Abstract

We analyze the increase in precision of parameters estimation for polarization-resolved second-harmonic generation imaging microscopy when two intensities are measured with two orthogonal analyzers. The analysis is performed for measuring anisotropy parameters and molecule orientation for samples with cylindrical symmetry in the presence of photon noise with Poisson statistics. The improvement in comparison to global intensity measurement (i.e., without analyzer) is discussed.

© 2012 Optical Society of America

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  1. I. Freund, M. Deutsch, and A. Sprecher, Biophys. J. 50, 693 (1986).
    [CrossRef]
  2. P. Stoller, B. M. Kim, A. M. Rubenchik, K. M. Reiser, and L. B. Da Silva, J. Biomed. Opt. 7, 205 (2000).
    [CrossRef]
  3. T. Yasui, K. Sasaki, Y. Tohno, and T. Araki, Opt. Quantum Electron. 37, 1397 (2005).
    [CrossRef]
  4. R. M. Williams, W. R. Zipfel, and W. W. Webb, Biophys. J. 88, 1377 (2005).
    [CrossRef]
  5. S. V. Plotnikov, A. Millard, P. Campagnola, and W. Mohler, Biophys. J. 90, 328 (2006).
    [CrossRef]
  6. F. Tiaho, G. Recher, and D. Rouède, Opt. Express 15, 4054 (2007).
    [CrossRef]
  7. 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]
  8. 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]
  9. D. Aït-Belkacem, A. Gasecka, F. Munhoz, S. Brustlein, and S. Brasselet, Opt. Express 18, 14859 (2010).
    [CrossRef]
  10. I. Gusachenko, Y. G. Houssen, V. Tran, J.-M. Allain, and M.-C. Schanne-Klein, Biophys. J. 102, 2220 (2012).
    [CrossRef]
  11. P. J. Su, W. L. Chen, Y. F. Chen, and C. Y. Dong, Biophys. J. 100, 2053 (2011).
    [CrossRef]
  12. Ph. Réfrégier, M. Roche, and S. Brasselet, Opt. Lett. 36, 2149 (2011).
    [CrossRef]
  13. V. Le Floc’h, S. Brasselet, J.-F. Roch, and J. Zyss, J. Phys. Chem. B 107, 12403 (2003).
    [CrossRef]
  14. S. Brasselet, V. Le Floc’h, F. Treussart, J.-F. Roch, and J. Zyss, Phys. Rev. Lett. 92, 207401 (2004).
    [CrossRef]
  15. J. Duboisset, D. Aït-Belkacem, M. Roche, H. Rigneault, and S. Brasselet, Phys. Rev. A 85, 043829 (2012).
    [CrossRef]
  16. H. V. Poor, An Introduction to Signal Detection and Estimation (Springer-Verlag, 1998).

2012 (2)

I. Gusachenko, Y. G. Houssen, V. Tran, J.-M. Allain, and M.-C. Schanne-Klein, Biophys. J. 102, 2220 (2012).
[CrossRef]

J. Duboisset, D. Aït-Belkacem, M. Roche, H. Rigneault, and S. Brasselet, Phys. Rev. A 85, 043829 (2012).
[CrossRef]

2011 (2)

P. J. Su, W. L. Chen, Y. F. Chen, and C. Y. Dong, Biophys. J. 100, 2053 (2011).
[CrossRef]

Ph. Réfrégier, M. Roche, and S. Brasselet, Opt. Lett. 36, 2149 (2011).
[CrossRef]

2010 (1)

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]

2007 (1)

2006 (1)

S. V. Plotnikov, A. Millard, P. Campagnola, and W. Mohler, Biophys. J. 90, 328 (2006).
[CrossRef]

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]

2004 (1)

S. Brasselet, V. Le Floc’h, F. Treussart, J.-F. Roch, and J. Zyss, Phys. Rev. Lett. 92, 207401 (2004).
[CrossRef]

2003 (1)

V. Le Floc’h, S. Brasselet, J.-F. Roch, and J. Zyss, J. Phys. Chem. B 107, 12403 (2003).
[CrossRef]

2000 (1)

P. Stoller, B. M. Kim, A. M. Rubenchik, K. M. Reiser, and L. B. Da Silva, J. Biomed. Opt. 7, 205 (2000).
[CrossRef]

1986 (1)

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

Aït-Belkacem, D.

J. Duboisset, D. Aït-Belkacem, M. Roche, H. Rigneault, and S. Brasselet, Phys. Rev. A 85, 043829 (2012).
[CrossRef]

D. Aït-Belkacem, A. Gasecka, F. Munhoz, S. Brustlein, and S. Brasselet, Opt. Express 18, 14859 (2010).
[CrossRef]

Allain, J.-M.

I. Gusachenko, Y. G. Houssen, V. Tran, J.-M. Allain, and M.-C. Schanne-Klein, Biophys. J. 102, 2220 (2012).
[CrossRef]

Amat-Roldan, I.

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]

Araki, T.

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

Artigas, D.

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]

Brasselet, S.

J. Duboisset, D. Aït-Belkacem, M. Roche, H. Rigneault, and S. Brasselet, Phys. Rev. A 85, 043829 (2012).
[CrossRef]

Ph. Réfrégier, M. Roche, and S. Brasselet, Opt. Lett. 36, 2149 (2011).
[CrossRef]

D. Aït-Belkacem, A. Gasecka, F. Munhoz, S. Brustlein, and S. Brasselet, Opt. Express 18, 14859 (2010).
[CrossRef]

S. Brasselet, V. Le Floc’h, F. Treussart, J.-F. Roch, and J. Zyss, Phys. Rev. Lett. 92, 207401 (2004).
[CrossRef]

V. Le Floc’h, S. Brasselet, J.-F. Roch, and J. Zyss, J. Phys. Chem. B 107, 12403 (2003).
[CrossRef]

Brustlein, S.

Campagnola, P.

S. V. Plotnikov, A. Millard, P. Campagnola, and W. Mohler, Biophys. J. 90, 328 (2006).
[CrossRef]

Chen, W. L.

P. J. Su, W. L. Chen, Y. F. Chen, and C. Y. Dong, Biophys. J. 100, 2053 (2011).
[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]

Chen, Y. F.

P. J. Su, W. L. Chen, Y. F. Chen, and C. Y. Dong, Biophys. J. 100, 2053 (2011).
[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 (2000).
[CrossRef]

Deutsch, M.

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

Dong, C. Y.

P. J. Su, W. L. Chen, Y. F. Chen, and C. Y. Dong, Biophys. J. 100, 2053 (2011).
[CrossRef]

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]

Duboisset, J.

J. Duboisset, D. Aït-Belkacem, M. Roche, H. Rigneault, and S. Brasselet, Phys. Rev. A 85, 043829 (2012).
[CrossRef]

Freund, I.

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

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.

I. Gusachenko, Y. G. Houssen, V. Tran, J.-M. Allain, and M.-C. Schanne-Klein, Biophys. J. 102, 2220 (2012).
[CrossRef]

Houssen, Y. G.

I. Gusachenko, Y. G. Houssen, V. Tran, J.-M. Allain, and M.-C. Schanne-Klein, Biophys. J. 102, 2220 (2012).
[CrossRef]

Kim, B. M.

P. Stoller, B. M. Kim, A. M. Rubenchik, K. M. Reiser, and L. B. Da Silva, J. Biomed. Opt. 7, 205 (2000).
[CrossRef]

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]

Le Floc’h, V.

S. Brasselet, V. Le Floc’h, F. Treussart, J.-F. Roch, and J. Zyss, Phys. Rev. Lett. 92, 207401 (2004).
[CrossRef]

V. Le Floc’h, S. Brasselet, J.-F. Roch, and J. Zyss, J. Phys. Chem. B 107, 12403 (2003).
[CrossRef]

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.

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]

Millard, A.

S. V. Plotnikov, A. Millard, P. Campagnola, and W. Mohler, Biophys. J. 90, 328 (2006).
[CrossRef]

Mohler, W.

S. V. Plotnikov, A. Millard, P. Campagnola, and W. Mohler, Biophys. J. 90, 328 (2006).
[CrossRef]

Munhoz, F.

Plotnikov, S. V.

S. V. Plotnikov, A. Millard, P. Campagnola, and W. Mohler, Biophys. J. 90, 328 (2006).
[CrossRef]

Poor, H. V.

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

Psilodimitrakopoulos, S.

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]

Recher, G.

Réfrégier, Ph.

Reiser, K. M.

P. Stoller, B. M. Kim, A. M. Rubenchik, K. M. Reiser, and L. B. Da Silva, J. Biomed. Opt. 7, 205 (2000).
[CrossRef]

Rigneault, H.

J. Duboisset, D. Aït-Belkacem, M. Roche, H. Rigneault, and S. Brasselet, Phys. Rev. A 85, 043829 (2012).
[CrossRef]

Roch, J.-F.

S. Brasselet, V. Le Floc’h, F. Treussart, J.-F. Roch, and J. Zyss, Phys. Rev. Lett. 92, 207401 (2004).
[CrossRef]

V. Le Floc’h, S. Brasselet, J.-F. Roch, and J. Zyss, J. Phys. Chem. B 107, 12403 (2003).
[CrossRef]

Roche, M.

J. Duboisset, D. Aït-Belkacem, M. Roche, H. Rigneault, and S. Brasselet, Phys. Rev. A 85, 043829 (2012).
[CrossRef]

Ph. Réfrégier, M. Roche, and S. Brasselet, Opt. Lett. 36, 2149 (2011).
[CrossRef]

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 (2000).
[CrossRef]

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]

Sasaki, K.

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

Schanne-Klein, M.-C.

I. Gusachenko, Y. G. Houssen, V. Tran, J.-M. Allain, and M.-C. Schanne-Klein, Biophys. J. 102, 2220 (2012).
[CrossRef]

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]

Stoller, P.

P. Stoller, B. M. Kim, A. M. Rubenchik, K. M. Reiser, and L. B. Da Silva, J. Biomed. Opt. 7, 205 (2000).
[CrossRef]

Su, P. J.

P. J. Su, W. L. Chen, Y. F. Chen, and C. Y. Dong, Biophys. J. 100, 2053 (2011).
[CrossRef]

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]

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]

Tiaho, F.

Tohno, Y.

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

Tran, V.

I. Gusachenko, Y. G. Houssen, V. Tran, J.-M. Allain, and M.-C. Schanne-Klein, Biophys. J. 102, 2220 (2012).
[CrossRef]

Treussart, F.

S. Brasselet, V. Le Floc’h, F. Treussart, J.-F. Roch, and J. Zyss, Phys. Rev. Lett. 92, 207401 (2004).
[CrossRef]

Webb, W. W.

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

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]

Zyss, J.

S. Brasselet, V. Le Floc’h, F. Treussart, J.-F. Roch, and J. Zyss, Phys. Rev. Lett. 92, 207401 (2004).
[CrossRef]

V. Le Floc’h, S. Brasselet, J.-F. Roch, and J. Zyss, J. Phys. Chem. B 107, 12403 (2003).
[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. (5)

I. Gusachenko, Y. G. Houssen, V. Tran, J.-M. Allain, and M.-C. Schanne-Klein, Biophys. J. 102, 2220 (2012).
[CrossRef]

P. J. Su, W. L. Chen, Y. F. Chen, and C. Y. Dong, Biophys. J. 100, 2053 (2011).
[CrossRef]

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

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

S. V. Plotnikov, A. Millard, P. Campagnola, and W. Mohler, Biophys. J. 90, 328 (2006).
[CrossRef]

J. Biomed. Opt. (2)

P. Stoller, B. M. Kim, A. M. Rubenchik, K. M. Reiser, and L. B. Da Silva, J. Biomed. Opt. 7, 205 (2000).
[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]

J. Phys. Chem. B (1)

V. Le Floc’h, S. Brasselet, J.-F. Roch, and J. Zyss, J. Phys. Chem. B 107, 12403 (2003).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Opt. Quantum Electron. (1)

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

Phys. Rev. A (1)

J. Duboisset, D. Aït-Belkacem, M. Roche, H. Rigneault, and S. Brasselet, Phys. Rev. A 85, 043829 (2012).
[CrossRef]

Phys. Rev. Lett. (1)

S. Brasselet, V. Le Floc’h, F. Treussart, J.-F. Roch, and J. Zyss, Phys. Rev. Lett. 92, 207401 (2004).
[CrossRef]

Other (1)

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

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Figures (2)

Fig. 1.
Fig. 1.

Notations used for the precision analysis when the intensities are measured with two orthogonal analyzers (corresponding to α and β).

Fig. 2.
Fig. 2.

Variance of different estimators of φ0 in radians (inset: of d2 and d3) as a function of the parameter μ (which is proportional to the photon mean number) for global intensity measurement (T) and for two intensity measurements (V). The CRB has also been reported. Estimator’s variances have been estimated with 300 simulation experiments when P=11, with φ0=π/12, d1=d2=1.0, and d3=1.5 and ψn=0. Values on the vertical axis have to be multiplied by 103.

Equations (11)

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

Aα(θ)=Au(θ)cos(φ0ψ)Av(θ)sin(φ0ψ),Aβ(θ)=Au(θ)sin(φ0ψ)+Av(θ)cos(φ0ψ),
Au(θ)=μd1+d32+μd3d12cos[2(θφ0)],Av(θ)=μd2sin[2(θφ0)],
(χ|p)=α(χ|p)+β(χ|p)
[IF(η)]i,j=n=1PpiIη(θn)pjIη(θn)Iη(θn),
IF,V=Pμ(3201200200120320000G)
var[φ^0V]CRBV[φ0]=1PμG,
var[d^jV]CRBV[dj]=AjPμ,
CRBT[φ0]3d12+4d22+2d1d3+3d32μP([(d1d3)24d22]2+4(d12d32)2).
Rn=(cos(φ0ψn)sin(φ0ψn)sin(φ0ψn)cos(φ0ψn)).
diA˜nTdjA˜n=diAnTdjAn,diA˜nTφ0A˜n=diAnTφ0An+diAnTUAn,[φ0A˜n]Tφ0A˜n=φ0ATφ0A+φ0AnTUAnAnTUφ0An+AnTAn,
U=RnTBn=(0110).

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