Fiber-based polarization-sensitive Fourier domain optical coherence tomography using B-scan-oriented polarization modulation method

Masahiro Yamanari; Shuichi Makita; Violeta Dimitrova Madjarova; Toyohiko Yatagai; Yoshiaki Yasuno

doi:10.1364/OE.14.006502

Optics Express
Vol. 14,
Issue 14,
pp. 6502-6515
(2006)
•https://doi.org/10.1364/OE.14.006502

Fiber-based polarization-sensitive Fourier domain optical coherence tomography using B-scan-oriented polarization modulation method

Masahiro Yamanari, Shuichi Makita, Violeta Dimitrova Madjarova, Toyohiko Yatagai, and Yoshiaki Yasuno

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Masahiro Yamanari, Shuichi Makita, Violeta Dimitrova Madjarova, Toyohiko Yatagai, and Yoshiaki Yasuno, "Fiber-based polarization-sensitive Fourier domain optical coherence tomography using B-scan-oriented polarization modulation method," Opt. Express 14, 6502-6515 (2006)

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- Medical Optics and Biotechnology
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About this Article
History
- Original Manuscript: April 18, 2006
- Revised Manuscript: June 28, 2006
- Manuscript Accepted: June 29, 2006
- Published: July 10, 2006
Virtual Issues
Virtual Journal for Biomedical Optics Vol. 1, Iss. 8

Abstract

Fiber-based high-speed polarization-sensitive Fourier domain optical coherence tomography (PS-FD-OCT) is developed at 840 nm wavelengh using polarization modulation method. The incident state of polarization is modulated along B-scan. The spectrometer has a polarizing beamsplitter and two line-CCD cameras operated at a line rate of 27.7 kHz. From the 0th and 1st orders of the spatial frequencies along the B-scanning, a depth-resolved Jones matrix can be derived. Since continuous polarization modulation along B-scan causes fringe washout, equivalent discrete polarization modulation is applied to biological measurements. For the demonstration, an in vitro chicken breast muscle, an in vivo finger pad, and an in vivo caries lesion of a human tooth are measured. Three dimensional phase retardation images show the potentials for applying the system to biological and medical studies.

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Supplementary Material (14)

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Fig. 1. Diagram of the PS-FD-OCT system. The notations imply the following: SLD: superluminescent diode, PC: polarization controller, ND: neutral density filter, LP: linear polarizer, EO: electro-optic modulator, M: mirror, G: grating, PBS: polarizing beamsplitter, CCD: line-CCD camera.

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Fig. 2. Depth-dependent phase difference of the OCT signals between horizontal and vertical channels. The interference signal is generated by the back surface of the slide glass and the mirror.

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Fig. 3. (a) measured orientations of LP and QWP. The rhombuses and squares are the measured cumulative orientation of LP and QWP relative to 0 degree, respectively. The solid and dashed lines are the linear least-squares fits of the orientations of LP and QWP, respectively. (b) measured phase retardation of QWP.

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Fig. 4. An intensity image (a) (1.83MB), the cumulative round-trip phase retardation image (b) (1.86MB), and the orientation image (c) (1.86MB) of chicken breast muscle. A median filter with a kernel size of 3×3 was applied to each B-scan of (b) and (c). Each frame has 1023 A-lines, and 128 frames are aqcuired in 5 seconds. The image size is 2 mm (x) ×2 mm (y) ×3.44 mm (z) in air. (6.80MB version (a), 6.80MB version (b), and 6.83MB version (c))

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Fig. 5. Images of chicken breast muscle with different modulations. Upper images (a)–(c) are measured with continuous polarization modulation, and lower images (d)–(f) are measured with discrete polarization modulation. (a) and (d) are the intensity images, (b) and (e) are the phase retardation images, and (c) and (f) are the orientation images. All images have 1023 A-lines, and axial 500 pixels. The image size is 2 mm (x) ×2.15 mm (z) in air.

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Fig. 6. An intensity image (a) (2.16MB), the cumulative round-trip phase retardation image (b) (2.18MB), and the orientation image (c) (2.17MB) of a human finger pad in vivo. A median filter with a kernel size of 3×3 was applied to each B-scan of (b) and (c). The volume is 4 mm (x) ×4 mm (y) ×1.75 mm (z) in air, or 1023 pixels ×128 pixels ×350 pixels. The measurement time is 5 seconds. (13.3MB version (a), 13.3MB version (b), and 13.3MB version (c))

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Fig. 7. (a): an intensity image (upper) and the cumulative round-trip phase retardation image (lower) of caries lesion of human canine tooth in vivo (1.86MB). A white arrow shows the enamel-dentin junction. The size is 6 mm (x) ×2.80 mm (z) in air, or 2046 pixels (x) ×650 pixels (z). 64 frames were scanned on 6 mm length and acquired in 5 s. (b): a enlarged intensity image of the 24th frame in the movie (a). The white arrows show the incremental lines in the enamel region. A green arrow shows the tufts and lamellae above the enamel-dentin junction. The image size is 2.5 mm (x) ×2.54 mm (z) in air. (4.28MB version)

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Tables (1)

Table 1. Typical approaches to obtain PS-OCT image. A: circularly polarized incident light, B: Stokes vector, C: Mueller matrix, D: Jones matrix with two incident polarizations, E: Jones matrix with polarization modulation method.

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Equations (27)

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I_{h} (x, ω) = {{∣ H_{ref} (x, ω) ∣}^{2} + ∣ H_{sam} (x, ω) ∣}^{2} + H_{ref} (x, ω) H_{sam}^{*} (x, ω) + c . c .,

{\tilde{I}}_{h} (x, z) = 𝓕_{z ω}^{- 1} [H_{ref} (x, ω) H_{sam}^{*} (x, ω)],

(\begin{matrix} \cos \frac{φ}{2} & i \sin \frac{φ}{2} \\ i \sin \frac{φ}{2} & \cos \frac{φ}{2} \end{matrix}),

(\begin{matrix} H_{sam} \\ V_{sam} \end{matrix}) = J_{all} (\begin{matrix} H_{i} \\ V_{i} \end{matrix}),

J_{all} = (\begin{matrix} J (1, 1) & J (1, 2) \\ J (2, 1) & J (2, 2) \end{matrix}),

(\begin{matrix} H_{i} \\ V_{i} \end{matrix}) = (\begin{matrix} i \sin \frac{φ}{2} \\ \cos \frac{φ}{2} \end{matrix}) .

(\begin{matrix} H_{sam} \\ V_{sam} \end{matrix}) = (\begin{matrix} J (1, 2) \cos \frac{φ}{2} + i J (1, 1) \sin \frac{φ}{2} \\ J (2, 2) \cos \frac{φ}{2} + i J (2, 1) \sin \frac{φ}{2} \end{matrix}) .

E_{ref} = (\begin{matrix} H_{ref} \\ V_{ref} \end{matrix}) = (\begin{matrix} H_{r} \\ V_{r} \end{matrix}) e^{- i \frac{φ}{2}},

𝓕_{xu} [{\tilde{I}}_{h} (x)] = 𝓕_{xu} [𝓕_{z ω}^{- 1} [H_{ref} (x, ω) H_{sam}^{*} (x, ω)]]

𝓕_{xu} [{\tilde{I}}_{h} (x)] = H_{r} 𝓕_{xu} [J^{*} (1, 2) \cos \frac{φ}{2} e^{- i \frac{φ}{2}} - i J^{*} (1, 1) \sin \frac{φ}{2} e^{- i \frac{φ}{2}}]

= \frac{H_{r}}{2} {𝓕_{xu} [J^{*} (1, 2) - J^{*} (1, 1)] + 𝓕_{xu} [J^{*} (1, 2) + J^{*} (1, 1)] * 𝓕_{xu} [e^{- i φ}]},

\sin [φ (x)] = \sum_{l = 0}^{\infty} 2 J_{2 l + 1} (A_{0}) \sin [(2 l + 1) ω_{m} x],

\cos [φ (x)] = J_{0} (A_{0}) + \sum_{l = 1}^{\infty} 2 J_{2 l} (A_{0}) \cos [(2 l) ω_{m} x],

𝓕_{x u} [e^{- i φ}] = \sum_{l = 0}^{\infty} [J_{2 l} (2.405) {δ (u - 2 l ω_{m}) + δ (u + 2 l ω_{m})}

+ J_{2 l + 1} (2.405) {δ (u - (2 l + 1) ω_{m}) - δ (u + (2 l + 1) ω_{m})}] .

{\tilde{I}}_{h} (0) = \frac{H_{r}}{2} (J^{*} (1, 2) - J^{*} (1, 1)),

{\tilde{I}}_{h} (ω_{m}) = \frac{J_{1} (2.405) H_{r}}{2} (J^{*} (1, 2) + J^{*} (1, 1)),

H_{r} J^{*} (1, 1) = - {{\tilde{I}}_{h} (0) - \frac{1}{J_{1} (2.405)} {\tilde{I}}_{h} (ω_{m})},

{H_{r} J}^{*} (1, 2) = {{\tilde{I}}_{h} (0) + \frac{1}{J_{1} (2.405)} {\tilde{I}}_{h} (ω_{m})} .

(\begin{matrix} H_{r}^{*} J (1, 1) & H_{r}^{*} J (1, 2) \\ V_{r}^{*} J (1, 1) & V_{r}^{*} J (1, 2) \end{matrix}) = (\begin{matrix} 1 & 0 \\ 0 & e^{i γ} \end{matrix}) J_{all} = J_{offset} J_{all},

J_{sur} = J_{out} J_{in},

J_{all} = J_{out} J_{sam} J_{in} .

{J_{offset} J_{all} (J_{offset} J_{sur})}^{- 1} = J_{offset} J_{out} J_{sam} J_{in} J_{in}^{- 1} J_{out}^{- 1} J_{offset}^{- 1}

= J_{offset} J_{out} J_{sam} J_{out}^{- 1} J_{offset}^{- 1}

= J_{U} (\begin{matrix} p_{1} e^{i \frac{η}{2}} & 0 \\ 0 & p_{2} e^{- i \frac{η}{2}} \end{matrix}) J_{U}^{- 1},

φ_{n} = \frac{\int_{2 π (n - 1) ⁄ N}^{2 π n ⁄ N} A_{0} \sin (ω_{m} x) d x}{2 π ⁄ N},

10 \log = {\frac{1}{2} ({∣ J (1, 1) ∣}^{2} {+ ∣ J (1, 2) ∣}^{2} {+ ∣ J (2, 1) ∣}^{2} {+ ∣ J (2, 2) ∣}^{2})},

	Time-domain		Fourier-domain
	Free space	Fiber-based	Free space	Fiber-based
A	Hee et al. [2] [de Boer et al. [3] Hitzenberger et al. [26]		Götzinger et al. [17]
B	de Boer et al. [29]	Saxer et al. [30]		Zhang et al. [31] Cense et al. [32]
C	Yao et al. [33]		Yasuno et al. [34]
D	Jiao et al. [38] Jiao et al. [39]	Park et al. [40]	Yasuno et al. [47]	Park et al. [41]
E		Jiao et al. [45]		⋄

Abstract

Supplementary Material (14)

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Figures (7)

Tables (1)

Equations (27)

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