Full-range depth-encoded swept source polarization sensitive optical coherence tomography

Tong Wu; Tong Wu; Hengyu Shi; Xinkang Zhou; Youwen Liu; Ling Wang; Yaoyao Shi; Jiming Wang; Yuangang Lu; Xiaorong Gu; Chongjun He

doi:10.1364/OE.510970

1. Introduction

Polarization sensitive optical coherence tomography (PS-OCT) is a functional extension of OCT, which can quantitatively measure the depth-resolved polarization properties of the birefringent sample [1]. PS-OCT is promising to be used in many biomedical applications, such as assessment of burn depth, early diagnosis of glaucoma and caries diagnosis [2,3].

The fiber-based PS-OCT system is desired in the clinical application, due to its advantage of miniaturization and compactness. Davé and Götzinger et al. proposed the polarization-maintaining (PM) fiber-based PS-OCT system [4–6]. However, the PM fiber would introduce polarization mode dispersion that may degrade the effective imaging [4]. Unmatched PM fiber length between the sample arm and reference arm will obscure the phase and retardation. In addition, cross-coupling between the polarization channels at the PM fiber connectors and splices can introduce ghost images and other artifacts [4,7]. Thus, it is more appropriate to use the single mode fiber (SMF) instead of the PM fiber to avoid these problems. However, the imperfection of the SMF will make the polarization state of the light transmitting through the fiber randomly vary, which will cause the polarization state of the light illuminated on the sample unknown. To overcome this problem one method is to use the polarization controllers to make the light illuminated on the sample has a deterministic polarization state. Trasischker presented a single input state PS-OCT based on all-SMF interferometer, using the complex calibration steps to control the polarization state throughout the fiber-based system [8].

In contrast, another method of the SMF-based PS-OCT uses two or more polarized light to illuminate the sample. Although the polarization state of the light illuminating the sample may be unknown, their relative positions on the Poincaré sphere are fixed. Saxer and Park et al. used a polarization modulator to generate two or four different polarized input light to illuminate the sample, and Jones matrix or Stokes vector analysis was used to calculate the birefringence of the sample [9,10]. However, the signal corresponding to the multiple polarized input light were probed sequentially [9,10], which imposed the strict requirements on both the stability of the sample and the synchronization of the devices. Kim et al. proposed the frequency multiplexing method to simultaneously measure the reflectance of the two incident polarization states [11,12], overcoming the concerns regarding the temporal variations of the catheter birefringence and the movement of the sample. But this method greatly increases the system complexity and cost. Subsequently, Baumann et al. proposed a depth-encoded method using a passive polarization delay unit (PDU) to generate orthogonal polarized input light with specific optical path difference (OPD), which does not require any expensive modulating devices or sophisticated synchronization control [13–15]. However, this depth-encoded method for PS-OCT actually sacrifices half of the imaging range, because the two OCT images corresponding to the orthogonal polarized input light need to be separated in the depth direction. In addition, to avoid overlapping with the complex conjugate artifacts, the two OCT images need to be located on the same side of the zero OPD position. However, the image further from the zero OPD position is more severely affected by the sensitivity roll-off effect. This requires the additional post-processing to compensate the sensitivity. These factors limit the system to obtain the polarization sensitive images with long range and high sensitivity.

In this paper, we propose a fiber-based full-range depth-encoded swept source PS-OCT (SS-PS-OCT) method, which can realize the high sensitivity PS-OCT imaging without sacrificing the imaging range. We utilize a passive PDU to separate the two OCT images corresponding to the orthogonal polarized input light in the depth direction, but located on the opposite sides relative to the zero OPD position. To eliminate the complex conjugate artifacts, the spatial phase modulation (SPM) was introduced in the spectral interference signal and the two full-range OCT images separated in the depth direction can be reconstructed by signal post-processing. We first demonstrate the principle of this method. Next, the detection sensitivity and complex conjugate suppression ratio of the proposed system were measured experimentally, verifying the feasibility of the SPM based full-range depth-encoded SS-PS-OCT imaging method. The phase retardation of the quarter-wave plate (QWP) with the different optic axis orientations was accurately measured. Finally, phase retardation images of biological tissue obtained using the system was demonstrated to verify the proposed method.

2. Methods

Figure 1(a) shows the working principle of the SMF-based full-range depth-encoded SS-PS-OCT method. The SS-PS-OCT system is based on a Mach-Zehnder interferometer. It consists of a sample arm with PDU, a reference arm with SPM unit, and a detection arm with the polarization diversity detection (PDD) unit. The SPM is used to eliminate the complex conjugate artifacts.

Fig. 1. The working principle of the fiber-based full-range depth-encoded SS-PS-OCT method. (a) The schematic of the fiber-based full-range depth-encoded SS-PS-OCT system. (b) The schematic of the galvo-based spatial phase modulation unit. FC: fiber coupler, C: circulator, G: galvo-scanner, L: lens, M: mirror.

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The Jones vector of the reference light arriving at the PDD unit can be expressed as

(1)$${E_R} = \left[ {\begin{array}{{c}} 1\\ 1 \end{array}} \right]{e^{i[{k{z_R} + \phi (x )} ]}}, $$

where k and z_R are the wavenumber and optical path length in the reference arm, respectively. ϕ(x) is the modulated phase term introduced by the SPM unit in the reference arm.

As shown in Fig. 1(b), by setting an offset s between the incident beam and the pivot axis of the galvo-scanner, the optical path can be modulated during the oscillation of the galvo-scanner. Considering the small mechanical scanning angle α of the galvo-scanner and the initial incident angle of 45°, the total phase change Φ in a B-scan can be derived as [16–21]

(2)$$\Phi = \frac{{16\pi \cdot s \cdot \alpha }}{\lambda }. $$

Thus, the modulated phase variation between the two adjacent A-lines can be expressed as

(3)$$\phi = \frac{\Phi }{N} = \frac{{16\pi \cdot s \cdot \alpha }}{{\lambda \cdot N}}, $$

where N is the number of A-lines per B-scan. Note that the modulated phase variation ϕ is proportional to the beam offset s. Therefore, for a given mechanical scanning angle and the number of A-lines, the offset necessary to generate the necessary modulation phase, e.g., ϕ=π/2, can be calculated according to the Eq. (3).

On the other hand, the Jones vectors of the orthogonal polarized light output from the PDU can be combined as a 2 by 2 matrix, and expressed as

(4)$${E_{in}} = \left[ {\begin{array}{{cc}} {E_{in}^{(1)}}&{E_{in}^{(2)}} \end{array}} \right] = \left[ {\begin{array}{{cc}} 1&0\\ 0&{{e^{ikd}}} \end{array}} \right]{e^{ikz^{\prime}}}, $$

where d and z’ are the OPD and the common optical path between the orthogonal polarized input light, respectively.

We denote the Jones matrix of the light path from the PDU to the sample surface as J_in, the round-trip Jones matrix of the sample as J_samp, and the Jones matrix of the light path from the sample surface to the PDD as J_out. Then, the Jones vector of the sample light arriving at the PDD can be expressed as

(5)$${E_S} = {J_{out}} \cdot {J_{samp}} \cdot {J_{in}} \cdot {E_{in}}, $$

the Eq. (5) can be rewritten as

(6)$${E_S} = J \cdot {E_{in}} = \left[ {\begin{array}{{cc}} {{J_{11}}}&{{J_{12}}}\\ {{J_{21}}}&{{J_{22}}} \end{array}} \right] \cdot \left[ {\begin{array}{{cc}} 1&0\\ 0&{{e^{ikd}}} \end{array}} \right]{e^{ik{z_1}}} = \left[ {\begin{array}{{cc}} {{J_{11}}{e^{ik{z_1}}}}&{{J_{12}}{e^{ik{z_2}}}}\\ {{J_{21}}{e^{ik{z_1}}}}&{{J_{22}}{e^{ik{z_2}}}} \end{array}} \right], $$

where J = J_out·J_samp·J_in, and z₂ is equal to z₁+ d.

The spectral interference signal can be expressed as

(7)$$I({x,k} )\sim S(k)({E_S}{E_R}^ \ast{+} {E_S}^ \ast {E_R}), $$

where S(k) represent the power spectral density of the light source. The horizontal and vertical components of the detected spectral interference signal detected by the PDD can be expressed as

(8)$${I_H}(x,k)\sim S(k)\int {[{{J_{11}}\cos (k \cdot \Delta {z_1} - \phi (x)) + {J_{12}}\cos (k \cdot \Delta {z_2} - \phi (x))} ]} dz, $$

(9)$${I_V}(x,k)\sim S(k)\int {[{{J_{21}}\cos (k \cdot \Delta {z_1} - \phi (x)) + {J_{22}}\cos (k \cdot \Delta {z_2} - \phi (x))} ]} dz, $$

respectively. Δz₁= z₁-z_R and Δz₂= z₂-z_R are the OPD between the orthogonal polarized input light and the reference arm, respectively.

The standard full-range demodulation process is conducted to the digitized spectral interference signal [16–21], and the full-range OCT images without the complex conjugate artifacts can be expressed as

(10)$${I_H}(x,z)\sim F{T^{ - 1}}[{S(k)} ]\otimes \sum {[{{J_{11}}\delta (z - \Delta {z_1}) + {J_{12}}\delta (z - \Delta {z_2})} ]} , $$

(11)$${I_V}(x,z)\sim F{T^{ - 1}}[{S(k)} ]\otimes \sum {[{{J_{21}}\delta (z - \Delta {z_1}) + {J_{22}}\delta (z - \Delta {z_2})} ]} . $$

Four OCT images corresponding to the orthogonal polarized input light can be captured by the PDD, and the four sets of OCT data are reconstructed into the Jones matrix of the sample. The Jones vector from the sample surface can be expressed as

(12)$${E_{surf}} = {J_{out}} \cdot {J_{in}} \cdot {E_{in}}, $$

To extract the phase retardation of the sample, E_s is multiplied by the inverse of E_surf. This yields the similar matrix of the sample Jones matrix M which can be expressed as,

(13)$$M = {E_S} \cdot E_{surf}^{ - 1} = {J_{out}} \cdot {J_{samp}} \cdot J_{out}^{ - 1}. $$

By performing the eigen-decomposition of M, the double-pass phase retardation (DPPR) can be calculated as

(14)$$\eta = \left|{\arg \frac{{{\lambda_1}}}{{{\lambda_2}}}} \right|, $$

where λ₁ and λ₂ are the eigenvalues of the similar matrix M.

3. Experiments

3.1 Experimental setup

The fiber-based full-range depth-encoded SS-PS-OCT system is illustrated in Fig. 2. The light source is a frequency swept source (Axsun Technology Inc.) with the center wavelength of 1310 nm and the sweeping range of 110 nm. The scanning rate is 50 kHz, and the average output power is 23 mW. The light is first split by a 90/10 single-mode optical fiber coupler (FC1). The 90% portion of the fiber coupler is connected to the sample arm. The light enters a free-space PDU after passing through a fiber-based polarization controller (PC1) and a fiber-optic collimator. The OPD d of the orthogonal polarized input light is generated by adjusting the position of the plane reflective mirrors in the PDU. The orthogonal polarized light from the PDU then enters the circulator (CIR1), and passes through a collimator, a dual-axis galvo-scanner (GVS002, Thorlabs Inc.) and a focusing lens to illuminate the sample. After passing through a polarization controller (PC2), the 10% portion of the light from the FC1 is connected to the reference arm consisting of a collimator, a single-axis galvo-scanner (GVS001, Thorlabs Inc.), a focusing lens and a reflective mirror through another circulator (CIR2). The single-axis galvo-scanner in the SPM is synced with the dual-axis galvo-scanner in the sample arm. The light reflected by the reference mirror passes through a linear polarizer to align the polarization state to 45°, and interferes with the backscattered light from the sample at the beam splitter. The interference light is split into the horizontal and vertical polarization components by the polarizing beam splitter and detected by the two balanced photodetectors, respectively. The electric signals from the photodetectors are then digitized by the two channels of the digitizer (ATS9350, AlazarTech Inc.) with 12-bit resolution simultaneously. The acquisition is triggered by the k-clock signal generated by the swept source. The axial and lateral resolution of the system are 7.57 µm and 15.68 µm, respectively.

Fig. 2. The system schematic of the fiber-based full-range depth-encoded SS-PS-OCT system. FC: fiber coupler, PC: polarization controller, CIR: circulator, C: collimator, P: polarizer, PBS: polarizing beam splitter, BS: beam splitter, G: galvo-scanner, L: lens, M: mirror.

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3.2 Data processing flow

The flow chart of the data processing is shown in the Fig. 3. Since the two OCT images corresponding to the orthogonal polarized input light can be captured in each polarization acquisition channel, the four polarization OCT images can be captured by the dual-channel acquisition. In conventional depth-encoded PS-OCT, inverse fast Fourier transform (FFT) is generally performed on the real-valued spectral interference signal, i.e., Eq. (8) and Eq. (9), along the wavenumber direction to reconstruct a depth-resolved image. After adding the SPM, the demodulation steps shown in the dotted box in the Fig. 3 is needed to be performed before calculating the phase retardation. An FFT is firstly performed along the scanning direction for each wavenumber. The OCT signal in the spatial frequency domain will be shifted to both the positive and negative spatial frequency range symmetrical to the zero frequency. Since the two spectral signals containing the same information are Hermitian, a band-pass filter is used to filter out the negative and zero frequency signals. By performing an inverse FFT on the spectral signal in the positive frequency range, the complex-valued interference signal can then be reconstructed back to the spatial domain. The full-range OCT images corresponding to Eqs. (10) and (11) can be obtained by performing an inverse FFT on the complex-valued interference signal along the wavenumber direction. The Jones matrix of the sample and its surface can be constructed by segmenting the full-range OCT images into four OCT images, and then the DPPR of the sample can be extracted according to Eqs. (13) and (14).

Fig. 3. The flow chart of the data processing.

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4. Results

4.1 Characterization of the full-range depth-encoded SS-PS-OCT system

To evaluate the detection performance of the system we measured the sensitivity of the horizontal and vertical detection channels, respectively. Taking the plane reflective mirror as the sample, we measured the A-line signals at different imaging depths by changing the OPD between the two arms to measure the system sensitivity. Figure 4(a) and (b) are the sensitivity roll-off curves measured for the horizontal and vertical channels of the system, respectively. It can be seen from the figure that the system sensitivity is highest near the zero OPD position, and decreased with the increasement of the imaging depth. When the imaging depth approaches to 2 mm, the sensitivity decreases from 67 dB to 63 dB.

Fig. 4. Sensitivity measurement for the (a) horizontal and (b) vertical detection channels.

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To verify that the full-range imaging can be realized by the proposed depth-encoded SS-PS-OCT system, we compared imaging results before and after removing the complex conjugate artifacts. Figure 5 shows the A-scan profiles for the horizontal and vertical detection channels, respectively. Before the removal of the complex conjugate artifacts, the A-scan profiles were symmetrically located on the opposite sides of the zero OPD position. However, after signal demodulation and reconstruction, the complex conjugate artifacts and the direct current term are mostly suppressed. The complex conjugate suppression ratio in both the horizontal and vertical detection channels is measured to be about 15 dB. Due to the strong signal from the surface reflection of the mirror, some residual signals from the complex conjugate artifacts remained. These results indicate that applying galvo-based SPM in the reference arm could effectively suppress the complex conjugate artifacts.

Fig. 5. A-scan profiles before (solid blue line) and after (dotted red line) the removal of the complex conjugate artifacts in the horizontal (a) and vertical (b) detection channels, respectively.

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Figure 6 compares the OCT images of the bovine tendon acquired using the conventional depth-encoded and the proposed full-range depth-encoded SS-PS-OCT system. The image shown in the Fig. 6(a) was obtained by the conventional depth-encoded SS-PS-OCT system. In order to avoid overlapping with the complex conjugate artifacts, the two OCT images corresponding to the orthogonal polarized input light should be located on the same side of the zero OPD position. For the sample occupying a long depth range the OCT image further away from the zero OPD position cannot be obtained completely, and was more severely affected by the sensitivity roll-off effect, resulting the lower sensitivity than that near the zero OPD position. The images shown in the Fig. 6(b) and (c) were obtained by the full-range depth-encoded SS-PS-OCT system. To realize the high sensitivity detection, the two OCT images corresponding to the orthogonal polarized input light were placed on the opposite sides of the zero OPD position. Before removing the complex conjugate artifacts, the two bovine tendon OCT images were overlapped with each other, and cannot be distinguished. After demodulation and reconstruction, the complex conjugate artifacts are mostly eliminated, and the two OCT images of the bovine tendon corresponding to the orthogonal polarized input light can be clearly distinguished with high sensitivity. To quantify the signal-to-noise ratio (SNR) improvement the profiles of the images at the same lateral position corresponding to the red dashed line in Fig. 6(a) and (c) are shown in the Fig. 6(d). As shown in the figures the full-range depth-encoded SS-PS-OCT achieves an enhancement of peak SNR of 5 dB compared with the conventional depth-encoded SS-PS-OCT.

Fig. 6. Intensity images of the bovine tendon obtained by the (a) conventional and (b) (c) full-range depth-encoded SS-PS-OCT system, and (d) depth profile of the intensity images.

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4.2 Imaging performance of the full-range depth-encoded SS-PS-OCT system

In order to verify the measurement accuracy of the full-range depth-encoded SS-PS-OCT method the DPPR of a piece of QWP (WAQ05ME-1310, Thorlabs Inc.) with different optic axis orientation was measured by the system. The sample was also measured by the conventional depth-encoded SS-PS-OCT method with and without sensitivity roll-off compensation. The measurement results are shown in Fig. 7. The result indicates that the DPPR values measured by the full-range depth-encoded SS-PS-OCT method is stable regardless of different axis orientation, and the average value of the measured DPPR was 2.88 rad which is expected to be 3.14 rad theoretically. The average value of the measured DPPR was 2.72 rad and 2.80 rad for the conventional depth-encoded SS-PS-OCT method without and with sensitivity roll-off compensation, respectively. As we can see the measurement accuracy of the retardation by the conventional depth-encoded SS-PS-OCT method is improved after the sensitivity roll-off compensation, and is comparable to that of the full-range depth-encoded SS-PS-OCT method.

Fig. 7. The measured DPPR of the QWP with different optic axis orientation measured by the full-range depth-encoded SS-PS-OCT method and the conventional depth-encoded SS-PS-OCT method with and without sensitivity roll-off compensation.

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To further demonstrate the proposed full-range depth-encoded SS-PS-OCT method the bovine tendon tissue was imaged by the system. Figure 8(a) and (c) show the DPPR images of the different regions of the bovine tendon tissue. Figure 8(c) is the DPPR image calculated from the long range imaging data corresponding to the Fig. 6(c). Figure 8(b) is the profile extracted from the DPPR image corresponding to the dashed red line shown in the Fig. 8(a). The periodic structure shown in the DPPR image and the profile indicates the birefringence of the bovine tendon. The skin of human fingertip was also imaged by the developed system. Figure 8(d) is the DPPR image of the skin tissue. The uneven surface of the image shows the outline of the fingerprint. The DPPR image of the skin tissue also indicates that the proposed system can be used to image the sample with uneven surface.

Fig. 8. (a) The DPPR images of the bovine tendon and (b) the profile of the DPPR image of the bovine tendon at the dotted red line obtained by the full-range depth-encoded SS-PS-OCT system, (c) (d) The DPPR images of the bovine tendon and skin of human fingertip obtained by the system.

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5. Conclusion

In this paper, we propose a SMF-based full-range depth-encoded SS-PS-OCT method and system. The measurement and imaging of the polarization optics and the biological tissue verify that the proposed full-range depth-encoded SS-PS-OCT system has the higher detection sensitivity and measurement accuracy. The DPPR images of the biological tissue demonstrate that the proposed system can obtain the high sensitivity PS-OCT images. It may have the considerable application prospects in the fields of biomedical imaging in future.

Funding

National Natural Science Foundation of China (62105146, 62175106).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

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Full-range depth-encoded swept source polarization sensitive optical coherence tomography

Abstract

1. Introduction

2. Methods

3. Experiments

3.1 Experimental setup

3.2 Data processing flow

4. Results

4.1 Characterization of the full-range depth-encoded SS-PS-OCT system

4.2 Imaging performance of the full-range depth-encoded SS-PS-OCT system

5. Conclusion

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (8)

Equations (14)

Optics Express