Birefringence imaging in biological tissue using polarization sensitive optical coherent tomography

[0002] The present application is a continuation in part of provisional application Ser. No. 60/049371 filed on Jun. 12, 1997 entitled Two Dimensional Birefringence Imaging And Biological Tissue Using Polarization Sensitive Optical Coherence Tomography.

[0004] 1. Field of the Invention

[0005] The invention relates to the field of optical imaging and in particular to the use of optical polarizations to create tomographic images.

[0006] 2. Description of the Prior Art

[0007] The demand for noninvasive optical images of biological tissue has led to the development of several techniques to circumvent the common problem of scattering in turbid media. Such techniques include diffusing wave spectroscopy A. Yodh, et al., “Spectroscopy and Imaging with Diffuse Light,” Physics Today 48, 34 (1995); F. Liu, et al., “Transmitted Photon Intensity through Biological Tissues within Various Time Windows,” Opt. Lett. 19, 740 (1994); W. Denk, et al., Handbook of Biological Confocal Microscopy, edited by J. B. Pawley (Plenum New York 1995) at p445; L. Wang, et al. “Continuous-Wave Ultrasonic Modulation of Scattered Laser Lidght to Image Objects in Turbid Media,” Opt. Lett. 20, 629 (1995); M. Kempe, et al., “Acousto-optic tomography with Multiple Scattered Light,” J. Opt. Soc. Am. A14 (1997); and D. Huang, et al. “Optical Coherence Tomography”, Science 254, 1178 (1991); and A. F. Fercher, “Optical Coherence Tomography”, J. Biomed. Opt. 1, 157 (1996).

[0008] Optical coherence tomography employs the partial coherence properties of a light source to image structures with high resolution, namely, in the range of one to fifteen microns, in turbid media such as biological tissue. The sample under study is positioned in one arm or sample arm of a two beam interferometer. The interference fringes are formed when the optical path length of the signal back scattered from the sample matches that from the reference arm to within the coherence length of the source light. The optical path length in the reference arm acts as a detection gate to thereby select only light back scattered from the sample that has traveled the same optical path length. By laterally and longitudinally scanning the sample, two dimensional optical coherence tomographic images are constructed that map the amplitude of light back scattered from the sample. Lateral resolution is determined by the spot size of the beam focus of incoming light and the collection aperture. Longitudinal resolution is determined by the coherence length of the source light.

[0009] Optical coherence-domain reflectometry is further described by Sorin, et al. “Polarization Independent Optical Coherence-Domain Reflectometry,” U.S. Pat. No. 5,202,745 (1993). Sorin describes the use of an incoherent light source in an interferometer in which the reference mirror is moved at a controlled velocity to produce a Doppler shift in the reference signal in the interferometer. The phase of the reference signal is also modulated by piezo-electric transducer to cause a further shift in the referenced signal frequency. The interference signals are detected and measured by a polarization diversity receiver. A linear polarizer and reference signal arm is adjusted to produce equal reference signal powers in each arm of the polarization diversity receiver in the absence of reflection signal from the test arm. The measured reflectometry signal is substantially independent of the state of polarization and the reflected signal from the device under test. The system is generally used to test the optical properties of optical fiber systems. Polarization stability can be a problem in such testing situations. Sorin is directed to a methodology to overcome the problem of polarization variations and distortions in optical fibers and system components. Sorin thus describes the system in which the polarization information returned from the sample or test object is treated as noise and is effectively disregarded.

[0010] Prior art examples of the use of optical coherence domain reflectometry is described in Swanson, et al. “Method and Apparatus for Performing Optical Measurements,” U.S. Pat. No. 5,459,570 (1995). The use of the method for performing optical imaging and sample using longitudinal scanning and positioning of a sample by varying the relative optical path lengths leading to the sample into a reference reflector or by varying the optical characteristic of the output from the optical source is shown and described in Swanson, et al., “Method and Apparatus for Optical Imaging with Means for Controlling the Longitudinal Range of the Sample,” U.S. Pat. No. 5,321,501 (1994).

[0011] Swanson '570 and '601 describes inter alia a system in which birefringence information may be obtained by polarizing the optical radiation used, by suitably modifying the polarization in the sample and reference paths, and by dividing the output into an orthogonal polarization outputs which are separately demodulated before processing. In particular, in FIG. 6 in Swanson '570 orthogonal polarized back scattered interference fringes are provided to two separate detectors 42C and 42D into a beam splitter in the return arm of an interferometer using a coherent light source 12 as the interferometer source signal. The interferometric signals detected by detectors 42C and D are separately processed in demodulators 46 and A-to-D converters 50 to produce two interferrometric signals, a horizontal amplitude component 11 and a vertical amplitude component 12. These signals are applied to computer 52 and used to determine the round trip birefringence retardation in the sample like path. Swanson does not in fact measure the phases from two detector outputs. The relative phase information is computed from measured amplitudes of the two orthogonal components under a set of special assumptions. In order to obtain computed phase information from the signals in Swanson, the optical birefringence axes in the sample must be constant.

[0012] Demodulator 46 for each of the signals is detailed further in FIG. 2. Demodulator 46 is comprised of a band pass filter 78 centered around the modulation frequency of the combined output signal and an envelope detector. The filter assures that only the signal of interest is looked at and removes noise from the output. The filter signal is applied to the envelope detector. The envelope detector is comprised of a rectifier 82 and a subsequent low pass filter 84. The rectifier output is proportional to the square of the sample reflectivity. The low pass filter removes any high frequency components from what is basically a base band signal. Demodulator 46 also includes a logarithmic amplifier 86 for dynamic range compression.

[0013] The effect of rectification of the signal is graphically illustrated by a comparison of FIGS. 5A and 5B. FIG. 5A illustrates the output waveform modulation frequency on which the envelope is superimposed. FIG. 5B is the wave form of FIG. 5A after demodulation by demodulator 46. Thus, it is clear from Swanson that the information contained within the fringes or oscillations of FIG. 5A are lost in the demodulation. As will be described below, it is this information in the undemodulated signal of Swanson that provides a basis when used according to the invention to develop a two dimensional birefringence imaging signal, and more generally create a polarization sensitive optical coherence tomograph using spatially resolved Stokes parameters of the backscattered light from highly scattering biological samples.

[0014] Many surgical procedures use laser radiation to selectively photocoagulate subsurface chromophores in biological tissue in order to obtain a desired therapeutic effect. What is needed is the diagnostic imaging system to provide real-time feedback control for optical laser dosimetry. Application of surgical techniques using radiative energy to selectively destroy chromophores in tissue is limited by the availability of feedback techniques for real-time control of the laser dosimetry. A generic radiative treatment apparatus consists of a generic radiative treatment apparatus and is comprised of five major subsystems, namely (1) a radiative source such as a laser; (2) a diagnostic imaging subsystem; (3) image processing and analysis subsystem; (4) a feedback control subsystem; and (5) a delivering device which delivers the radiative energy to the sample.

[0015] Two non-contact methods have been proposed and tested as diagnostic imaging techniques for use in a generic radiative treatment apparatus. These methods include infrared imaging radiometry and polarization sensitive detection of the remitted backscattered light intensity. Both techniques are limited by poor spatial resolution of the inferred structural changes in the tissue which is induced by the incident radiation.

[0016] Infrared imaging radiometry uses a detector to measure temperature rises in a tissue induced by pulsed laser radiation. The temperature rise due to selective optical absorption of pulse laser light, creates an increase in infrared blackbody emission which is measured by the detector. Because biological materials are composed primarily of water, blackbody emission from tissue originates from a thin 5 to 50 μm superficial layer on the tissue surface. Therefore, infrared imaging radiometry provides little useful information in the temperature distribution and result in structural changes at deep positions in the irradiated tissue. Furthermore, because the transport of thermal energy from deep portions to the tissue surface is a diffusive process, determination of underlying tissue changes is an ill-posed inverse problem that requires application of a computational algorithm to analyze the time sequence of infrared emission images. The ill-posed nature of the problem places severe limitations on the spatial resolution that can be realized from measurements through infrared imaging radiometry.

[0017] Polarization sensitive detection of remitted backscattered light intensity has recently been proposed as a non-contact imaging technique to monitor changes and tissue birefringence during laser irradiation. This technique relies on changes and the birefringence of native collagen in tissue upon exposure to laser irradiation. As collagen is subjected to higher temperatures over prolonged times, the molecular helix begins to unwind and birefringence is lost. If incident diagnostic light is linearly polarized, detected intensity changes of the remitted backscattered light from the tissue in the orthogonal polarization mode may indicate partial loss of collagen birefringence. Although this technique has been demonstrated to provide an average measure of bulk tissue birefringence changes, spatially resolved measurements have not been possible. Because this technique does not discriminate between the multitude of optical paths contained in remitted backscattered light from the tissue, spatial resolution in the lateral and longitudinal directions is limited by, respectively, the scattering anisotropy coefficient and the optical penetration depth. In the visible near infrared spectral regions, lateral and longitudinal spatial resolution is approximately 500 μm.

[0018] The invention is an apparatus for polarization sensitive optical coherence tomography of a sample characterized by optical birefringence comprising an interferometer having a source arm, a reference arm, a sample arm and a detector arm. A source of at least partially coherent polarized light is coupled to the source arm. A polarization modulator is provided, typically in the reference or sample arm. The polarization modulated light is returned to the detector arm from the reference arm and is incident on the sample. Arbitrarily polarized light is returned to the detector arm from the sample arm according to sample birefringence. The returned light from the reference arm and sample arm interfers in the detector arm. A polarization demodulator demodulates the polarization modulated interference fringes to generate a complete polarization state description of the backscattered light from the sample.

[0019] The apparatus further comprises a scanner for laterally moving the sample and the sample arm relative to one another transverse to the longitudinal direction along which the light is incident on the sample, and for longitudinally moving the sample and sample arm relative to one another to obtain a two dimensional image of the sample.

[0020] In the illustrated embodiment the polarization modulator circularly polarizes orthogonal states of the polarization modulated light. The polarization modulator may generate either uniformly or nonuniformly rotating linear polarized light to be returned to the detector arm from the reference arm. In the illustrated embodiment an uniformly rotating quarter wave plate rotates linearly polarized light in the reference arm. The polarization modulator rotates linearly polarized light in the reference arm through at least part of the Poincare sphere. In another embodiment the polarization modulator comprises an electro-optical variable waveplate. The type of polarization modulation which may be used is, however, completely arbitrary and must be understood to be completely general in its scope.

[0021] In a first embodiment the polarization demodulator comprises a single detector which detects polarization modulation of the polarization modulated light to obtain relative phase differences between orthogonal components of the polarization modulated light. In a second embodiment the polarization demodulator comprises two detectors. Each of the two detectors detects over time a separate orthogonal component of the polarization modulated light to obtain a complete set of polarization states of the Poincare sphere sufficient to determine orientation of optical axes of the sample and birefringence of the sample.

[0022] The polarization demodulator averages the demodulated, orthogonal polarization states of interference fringes according to a weighted average to obtain a value for a pixel image.

[0023] The apparatus further comprises a rapid spectral optical delay line to provide for longitudinal scanning of the sample. In this case the apparatus further comprises a phase modulator in the sample arm or reference arm to decouple longitudinal scan speed and modulation frequency of the rapid spectral optical delay line.

[0024] In one embodiment the demodulator generates the Stokes parameters, I, Q, U, and V and the degree of polarization, P, from the orthogonal signal components of the intensity of backscattered light from the sample. The invention is also defined as a method for performing polarization sensitive optical coherence tomography of a sample characterized by optical birefringence comprising the steps of providing a source of at least partially coherent light coupled to an interferometer having a source arm, a reference arm, a sample arm and a detector arm. The light is polarization modulated in at least the reference arm or sample arm. Polarization modulated partially coherent light is returned to the detector arm from the reference arm and the sample arm. The polarization modulated partially coherent light is incident on the sample and arbitrarily polarized light is returned to the detector arm from the sample arm according to sample birefringence. The returned light from the reference arm and sample arm interferes in the detector arm to coherently gate the returned light from the sample arm in the detection arm in order to select between a multiplicity of optical paths of backscattered light returned from the sample arm. The polarization modulated interference fringes are demodulated in the detector arm to provide a data signal indicative the optical birefringence of the sample.

[0025] The step of providing the source of polarization modulated partially coherent light comprises in one embodiment uniformly or nonuniformly rotating the linearly polarized partially coherent light in the reference arm or sample arm.

[0026] The step of demodulating phase sensitive, orthogonal polarization states of the interference fringes in the detector arm to provide a data signal indicative the optical birefringence of the sample further comprises the step of generating the Stokes parameters, I, Q, U and V from the orthogonal signal components of the intensity of backscattered light from the sample to provide a complete polarization state description of the backscattered light from the sample.

[0027] The invention is more generally defined as a method for performing polarization sensitive optical coherence tomography of a sample characterized by optical birefringence comprising the steps of generating two polarization-modulated orthogonal polarization states of an at least partially coherent light signal. Interference fringes of two polarization-modulated orthogonal polarization states are generated from a reference signal and a backscattered sample signal. The fringes have an amplitude and relative phase with respect to the other modulated orthogonal polarization state for each of the two polarization-modulated orthogonal polarization states. The amplitude and phases of the interference fringes of the two polarization-modulated orthogonal polarization states are measured. The amplitude and phases of the interference fringes of the two polarization-modulated orthogonal polarization states are polarization demodulated to obtain the full polarization state of the backscattered sample signal to obtain structural information pertaining to the sample.

[0028] The invention and its various embodiment as briefly summarized above can be better visualized by turning to the following drawings wherein like elements are referenced by like numerals.

[0029] FIG. 1 is a diagram of an apparatus or interferometer system in which the invention may be practiced.

[0030] FIG. 2ais a birefringence image of fresh bovine tendon.

[0031] FIG. 2bis a computer tomograph birefringence of laser radiated bovine tendon shown in FIG. 2a.

[0032] FIG. 2cis a conventional light optical coherence tomography of the bovine tendon of FIGS. 2aand b.

[0033] FIG. 3 is a diagram of a second embodiment of the apparatus of FIG. 1 wherein the polarization states of the detected signal are separately detected.

[0034] FIG. 4 is a diagram of a third embodiment of the apparatus of either FIGS. 1 or 3 where the optical paths are provided not in free space, but through optical fibers.

[0035] FIG. 5ais a digital graphic depiction of the Stokes vector I, for a sample of skeletal rat muscle derived from experimental data.

[0036] FIG. 5bis a digital graphic depiction of the Stokes vector Q, for the sample of skeletal rat muscle of FIG. 5aderived from experimental data.

[0037] FIG. 5cis a digital graphic depiction of the Stokes vector U, for the sample of skeletal rat muscle of FIG. 5aderived from experimental data.

[0038] FIG. 5dis a digital graphic depiction of the Stokes vector V for the sample of skeletal rat muscle of FIG. 5aderived from experimental data.

[0039] FIG. 5eis a digital graphic depiction of the degree of polarization P for the sample of skeletal rat muscle of FIG. 5aderived from experimental data.

[0040] FIG. 6ais a digital graphic depiction of the Stokes vector I, for a sample of rat bone derived from experimental data.

[0041] FIG. 6bis a digital graphic depiction of the Stokes vector Q, for the sample of rat bone of FIG. 6aderived from experimental data.

[0042] FIG. 6cis a digital graphic depiction of the Stokes vector U, for the sample of rat bone of FIG. 6aderived from experimental data.

[0043] FIG. 6dis a digital graphic depiction of the Stokes vector V for the sample of rat bone of FIG. 6aderived from experimental data.

[0044] FIG. 6eis a digital graphic depiction of the degree of polarization P for the sample of rat bone of FIG. 6aderived from experimental data.

[0045] FIGS. 7, 7aand 7bare digital graphs of data showing the spatial evolution of the polarization of the E wave in rat muscle derived from experimental data.

[0046] FIG. 8 is a third embodiment of the invention that employs a rapid spectral optical delay line to allow a longitudinal scan speed and modulation frequency or Doppler shift to be set independently.

[0047] FIG. 8ais schematic diagram of a fourth embodiment of the invention similar to that shown in FIG. 8, except the phase modulator is disposed in the sample arm instead of the reference arm.

[0048] FIG. 8bis schematic diagram of a fifth embodiment of the invention similar to that shown in FIG. 8, wherein the phase modulator is moved from the source arm to the sample arm, or alternatively a second phase modulator is disposed in the sample arm instead of the reference arm.

[0049] The invention now having been illustrated in the foregoing drawing can now be better understood by turning to the following detailed description of the preferred embodiments.

[0050] The present invention combines optical coherence tomography (see M. R. Hee, et al., J. Opt. Soc. Am. B9, 903 (1992) with polarization sensitive detection to record two dimensional images of the change of polarization of circularly polarized incoming light which is backscattered from a turbid birefringent sample, typically a biological sample. In contrast with conventional optical coherence tomography where the magnitude of the backscattered light is imaged as a function of depth, backscattered light is used in the invention to image the magnitude of the birefringence in the sample as a function of depth. Two dimensional maps of the optical birefringence of biological materials reveal important structural information in the biological sample that is otherwise difficult to resolve using other imaging techniques. For example, partial loss of birefringence is known to be an early indication of thermal damage in tissue such as in burns or laser treatments.

[0051] It will demonstrated below that polarization sensitive optical coherence tomography of the invention reveals structural information on birefringent turbid media, such as biological tissue, which is not available when using polarization insensitive optical coherent tomography. Polarization sensitive optical coherent tomography has potential to provide guidance regarding optical dosimetry for thermally mediated laser therapeutic medical procedures by allowing real-time diagnosis at each irradiated sight through detection of changes in the sample birefringence associated with thermal damage at pathological condition. This permits semi-quantitative evaluation of the efficacy of laser therapy as a function of the incident light dosage.

[0052] Thus, it is understood that polarization sensitive optical coherence tomography as disclosed herein can be employed for real-time diagnostic imaging for surgical procedures in general. Surgical procedures involve the use of several types of energy and techniques to modify biological tissues to obtain the desired therapeutic effect. For example, mechanical, acoustical, thermal, cryogenic and radiative electromagnetic energy sources can be applied while schemic and pharmacological techniques practiced. In all procedures, real-time feedback on the induced changes in tissue would be extremely useful to the procedure. What is described here is a polarization sensitive optical coherent tomographic system 10 for use as a diagnostic imaging subsystem in a generic treatment apparatus. Although the illustrative embodiment is described in a context thermally mediated laser surgery, the invention is not limited to this application but may be applied to any tissue mediation procedure or system.

[0053] The present invention uses a coherence gate to discriminate between the multitude of optical paths contained in the diagnostic light backscattered from a tissue to substantially improve spatial resolution of birefringence changes caused by higher temperatures. Lateral and longitudinal spatial resolution of polarization sensitive optical coherence tomography is limited by, respectively, the numerical aperture and the coherence length of the source light which in practice is about 2-15 μm.

[0054] The details of specific implementation of polarization sensitive optical coherence tomography are described below. First, consider the apparatus as diagrammatically shown in FIG. 1. Interferometer system 10 uses a partially coherent light source 12, such as a super luminescent diode having a linearly polarized output. In the illustrated embodiment light source 12 has an output of 0.8 mW at a wave length of 856 nm with a spectral full width half maximum of 25 nm. Light from diode source 12 passes through a Glan-Thompson polarizer 14 which selects a pure linear vertical input state. Light is then spread by a beam splitter 16 into a reference arm 18 and sample arm 20 of a Michelson interferometer. Beam splitter 16 has a reflection and transmission coefficient for linear vertical and horizontal polarization states of 0.5±0.05. Light in reference arm 18 passes through a zero order quarter wave plate 22, which quarter wave plate 22 rotates the light at a rate of 200 π radians per second. To measure the relative phases of the two orthogonal polarization components, the rotation rate of the linear polarization due to the quarter wave plate must exceed the frequency generated by relative changes in the optical path lengths of the sample and reference arms, such as due to the longitudinal scanning of the sample. Accuracy of the relative phase measurement increases as the frequency separation between the rotation rate of the quarter wave and the frequency generated by relative changes in the optical path lengths of the sample and reference arms increases. Light impinges upon a planar mirror 24 and makes a return pass through quarter wave plate 22. Light in reference arm 18 therefore has a rotating linear polarization of 400 π radians per second. Improvement of the signal-to-noise ratio is obtained by a neutral density filter 26 which is placed in reference arm 18 to reduce intensity of the noise by a factor of 50. Light split by beam splitter 16 into sample arm 20 passes through a quarter wave plate 28, oriented at 45° to the incident vertical polarization, to give circularly polarized light. The circularly polarized light from quarter wave plate 28 is focused by lens 30 to a spot size of 17 microns in diameter on sample 32. In the illustrated embodiment the focal length of lens 30 is 50 millimeters. Backscattered light from sample 32 passes again through lens 30 and quarter wave plate 28 to result in light with an elliptical polarization state as determined by the sample birefringence properties.

[0055] Light from reference arm 18 and sample arm 20 are then recombined in detection path 34. In the illustrated embodiment of FIG. 1 the combined light then impinges upon detector 36. In the second embodiment of the invention such as shown in FIG. 3, detector 36 is replaced by detectors 36A and 36B to which polarized light in detection arm 34 is split by a polarizing beam splitter 38 and focused on a 25 micron diameter pin hole placed directly in front of detectors 36A and 36B to detect a single spatial mode as described below. It should be understood that detector 36 or 36A and B as appropriate, are coupled to appropriate signal conditioning and data processing circuits or computers (not shown) which perform the data reductions required by the equations set forth in this specification according to well known means. Therefore, the term “detectors” or “demodulators” is to be understood not only to include optical detection devices and circuits, but to also include demodulation and data processing circuits and software controlled processors as may be required from context.

[0056] Returning to the embodiment of FIG. 1 the intensity of detector 36 is given by recombination of the light in both arms 18 and 20 of interferometer 10 is given by equation 1 below.

[0057] I_rs+2Re[<{right arrow over (Ψ)}_r^*(t,z_r)·{right arrow over (Ψ)}_s(t,z_s)>]  (1)

[0058] Where {right arrow over (Ψ)} (t,z) is the light amplitude field vector, subscripts r, s, denote the reference and sample arms respectively, the z_r,sare the optical path lengths of the same, and angular brackets denote ensemble averaging. The source spectral density S (ω) is assumed to be Gaussian, that is proportional to exp [−( ω−ω₀)²/Ω²] with a full width half maximum of 2Ω{square root over (1+L n_Hand vertical A_Vcomponents that are proportional to the light amplitude fields backscattered from sample 32 as given by equations 2 below.

[0059] Re[<{right arrow over (Ψ)}_r^*(t,z_r)·{right arrow over (Ψ)}_rs^*(t,z_sr)>]=A_H+A_V;

[0060] A_H≈sin(2{dot over (Θ)}t)cos(2k₀Δz)e^{−(ΩΔz/c)2}cos(k₀zδ),

[0061] A_V≈cos(2{dot over (Θ)}t)cos(2k₀Δz+2α)e^{−(ΩΔz/c)2}sin(k₀zδ),  (2)

[0062] Δz is the optical path link difference between sample arm 20 and reference arm 18 of interferometer 10. In the apparatus of FIG. 1, Δz is a function of time and longitudinal velocity of sample 32, z is the backscattered depth within sample 32, k₀=2π/λ₀, c the speed of light in the vacuum, δ the difference in refractive indices along the fast and slow axis of the birefringent (n_s−n_f), and {dot over (Θ)} is the rotation speed of quarter wave plate 22 in reference arm 18 and α is the angle of the fast optical axis of birefringent sample 32 with the horizontal. The only approximation in equation 2 above is that of the product of birefringence and propagation depth in sample 32, which in the illustrated embodiment was z δ≦2.6 microns, which is much smaller than the width of the coherence envelope, which again in the illustrated embodiment was 2c/Ω=19 microns.

[0063] Phase sensitive demodulation of the recorded signal in detector 36 with respect to the modulation of the polarization, namely the angular position, ({dot over (Θ)}t), of the rotating quarter wave plate 22, allows separation of the signal amplitudes of the vertical and horizontal polarized light components. In addition to the carrier frequency of 2k₀Δz within the coherence envelope, exp[−(ΩΔz/c)²], both signals show an oscillation with a periodicity determined by the product of sample birefringence, δ, and the propagation depth, z, that allows for birefringent imaging.

[0064] Scans are made by moving sample 32 at a constant velocity v=1 mm/s giving a carrier frequency v=2v/λ₀=2.4 kHz. To form two-dimensional images, a longitudinal scan is recorded after each 10 microns of lateral displacement of sample 32. A 4 millimeter diameter beam, focused on sample 32 by lens 30 gave a 14 micron beam waste diameter. In air, sample arm 20 was matched in length to reference arm 18 at a position 200 microns past the focal point of lens 30, leading to a matched length in the beam focus of approximately 400 microns deep into sample 32 with a refractive index of 1.4. Detector 36 was AC coupled with signal amplified, highpass filtered at 1 kHz with 18 dB per octave roll-off and digitized with 16 bit resolution at 50 k points per second.

[0065] Signal processing was comprised of the steps of squaring the detected signal and phase sensitive demodulation with respect to {dot over (Θ)}t to separate the horizontal I_Hand vertical I_Vcomponents of the backscattered light. Subsequently within each longitudinal scan, data points were averaged with a Gaussian weight function (FWHM=700 data points), to form one image pixel. The resulting signals gave the backscatted horizontal and vertical intensities as a function of z with a resolution of 10 μm physical distance, modulated with their respective birefringence dependent terms given by equation 3 below.

[0066] I_H(z)∝cos²(k₀zδ); I_v(z)∝sin²(k₀zδ);  3

[0067] FIG. 2ais a birefringence image of fresh bovine tendon. In the illustrated embodiment below to demonstrate polarization sensitive optical coherence tomography, 1 mm wide by 700μ deep images of bovine tendon birefringence are shown and described before and after pulsed laser irradiation. It is to be expressly understood that the tomographic imaging technique of the invention is intended to be applied to any tissue or turbid medium. Measurements on a 1 cm samples at least 1 cm thick were done within 48 hours of sacrifice. The banded structure shown in FIG. 2ais indicative of birefringence and is clearly visible up to a physical depth of about 700 μm. The average refractive index of the tendon used in FIG. 2awas found to be 1.42±0.03 by measuring optical versus physical thicknesses of a thin slice. Birefringence was determined by measuring the average distance between the start or zero crossing between the first and second band over the full width of FIG. 2a, which was 100 lateral scans. The average distance {overscore (z)}=116±13 μm corresponds to a full period of sine squared in Eq. (3) above, k₀{overscore (z)}δ=π. The measured birefringence δ was 3.7±0.4×10⁻³of bovine tendon which is predominantly a type I collagen, which is in good agreement with reported values of 3.0±0.6×10⁻³and 2.8-3.0×10⁻³. The fit of an exponential e^−2z/γ, between z=150-600 μm depth to a total backscattered intensity in the sample 32, I_b(z), averaged over the image of FIG. 2 gives γ approximately equal to 0.2 millimeters, where γ is the optical penetration depth. Decay of total backscattered light intensity with depth depends on several factors, among them attenuation of the partially coherent beam by scattering and geometry of the collection optics.

[0068] Each pixel in FIGS. 2a-crepresents an area of 10×10 microns². In FIGS. 2aand bfalse color images were generated by computing sgn[I_H(z)−I_V(z)] 10 log |I_H(z)−I_V(z)|. Positive values were colored green-yellow, lower signals graded to red, negative values were colored green-blue and lower signals graded to deep blue. In FIG. 2cfalse color images were generated by computing 10 log |I_H(z)+I_V(z)|, which were colored red-yellow to green-blue for lower signals over a dynamic range of 48 dB. A gray grayscale conversion has been made of the false color grading of FIGS. 2a-cfor the purposes of the patent specification.

[0069] FIG. 2bis a computer tomograph birefringence of laser radiated bovine tendon shown in FIG. 2a. The image of FIG. 2bclearly shows a decrease in the birefringence of the center of the radiation zone which is in the center of the image extending into the tendon over the full depth of the image of 700 μm. Furthermore, the direction of incoming laser light from the upper left corner at an angle of 35° with respect to the normal surface is observable in the image of FIG. 2b. Surface temperature of the tendon was monitored during laser radiation using infrared radiometry. By comparison in FIG. 2can optical coherence tomographic image of the total backscattered intensity I_b(z) is shown. Although less backscattered light from the irradiated area is observable, the polarization sensitive image shown in FIG. 2breveals important structural information which is clearly not shown in the conventional prior art optical coherence tomograph of FIG. 2c.

[0070] FIG. 4 shows a schematic diagram of an implementation using polarization preserving optical fibers. The apparatus of FIG. 4 differs from that shown in FIGS. 1 and 3 in that in additional to the optical paths being defined within polarizing preserving optical fibers 40, a polarization modulator 42 provided is provided in reference arm 18 or may be placed in the sample arm. A phase modulator 45 is shown in sample arm 20, but may be alternatively placed in reference arm 18 if desired. Modulator 42 is an electro-optical device that rotates the polarization of the light in a controlled manner upon double passage through modulator 42. Rotating the polarization of the light in reference arm 18 in a linear or non-linear manner permits detection of two independent polarization states of light backscatted from tissue 32. Planar mirror 24 may be replaced by a corner cube or cat's eye retroreflector if desired. Thus, the polarization state of light backscattered from tissue 32 is determined after demodulation of the interference fringe intensity signal at detector 36aand b. The demodulation technique described is a specific example of particular methodology and is not intended to be general description. In particular, the polarization modulation frequency is higher than the carrier frequency resulting from the optical path length reference and sample arm modulation. Digital data acquisition and processing permits the independent determination of the phase and amplitude of the two independent polarization states of remitted backscattered light from tissue 32. Summing of the amplitude of the orthogonal polarized light signal fringes permits the determination of the total remitted backscattered light independent of the polarization state. A notable improvement over existing devices is that the indicated modulation technique is simpler and permits the use of a single light detector without the need of a beam splitter.

[0071] Consider now how polarization sensitive optical coherence tomography is used to determine the spatially resolved Stokes parameters of light backscattered from highly scattering biological samples. Changes in the Stokes parameters due to the optical phase delay between light propagating along the fast and slow axis of birefringence is measured through simultaneous detection of amplitude and relative phase of signal fringes and othoginal polarization states in the backscattered light formed by interference of light backscatted from biological sample 32 in sample arm 20 and from mirror 24 in reference arm 18.

[0072] The method can also be applied to the investigation of birefringence and highly scattering materials of any nature including ceramics and crystals. In contrast to the prior art where only the amplitude of the signal fringes in two othoginal polarization states was used, the present invention incorporates the phase relationship between interference fringes in each polarization channel to completely characterize the polarization state of light backscattered from the sample. Depth resolved changes in the Stokes parameters of light backscattered from sample 32 allow better understanding of the spatial variation in the sample birefringence and corresponding structural properties.

[0073] Consider now the signal developed in the device of FIG. 3 which was described above. Two dimensional images have formed of sample 32 in the device of FIG. 3 by lateral movement to sample 32 at 1 mm per second in the x direction which is repeated after each 10 μm incremental longitudinal displacement in the z direction, which is the direction of propagation of light. Active beam focus tracking in sample 32 was achieved by translating a piezoelectric transducer retroreflector assembly 43 after each transverse scan. The interference fringe carrier frequency of about 6 kHz was generated by modulating optical path lengths of reference arm 18 over about 20 μm with a 50 Hz triangular waveform driving assembly 43. An image pixel is calculated using the interference signal recorded over the central 10 μm of the reference arm modulation. Transverse and longitudinal pixel dimensions in the images were 10 μm by 10 μm.

[0074] To derive the expression of the Stokes parameters of the light in sample arm 20 in terms of the amplitude and relative phase of the interference fringes in othogonal polarization states, the electric fields are represented in the complex analytical form E(z)=∫{tilde over (e)}(k)exp(−ikz)dk with k=2π/λ and {tilde over (e)}(k)=0 if k<0 where {tilde over (e)}(k)is the wave field spectral amplitude. From the Wiener-Khinchine theorem, it follows that<{tilde over (e)}^*(k){tilde over (e)}(k′)>=S(k)δ(k-k′), with δ(k-k′) the Dirac delta function, and S(k) the spectral density of a source. Since light from the reference arm was split equally into the horizontal and vertical polarization states, the electric field in reference arm is given by Eq. (4) below. $\begin{array}{cc}{E}_{x,y}\left(z_r\right)={\int }_{-\infty }^{\infty }\tilde{e}\left(k\right)\exp \left(-2ik{z}_r\right)dk& \mathrm{Eq}.4\end{array}$

[0075] with z_rthe length of the reference arm 18. Electric field and sample arm 20 is given by Eq. (5) below. $\begin{array}{cc}\stackrel{->}{E}\left(z_s\right)={\int }_{-\infty }^{\infty }\sqrt{R\left(z_s\right)}\stackrel{->}{a}\left(k,z_s\right)\tilde{e}\left(k\right)\exp \left(-2ik{z}_s\right)dk& \mathrm{Eq}.5\end{array}$

[0076] with {square root over (R(z_s+L ))} describing the reflectivity at z_sand the decay of the coherent beam in sample 32 and {right arrow over (a)}(k,z_s) being the normalized complex vector amplitude of the polarization state of the light that was backscattered at depth z_swith {right arrow over (a)}^*(k,z_s)•{right arrow over (a)}(k,z_s)=1. The measured phase information is included in the normalized complex vector amplitude, {right arrow over (a)}(k,z_s). The Stokes parameters, I, Q, U and V, of the electric field are calculated to be given by equations 6 and 7 below. $\begin{array}{cc}\begin{array}{c}I\left(z_s\right)=R\left(z_s\right)\int \left[a_x^{*}\left(k,z_s\right)a_x\left(k,z_s\right)+a_y^{*}\left(k,z_s\right)a_y\left(k,z_s\right)\right]S\left(k\right)dk\\ Q\left(z_s\right)=R\left(z_s\right)\int \left[a_x^{*}\left(k,z_s\right)a_x\left(k,z_s\right)+a_y^{*}\left(k,z_s\right)a_y\left(k,z_s\right)\right]S\left(k\right)dk\\ U\left(z_s\right)=R\left(z_s\right)\int 2\mathrm{Re}\left[a_y^{*}\left(k,z_s\right)a_x\left(k,z_s\right)\right]S\left(k\right)dk\\ V\left(z_s\right)=R\left(z_s\right)\int 2\mathrm{Im}\left[a_y^{*}\left(k,z_s\right)a_x\left(k,z_s\right)\right]S\left(k\right)dk\end{array}& \mathrm{Eq}.6\end{array}$

[0077] The interference intensity between light and sample path 20 and reference path 18 is given by equation 7. $\begin{array}{cc}\stackrel{\rightharpoonup }{I}\left(z_s,2k\right)=\frac{1}{2\pi }\sqrt{R\left(z_s\right)}\overrightarrow{a}\left(k,z_s\right)S\left(k\right)& \mathrm{Eq}.\left(7\right)\end{array}$

[0078] where Δz=zs-zr. The Fourier transform of {right arrow over (I)}(z_s,Δz) with respect to Δz is given by equation 8. $\begin{array}{cc}\stackrel{\overrightarrow{~}}{I}\left(z_s,2k\right)=\frac{1}{2\pi }\sqrt{R\left(z_s\right)}\overrightarrow{a}\left(k,z_s\right)S\left(k\right)& \text{Eq. 8}\end{array}$

[0079] Using equation 8 in the Stokes parameters in equations 7 expressed in terms of the Fourier transform by equation 9. $\begin{array}{cc}\begin{array}{c}I\left(z_s\right)={\left(2\pi \right)}^2\int \left[{\tilde{I}}_x^{*}\left(z_s,2k\right){\tilde{I}}_x\left(z_s,2k\right)+{\tilde{I}}_y^{*}\left(z_s,2k\right){\tilde{I}}_y\left(z_{s}2k\right)\right]/Sdk\\ Q\left(z_s\right)={\left(2\pi \right)}^2\int \left[{\tilde{I}}_x^{*}\left(z_s,2k\right){\tilde{I}}_x\left(z_s,2k\right)+{\tilde{I}}_y^{*}\left(z_s,2k\right){\tilde{I}}_y\left(z_{s}2k\right)\right]/Sdk\\ U\left(z_s\right)={\left(2\pi \right)}^2\int 2\mathrm{Re}\left[{\tilde{I}}_y^{*}\left(z_s,2k\right){\tilde{I}}_x\left(z_s,2k\right)\right]/Sdk\\ V\left(z_s\right)={\left(2\pi \right)}^2\int -2\mathrm{Im}\left[{\tilde{I}}_y^{*}\left(z_s,2k\right){\tilde{I}}_x\left(z_s,2k\right)\right]/Sdk\end{array}& \mathrm{Eq}.9\end{array}$

[0080] It is to be expressly understood that many other formulas or algorithms exist for derivation of the Stokes parameters than those listed above. Therefore, the invention is not limited to the particular computational approach to the Stokes parameters which is discussed above, but explicitly includes all known or later derived methods for their derivation. The signals I_x(z_s, Δz) and I_y(z_s, Δz) are bandpass filtered between 3 and 10 kHz and digitized at 5×10⁴points per second each. For each pixel in an image, the Fourier transform of the central 10 μm are 256 points of the reference arm modulation is taken and digitally bandpass filtered between 5 and 7 kHz. The Stokes parameters for each pixel are calculated according to equation 9 with the spectral density of estimated by S(k) proportional to $\left|\overrightarrow{I}\left(z_s,2k\right)\right|=\frac{1}{2\pi }\sqrt{R\left(z_s\right)}S\left(k\right).$

[0081] To determine the polarization state reflected from the sample, the Stokes vectors need to be multiplied by the inverse of the Mueller matrix associated with quarter wave plate 28 in sample arm 20 with II, Q−V, UU and VU. I is the backscattered intensity summed over both polarization channels. Q and U characterize linear polarization in frames rotated over 45° with respect to each other. The signs of Q and U indicate a predominant linear polarization and either of two othoginal planes. V describes circular polarization. The sign of V denotes the handedness. The Stokes parameters, I, Q, U and V satisfy the relationship, I²≧Q²+U²+V²and a parameter $P=\sqrt{\left(Q^2+U^2+V^2\right)/I}$

[0082] can be defined that ranges from 0 to 1 and describes the degree of polarization.

[0083] Tomographic images of the Stokes parameters were formed by grayscale coding the common log of I from 0 to −48 dB where the 0 dB level corresponded to the maximum signal in an image. The polarization state parameters Q, U and V were grayscale coded by normalizing on the intensity I from −1 to 1 and P from 0 to 1. Contour lines indicating −⅓ and +⅓ fractions of the normalized parameters, Q, U and V were calculated after low pass filtering by convolving the images with a Gaussian filter of 4×4 pixels and overlaid with an original image.

[0084] FIGS. 5a-dand 6a-eshow the four Stokes parameters measured in an ex vivo rat skeletal muscle and bone, respectively. The image of the Stokes parameter V is similar to that obtained by grayscale coding the birefringence induced phase retardation $\phi =\arctan \sqrt{I_x^2\left(z\right)/I_y^2\left(z\right)}=k_{o}z\delta$

[0085] with the exact relationship being V=cos 2ø.

[0086] The birefringence in FIG. 5 is attributed to the high structural order or anisotropy of skeleton muscle fibers. Several periods of Q, U and V, cycling back and forth between 1 and −1 are observed. FIG. 5ais a depiction of I, FIG. 5ba depiction of Q, FIG. 5ca depiction of U, FIG. 5da depiction of V and FIG. 5ethe degree of polarization P. The birefringence was determined by measuring the distance of a full period of V which corresponds to a phase retardation of π=kozΔ2.4×10^−3.The greater birefringence in skeletal muscles compared to myocardium has been attributed to the structural differences between these two different types of muscle. The myocardium muscles fibers are oriented in different directions and not necessarily parallel to the muscle surface. The skeletal muscle image in FIGS. 5a-5eshows 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 Q or U and what resulted in an angle of −7° with respect to the vertical of one of the optical axis which is in good agreement with the fiber direction which was approximately perpendicular to the horizontal scan direction.

[0087] The birefringence depicted in FIGS. 6a-6ealso depicting the Stokes parameters I, Q, U, V and the degree of polarization P respectively, is attributed to the presence of collagen. The V parameter image of FIG. 6dshows an apparent loss of birefringence. However, the Q parameter image of FIG. 6breveals that the predominant orientation of the linear polarization in either of the two othoginal planes is reversed around the region showing the apparent loss of birefringence. This indicates that in the region showing loss of birefringence in FIG. 5d, there is a transition of a dominant orientation of the optical axis.

[0088] Therefore, a determination as shown in FIGS. 5a-5eand 6a-6eof examples of the spatially resolved Stokes parameters of light reflected from turbid sample 32 reveals substantial additional structural information than was previously obtainable by prior art methods that used only the intensity in two orthogonal polarization channels. In samples with a constant orientation of the optical axes, birefringence and the orientation of the optical axes can be determined. Parameter, P, reveals information on a multiply scattered light in optical coherence tomographic images through the decrease of the degree of polarization. An analysis of the evolution of the Stokes parameters in a biological sample allows determination of the changes and birefringence and in the orientation of the optical axis and turbid samples during radiative mediation.

[0089] FIG. 7, 7aand 7bare a digital graphs of data showing the evolution of a reflected light propagating through the birefringent murine muscle as seen in the detection arm of apparatus 10 of the invention. The electromagnetic wave is reconstructed in FIG. 7 from the horizontal amplitude A_Hand the vertical amplitude A_Vpolarized components and relative phase of the interference fringes detected in the device of FIG. 3. The evolution of the wave shown in FIG. 7 is a small section of the longitudinal scan taken from the middle of an image of murine muscle. The length of the section of the scan depicted in FIG. 7 is 38 μm within sample 32 in which a sample refractive index of 1.4 is realized. The initial portion 44 of the scan shown on FIG. 7 is the reflection from the sample surface modulated by the coherence envelope.

[0090] Inserts FIG. 7aand 7bare cross-sectional diagrams of the electromagnetic wave taken over full cycle in a direction perpendicular to the propagation at 5.7 and 35.7 μm from beginning 46 of the section scan. As FIG. 7 graphically depicts as interpreted by insets FIGS. 7aand 7b, the initial polarization is linear along one of the displayed axis and changes to an elliptical polarization state as shown in FIG. 7bdeeper within the tissue sample 32.

[0091] In the third embodiment of FIG. 8 apparatus 10 employs two detectors 36aand 36band the detection 34 of Michelson interferometer 10 to detect to orthogonal polarization states. Apparatus 10 allows measurement of the changes of polarization state and the intensity with high spatial resolution of between 1 to 10 μm and high sensitivity, greater than 100 dB, of light that is backscattered from a transparent or turbid medium or sample 32. The information is used to determine birefringence and the optical axes of birefringence or optical activity and transparent and turbid media for use in biomedical imaging, or to determine stress or lattice deformation or other structural information in materials such as crystals and ceramics.

[0092] Apparatus 10 of FIG. 8 does not employ polarization preserving fibers. Modulation of the input polarization state incident on sample 32 is at an arbitrary frequency. Data processing algorithms allow the optical axis and birefringent nature of the sample to be determined, because at any location inside sample 32 sample-induced changes in both the linear and circular polarization are measured. The embodiment of FIG. 8 employs a rapid spectral optical delay line 46 that allows a longitudinal scan speed and modulation frequency or Doppler shift to be set independently. This is achieved by placement of a fiber optic phase modulator in either reference arm 18 or sample arm 20 of interferometer 10. In the illustration in FIG. 8 phase modulator 42 is shown in reference arm 18.

[0093] Light source 12 of FIG. 8 has low temporal and high spatial coherence. Source 12 can either be polarized in a single state or can be polarized by polarizer and wave plates in an arbitrary single state. An aiming beam of visible light can be combined with light source 12 if desired. Polarization modulator 48, such as an eletrooptic wave plate(s) or other equivalent device(s) or combination of devices, modulates the pure polarization state to map out part of or, with a combination of polarization devices, the complete Poincare sphere which completely describes the polarization state of light. Polarization modulator 48 is placed either in light source arm 50 or sample arm 20. As a result, the input polarization state of light incident upon sample 32 samples part of or the complete Poincare sphere. Since each spatial location of sample 32 is probed with a complete set of polarization states, the local optical axes of birefringence can be determined.

[0094] Rapid spectral optical delay line 46 of FIG. 8 is used as a longitudinal or depth scanning mechanism and is known in the art as described by G. J. Tearney, et al. Opt. Left. 22, 1811 (1997). Rapid spectral optical delay line 46 is modified by adding a phase modulator 42 in reference arm 18. The advantage of phase modulator 42 and reference arm 18 is a decoupling of the longitudinal scan speed in the modulation frequency or Doppler shift of rapid spectral optical delay line 46. Phase modulator 42 modulates optical length to reference arm 18 within a few wave lengths. Phase modulator 42 can be driven by any one of several different types of waveforms, such as sawtooth, triangular, sinusoidal or a combination of sinusoids. Although the sawtooth and triangular waveforms are the simplest driving signals to implement, driving phase modulator 42 with a special combination of sinusoids, such as a fundamental frequency and higher harmonics, allows demodulation of the signal at the fundamental frequency while phase information is preserved. The improved quality of frequency modulated signal at detectors 36aand 36ballows for better determination of the polarization state of the light. In addition, it improves the quality of Doppler flow velocity analysis of the signal.

[0095] In detection arm 34 of inferometer 10 of FIG. 8 a polarizing beam splitter 38 separates the detected light into two othoginal polarization states before being detected. Throughout the design, static polarization controllers can be added to manipulate the polarization into a desired state such as static quarterwave plates 60 shown in FIGS. 8aand 8b.

[0096] Many alterations and modifications may be made by those having ordinary skill in the art without departing from the spirit and scope of the invention. Therefore, it must be understood that the illustrated embodiment has been set forth only for the purposes of example and that it should not be taken as limiting the invention as defined by the following claims.

[0097] The words used in this specification to describe the invention and its various embodiments are to be understood not only in the sense of their commonly defined meanings, but to include by special definition in this specification structure, material or acts beyond the scope of the commonly defined meanings. Thus if an element can be understood in the context of this specification as including more than one meaning, then its use in a claim must be understood as being generic to all possible meanings supported by the specification and by the word itself.

[0098] The definitions of the words or elements of the following claims are, therefore, defined in this specification to include not only the combination of elements which are literally set forth, but all equivalent structure, material or acts for performing substantially the same function in substantially the same way to obtain substantially the same result. In this sense it is therefore contemplated that an equivalent substitution of two or more elements may be made for any one of the elements in the claims below or that a single element may be substituted for two or more elements in a claim.

[0099] Insubstantial changes from the claimed subject matter as viewed by a person with ordinary skill in the art, now known or later devised, are expressly contemplated as being equivalently within the scope of the claims. Therefore, obvious substitutions now or later known to one with ordinary skill in the art are defined to be within the scope of the defined elements.

[0100] The claims are thus to be understood to include what is specifically illustrated and described above, what is conceptionally equivalent, what can be obviously substituted and also what essentially incorporates the essential idea of the invention.