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We report a novel polarization-maintaining fiber based optical coherence tomography for single detector imaging of tissue reflectivity and birefringence. A single depth scan yields quantitative birefringence information along the A-line accurately. Since the orthogonal polarization channels are frequency multiplexed, the polarization information is extracted by using digital band-pass filters. Here, we introduce the optical system and present the reflectivity and birefringence images of biological tissues with an axial resolution of 7.9 µm and SNR of 30 dB.
©2008 Optical Society of America
1. Introduction
Polarization-sensitive optical coherence tomography (PS-OCT) has been proposed to utilize tissue birefringence to obtain an improved contrast in OCT imaging [1–4]. By measuring polarization state of light reflecting or scattering back from tissue, PS-OCT quantitatively images depth-resolved birefringence, which originates from the difference between the refractive indices for polarized light propagating parallel and perpendicular to the axis of anisotropy. Birefringence information is particularly useful when the nano-scale organization of tissue, such as collagen fibrils density and alignment, is altered due to a disease or tissue response to injury. Applications include investigation of tissue collagen alteration due to thermal damage [5] or burn [6], early detection of osteoarthritis [7], and differentiation of atherosclerotic plaques [8]. Birefringence exhibited by nerve fibers bundled in parallel in retinal nerve fiber layer has been suggested for glaucoma diagnosis [9]. PS-OCT is also important for accurate interpretation of conventional OCT images of birefringent tissue, which renders misleading bands due to polarization state alteration [10, 11].
Bulk PS-OCT interferometers with dual or single detector setups have been reported in literature. Dual-detector time-domain systems with circularly polarized light incident on the sample successfully measures retardance [1, 2] and fast axis orientation [12] in a single Ascan. Another dual-detector system has been demonstrated to generate the Stokes parameters of the sample [3]. In this system, three measurements were required to verify the optical axis orientation. A single-detector free space system has been proposed to generate the Mueller matrix of birefringent samples [4] by using four consecutive A-scans with an independent polarization state incident in each case. Free space bulk systems, however, are not as convenient as fiber based systems especially when it comes to endoscopic applications.
Fiber based OCT implementations offer easy alignment, compact size, and the capability to be used with endoscopes. In the single-mode (SM) fibers, however, the polarization state of the propagating light can be altered by fiber imperfections, environmental perturbations, and stresses on the freely moving waveguide that induce static and dynamic birefringence within the fiber. Nevertheless, a SM fiber based system with two detectors has been reported for generating the Stokes parameters [13]. Four fast consecutive A-scans were acquired while light in the input arm was modulated by a polarization modulator. A single-detector SM fiber based interferometer [14] has been designed to obtain retardance and optical axis orientation of birefringent samples. In this design, A-lines with at least three different polarization states incident on the sample had to be sequentially acquired.
Fourier-domain OCT systems bear the advantage of speed and sensitivity [15–17] over the time-domain systems. Spectral-domain PS-OCT systems equipped with two line scan cameras have been demonstrated in free-space [18], and with a SM fiber implementation that requires at least three incident polarization states [19]. Single camera-based spectral-domain PS-OCT systems have also been reported in free-space [20], and with SM fiber implementation that requires two consecutive A-scans [21]. Swept-source PS-OCT system has been demonstrated with dual-detectors requiring two consecutive scans to quantify birefringence [22]. Fiberbased swept-source PS-OCT systems have been reported for quantifying birefrigence in single A-scan using dual-detector setups [23, 24]. A single-detector swept-source PS-OCT with the incident polarization state circumnavigates Poincaré sphere during a single A-scan [25] has been published very recently. Optical axis orientation measurement has also been demonstrated [18–20, 24].
Polarization maintaining (PM) fibers, unlike the conventional (non-PM) single mode fibers, have two stress elements installed parallel to the fiber core along the cladding. The resulting unidirectional stress enhances ordinary and extraordinary refractive indexes in the PM fiber, allowing light propagation in two linear orthogonal channels (fast and slow). Typical polarization isolation is 40 dB for 4 m of PM-850 fiber. A PM fiber interferometer, which employs two detectors to measure the interference patterns on the orthogonal channels, has been reported for differential phase measurement of optical path length change between two spatial points [26]. With inclusion of a Y-waveguide LiNbO3 phase modulator, up to four spatially distinct sample points have been utilized for differential phase measurements by frequency multiplexing [27]. Later on, the first PM fiber based OCT system has been reported for birefringence measurements [28]. This dual-detector system was capable of characterizing both retardance and axis orientation of a birefringent plate with a single A-scan.
In this paper, we introduce a PM fiber-based PS-OCT (PM-OCT) system capable of generating depth resolved reflectivity and birefringence images of biological tissue with a single photo-detector. A single depth scan is adequate to quantify birefringence along the Aline accurately as shown with the characterization experiments of a variable retarder. Another advantage of the PM-OCT is that the retardance is measured without any compensation. The design eliminates ghost images due to the cross-coupling in PM fiber components within the OCT imaging range. Like other PS-OCT implementations, the reflectivity measurement of PM-OCT for birefringent tissue is inherently stable and representative. Because the PM-OCT maintains polarization state of the light under mechanical disturbances such as fiber movement and rotation, and does not use any polarization controller, it may become popular for clinical applications. Furthermore, the PM-fiber approach can be utilized for simple PMOCT implementations in Fourier domain to improve the imaging speed considerably.
2. System description
Figure 1 illustrates a schematic diagram for the PM-OCT system. The light source is a 5 mW superluminescent diode operating at 855 nm (λ c) with a full-width half-maximum bandwidth of 32 nm. Hence, a theoretical axial resolution of 7.1 µm is expected. Light transmitted through a free-space isolator is coupled into the slow channel of the PM-fiber system.
A 2×2 PM-coupler launches 30% of the light into the sample arm. A quarter-wave plate inserted at 45° with respect to the slow axis of the fiber creates circularly polarized light incident on the sample. The birefringence of sample alters the polarization state, therefore, the back-scattered light couples into the slow and fast axes of the PM fiber. Here, the mode that propagates both ways in the slow axis is denoted by S, and the mode cross-coupled into the fast axis is denoted by SF. Similar denotation in small letters (s and sf) is used for modes in the reference arm.
In the reference arm, a fiber-based polarization splitter/combiner directs the light to a Ywaveguide LiNbO3 electro-optic phase modulator through a 0° splice. After modulated, the light in the slow channel enters a galvanometer-equipped rapid scanning optical delay line (RSOD) [29, 30] that is employed in the bulk portion of the reference arm. The RSOD provides high-speed axial scanning (up to 500 scans/s), and compensates for dispersion imbalance in the interferometer in order to achieve the theoretical axial resolution by adjusting the separation between the grating and lens. The rotating mirror on the fast galvanometer is laterally centered with the optical axis of the lens, so that the RSOD linearly scans the reference arm length without inducing fringe modulation. The fringes are formed at desired frequencies by means of the LiNbO3 phase modulator.
Light returning back from the RSOD is equally split at the Y-connection of the phase modulator. In order to modulate the s and sf components, two sawtooth waveforms are applied to the phase modulator. The waveforms are synchronized in phase and oscillate at frequency f 1, with voltage amplitudes V π and V 3π, respective to s and sf. Hence, double pass optical path length changes as a result of phase modulation are one central wavelength (2π) for s, and two central wavelengths (4π) for sf. The x-cut y-propagating modulator only transmits and modulates the polarization channel aligned with the LiNbO3 TE plane, which is aligned with the slow channel of the PM fiber. Therefore, the sf component is then coupled into the fast channel of the PM fiber by a 90° splice between the modulator and polarization splitter/ combiner.
Fig. 1. Schematic diagram of the interferometer. All fibers are polarization maintaining. SLD - Superluminscent diode, FB - fiber bench, FSI - free-space isolator, C - collimator, PSC - polarization splitter/combiner, PMod - phase modulator (LiNbO3), FG - function generator, G - grating, , L - lens, GM - galvo mirror, M - mirror, BCW - birefringent calcite wedges, QWP - quarter-wave plate
When the reference and sample path lengths are equal, s and S, and sf and SF interfere in the PM coupler. The corresponding coherence functions will appear at different locations, if the optical path length differences between the reference and sample arms for the slow and fast channels are unequal. In order to position the coherence functions at a same location, a pair of birefringent wedges is inserted in the sample arm with optical axis aligned with that of the PM fiber. For accurate alignment, the effective thickness adjusted by the wedges must be equal to the displacement divided by the birefringence of the wedge material. The wedges must be aligned with precision. For instance, 100 µm lateral translation of a 7.5° calcite wedge (Δn≅0.17) induces an optical path difference of 2.2 µm, which is within the axial resolution. Therefore, translation of the wedge is achieved by means of a manual translational stage.
A photo-detector in the detection arm detects and amplifies the frequency-multiplexed interference signal, which consists of two distinct fringe frequencies. The component at frequency f 1 corresponds to the interference between s and S; whereas the interference between sf and SF appears at frequency 2f 1. Using a 12-bit, 5 Msample/s analog to digital converter, the analog signal is acquired to a personal computer for data processing and image display.
A dual-channel configuration is utilized for relative optic axis orientation measurement. In this configuration, a Wollaston prism in the detection arm separates and diverts the orthogonal polarization channels onto the detectors. In this case, the phase modulator driven by sawtooth amplitudes of V π does not induce frequency multiplexing; therefore, both detectors detect interference at frequency f 1.
3. Algebraic formulation and signal processing
The sample is treated as a linear retarder with retardance δ and optical axis orientation θ at a given depth. For circularly polarized light incident on sample, the electrical field of light back-scattered from the sample can be represented by using Jones calculus as [5]
where R is sample’s reflectivity, and the first element of the vector represents the slow axis. The variables in Eq. (1) are depth-dependent. It must be noted that this equation applies only when circularly polarized light is incident on the observed depth point. Both birefringence and polarization-independent reflectivity can be mapped from the acquired signal. The DC-blocked interference signal observed on the detector can be written as
where k is a constant related to detector’s quantum efficiency, Δd is the optical path length mismatch between the two arms of the interferometer, and lc is the source’s coherence length. Digital band-pass filters centered at f 1 and 2f 1 with similar bandwidths separates the two bracketed terms in Eq. (2). The intensity image that shows tissue reflectivity is obtained by mapping the reflectance signal, which is calculated by [1]
where U 1 and U 2 are the depth-resolved amplitudes (envelopes of the coherence functions) for the slow and fast channels, respectively. Phase retardance image is constructed by mapping the quantity [1]
The phase difference between the fringes can be utilized for observing variations in optical axis orientation using a dual-detector setup. The relative optical axis orientation is given by
where ϕ 1 and ϕ 2 are the phase information on the slow and fast channels, respectively. The differential phase operation in Eq. (5) provides common mode noise rejection, as well. The phase and amplitude terms can be calculated by using the Hilbert transform: ϕm=arctan(H{Im}/Im) and Um=(I 2 m+H{Im}2)1/2, where H indicates the Hilbert operator, and m indicates a particular channel.
4. Results
4.1 System characterization
A liquid crystal variable retarder (LCVR) is inserted in the sample arm between the quarter wave-plate and the lens. Figure 2 shows the retardance measurement versus the LCVR’s driving voltage using the single- and dual-detector setups. Because the amplitude ratio in Eq. (4) is always positive, the phase retardance calculated using the arctangent function is bounded between zero and 90° as shown in Fig. 2(a). After correcting for this anomaly, the retardance curves in Fig. 2(b) are obtained, and plotted with the manufacturer’s test data of the variable retarder. Slight difference between the PM-OCT and manufacturer’s curves can be accounted for misalignments, mismatch between the design wavelength of our quarter-wave plate (830 nm) and the PM-OCT’s operating wavelength (855 nm), a different wavelength (848.7 nm) used for manufacturer’s test, and the temperature dependence of the LCVR. The results are in good agreement with each other, and show the efficacy of the single-detector frequency multiplexed design aided by digital filtering.
Fig. 2. (a). Phase retardance measurement of a voltage controlled liquid crystal variable retarder using single- and dual-detector PM-OCT setups. (b) Retardance after the phase anomaly is corrected, and the manufacturer’s test data.
Figure 3 demonstrates the measurement of optical axis orientation with dual-detector setup. The LCVR with its retardance fixed is rotated 180° in the sample path with 5° incremental steps. Figure 3(a) shows the measured fast axis orientation. The slope for the data set is 1.08. Retardance measurement insensitivity to sample rotation is shown in Fig. 3(b). The mean and standard deviation of the phase retardance measurement are 43.65° and 0.79°, respectively. Set value for phase retardance when the LCVR is driven by 7 V is 42.11°. Errors in data shown in Fig. 3 may originate from imperfect polarization components and alignments as discussed above.
Fig. 3. Measurements of the LCVR’s fast axis orientation, and rotation insensitivity for phase retardance
4.2 Imaging
A mouse tail with tendons exposed is placed under the sample arm of the PM-OCT. While rapid axial scans are performed in the reference arm, the sample light is laterally scanned over the tissue using a galvanometer-based mirror scanner. Correspondingly, cross-sectional images are obtained. Each frame consists of 400 A-lines, and is recorded in 4 seconds. If the detector bandwidth (150 kHz) is increased, the axial scanning speed (100 Hz) can be improved.
Figure 4 shows the reflectivity and retardance images acquired by the single-detector PMOCT setup. The optical power incident on the tissue is approximately 1 mW. The interference signal consisting of 60 kHz and 120 kHz modulations is digitized at 3 Msamples/s. The polarization-insensitive reflectance image shows the tissue reflectivity in Fig. 4(a) with 7.9 µm axial resolution, 27 µm lateral resolution, and 30 dB dynamic range. The image shows the tendons (bright structures on the sides), and an artery in the middle. Like in other PS-OCT implementations, tissue birefringence does not induce misleading bands in the reflectivity image.
Tissue birefringence results in a banding pattern as shown in the retardance image, Fig. 4(b). The figure shows that the tendons are highly birefringent. To avoid as much systematic error as possible [5], the regions having low SNR (<3 dB) in the intensity image are masked in Fig. 5(b).
Fig. 4. Single-detector PM-OCT images of a mouse tail. (a) Polarization-insensitive reflectivity image, (b) retardance image shows a banding pattern that is due to tissue birefringence.
Using a mode-locked Ti-Sapph laser with 45 nm bandwidth centered at 835 µm, an exposed mouse foot is imaged by the dual-detector PM-OCT setup. The optical power incident on the tissue is 3 mW. Figure 5(a) shows the reflectivity image with 6.8 µm theoretical axial resolution, 26.6 µm lateral resolution, and 26 dB dynamic range. The extensor tendons are not easily distinguished in the reflectivity image. However, the banding patterns due to the tissue birefringence clearly indicate the location of the tendons in the retardance image, Fig. 5(b). The relative angular divergence of the tendons is obtained from the optical axis orientation image shown in Fig. 5(c). The low SNR (<8 dB) regions in the intensity image are masked in Fig. 5(b) and 5(c). In this experiment, the interference channels modulated at 80 kHz are sampled at 2 Msamples/s.
Fig. 5. Dual-detector PM-OCT images of a mouse foot. (a) Polarization-insensitive intensity image, (b) retardance image, and (c) relative fast axis orientation image. The retardance image clearly shows the extensor tendons that are not easily recognized in the intensity image.
We also compared single-detector reflectivity and retardance images to their corresponding dual-detector images and found that they were alike.
5. Discussion
PM-OCT design eliminates ghost lines within the OCT imaging range (2 mm). The PM fiber splices, if the segments are not precisely oriented, can induce cross-coupling between the channels, which results in ghost images. Other factors creating ghost images are the imperfect PM fiber orientation in the polarization components, and stress applied to the fiber by these components. In the reference arm, cross-coupling into the fast channel is eliminated by the phase modulator, and cross-coupling of the returning light in the modulator is eliminated by the polarization combiner. If a ghost image cannot be removed by precise implementation, it can be displaced out of the OCT range by using longer PM fiber segments. In our implementation, splice losses have ranged between 0.1 and 1.2 dB, regardless of the splice angle.
Another design concern is the unequal transmission loss of the orthogonal modes in the reference arm. The transmission efficiencies of the polarization splitter/combiner and Ywaveguide phase modulator for the orthogonal polarization channels as well as the quality of fiber splices can cause intensity imbalance between the polarization channels. The ratio of the fringe amplitudes in PM-OCT channels was 0.88, and the effect on measurements was avoided by rescaling the interference signals.
Light in the orthogonal channels travel different optical paths. As a result, the dispersion imbalances between the reference and sample arms may not be identical for the two channels. Hence, the RSOD may not compensate the dispersion for both channels at the same gratingmirror distance. Using the superluminescent diode, we obtained coherence lengths that deviate 0.8 µm from the theoretical value. Therefore, the effect was negligible. However, if broader optical bandwidths are required for ultrahigh axial resolution, the system must be implemented with additional care.
An advantage of PM-OCT over non-PM fiber-based PS-OCT systems is that the retardance measurement does not require compensation for polarization transformations known in non-PM single-mode fibers. The axis orientation image, which is calculated from the phase difference, is sensitive to dynamic external perturbations, for which the fiber-based components of the PM-OCT are kept in polystyrene enclosure. The image shown in Fig. 5(c) does not suffer such perturbations within four seconds of acquisition time while the sample arm fiber is not disturbed. Since light between the phase modulator and the RSOD propagates in the slow axis, perturbations on the exposed fiber of the reference arm are not problematic. Contrary to the bulk PS-OCT implementations that yield absolute axis orientation [12], PMOCT produces relative axis orientation images.
Images are generated with circularly polarized light incident on sample permitting a retardance measurement that is insensitive to sample rotation in plane perpendicular to ranging. However, a probe designed for endescopic applications needs to house the quarter waveplate. Such a probe does not have to house the wedges, which can be located between the probe and the sample arm fibers, or the alignment of coherence functions can be made in the reference arm.
6. Conclusion
We have demonstrated a novel design of a PM-fiber based polarization sensitive optical coherence tomography for imaging tissue reflectivity and birefringence. The PM-OCT system quantitatively maps the retardance along the A-line with a single detector and a single A-scan. The system is characterized with both pre-proposed dual-detector setup and the new frequency multiplexed single-detector design. The PM-OCT is also the first PM-fiber based system demonstrating images with high dB range. Because the polarization is maintained in the PM fiber and there is no need for polarization controllers, the PM-OCT system may become attractive for clinical and endoscopic applications.
Acknowledgments
This work was supported in part by research grants from the National Institutes of Health (R21 EB006588) and the University of Minnesota (Grant-In-Aid program).
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