Stokes parameters imaging of light reflected from biological tissue using polarization-sensitive optical coherence tomography

Polarization sensitive optical coherence tomography (PS-OCT) was used to determine the depth resolved Stokes parameters of light backscattered from highly scattering biological samples. Through simultaneous detection of the amplitude and relative phase of signal fringes in orthogonal polarization states formed by interference of light backscattered from turbid media and a mirror in the reference arm of a Michelson interferometer, changes in the Stokes parameters due to the optical phase delay between light propagating along the fast and slow axes of birefringent media were measured. Inasmuch as fibrous structures in many biological tissues influence the polarization state of light backscattered, PS-OCT is a potentially useful technique to image the structural properties of turbid biological materials. The method can also be applied to the investigation of birefringent properties in highly scattering materials such as ceramics and crystals.


INTRODUCTION
First reported in the field of fiber optics,'3 optical coherence tomography (OCT) has become an important high resolution technique for biomedical imaging. OCT utilizes a Michelson interferometer with a broadband source with high spatial coherence to measure light backscattered from turbid media with high spatial resolution ( 10 ,um) and sensitivity (>100 dB). 4 In general, OCT images display the depth resolved magnitude of backscattered light. Except for an early study by Hee et al.,5 the polarized nature of light was not considered until recently when depth resolved birefringence images of bovine tendon6'7 and myocardium8 were reported. In this letter we present an analysis to determine the depth resolved Stokes parameters of light backscattered from turbid media using polarization sensitive optical coherence tomography (PS-OCT). Compared to previous methods, where only the fringe intensity in two orthogonal polarization states was used in the signal analysis,68 the present work incorporates the phase relationship between interference fringes in each polarization channel to characterize completely the polarization state. Analysis of depth resolved changes in the Stokes parameters of light backscattered from the sample provides a means to determine spatial variations in sample birefringence and corresponding structural properties. Figure 1 shows a schematic of the PS-OCT system used in our experiments. Light from a superluminescent diode (0.8 mW, A0 = 856 rim and spectral FWHM &\ = 25 nm) was linearly polarized. A quarter wave plate (QWP) positioned in the reference path produced linearly polarized light at 45° with respect to the vertical after double passage. The intensity noise was reduced by a factor of 50 by placing a neutral density filter in the reference path.9 A second QWP in the sample path produced circularly polarized light that was focused (f=50 mm) to a spot size of 17im diameter on the sample. After double passage through the QWP, light in the sample arm was in an arbitrary (elliptical) polarization state, determined by the sample birefringence. After recombination in the detection path, the light was split into horizontal and vertical components by a polarizing beamsplitter (PBS) and focused (f=50 mm) on 25 m diameter pinholes placed directly in front of the detectors to detect a single spatial mode. Two dimensional images were formed by lateral movement of the sample at 1 mm/s (x-direction), repeated after each 10 jim incremental longitudinal displacement (z-direction). Active beam focus tracking in the tissue (n = 1 .4) was achieved by translating the PZT retroreflector assembly after each transverse scan. 10 The interference fringe carrier frequency (t..) 6 kllz) was generated by modulating the optical path length of the reference arm over 20 1am with a 50 Hz triangular waveform. An image pixel was calculated using the interference signal recorded over the central 10 ,um of the 20 1um reference arm modulation. Transverse and longitudinal pixel dimensions in the images were 1 0 tm by 10 1tm.

THEORY
An expression for the depth resolved Stokes parameters of light backscattered from a turbid birefringent sampie was derived in terms of the measured amplitude and relative phase of the interference fringes in orthogonal polarization states.11 In our analysis, the electric fields are represented in their complex analytic form,'2 From the Wiener-Khinchine theorem, it follows (ë*(k)ë(kI)) = S(k)5(kk'), which defines in terms of the spectral density S(k) of the source, and angular brackets denote ensemble averaging. Since light from the reference arm was split equally into the horizontal and vertical polarization states, the electric field in the reference arm is given by Ex,y(Zr) = L: exp(-2ikzr)dk (1) with Zr the length of the reference arm. The electric field in the sample arm is given by, (2) where \/ikG;-) describes the reflectivity at depth z and the attenuation of the coherent beam by scattering, and a(k, z) characterizes the polarization state of light backscattered from depth z8, with a*(k, z5).O(k, z8) = 1 . Following the definitions in Mandel and Wolf13 the Stokes parameters s2 with j = 0, 1, 2, 3 of the electric field E(z8) are

RESULTS
OCT images of the Stokes parameters were formed by grayscale coding 20 log SO(Z8)from 0 to -48 dB, where the 0 dB level corresponded to the maximum signal in an image, and by grayscale coding the polarization state parameters Si , S2 and s3 normalized on the intensity s0 from 1 to -1 , and P from 1 to 0. Contour lines indicating 1/3 and -1/3 fractions of the normalized parameters Si , S2 and S3 were calculated after low pass filtering by convolving the images with a Gaussian filter of 4 x 4 pixels and overlaid with the original image. Figures 2 and 3 show the four Stokes parameters, measured in ex vivo rat skeletal muscle and bone, respectively. In our experimental configuration, the image of the Stokes parameter S3 5 similar to that obtained by grayscale coding the birefringence induced phase retardation, q = arctan y1I(z)/I(z) k0zS, as was done previously,5'7'8 with the exact relationship being s3/so = cos2çb. The birefringence in Figure 2 is attributed to the high structural order (anisotropy) of skeletal muscle fibers. Several periods of Si, S2 and s3, cycling back and forth between 1 and -1, are observed. The birefringence S was determined by measuring the distance of a full S3 period, which corresponds to a phase retardation of r = k0z6, giving 6 = 2.4 x i0. The greater birefringence in skeletal muscle as compared to the myocardium reported by Everett et al.8 is attributed to structural differences. In myocardium, the fibers are oriented in different directions, and not necessarily parallel to the tissue surface. The skeletal muscle imaged in Figure 2 shows a high degree of muscle fiber alignment, the orientation of which can be determined by finding the rotation of the reference frame that minimizes the variance in either .si or S2 . Our analysis of this image gives an angle of _70 with respect to the vertical of one of the optic axes, consistent with a fiber direction that was almost perpendicular to the horizontal scan direction.
In Figure 3 an interesting feature in a portion of the S3 parameter image of ex-vivo rodent bone is the apparent loss of birefringence. However, the s1 parameter image reveals that the predominant orientation of the linear polarization in either of two orthogonal planes is reversed around the region showing the apparent loss of birefringence. The region indicating birefringence loss (s3-image) may represent a transition of the dominant orientation of the optic axis.

DISCUSSION
Determination of the depth resolved Stokes parameters of light backscattered from turbid birefringent media using PS-OCT reveals structural information that can not be determined by previous methods58 that only analyzed the intensity in two orthogonal polarization channels. In a sample wherethe optical axes were constant, the birefringence and axes orientations were determined. A future analysis of the evolution of the Stokes parameters will allow depth resolved determination of the birefringence and changes in the orientation of the optical axes in turbid birefringent media. Also of interest for future study is the parameter P that may reveal information on the presence of multiply scattered light in OCT images through a decrease in the degree of polarization. I Figure 2. PS-OCT images of ex vito rat muscle. 1 mm x 1 mm. pixel size 10 irn x 10 sum. From left to right, the Stokes parameters s1. S2. S3 and degree of polarization P. The gray scale to the right gives the magnitude of signals, ranging from 0 to -48 dB for s0, from 1 to -1 for .s. s2 and S3, arid from 1 to U for P. White lines in images s1, s2 and .53 are contours at 1/3 (white to gray transition) and -1/3 (gray to black transition) signal levels. respectively. Figure 3. PS-OCT images of cx vivo rat bone. 1 mm x 1 mm, pixel size 10 /tm x 10 pm. From left to right, the Stokes parameters s0, Si. and s3. and degree of polarization P. The gray scale to the right gives the magnitude of signals. ranging from 0 to -48 dB for o, from 1 to -1 for Si, s2 and 83, and from 1 to 0 for P. White lines in images i, 2 and S3 are contours at 1/3 (white to gray transition) and -1/3 (gray to black transition) signal levels. respectively.