Determination of birefringence and absolute optic axis orientation using polarization-sensitive optical coherence tomography with PM fibers

Jun Zhang; Shuguang Guo; Woonggyu Jung; J. Stuart Nelson; Zhongping Chen

doi:10.1364/OE.11.003262

Optics Express
Vol. 11,
Issue 24,
pp. 3262-3270
(2003)
•https://doi.org/10.1364/OE.11.003262

Determination of birefringence and absolute optic axis orientation using polarization-sensitive optical coherence tomography with PM fibers

Jun Zhang, Shuguang Guo, Woonggyu Jung, J. Stuart Nelson, and Zhongping Chen

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Jun Zhang, Shuguang Guo, Woonggyu Jung, J. Stuart Nelson, and Zhongping Chen, "Determination of birefringence and absolute optic axis orientation using polarization-sensitive optical coherence tomography with PM fibers," Opt. Express 11, 3262-3270 (2003)

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Abstract

A novel polarization-sensitive optical coherence tomography (PS-OCT) system was developed using polarization maintaining (PM) optical fibers and fiber coupler to measure birefringence properties of samples. Polarization distortion due to PM fibers and coupler can be calibrated with different polarization states during two consecutive A-scans. By processing the analytical interference fringe signals derived from two orthogonal polarization detection channels, the system can be used to measure phase retardation and optic axis orientation. Standard wave plates with different orientation and retardation were used as samples to test the system and calibrating method. We have also applied this system to image biological sample such as beef tendon.

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Fig. 1. Schematic of the PM fiber-based PS-OCT system. SLD: superluminescent diode at 1310nm with a FWHM bandwidth of 80 nm. P: Vertically polarized in line polarizer. Pol. Mod.: polarization modulator, Phase Mod.: phase modulator, PBS: polarization beam splitter, RSOD: rapid scanning optical delay line, Galvo: Galvanometer scanner, D1, D2: detectors. Amp1, Amp2: low noise preamplifier.

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Fig. 2. Poincaré’s sphere showing the polarization states of the light. S₁ and S₂ are the Stokes vectors of the light after the polarization modulator in the forward propagation. S’₁ and S’₂ show the possible polarization states of the light reflected from the surface before the polarization modulator in the backward propagation. S”₁ and S”₂ are the possible Stokes vectors of the reflected light from the surface after the PM coupler in the backward propagation.

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Fig. 3. (a) Measured fast axis orientation as a function of set orientation from 0° to 180° in steps of 10° for different wave plates. The solid line represents the set orientation and the points represent the measured orientation; (b) Measured retardation versus the actual retardation for a fast axis orientation of 80°. The retardation values of the wave plates for measurement are 45°, 55°, 70°, 90°and 143° respectively. The solid line represents the actual retardation and the points represent the measured retardation.

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Fig. 4. Images of the intensity, phase retardation and optic axis orientation in beef tendon. (a): structural (intensity) image; (b): phase retardation image; (c): fast axis orientation image;

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Equations (7)

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S = [\begin{matrix} I \\ Q \\ U \\ V \end{matrix}] = [\begin{matrix} a_{x}^{2} + a_{y}^{2} \\ a_{x}^{2} - a_{y}^{2} \\ 2 a_{x} a_{y} \cos φ \\ 2 a_{x} a_{y} \sin φ \end{matrix}]

S_{2} = [\begin{matrix} I_{2} \\ Q_{2} \\ U_{2} \\ V_{2} \end{matrix}] = M S_{1} = [\begin{matrix} M_{00} & M_{01} & M_{02} & M_{03} \\ M_{10} & M_{11} & M_{12} & M_{13} \\ M_{20} & M_{21} & M_{22} & M_{23} \\ M_{30} & M_{31} & M_{32} & M_{33} \end{matrix}] [\begin{matrix} I_{1} \\ Q_{1} \\ U_{1} \\ V_{1} \end{matrix}]

S_{o} = M_{c} M_{\mod} M_{pf} M_{s} M_{pf} M_{\mod} S_{i}

M_{c} = [\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & \cos γ & \sin γ \\ 0 & 0 & - \sin γ & \cos γ \end{matrix}]

M_{\mod} = [\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{matrix}] or M_{\mod} = [\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & \frac{\sqrt{2}}{2} & 0 & - \frac{\sqrt{2}}{2} \\ 0 & 0 & 1 & 0 \\ 0 & \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \end{matrix}]

M_{pf} = [\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & \cos δ_{f} & 0 & - \sin δ_{f} \\ 0 & 0 & 1 & 0 \\ 0 & \sin δ_{f} & 0 & \cos δ_{f} \end{matrix}]

M_{s} = [\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 - (1 - \cos δ) \sin^{2} 2 θ & (1 - \cos δ) \sin 2 θ \cos 2 θ & - \sin δ \sin 2 θ \\ 0 & (1 - \cos δ) \sin 2 θ \cos 2 θ & 1 - (1 - \cos δ) \cos^{2} 2 θ & \sin δ \cos 2 θ \\ 0 & \sin δ \sin 2 θ & - \sin δ \cos 2 θ & \cos δ \end{matrix}]

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