1. Introduction

Second harmonic generation (SHG) is becoming increasingly recognized as a viable microscope imaging mechanism for visualization of tissue structure without the use of exogenous labels. Specifically, it has been demonstrated that structural protein arrays consisting of collagen,1–3 acto-myosin,4 and tubulin1, 5 exhibit large hyperpolarizabilities that produce bright SHG contrast. Due to the near infrared fundamental wavelengths that are typically used, this imaging modality is well-suited for imaging deep (several hundred microns) into highly scattering specimens. Perhaps the main power in SHG microscopy lies in the fact that the signal intensities are exquisitely sensitive to the assembly of protein molecules in tissue. Specifically, the SHG intensity depends on the concentration, fibrillar organization as well as the crosslink density. Additionally, due to the SHG photophysics, complete molecular anisotropy information is retained in the signal, so SHG provides more structural level data than either two-photon excited fluorescence (TPEF) or polarization microscopy. For example, we recently showed that the SHG signal intensity dependence on the laser polarization can be used to extract the helical pitch angle in collagen and myosin.4 While other publications have also reported the use of polarization analysis,6 this unique aspect of SHG imaging is just beginning to be exploited for its full capability.

This benefit is especially promising for imaging applications in biomedical research and in the clinic where a non-invasive three-dimensional in vivo “optical biopsy” can be developed via SHG imaging. For example, it has been postulated that such assembly may be different in normal and diseased tissues.7 While SHG has shown promise as a disease diagnostic, more still needs to be understood about the contrast mechanism in terms of how the observed signals are correlated with the organization of the tissue over length scales ranging from the molecular level to the fiber level.

In this paper we consider two general (and related) approaches to this problem. The first scheme analyzes the depth dependence of directionality of the detected SHG contrast. Specifically, since SHG is a coherent process, phase information is conserved and this can be exploited for tissue characterization. The second tactic measures the dependence of the SHG intensity of the polarized laser excitation as well as the anisotropy of the SHG signal as a function of depth into the tissue. Since SHG is governed by the electric dipole interaction, the initial emission pattern is defined by the size of the scattering objects. Small scatterers, i.e. much smaller than the excitation wavelength, produce a “figure 8” spatial pattern.8 When the dipoles of adjacent molecules form aligned structures comparable or larger than λ (in the axial dimension) the emission becomes highly forward directed. Because of the coherence of SHG, different fibril morphology can be observed in the forward and backwards channels. Specifically, smaller features can appear in the backwards signal due to incomplete destructive interference. This effect has recently been observed in collagen tendon and cornea by Williams et al3 and Han et al9, respectively. In addition to this size dependent coherent backwards emission in highly scattering tissues, the emitted SHG forward signal will undergo multiple scattering events, producing an incoherent backwards SHG signal.2 This contribution will become significant at SHG depths exceeding one mean free path (MFP) or 1/μ_s of the matrix. For this scattered component (i.e. the incoherent part of the signal), the depth dependence of the ratio of the forward to backwards intensities contains information on the scattering properties of the matrix, i.e. the scattering coefficient μ_s, and the scattering anisotropy, g, where these are related by the reduced scattering coefficient μ_s’:

Based on models of multiple scattering in the tissue spectroscopy literature,10, 11 it has been shown that for efficient backscattering to occur, a distance of one MFP from point of focus until the exit of the tissue is required. Thus at greater imaging depths, the probability of scattering collisions is decreased as the exit is approached and the F/B ratio must increase. Concurrently, the backwards signal becomes increasingly incoherent. It should be noted that the propagation of a photon of a given wavelength will be based on μ_s and g of the scattering matrix at that wavelength and will be independent of the contrast mechanism that created it. This was also recently suggested for CARS and SHG imaging by Xie and coworkers.12

Backwards collected SHG is of particular interest for in vivo applications which would likely require the use of the same optics for the excitation and signal collection. As certain connective tissue pathologies may display significantly different mean free paths, this scheme of analyzing the depth dependence of the F/B could then be utilized for analysis of tissue biopsies. A fundamental and related question regarding the backscattered SHG component is the extent that the SHG polarization properties are retained in a highly scattering environment.

Here we examine the depth dependence of the F/B in conjunction with polarization analysis in purified fibrous cellulose specimens. These are prototypical fibrillar system having analogous hierarchical-assembly as collagen, where the latter assembles into progressively higher ordered structures, beginning with the nanometer level (microfibril) that then become organized into fibrils (~100 nm), which assemble into fibers (~microns), and finally fascicles (~10–100 microns).13, 14 Cellulose similarly evolves through a progression of well- ordered molecular chains which crystallize into microfibrils.15 The supramolecular structure of these materials also parallels that of structural proteins in that it highly birefringent, and strongly chiral. From our previous work with collagen4 and cellulose16 we have determined that the polarization dependence of the SHG from the latter is characterized by a simpler profile. This is a powerful analysis as we have shown that these measurements can yield the angle of the dipole moment with respect to the fiber symmetry axis.4 Furthermore, the fibrillar structure of the cellulose matrices is highly regular and displays high anisotropy, thus providing a convenient environment to study the signal propagation and polarization properties. Additionally, some forms of cellulose, including Acetobacter (studied here) have attracted attention as tissue engineering scaffolds for implantable devices.17 Thus high-resolution optical imaging of these structures may be relevant for future in vivo imaging applications.

Previously we reported that thin sections of Acetobacter xylinum and Valonia ventricosa produced SHG signals with high contrast in forward directed SHG.16 In this paper we present our efforts to extensively characterize the SHG signal propagation and polarization signatures for both the forward and backscattered components in these scattering environments in specimens up to 500 μm in thickness. To this end, we compare morphologies throughout the thickness as well as analyze the depth dependence of the ratio of the forward to backward (F/B) intensities. We observed both direct coherent backwards emission as well as that arising from multiple scattered forward directed SHG. Specifically, the backwards channel in regions near the surface displays small fibrils not present in the forward emission, suggesting this component is largely coherent. In addition, at depths beyond one MFP the fibril morphologies become highly similar, suggesting the backwards contrast is increasingly mixed with multiple scattered photons of the initially forward directed wave. The depth dependence of the F/B ratio consistent with our Monte Carlo simulations based a photon diffusion model using the measured scattering coefficient μ_s of 75 cm^-1 and anisotropy g=0.94 at the SHG wavelength. We also show that the polarization dependence of the intensity of SHG signal as well as the signal anisotropy are similar for forwards and backwards SHG and that their respective information content is largely retained throughout the specimen thickness.

2. Experimental methods

The SHG imaging system consists of a laser scanning head (Olympus Fluoview 300) mounted on upright microscope, coupled to a mode-locked Titanium Sapphire laser. All measurements were performed with a laser fundamental wavelength of 900 nm with average power of 50 mW at the sample. The system is designed for simultaneous SHG detection of the forward and backscattered components. In the former, a long working distance 40X 0.8 N.A. water-immersion objective and a 0.9 N.A. condenser provide excitation and signal collection, respectively. The backwards component is collected in a non-descanned configuration. In both geometries, the SHG signal is isolated with a longwave pass dichroic mirror and 10 nm bandpass filters (450 nm). The signals are detected by a pair of identical photon-counting photomultiplier modules (Hamamatsu). The SHG wavelength (450 nm) was confirmed with a fiber optic spectrometer (Ocean Optics). There is no auofluorescence for cellulose at this excitation wavelength.

3D SHG image stacks were quantitatively analyzed with ImageJ software (http://rsb.info.nih.gov/ij/). A coumarin dye slide emitting at the SHG wavelength was used to calibrate both signal collection channels to account for uneven losses in optical paths and relative collection efficiency of the two detectors. Since forward-to-backward fluorescence ratio from a dye slide is assumed to be one, it becomes the normalization factor for the two channels.

The input polarization is controlled by a set of half- and quarter-wave plates. We de facto determined the polarization of excitation light at the focal plane by matching SHG maxima and minima to those previously measured for linear (myofibrils) and spherical (circular cells) specimens. We acquired the dependence of the SHG intensity on the angle between the axis of a single fibril and input laser polarization by two equivalent approaches. In the first, the laser polarization was rotated with a half-wave plate and the specimen was imaged at high zoom (8X). To investigate whether any ellipticity was introduced by the scanning system, we also fixed the input laser polarization and rotated the sample with a centered circular rotation stage while imaging at high zoom (8X) from a region in the middle of the field. Results from both methods were in excellent agreement. For measurements not involving polarization analysis, circular polarization of the laser fundamental was used for the excitation. We adapted both acquisition channels for analysis of the polarization of the resulting SHG signals by addition of collimation lenses a Glan laser polarizer. Images were taken with the analyzing polarizers in the parallel and orthogonal positions to the excitation light.

Monte Carlo simulations based on photon diffusion were performed as a comparison to the experimental F/B data to determine if multiple scattering can occur in these fibrillar specimens. To this end, we adapted a previous model by Wang et al10 to calculate the escape probabilities for the forward and backwards channels. The simulation requires the scattering coefficient and anisotropy, g, for both the fundamental and SHG wavelengths. Optical sectioning is simulated by calculating the fraction of laser photons that arrive at the focal point at a given depth, and the SHG intensity is then calculated based on resulting laser intensity after scattering losses. To the best of our knowledge, the scattering parameters for Acetobacter and Valonia celluloses have not been reported, thus we determined them at 450 and 900 nm using the following measurements. The diffuse reflected and transmitted intensities were measured using a dual integrating sphere technique, where the specimen was placed between 3 and 2 port spheres. The refractive indices were determined using the method of Li18 where the specimen is placed on a cylindrical lens and the critical angle for total internal reflection is measured. From the sphere measurements and using the measured refractive indices, following Reichman19 we numerically determine the absorption coefficient μ_a and reduced scattering coefficient μ_s’. Since integrating spheres cannot independently determine μ_s and the anisotropy, g, we measured the latter by the method of Marchesisi et al20 where the rotation of a centered detector is used to determine the Henyey-Greenstein function.

Acetobacter xylinum and Valonia ventricosa were gifts from Prof. Malcolm Brown. Both materials were stored in absolute methanol until used. A thick slice was cut from the never-dried sample, repeatedly washed in deionized water, mounted on a slide, and kept hydrated during image acquisition.

3. Results and discussion

3.1 SEM and scattering characterization of cellulose specimens

In order to provide some background into the SHG imaging studies of these fibrillar specimens, we begin by showing the higher resolution scanning electron microscopy (SEM) images from Acetobacter xylinum and Valonia ventricosa. Given the similarity in the supramolecular assembly to collagen, by analogy, it is anticipated that the fibrillar structure of cellulose will display a high degree of regularity. This is borne out by the typical SEM images shown in Fig. 1. In the case of Valonia (Fig. 1(a)) every lateral section has some dominant direction of fibril axis orientation with orthogonally aligned fibrils in adjacent planes. Fibrils composing Acetobacter cellulose are much more densely packed and tightly woven but less regularly ordered. Through analysis of the SEM images, we determined the average fibril sizes for Acetobacter and Valonia grown under these culture conditions to be 77 ± 21 and 36±8 nm, respectively. The spacing between the axially adjacent lamella in Valonia allows the fibrils to be imaged within one optical section at 0.8 NA with little to no contribution from the next orthogonally oriented layer (even with the use of circularly polarized light).

 

Fig. 1. Scanning electron microscope images of (a) Valonia cellulose (scale bar: 1 μm) and (b) Acetobacter cellulose (scale bar: 1 μm).

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Using the techniques described in the methods, we determined n, μ_a, μ_s, μ_s,’, and g for these specimens. The refractive indices and anisotropies, g, for both specimens were 1.37±.02 and 0.94± .02, at 457 nm respectively. Variations of these indices at 900nm were within our experimental error and assumed to be the same. The Valonia specimens were too thin (20 microns) to permit sufficient attenuation in the integrating spheres measurement, and the determination of μ_s’ and thus μ_s was only possible for Acetobacter. After determining the anisotropy, a value of μ_s=75 cm^-1 was determined at 457 nm. By comparison, a turbid tissue such as skin is characterized by values ~100–200 cm^-1. From these measurements we conclude that this cellulose does form a scattering environment. Similarly, this scattering anisotropy is comparable to that of highly ordered tissues such as tendon. The absorption coefficients were less than 1 cm^-1.

3.2 Directionality of detected SHG

As described in the Introduction, SHG detected in the backwards direction can arise from direct coherent emission from small fibrils, or from forward directed SHG that undergoes multiple scattering events resulting in an incoherent backward component. Here we show that the SHG contrast in cellulose matrices is consistent with contributions from both mechanisms, and that the relative contributions display a depth-dependence. The coherent backwards emission can result in the observation of different fibril morphologies of the forward and backwards channels. This is because the forward SHG contrast can display enhanced intensity from thicker or parallel-overlapped fibrils due to constructive interference between the signals emanating from them. Backscattered SHG from such fibrils may appear with lower intensity due to incomplete destructive interference. This has also been demonstrated by Xie and coworkers for the analogous case of Coherent Anti-Stokes Raman Scattering (CARS) imaging in tissue culture cells.8 We first show this behavior occurs in Valonia, where these specimens have insufficient thickness (~50 microns) to produce multiple scattering with high probability. Thus the coherent backwards component dominates in this material. Representative images of the forward and backwards channels are shown in Figure 2(a) and 2(b) respectively. It is seen that the backwards channel reveals smaller, segmented fibrils, whereas these fibrils in the forward channel have a continuous appearance. In this case, the backwards signal likely arises from spatially varying incomplete destructive interference along the length of a fibril due to local changes in thickness or density of glucan chains. This is consistent with the observations of Williams et al3 where they reported that immature rat tail tendon fibrils with local size variations were more evident in the backwards direction, whereas the observed morphology of mature, larger fibrils was more similar in the two channels.

 

Fig. 2. Forward (a) and Backwards (b) images of Valonia at an image depth of 10 microns. The backwards channel has smaller, more segmented fibrils. The 2 color overlap, where magenta and green are the forward and backward channels, respectively are shown in raw contrast in (c) and the forward channel multiplied by 3 in (d) to reveal weaker features. Scale bar=10 microns

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Inspection of the 2- color overlap in Fig. 2(c) reveals some features that appear only in the backwards channel, suggesting a measured value for the F/B ratio of less than unity. This arises in part due to the limited range dynamic range in the backwards channel, analogous to that pointed out by Tai et al21 on SHG imaging of skin. If the contrast level of the forward signal is multiplied by 3 fold (Fig 2(d)) such that the brighter features become saturated, the same fibrils are observed in both channels. It would appear to be physically unreasonable than an initial F/B<1 can occur in the SHG process, however, such a measured value this can result from reflection or scattering events following the generation. While we pointed out above that the Valonia had insufficient thickness (10’s of microns) to support scattering events, we must consider that the scattering coefficient μ_s is an ensemble averaged value. Thus in an inhomogeneous tissue such as cellulose, μ_s is highly averaged over denser and less dense regions. For Valonia (Fig 2(c)) and Acetobacter (not shown) we note that fibrils that appear brighter in the backwards channel occur in regions of locally high density. We then suggest that propagation of the SHG through these regions can result in scattering events, such that a portion of the forward directed intensity then contributes to the observed backwards signal, resulting in a measured F/B value of less than unity. While not explicitly discussed, this effect was also seen by Williams et al3 where brighter spots were observed in the backwards channel in locally dense regions.

While this work on collagen showed conclusively the size and shape dependence of the forward and backwards components, only this coherent aspect of the emission was considered, i.e no investigation of the multiple scattered component or depth dependence was attempted. Here we investigate the multiple scattered component of the backwards signal in cellulose matrices. We determined the scattering coefficient of Acetobacter to be 75 cm^-1. Thus photon propagation through a specimen of thickness 300– 500 microns should result in multiple scattering events as this corresponds to a mean

 

Fig. 3. SHG images of Acetobacter at depths of 5 (a,b) and 200 microns (c,d) where the left and right panels are the forward and backwards channels, respectively. The arrows in (a) and ( b) denote the same fibrils. Field size=50 microns.

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free path (~1/μ_s) of ~135 microns. While we observed that coherent backwards SHG reveals fibrils of different morphology than the forward component, backwards collected contrast from fibrils arising from multiple scattering (incoherent component) of initially forward directed photons would be expected to have the same morphology as the forward channel but appear with lower intensity. Since the Valonia specimens lack sufficient thickness to display significant multiple scattering, we compared the morphology of the observed fibrils in forward and backwards SHG contrast in Acetobacter at depths between 5 and 500 microns.

Typical forward and backwards SHG images of single optical sections at depths of 5 μm and 200 μm are shown in Fig. 3(a,b) and Fig. 3(c,d), respectively, where the field sizes are 50 microns. Similar to Valonia, in the backwards channel the fibrils near the surface are smaller, more segmented and show punctuate spots. By contrast, the forward signal is comprised of more continuous fibrils. As an example, the arrows in Fig. 3(a) and 3(b) denote the same regions in the matrix. The images in 3(c) and 3(d) were taken at 200 microns into the tissue and are deeper than one MFP and should contain a scattered component. While the backwards signal is much weaker than it is that near the surface, the observed contrast is more similar to that of the forward channel. While some smaller spots can still be seen, the fibrils now appear more continuous. Given the clear morphological differences in the two channels near the top of the specimen, this similarity at a depth greater than one mean free path is indicative of a multiple scattered component of the forward signal contributing to the total backwards intensity. This similarity in the morphology is continued to be observed at depths beyond this point as well (not shown). These images suggest that the backwards signal near the surface is dominated by the coherent component, and that deep into the tissue results from a mixing of the coherent and multiple scattered components. The measured anisotropy, g, of 0.94 suggests the forward channel consists largely, but not exclusively of the coherent component.

We can further investigate this scenario by examining the ratio of the forward and backwards channels as a function of the depth into the Acetobacter, where this dependence is plotted in Figure 4. These values were obtained by integrating the entire intensity in the field and were repeated for many fields. Inspection of Fig. 4 reveals two distinct slopes of the F/B with a change occurring at about 40 microns. This result is observed in all stacks and it is possible that near the surface this lower F/B ratio is due to a greater contribution of the direct coherent backwards SHG emission. This suggestion is consistent with the appearance of smaller fibrils in the backwards channel at imaging depths near the surface. It should be noted that while infinitely thin fibrils would have an initial F/B of unity for the coherent component, a measured F/B value of less than one would be obtained due to the scattering losses upon propagation through the 500 micron depth. We have verified this trend through Monte Carlo simulations (discussed further below). In the current case, however, the average widths of the Acetobacter fibrils are 75 nm, or about λ/6, and a higher initial ratio than 1-1 for the coherent component would be expected (estimated to be 4:1 below). Thus the measured F/B of about unity at the surface arises from losses and does not represent the initial distribution of coherent emission.

 

Fig. 4. Forward vs Backward SHG ratio of Acetobacter as a function of depth into the specimen. The arrow denotes a change in slope.

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The change in slope beginning at about 40 microns of depth and continuing through the entire thickness of the specimen can be attributed to the increased probability at these depths that the initially produced SHG photons undergo scattering collisions at depths approaching and beyond one MFP. The observations are also consistent with the near constant slope in this region of depths, where the F/B increases from 2.3 to 6.2. This is because, based on photon diffusion theory, at least one transport MFP is required between the location of the emitted photon to the forward boundary of the specimen for efficient multiple scattering to occur.10 Thus at increasing focal depths, the probability of scattering collisions is decreased as the exit is approached and the F/B ratio must therefore increase. In addition, at all depths before the exit surface materials of lower scattering coefficient will have a higher F/B than those with larger μ_s since the MFP is longer, and scattering collisions are less probable. As shown on Figure 5, we have verified these probabilities for the 450 nm SHG wavelengths by Monte Carlo simulations for a range of 10 fold in the scattering coefficient (10–100 cm^-1) at constant g=0.94. We find that at the lower range, corresponding to a mean free path of 1 mm (10 cm_-1), the SHG is very highly forward directed and there is little to no multiple scattered component. Note that in this model for the F/B ratios for all scattering coefficients all must converge at the exit surface, as no depth is available for scattering. It must be further noted that this specific simulation is based on photon diffusion and only considers the propagation of photons produced in the forward direction, i.e. the coherent part of the backwards emission is not yet taken into consideration (below we will also heuristically consider this aspect of the emission).

 

Fig. 5. Monte Carlo simulations of the F/B as a function of depth for scattering coefficients μ_s 10–100 cm^-1, where g was held at 0.94 for all of the simulations.

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Next we examine the resulting simulation for the specific case of our specimen with scattering parameter μ_s=75 cm^-1 and g=0.94 (blue diamonds in Figure 5). Our simulation overestimated the magnitude of the F/B as it is based on photon diffusion and does not consider the direct backwards coherent SHG. However, if we consider the region of the plot from 40 microns through 500 microns, where similar morphology of the fibrils in both channels is also observed (see Figure 3), we find a comparable increase of ~2 fold in the F/B as also seen in the experimental data plotted in Figure 4. The good agreement for slope as a function of excitation depth between simulated and experimental F/B supports the argument that the depth dependence is driven by multiple scattering. We can obtain an estimate of initially emitted forwards and backwards components by varying these conditions in a series of simulations and to attempt to match the F/B plot shown in Figure 4. We find that initial forward and backwards fractions of 0.8 and 0.2, respectively, result in an increase in the F/B of 2–4 over the range of 50–500 microns (not shown), approximating the trend in the experimental data. In these simulations we also observe that the backwards channel becomes increasingly incoherent with increasing depth.

We note that this increase in F/B as a function of depth into the specimen will be observed for any scattering material of sufficient thickness to support multiple scattering collisions. Additionally, the propagation of a photon of a given wavelength will be independent of the contrast mechanism that created it. To investigate this for the case of fluorescence we attempted to image fluorescent beads (emitting at the same wavelength as the SHG) embedded in the cellulose matrix. We were not able to inject beads into the cellulose, but we placed beads in between several layers of Acetobacter and we observed a similar F/B (7 fold increase through the same 500 microns depth) as that of the SHG.

3.3 Polarization dependencies and SHG signal anisotropy

As we have previously suggested1, 4 much of the potential power of SHG imaging lies in polarization analysis, both in terms of the dependence of the SHG intensity on the laser polarization as well as the polarization anisotropy of the signal. It is conceivable that the structural information carried in the forward SHG signal might be lost or at least deteriorated in the backward signal due to multiple scattering events. This outcome would somewhat diminish the impact of SHG imaging for some clinical applications, as the polarization data may well encode diagnostic information. Here we investigate these issues by characterizing the forward and backward polarization profiles for both Acetobacter and Valonia fibrils.

First we consider the SHG intensity dependence on the laser polarization. We perform this analysis for individual fibrils at high zoom (8x). As opposed to averaging intensities for the whole field of view this approach reduces the undesired contributions from orthogonally oriented fibrils in adjacent layers (see Fig 1(a)). Single fibrils were chosen that displayed similar morphology in the forwards and backwards channels. These were further chosen such that the orientation was parallel to the primary direction of the fibrils in that field of view. At fixed z positions, we simultaneously acquired forward and backward SHG images at 4° steps through 180° of rotation. For the case of the dipole moment lying parallel to the fiber axis, the SHG intensity profile as a function of polarization angle θ will exhibit a sinusoidal pattern with a period of 180 degrees where the maxima and minima occur at 0 and 90 degrees, respectively. The results (blue square icons) for Valonia and Acetobacter along with the fit to the expected cos²θ function are shown in Fig 6(a) and Fig. 6(b) respectively, excellent agreement is observed. The high extinction at 90 degrees points to the importance of performing polarization analysis on an individual fibril basis. By contrast, a much poorer fit was observed when we previously measured this dependence from entire fields of view.16 The fit is not quite as good for Acetobacter, as it is more difficult to isolate fibrils without contributions from neighboring fibrils.

We extend this analysis to the polarization profiles for the backwards collected SHG as well (Fig. 6(a), red circles). We observe the same the dependence on the laser polarization, with the same maxima and minima. Additionally, the overlap between the two channels is excellent. We have also performed these measurements on smaller features in Valonia that only were revealed in the backwards channel. These fibrils also display the same polarization dependence (not shown). We have previously shown that analysis of this plot can be fit to provide the angle between the dipole moment and symmetry axis of the fiber.4 From these data on the cellulose specimens, we conclude that this information is also attainable in both the forward and backwards channels. Furthermore, we have performed thee measurements in Acetobacter at several hundred microns into the specimen and observed the same polarization dependence, indicating that these measurements can be performed in a scattering environment without loss of information content. We note that this facilitated by the use of the 900 nm laser fundamental wavelength where μ_s=12 cm^-1.

 

Fig. 6 Polarization dependence of the forward and backwards SHG intensity in a) Valonia and b) Acetobacter. The solid line is the fit to the expected cos²θ function. This plot indicates the dipole moment is parallel to the fiber axis for both channels.

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A related question is whether the SHG signal anisotropy. is retained in these scattering media. We previously showed for collagen in thin fish scales (~30 microns) that the polarization of the forward directed signal was primarily aligned parallel to that of the laser, with anisotropy parameter β of 0.7. 1 Please note that this signal anisotropy is independent of the scattering anisotropy g described above. Here we investigate the forward and backwards anisotropy in Acetobacter specimens at depths up to several hundred microns to determine the effect of scattering events on the polarization state of the SHG signal following propagation through the tissue. To determine this, images of single x-y optical sections at preset z positions were taken with fixed linear input polarization. Each section was imaged twice (Zoom 8x) with the polarizers oriented parallel and then perpendicular to the laser polarization. The SHG signal anisotropy parameter β was calculated from individual fibril analysis by Equation 2:

where I_par and I_orth are intensities of SHG signals polarized parallel and orthogonal to the polarization of excitation laser. This parameter can vary between -0.5 and 1 with a value of 0 representing the isotropic situation where I_par and I_orth are equal. In principle, any decrease of β relative to the forward channel, and/or with increasing depth would suggest depolarization of the SHG signal, the laser excitation, or both. However, the data in Fig. 6 suggests that little depolarization of the excitation occurred.

The depth dependence of the anisotropy parameter for Acetobacter for the forward and backward channels is plotted in Fig. 7, where the error bars represent the standard deviation over 10 fibrils. We observe that the forward SHG is more highly polarized parallel to the laser polarization, where β has an average value of 0.7±0.1 as opposed to 0.5±0.1 for backscattered signal. Additionally, the forward directed shows a slight increase in anisotropy with increasing depth into the specimen, where β ranges from 0.62 to 0.74. This suggests the forward directed signal remains largely coherent with a small incoherent component, as is also borne out by the high value of the scattering anisotropy g=0.94. The slight increase is consistent with an increase in the coherence due to the decreased probability of scattering collisions as the generation plane approaches the exit surface. The anisotropy more markedly decreases for the backwards component at points deeper into the Acetobacter, as would be expected for the signal that undergoes multiple scattering events and becomes increasingly incoherent. By contrast, the thin (~20 microns) Valonia specimens, which display essentially only direct backwards SHG emission, have similar initial scattering anisotropy, g, were characterized by β of near unity in both channels. This further supports the conclusion that the lower anisotropy in the 500 micron thick Acetobacter is in fact due to scattering. We also note that the Valonia data is analogous to the findings of Williams et al,3 where they also observed similar anisotropies when comparing the coherent forwards and backwards emission of collagen fibrils in tendon.

 

Fig. 7. Anisotropy parameters β calculated for forward (blue) and backscattered (red) SHG as a function of depths in Acetobacter cellulose.

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It should be noted that when averaging intensities over the whole image, rather than making the measurement on individual fibrils, much lower anisotropy parameters (0.5 and 0.4 for forward and backward, respectively; data not shown) are obtained. Thus, similar to the data in Figure 6, these results point out the importance of measuring polarization profiles on individual fibrils, as averaging over larger areas results in a loss of information due to distribution of orientation of fibrils in the specimen.

4. Conclusions

In summary, we investigated the emission direction and polarization profiles of SHG from highly scattering cellulose specimens. We observe that the backwards contrast in the SHG image is comprised of direct emission from smaller fibrils, as well as a component arising from multiple scattering of the forward directed signal. Furthermore, this mixing is depth dependent, where the coherence of the backwards signal decreases at greater focal depths into the specimen. This is borne out by morphological comparisons as well as analysis of the depth dependence of the forward/backwards ratio. The latter was also compared to Monte Carlo simulations based on our measured scattering parameters in these specimens, and yields a similar depth dependent slope of the F/B ratio. We also find that polarization of the SHG signal is largely preserved in both forward and backscattered SHG originated as deep as 500 μm. Because the SHG polarization profiles contain information on the structural aspects of the matrix, retention of this information in highly scattering media suggests great promise for future biomedical and clinical SHG imaging applications.