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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 5, Iss. 12 — Sep. 30, 2010
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Fast image analysis in polarization SHG microscopy.

Ivan Amat-Roldan, Sotiris Psilodimitrakopoulos, Pablo Loza-Alvarez, and David Artigas  »View Author Affiliations


Optics Express, Vol. 18, Issue 16, pp. 17209-17219 (2010)
http://dx.doi.org/10.1364/OE.18.017209


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Abstract

Pixel resolution polarization-sensitive second harmonic generation (PSHG) imaging has been recently shown as a promising imaging modality, by largely enhancing the capabilities of conventional intensity-based SHG microscopy. PSHG is able to obtain structural information from the elementary SHG active structures, which play an important role in many biological processes. Although the technique is of major interest, acquiring such information requires long offline processing, even with current computers. In this paper, we present an approach based on Fourier analysis of the anisotropy signature that allows processing the PSHG images in less than a second in standard single core computers. This represents a temporal improvement of several orders of magnitude compared to conventional fitting algorithms. This opens up the possibility for fast PSHG information with the subsequent benefit of potential use in medical applications.

© 2010 OSA

1. Introduction

Second harmonic generation (SHG) laser scanning microscopy is considered nowadays one of the most promising minimally invasive, high-resolution optical techniques for clinical applications [1

1. P. J. Campagnola, M. D. Wei, A. Lewis, and L. M. Loew, “High-resolution nonlinear optical imaging of live cells by second harmonic generation,” Biophys. J. 77(6), 3341–3349 (1999). [CrossRef] [PubMed]

]. Because of recent technological advantages in micro-endoscopes/fibers [2

2. M. E. Llewellyn, R. P. J. Barretto, S. L. Delp, and M. J. Schnitzer, “Minimally invasive high-speed imaging of sarcomere contractile dynamics in mice and humans,” Nature 454(7205), 784–788 (2008). [PubMed]

4

4. H. Bao, A. Boussioutas, R. Jeremy, S. Russell, and M. Gu, “Second harmonic generation imaging via nonlinear endomicroscopy,” Opt. Express 18(2), 1255–1260 (2010). [CrossRef] [PubMed]

] and laser sources [5

5. E. U. Rafailov, M. A. Cataluna, and W. Sibbett, “Mode-locked quantum-dot lasers,” Nat. Photonics 1(7), 395–401 (2007). [CrossRef]

], SHG imaging shows a great potential for clinical usage as an optical biopsy tool [6

6. 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,” Biophys. J. 82(1), 493–508 (2002). [CrossRef]

].

Earlier, numerous studies on the SHG contrast have demonstrated that collagen, myosin, and microtubules are effective SHG converters in tissues [1

1. P. J. Campagnola, M. D. Wei, A. Lewis, and L. M. Loew, “High-resolution nonlinear optical imaging of live cells by second harmonic generation,” Biophys. J. 77(6), 3341–3349 (1999). [CrossRef] [PubMed]

]. Consequently, biological structures that are consisting of the above endogenous SHG sources can be imaged using intensity-based SHG microscopy. Despite the fact that the SHG intensity is the only contrast mechanism for generating the images, several morphological parameters can be obtained [7

7. R. M. Williams, W. R. Zipfel, and W. W. Webb, “Interpreting second-harmonic generation images of collagen I fibrils,” Biophys. J. 88(2), 1377–1386 (2005). [CrossRef]

]. For example, by comparing the forward and epi-detected SHG signals, conclusions on the dimensions of collagen fibrils can be obtained [8

8. S.-W. Chu, S.-P. Tai, M.-C. Chan, C.-K. Sun, I.-C. Hsiao, C.-H. Lin, Y.-C. Chen, and B.-L. Lin, “Thickness dependence of optical second harmonic generation in collagen fibrils,” Opt. Express 15(19), 12005–12010 (2007). [CrossRef] [PubMed]

]. Other methodologies take advantage of the characteristic striation pattern for quantitative interpretation and extraction of information in muscles [9

9. G. Recher, D. Rouède, P. Richard, A. Simon, J.-J. Bellanger, and F. Tiaho, “Three distinct sarcomeric patterns of skeletal muscle revealed by SHG and TPEF microscopy,” Opt. Express 17(22), 19763–19777 (2009). [CrossRef] [PubMed]

]. In such cases, the analysis of the sarcomere pattern was used for the study of rare diseases, including muscular dystrophy [10

10. S. V. Plotnikov, A. M. Kenny, S. J. Walsh, B. Zubrowski, C. Joseph, V. L. Scranton, G. A. Kuchel, D. Dauser, M. Xu, C. C. Pilbeam, D. J. Adams, R. P. Dougherty, P. J. Campagnola, and W. A. Mohler, “Measurement of muscle disease by quantitative second-harmonic generation imaging,” J. Biomed. Opt. 13(4), 044018 (2008). [CrossRef] [PubMed]

] and osteogenesis imperfecta [11

11. O. Nadiarnykh, S. Plotnikov, W. A. Mohler, I. Kalajzic, D. Redford-Badwal, and P. J. Campagnola, “Second harmonic generation imaging microscopy studies of osteogenesis imperfecta,” J. Biomed. Opt. 12(5), 051805 (2007). [CrossRef] [PubMed]

]. More recently, the use of image processing based on spatial Fourier analysis has been used to infer properties of tissue and molecules of the intensity-based SHG imaging [12

12. S. Plotnikov, V. Juneja, A. B. Isaacson, W. A. Mohler, and P. J. Campagnola, “Optical clearing for improved contrast in second harmonic generation imaging of skeletal muscle,” Biophys. J. 90(1), 328–339 (2006). [CrossRef]

]. Specifically, bidimensional (2D) Fourier transform (FT) was used to spatially quantify the disorganization of collagen fibres due to photo-thermal damage in porcine corneas [13

13. P. Matteini, F. Ratto, F. Rossi, R. Cicchi, C. Stringari, D. Kapsokalyvas, F. S. Pavone, and R. Pini, “Photothermally-induced disordered patterns of corneal collagen revealed by SHG imaging,” Opt. Express 17(6), 4868–4878 (2009). [CrossRef] [PubMed]

]. It was found that the regularities in fibres organization leads to an elliptical distribution in the bidimensional (2D-FT) transformed space, whereas randomness leads to a more circular distribution [14

14. R. Cicchi, D. Kapsokalyvas, V. De Giorgi, V. Maio, A. Van Wiechen, D. Massi, T. Lotti, and F. S. Pavone, “Scoring of collagen organization in healthy and diseased human dermis by multiphoton microscopy,” J Biophoton. 3(1-2), 34–43 (2010). [CrossRef]

]. Also very recently, it was presented that additional information on collagen fibre orientation and maximum spatial frequency can be obtained using 2D-FT in an SHG image [15

15. R. A. Rao, M. R. Mehta, and K. C. Toussaint Jr., “Fourier transform-second-harmonic generation imaging of biological tissues,” Opt. Express 17(17), 14534–14542 (2009). [CrossRef] [PubMed]

]. Likewise, it was shown that the 2D-FT can also be performed in the epi-detection [16

16. R. A. R. Rao, M. R. Mehta, S. Leithem, and K. C. Toussaint Jr., “Quantitative analysis of forward and backward second-harmonic images of collagen fibers using Fourier transform second-harmonic-generation microscopy,” Opt. Lett. 34(24), 3779–3781 (2009). [CrossRef] [PubMed]

].

In this work, we present a polarization 1-D FT analysis of the anisotropy curve to retrieve the biophysical parameters of the proposed model, referred to us as Fast Fourier Polarization SHG (FF-PSHG) analysis, to obtain the same information as with the iteration fitting-based procedure, but instead of hours, in a few hundreds of milliseconds using a regular processor. Considering a PSHG image of a three dimensional data set, I(x,y,α), where x-y refer to the spatial axis of the image and α refers to the polarization dependency of the SHG image (anisotropy curve), this FF-PSHG analysis is performed only on the polarization axis, α, of every pixel. This is in contrast to the spatial image processing methods using 2D-FT in the (x,y) axis discussed above [15

15. R. A. Rao, M. R. Mehta, and K. C. Toussaint Jr., “Fourier transform-second-harmonic generation imaging of biological tissues,” Opt. Express 17(17), 14534–14542 (2009). [CrossRef] [PubMed]

, 16

16. R. A. R. Rao, M. R. Mehta, S. Leithem, and K. C. Toussaint Jr., “Quantitative analysis of forward and backward second-harmonic images of collagen fibers using Fourier transform second-harmonic-generation microscopy,” Opt. Lett. 34(24), 3779–3781 (2009). [CrossRef] [PubMed]

].

2. Theory

The biophysical model used here (see refs [20

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

,21

21. S. Psilodimitrakopoulos, S. I. Santos, I. Amat-Roldan, A. K. Thayil, D. Artigas, and P. Loza-Alvarez, “In vivo, pixel-resolution mapping of thick filaments’ orientation in nonfibrilar muscle using polarization-sensitive second harmonic generation microscopy,” J. Biomed. Opt. 14(1), 014001 (2009), http://spiedl.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JBOPFO000014000001014001000001&idtype=cvips&prog=normal. [CrossRef] [PubMed]

,23

23. S. Psilodimitrakopoulos, D. Artigas, G. Soria, I. Amat-Roldan, A. M. Planas, and P. Loza-Alvarez, “Quantitative discrimination between endogenous SHG sources in mammalian tissue, based on their polarization response,” Opt. Express 17(12), 10168–10176 (2009). [CrossRef] [PubMed]

25

25. S. Psilodimitrakopoulos, V. Petegnief, G. Soria, I. Amat-Roldan, D. Artigas, A. M. Planas, and P. Loza-Alvarez, “Estimation of the effective orientation of the SHG source in primary cortical neurons,” Opt. Express 17(16), 14418–14425 (2009). [CrossRef] [PubMed]

]) refers to an SHG active supramolecular assembly with cylindrical symmetry. The SHG signal dependency of such structures on the input polarization of the fundamental beam can be written as:
ISHG(ϕ)=C2sin2[2(ϕα)]+[Asin2(ϕα)+Bcos2(ϕα)]2,
(1)
where ϕ and α are the orientation of the long axis of the cylinder, which we assume coincides with the supramolecular assembly alignment, and the angle of the fundamental beam polarization, respectively, defined with respect the lab x-axis [21

21. S. Psilodimitrakopoulos, S. I. Santos, I. Amat-Roldan, A. K. Thayil, D. Artigas, and P. Loza-Alvarez, “In vivo, pixel-resolution mapping of thick filaments’ orientation in nonfibrilar muscle using polarization-sensitive second harmonic generation microscopy,” J. Biomed. Opt. 14(1), 014001 (2009), http://spiedl.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JBOPFO000014000001014001000001&idtype=cvips&prog=normal. [CrossRef] [PubMed]

]. A = I0 d31, B = I0 d33 and C = I0 d15, where I0 is proportional to the intensity of the excitation fundamental field, and d31, d33 and d31 are the non-zero elements of the nonlinear susceptibility tensor characterizing the tissue under cylindrical symmetry assumption [21

21. S. Psilodimitrakopoulos, S. I. Santos, I. Amat-Roldan, A. K. Thayil, D. Artigas, and P. Loza-Alvarez, “In vivo, pixel-resolution mapping of thick filaments’ orientation in nonfibrilar muscle using polarization-sensitive second harmonic generation microscopy,” J. Biomed. Opt. 14(1), 014001 (2009), http://spiedl.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JBOPFO000014000001014001000001&idtype=cvips&prog=normal. [CrossRef] [PubMed]

].

The free parameters A, B, C and ϕ are usually obtained by fitting the experimental SHG images for every polarization α to Eq. (1). To do that, an iterative nonlinear algorithm is usually utilized. However, this is a lengthy task as, depending on the size of the image, this fitting procedure may take several hours. To speed up such process, Eq. (1) can be rewritten in a more convenient form as a sum of cosine frequency components as follows:
ISHG(ϕ)=α0+α2cos2(ϕα)+α4cos4(ϕα),
(2)
where a0 =C2/2 +3/8 (A2 +B2) +AB/4, a2 = B2/2-A2/2 and a4 = (A-B)2/8 – C2/2. Note that the parameters ϕ, a0, a2 and a4 contain now the whole information relative to our biophysical model (tensor elements). In what follows, we show that these components can be readily obtained by our FF-PSHG analysis in an efficient manner.

As commented in the introduction, in this work we are going to perform the 1D-FT only on the polarization axis, α as i(x,y,Ω)=Fα{I(x,y,α)}. By doing so, the Fourier transform of Eq. (2) in a pixel, determined by (x,y), with a polarization sampling between 0° and 180°, results in
i(Ω)=α0δ(0)+α2exp(i2ϕ)δ(1Ω)+α4exp(i4ϕ)δ(2Ω)+c.c.,
(3)
where c.c. indicates complex conjugated. From Eq. (3), we can now directly retrieve the different cosine components and therefore, extract the elements’ ratio of the second order susceptibility tensor of our model, in a pixel by pixel fashion. Note that since in an experiment the polarization intensity period is 180°, a sampling has therefore be considered in the 0° to 180° range. Polarization sampling performed between 0° and 360° is in fact reproducing the measurement twice (α is equivalent to α+180°). In this case the FF-PSHG analysis can be used by transforming the Dirac delta into δ(2−Ω) and δ(4−Ω) respectively, with the advantage that an immediate averaging of the two set of results (from 0° to 180° and from 180° to 360°) is obtained. In the rest of the document, for simplicity we assume the sampling is in the range from 0° to 180°. Note that the quadratic nature of PSHG response [see Eq. (1)] generates a symmetric polarization response in the polarization intervals α ∈ [0, π], therefore ϕ has the same periodicity, which for convenience we chose the range ϕ ∈ [- π/2, π/2].

Before go further, it is worth to note that Eq. (1) possesses a mathematical intrinsic ambiguity that affects any PSHG experiment. This ambiguity is apparent when the same result is obtained by exchanging A and B and adding π/2 phase to the orientation ϕ [21

21. S. Psilodimitrakopoulos, S. I. Santos, I. Amat-Roldan, A. K. Thayil, D. Artigas, and P. Loza-Alvarez, “In vivo, pixel-resolution mapping of thick filaments’ orientation in nonfibrilar muscle using polarization-sensitive second harmonic generation microscopy,” J. Biomed. Opt. 14(1), 014001 (2009), http://spiedl.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JBOPFO000014000001014001000001&idtype=cvips&prog=normal. [CrossRef] [PubMed]

]. From a physical point of view, this ambiguity appears because the model is build in a manner that assumes a minimum SHG signal when the incident polarization is perpendicular to the cylinder’s long axis. Experimentally, this has been reported to occur in several biosamples such as microtubulin of axons [25

25. S. Psilodimitrakopoulos, V. Petegnief, G. Soria, I. Amat-Roldan, D. Artigas, A. M. Planas, and P. Loza-Alvarez, “Estimation of the effective orientation of the SHG source in primary cortical neurons,” Opt. Express 17(16), 14418–14425 (2009). [CrossRef] [PubMed]

], collagen [18

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

] or starch [26

26. S. Psilodimitrakopoulos, I. Amat-Roldan, P. Loza-Alvarez, and D. Artigas, “Estimating the helical pitch angle of amylopectin in starch using polarization second harmonic generation microscopy,” J. Opt. 12(8), 084007 (2010). [CrossRef]

], and results in B/C >A/C ≈1. However, muscle [20

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

] shows the minimum SHG signal when the incident polarization is parallel to the thick filaments orientation (assumed to posses the cylindrical symmetry), with B/C <A/C ≈1. Since the ambiguity cannot be solved using mathematical criteria, a priori knowledge on the different sample PSHG response was needed. When using the fitting algorithm, the ambiguity is solved in every pixel by assigning the value closer to the unity to A/C. Then if this value is associated to the sinus in Eq. (1) the orientation is directly the retrieved angle ϕ. On the contrary, if A/C is associated to the cosine in Eq. (1), the actual orientation isϕ+π/2.

2.1. Determining the orientation of the supramolecular assembly ϕ

The above ambiguity also affects our FF-PSHG analysis, particularly in the orientation ϕ. Direct observation of Eq. (2) shows that ϕ only affects the cosine argument. Therefore, when performing Fourier transform to Eq. (3), it will appear as a phase in the first and second (second and four) coefficients when performing the sampling between 0° and 180° (0° and 360°). Then, the extraction of the orientation ϕ consists in computing the complex argument of the second coefficient as

ϕ'=arg[α2exp(i2ϕ)]/2
(4)

In Eq. (4), the ambiguity is apparent in the fact that the obtained angle ϕ' and the orientation ϕ can be different, since ϕ' also include information on the sign of a2. This is because a2 = B2/2-A2/2 can either be positive (|B|>|A|) or negative (|B|<|A|). This unknown sign is transformed in the intrinsic ambiguity of π/2 in calculating the angle orientation ϕ. This is totally equivalent to the ambiguity in Eq. (1) by exchanging A and B and adding π/2 to the orientation ϕ [21

21. S. Psilodimitrakopoulos, S. I. Santos, I. Amat-Roldan, A. K. Thayil, D. Artigas, and P. Loza-Alvarez, “In vivo, pixel-resolution mapping of thick filaments’ orientation in nonfibrilar muscle using polarization-sensitive second harmonic generation microscopy,” J. Biomed. Opt. 14(1), 014001 (2009), http://spiedl.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JBOPFO000014000001014001000001&idtype=cvips&prog=normal. [CrossRef] [PubMed]

]. Similarly, the condition used with iterative fitting algorithms, |A/C|<|B/C|, results in a 2>a 4, characteristic of collagen and starch, while |A/C|>|B/C| results in a 2<a 4, which is typical in myosin. Therefore, by comparing a 2 and a 4 it is possible to solve the indetermination as follows:

ϕ=|ϕ'2fora2a4ϕ'2+π/2fora2<a4
(5)

For other tissues it will be possible to design different strategies and define specific criteria. Also note that since the extraction of ϕ.is based on the phase of the polarization-spectral components, it is, in principle, independent of possible errors affecting the amplitudes a0, a2 and a4, adding robustness to the method.

2.2. Extraction of the biophysical parameters

cos2θe=B/(2A+B).
(7)

2.3. Pixels with erroneous results

In addition to this filtering, the noise at components Ω > 2 can be used to estimate the total amount of error in the coefficients a0, a2 and a4. To do that, we assume that the error in the frequency components at Ω = 0, 1 and 2 (related with a0, a2 and a4) is affected in a similar way as those components with Ω > 2. Therefore the experimental error in determining a0, a2 and a4 in a pixel can be estimated comparing the spectral components as

e(x,y)=[mean(i(x,y,Ω),Ω>2)]/[mean(α0,α2,α4)]
(8)

For example, the signal detected in pixels in areas outside any SHG active tissue is noise in nature and therefore results in a value of e ≈1. However, pixels in areas with a good signal to noise ratio will result in e ≈0. Then, since e quantifies the error in a pixel, it can be used to filter out pixels with e above a certain threshold value, e th, which are considered erroneous [i.e., do not match Eqs. (1)(3)]. Typical values for the threshold are in the range e th ≈0.02-0.1.

3 Results-discussion

In this section, we show the capability of determining the orientation of the supramolecular assembly ϕ, also referred as fiber orientation, discussing the ambiguity described in subsection 2.1, and the determination of θe. This is followed by two methods to perform discrimination among tissues.

3.1 Single SHG-active structure images

To show the ability of the algorithm to locally determine the orientation of the supramolecular assembly we analyze a representative case: a granule of starch. A granule of starch has been previously reported to possess a radial molecular orientation [26

26. S. Psilodimitrakopoulos, I. Amat-Roldan, P. Loza-Alvarez, and D. Artigas, “Estimating the helical pitch angle of amylopectin in starch using polarization second harmonic generation microscopy,” J. Opt. 12(8), 084007 (2010). [CrossRef]

]. This sample is ideal to show the performance of the method since it allows obtaining data within the whole orientation range, from 0° to 180°. The multiphoton microscope used to acquire the PSHG images has been thoroughly described in Refs [21

21. S. Psilodimitrakopoulos, S. I. Santos, I. Amat-Roldan, A. K. Thayil, D. Artigas, and P. Loza-Alvarez, “In vivo, pixel-resolution mapping of thick filaments’ orientation in nonfibrilar muscle using polarization-sensitive second harmonic generation microscopy,” J. Biomed. Opt. 14(1), 014001 (2009), http://spiedl.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JBOPFO000014000001014001000001&idtype=cvips&prog=normal. [CrossRef] [PubMed]

,23

23. S. Psilodimitrakopoulos, D. Artigas, G. Soria, I. Amat-Roldan, A. M. Planas, and P. Loza-Alvarez, “Quantitative discrimination between endogenous SHG sources in mammalian tissue, based on their polarization response,” Opt. Express 17(12), 10168–10176 (2009). [CrossRef] [PubMed]

,25

25. S. Psilodimitrakopoulos, V. Petegnief, G. Soria, I. Amat-Roldan, D. Artigas, A. M. Planas, and P. Loza-Alvarez, “Estimation of the effective orientation of the SHG source in primary cortical neurons,” Opt. Express 17(16), 14418–14425 (2009). [CrossRef] [PubMed]

,26

26. S. Psilodimitrakopoulos, I. Amat-Roldan, P. Loza-Alvarez, and D. Artigas, “Estimating the helical pitch angle of amylopectin in starch using polarization second harmonic generation microscopy,” J. Opt. 12(8), 084007 (2010). [CrossRef]

]. The linear polarization at the sample plane exhibited an extinction ratio of 25:1. By comparing the summed reconstruction of linear polarization images with the image created using circular polarization, we found this ratio adequate. Figure 1
Fig. 1 Calculation of fiber orientationϕ in starch: (a) Mean SHG intensity of the 9 PSHG images. Scale bar shows 10μm. (b) FF-PSHG analysis using 9 polarizations and (c) iterative fitting algorithm using 8 polarizations.
shows the results, measuring the angle ϕ using both the FF-PSHG analysis, which is obtained in 100 ms, and a fitting algorithm, which lasted ~6 hours with 400 iterations per pixel. The results are very similar, clearly retrieving the radial-like structure. The small deviation of the radial symmetry in Fig. 1 might be attributed to the imperfections on the starch granule. We can also observe that a smooth change from pixel to pixel is obtained with FF-PSHG analysis, without the need of pixel averaging, as is the case in the image obtained with the iterative algorithm. We attribute this smooth variation to the filtering process intrinsic in the FF-PSHG analysis. In addition to this filtering procedure, pixels with e > 0.05 have been removed from the image (black color). Notice that only points near the external surface of the starch granule disappears, denoting the quality of the measurement. In the case of the fitting algorithm, pixels with coefficient of determination r2<90%, has been filtered out. Finally, when using a fitting algorithm, final results slight change depending on the initial conditions and number of iterations. This is not the case in our FF-PSHG analysis, since its analytical nature always provides the same results. This adds robustness and consistency to the analysis.

With the above results, the reliability of the method to determine any fiber orientation change is clearly demonstrated. This allows analyze complicated situations and go a step forward to obtain the helical pitch angle in a sample, with pixel resolution, and compare the results obtained with the fitting algorithm and the FF-PSHG analysis. The results, corresponding to bundle of collagen fibers oriented in different directions, are showed in Fig. 3
Fig. 3 Lyophilized Achilles’ tendon collagen. (a) Superposition of the SHG intensity images for eight polarizations. Scale bar shows 10μm. (b) Image showing the helical pitch angle in every pixel obtained using an iterative fitting algorithm and its frequency distribution in (c). Similarly, (d) shows the helical pitch angle in every pixel and its frequency distribution in (e), this time using the FF-PSHG analysis.
(the corresponding fiber orientation is shown in Fig. 2c). Figure 3(a) shows the superposition of the SHG intensity images for all the polarizations. This figure show the difficulties to obtain SHG signal in some areas, specifically in most of the points in the top part of the collagen bundle that will result in a poor noise to signal ratio. As a consequence, the analysis performed using the iterative algorithm, shown in Fig. 3(b), lacks important parts of the image, which has been filtered out due to the low quality of fitting in the top part of the image (points with coefficient of determination, r2<85% where removed). In spite of the decrease of useful pixel, the fitting algorithm is able to correctly retrieve the helical pitch angle, whose distribution is shown in Fig. 3(c), with the maximum frequency at θ e = 44.4° and a distribution width of Δθ e = 5.4° (the helical pitch angle obtained with X-ray diffraction measurements is ~45°). On the contrary, the FF-PSHG analysis shown in figure Fig. 3(d) is able to map θ e in the entire sample, even for those areas with low SHG signal quality (notice the top part of the bundle of collagen fibers). This is possible to the noise filtering intrinsic to the method. The image shows smooth changes that give the impression of volume, which correlates well with the contour of Fig. 3(a). This makes us suspect that the variation in θ e can be attributed to be mainly produced by out of plane fiber axis orientations. The θ e frequency distribution obtained with the FF-PSHG analysis is shown in Fig. 3(e), showing a displacement of the maximum, at θ e = 42.3° and a distribution width of Δθ e = 4.9°. This displacement of the maximum is attributed to major number of pixels with θ e ≈40°, appearing in the top part of the bundle of collagen fibers, which are filtered out by the fitting algorithm in Fig. 3(c).

Regarding the time required to compute the above Figs. 2-3 (500 x 500 pixels), the FF-PSHG analysis lasted around 100 ms to compute the fiber orientation, while the calculus of θ e required less than 300 ms. Figures obtained with the fitting algorithm, where obtained with 400 iterations per pixel and lasted ~6 hours.

3.2 Multiple SHG-active structure images

PSHG offers the unique characteristic of identifying and discriminating different SHG active molecules, with pixel resolution, in the same image [23

23. S. Psilodimitrakopoulos, D. Artigas, G. Soria, I. Amat-Roldan, A. M. Planas, and P. Loza-Alvarez, “Quantitative discrimination between endogenous SHG sources in mammalian tissue, based on their polarization response,” Opt. Express 17(12), 10168–10176 (2009). [CrossRef] [PubMed]

]. In this section we show that our FF-PSHG analysis can also be used with discrimination purposes by computing B/A parameter and θ e in every pixel [using Eq. (7)]. The results for unstained temporalis muscle from rat are shown in Fig. 4(a), where it is possible to observe a clear discrimination between two tissues, orange corresponding to muscle and blue to collagen. In this case, the time required to compute Fig. 4(a) was less than 300 ms.

In addition to the discrimination method described above, the FF-PSHG analysis offers a simple discrimination alternative based on directly mapping the cosine frequency components a0, a2 and a4 into RGB images. Since the values of a0, a2 and a4 depend on the actual SHG molecule, the weight for every RGB channel is different for different tissues. Therefore, different tissues appear with different pseudocolor in the same image. The results are shown in Fig. 4(b). We can observe that both tissues are clearly differentiated. In order to identify what are the actual tissues displayed, the typical relation among values a0, a2 and a4 must be characterized. In the case of Fig. 4(b), and by comparing with Fig. 4(a), in the RGB representation yellow corresponds to collagen and purple to myosin. This provides a simple method to discriminate among different tissues, getting an instantaneous perception of the image, with the advantage that the time required to compute Fig. 4(b) was less than 100 ms, in a single core computer, after acquiring the corresponding PSHG data.

Comparing Figs. 4(a) and 4(b), we see that both methods provide similar discrimination capabilities, the main difference being the image appearance. This differences in the images appears because the cosine frequency components a0, a2 and a4 contains information on the ratio among a0, a2 and a4, which is always the same for a tissue (providing the discrimination capability), and on the intensity, providing smoother changes in the image. This results in an apparent better quality of Fig. 4(b) when compared with Fig. 4(a). However, although the RGB representation provides the fastest method to discriminate between different SHG sources, the standard method has the advantage that the tissue identification is based on a known intrinsic characteristic of the SHG active molecule, as is the helical pitch angle, providing a clear criterion in case of ambiguous situations. This is clearly apparent when plotting the frequency distribution for the helical pitch angle as showed in Fig. 4(c). The two well separated, not overlapping peaks centered at 43° and 64° for collagen and muscle, respectively, show the ability of the method to unambiguously distinguish between tissues in the same image.

4. Conclusions

Polarization-sensitive Second Harmonic Generation is a promising imaging modality that enables statistically studying the orientational distribution of the β( 2) dominant axis (related to the helical pitch angle) of a number of molecules which play a role in many biological processes: collagen, microtubulin and myosin and additional structures, like starch, which has been also used to probe polarization state in a microscope [27

27. S. Psilodimitrakopoulos, I. Amat-Roldan, S. Santos, M. Mathew, A.K.N. Thayil, D. Zalvidea, D. Artigas, and P. Loza-Alvarez, “Starch granules as a probe for the polarization at the sample plane of a high resolution multiphoton microscope,” SPIE, 68600E (2008).

]. Especially when optical clearing is used, this information can be acquired several hundreds of microns deep in tissues [28

28. O. Nadiarnykh and P. J. Campagnola, “Retention of polarization signatures in SHG microscopy of scattering tissues through optical clearing,” Opt. Express 17(7), 5794–5806 (2009). [CrossRef] [PubMed]

]. Therefore, many applications can be enhanced by the development of new and faster algorithms than the current ones, which are executed “offline”, requiring from minutes to hours to process an image of 500 by 500 pixels, even with multi-core computers.

In this paper, we have presented for the first time an approach that allows processing in few milliseconds an image based on 1D Fourier analysis of the PSHG modulation response obtaining a temporal improvement of near five orders of magnitude. This opens the possibility for PSHG imaging to penetrate new fields in medicine at video rates, acting for example as an instantaneous diagnostic supporting method in surgery. The results are in total agreement of those obtained by conventional fitting algorithms, where the intrinsic noise filtering results in a smother response and a better contrast, while its analytical nature provides robustness and consistency to the analysis. In conclusion, we have presented a sub-second method to process PSHG images to extract full biophysical meaning and straight visualization methods that can be useful for many fields in microscopy and biomedicine that possess additional advantages that do not possess its prior competitors.

Acknowledgments

This work is supported by the Generalitat de Catalunya grant 2009-SGR-159 and by the Spanish government grant TEC2009-09698 Authors also acknowledge the Laserlab-Europe Cont (JRA4: Optobio212025) and the Photonics4Life networks of excellence. This research has been partially supported by Fundació Cellex Barcelona.

References and links

1.

P. J. Campagnola, M. D. Wei, A. Lewis, and L. M. Loew, “High-resolution nonlinear optical imaging of live cells by second harmonic generation,” Biophys. J. 77(6), 3341–3349 (1999). [CrossRef] [PubMed]

2.

M. E. Llewellyn, R. P. J. Barretto, S. L. Delp, and M. J. Schnitzer, “Minimally invasive high-speed imaging of sarcomere contractile dynamics in mice and humans,” Nature 454(7205), 784–788 (2008). [PubMed]

3.

L. Fu and M. Gu, “Polarization anisotropy in fiber-optic second harmonic generation microscopy,” Opt. Express 16(7), 5000–5006 (2008). [CrossRef] [PubMed]

4.

H. Bao, A. Boussioutas, R. Jeremy, S. Russell, and M. Gu, “Second harmonic generation imaging via nonlinear endomicroscopy,” Opt. Express 18(2), 1255–1260 (2010). [CrossRef] [PubMed]

5.

E. U. Rafailov, M. A. Cataluna, and W. Sibbett, “Mode-locked quantum-dot lasers,” Nat. Photonics 1(7), 395–401 (2007). [CrossRef]

6.

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,” Biophys. J. 82(1), 493–508 (2002). [CrossRef]

7.

R. M. Williams, W. R. Zipfel, and W. W. Webb, “Interpreting second-harmonic generation images of collagen I fibrils,” Biophys. J. 88(2), 1377–1386 (2005). [CrossRef]

8.

S.-W. Chu, S.-P. Tai, M.-C. Chan, C.-K. Sun, I.-C. Hsiao, C.-H. Lin, Y.-C. Chen, and B.-L. Lin, “Thickness dependence of optical second harmonic generation in collagen fibrils,” Opt. Express 15(19), 12005–12010 (2007). [CrossRef] [PubMed]

9.

G. Recher, D. Rouède, P. Richard, A. Simon, J.-J. Bellanger, and F. Tiaho, “Three distinct sarcomeric patterns of skeletal muscle revealed by SHG and TPEF microscopy,” Opt. Express 17(22), 19763–19777 (2009). [CrossRef] [PubMed]

10.

S. V. Plotnikov, A. M. Kenny, S. J. Walsh, B. Zubrowski, C. Joseph, V. L. Scranton, G. A. Kuchel, D. Dauser, M. Xu, C. C. Pilbeam, D. J. Adams, R. P. Dougherty, P. J. Campagnola, and W. A. Mohler, “Measurement of muscle disease by quantitative second-harmonic generation imaging,” J. Biomed. Opt. 13(4), 044018 (2008). [CrossRef] [PubMed]

11.

O. Nadiarnykh, S. Plotnikov, W. A. Mohler, I. Kalajzic, D. Redford-Badwal, and P. J. Campagnola, “Second harmonic generation imaging microscopy studies of osteogenesis imperfecta,” J. Biomed. Opt. 12(5), 051805 (2007). [CrossRef] [PubMed]

12.

S. Plotnikov, V. Juneja, A. B. Isaacson, W. A. Mohler, and P. J. Campagnola, “Optical clearing for improved contrast in second harmonic generation imaging of skeletal muscle,” Biophys. J. 90(1), 328–339 (2006). [CrossRef]

13.

P. Matteini, F. Ratto, F. Rossi, R. Cicchi, C. Stringari, D. Kapsokalyvas, F. S. Pavone, and R. Pini, “Photothermally-induced disordered patterns of corneal collagen revealed by SHG imaging,” Opt. Express 17(6), 4868–4878 (2009). [CrossRef] [PubMed]

14.

R. Cicchi, D. Kapsokalyvas, V. De Giorgi, V. Maio, A. Van Wiechen, D. Massi, T. Lotti, and F. S. Pavone, “Scoring of collagen organization in healthy and diseased human dermis by multiphoton microscopy,” J Biophoton. 3(1-2), 34–43 (2010). [CrossRef]

15.

R. A. Rao, M. R. Mehta, and K. C. Toussaint Jr., “Fourier transform-second-harmonic generation imaging of biological tissues,” Opt. Express 17(17), 14534–14542 (2009). [CrossRef] [PubMed]

16.

R. A. R. Rao, M. R. Mehta, S. Leithem, and K. C. Toussaint Jr., “Quantitative analysis of forward and backward second-harmonic images of collagen fibers using Fourier transform second-harmonic-generation microscopy,” Opt. Lett. 34(24), 3779–3781 (2009). [CrossRef] [PubMed]

17.

K. M. Reiser, C. Bratton, D. R. Yankelevich, A. Knoesen, I. Rocha-Mendoza, and J. Lotz, “Quantitative analysis of structural disorder in intervertebral disks using second harmonic generation imaging: comparison with morphometric analysis,” J. Biomed. Opt. 12(6), 064019 (2007). [CrossRef]

18.

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

19.

S. Plotnikov, V. Juneja, A. B. Isaacson, W. A. Mohler, and P. J. Campagnola, “Optical clearing for improved contrast in second harmonic generation imaging of skeletal muscle,” Biophys. J. 90(1), 328–339 (2006). [CrossRef]

20.

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

21.

S. Psilodimitrakopoulos, S. I. Santos, I. Amat-Roldan, A. K. Thayil, D. Artigas, and P. Loza-Alvarez, “In vivo, pixel-resolution mapping of thick filaments’ orientation in nonfibrilar muscle using polarization-sensitive second harmonic generation microscopy,” J. Biomed. Opt. 14(1), 014001 (2009), http://spiedl.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JBOPFO000014000001014001000001&idtype=cvips&prog=normal. [CrossRef] [PubMed]

22.

C. Odin, T. Guilbert, A. Alkilani, O. P. Boryskina, V. Fleury, and Y. Le Grand, “Collagen and myosin characterization by orientation field second harmonic microscopy,” Opt. Express 16(20), 16151–16165 (2008). [CrossRef] [PubMed]

23.

S. Psilodimitrakopoulos, D. Artigas, G. Soria, I. Amat-Roldan, A. M. Planas, and P. Loza-Alvarez, “Quantitative discrimination between endogenous SHG sources in mammalian tissue, based on their polarization response,” Opt. Express 17(12), 10168–10176 (2009). [CrossRef] [PubMed]

24.

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, “Second harmonic generation chi tensor microscopy for tissue imaging,” Appl. Phys. Lett. 94, 3 (2009).

25.

S. Psilodimitrakopoulos, V. Petegnief, G. Soria, I. Amat-Roldan, D. Artigas, A. M. Planas, and P. Loza-Alvarez, “Estimation of the effective orientation of the SHG source in primary cortical neurons,” Opt. Express 17(16), 14418–14425 (2009). [CrossRef] [PubMed]

26.

S. Psilodimitrakopoulos, I. Amat-Roldan, P. Loza-Alvarez, and D. Artigas, “Estimating the helical pitch angle of amylopectin in starch using polarization second harmonic generation microscopy,” J. Opt. 12(8), 084007 (2010). [CrossRef]

27.

S. Psilodimitrakopoulos, I. Amat-Roldan, S. Santos, M. Mathew, A.K.N. Thayil, D. Zalvidea, D. Artigas, and P. Loza-Alvarez, “Starch granules as a probe for the polarization at the sample plane of a high resolution multiphoton microscope,” SPIE, 68600E (2008).

28.

O. Nadiarnykh and P. J. Campagnola, “Retention of polarization signatures in SHG microscopy of scattering tissues through optical clearing,” Opt. Express 17(7), 5794–5806 (2009). [CrossRef] [PubMed]

OCIS Codes
(100.2960) Image processing : Image analysis
(170.0170) Medical optics and biotechnology : Medical optics and biotechnology
(170.3880) Medical optics and biotechnology : Medical and biological imaging
(180.0180) Microscopy : Microscopy
(180.6900) Microscopy : Three-dimensional microscopy
(190.4160) Nonlinear optics : Multiharmonic generation
(180.4315) Microscopy : Nonlinear microscopy

ToC Category:
Microscopy

History
Original Manuscript: May 12, 2010
Revised Manuscript: July 8, 2010
Manuscript Accepted: July 15, 2010
Published: July 29, 2010

Virtual Issues
Vol. 5, Iss. 12 Virtual Journal for Biomedical Optics

Citation
Ivan Amat-Roldan, Sotiris Psilodimitrakopoulos, Pablo Loza-Alvarez, and David Artigas, "Fast image analysis in polarization SHG microscopy.," Opt. Express 18, 17209-17219 (2010)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-18-16-17209


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References

  1. P. J. Campagnola, M. D. Wei, A. Lewis, and L. M. Loew, “High-resolution nonlinear optical imaging of live cells by second harmonic generation,” Biophys. J. 77(6), 3341–3349 (1999). [CrossRef] [PubMed]
  2. M. E. Llewellyn, R. P. J. Barretto, S. L. Delp, and M. J. Schnitzer, “Minimally invasive high-speed imaging of sarcomere contractile dynamics in mice and humans,” Nature 454(7205), 784–788 (2008). [PubMed]
  3. L. Fu and M. Gu, “Polarization anisotropy in fiber-optic second harmonic generation microscopy,” Opt. Express 16(7), 5000–5006 (2008). [CrossRef] [PubMed]
  4. H. Bao, A. Boussioutas, R. Jeremy, S. Russell, and M. Gu, “Second harmonic generation imaging via nonlinear endomicroscopy,” Opt. Express 18(2), 1255–1260 (2010). [CrossRef] [PubMed]
  5. E. U. Rafailov, M. A. Cataluna, and W. Sibbett, “Mode-locked quantum-dot lasers,” Nat. Photonics 1(7), 395–401 (2007). [CrossRef]
  6. 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,” Biophys. J. 82(1), 493–508 (2002). [CrossRef]
  7. R. M. Williams, W. R. Zipfel, and W. W. Webb, “Interpreting second-harmonic generation images of collagen I fibrils,” Biophys. J. 88(2), 1377–1386 (2005). [CrossRef]
  8. S.-W. Chu, S.-P. Tai, M.-C. Chan, C.-K. Sun, I.-C. Hsiao, C.-H. Lin, Y.-C. Chen, and B.-L. Lin, “Thickness dependence of optical second harmonic generation in collagen fibrils,” Opt. Express 15(19), 12005–12010 (2007). [CrossRef] [PubMed]
  9. G. Recher, D. Rouède, P. Richard, A. Simon, J.-J. Bellanger, and F. Tiaho, “Three distinct sarcomeric patterns of skeletal muscle revealed by SHG and TPEF microscopy,” Opt. Express 17(22), 19763–19777 (2009). [CrossRef] [PubMed]
  10. S. V. Plotnikov, A. M. Kenny, S. J. Walsh, B. Zubrowski, C. Joseph, V. L. Scranton, G. A. Kuchel, D. Dauser, M. Xu, C. C. Pilbeam, D. J. Adams, R. P. Dougherty, P. J. Campagnola, and W. A. Mohler, “Measurement of muscle disease by quantitative second-harmonic generation imaging,” J. Biomed. Opt. 13(4), 044018 (2008). [CrossRef] [PubMed]
  11. O. Nadiarnykh, S. Plotnikov, W. A. Mohler, I. Kalajzic, D. Redford-Badwal, and P. J. Campagnola, “Second harmonic generation imaging microscopy studies of osteogenesis imperfecta,” J. Biomed. Opt. 12(5), 051805 (2007). [CrossRef] [PubMed]
  12. S. Plotnikov, V. Juneja, A. B. Isaacson, W. A. Mohler, and P. J. Campagnola, “Optical clearing for improved contrast in second harmonic generation imaging of skeletal muscle,” Biophys. J. 90(1), 328–339 (2006). [CrossRef]
  13. P. Matteini, F. Ratto, F. Rossi, R. Cicchi, C. Stringari, D. Kapsokalyvas, F. S. Pavone, and R. Pini, “Photothermally-induced disordered patterns of corneal collagen revealed by SHG imaging,” Opt. Express 17(6), 4868–4878 (2009). [CrossRef] [PubMed]
  14. R. Cicchi, D. Kapsokalyvas, V. De Giorgi, V. Maio, A. Van Wiechen, D. Massi, T. Lotti, and F. S. Pavone, “Scoring of collagen organization in healthy and diseased human dermis by multiphoton microscopy,” J Biophoton. 3(1-2), 34–43 (2010). [CrossRef]
  15. R. A. Rao, M. R. Mehta, and K. C. Toussaint., “Fourier transform-second-harmonic generation imaging of biological tissues,” Opt. Express 17(17), 14534–14542 (2009). [CrossRef] [PubMed]
  16. R. A. R. Rao, M. R. Mehta, S. Leithem, and K. C. Toussaint., “Quantitative analysis of forward and backward second-harmonic images of collagen fibers using Fourier transform second-harmonic-generation microscopy,” Opt. Lett. 34(24), 3779–3781 (2009). [CrossRef] [PubMed]
  17. K. M. Reiser, C. Bratton, D. R. Yankelevich, A. Knoesen, I. Rocha-Mendoza, and J. Lotz, “Quantitative analysis of structural disorder in intervertebral disks using second harmonic generation imaging: comparison with morphometric analysis,” J. Biomed. Opt. 12(6), 064019 (2007). [CrossRef]
  18. P. Stoller, K. M. Reiser, P. M. Celliers, and A. M. Rubenchik, “Polarization-modulated second harmonic generation in collagen,” Biophys. J. 82(6), 3330–3342 (2002). [CrossRef] [PubMed]
  19. S. Plotnikov, V. Juneja, A. B. Isaacson, W. A. Mohler, and P. J. Campagnola, “Optical clearing for improved contrast in second harmonic generation imaging of skeletal muscle,” Biophys. J. 90(1), 328–339 (2006). [CrossRef]
  20. F. Tiaho, G. Recher, and D. Rouède, “Estimation of helical angles of myosin and collagen by second harmonic generation imaging microscopy,” Opt. Express 15(19), 12286–12295 (2007). [CrossRef] [PubMed]
  21. S. Psilodimitrakopoulos, S. I. Santos, I. Amat-Roldan, A. K. Thayil, D. Artigas, and P. Loza-Alvarez, “In vivo, pixel-resolution mapping of thick filaments’ orientation in nonfibrilar muscle using polarization-sensitive second harmonic generation microscopy,” J. Biomed. Opt. 14(1), 014001 (2009), http://spiedl.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JBOPFO000014000001014001000001&idtype=cvips&prog=normal . [CrossRef] [PubMed]
  22. C. Odin, T. Guilbert, A. Alkilani, O. P. Boryskina, V. Fleury, and Y. Le Grand, “Collagen and myosin characterization by orientation field second harmonic microscopy,” Opt. Express 16(20), 16151–16165 (2008). [CrossRef] [PubMed]
  23. S. Psilodimitrakopoulos, D. Artigas, G. Soria, I. Amat-Roldan, A. M. Planas, and P. Loza-Alvarez, “Quantitative discrimination between endogenous SHG sources in mammalian tissue, based on their polarization response,” Opt. Express 17(12), 10168–10176 (2009). [CrossRef] [PubMed]
  24. 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, “Second harmonic generation chi tensor microscopy for tissue imaging,” Appl. Phys. Lett. 94, 3 (2009).
  25. S. Psilodimitrakopoulos, V. Petegnief, G. Soria, I. Amat-Roldan, D. Artigas, A. M. Planas, and P. Loza-Alvarez, “Estimation of the effective orientation of the SHG source in primary cortical neurons,” Opt. Express 17(16), 14418–14425 (2009). [CrossRef] [PubMed]
  26. S. Psilodimitrakopoulos, I. Amat-Roldan, P. Loza-Alvarez, and D. Artigas, “Estimating the helical pitch angle of amylopectin in starch using polarization second harmonic generation microscopy,” J. Opt. 12(8), 084007 (2010). [CrossRef]
  27. S. Psilodimitrakopoulos, I. Amat-Roldan, S. Santos, M. Mathew, A.K.N. Thayil, D. Zalvidea, D. Artigas, and P. Loza-Alvarez, “Starch granules as a probe for the polarization at the sample plane of a high resolution multiphoton microscope,” SPIE, 68600E (2008).
  28. O. Nadiarnykh and P. J. Campagnola, “Retention of polarization signatures in SHG microscopy of scattering tissues through optical clearing,” Opt. Express 17(7), 5794–5806 (2009). [CrossRef] [PubMed]

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