Wavelength-dependent, polarized, elastic-scatter spectra of tissue phantoms and in vitro tissue are presented. These measurements are shown to be sensitive to very small changes in composition of the scattering medium. A simple physical explanation of the wavelength-dependent polarization phenomena observed for media consisting only of spherical particles is given and the relevance of wavelength-dependent, polarized, elastic-scatter spectra to in vivo applications is discussed.
© 1999 Optical Society of America
Diagnosis of disease by a pathologist is frequently based on changes in the morphological structure of tissue. Therefore, other methods of interrogating tissue that are sensitive to morphological structure may also be useful for diagnosing diseases such as cancer. The transport of light through tissue is one such method which lends itself to noninvasive implementation. Structures in tissue strongly scatter visible and NIR light, therefore light transport should depend on the morphological features of tissue.
There are several methods of measuring light transmission through tissue that are sensitive to scattering properties1(see footnote). For application to tissue, backscattering geometries can be used so that the measurement is noninvasive. Typically light is incident on the tissue surface at one location and light which has traveled through the tissue is collected at a lateral position. Methods for quantitatively determining the reduced scattering coefficient, μs′, have been developed for backscattering measurement geometries in which the source and detector locations are sufficiently separated such that the diffusion approximation holds1–3. These measurements give important quantitative information but they are not sensitive to the nuances of the scattering properties of tissue such as the separate values of μs and g or details of the phase function P(θ). When the source and detector are in closer proximity it is expected that the collected light will depend on the details of the scattering properties4 and therefore be more sensitive to small changes in scattering properties.
In addition to placing the source and detector in close proximity, another method of increasing the sensitivity of cw light transport to morphological features may be to measure additional parameters such as polarization properties. The aim of this work is to investigate polarized, wavelength-dependent measurements as a method for characterizing scattering media, and to understand the physical principles behind the wavelength-dependent polarization intensities which are observed. Our results are discussed in the context of previously published work on polarized diffuse backscattering measurements of turbid media in Section 5.
2.1 Tissue phantoms
Suspensions of polystyrene spheres (Duke Scientific, Palo Alto, CA) were used as tissue phantoms. Polystyrene spheres are a very reproducible system for developing and testing a new experimental method. In order to very roughly simulate tissue, we used mixtures of small and large spheres and varied their relative concentrations. In all cases the number density of the small (0.505 ± 0.0094 μm diameter) spheres was much greater than the number density of the large (8.1 ± 1.3 μm diameter) spheres. The reduced scattering coefficient was between 5.1 and 5.3 cm-1 for the data in figures 2–4 and 9, and between 10.3 and 10.6 cm-1 for the data in figure 5. As an absorber blue dye (Direct Blue Dye #71, CAS #4399-55-7) was added.
2.2 Measurement methods
Polarization sensitive light transport measurements were made by placing a fiber optic probe on the surface of the tissue or tissue phantom to be measured. The fiber-optic probe used for this work had a cross shaped geometry as shown in Fig. 1. The center fiber was used for light delivery while the four fibers arranged in a cross through the delivery fiber collected light which had been scattered within the turbid media. From symmetry considerations, fiber 1 measures the same signal as fiber 3. Similarly, fiber 2 measures the same signal as fiber 4. All five fibers in this probe had a 200 μm diameter core, a 400 μm buffer+core diameter and the numerical aperture was 0.22. In order to make the polarized measurements, a linear polarizer (Tech spec linear polarizing laminated film, Edmund Scientific, Barrington, NJ) was placed on the surface of the probe. The polarizer was an integral part of a cap that was firmly attached to the end of the probe. Optical coupling between the fiber optics and the polarizer was assured by using Optical Couplant (Dow Corning Q2-3067, Midland, Mi) between the fibers and the polarizer. The wavelength dependent properties of the polarizer were characterized. The ratio of transmission through crossed polarizers to transmission through parallel polarizers was less than 0.009 between 500 and 683 nm, increased to a value of 0.024 at 700 nm, and by 900 nm was 1.0. Fig. 1 shows the orientation of the electric field transmitted by the polarizer with regards to the orientation of the probe. The thickness of the polarizer was 0.75 mm. Due to the fact that the spacing between the fibers (side-to-side) was 200 μm, specular reflectance off of the polarizer to scattering medium interface was a concern. This specular reflectance was measured in nanopure water and subtracted from the signal measured from the tissue and tissue phantoms. The specular reflectance was less than 4% of the intensity measured from polystyrene sphere suspensions.
In addition to the fiber optic probe, the measurement system was composed of a Tungsten lamp (Gilway Technical Lamp L1041, Woburn, Ma) for illumination through the delivery optical fiber, a spectrograph (Acton 275i, Acton Research Corp, Acton, Ma) for dispersion of the collected light and a TE cooled CCD array (Princeton, Instruments, Trenton, NJ) for light detection. One axis of the CCD camera corresponded to the four different collection fibers, while the other axis was wavelength. Consequently, the light intensity from all four fibers was measured simultaneously. Approximately 1.2 mW of light was incident on the sample through the delivery fiber. A measurement of a diffusely reflecting material (Spectralon, Labsphere, Inc, N. Sutton NH) was made and used to account for the wavelength dependent efficiencies of the lamp, the fibers, the grating, and the detector.
2.3 In vitro measurements of tissue
Chicken breast and chicken liver were obtained from a local grocery store. Polarized, wavelength dependent elastic-scatter measurements were made by placing the probe shown schematically in Fig. 1 in direct contact with the tissue.
Polarization images were obtained by methods similar to those described by Mehrübeoglu et al.5 Briefly, a linearly polarized laser beam (633 nm, 1 mm diameter) was incident on the center of the tissue to be examined. An area centered on the laser illumination spot was then imaged onto a CCD camera through a linear polarizer. The data was smoothed once by averaging each data point with its eight neighbors. All measurements were divided by an image taken with no polarizers present.
2.4 Data fitting
Data was fit by using a Levenberg-Marquart routine to search for coefficient values which minimizedχ2.
3.1 Measurements on polystyrene spheres
Polarized, wavelength dependent measurements of polystyrene spheres were made in order to 1) determine if these measurements can differentiate similar scattering media, 2) understand the effects of a small, possibly unknown absorption on the measurements, and 3) provide a well-characterized system with which to obtain a fundamental understanding of the polarized wavelength-dependent measurements.
For the polarized measurements, fibers 1 and 3 measure a different signal than fibers 2 and 4. We define a polarization ratio, R(λ), in Eq. 1 where I1 - I4 are the intensities of light collected by fibers 1 - 4 respectively. This ratio is plotted in Fig. 2 where the areas under the curve from 500 to 700 nm were made equal for all of the data in order to emphasize wavelength dependent effects. The width of the curves at each point is the standard deviation calculated from five independent measurements of each suspension. The ratio, R(λ), is shown for one measurement without the polarizer on the probe. The deviation of R(λ) from a straight line at 1.0 for this measurement is probably due to small differences in the distances of the collection fibers from the light delivery fiber.
The polarization ratios for the polarized measurements of polystyrene spheres shown in Fig. 2 have a dip near 525 nm and a peak near 625 nm. The general shape of R(λ) is discussed in detail in Section 4. Here it is interesting to note that the exact shape of the curves depends on the amount of 8.1 μm polystyrene spheres which are present. At both 525 nm and 625 nm, the change in the polarization ratios upon addition of 0.005% by number 8.1 μm spheres is greater than the standard deviations of the measurements.
An absolute measurement of the polarization ratio rather than a relative measurement can be obtained by taking advantage of the fact that past 900 nm, the polarizer no longer polarizes the light. At wavelengths longer than 900 nm the signal obtained on all four fibers should theoretically be identical if the collection efficiencies of all four fibers is the same. This means that R(λ) should have a value of 1.0 for wavelengths longer than 900 nm. This fact can be used to account for variations in collection efficiencies of the fibers caused by effects such as small differences in the polish. The polarization ratios shown in Fig. 3 were multiplied by a constant in order to have a value of 1.0 at wavelengths between 965 and 1000 nm. This figure shows that as the concentration of 8.1 μm polystyrene spheres increases, the polarization ratio decreases. As in Fig. 2 error bars on the measurements are included and are the standard deviation for five measurements of each solution. Fig. 3 demonstrates that absolute measurement of the R(λ) provides improved discrimination over relative measurement of R(λ) for turbid media with slightly different scattering properties.
Unpolarized measurements of the suspensions were also performed. The results are shown in Fig. 4 where the areas under the curve were made equal from 500 to 700 nm.
To quantitate the relative ability of the polarized and unpolarized wavelength dependent measurements to differentiate scattering media, the percent change in signal upon addition of 8.1 μm diameter polystyrene spheres to the suspension of 0.505 μm diameter polystyrene spheres was measured in the wavelength region showing the greatest differentiation. For the relative (Fig. 2) and absolute (Fig. 3) measurements of R(λ), the change in signal in the wavelength range from 624 to 627 nm was computed and the results are shown in columns 2 and 3 of Table 1. There is a 1% and 2.9% change for the relative and absolute measurements of R(λ) respectively, when the fraction of 8.1 μm polystyrene spheres is increased from 0 to 0.5×10-4. For the unpolarized measurements the percent change in R(λ) was calculated from 500 to 503 nm (column 5 of Table 1). There is a 0.9% change when the fraction of 8.1 μm polystyrene spheres is increased from 0 to 0.5×10-4. Clearly the absolute measurements of R(λ) show the greatest sensitivity to the addition of 8.1 μm diameter spheres. However, these measurements also have larger errors than the unpolarized measurements. These errors can be reduced assuming that the noise at different wavelengths is uncorrelated. The average change in signal over a wider range of wavelengths for the asolute measurements of R(λ) is shown in column 4. There is very little change in the sensitivity (a 10% decrease), but a significant change in the noise. A similar widening of the range used for the unpolarized measurements leads to a 30% decrease in sensitivity.
All of the results presented in Figs.2–4 are measurements performed in the absence of absorbance. We wish to address the general case of measurements in the presence of a small but unknown absorbance as might occur in the NIR region of tissue. Both polarized and unpolarized measurements were made in the presence of a small amount of blue dye. The goal was to determine the effect of a small absorption on both the polarized and unpolarized measurements. The blue curve in Fig. 5a is a ratio of unpolarized measurements with and without the addition of blue dye for the solution. For comparison, the wavelength dependence of the absorption coefficient in the suspension containing blue dye is shown in Fig. 5b. Clearly, absorption has a strong effect on the unpolarized measurements. The effect of absorption on the polarization ratio, R(λ), is much less pronounced. The red curve in Fig. 5a is a division of the polarization ratio without blue dye by the polarization ratio determined with blue dye present. Comparison of Figs. 5a and 5b demonstrate that an absorption coefficient of 0.3 cm-1 has only a 3% effect on the measured polarization ratio.
An important question is whether the polarization patterns which have been observed in polystyrene spheres and in cell suspensions are present in a wide variety of tissues. Polarization patterns were observed on the retina many years ago6. An image of the relative polarization for human skin has also been reported, although the contrast is weak7. Figs. 6a and 6b show polarization images (i.e. images obtained with polarizers present divided by images with no polarizers present) of liver tissue. The images are qualitatively similar to those which have been observed for polystyrene sphere suspensions, cell suspensions and on the surface of the retina8–10. For chicken breast tissue the images showed less contrast and were distorted by the fact that light propagation is not isotropic in chicken breast (as discussed below).
Polarized, wavelength-dependent elastic-scatter measurements were also made for chicken liver and chicken breast and the results are shown in Fig. 7. The data were normalized to one in the wavelength range 965 to 1000 nm to account for differences in efficiencies of the collection fibers. The polarization ratios can then be compared at wavelengths below 700 nm. Clearly, the polarization ratio is greater for the liver tissue than for breast tissue.
For the chicken breast, measurements were made in two orientations; one with fibers 1 and 3 lined up along the axis of the fibers in the tissue, and the other with the fiber-optic probe rotated 90 degrees. That the polarization ratio is different for these two geometries is not surprising as an anisotropy in the reduced scattering coefficient of chicken breast tissue was previously reported11.
4. Physical explanation of R(λ)
One goal of making measurements of polystyrene spheres was to develop a simple physical understanding of polarization-sensitive wavelength-dependent measurements of light transport. Before beginning a physical explanation of the wavelength-dependent measurements, we first describe a simple model that explains the relevant features of the polarization images obtained at a single wavelength with linear parallel polarizers. (A discussion of similar models is given in Section 5.2) This explanation of the features in polarization images at positions that correspond to the locations of collection fibers (when Fig. 1 is superimposed on e.g. Fig. 6a) will facilitate a discussion of the wavelength dependent measurements.
The initial assumptions of the model are:
- Light is incident normal to the surface of the scattering media and the delivery and detection are polarized along the x-axis. This geometry is shown in Fig. 1.
- All of the scattering events for photons collected by fibers 1 and 3 take place in the Y-Z plane and all of the scattering events for photons collected by fibers 2 and 4 take place in the X-Z plane.
- The photons undergo two scattering events before entering a collection fiber.
Phase functions for 633 nm light scattering off of 1.0 μm and 0.01 μm radius polystyrene spheres are shown in Figs. 8a and 8b respectively. Because the incident light is polarized along the x-axis, the relevant phase functions for scattering events in the X-Z and Y-Z planes are P∥ and P⊥, respectively. From examination of Fig. 8b, it is clearly more likely for a photon scattering off of a 0.01 μm radius polystyrene sphere to undergo two 90 degree scattering events in the Y-Z plane than in the X-Z plane. Consequently more photons are collected by fibers 1 and 3 than by fibers 2 and 4 when the scattering suspension consists of 0.01 mm radius spheres. For 1.0 μm radius spheres the relevant phase functions are shown in Fig. 8a and it is expected that the amount of light collected by fibers 1 and 3 would be similar to that collected by fibers 2 and 4. These very qualitative predictions of the amount of light collected by fibers 1 and 3 versus fibers 2 and 4 for relatively large and small spheres are consistent with images obtained by both Hielscher et al.8 and Carswell et al.9 for a wide variety of polystyrene sphere sizes. In reality, all of the photons that are collected do not simply undergo two 90 degree scattering events, rather there is a distribution of scattering events including angles both above and below 90 degrees. The relaxation of assumption 3 does not qualitatively change the results of the model. One would simply expect the difference in the amount of light collected in the two orientations to be smaller because P∥ and P⊥ differ less at angles other than 90 degrees.
The wavelength dependence of the absolute polarization ratios, R(λ), in Fig. 3 can also be understood by examination of the P∥ and P⊥ phase functions. The model is based on the same principles as above. P⊥ controls the scattering of light that can be collected by fibers 1 and 3 and P∥ controls the scattering of light that can be collected by fibers 2 and 4. P⊥ and P∥ are shown in Fig. 9 for 0.505 mm diameter polystyrene spheres at 650 nm. The amount of light collected by each fiber is composed of a part that is the same for all fibers (because many of the scattering events have the same or very similar probabilities for both P∥ and P⊥ phase functions) as well as a part that is different for fibers 1 and 3 than for fibers 2 and 4. For fibers 1 and 3 the amount of collected light is given by Eq. 2. A similar equation applies for fibers 2 and 4 where P⊥ is replaced by P∥. The polarization ratio is then given by Eq. 3 (assuming C1 ∝ μs). θ1 and θ2 define the range of angles for which the probability of scattering is significantly different for P∥ and P⊥. Another way to think about the model is that the first term (of either the numerator or denominator of Eq. 3) represents light which travels by paths that are equally likely in either the Y-Z or the X-Z plane and the second term represents photons paths in which one of the scattering events has a different probability for P⊥ than P∥ phase functions. Obviously, there should be higher order terms, representing photon paths for which several of the scattering events have a different probability for P⊥ than P∥. However, these terms are not necessary to describe the basic physical principles and would add more parameters to the fit.
The data in Fig. 3 for the suspension of 100% 0.505 μm diameter polystyrene spheres was fit to Eq. 3 using the appropriate phase functions for 0.505 μm diameter spheres and the results are presented in Fig. 10. Because, it was not clear exactly what values should be chosen for 81 and 82, these parameters as well as C were varied. The resultant values from the fits are θ1 = 80°, θ2 = 180°, and C = 0.021. From examination of Fig. 9, these values of θ1 and θ2 essentially bracket the range where P⊥ and P∥ are signficantly different. A measurement of absolute R(λ) for 2.02 μm diameter spheres was also fit to Eq.3 and is shown in Fig. 10. This fit gave θ1 = 63°, θ2 = 164°, and C = 0.013. It is a little surprising that θ1 has a value as low as 63°. Nonetheless, θ1 and θ2 again bracket the range where P⊥ and P∥ are signficantly different as can be seen from Fig. 8a.
The model described above is very simple, however it can predict some general features of the polarization ratio. Using the parameters obtained from the fits of the measured polarization ratio for the 0.505 μm polystyrene spheres, the absolute polarization ratio of the for a mix of 0.505 and 8.1 μm diameter spheres was calculated. Specifically the ratio of 8.1 to 0.505 μm diameter spheres was 2.3 × 10-4. The prediction of the model is compared to the measured polarization ratio for this mixture of spheres in Fig. 9. While there are some discrepancies, the general wavelength dependence of the polarization ratio is correctly predicted as is the fact that the magnitude is decreased from that of a pure suspension of 0.505 μm diameter spheres.
5.1 Differentiating scattering media
Polarization ratios, R(λ) are shown in Figs. 2 and 3 for several suspensions of 0.505 μm diameter spheres containing a small number of 8.1 μm diameter spheres. The choice of suspensions containing many more small than large scatterers was motivated by the fact that tissue has been shown to have a distribution of scatterer sizes13 and biological cells generally contain many more small scatterers than large scatterers as evidenced by the power spectrum of index variations14. Furthermore, there is evidence that differences in scattering properties of a pair of tumorigenic and nontumorigenic cells are due to a change in the average size of the scattering centers15. We are, therefore, interested in whether a small change in the relative number of small and large scattering particles can be measured by wavelength-dependent, polarized, light-scattering measurements. Table 1 demonstrates that measurements of the absolute polarization ratio, R(λ), are more sensitive to changes in scattering properties than are unpolarized measurements.
An additional advantage of making polarized measurements is that they are less affected by a small change in absorption than are the unpolarized measurements as is illustrated by Fig. 5.
In Figs. 2–4 error bars are provided which are the standard deviations of multiple measurements. There are also systematic errors in the measurements. Here we discuss these errors and demonstrate that they did not have an effect on the ability of the wavelength dependent measurements to differentiate scattering media. One systematic error is that the collection fibers are not all exactly the same distance from the delivery fiber. This error could cause a slight distortion of the wavelength dependence or a slight change in the amplitude of the absolute measurement of R(λ). The wavelength dependent effect was shown to be <0.9% at 700 nm and <0.4% at wavelengths below 650 nm by the black curve of Fig. 2. This error is not expected to change significantly for the different suspensions which have similar scattering properties. Therefore, it should not have had a signficant effect on the ability of the wavelength-dependent measurements to differentiate scattering media, particularly at wavelengths below 650 nm. The other systematic error is the small amount of light transmitted by the polarizer with a polarization perpendicular to the primary axis. This error is greatest at 700 nm where it causes about 2.4% of the incident light to have the wrong polarization. The real issue is how much light of the wrong polarization is collected. At the positions of our fibers the majority of light reaching the surface will have the same polarization as the incident polarization7. If we estimate that 25% of the light at the position of the collection fibers was polarized perpendicular to the incident polarization, then the amount of collected light is increased 1.3% over what it would be for an ideal polarizer. Of course this error is slightly different for fibers 1 and 3 than for fibers 2 and 4 and it is only this difference that matters because R(λ) is a ratio of intensities. Therefore, we conclude that this systematic error has significantly less than a 1% effect even at its maximum. Finally because it is a systematic error and present in (albeit slightly varying amounts) in all measurements it would not have had a significant effect on using R(λ) to differentiate scattering media.
5.2 A simple physical understanding of polarization effects
Polarization patterns observed due to diffuse backscattering of light from turbid media have intrigued many researchers, and several models to explain these images have been developed. In an early work, Pal and Carswell16 calculated intensities for single scattering events with final polarization both perpendicular and parallel to the incident polarization as a function of the azimuthal angle of the scattering event. From a comparison of these calculations to experimental measurements of backscattering from clouds they concluded that the experimentally observed polarization anisotropy arises from the basic polarization properties of single scattering events. Both Dogariu et al.17 and Dogariu and Asakaru12 describe how geometrical factors of different, planar, two-event scattering trajectories affect the polarization vector of light exiting the medium. In Dogairu et al.17, a Gaussian distributed random variable with a zero mean is introduced to describe the rotation of the electric vector due to nonplanar scattering events and other sources of depolarization. The authors were then able to describe the main features of the polarization patterns they observed for carbonyl iron and cerium oxide particles. Dogairu and Asakura12 take a slightly different approach to describing the patterns that incorporates approximations to an equation that describes depolarization as a function of the number of scattering events for isotropic scatterers. It is interesting that niether of the above two papers use the basic polarization properties of single scattering events, which are described by the P∥ and P⊥, in their models. Rakovic and Kattawar18 have given a mathematically rigorous analysis of double scattering events which qualitatively describes polarization patterns for both parallel and crossed polarizers. Their model does incorporate phase functions for single scattering events. Finally, Monte Carlo simulations based on the single scattering Mueller matrix have been shown to reproduce all 16 elements of the backscattering Mueller matrix from a suspension of polystyrene spheres19.
The model in Section 4 is based on polarization properties of single scattering events as well as geometrical factors. It does not assume a specific number of scattering events. The basic principle of the model is that differences in the amount of light collected by fibers in different locations are due to disparities between the phase functions which govern scattering in the planes containing the fiber of interest, and the delivery fiber (and of course the z axis). For a photon to be collected it must undergo a sequence of scattering events that result in a polarization at the collection fiber which is identical to the polarization at the delivery fiber. Scattering events in a plane will preserve the polarization of the light (assuming spherical scatterers and a non-optically active scattering media). We hypothesize that scattering in planes containing light delivery and collection fibers is the primary mechanism of scattering that results in the contrast between the amount of light collected by fibers 1 and 3 and that collected by fibers 2 and 4. From geometrical considerations we know that the probability distribution governing scattering events in the plane containing fibers 1 and 3 and the z-axis is different than the probability distribution governing scattering events in the plane containing fibers 2 and 4. These probability distributions, P∥ and P⊥ are not different at all angles, but rather differ significantly only over a range of angles θ1 to θ2. We expect that the difference in the amount of collected light should be related to this difference in the P∥ and P⊥ functions. In our model, the collected light is separated into two components; one for photon trajectories which are equally likely for either P∥ or P⊥, and another term for photon paths which include scattering events at angles between θ1 and θ2. An expression for the polarization ratio is given in Eq. 3. Since we did not know the exact values of θ1 and θ2, these parameters were determined by fitting the experimental data. The model describes the experimentally measured data fairly well (see Fig. 10), and the values obtained for θ1, θ2 and C are reasonable in that θ1 and θ2 bracket the range of angles for which P∥ and P⊥ are different, and C is positive.
Within the physical model of Section 4, the decrease of the polarization ratio upon the addition of 8.1 μm spheres to the suspension of 5.1 μm polystyrene spheres (see Fig. 3), can be easily understood. For 8.1 μm polystyrene spheres, P∥ and P⊥ are very similar and the polarization ratio for a suspension of 8.1 μm spheres would be very nearly one. Therefore, as the 8.1 μm diameter spheres are added to the suspension of 5.1 μm polystyrene spheres, the polarization ratio decreases. Using, the values of θ1, θ2 and C obtained for the suspension of 0.505 μm diameter spheres, the decrease upon addition of 8.1 μm diameters spheres was computed and compared to a measurement in Fig. 10.
Based on the fact that θ1 is greater than 60° for both sizes of spheres, the amount of light collected for which the polarization properties are preserved is related to the probability of medium and high angle scattering events. In other words, the wavelength dependence of the polarization ratio is related to the polarization properties of single scattering events at medium to high angles. Scattering at medium and high angles in cell suspensions are believed to be due to scattering from internal organelles13, therefore the polarization ratio should be a function of the morphology of these organelles.
5.3 Polarized diffuse backscattering measurements of tissue
Polarization patterns due to backscattering of light from the retina were observed many years ago6,10. Here, we have shown that polarization images from liver are also easily obtainable. Polarization images of chicken breast tissue were more difficult to obtain presumably because the intrinsic anisotropy of the tissue scattering properties distorts the polarization images.
The wavelength dependent measurements provide a convenient method for determining the absolute value of the polarization ratio as a function of wavelength. Fig. 7 shows that the polarization ratio is significantly larger for liver tissue than for breast tissue. Differences in polarization properties of fat and tumor tissue, and between white and gray matter have also been reported20,21. Earlier measurements of polarized diffuse backscattering images of highly-scattering media have demonstrated that for spherical particles, the polarization ratio (i.e. the ratio of intensities at 0° and 90° in Hielscher et al8) is related to particle size (for suspensions with similar values of μs′. Therefore based on figure 7, the scattering particles in chicken breast are expected to be larger than those in chicken liver, although a better understanding of the relative contributions of particle size and μs′ to R(λ) is needed. Scattering from the liver tissue is likely dominated by scattering from mitochondria22 which are small ellipsoidal organelles with the long axis being on the order of 1 μm. There are a broad range of size scales in muscle, some of them larger than 1 μm.
In the measurements of liver tissue, the polarization ratio increases at the α and β absorption bands of hemoglobin. At these wavelengths, the increased absorption dictates that longer pathlengths are less likely. Therefore, the contribution of light which has had its polarization randomized is decreased resulting in an increased polarization ratio. In chicken breast where the absorption is not so great (although still easily observable in unpolarized elastic-scatter measurements), the absorption is not sufficient to affect the polarization ratio.
5.4 Polarization properties of scattering from non-spherical particles
For spheres, a single scattering event does not change the polarization in the scattering plane. If light is polarized parallel to the scattering plane before the scattering event, it is polarized parallel to the scattering plane after the scattering event. The same is true for light initially polarized perpendicular to the scattering plane. For nonspherical particles, however, a scattering event can change the polarization of the light in the scattering plane23.
In tissue the scattering centers are not perfectly homogeneous, spherical particles. The implications of scattering from inhomogeneous, nonspherical particles on the polarization ratio is not yet understood, although it is being considered as an explanation for polarization effects in optical coherence tomography24. The presence of easily observable polarization patterns that are very similar to those measured for polystyrene sphere suspensions in liver tissue implies that the presence of nonspherical rather than spherical particles is not a major perturbation. However, more work in this area is needed.
6. Summary and Conclusions
A fiber optic probe that should be relatively easy to implement in vivo has been designed for measuring polarization properties of highly-scattering media. Wavelength dependent measurements of diffuse backscattering with parallel polarization for light delivery and detection are presented. A polarization ratio is defined as the ratio of light collected by fibers at 90° and 0°, where the delivery fiber is at the origin and 0° is defined by the oscillation direction of the electric field passed by the polarizer. The wavelength dependence of the polarization ratio can be measured in an absolute manner by taking advantage of the fact that the polarizer used did not polarize light with a wavelength greater than 900 nm. This polarization ratio provides better sensitivity than unpolarized measurements and can be used to distinguish very similar suspensions of polystyrene spheres containing slightly different amounts of small and large spheres. In addition, it is found that the polarization ratio is very different for liver and chicken tissue. Finally, the polarization ratio was found to be only weakly dependent on the absorption properties of the medium and therefore may be particularly useful for comparing scattering media with slightly different absorption properties.
A very simple model based on the polarization properties of single scattering events of spheres reproduces the experimentally determined polarization ratio reasonably well. Based on this model it is inferred the probability of scattering events at medium and large angles controls the amount of light that is collected with its polarization properties preserved. Since scattering from biological cells at these angles is believed to be due to scattering from internal structures of the cells, the polarization ratio should be sensitive to changes in the internal morphology of biological cells.
We thank James P. Freyer and Murat Canpolat for useful discussions. This work was funded by NIH grant R01 CA71898.
|1.||The scattering properties used in this paper are; the scattering coefficient μs, which is the inverse of the mean free path between scattering events; the phase function P(θ) which is the probablity of scattering through an angle θ; and the reduced scattering coefficient μs′ = μs(1-g) where g is the average cosine of the scattering angle, <cos θ>.|
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