1. Introduction

Optical coherence tomography (OCT) [1–3] is a non-invasive imaging technique, capable of optical ranging within a highly scattering sample, such as biological tissue, with visualization of microstructures at a resolution approaching that of conventional histology. The technique, based on the optical scattering properties of tissue, is feasible because most biological tissues have a sufficient number of complex microscopic scattering elements to produce good contrast for OCT images. The development of polarization sensitive (PS) OCT [4–8] has enabled OCT to sense the birefringence properties of biological tissue that are not provided by the conventional OCT. Since its first description in 1992 by Hee et al [4], a number of medical applications for PSOCT have emerged over the last decade, for example burn assessment in skin [9–14], caries research in tooth [15–18], diagnostics of cornea [19–20] and retina [21–26] in ophthalmology, rheumatology [27–32], among the others. Recent report has shown the potential of PSOCT to detect ultra-structural changes in a muscle using the changes in the form birefringence related to dystrophy [33].

Because of the significant sensitivity and imaging speed advantages of spectral domain (SD) OCT over the time domain OCT [34,35], the recent development of PSOCT has also shifted its emphasis on the spectral domain implementations. Yasuno et al was the first to demonstrate measurements on human skin in vitro using a SD-PSOCT system [36]. SD-PSOCT systems for in vivo applications have only been developed recently thanks to the state-of-the-art light sources and high speed detection systems recently available [37–39]. Generally speaking, in conventional PSOCT, the interference signal emerging at the output of an interferometer has to be split into horizontal and vertical polarization channels for separate detections [4]. In SD-PSOCT this usually translates into the requirement for two separate spectrometer cameras [37–39]. Such requirement adds additional costs and demands the strict triggering in hardware and software to avoid any time delays between the signal acquisition of the two cameras which is required if the phase based PS-OCT algorithms are used [40]. To address these problems, single camera spectrometer detection system has been most recently proposed where the CCD array is split into two halves for accommodating, side by side, the spectral interferograms formed by the horizontally and vertically polarizing beam components. This was made possible by either shining the two orthogonal states of light at a different angle onto the dispersive grating [41] or placing a specialized Wollaston prism into the light path in the detection spectrometer [42]. This requires the uniform sensitivity across the detector array that is usually difficulty to achieve in practice. In addition, the possible imaging depth in the tissue is reduced by a factor of two because the number of pixels available for each spectrum is reduced by a factor of two. Furthermore, in the case of [41], a slight different angle for each spectrum impinging onto the grating causes different diffraction efficiency, leading to distorted spectrum mismatch between orthogonally polarized beam components. As discussed in [41], since the single camera system does not have enough degrees of freedom to achieve the pixel-to-pixel correspondence between two spectra of orthogonal beam components by a pure hardware alignment, software based correction of the distorted spectra is required. Apart from a shift correction, a size correction of the spectra is also required which means an additional calibration step is needed.

In this paper, we report an alternative approach that also uses a single-camera configuration for SD-PSOCT system to achieve the polarization sensitive imaging that eliminates the above mentioned problems. We will first describe the system design associated with some theoretical considerations. We then give experimental demonstrations of the system both for in vitro and in vivo cases with an imaging rate at 10,000 A scans per second which is currently limited by the light source power used.

2. Methods

The schematic diagram of the system that uses a single camera for spectral interferogram detection to perform polarization sensitive imaging is illustrated in Fig. 1. The system used a superluminescent diode (InPhenix, USA) with a central wavelength of 850 nm and FWHM bandwidth of 30 nm that yields a measured axial resolution of ~12 μm in air. The collimated light (~3mm diameter) from the light source was made vertically polarized by a linear polarizer and then coupled into a polarization sensitive low coherence interferometer that is similar to a PSOCT system described previously [38]. The reference light was delivered into a reference delay-line assembly (RDA). Within RDA, the vertically polarized light was split by a non-polarization beam splitter into two equal beams. One beam was passed through a quarter wave plate (QWP) with its fast axis oriented at 45° and reflected by a staggered reference mirror. This beam was then passed through QWP again to become horizontally polarized beam. Another beam was bended by a mirror, reflected back by the same staggered reference mirror as above to join with the horizontally polarized beam. The joined beam was then routed back into the interferometer. Neutral density filters were placed in one or both of the beam paths to make sure that the light for two orthogonally polarized beam components impinged onto the detector has equal strength. With such design, RDA provided a fixed optical pathlength difference (OPD) between these two orthogonally polarized lights. The fixed OPD can be adjusted according to the needs for different applications. In the current study, OPD between the vertically and horizontally polarized lights was ~2.0 mm. This made it possible to separate the OCT images formed by two orthogonally polarized beam components at the output plane of Fourier space after processing the mixed spectral interferograms captured by the CCD camera (see below).

The sample light was first passed through a QWP with its fast axis oriented at 45° that transforms the light into a circularly polarized light. And then it was delivered onto the sample by an X galvanometer scanner and an achromatic lens with a focal length of 100mm. The theoretical lateral imaging resolution and the depth of focus of the probe beam were approximately 28 μm and 4.2 mm, respectively. The light power shone onto the sample was ~2.0 mW. The light returning from the reference and sample arms was recombined and coupled into a single mode fiber which was then sent to a custom built high speed spectrometer, consisting of a 30mm focal length collimator, a 1200 lines/mm polarization-insensitive volume-phase-holographic transmission gratings (Wasatch Photonics, USA) and an achromatic focusing lens with 190 mm focal length. The focused light spectra that includes both orthogonally polarized beam components were captured in parallel by a line scan charge coupled device (CCD) (Atmel, USA) consisting of 1024 pixels, each with 14×14 microns in size and 12 bits in digital depth, and capable of 53 kHz line rate. Polarization controller was used in the single mode fiber in order to fine tune the polarization states of light in the spectrometer system. Note here that the propagating beam paths for vertically and horizontally polarized light components are totally identical in the spectrometer, and their spectra are captured by the identical CCD pixel array in parallel, thus the requirement for careful calibration of the spectral components on the CCD array like in [41, 42] is avoided. The spectrometer has a designed imaging depth of approximately 8.2 mm in air, i.e. the full depth in the Fourier space that was used for imaging (see below), rather than half of space used in the conventional SD-PSOCT. The camera integration time was set at 100 μs for imaging, and the spectral data from CCD (1024 pixels, A scan) was downloaded to the host computer via CameraLink™ and a high-speed frame grabber board (PCI 1428, National Instruments, USA). This means that the CCD line scan rate was 10 kHz for the current study. This imaging speed was limited by the output power of the light source used which is ~5mW in the current system because of the power loss in RDA and coupling efficiency of the interference light coupled into the single mode fiber for detection in spectrometer. The signal sensitivity of 100 dB was measured at z=+0.5 mm and dropped to ~85 dB at z=+3.5 mm when the camera integration time was set at 100 μs. The light energy in the reference arm was adjusted such that the maximum intensity on the linear CCD array detector achieved approximately 40% of the camera’s saturation level for each polarization beam components. The remaining 20% of the dynamic range of the camera was available to fill up the polarization interference fringes.

 

Fig. 1. Schematic of the SD-PSOCT system where SLD represents the superluminescent diode, L the lens, P the linear polarizer, BS the polarization-insensitive beam splitter, QWP the quarter wave plate, M the mirror, N the neutral density filter, PC the polarization controller, C the collimator, TG the transmission grating, and CCD the charge coupled device.

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The normal procedures for deriving the spectral interference in a polarization sensitive interferometer can be equally applied here. However, for clarity of the system presented here, we show below some basic elements that incorporate the effect of RDA in Fig. 1. An equivalent schematic to show the relationship between the focused sample beam and the effective positions for the reference mirror is illustrated in Fig. 2. If we assume the coordinate origin along the depth direction, z, is at the focal spot for simplicity, then the optical fields in the reference arm for the vertically and horizontally polarized lights can be expressed as:

where H and V refer to the signals from the horizontal and vertical polarization channels; R is the reflectivity in the reference arm; k is the wavenumber, d is the distance of the mirror position relative to the focal spot, and r is the matching distance between the reference mirror and the beam splitter in the interferometer. In the sample arm, the optical fields that are decomposed into the vertically and horizontally polarized light can be written as:

where S_H,V(z) represents the strengths of backscattering light at optical depth z in the sample in the respective polarization direction. Thus, considering that the vertically and horizontally polarized beam components are independent, the spectral interferogram detected at the CCD camera can be described as:

 

Fig. 2. Schematic of the relationship between the mirror position and the sample beam.

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Because of the linear relationship between the contributions from different optical depth z from within a sample to Eq. (2), spectral interferograms detected by the CCD camera at wavenumber k can be bundled and simplified by ignoring the terms that do not contribute to the useful signals, without loss of generality, as

where A_H,V(z) are the magnitude of envelopes of interferograms formed by the respective polarization components and φ_H,V(z) are the random phase term that is due to the optical properties of sample. As it can be seen, the interferograms formed by the vertical and horizontal polarization beam components are simply added together at the CCD camera.

Because of limited capability of CCD to digitize the spectral components, the SDOCT shows systematic sensitivity falling off along the imaging depth. It is highly desirable to place the target near to the zero phase delay line where the sensitivity is highest. Thus, we placed the OCT images formed by the two orthogonally polarized states side by side (2 mm apart) approximately centered at the zero delay line. However, because the spectral interferograms captured by the CCD are real-valued components, its Fourier transform produces a complex conjugate artifact that mirrors with the desired true image about the zero-phase delay in the entire complex space, leading to un-resolved positive and negative distances. To solve this problem, we adopted the in vivo full-range complex Fourier domain OCT technique recently developed in our group [43, 44] in which a constant modulation frequency was introduced into the spatial spectral interferograms when the probe beam was scanned over the sample. In the current SD-PSOCT setup, this was achieved by mounting the reference mirror in the reference arm onto a linear Piezo-translation stage (Fig.1) that moved the mirror at a constant velocity across the B scan (i.e. x direction scan). As a consequence, a constant modulation frequency f ₀ is introduced in Eq. (4),

where t is the timing of the x scanner when it scans over the B scan. t=0 would be the start of the B scan. To eliminate the complex conjugate mirror images from the output plane of Fourier space, Hilbert transformation was first applied to Eq. (5) against t to obtain the analytic function,

As a consequence, a final Fourier transformation against 2z as in conventional SD-OCT will retrieve the depth information of the sample with the complex conjugate mirror terms removed from the output plane. It is clear from Eq. (6) that the images formed by the vertically and horizontally polarized beam components are separated by 2d around the zero delay line that is determined by the RDA setup as described above.

In this study, the modulation frequency introduced in the spectral interferograms was 1.25 kHz with the CCD line rate set at 10 kHz. Because the introduced modulation frequency is one eighth of the data acquisition rate, the phenomenon on the spectral interference fringe washout at the CCD camera can be neglected. In the x direction, there were 1000 discrete points measured that makes up a data matrix of 1000 by 1024 elements (slice, B scan) from which the OCT images formed by two orthogonally polarized beam components were computed at once.

After the data had been acquired, several steps of post-processing were performed. First the average over 1000 A-lines was subtracted from the raw data, followed by fixed pattern noise removal. This operation effectively removes/minimizes autocorrelation, self-cross correlation, and camera noise artifacts presented in the final images [45] that considerably improves the image quality. The subtracted spectral interferograms are then converted into the equal frequency space by use of the spline interpolation method as usually done in the SD-OCT [46]. Then the full range complex imaging processing method [43, 44] were applied to the processed data to remove the complex conjugate images presented in the Fourier output plane, leaving two OCT images side by side separated by 2d = 2mm as described above. These two images represented the images formed in the horizontal and vertical polarization channels, respectively. Finally, one of the images was shifted by the fixed delay (2.0 mm) to coincide with the other image. In the images, the A-scan signals of the object structure was obtained in form of A_H,V(z) exp[i Φ _H,V(z)]. From the magnitude of envelopes A_V(z) and A_H(z) of interferograms, the depth-resolved retardation δ(z) using the formula derived by Hee et al [4] can be expressed as:

and depth-resolved reflectivity R(z) is

Since A_V(z) and A_H(z) are determined by amplitude of the sample electrical field, not their phase, measurements of retardation and reflectivity can be performed with substantial less noise. Fast axis direction θ(z) derived by Hitzenberger et al [40] is equally applied to the case presented in this study:

The measured values for δ(z)and θ(z) are unambiguous in the range of [0 90] and [0 180] degrees, respectively.

To test the accuracy of the SD-PSOCT system described above, we used a QWP inserted into the sample arm with a mirror as the sample placed at ~1mm away from the zero-delay line, and followed the steps that were described previously by e.g. [39–41]. With rotating QWP from 0 to 180 degrees, the measured optic axis orientation appeared to be approximately linear with the preset values with an amplitude oscillation of ~9 degrees, and the measured retardation was at a constant value of 82±4 degrees. These values are consistent with the values published previously, thus the SD-PSOCT system is working properly.

3. Results and Discussion

To validate that the SD-PSOCT system described here can provide the polarization sensitive imaging of the biological samples, first, we performed experiments to confirm that the system is capable of separating the OCT images formed by the two orthogonally polarized beam components by use of the RDA and full-range complex imaging technique as described in Section 2. Figure 3 gives the in vitro results captured from a fresh chicken breast sample. Figure 3(A) shows the reconstructed in-depth OCT images formed by two orthogonal states of light by use of the standard FDOCT method. As expected, RDA separates the images by ~2mm centered at zero-delay line. However, because of the property of real valued function of spectral interferograms captured by the CCD camera, the true image was completely deteriorated by the overlapped complex conjugate image, causing the separation of the two images formed by orthogonally polarized light impossible. Figure 3(B) shows the reconstructed images by use of the full range complex imaging technique, i.e. modulating the spectral interferograms across B scan at a constant frequency induced by the movement of the reference mirror [43, 44]. It is clear that the full range complex imaging was achieved with the complex conjugate image almost completely removed, where the image formed by the vertically polarized beam component is on the top of that formed by the horizontally polarized light.

 

Fig. 3. OCT images of a chicken breast sample acquired using the SD-PSOCT system: (A) direct reconstruction using standard FDOCT algorithm, and (B) reconstruction by use of the full range complex OCT method leading to the OCT images formed by the vertically and horizontally polarized beam components displayed side by side, respectively.

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With such unambiguous determination of OCT signals from two orthogonal light beams, the polarization sensitive imaging is therefore possible by simply shifting one of the images with a known amount of optical delay in the depth direction, where in this case it was 2.0 mm. Note that a horizontal line visible near the surface of the sample (Fig. 3(B)) maybe an artifact caused by interference of the two reference mirrors resulting from imperfect quarter wave plate in the reference ram.

Although the full range complex imaging technique enables the OCT images formed by two orthogonal polarization beam components to be separated and centered about the zero delay line where the sensitivity of the spectrometer is highest, the sensitivity-falling-off characteristic of the system will still has the effect on the final determination of the retardation values of the sample. The accurate determination of retardation using Eq. (7) requires that the system sensitivity at corresponding depths of two images formed by orthogonal polarization beam components are equal. To solve this issue, we used the measured curve of the system sensitivity to retrospectively correct the OCT signals A(z) along the depth, applied for example to Fig. 3(B), so that the sensitivity along the depth is approximately flat. This approach is similar to that used previously to correct the sensitivity decay in SDOCT [47]. Fig. 4 shows the system sensitivity measured along the depth up to 3.5mm, where it can be seen that for the imaging depth near to the zero delay line the sensitivity is about 100 dB and this value drops to about 85 dB at the depth of ±3.5mm for both polarization channels. From the measured data, we obtained a correction curve, c(z), by a polynomial curve fitting to a 4^th order that was then normalized resulting in c(z) having a maximum value of unity. Thereafter, the corrected OCT signals along the depth were calculated by

Finally, the shift operation was taken place in order to coincide the two images formed by orthogonal polarization beam components, respectively, to obtain the depth-resolved retardation δ(z) and reflectivity R(z), i.e. Eq. 7 and Eq. 8. Note that this correction does not effect the optic axis calculation in Eq. 9. The final results are given in Fig. 5. In obtaining Fig. 5, a simple algorithm was used to find the surface of the sample, and then a signal band strip was isolated which stands for an optical length of 2.00 mm from the surface. The signals in the other areas were forced to zero as there contains no useful OCT signals for calculation of the polarization sensitive images.

 

Fig. 4. Measured system sensitivity against imaging depth for vertically (red squares) and horizontally (blue circles) polarized channels. The solid curve was resulted from the 4^th order polynomial curve fitting to the measured data.

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Figure 5(A) gives the structural OCT image of the interrogated sample with the polarization artifact diminished. The straight-line presented in the figure is an artifact from the zero delay line that is a residue of the autocorrelation signal, not completely removed by the pre-processing method. However, the presence of this artifact would have a minimum effect on the interpretation of the sample. Figure 5(B) is a cumulative round-trip phase retardation image. The phase retardation map of the sample is gray-scale coded from 0 to 90 degrees. Because of the cumulative nature, it appears periodic changes along the depth. The non-uniformity of the periodic phase appearance is not an artifact, but reveals certain organization information of the tissue components that make up the sample. The fast axis orientation image in Fig. 5(C) shows abrupt phase changes that are due to the retardation-dependent algorithm used for determination of fast axis orientation. Thus, whenever retardation values exceed the limits of the unambiguous range, it would cause a 90 degree-shift of axis orientation.

 

Fig. 5. Polarization sensitive SD-PSOCT images (B scan) of chicken breast tissue in vitro. (A) Intensity (log scale). (B) Retardation with display scale 0 (black) and 90 (white) degrees. (C) Fast axis orientation with display scale from 0 (black) and 180 (white) degrees. Image size is 3×4 mm̂2 (depth x lateral).

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It, however, has to be pointed out that the separation distance between the two images formed by orthogonally polarized beam components and determined by the RDA design limits the imaging depth that the system can achieve. The current study sets the separation distance to be 2.0mm. This would probably serve the purpose for imaging of most biological tissues which are usually highly scattering in nature, e.g. retina and skin, and also thin samples, such as human cornea. For most highly scattering biological tissues, the OCT signals would rapidly fall into the noise floor for the optical depth beyond 2.0mm. However, for the biological samples that are relatively transparent, one could simply increase the separation distance by adjusting the RDA delay line to increase the imaging depth.

Another disadvantage of the current system is that it requires a relatively large depth of focus of the focusing sampling beam volume in order to keep the system sensitivity as uniform as possible along the depth because the two (virtual) reference mirrors are 2 mm apart. This can be easily understood by Fig. 2. We should appreciate that this is different from the sensitivity falling off characteristics of the spectrometer due to the finite number of CCD arrays. In the current study, we used an objective lens with a focal length of 100 mm that gives a depth of focus of ~4.2mm to satisfy this requirement. This however trades off the lateral imaging resolution that can be achieved. To solve this problem, an axicon lens may be used in the sample arm to focus the beam into the sample that would give us the required depth of focus while keeping the lateral resolution high. The axicon lens has been successfully used in the OCT previously [48], thus it should be feasible here too.

Note also that we have used the measured system sensitivity curve to retrospectively correct the OCT signals in order to account for depth dependent sensitivity of the system. However, in applying this amplitude-flattening to the vertical (reversed) polarization channel, noise in the upper region of the image would be amplified as well. Such operation would result in unmatched noise properties versus depth for the two polarization modes and could introduce an error in calculation of retardation values. Under this condition, Eq.(7) can be rewritten as:

where N represents the system noises that include shot noise, intensity fluctuation noise and electronic noise present in the system. From Fig. 4, the correction by use of the measured curve could have a maximum amplification factor of 6.25 applied to the noise if the maximum depth of 3.5mm is used for imaging, while for our current system it was 1.82, i.e. imaging depth of 2.0mm. Assuming the system noise floor is at 20dB as in our current system, the maximum errors accrued in the retardation over the imaging depth range of 3.5mm and 2.0mm are respectively plotted in Fig. 6 by use of the OCT signal strength at the zero-delay line (ZDL) as a variable. As it expected, the error is highly dependent on the OCT signal strength received from the sample. If the sample is placed far away from ZDL (>2.0mm), the calculation uncertainty could amount to ~27 degrees for the weak OCT signal of 30dB. This value is however greatly reduced if the sample is placed around ZDL where the system sensitivity is highest. Because typical OCT signals reflected from biological tissues have SNRs below 50dB, the maximum measuring errors of retardation induced by the system sensitivity curve correction is in a range between 1 degree for 50dB and 14 degrees for 30dB OCT signals for the system used in this study as it can be seen from Fig. 6.

 

Fig. 6. Plots show the maximum errors of retardation, due to the correction of depth-dependent system sensitivity, against OCT signal strength at ZDL received from the sample. The simulations considered are for maximum errors incurred for the imaging depth up to 3.5mm (top blue curve), and 2.0 mm as in our current system (bottom red curve).

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Finally, in vivo experiments were performed using the current system. Fig. 7 and associated videos are the SD-PSOCT images captured from the proximal nail fold of a human volunteer. The scan covers an area 4 mm wide by 1.3 mm deep (scaled by average refractive index of 1.35 [49]). The imaging rate was set at 10 frames per second with each frame covering 1000 A scans. The intensity image shown in Fig. 7(A) clearly delineates the epidermal and dermal regions near to the nail fold, cuticle, nail plate, and nail bed. The phase retardation image in Fig. 7(B) shows the highly birefringent property of the lower half of nail plate that gives a banded structure as the amount of phase retardation wraps several times from 0 to 90 degrees. At the epidermal-dermal boundary of the nail fold, the transition from white to black indicates the light experiences a change in phase retardation angle with increasing depth due to the presence of birefringent tissue there. The dermis region near to the nail fold appears homogeneous in the intensity image, whereas it shows structural appearance in the retardation image, indicating that the collagen fiber organization in this region is inhomogeneous. These results are consistent with those reported previously [50]. The same tissue properties observed in retardation image are also evident in the fast axis orientation image as shown in Fig. 7(C). The associated videos are played back in 10 frames per second at the true system imaging rate, and continuously updated for time duration of 14 seconds.

 

Fig. 7. In vivo SD-PSOCT results of the proximal nail fold of a human volunteer showing (A) Intensity (2.6MBytes) [Media 1], (B) phase retardation (2.6MBytes) [Media 2], and (C) fast axis orientation (2.6MBytes) [Media 3] images, respectively. Within images, E and D represent the epidermis and dermis near to the nail fold; C, the cuticle; P, the nail plate; B, the nail bed; EDB, the epidermal-dermal boundary; and LH, the lower half of the nail plate. Note that (A) is displayed in log scale. (B) is coded from 0 to 90 degrees and (C) from 0 to 180 degrees.

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4. Summary

We have demonstrated a novel SD-PSOCT system by employing one single line scan camera for detection of the polarization sensitive spectral interferograms formed by the vertically and horizontally polarized beam components, respectively. The OCT images from orthogonal polarization channels are separated by a fixed distance at the output plane of Fourier space enabled by a reference delay line assembly installed in the reference arm. To separate these two images in the output plane so that the polarization sensitive imaging can be performed, the complex conjugate mirror images is eliminated by introducing a constant frequency modulation in the spatial varying spectral interferograms when the probe beam is swept over the sample (B scan). Because the orthogonally polarized beam components travel in the identical beam path in the spectrometer, the distortion between spectra and therefore a careful calibration between them in order to achieve strict pixel-by-pixel correspondence are avoided. We have also experimentally demonstrated that the system is capable of polarization-sensitive imaging for both the in vitro and in vivo cases at an imaging rate of 10,000 A scan per second which is currently limited by the availability of power of the light source used.