All single-mode fiber-based polarization-sensitive spectral domain optical coherence tomography system

Our SMF-based OCT system is shown in figure 1 which is based on the Michelson interferometer. Figures 1(a) and (b) show the schematic and prototype of the handheld probe, respectively. The source used in our system was a superluminescent diode (SLD) with a center wavelength of 840 nm and a spectral bandwidth of approximately 50 nm. Thus an axial resolution of the system is 6.2 μm in air. The maximum power of the laser source was 54 mW. The light from SLD was guided into one port of the 2 × 2 fiber coupler without any polarizing components, and split equally into the reference and the sample arms of interferometer. In the reference arm, the light was reflected from a reference mirror. In the sample arm, a handheld probe was implemented with a galvanoscanner mirror for imaging tissues. The light backscattered from within the sample in the sample arm and the light reflected from the reference mirror were recombined at the fiber coupler and the interferogram generated was measured by a home-made spectrometer. The interference signal was then collimated by focusing lens with a focal length of 50 mm, dispersed by a transmission grating of 1200 lines/mm, focused by an achromatic focusing lens with a focal length of 300 mm. The light were then separated by a polarization beam splitter (PBS) into horizontal and vertically components which were independently directed toward two line-scan CCD cameras of 2048 and a line scan acquisition rate of 70 kHz (AVIIVA M2 CL 2014, Atmel, CA, USA). Digitized spectral fringe profiles from the camera were acquired by data acquisition (DAQ) boards and transferred to a computer for further processing. DAQ boards and the galvanometer-based mirror were synchronized by a signal generated by an analog output device (PCI-6733, National Instruments). The data acquisition and transfer were triggered by a signal generated by a computer synchronized with the ramp function that drives the x-direction scanning galvanometer. The polarization controller (PC1) was aligned to modify the polarization of the light from the source to ensure maximum power. PC2 and PC4 allowed us to adjust the polarization of the light to achieve equal reference illumination power at the detector outputs in the SMF-based system.

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In the SMF-based system, the polarization information of sample and system are mixed together. It is difficult to directly extract the sample polarization information from the output signals with single IPS because the polarization information of fiber and fiber components are unknown. It has been shown that to extract the polarization properties of sample, it is required that the phase retardance of SMF system to be equal to a half-wave plate or full-wave plate by adjusting PCs.

In our analysis, the Stokes vector is used to represent the polarization state of the light from the horizontal and vertical (H & V) channels, and Muller matrix is used for describing the effects of SMF and optical components, and sample on the polarization of the light. Let H(z) and V(z) donate the interference fringe signals from a specific depth z, the output Stokes vector from spectrometer can be expressed as:

$$\begin{eqnarray}&&{S}_{out}\left(z\right)=\left[\begin{array}{l}{S}_{1}\left(z\right)\\ {S}_{2}\left(z\right)\\ {S}_{3}\left(z\right)\end{array}\right]=\left[\begin{array}{l}H\left(z\right){H}^{\ast }\left(z\right)-V\left(z\right){V}^{\ast }\left(z\right)\\ H\left(z\right){V}^{\ast }\left(z\right)+{H}^{\ast }\left(z\right)V\left(z\right)\\ i\left[H\left(z\right){V}^{\ast }\left(z\right)-{H}^{\ast }\left(z\right)V\left(z\right)\right]\end{array}\right].\end{eqnarray} \tag{ 1 }$$

For a circularly polarized incident light and a bulk PS-OCT system, the Stokes vector of the backscattered light is [6, 34]:

$$\begin{eqnarray}&&{S}_{out}=\left[\begin{array}{l}{S}_{1}\\ {S}_{2}\\ {S}_{3}\end{array}\right]={M}_{S}\left[\begin{array}{l}0\\ 0\\ 1\end{array}\right]=\left[\begin{array}{l}\sin \left(2\alpha \right)\sin \,{\delta }_{S}\\ \cos \left(2\alpha \right)\sin \,{\delta }_{S}\\ \cos \,{\delta }_{S}\end{array}\right],\end{eqnarray} \tag{ 2 }$$

The phase retardance and optical axis orientation of sample are then given by:

$$\begin{eqnarray}&&\begin{array}{l}{\delta }_{S}=arc\,\cos \,{S}_{3}\\ \alpha =\displaystyle \frac{1}{2}\arctan \left(\displaystyle \frac{{S}_{1}}{{S}_{2}}\right)\end{array}\end{eqnarray} \tag{ 3 }$$

To derive the information about the changes in polarization state, we will use a modified model of the Muller matrix measurement. Figure 2 shows a simplified schematic of Muller matrix measurement with an all SMF-based PS-SDOCT, where M_in represents Muller matrix of the illumination optics, M_out is the Muller matrix of the fiber path from the sample surface to the interferometer output, and M_s is a round-trip cumulative Muller matrix of a sample, S_out (z_surf) and S_out (z) are the Stokes vectors of the light from surface and the specific depth z of the sample, respectively. With the help of schematic in figure 2, equation (1) can be rewritten as:

$$\begin{eqnarray}&&{S}_{out}\left(z\right)={M}_{out}{M}_{s}\left(z\right){S}_{in}.\end{eqnarray} \tag{ 4 }$$

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The output Stokes vector from the sample surface in the system, S_out (z_surf) could be written as:

$$\begin{eqnarray}&&{S}_{out}\left({z}_{surf}\right)={M}_{out}{S}_{in}.\end{eqnarray} \tag{ 5 }$$

Note that we do not change the coordinate orientation for back-reflected light. Thus, the light reflected from the surface is equal to S_in. From equation (5), we have:

$$\begin{eqnarray}&&{S}_{in}={M}_{out}^{-1}{S}_{out}\left({z}_{surf}\right).\end{eqnarray} \tag{ 6 }$$

On substituting (6 ) into equation (4), we have:

$$\begin{eqnarray}&&{S}_{out}\left(z\right)={M}_{out}{M}_{s}\left(z\right){S}_{in}={M}_{out}{M}_{s}\left(z\right){M}_{out}^{-1}{S}_{out}\left({z}_{surf}\right).\end{eqnarray} \tag{ 7 }$$

Equation (7) shows that M_s is mixed with M_out in the measured signals. For a linear retardar with an optical axis θ and retardance δ, its general expression can be written as:

$$\begin{eqnarray}&&\begin{array}{l}M=R\left(\theta \right)M\left(\delta \right)R\left(-\theta \right)\\ \,\,=\,\left[\begin{array}{ccc}\cos \,2\theta & -\,\sin \,2\theta & 0\\ \sin \,2\theta & \cos \,2\theta & 0\\ 0 & 0 & 1\end{array}\right]\left[\begin{array}{ccc}1 & 0 & 0\\ 0 & \cos \,\delta & \sin \,\delta \\ 0 & \sin \,\delta & \cos \,\delta \end{array}\right]\left[\begin{array}{ccc}\cos \,2\theta & \sin \,2\theta & 0\\ -\,\sin \,2\theta & \cos \,2\theta & 0\\ 0 & 0 & 1\end{array}\right]\end{array}\end{eqnarray} \tag{ 8 }$$

In our system, diattenuation of the polarizing components can be neglected. In this case, the unknown Muller matrix M_out, can be expressed as a product of a linear retardance matrix M_L and circular retardance matrix M_C:

$$\begin{eqnarray}&&{M}_{out}={M}_{C}{M}_{L}=R\left(-\varphi \right)R\left({\theta }_{L}\right)M\left({\delta }_{L}\right)R\left(-{\theta }_{L}\right),\end{eqnarray} \tag{ 9 }$$

where φ is the circular phase retardance value of circular retardance matrix, and θ_L and δ_L are the optical axis orientation and the phase retardance of linear birefringence, respectively.

For an ideal sample with an optical axis orientation θ_S and the round-trip cumulative phase retardance δ_S, its general expression M_S can be written as:

$$\begin{eqnarray}&&{M}_{s}=R\left({\theta }_{s}\right)M\left({\delta }_{s}\right)R\left(-{\theta }_{s}\right).\end{eqnarray} \tag{ 10 }$$

Note that M_out is an orthogonal matrix [18], we have ${M}_{out}^{-1}={M}_{out}^{T}.$ By substituting equations (9) and (10) into equation (7), we have:

$$\begin{eqnarray}&&\begin{array}{l}{S}_{out}={M}_{out}{M}_{ST}{M}_{out}^{T}{S}_{out}\left({z}_{surf}\right)\\ \,\,\,=\,R\left(-\varphi \right)R\left({\theta }_{L}\right)M\left({\delta }_{L}\right)R\left(-{\theta }_{L}\right)R\left({\theta }_{s}\right)M\left({\delta }_{s}\right)R\left(-{\theta }_{s}\right)\\ \,\,R\left({\theta }_{L}\right)M\left({\delta }_{L}\right)R\left(-{\theta }_{L}\right)R\left(\varphi \right){S}_{out}\left({z}_{surf}\right)\end{array}\end{eqnarray} \tag{ 11 }$$

By adjusting the polarization controller in the sample arm (PC3), the system phase retardance is equal to that of a half-wave plate or full-wave plate, the output Stokes vector of the light refelceted from the sample surface is ${\left[0,{\rm{0}},{\rm{1}}\right]}^{T}.$ Thus, M(δ_L) is expressed as:

$$\begin{eqnarray}M\left({\delta }_{L}\right)=\left[\begin{array}{ccc}1 & 0 & 0\\ 0 & -1 & 0\\ 0 & 0 & -1\end{array}\right]or\left[\begin{array}{ccc}1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1\end{array}\right].\end{eqnarray} \tag{ 12 }$$

Therofore, ${M}_{out}{M}_{ST}{M}_{out}^{T}$ could be considered as a new retardar with an axis orientation α and phase retardance δ_s, equation (11) could be simplified as:

$$\begin{eqnarray}&&{S}_{out}=\left[\begin{array}{l}{S}_{1}\\ {S}_{2}\\ {S}_{3}\end{array}\right]=R\left(\alpha \right)M\left({\delta }_{s}\right)R\left(-\alpha \right)\left[\begin{array}{l}0\\ 0\\ 1\end{array}\right],\end{eqnarray} \tag{ 13 }$$

where $\alpha =\varphi +{\theta }_{S}or\alpha =\varphi +{\theta }_{S}-{\theta }_{L}.$

If the SMF system is so stable enough that φ and θ_L remain unchanged, the phase retardance δ_S and axis orientation θ_s of the sample can be extracted from equation (3) and can be expressed as:

$$\begin{eqnarray}&&\begin{array}{l}{\delta }_{S}=arc\,\cos \,{S}_{3}\\ {\theta }_{S}=\left\{\begin{array}{c}\displaystyle \frac{1}{2}\arctan \left(\displaystyle \frac{{S}_{1}}{{S}_{2}}\right)-\varphi ,\,\,\,\,{\delta }_{L}=2\pi \\ \displaystyle \frac{1}{2}\arctan \left(\displaystyle \frac{{S}_{1}}{{S}_{2}}\right)-\varphi +2{\theta }_{L},\,\,\,{\delta }_{L}=\pi \end{array}\right..\end{array}\end{eqnarray} \tag{ 14 }$$

Equation (13) shows that when the output Stokes vectors from the sample surface is ${\left[0,{\rm{0}},{\rm{1}}\right]}^{T}$ and the system retardance is equal to π or 2π by employing the PC3, the optical axis orientation and phase retardance of the sample can be measured with the SMF-based system. These prerequisites of system adjustment can be realized by using a quarter wave plate (QWP) [27]. In this case, the light incident on the sample is a circular polarized light, which can be verified by calculating the Stokes vector S_inof the light incident on the sample with equation (5).

In OCT imaging, the single scattered signal is particularly useful as it provides the localized optical information about the scatterers; while the multiply scattered signals photons degrades the detected signal. Therefore, determination of the tissue scattering coefficient, quantitative depth ranging, and flow measurement with OCT are generally based on single backscattered light. However, in tissue imaging, multiple scattered light is also present in the OCT signals due to the finite collection numerical aperture of the objective lens in the sample arm and partial coherence of the multiply scattered light.

In PS-SDOCT system, the light incident on the sample is illuminated by a polarized beam. The light measured by spectrometer has two components: single backscattered light I^s and multi-scattered light I^m. I^s is decomposed into two orthogonal components ${I}_{H}^{s}$ and ${I}_{V}^{s}$ components in horizontal and vertical channels, respectively. If we use ${I}_{H}^{m}$ and ${I}_{V}^{m}$ to represent multiply scattered light in the horizontal and vertical channels, we have ${I}_{H}^{m}\approx {I}_{V}^{m}$ [33], due to the multiple scattering processes. Thus, the residual spectra of the emerging light can be expressed as:

$$\begin{eqnarray}&&{I}_{d}={I}_{H}-{I}_{V}\approx {I}_{H}^{s}-{I}_{V}^{s}.\end{eqnarray} \tag{ 15 }$$

It can be seen from equation (15) that the contributions of the multiply scattered light are removed, resulting in a potential improvement of the signal-to-noise ratio (SNR) of the image.

In order to prove the ability of our SMF-based PS-SDOCT system, different tissues, including in vivo finger nail and fingertip skin, ex vivo pork cartilage, and normal and burned chicken breast have been imaged. Figure 3 shows the intensity, phase retardation and optical axis orientation images of pork cartilage ex vivo, human finger nail, fingertip skin and normal and burned chicken breast, where glycerin was applied on the tissue surface before the imaging. The PS-SDOCT system was configured at an A-line acquisition rate of 70 kHz and consisted of 500 A-lines per image frame at a scanning width of 2 mm with the maximum imaging depth of 2.5 mm. Figure 3(a) was the intensity image which showed relatively homogeneous structure in the pork cartilage. The periodical stripe appearances in the phase retardation image figure 3(b), and optical axis orientation image figure 3(c) distributed in the PS-OCT signals were easily observed due to the existence of strong birefringence in pork cartilage. The retardance on the tissue surface was zero (black) and it changed with the increase of depth in the tissues. The PS images of in vivo finger nail were presented in figures 3(d)–(f). Figures 3(e) and (f) were phase retadance and optical axis orientation that also indicated distinct layered patterns. It was obvious that the phase retardation in figure 3(e) varied between 0 and 180 deg with the imaging depth. For the intensity image of fingertip skin in figure 3(g), it was easy to observe the typical layered structure of human skin, including the thick stratum corneum and dermis. For the polarization images in figures 3(h) and (i), it was evident that tissue birefringence varied within the images: the phase retardation in some regions was high (yellow) while the retardation in neighboring regions remains low (black). Consequently, these results show that our all SMF-based PS-SDOCT system with a single IPS is able to achieve quantitative measurements of phase retardance in biological tissues.

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Figures 3(j)–(l) present the cross sectional images of structural, phase retardation and optical axis orientation imaging of normal and burned chicken breast, respectively. The images were obtained by scanning the probing beam of light across the boundary of normal and burned breast of chicken in vitro. The right part of the images in figures 3(j)–(l) was the images of the burned structure. The left part of the images in figures 3(k) and (l) demonstrated the chnages in polarization properties of chicken breast before being heated. Note that in the normal chicken breast, the variation of the relative phase with depth could be seen clearly and the characteric structures disappeared in the heated part of the tissue. It was also noted that there existed a visible boundary between the normal and the burned area in the phase retardance image (see the blue arrow in figure 3(k)), which was not evident in the intensity image (see figure 3(j)).

To demonstrate the capability of our method for removing the effects of the multiply scattered light, figure 4 shows cross-sectional images in human fingertip skin. Figures 4(a) and (b) were obtained by the two CCDs, respectively, and figure 4(c) was achieved by spectral subtraction to eliminate the multi-scattering light in tissues from equation (15). On comparison of the images, it was easily observed that the results were quitely similar to those obtained in the previous experiment results, and figure 4(c) had the higher image contrast than the other images. Here, it is evident that multiple scattering light acts as background noise, seriously degrading image quality. Compared regions with the white arrows in figures 4(a)–(c), it was obvious that the interface of stratum corneum and dermis in figures 4(a) and (b) was blurred, and the interface in figure 4(c) was really clear and continuous. Thus, the noise artifacts were greatly suppressed by removing the multi-scattered light. In addition, from the red circles in three structural images of fingertip skin, depth range in figure 4(c) was also extended due to the increasing sensitivity.

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Figure 4(d) showed the mean intensity of A-scans in selected regions from figures 4(a)–(c) at several depths. It is obvious to directly observe the signal improvement without multi-scattered light, especially at depths from 450 μm to 700 μm.

To quantify the improvement of our method, the SNR of cross-sectional images was analyzed. First choosing regions in the structural image in human skin (marked as the blue rectangle and the green rectangle in figure 4(a)), the signal and noise regions are represented by the image gray scale. Here The SNR is defined as:

$$\begin{eqnarray}&&Intensity\,SNR=\left\langle 20\,\mathrm{log}\left(S/\sigma \right)\right\rangle ,\end{eqnarray} \tag{ 16 }$$

where the angle brackets represent the average over the values of selected regions. It should be noted that the intensity SNR evaluated here indicates a metric for image contrast, rather than the sensitivity of the system used. Similarly, the SNR of corresponding regions in figures 4(b) and (c) could be calculated. The SNR values of two images in figures 4(a) and (b) obtained by two CCDs were 48.9 dB and 49.5 dB. In contrast, by spectral subtraction to eliminate the multi-scattering light from equation (16), the SNR of the image in figure 4(c) was increased to 52.1 dB. As a consequence, it was obvious that our method resulted in a SNR increase of at least 2.6 dB comparing to single CCD.