Abstract

Second harmonic generation microscopy(SHGM) has become widely used to image biological samples. Due to the complexity of biological samples, more and more effort has been put on polarization imaging in SHGM technology to uncover their structures. In this work, we put forward a novel stitching method based on careful mathematical calculation, and accomplish it by rotating laser polarization. We first show its validity in imaging a perfectly synthesized bio-origin polymer poly (3-hyroxybutyrate-co-3-hydroxyhexanoate) (PHBHHx). Then, we test its power by getting a true image of fibrillar collagen structure of rat-tail tendon.

© 2006 Optical Society of America

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  1. P. A. Franken, A. E. Hill, C. W. Peters and G. Weinreich, "Generation of Optical Harmonics," Phys. Rev. Lett. 7,118-119 (1961).
    [CrossRef]
  2. R. Hellwarth and P. Christensen, "Nonlinear optical microscopic examination of structure in polycrystalline ZnSe," Opt. Commun. 12,318-322 (1974)
    [CrossRef]
  3. S. Roth and I. Freund, "Second harmonic in collagen," J. Chem. Phys. 70,1637-1643 (1979)
    [CrossRef]
  4. G. Cox, E. Kable, A. Jones, I. K. Fraser, F. Manconi and M. D. Gorrell, "3-dimensional imaging of collagen using second harmonic generation," J. Structural Biol. 141,53-62 (2003)
    [CrossRef]
  5. I. Freund, M. Deutsch and A. Sprecher, "Connective Tissue Polarity Optical Second-harmonic Microscopy, Crossed-beam Summation, and Small-angle Scattering in Rat-tail Tendon," Biophy. J. 50,693-712 (1986)
    [CrossRef]
  6. B. M. Kim, J. Eichler and L. B. Da Silva, "Frequency doubling of ultrashort laser pulses in biological tissues," Appl. Opt. 38,7145-7150 (1999)
    [CrossRef]
  7. T. Yasui, Y. Tohno and T. Araki, "Characterization of collagen orientation in human dermis by two-dimensional second-harmonic-generation polarimetry," J. Biomed. Opt. 9,259-264 (2004).
    [CrossRef] [PubMed]
  8. S. W. Chu, S. Y. Chen, G. W. Chern, T. H. Tsai, Y. C. Chen, B. L. Lin and C. K. Sun, "Studies of x((2))/x((3)) tensors in submicron-scaled bio-tissues by polarization harmonics optical microscopy," Biophy. J. 86,3914-3922 (2004)
    [CrossRef]
  9. T. Yasui, Y. Tohno and T. Araki "Determination of collagen fiber orientation in human tissue by use of polarization measurement of molecular second-harmonic-generation light," Appl. Opt. 43,2861-2867 (2004)
    [CrossRef] [PubMed]
  10. P. Stoller, K. M. Reiser, P. M. Celliers and A. M. Rubenchik, "Polarization-modulated second harmonic generation in collagen," Biophy. J. 82,3330-3342 (2002)
    [CrossRef]
  11. R. M. Williams, W. R. Zipfel and W. W. Webb, "Interpreting second-harmonic generation images of collagen I fibrils," Biophy. J. 881377-1386 (2005)
    [CrossRef]
  12. Y. Z. Qiu, S. P. Ouyang, Z. Y. Shen, Q. Wu and G. Q. Chen, "Metabolic engineering for the production of copolyesters consisting of 3-hydroxybutyrate and 3-hydroxyhexanoate by Aeromonas hydrophila," Macromol. Biosci 4255-261 (2004)
    [CrossRef] [PubMed]
  13. P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone and W. A. Mohler, "Three dimensional high-resolution second-harmonic generation imaging of endogenous structural proteins in biological tissues," Biophy. J. 82,493-508 (2002).
    [CrossRef]
  14. S. W. Chu, S. Y. Chen, T. H. Tsai, T. M. Liu, C. Y. Lin, H. J. Tsai and C. K. Sun, "In vivo developmental biology study using noninvasive multi-harmonic generation microscopy," Opt. Express 11,3093-3099 (2003).
    [CrossRef] [PubMed]

2005

R. M. Williams, W. R. Zipfel and W. W. Webb, "Interpreting second-harmonic generation images of collagen I fibrils," Biophy. J. 881377-1386 (2005)
[CrossRef]

2004

Y. Z. Qiu, S. P. Ouyang, Z. Y. Shen, Q. Wu and G. Q. Chen, "Metabolic engineering for the production of copolyesters consisting of 3-hydroxybutyrate and 3-hydroxyhexanoate by Aeromonas hydrophila," Macromol. Biosci 4255-261 (2004)
[CrossRef] [PubMed]

T. Yasui, Y. Tohno and T. Araki, "Characterization of collagen orientation in human dermis by two-dimensional second-harmonic-generation polarimetry," J. Biomed. Opt. 9,259-264 (2004).
[CrossRef] [PubMed]

S. W. Chu, S. Y. Chen, G. W. Chern, T. H. Tsai, Y. C. Chen, B. L. Lin and C. K. Sun, "Studies of x((2))/x((3)) tensors in submicron-scaled bio-tissues by polarization harmonics optical microscopy," Biophy. J. 86,3914-3922 (2004)
[CrossRef]

T. Yasui, Y. Tohno and T. Araki "Determination of collagen fiber orientation in human tissue by use of polarization measurement of molecular second-harmonic-generation light," Appl. Opt. 43,2861-2867 (2004)
[CrossRef] [PubMed]

2003

S. W. Chu, S. Y. Chen, T. H. Tsai, T. M. Liu, C. Y. Lin, H. J. Tsai and C. K. Sun, "In vivo developmental biology study using noninvasive multi-harmonic generation microscopy," Opt. Express 11,3093-3099 (2003).
[CrossRef] [PubMed]

G. Cox, E. Kable, A. Jones, I. K. Fraser, F. Manconi and M. D. Gorrell, "3-dimensional imaging of collagen using second harmonic generation," J. Structural Biol. 141,53-62 (2003)
[CrossRef]

2002

P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone and W. A. Mohler, "Three dimensional high-resolution second-harmonic generation imaging of endogenous structural proteins in biological tissues," Biophy. J. 82,493-508 (2002).
[CrossRef]

P. Stoller, K. M. Reiser, P. M. Celliers and A. M. Rubenchik, "Polarization-modulated second harmonic generation in collagen," Biophy. J. 82,3330-3342 (2002)
[CrossRef]

1999

1986

I. Freund, M. Deutsch and A. Sprecher, "Connective Tissue Polarity Optical Second-harmonic Microscopy, Crossed-beam Summation, and Small-angle Scattering in Rat-tail Tendon," Biophy. J. 50,693-712 (1986)
[CrossRef]

1979

S. Roth and I. Freund, "Second harmonic in collagen," J. Chem. Phys. 70,1637-1643 (1979)
[CrossRef]

1974

R. Hellwarth and P. Christensen, "Nonlinear optical microscopic examination of structure in polycrystalline ZnSe," Opt. Commun. 12,318-322 (1974)
[CrossRef]

1961

P. A. Franken, A. E. Hill, C. W. Peters and G. Weinreich, "Generation of Optical Harmonics," Phys. Rev. Lett. 7,118-119 (1961).
[CrossRef]

Araki, T.

T. Yasui, Y. Tohno and T. Araki, "Characterization of collagen orientation in human dermis by two-dimensional second-harmonic-generation polarimetry," J. Biomed. Opt. 9,259-264 (2004).
[CrossRef] [PubMed]

T. Yasui, Y. Tohno and T. Araki "Determination of collagen fiber orientation in human tissue by use of polarization measurement of molecular second-harmonic-generation light," Appl. Opt. 43,2861-2867 (2004)
[CrossRef] [PubMed]

Campagnola, P. J.

P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone and W. A. Mohler, "Three dimensional high-resolution second-harmonic generation imaging of endogenous structural proteins in biological tissues," Biophy. J. 82,493-508 (2002).
[CrossRef]

Celliers, P. M.

P. Stoller, K. M. Reiser, P. M. Celliers and A. M. Rubenchik, "Polarization-modulated second harmonic generation in collagen," Biophy. J. 82,3330-3342 (2002)
[CrossRef]

Chen, G. Q.

Y. Z. Qiu, S. P. Ouyang, Z. Y. Shen, Q. Wu and G. Q. Chen, "Metabolic engineering for the production of copolyesters consisting of 3-hydroxybutyrate and 3-hydroxyhexanoate by Aeromonas hydrophila," Macromol. Biosci 4255-261 (2004)
[CrossRef] [PubMed]

Chen, S. Y.

S. W. Chu, S. Y. Chen, G. W. Chern, T. H. Tsai, Y. C. Chen, B. L. Lin and C. K. Sun, "Studies of x((2))/x((3)) tensors in submicron-scaled bio-tissues by polarization harmonics optical microscopy," Biophy. J. 86,3914-3922 (2004)
[CrossRef]

S. W. Chu, S. Y. Chen, T. H. Tsai, T. M. Liu, C. Y. Lin, H. J. Tsai and C. K. Sun, "In vivo developmental biology study using noninvasive multi-harmonic generation microscopy," Opt. Express 11,3093-3099 (2003).
[CrossRef] [PubMed]

Chen, Y. C.

S. W. Chu, S. Y. Chen, G. W. Chern, T. H. Tsai, Y. C. Chen, B. L. Lin and C. K. Sun, "Studies of x((2))/x((3)) tensors in submicron-scaled bio-tissues by polarization harmonics optical microscopy," Biophy. J. 86,3914-3922 (2004)
[CrossRef]

Chern, G. W.

S. W. Chu, S. Y. Chen, G. W. Chern, T. H. Tsai, Y. C. Chen, B. L. Lin and C. K. Sun, "Studies of x((2))/x((3)) tensors in submicron-scaled bio-tissues by polarization harmonics optical microscopy," Biophy. J. 86,3914-3922 (2004)
[CrossRef]

Christensen, P.

R. Hellwarth and P. Christensen, "Nonlinear optical microscopic examination of structure in polycrystalline ZnSe," Opt. Commun. 12,318-322 (1974)
[CrossRef]

Chu, S. W.

S. W. Chu, S. Y. Chen, G. W. Chern, T. H. Tsai, Y. C. Chen, B. L. Lin and C. K. Sun, "Studies of x((2))/x((3)) tensors in submicron-scaled bio-tissues by polarization harmonics optical microscopy," Biophy. J. 86,3914-3922 (2004)
[CrossRef]

S. W. Chu, S. Y. Chen, T. H. Tsai, T. M. Liu, C. Y. Lin, H. J. Tsai and C. K. Sun, "In vivo developmental biology study using noninvasive multi-harmonic generation microscopy," Opt. Express 11,3093-3099 (2003).
[CrossRef] [PubMed]

Cox, G.

G. Cox, E. Kable, A. Jones, I. K. Fraser, F. Manconi and M. D. Gorrell, "3-dimensional imaging of collagen using second harmonic generation," J. Structural Biol. 141,53-62 (2003)
[CrossRef]

Da Silva, L. B.

Deutsch, M.

I. Freund, M. Deutsch and A. Sprecher, "Connective Tissue Polarity Optical Second-harmonic Microscopy, Crossed-beam Summation, and Small-angle Scattering in Rat-tail Tendon," Biophy. J. 50,693-712 (1986)
[CrossRef]

Eichler, J.

Franken, P. A.

P. A. Franken, A. E. Hill, C. W. Peters and G. Weinreich, "Generation of Optical Harmonics," Phys. Rev. Lett. 7,118-119 (1961).
[CrossRef]

Fraser, I. K.

G. Cox, E. Kable, A. Jones, I. K. Fraser, F. Manconi and M. D. Gorrell, "3-dimensional imaging of collagen using second harmonic generation," J. Structural Biol. 141,53-62 (2003)
[CrossRef]

Freund, I.

I. Freund, M. Deutsch and A. Sprecher, "Connective Tissue Polarity Optical Second-harmonic Microscopy, Crossed-beam Summation, and Small-angle Scattering in Rat-tail Tendon," Biophy. J. 50,693-712 (1986)
[CrossRef]

S. Roth and I. Freund, "Second harmonic in collagen," J. Chem. Phys. 70,1637-1643 (1979)
[CrossRef]

Gorrell, M. D.

G. Cox, E. Kable, A. Jones, I. K. Fraser, F. Manconi and M. D. Gorrell, "3-dimensional imaging of collagen using second harmonic generation," J. Structural Biol. 141,53-62 (2003)
[CrossRef]

Hellwarth, R.

R. Hellwarth and P. Christensen, "Nonlinear optical microscopic examination of structure in polycrystalline ZnSe," Opt. Commun. 12,318-322 (1974)
[CrossRef]

Hill, A. E.

P. A. Franken, A. E. Hill, C. W. Peters and G. Weinreich, "Generation of Optical Harmonics," Phys. Rev. Lett. 7,118-119 (1961).
[CrossRef]

Hoppe, P. E.

P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone and W. A. Mohler, "Three dimensional high-resolution second-harmonic generation imaging of endogenous structural proteins in biological tissues," Biophy. J. 82,493-508 (2002).
[CrossRef]

Jones, A.

G. Cox, E. Kable, A. Jones, I. K. Fraser, F. Manconi and M. D. Gorrell, "3-dimensional imaging of collagen using second harmonic generation," J. Structural Biol. 141,53-62 (2003)
[CrossRef]

Kable, E.

G. Cox, E. Kable, A. Jones, I. K. Fraser, F. Manconi and M. D. Gorrell, "3-dimensional imaging of collagen using second harmonic generation," J. Structural Biol. 141,53-62 (2003)
[CrossRef]

Kim, B. M.

Lin, B. L.

S. W. Chu, S. Y. Chen, G. W. Chern, T. H. Tsai, Y. C. Chen, B. L. Lin and C. K. Sun, "Studies of x((2))/x((3)) tensors in submicron-scaled bio-tissues by polarization harmonics optical microscopy," Biophy. J. 86,3914-3922 (2004)
[CrossRef]

Lin, C. Y.

Liu, T. M.

Malone, C. J.

P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone and W. A. Mohler, "Three dimensional high-resolution second-harmonic generation imaging of endogenous structural proteins in biological tissues," Biophy. J. 82,493-508 (2002).
[CrossRef]

Manconi, F.

G. Cox, E. Kable, A. Jones, I. K. Fraser, F. Manconi and M. D. Gorrell, "3-dimensional imaging of collagen using second harmonic generation," J. Structural Biol. 141,53-62 (2003)
[CrossRef]

Millard, A. C.

P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone and W. A. Mohler, "Three dimensional high-resolution second-harmonic generation imaging of endogenous structural proteins in biological tissues," Biophy. J. 82,493-508 (2002).
[CrossRef]

Mohler, W. A.

P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone and W. A. Mohler, "Three dimensional high-resolution second-harmonic generation imaging of endogenous structural proteins in biological tissues," Biophy. J. 82,493-508 (2002).
[CrossRef]

Ouyang, S. P.

Y. Z. Qiu, S. P. Ouyang, Z. Y. Shen, Q. Wu and G. Q. Chen, "Metabolic engineering for the production of copolyesters consisting of 3-hydroxybutyrate and 3-hydroxyhexanoate by Aeromonas hydrophila," Macromol. Biosci 4255-261 (2004)
[CrossRef] [PubMed]

Peters, C. W.

P. A. Franken, A. E. Hill, C. W. Peters and G. Weinreich, "Generation of Optical Harmonics," Phys. Rev. Lett. 7,118-119 (1961).
[CrossRef]

Qiu, Y. Z.

Y. Z. Qiu, S. P. Ouyang, Z. Y. Shen, Q. Wu and G. Q. Chen, "Metabolic engineering for the production of copolyesters consisting of 3-hydroxybutyrate and 3-hydroxyhexanoate by Aeromonas hydrophila," Macromol. Biosci 4255-261 (2004)
[CrossRef] [PubMed]

Reiser, K. M.

P. Stoller, K. M. Reiser, P. M. Celliers and A. M. Rubenchik, "Polarization-modulated second harmonic generation in collagen," Biophy. J. 82,3330-3342 (2002)
[CrossRef]

Roth, S.

S. Roth and I. Freund, "Second harmonic in collagen," J. Chem. Phys. 70,1637-1643 (1979)
[CrossRef]

Rubenchik, A. M.

P. Stoller, K. M. Reiser, P. M. Celliers and A. M. Rubenchik, "Polarization-modulated second harmonic generation in collagen," Biophy. J. 82,3330-3342 (2002)
[CrossRef]

Shen, Z. Y.

Y. Z. Qiu, S. P. Ouyang, Z. Y. Shen, Q. Wu and G. Q. Chen, "Metabolic engineering for the production of copolyesters consisting of 3-hydroxybutyrate and 3-hydroxyhexanoate by Aeromonas hydrophila," Macromol. Biosci 4255-261 (2004)
[CrossRef] [PubMed]

Sprecher, A.

I. Freund, M. Deutsch and A. Sprecher, "Connective Tissue Polarity Optical Second-harmonic Microscopy, Crossed-beam Summation, and Small-angle Scattering in Rat-tail Tendon," Biophy. J. 50,693-712 (1986)
[CrossRef]

Stoller, P.

P. Stoller, K. M. Reiser, P. M. Celliers and A. M. Rubenchik, "Polarization-modulated second harmonic generation in collagen," Biophy. J. 82,3330-3342 (2002)
[CrossRef]

Sun, C. K.

S. W. Chu, S. Y. Chen, G. W. Chern, T. H. Tsai, Y. C. Chen, B. L. Lin and C. K. Sun, "Studies of x((2))/x((3)) tensors in submicron-scaled bio-tissues by polarization harmonics optical microscopy," Biophy. J. 86,3914-3922 (2004)
[CrossRef]

S. W. Chu, S. Y. Chen, T. H. Tsai, T. M. Liu, C. Y. Lin, H. J. Tsai and C. K. Sun, "In vivo developmental biology study using noninvasive multi-harmonic generation microscopy," Opt. Express 11,3093-3099 (2003).
[CrossRef] [PubMed]

Terasaki, M.

P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone and W. A. Mohler, "Three dimensional high-resolution second-harmonic generation imaging of endogenous structural proteins in biological tissues," Biophy. J. 82,493-508 (2002).
[CrossRef]

Tohno, Y.

T. Yasui, Y. Tohno and T. Araki "Determination of collagen fiber orientation in human tissue by use of polarization measurement of molecular second-harmonic-generation light," Appl. Opt. 43,2861-2867 (2004)
[CrossRef] [PubMed]

T. Yasui, Y. Tohno and T. Araki, "Characterization of collagen orientation in human dermis by two-dimensional second-harmonic-generation polarimetry," J. Biomed. Opt. 9,259-264 (2004).
[CrossRef] [PubMed]

Tsai, H. J.

Tsai, T. H.

S. W. Chu, S. Y. Chen, G. W. Chern, T. H. Tsai, Y. C. Chen, B. L. Lin and C. K. Sun, "Studies of x((2))/x((3)) tensors in submicron-scaled bio-tissues by polarization harmonics optical microscopy," Biophy. J. 86,3914-3922 (2004)
[CrossRef]

S. W. Chu, S. Y. Chen, T. H. Tsai, T. M. Liu, C. Y. Lin, H. J. Tsai and C. K. Sun, "In vivo developmental biology study using noninvasive multi-harmonic generation microscopy," Opt. Express 11,3093-3099 (2003).
[CrossRef] [PubMed]

Webb, W. W.

R. M. Williams, W. R. Zipfel and W. W. Webb, "Interpreting second-harmonic generation images of collagen I fibrils," Biophy. J. 881377-1386 (2005)
[CrossRef]

Weinreich, G.

P. A. Franken, A. E. Hill, C. W. Peters and G. Weinreich, "Generation of Optical Harmonics," Phys. Rev. Lett. 7,118-119 (1961).
[CrossRef]

Williams, R. M.

R. M. Williams, W. R. Zipfel and W. W. Webb, "Interpreting second-harmonic generation images of collagen I fibrils," Biophy. J. 881377-1386 (2005)
[CrossRef]

Wu, Q.

Y. Z. Qiu, S. P. Ouyang, Z. Y. Shen, Q. Wu and G. Q. Chen, "Metabolic engineering for the production of copolyesters consisting of 3-hydroxybutyrate and 3-hydroxyhexanoate by Aeromonas hydrophila," Macromol. Biosci 4255-261 (2004)
[CrossRef] [PubMed]

Yasui, T.

T. Yasui, Y. Tohno and T. Araki "Determination of collagen fiber orientation in human tissue by use of polarization measurement of molecular second-harmonic-generation light," Appl. Opt. 43,2861-2867 (2004)
[CrossRef] [PubMed]

T. Yasui, Y. Tohno and T. Araki, "Characterization of collagen orientation in human dermis by two-dimensional second-harmonic-generation polarimetry," J. Biomed. Opt. 9,259-264 (2004).
[CrossRef] [PubMed]

Zipfel, W. R.

R. M. Williams, W. R. Zipfel and W. W. Webb, "Interpreting second-harmonic generation images of collagen I fibrils," Biophy. J. 881377-1386 (2005)
[CrossRef]

Appl. Opt.

Biophy. J.

S. W. Chu, S. Y. Chen, G. W. Chern, T. H. Tsai, Y. C. Chen, B. L. Lin and C. K. Sun, "Studies of x((2))/x((3)) tensors in submicron-scaled bio-tissues by polarization harmonics optical microscopy," Biophy. J. 86,3914-3922 (2004)
[CrossRef]

P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone and W. A. Mohler, "Three dimensional high-resolution second-harmonic generation imaging of endogenous structural proteins in biological tissues," Biophy. J. 82,493-508 (2002).
[CrossRef]

I. Freund, M. Deutsch and A. Sprecher, "Connective Tissue Polarity Optical Second-harmonic Microscopy, Crossed-beam Summation, and Small-angle Scattering in Rat-tail Tendon," Biophy. J. 50,693-712 (1986)
[CrossRef]

P. Stoller, K. M. Reiser, P. M. Celliers and A. M. Rubenchik, "Polarization-modulated second harmonic generation in collagen," Biophy. J. 82,3330-3342 (2002)
[CrossRef]

R. M. Williams, W. R. Zipfel and W. W. Webb, "Interpreting second-harmonic generation images of collagen I fibrils," Biophy. J. 881377-1386 (2005)
[CrossRef]

J. Biomed. Opt.

T. Yasui, Y. Tohno and T. Araki, "Characterization of collagen orientation in human dermis by two-dimensional second-harmonic-generation polarimetry," J. Biomed. Opt. 9,259-264 (2004).
[CrossRef] [PubMed]

J. Chem. Phys.

S. Roth and I. Freund, "Second harmonic in collagen," J. Chem. Phys. 70,1637-1643 (1979)
[CrossRef]

J. Structural Biol.

G. Cox, E. Kable, A. Jones, I. K. Fraser, F. Manconi and M. D. Gorrell, "3-dimensional imaging of collagen using second harmonic generation," J. Structural Biol. 141,53-62 (2003)
[CrossRef]

Macromol. Biosci

Y. Z. Qiu, S. P. Ouyang, Z. Y. Shen, Q. Wu and G. Q. Chen, "Metabolic engineering for the production of copolyesters consisting of 3-hydroxybutyrate and 3-hydroxyhexanoate by Aeromonas hydrophila," Macromol. Biosci 4255-261 (2004)
[CrossRef] [PubMed]

Opt. Commun.

R. Hellwarth and P. Christensen, "Nonlinear optical microscopic examination of structure in polycrystalline ZnSe," Opt. Commun. 12,318-322 (1974)
[CrossRef]

Opt. Express

Phys. Rev. Lett.

P. A. Franken, A. E. Hill, C. W. Peters and G. Weinreich, "Generation of Optical Harmonics," Phys. Rev. Lett. 7,118-119 (1961).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Illustration of fiber orientation and laser beam propagation direction and polarization

Fig. 2.
Fig. 2.

Angle α dependence of SHG signal for collagen in three complementary images and stitched image (α here represents the angle between the laser polarization and axis of collagen in the first measurement, which we can not predict). Under an arbitrary α, we get the first picture. Then we rotate the half wave plate to make this angle increase π/3 in the second measurement and 2π/3 in the third measurement to get the second and third pictures. S1, S2, S3 and Sum stands for the SHG intensity depending on initial angle α in these complementary images and final stitched image respectively(S1, S2, S3 have been normalized).

Fig. 3.
Fig. 3.

Experimental setup. PMT: photomultiplier; GL: Glan polarizer lens. The SHG signal is collective in the forward direction. GL is used to make the incident laser purely polarized. Half wave plate is used to rotate the laser polarization to the angle we need.

Fig. 4.
Fig. 4.

Stitching SHG images of PHBHHx. (a), (b), (c) are three complementary SHG images and are obtained under linear polarized laser, in which angles between laser polarization and the axis of PHBHHx are α, α+π/3, α+2π/3 respectively. (d) is the final stitched image of three complementary images. Scale bar: 30µm

Fig. 5.
Fig. 5.

Stitching SHG images of collagen. (a), (b), (c) are three complementary SHG images and are obtained under linear polarized laser, in which angles between laser polarization and the axis of collagen are α, α+π/3, α+2π/3 respectively. (d) is the final stitched image of three complementary images. Scale bar: 15µm

Equations (13)

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I SHG ( P · s ) 2 + ( P · ( s × k ) ) 2
I 1 2 ( 3 + 20 γ + 40 γ 2 ) + 1 2 ( 1 + 6 γ + 8 γ 2 ) cos 2 α + 1 8 ( 1 + 4 γ ) cos 4 α
Δ ϕ = 2 π f Δ t
I total = B α 0 α 0 + Δ ϕ [ 1 8 ( 3 + 20 γ + 40 γ 2 ) + 1 2 ( 1 + 6 γ + 8 γ 2 ) cos 2 α + 1 8 ( 1 + 4 γ ) cos 4 α ] d α
I total = B [ 1 8 Δ ϕ ( 3 + 20 γ + 40 γ 2 )
+ 1 4 ( 1 + 6 γ + 8 γ 2 ) sin 2 α α 0 α 0 + Δ ϕ + 1 32 ( 1 + 4 γ ) sin 4 α α 0 α 0 + Δ ϕ ]
I 1 = A [ 1 8 ( 1 + 20 γ + 40 γ 2 ) + 1 2 ( 1 + 6 γ + 8 γ 2 ) cos 2 α + 1 8 ( 1 + 4 γ ) cos 4 α ]
I 2 = A [ 1 8 ( 1 + 20 γ + 40 γ 2 ) + 1 2 ( 1 + 6 γ + 8 γ 2 ) cos 2 ( α + π 3 ) + 1 8 ( 1 + 4 γ ) cos 4 ( α + π 3 ) ]
I 3 = A [ 1 8 ( 1 + 20 γ + 40 γ 2 ) + 1 2 ( 1 + 6 γ + 8 γ 2 ) cos 2 ( α + 2 π 3 ) + 1 8 ( 1 + 4 γ ) cos 4 ( α + 2 π 3 ) ]
I total = I 1 + I 2 + I 3
= A { 3 8 ( 1 + 20 γ + 40 γ 2 ) + 1 2 ( 1 + 6 γ + 8 γ 2 ) [ cos 2 α + cos ( 2 α + 2 π 3 ) + cos ( 2 α + 4 π 3 ) ]
+ 1 8 ( 1 + 4 γ ) [ cos 4 α + cos ( 4 α + 4 π 3 ) + cos ( 4 α + 8 π 3 ) ] }
= 3 A 8 ( 1 + 20 γ + 40 γ 2 )

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