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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 18 — Aug. 30, 2010
  • pp: 19339–19352
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Polarization-resolved Second Harmonic microscopy in anisotropic thick tissues

Ivan Gusachenko, Gaël Latour, and Marie-Claire Schanne-Klein  »View Author Affiliations


Optics Express, Vol. 18, Issue 18, pp. 19339-19352 (2010)
http://dx.doi.org/10.1364/OE.18.019339


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Abstract

We thoroughly analyze the linear propagation effects that affect polarization-resolved Second Harmonic Generation imaging of thick anisotropic tissues such as collagenous tissues. We develop a theoretical model that fully accounts for birefringence and diattenuation along the excitation propagation, and polarization scrambling upon scattering of the harmonic signal. We obtain an excellent agreement with polarization-resolved SHG images at increasing depth within a rat-tail tendon for both polarizations of the forward SHG signal. Most notably, we observe interference fringes due to birefringence in the SHG depth profile when excited at π/4 angle from the tendon axis. We also measure artifactual decrease of ρ = χxxx /χxyy with depth due to diattenuation of the excitation. We therefore derive a method that proves reliable to determine both ρ and the tendon birefringence and diattenuation.

© 2010 Optical Society of America

1. Introduction

Second Harmonic Generation (SHG) microscopy is an efficient imaging technique to visualize the three-dimensional (3D) distribution of fibrillar collagen in biological tissues [1

1. P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone, and W. Mohler, “Three-Dimensional High-Resolution Second-Harmonic Generation Imaging of Endogenous Structural Proteins in Biological Tissues,” Biophys. J. 82, 493–508 (2002). [CrossRef]

, 2

2. W. R. Zipfel, R. Williams, R. Christie, A. Nikitin, B. Hyman, and W. Webb, “Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation.” Proc. Natl. Acad. Sci. USA 100, 7075–7080 (2003). [CrossRef] [PubMed]

]. Incident circular polarization is usually used since it enables imaging of fibrils independently of their orientation in the focal plane. This approach is particularly relevant for quantitative biomedical studies such as fibrosis scoring [3

3. A.-M. Pena, A. Fabre, D. Débarre, J. Marchal-Somme, B. Crestani, J.-L. Martin, E. Beaurepaire, and M.-C. Schanne-Klein, “Three-dimensional investigation and scoring of extracellular matrix remodeling during lung fibrosis using multiphoton microscopy.” Microsc. Res. Tech. 70(2), 162–170 (2007). [CrossRef]

, 4

4. M. Strupler, M. Hernest, C. Fligny, J.-L. Martin, P.-L. Tharaux, and M.-C. Schanne-Klein, “Second Harmonic Microscopy to Quantify Renal Interstitial Fibrosis and Arterial Remodeling,” J. Biomed. Optics 13, 054041 (2008). [CrossRef]

]. However, fibrillar collagen exhibits a structural anisotropy that may be interesting to characterize for many applications. For that purpose, polarization-resolved SHG provides complementary information about the 3D distribution of nonlinear dipoles within the focal volume [5

5. S. V. Plotnikov, A. Millard, P. Campagnola, and W. Mohler, “Characterization of the myosin-based source for second-harmonic generation from muscle sarcomeres,” Biophys. J. 90, 328–339 (2006). [CrossRef]

, 6

6. F. Tiaho, G. Recher, and D. Rouède, “Estimation of helical angle of myosin and collagen by second harmonic generation imaging microscopy,” Opt. Express 15(19), 12286–12295 (2007). [CrossRef] [PubMed]

, 7

7. A. Deniset-Besseau, J. Duboisset, E. Benichou, F. Hache, P.-F. Brevet, and M.-C. Schanne-Klein, “Measurement of the second order hyperpolarizability of the collagen triple helix and determination of its physical origin.” J. Phys. Chem. B 113(40), 13437–13445 (2009). [CrossRef] [PubMed]

, 8

8. V. Nucciotti, C. Stringari, L. Sacconi, F. Vanzi, L. Fusi, M. Linari, G. Piazzesi, V. Lombardi, and F. S. Pavone, “Probing myosin structural conformation in vivo by second-harmonic generation microscopy,” Proc. Natl. Acad. Sci. USA 107(17), 7763–7768 (2010). [CrossRef] [PubMed]

]. The usual approach is to measure the ratio ρ of the two main tensorial components of the nonlinear response, considering a cylindrical symmetry for fibrillar collagen [9

9. S. Roth and I. Freund, “Second harmonic generation in collagen,” J. Chem. Phys. 70(04), 1637–1643 (1979). [CrossRef]

, 10

10. P. Stoller, K. Reiser, P. Celliers, and A. Rubenchik, “Polarization-modulated second harmonic generation in collagen,” Biophys J. 82(6), 3330–3342 (2002). [CrossRef] [PubMed]

, 11

11. P. Stoller, P. Celliers, K. Reiser, and A. Rubenchik, “Quantitative second-harmonic generation microscopy in collagen,” Appl. Opt. 42(25), 5209–5219 (2003). [CrossRef] [PubMed]

, 12

12. R. Williams, W. R. Zipfel, and W. Webb, “Interpreting second-harmonic generation images of collagen fibrils,” Biophys. J. 88, 1377–1386 (2005). [CrossRef]

, 13

13. A. Erikson, J. Örtegren, T. Hompland, C. de Lange Davies, and M. Lindgren, “Quantification of the second-order nonlinear susceptibility of collagen I using a laser scanning microscope,” J. Biomed. Optics 12(4), 044002 (2007). [CrossRef]

, 14

14. X. Han, R. M. Burke, M. L. Zettel, P. Tang, and E. B. Brown, “Second harmonic properties of tumor collagen: determining the structural relationship between reactive stroma and healthy stroma,” Opt. Express 16(3), 1846–1859 (2008). [CrossRef] [PubMed]

]. This ratio depends on the orientational distribution of the collagen triple helices and on the orientation of the nonlinear dipoles (along the peptidic bonds) within the triple helix. ρ therefore provides information about the ordering of collagen molecules or fibrils within the focal volume. It has been measured in various collagenous tissues and showed a wide dispersion of values (1.2 to 2.6). Comparison of healthy and pathological tissue however requires to characterize the accuracy of ρ measurements and their sensitivity to various artifacts. In particular, the anisotropy of many collagenous tissues may affect polarization-resolved SHG experiments as reported in tendons [10

10. P. Stoller, K. Reiser, P. Celliers, and A. Rubenchik, “Polarization-modulated second harmonic generation in collagen,” Biophys J. 82(6), 3330–3342 (2002). [CrossRef] [PubMed]

, 15

15. J. C. Mansfield, C. P. Winlove, J. Moger, and S. J. Matcher, “Collagen fiber arrangement in normal and diseased cartilage studied by polarization sensitive nonlinear microscopy,” J. Biomed. Optics 13(4), 044020 (2008). [CrossRef]

, 16

16. D. Aït-Belkacem, A. Gasecka, F. Munhoz, S. Brustlein, and S. Brasselet, “Influence of birefringence on polarization resolved nonlinear microscopy and collagen SHG structural imaging,” Opt. Express 18(14), 14859–14870 (2010). [CrossRef] [PubMed]

]. Polarization-resolved image processing improved when taking into account diattenuation [15

15. J. C. Mansfield, C. P. Winlove, J. Moger, and S. J. Matcher, “Collagen fiber arrangement in normal and diseased cartilage studied by polarization sensitive nonlinear microscopy,” J. Biomed. Optics 13(4), 044020 (2008). [CrossRef]

] and birefringence [10

10. P. Stoller, K. Reiser, P. Celliers, and A. Rubenchik, “Polarization-modulated second harmonic generation in collagen,” Biophys J. 82(6), 3330–3342 (2002). [CrossRef] [PubMed]

, 16

16. D. Aït-Belkacem, A. Gasecka, F. Munhoz, S. Brustlein, and S. Brasselet, “Influence of birefringence on polarization resolved nonlinear microscopy and collagen SHG structural imaging,” Opt. Express 18(14), 14859–14870 (2010). [CrossRef] [PubMed]

]. Furthermore, polarization scrambling due to scattering has been shown in tendons and other biological tissues [17

17. O. Nadiarnykh and P. J. Campagnola, “Retention of polarization signatures in SHG microscopy of scattering tissues through optical clearing,” Opt. Express 17, 5794–5806 (2009). [CrossRef] [PubMed]

].

The aim of this paper is therefore to thoroughly characterize the linear propagation effects that affect polarization-resolved SHG experiments in anisotropic tissues and to develop a reliable method to determine ρ in collagenous tissues. For this purpose, we first develop a theoretical model that fully accounts for birefringence, diattenuation and polarization scrambling upon scattering. We then record polarization-resolved SHG images in rat-tail tendons that is a model tissue composed of aligned collagen fibrils. We finally compare simulated and experimental data that show an excellent agreement and give insight into the linear and nonlinear optical properties of the tendon. Most notably, we observe interference fringes in the SHG depth profiles when excited at π/4 angle from the tendon axis, and artifactual decrease of ρ with depth due to diattenuation of the excitation. We conclude that the correction for these effects enables a reliable determination of ρ.

2. Experimental setup

2.1. Tendon preparation

Tendons were extracted from Sprague-Dawley rat-tails (female, ≈ 300g), centrifugated at 4700 rpm and stored at 4° in phosphate buffer saline (PBS). Imaging was performed within a few days using a water-immersion objective. Tendons were first labelled with fluorescent latex beads to enable precise location of the tissue surface (1µm diameter, L1030, Sigma-Aldrich). After rinsing, they were fixed at both extremities and streched to get rid of the crimps and facilitate alignment of the fibrillar pattern along the x direction of the microscope stage. They were kept in PBS on a glass coverslip that maintained them in the focal plane of the microscope.

2.2. Imaging setup

2.3. Polarization-resolved measurements

The laser polarization at the back pupil of the objective was approximately along the x direction but exhibited a 14% ellipticity due to the optical components within the microscope (9% ellipticity without the dichroic mirror for epi-detection). We therefore inserted an infrared polarizer and achieved an ellipcity less than 1% with small scanning angles. This linear polarization was tuned from −2π/3 to 2π/3 (usually with π/12 steps) by rotating an achromatic half waveplate (MWPAA2-22-700-1000, CVI-Melles Griot) placed just before the objective (see fig. 1.a). Forward SHG signals were analyzed using a polarizing beamsplitter cube (BBPC-550, CVI- Melles Griot). To improve the extinction ratio of the x- and y-polarized detection channels, linear polarizers (03FPG021, CVI- Melles Griot) were set in front of the detectors. The relative transmission of these two channels was calibrated using a fluorescent slide (Chroma): we took advantage of the isotropy of the setup within the xy plane and compared the x-polarized signal to the y-polarized one excited with polarizations shifted by π/2 angle (see fig.1.b). The ratio of both channels was typically 1.1. Calibration was performed before every experiment and enabled quantitative comparison between x- and y-polarized signals.

Fig. 1. Experimental setup. (a) Laser scanning multiphoton microscope showing polarization-resolved detection of forward SHG signal and epi-detection of 2PEF signal and possibly of SHG signal. The insert displays the incident electric field relative to the tendon geometry in the focal plane. (b) x- and y-polarized forward 2PEF signal from a fluorescent slide for variable incident polarization angles. The ratio of the 2 maxima is used for calibration of polarization-resolved SHG signals. (c) Combined 2PEF (red) and SHG (green) image of a tendon labeled with fluorescent latex beads. The image is the summation of 15 images acquired 2µm apart from the tendon upper surface, with enhanced contrast. The yellow box shows a typical Region of Interest used for plotting depth-polar diagrams as in fig. 5. Scale bar: 50µm.

3. Theoretical background

3.1. Polarization-resolved SHG

Let’s consider the nonlinear optical interaction of the incident laser beam with a rat-tail tendon. The polarization induced in the medium by the elecric field E is given by:

Pi=χij(1)Ej+χijk(2)EjEk
(1)

where we considered only the first- and second-order electric susceptibility tensors χ (1),(2). Rattail tendon is commonly assumed to have a cylindrical symmetry (C 6v symmetry) [9

9. S. Roth and I. Freund, “Second harmonic generation in collagen,” J. Chem. Phys. 70(04), 1637–1643 (1979). [CrossRef]

, 10

10. P. Stoller, K. Reiser, P. Celliers, and A. Rubenchik, “Polarization-modulated second harmonic generation in collagen,” Biophys J. 82(6), 3330–3342 (2002). [CrossRef] [PubMed]

, 7

7. A. Deniset-Besseau, J. Duboisset, E. Benichou, F. Hache, P.-F. Brevet, and M.-C. Schanne-Klein, “Measurement of the second order hyperpolarizability of the collagen triple helix and determination of its physical origin.” J. Phys. Chem. B 113(40), 13437–13445 (2009). [CrossRef] [PubMed]

], which reduces the number of independent nonvanishing χ (2) components. Moreover, we assume that the Kleinman symmetry is valid as usually considered because of the nonresonant character of the interaction. Within these approximations, there are only 2 independent nonvanishing χ (2) tensorial components: χxxx and χxyy = χxzz = χyxy = χzxz = χyyx = χzzx, where x represents the main axis of the tendon [19

19. R. Boyd, Nonlinear optics (Academic press, London, 2003).

]. Considering a laser beam propagating in the z direction with a linear polarization at angle α to the tendon lying in the xy plane (see fig. 1.a), the electric fields reads: Eωx = E 0 cos α and Eωy = E 0 sin α near the focus and induces a SH polarization:

Px2ω(χxxxcos2α+χxyysin2α)E02
Py2ω(χxyysin2α)E02
(2)

which radiates at frequency 2ω. In this paper, we are interested in ratiometric measurement of the second-order response and we consider the ratio of the two independent tensorial components of the second-order susceptibility: ρ = χxxx/χxyy. This ratio provides insight into the orientational distribution of the collagen molecules within the focal volume. It is taken to be real in the Kleiman approximation. The SH intensity detected for each polarisation then reads:

Ix2ω=Kρcos2α+sin2α2
(3a)
Iy2ω=K2sinαcosα2
(3b)

where K is a constant merging various parameters such as setup geometry and squared incident beam intensity I 2 0. Polar diagrams of eq. (3) are displayed in fig. 2.a and b using ρ = 1.4. A common method to determine ρ from polarization-resolved SH experiments is to fit Ix 2ω using eq. (3a).

In the following, we propose a more general method. Since Ix 2ω and Iy 2ω are even functions of α and contain only even powers of trigonometric functions, they can be represented as a sum of cos2 functions:

Ix2ω=Acos4α+Bcos2α+C
(4a)
Iy2ω=K2(cos4α+1)
(4b)

where

A=K2(ρ12)2
(5a)
B=2K(ρ12)(ρ+12)
(5b)
C=K2(ρ12)2+K(ρ+12)2
(5c)

In that framework, one can notice that:

ρ2=A+B+CAB+C
(6)

This expression enables the determination of ρ from polarization-resolved SH data by fitting Ix 2ω using eq. (4a). The advantage of this method is that it can take into account various physical effects that appear to modify the expression of Ix 2ω but not its representation as a sum of cos2 functions. These physical effects will be presented in the following sections and the new expressions of the A,B and C parameters will be derived.

Fig. 2. Simulated polar diagrams of polarization-resolved SH intensity generated by a tendon aligned along x axis. The angle represents the direction of the excitation polarization to the tendon direction (see fig. 1.a). (a) Ix 2ω and (b) Iy 2ω in a non-birefringent, non-scattering medium without diattenuation (see eq. (2)). (c) Ix 2ω and (d) Iy 2ω at 24µm depth considering birefringence (Δn = 0.0066), diattenuation (Δla = 175µm) and polarisation cross-talk due to scattering (ηxy = 0.13) (see Eq. (11)). ρ = 1.40 in all simulations.

3.2. Tendon birefringence

In the former derivation of I 2ω, we have assumed that the electric field propagation takes place in an isotropic medium. Nevertheless, the tendon is considered to exhibit a C 6v symmetry, so that the permittivity tensor ε 0 (1+χ (1) ij) has two different components and the tendon is analogous to a uniaxial birefringent crystal. Indeed, it has been reported that birefringence Δn = neno attains 5 · 10−3 [20

20. N. J. Kemp, H. N. Zaatari, J. Park, H. G. Rylander, and T. E. Milner, “Form-biattenuance in fibrous tissues measured with polarization-sensitive optical coherence tomography (PS-OCT),” Opt. Express 13(12), 4611–4628 (2005). [CrossRef] [PubMed]

, 21

21. J. Park, N. J. Kemp, H. G. Rylander, and T. E. Milner, “Complex polarization ratio to determine polarization properties of anisotropic tissue using polarization-sensitive optical coherence tomography,” Opt. Express 17(16), 13402–13417 (2009). [CrossRef] [PubMed]

] in tendon. As a consequence, the x (extraordinary wave) and y (ordinary wave) excitation field components undergoes a relative phase retardation when propagating within the tendon. SH intensity then reads:

Ix2ω(z)=Kρcos2αeiϕ+sin2α2=K(ρcos2α+sin2α2+ρ2sin22α(cosϕ1))
(7a)
Iy2ω(z)=Ksin2αei2π(ne+no)λz2=Ksin2α2
(7b)

where ϕ=4π(neno)zλ accounts for the birefringence in the excitation propagation (SHG intensity is unaffected by birefringence in the harmonic propagation). Note that z represents the depth in tendon at which SH takes place: due to index mismatch, z = dzlens ntendon/nwater, where dzlens is the microscope lens displacement from the tendon upper surface.

These expressions show that Iy 2ω is unaffected by birefringence, while Ix 2ω has a supplementary term compared to eq. (4). Decomposing Ix 2ω in the cos2 basis, we get:

Abiref=K[12(ρ12)2+ρ4(1cosϕ)]
(8a)
Bbiref=2K(ρ12)(ρ+12)
(8b)
Cbiref=K[12(ρ12)2+(ρ+12)2ρ4(1cosϕ)]
(8c)

One observes that Bbiref = B and Abiref+Cbiref = A+C, so that ρ can be determined using eq. 6 as in section 3.1. To get better insight into the effect of birefringence, we have plotted in fig. 3 the variation of Ix 2ω and Ix 2ω as a function of the incident polarization angle α for increasing depth within the tendon. Comparison of model calculations with and without birefringence shows that birefringence results in interference fringes in the x-polarized SH intensity Ix 2ω when excited with a linear polarization at π/4 from the tendon axis, as shown by the cosΔϕ term in eq. 7a (see z-profiles in 3.k and 3.n).

3.3. Polarization cross-talk

Ix2ω(z)=Kρcos2α+sin2α2+ηXYKsin2α2
(9a)
Iy2ω(z)=ηYXKρcos2α+sin2α2+Ksin2α2
(9b)

Decomposing Ix 2ω in the cos2 basis, we obtain:

Apol=K[12(ρ12)2ηXY2]
(10a)
Bpol=2K(ρ12)(ρ+12)
(10b)
Cpol=K[12(ρ12)2+(ρ+12)2+ηXY2]
(10c)

Once again, Bpol = B and Apol+Cpol = A+C, and ρ can be determined as before. Fig. 3.b and g show that the angular profiles of Ix 2ω and Iy 2ω are slightly modified by polarization cross-talk.

3.4. Diattenuation in tendon

Multiphoton microscopy uses near-infrared excitation which minimizes absorbance and scattering in biological tissues. Nevertheless, light scattering and spherical aberrations cause focal volume deterioration upon propagation within the tendon, which results in smaller excitation intensity and weaker SH signal. For simplicity, we assume that the excitation intensity undergoes exponential attenuation with depth. Due to the tendon anisotropy, the effective attenuation lengths for Iωx and Iωy are different and the excitation light experiences diattenuation. These attenuation lengths will be noted as lea and loa to account for the uniaxial symmetry of the tendon. We assume that diattenuation of the SH signal is negligible because signal forward-detection in multiphoton setups is not much sensitive to light scattering and aberrations. I 2ω x,y then reads:

Ix2ω(z)=Kρcos2αezlae+sin2αezlao2=Ke2zlaoρezlacos2α+sin2α2
(11a)
Iy2ω(z)=Ksin2αez2laoez2lae2=Ke2zlaoezlasin2α2
(11b)

where 1la=1lae1lao. . The expression of the A,B and C parameters are the same as in eq. 5 with the modified parameters: KKe2zlao and ρρezla . Consequently, once Δla is known, ρ can be determined in a similar way as in section 3.1. Note that this approach can be generalized to an arbitrary diattenuation profile fa(z) = fxa (z)/fya (z) by using the transformation ρρ fa(z) in eq. 6. Fig. 3.c, h and m show the modifications of Ix 2ω and Iy 2ω induced by diattenuation. In particular, z-profiles for an incident polarization parallel (resp. perpendicular) to the tendon exhibit a lea (resp. loa) exponential decay.

Fig. 3. Numerical calculation of polarization-resolved SH intensity as a function of incident polarisation angle α (see fig. 1) and depth z within tendon for different parameters. (a)–(e) Ix 2ω, (f)–(j) Iy 2ω and (k)–(o) z-profiles of Ix 2ω for α = 0 (green dotted line), α = π/4 (blue dashed line) and α = π/2 (red dash-dot line). (a), (f), (k) tendon with uniform depthattenuation: lax = lay = 190µm. (b), (g), (l) tendon with polarization cross-talk: ηxy = 0.13, ηyx = 0.2 (constant with depth). (c), (h), (m) tendon with diattenuation: lea = 91µm and loa = 190µm. (d), (i), (n) tendon with birefringence Δn = 0.0066. (e), (j), (o) tendon with diattenuation, birefringence and polarisation cross-talk (same parameters). ρ is equal to 1.40 for all calculations.

3.5. Combined effects of birefringence, polarization cross-talk and diattenuation

When taking into account all the effects introduced above, we obtain the following expression:

Ix2ω(z)=Ke2zlao(ρezlacos2αeiϕ+sin2α2+ηXYezlasin2α2)
(12)

Fig. 2.c and d display the polar diagrams of this expression along with the similar expression for Iy 2ω. They clearly look very different from the polar diagrams a and b plotted from the simplified model (eq. 3). It shows that determination of ρ using eq. 3a is hazardous. Conversely, Ix 2ω can still be decomposed as a sum of cos2 functions as in eq. 4a: the parameters Aeff,Beff and Ceff are obtained by combining the effects of birefringence (eq. 8) and polarization crosstalk (eq. 10) only, and considering the modified parameters: KKe2zlao , ρρezla and ηxyηxyezla. . In that framework, ρ can be determined as follows:

ρ2e2zla=Aeff+Beff+CeffAeffBeff+Ceff
(13)

given that z-profiles of Ix 2ω for α = 0 and π2 can be used to determine lea and loa (or fa(z) in a more general case).

The right hand side of fig. 3 displays the x- and y-polarized SH signal given by eq. 12: diattenuation is revealed by differences in z attenuation for incident polarization parallel and perpendicular to the tendon axis, birefringence by oscillations in the z-profile at π/4 polarization angle from the tendon axis and polarization cross-talk by deformation of the angular profiles. In order to better evidence the latter two effects, we introduce the parameter Δ that sorts out the contributions of Δϕ and ηXY to Aeff and Ceff:

(z)=C3A(A+C)2B22(AB+C)
(14a)
(z)=fa[ηXYρ2(1cosϕ)]
(14b)

At a given depth, contributions of birefringence and polarization cross-talk are intrinsically mixed, but information on these effects can be obtained by analysis of Δ depth variation.

4. Results

Fig. 4 displays typical x- and y-polarized SHG images obtained at various depths within a tendon for an incident beam polarized at π/4 from the tendon axis. Transverse profiles show that the SHG signal is higher at the tendon edges as expected because of the cylindrical shape of the tendon: attenuation of the excitation beam is more effective in the center of the section when the incident light propagates along a larger distance within the tendon. However, the x- and y-polarized SHG transverse profiles exhibit different behaviour as a function of the depth from the tendon upper surface. In fig. 4.a and b, the x-polarized SHG image is more attenuated than the y-polarized SHG image at the tendon center, whereas it is not the case in fig. 4.c and d. Moreover, the x-polarized SHG image at 57µm (fig. 4.c) displays more signal at the center than at intermediate positions along the transverse profile. This complex behaviour is characteristic for birefringence effects. The x and y components of the π/4-polarized incident beam experience different optical indices when propagating within the tendon and accumulate a relative phase shift. The tensorial components of the nonlinear response excited by the x and y components of the π/4-polarized incident beam then interfere in a constructive or destructive way, depending on the propagation distance within the tendon. It results in interference fringes in the depth profile of the SHG signal for incident excitation mixing up x and y-polarization components. These fringes appear only in x-polarized SHG images because they result from the coherent summation of two tensorial components excited along x and y polarizations respectively (see eq. 2). Conversely, y-polarized SHG images are not sensitive to birefringence because they probe only one tensorial component.

Fig. 4. Polarization-resolved SH images of a tendon upon excitation polarized at π/4 from the tendon axis. (a)–(c) x- and (b)–(d) y-polarized SH images and transverse profiles of a tendon aligned along x axis at (a)–(b) 39 µm depth and (c)–(d) at 57 µm depth from the tendon upper surface. x-polarisation images shows dark fringes (red arrows), whereas y-polarisation has almost uniform intensity profile in the tendon center. Scale bar: 50 µm.

To get a better insight into the physics of polarization-resolved SHG images, we carried out SHG experiments at increasing depth within the tendon. Fig. 5.a and b display typical x- and y-polarized SHG signals in 28 × 20µm regions of interest such as the one depicted in fig. 1.a. The depth profile of the 2PEF signal from the latex beads is also displayed in fig. 5.c. It enables the location of the tendon surface z 0 that corresponds to the maximum of the 2PEF peak. The specific patterns observed in the SHG images were consistently observed in all our samples provided that the ellipticity of the incident polarization was negligible. Practically, experiments performed without a linear polarizer at the back pupil of the objective lens exhibited a non symmetrical pattern relative to the tendon axis (α = 0).

Finally, fig. 5.d and e display Ix 2ω and Iy 2ω at the surface of the tendon (z = z 0) where birefringence and diattenuation effects do not apply. We therefore fit our data using eq. 9 that accounts only for polarization cross-talk due to light scattering (or equivalently, using eq. 12 with z = 0 and Δϕ = 0). We observe that the experimental data are better fitted using eq. 9 than in the simplified approach (eq. 3). It shows that polarization cross-talk due to light scattering significantly distorts the polarization pattern at the tendon surface.

Fig. 5. Experimental polarization-resolved SH intensity from a tendon. (a) Ix 2ω and (b) Iy 2ω as a function of incident polarisation angle α (see fig. 1) and lens displacement. (c) z-profile of fluorescence signal from latex beads, peaking at the tendon surface z 0. (d) Ix 2ω (α) and (e) Iy 2ω (α) at the tendon surface (black dots), along with fits using the simplified approach (eq. 3, red line) or accounting for polarization cross-talk (eq. 9, blue line). (f) experimental z-profiles of Ix 2ω for α = 0 (green dotted line), α = π/4 (blue dashed line) and α = π/2 (red dash-dot line).

Altogether, these experimental observations show that the usual approach with eq. 3 does not satisfactorily account for polarization-resolved SHG imaging in thick tendons. Birefringence, diattenuation and polarization cross-talk due to scattering must all be taken into account to explain experimental data. Accordingly, we used eq. 4 with parameters Aeff,Beff and Ceff to fit our data. Note that we introduced an angular shift α 0 to account for possible slight misalignment of the tendon axis from x direction (−2° <α 0 <2° for all our data). We then calculated ρezla by use of eq. 13. This value was subsequently corrected for diattenuation using lea = 91µm and loa = 190µm obtained from exponential fitting of Ix 2ω (α = 0) and Ix 2ω (α = π/2). Both the raw and corrected values of ρ are depicted in fig. 6.b. Diattenuation correction successfully removes the artifactual variation of ρ with depth and enables the reliable determination of this parameter: ρ = 1.40±0.03. Moreover, as already stated, this approach is applicable to any attenuation profile fa(z). To fully characterize the optical response of our sample, we also calculated the parameter Δ(z) from eq. 14a and plotted its depth profile in fig. 6.c. Eq. 14b shows that the values at the maxima (Δϕ = 2πk with k integer) reduce to ηxy. The first maximum is obtained at the tendon surface: ηxy = 0.13. The second maximum is zero which shows that ezlaηxy is negligible ≈ 60µm deep within the tendon. We then consider that ηxy diminishes exponentionally from 0.13 to 0 within the first 40µm from the surface and we get Δn = 0.0066 by fitting our data using eq. 14bn = 0.0074 without any index mismatch correction).

Finally, to verify the consistency of our data processing, let’s compare our experimental data (fig. 5.a and b) to the simulations using our experimentally determined parameters for birefringence, diattenuation and polarization cross-talk (fig. 3.e and j). The theoretical and experimental intensity maps are in excellent agreement which proves that our theoretical approach satisfactorily reproduces polarization-resolved SHG experiments in tendons.

Fig. 6. Determination of tendon characteristic parameters from experimental SH depthprofiles. (a) Ix 2ω (α = 0) (blue dots) and Ix 2ω (α = π/2) (red squares) showing diattenuation: the solid lines correspond to exponential fitting with lea = 91µm and loa = 190µm. (b) ρ determined from polarization-resolved SHG measurements with (black) and without (green) correction for diattenuation. (c) Δ parameter evidencing birefringence (oscillations), polarization cross-talk due to scattering (non-vanishing value at the tendon surface) and diattenuation (exponential attenuation with depth). The solid line represents fitting with the following parameters: Δn = 1.40, ηxy = 0.13 near the surface and Δla = 134µm.

5. Discussion

Most importantly, our measurements show that the raw value of ρ varies a lot with depth as depicted in fig. 6.b. It decreases from 1.40 at the surface of the tendon to 0.8 at ≈ 90µm depth within the tendon. These data proves that correction for diattenuation is essential for reliable measurements of ρ in thick anisotropic tissues and that our model provides an efficient correction along the full stack of data. We expect that the determination of ρ deeper in the tissue would be hampered because of the low signal to noise ratio. When possible, the most reliable method is to perform polarization-resolved measurements at the sample surface to get rid of diattenuation and birefringence effects.

6. Conclusion

In this paper, we combined model calculation and experiments in rat-tail tendon to characterize linear optical effects that affect the polarization in polarization-resolved SHG experiments. We evidenced that birefringence, diattenuation and polarization scrambling upon scattering significantly distort the SHG response for tunable incident linear polarizations. In particular, birefringence results in interference fringes in the depth profile of the SHG signal excited with polarization at π/4 angle from the tendon axis. Most importantly, diattenuation results in an artifactual decrease of ρ with the depth within the tendon. To address these problems, we derived a method to process polarization-resolved SHG data and we successfully retrieved relevant optical parameters in rat-tail tendon. This method is applicable to any anisotropic sample that exhibits SHG signals, including other collagenous tissues and presumably skeletal muscles. It may also be generalized to other nonlinear optical processes, that is 2PEF, THG, CARS or SRS polarization-resolved microscopies. Altogether, our work proves unambiguously that uncorrecting for polarization distortion results in misleading determination of the tensorial nonlinear response in anisotropic thick tissues.

Acknowledgements

We gratefully acknowledge G. Liot from Institut Curie, Université Paris XI, for providing us with the rat-tails, X. Solinas and J.-M. Sintès for technical implementation of the setup, A. de Martino, E. Beaurepaire and D. Débarre for fruitful discussions, and F. Hache for critical reading of this manuscript. G. Latour was supported by RTRA-Triangle de la Physique.

References and links

1.

P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone, and W. Mohler, “Three-Dimensional High-Resolution Second-Harmonic Generation Imaging of Endogenous Structural Proteins in Biological Tissues,” Biophys. J. 82, 493–508 (2002). [CrossRef]

2.

W. R. Zipfel, R. Williams, R. Christie, A. Nikitin, B. Hyman, and W. Webb, “Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation.” Proc. Natl. Acad. Sci. USA 100, 7075–7080 (2003). [CrossRef] [PubMed]

3.

A.-M. Pena, A. Fabre, D. Débarre, J. Marchal-Somme, B. Crestani, J.-L. Martin, E. Beaurepaire, and M.-C. Schanne-Klein, “Three-dimensional investigation and scoring of extracellular matrix remodeling during lung fibrosis using multiphoton microscopy.” Microsc. Res. Tech. 70(2), 162–170 (2007). [CrossRef]

4.

M. Strupler, M. Hernest, C. Fligny, J.-L. Martin, P.-L. Tharaux, and M.-C. Schanne-Klein, “Second Harmonic Microscopy to Quantify Renal Interstitial Fibrosis and Arterial Remodeling,” J. Biomed. Optics 13, 054041 (2008). [CrossRef]

5.

S. V. Plotnikov, A. Millard, P. Campagnola, and W. Mohler, “Characterization of the myosin-based source for second-harmonic generation from muscle sarcomeres,” Biophys. J. 90, 328–339 (2006). [CrossRef]

6.

F. Tiaho, G. Recher, and D. Rouède, “Estimation of helical angle of myosin and collagen by second harmonic generation imaging microscopy,” Opt. Express 15(19), 12286–12295 (2007). [CrossRef] [PubMed]

7.

A. Deniset-Besseau, J. Duboisset, E. Benichou, F. Hache, P.-F. Brevet, and M.-C. Schanne-Klein, “Measurement of the second order hyperpolarizability of the collagen triple helix and determination of its physical origin.” J. Phys. Chem. B 113(40), 13437–13445 (2009). [CrossRef] [PubMed]

8.

V. Nucciotti, C. Stringari, L. Sacconi, F. Vanzi, L. Fusi, M. Linari, G. Piazzesi, V. Lombardi, and F. S. Pavone, “Probing myosin structural conformation in vivo by second-harmonic generation microscopy,” Proc. Natl. Acad. Sci. USA 107(17), 7763–7768 (2010). [CrossRef] [PubMed]

9.

S. Roth and I. Freund, “Second harmonic generation in collagen,” J. Chem. Phys. 70(04), 1637–1643 (1979). [CrossRef]

10.

P. Stoller, K. Reiser, P. Celliers, and A. Rubenchik, “Polarization-modulated second harmonic generation in collagen,” Biophys J. 82(6), 3330–3342 (2002). [CrossRef] [PubMed]

11.

P. Stoller, P. Celliers, K. Reiser, and A. Rubenchik, “Quantitative second-harmonic generation microscopy in collagen,” Appl. Opt. 42(25), 5209–5219 (2003). [CrossRef] [PubMed]

12.

R. Williams, W. R. Zipfel, and W. Webb, “Interpreting second-harmonic generation images of collagen fibrils,” Biophys. J. 88, 1377–1386 (2005). [CrossRef]

13.

A. Erikson, J. Örtegren, T. Hompland, C. de Lange Davies, and M. Lindgren, “Quantification of the second-order nonlinear susceptibility of collagen I using a laser scanning microscope,” J. Biomed. Optics 12(4), 044002 (2007). [CrossRef]

14.

X. Han, R. M. Burke, M. L. Zettel, P. Tang, and E. B. Brown, “Second harmonic properties of tumor collagen: determining the structural relationship between reactive stroma and healthy stroma,” Opt. Express 16(3), 1846–1859 (2008). [CrossRef] [PubMed]

15.

J. C. Mansfield, C. P. Winlove, J. Moger, and S. J. Matcher, “Collagen fiber arrangement in normal and diseased cartilage studied by polarization sensitive nonlinear microscopy,” J. Biomed. Optics 13(4), 044020 (2008). [CrossRef]

16.

D. Aït-Belkacem, A. Gasecka, F. Munhoz, S. Brustlein, and S. Brasselet, “Influence of birefringence on polarization resolved nonlinear microscopy and collagen SHG structural imaging,” Opt. Express 18(14), 14859–14870 (2010). [CrossRef] [PubMed]

17.

O. Nadiarnykh and P. J. Campagnola, “Retention of polarization signatures in SHG microscopy of scattering tissues through optical clearing,” Opt. Express 17, 5794–5806 (2009). [CrossRef] [PubMed]

18.

M. Strupler, A.-M. Pena, M. Hernest, P.-L. Tharaux, J.-L. Martin, E. Beaurepaire, and M.-C. Schanne-Klein, “Second harmonic imaging and scoring of collagen in fibrotic tissues,” Opt. Express 15(7), 4054–4065 (2007). [CrossRef] [PubMed]

19.

R. Boyd, Nonlinear optics (Academic press, London, 2003).

20.

N. J. Kemp, H. N. Zaatari, J. Park, H. G. Rylander, and T. E. Milner, “Form-biattenuance in fibrous tissues measured with polarization-sensitive optical coherence tomography (PS-OCT),” Opt. Express 13(12), 4611–4628 (2005). [CrossRef] [PubMed]

21.

J. Park, N. J. Kemp, H. G. Rylander, and T. E. Milner, “Complex polarization ratio to determine polarization properties of anisotropic tissue using polarization-sensitive optical coherence tomography,” Opt. Express 17(16), 13402–13417 (2009). [CrossRef] [PubMed]

22.

N. Olivier and E. Beaurepaire, “Third-harmonic generation microscopy with focus-engineered beams: a numerical study,” Opt. Express 16(19), 14703–14715 (2008). [CrossRef] [PubMed]

23.

P. Schön, M. Behrndt, D. Aït-Belkacem, H. Rigneault, and S. Brasselet, “Polarization and phase pulse shaping applied to structural contrast in nonlinear microscopy imaging,” Phys. Rev. A 81(1), 013809 (2010). [CrossRef]

24.

X. D. Wang and L. H. V. Wang, “Propagation of polarized light in birefringent turbid media: A Monte Carlo study,” J. Biomed. Optics 7, 279–290 (2002). [CrossRef]

25.

R. LaComb, O. Nadiarnykh, S. Carey, S. Campagnola, and P. J. Campagnola, “Quantitative second harmonic generation imaging and modeling of the optical clearing mechanism in striated muscle and tendon,” J. Biomed. Optics 13, 021109 (2008). [CrossRef]

26.

T. Boulesteix, A. Pena, N. Pagès, G. Godeau, M.-P. Sauviat, E. Beaurepaire, and M. Schanne-Klein, “Micrometer scale ex vivo multiphoton imaging of unstained arterial wall structure,” Cytometry 69A(1), 20–26 (2006). [CrossRef]

OCIS Codes
(120.5410) Instrumentation, measurement, and metrology : Polarimetry
(170.3660) Medical optics and biotechnology : Light propagation in tissues
(190.2620) Nonlinear optics : Harmonic generation and mixing
(180.4315) Microscopy : Nonlinear microscopy
(170.6935) Medical optics and biotechnology : Tissue characterization

ToC Category:
Microscopy

History
Original Manuscript: July 13, 2010
Revised Manuscript: August 20, 2010
Manuscript Accepted: August 22, 2010
Published: August 26, 2010

Virtual Issues
Vol. 5, Iss. 13 Virtual Journal for Biomedical Optics

Citation
Ivan Gusachenko, Gaël Latour, and Marie-Claire Schanne-Klein, "Polarization-resolved Second Harmonic microscopy in anisotropic thick tissues," Opt. Express 18, 19339-19352 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-18-19339


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References

  1. P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone, and W. Mohler, “Three-dimensional high-resolution second-harmonic generation imaging of endogenous structural proteins in biological tissues,” Biophys. J. 82, 493–508 (2002). [CrossRef]
  2. W. R. Zipfel, R. Williams, R. Christie, A. Nikitin, B. Hyman, and W. Webb, “Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation,” Proc. Natl. Acad. Sci. U.S.A. 100, 7075–7080 (2003). [CrossRef] [PubMed]
  3. A.-M. Pena, A. Fabre, D. Débarre, J. Marchal-Somme, B. Crestani, J.-L. Martin, E. Beaurepaire, and M.-C. Schanne-Klein, “Three-dimensional investigation and scoring of extracellular matrix remodeling during lung fibrosis using multiphoton microscopy,” Microsc. Res. Tech. 70(2), 162–170 (2007). [CrossRef]
  4. M. Strupler, M. Hernest, C. Fligny, J.-L. Martin, P.-L. Tharaux, and M.-C. Schanne-Klein, “Second harmonic microscopy to quantify renal interstitial fibrosis and arterial remodeling,” J. Biomed. Opt. 13, 054041 (2008). [CrossRef]
  5. S. V. Plotnikov, A. Millard, P. Campagnola, and W. Mohler, “Characterization of the myosin-based source for second-harmonic generation from muscle sarcomeres,” Biophys. J. 90, 328–339 (2006). [CrossRef]
  6. F. Tiaho, G. Recher, and D. Rouède, “Estimation of helical angle of myosin and collagen by second harmonic generation imaging microscopy,” Opt. Express 15(19), 12286–12295 (2007). [CrossRef] [PubMed]
  7. A. Deniset-Besseau, J. Duboisset, E. Benichou, F. Hache, P.-F. Brevet, and M.-C. Schanne-Klein, “Measurement of the second order hyperpolarizability of the collagen triple helix and determination of its physical origin,” J. Phys. Chem. B 113(40), 13437–13445 (2009). [CrossRef] [PubMed]
  8. V. Nucciotti, C. Stringari, L. Sacconi, F. Vanzi, L. Fusi, M. Linari, G. Piazzesi, V. Lombardi, and F. S. Pavone, “Probing myosin structural conformation in vivo by second-harmonic generation microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107(17), 7763–7768 (2010). [CrossRef] [PubMed]
  9. S. Roth and I. Freund, “Second harmonic generation in collagen,” J. Chem. Phys. 70(04), 1637–1643 (1979). [CrossRef]
  10. P. Stoller, K. Reiser, P. Celliers, and A. Rubenchik, “Polarization-modulated second harmonic generation in collagen,” Biophys. J. 82(6), 3330–3342 (2002). [CrossRef] [PubMed]
  11. P. Stoller, P. Celliers, K. Reiser, and A. Rubenchik, “Quantitative second-harmonic generation microscopy in collagen,” Appl. Opt. 42(25), 5209–5219 (2003). [CrossRef] [PubMed]
  12. R. Williams, W. R. Zipfel, and W. Webb, “Interpreting second-harmonic generation images of collagen fibrils,” Biophys. J. 88, 1377–1386 (2005). [CrossRef]
  13. A. Erikson, J. Örtegren, T. Hompland, C. de Lange Davies, and M. Lindgren, “Quantification of the second-order nonlinear susceptibility of collagen I using a laser scanning microscope,” J. Biomed. Opt. 12(4), 044002 (2007). [CrossRef]
  14. X. Han, R. M. Burke, M. L. Zettel, P. Tang, and E. B. Brown, “Second harmonic properties of tumor collagen: determining the structural relationship between reactive stroma and healthy stroma,” Opt. Express 16(3), 1846–1859 (2008). [CrossRef] [PubMed]
  15. J. C. Mansfield, C. P. Winlove, J. Moger, and S. J. Matcher, “Collagen fiber arrangement in normal and diseased cartilage studied by polarization sensitive nonlinear microscopy,” J. Biomed. Opt. 13(4), 044020 (2008). [CrossRef]
  16. D. Aït-Belkacem, A. Gasecka, F. Munhoz, S. Brustlein, and S. Brasselet, “Influence of birefringence on polarization resolved nonlinear microscopy and collagen SHG structural imaging,” Opt. Express 18(14), 14859–14870 (2010). [CrossRef] [PubMed]
  17. O. Nadiarnykh, and P. J. Campagnola, “Retention of polarization signatures in SHG microscopy of scattering tissues through optical clearing,” Opt. Express 17, 5794–5806 (2009). [CrossRef] [PubMed]
  18. M. Strupler, A.-M. Pena, M. Hernest, P.-L. Tharaux, J.-L. Martin, E. Beaurepaire, and M.-C. Schanne-Klein, “Second harmonic imaging and scoring of collagen in fibrotic tissues,” Opt. Express 15(7), 4054–4065 (2007). [CrossRef] [PubMed]
  19. R. Boyd, Nonlinear optics (Academic Press, 2003).
  20. N. J. Kemp, H. N. Zaatari, J. Park, H. G. Rylander, and T. E. Milner, “Form-biattenuance in fibrous tissues measured with polarization-sensitive optical coherence tomography (PS-OCT),” Opt. Express 13(12), 4611–4628 (2005). [CrossRef] [PubMed]
  21. J. Park, N. J. Kemp, H. G. Rylander, and T. E. Milner, “Complex polarization ratio to determine polarization properties of anisotropic tissue using polarization-sensitive optical coherence tomography,” Opt. Express 17(16), 13402–13417 (2009). [CrossRef] [PubMed]
  22. N. Olivier and E. Beaurepaire, “Third-harmonic generation microscopy with focus-engineered beams: a numerical study,” Opt. Express 16(19), 14703–14715 (2008). [CrossRef] [PubMed]
  23. P. Schön, M. Behrndt, D. Aït-Belkacem, H. Rigneault, and S. Brasselet, “Polarization and phase pulse shaping applied to structural contrast in nonlinear microscopy imaging,” Phys. Rev. A 81(1), 013809 (2010). [CrossRef]
  24. X. D. Wang and L. H. V. Wang, “Propagation of polarized light in birefringent turbid media: a Monte Carlo study,” J. Biomed. Opt. 7, 279–290 (2002). [CrossRef]
  25. R. LaComb, O. Nadiarnykh, and S. Carey, S. and P. J. Campagnola, “Quantitative second harmonic generation imaging and modeling of the optical clearing mechanism in striated muscle and tendon,” J. Biomed. Opt. 13, 021109 (2008). [CrossRef]
  26. T. Boulesteix, A. Pena, N. Pagès, G. Godeau, M.-P. Sauviat, E. Beaurepaire, and M. Schanne-Klein, “Micrometer scale ex vivo multiphoton imaging of unstained arterial wall structure,” Cytometry 69A(1), 20–26 (2006). [CrossRef]

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