Volume 111, Issue 7, Pages 1361-1374 (October 2016) Imaging the Nonlinear Susceptibility Tensor of Collagen by Nonlinear Optical Stokes Ellipsometry  Ximeng Y. Dow, Emma L. DeWalt, Shane Z. Sullivan, Paul D. Schmitt, James R.W. Ulcickas, Garth J. Simpson  Biophysical Journal  Volume 111, Issue 7, Pages 1361-1374 (October 2016) DOI: 10.1016/j.bpj.2016.05.055 Copyright © 2016 Terms and Conditions

Figure 1 General process of solving for a global χ⇀l(2) and sample orientation using the iterative analysis or for solving for χ⇀l(2) at every pixel using the pixel-by-pixel analysis. Biophysical Journal 2016 111, 1361-1374DOI: (10.1016/j.bpj.2016.05.055) Copyright © 2016 Terms and Conditions

Figure 2 Hyperellipsoid representation of hyperpolarizability tensor of (a) NMA; (b) a collagen triple helix; (c) a collagen fibril; and (d) the second-order susceptibility tensor of collagen, which exhibits a distribution in fibril tilt angles. To see this figure in color, go online. Biophysical Journal 2016 111, 1361-1374DOI: (10.1016/j.bpj.2016.05.055) Copyright © 2016 Terms and Conditions

Figure 3 Instrument and timing schematic for NOSE instrumentation capable of rapid polarization modulation and synchronous digitization. To see this figure in color, go online. Biophysical Journal 2016 111, 1361-1374DOI: (10.1016/j.bpj.2016.05.055) Copyright © 2016 Terms and Conditions

Figure 4 The process of linear fitting to recover Fourier coefficients for collagen fibers in a porcine ear sample. A set of 10 unique polarization-dependent images for the vertical PMT are shown in (a) and a representative linear fit to recover Fourier coefficients for a single pixel is shown in (b). The five Fourier coefficient images were assigned a unique color (red, green, blue, cyan, and magenta) (c) before being merged into a single five-color image, shown in (d). To see this figure in color, go online. Biophysical Journal 2016 111, 1361-1374DOI: (10.1016/j.bpj.2016.05.055) Copyright © 2016 Terms and Conditions

Figure 5 Fourier coefficient color maps for mouse tail, porcine ear, and porcine skin for the horizontal and vertical detectors (H-PMT and V-PMT, respectively). To see this figure in color, go online. Biophysical Journal 2016 111, 1361-1374DOI: (10.1016/j.bpj.2016.05.055) Copyright © 2016 Terms and Conditions

Figure 6 Orientation images of the azimuthal angle ϕ for a single FOV of mouse tail section (left) from OrientationJ and (right) from the iterative analysis. To see this figure in color, go online. Biophysical Journal 2016 111, 1361-1374DOI: (10.1016/j.bpj.2016.05.055) Copyright © 2016 Terms and Conditions

Figure 7 The out-of-plane tilt angle of the collagen fibers from three different types of samples. To see this figure in color, go online. Biophysical Journal 2016 111, 1361-1374DOI: (10.1016/j.bpj.2016.05.055) Copyright © 2016 Terms and Conditions

Figure 8 Normalized local-frame tensor elements for the three tissue types for (a) pooled analysis and (b) pixel-by-pixel analysis. Error bars indicate 95% CI within each sample set. To see this figure in color, go online. Biophysical Journal 2016 111, 1361-1374DOI: (10.1016/j.bpj.2016.05.055) Copyright © 2016 Terms and Conditions

Figure 9 Images representing the relationships between the three unique local frame tensor elements, χxxz(2), χzxx(2), and χzzz(2) for the three tissue types. Images were created by assigning each tensor image acquired from the pixel-by-pixel analysis a unique color (green, blue, and red for χxxz(2), χzxx(2), and χzzz(2), respectively) and overlaying them on the same intensity scale. Image brightness represents overall SHG intensity and the hue of the image represents the relative magnitudes of χxxz(2), χzxx(2), and χzzz(2). To see this figure in color, go online. Biophysical Journal 2016 111, 1361-1374DOI: (10.1016/j.bpj.2016.05.055) Copyright © 2016 Terms and Conditions

Figure 10 (a) The ratio of χl,zzz(2)/χl,zxx(2) as a function of the spread of the tilt-angle distribution of triple helices given different input values of βz′z′z′(2)/βz′x′x′(2). (b) The ratio of χl,zzz(2)/χl,zxx(2) as a function of tilt angle of triple helices given different input values of βz′z′z′(2)/βz′x′x′(2). Biophysical Journal 2016 111, 1361-1374DOI: (10.1016/j.bpj.2016.05.055) Copyright © 2016 Terms and Conditions

Figure 11 Bimodal distribution of the triple-helix tilt angles with respect to the fiber axis. Biophysical Journal 2016 111, 1361-1374DOI: (10.1016/j.bpj.2016.05.055) Copyright © 2016 Terms and Conditions