne-Klein, M.-C.

So, P. T. C.

W.-L. Chen, T.-H. Li, P.-J. Su, C.-K. Chou, P. T. Fwu, S.-J. Lin, D. Kim, P. T. C. So, and C.-Y. Dong, Appl. Phys. Lett. 94, 183902 (2009).
[CrossRef]

Sprecher, A.

I. Freund, M. Deutsch, and A. Sprecher, Biophys. J. 50, 693 (1986).
[CrossRef] [PubMed]

Stoller, P.

P. Stoller, B. M. Kim, A. M. Rubenchik, K. M. Reiser, and L. B. Da Silva, J. Biomed. Opt. 7, 205 (2002).
[CrossRef] [PubMed]

Strupler, M.

M. Strupler, M. Hernest, C. Fligny, J. L. Martin, P.-L. Tharaux, and M. C. Schanne-Klein, J. Biomed. Opt. 13, 054041 (2008).
[CrossRef] [PubMed]

Su, P.-J.

W.-L. Chen, T.-H. Li, P.-J. Su, C.-K. Chou, P. T. Fwu, S.-J. Lin, D. Kim, P. T. C. So, and C.-Y. Dong, Appl. Phys. Lett. 94, 183902 (2009).
[CrossRef]

Terasaki, M.

P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone, and W. A. Mohler, Biophys. J. 82, 493 (2002).
[CrossRef]

Tharaux, P.-L.

M. Strupler, M. Hernest, C. Fligny, J. L. Martin, P.-L. Tharaux, and M. C. Schanne-Klein, J. Biomed. Opt. 13, 054041 (2008).
[CrossRef] [PubMed]

Thayil, A. K. N.

S. Psilodimitrakopoulos, S. I. C. O. Santos, I. Amat-Roldan, A. K. N. Thayil, D. Artigas, and P. Loza-Alvarez, J. Biomed. Opt. 14, 014001 (2009).
[CrossRef] [PubMed]

Tiaho, F.

Tohno, Y.

T. Yasui, K. Sasaki, Y. Tohno, and T. Araki, Opt. Quantum Electron. 37, 1397 (2005).
[CrossRef]

Török, P.

Vishwasrao, H. D.

D. A. Dombeck, K. A. Kasischke, H. D. Vishwasrao, M. Ingelsson, B. T. Hyman, and W. W. Webb, Proc. Natl. Acad. Sci. USA 100, 7081 (2003).
[CrossRef] [PubMed]

Webb, W. W.

R. M. Williams, W. R. Zipfel, and W. W. Webb, Biophys. J. 88, 1377 (2005).
[CrossRef]

D. A. Dombeck, K. A. Kasischke, H. D. Vishwasrao, M. Ingelsson, B. T. Hyman, and W. W. Webb, Proc. Natl. Acad. Sci. USA 100, 7081 (2003).
[CrossRef] [PubMed]

Williams, R. M.

R. M. Williams, W. R. Zipfel, and W. W. Webb, Biophys. J. 88, 1377 (2005).
[CrossRef]

Yasui, T.

T. Yasui, K. Sasaki, Y. Tohno, and T. Araki, Opt. Quantum Electron. 37, 1397 (2005).
[CrossRef]

Zipfel, W. R.

R. M. Williams, W. R. Zipfel, and W. W. Webb, Biophys. J. 88, 1377 (2005).
[CrossRef]

Appl. Phys. Lett. (1)

W.-L. Chen, T.-H. Li, P.-J. Su, C.-K. Chou, P. T. Fwu, S.-J. Lin, D. Kim, P. T. C. So, and C.-Y. Dong, Appl. Phys. Lett. 94, 183902 (2009).
[CrossRef]

Biophys. J. (3)

I. Freund, M. Deutsch, and A. Sprecher, Biophys. J. 50, 693 (1986).
[CrossRef] [PubMed]

P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone, and W. A. Mohler, Biophys. J. 82, 493 (2002).
[CrossRef]

R. M. Williams, W. R. Zipfel, and W. W. Webb, Biophys. J. 88, 1377 (2005).
[CrossRef]

J. Biomed. Opt. (3)

M. Strupler, M. Hernest, C. Fligny, J. L. Martin, P.-L. Tharaux, and M. C. Schanne-Klein, J. Biomed. Opt. 13, 054041 (2008).
[CrossRef] [PubMed]

P. Stoller, B. M. Kim, A. M. Rubenchik, K. M. Reiser, and L. B. Da Silva, J. Biomed. Opt. 7, 205 (2002).
[CrossRef] [PubMed]

S. Psilodimitrakopoulos, S. I. C. O. Santos, I. Amat-Roldan, A. K. N. Thayil, D. Artigas, and P. Loza-Alvarez, J. Biomed. Opt. 14, 014001 (2009).
[CrossRef] [PubMed]

Opt. Express (4)

Opt. Lett. (1)

Opt. Quantum Electron. (1)

T. Yasui, K. Sasaki, Y. Tohno, and T. Araki, Opt. Quantum Electron. 37, 1397 (2005).
[CrossRef]

Proc. Natl. Acad. Sci. USA (1)

D. A. Dombeck, K. A. Kasischke, H. D. Vishwasrao, M. Ingelsson, B. T. Hyman, and W. W. Webb, Proc. Natl. Acad. Sci. USA 100, 7081 (2003).
[CrossRef] [PubMed]

Other (1)

H. V. Poor, An Introduction to Signal Detection and Estimation (Springer-Verlag, 1998).

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Figures (1)

Fig. 1
Fig. 1

Estimated efficiency of different estimators of φ 0 as a function of the noise variance and φ ^ 0 Poisson FF ( χ ) , φ ^ 0 Poisson FT 1 ( χ ) correspond to results of φ ^ 0 FF ( χ ) and φ ^ 0 FT 1 ( χ ) in the presence of Poisson noise. Estimator’s variances have been estimated with 400 simulation experiments when P = 30 , N = 3 with φ 0 = 6 ° , α 0 = 16.75 , α 1 = 5.0 , and α 2 = 3.75 .

Equations (10)

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

I 0 ( θ ) = α 0 8 + α 1 8 cos ( 2 θ 2 φ 0 ) + α 2 8 cos ( 4 θ 4 φ 0 ) ,
α 0 = μ [ 3 ( d 31 2 + d 33 2 ) + 4 d 15 2 + 2 d 31 d 33 ] α 1 = μ [ 4 ( d 33 2 d 31 2 ) ] α 2 = μ [ ( d 31 d 33 ) 2 4 d 15 2 ] ,
( χ | p ) = j = 1 Q [ I ( θ j ) I 0 ( θ j ) ] 2 2 σ 2 1 2 Q ln [ 2 π σ 2 ] .
I 0 ( θ ) φ 0 = 1 4 [ α 1 + 4 α 2 cos ( 2 θ 2 φ 0 ) ] sin ( 2 θ 2 φ 0 ) I 0 ( θ ) α n = 1 8 cos [ 2 n ( θ φ 0 ) ] ,
[ φ ^ 0 ( χ ) φ 0 ] 2 32 α 1 2 + 4 α 2 2 σ 2 P N ,
[ α ^ n ( χ ) α n ] 2 A n σ 2 P N ,
φ ^ 0 FT 1 ( χ ) = 1 2 arctan ( S 1 C 1 ) ,
φ ^ 0 FT 2 ( χ ) = 1 4 arctan ( S 2 C 2 ) ,
φ ^ 0 FF ( χ ) = η ^ ( χ ) φ ^ 0 FT 1 ( χ ) + [ 1 η ^ ( χ ) ] φ ^ 0 FT 2 ( χ ) ,
4 α 0 β ( α 1 2 + 4 α 2 2 ) P N .

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