## Abstract

We report that the complex conjugate artifact in Fourier domain optical coherence tomography approaches (including spectral domain and swept source OCT) may be resolved by the use of novel interferometer designs based on 3×3 and higher order fiber couplers. Interferometers built from NxN (N>2) truly fused fiber couplers provide simultaneous access to non-complementary phase components of the complex interferometric signal. These phase components may be converted to quadrature components by trigonometric manipulation, then inverse Fourier transformed to obtain A-scans and images with resolved complex conjugate artifact. We demonstrate instantaneous complex conjugate resolved Fourier domain OCT using 3×3 couplers in both spectral domain and swept source implementations. Complex conjugate artifact suppression by factors of ~20dB and ~25dB are demonstrated for spectral domain and swept source implementations, respectively.

© 2005 Optical Society of America

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### Equations (8)

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(1)
$${\hat{D}}_{i}\left[{k}_{m}\right]\propto \rho \xb7\hat{S}\left[{k}_{m}\right]\xb7\left({R}_{R}+{R}_{S}+2\sqrt{{R}_{R}{R}_{S}}\mathrm{cos}\left(2\Delta x{k}_{m}+{\phi}_{i}\right)\right),$$
(2)
$${D}_{i}\left[{x}_{n}\right]=\sum _{m=1}^{M}{\hat{D}}_{i}\left[{k}_{m}\right]{e}^{-\left(j2\pi \left(2{k}_{m}{x}_{n}\right)\right)},\phantom{\rule{.5em}{0ex}}n\in \{1,M\}.$$
(3)
$${D}_{i}\left[{x}_{n}\right]\propto S\left[{x}_{n}\right]\otimes \left[\left({R}_{R}+{R}_{S}\right)\delta \left({x}_{n}\right)+2\sqrt{{R}_{R}{R}_{S}}\left(\delta \left({x}_{n}+\Delta x\right)+\delta \left({x}_{n}-\Delta x\right)\right)\right].$$
(4)
$${\hat{D}}_{i}\left[{k}_{m}\right]={\hat{D}}_{i}^{0}\left[{k}_{m}\right]+j{\hat{D}}_{i}^{90}\left[{k}_{m}\right].$$
(5)
$${\hat{D}}_{i}\left[{k}_{m}\right]\propto \hat{S}\left[{k}_{m}\right]\xb7\left[2\left({R}_{R}+{R}_{S}\right)+2\sqrt{{R}_{R}{R}_{S}}\mathrm{cos}\left(2\Delta x{k}_{m}+{\phi}_{i}\right)+j2\sqrt{{R}_{R}{R}_{S}}\mathrm{sin}\left(2\Delta x{k}_{m}+{\phi}_{i}\right)\right],$$
(6)
$${D}_{i}\left[{x}_{n}\right]\propto S\left[{x}_{n}\right]\otimes \left[2\left({R}_{R}+{R}_{S}\right)\xb7\delta \left({x}_{n}\right)+4\sqrt{{R}_{R}{R}_{S}}\delta \left({x}_{n}+\Delta x\right)\right].$$
(7)
$${\hat{D}}_{i}\left[{k}_{m}\right]=\left({\hat{D}}_{i}^{0}\left[{k}_{m}\right]-{\hat{D}}_{i}^{\mathit{DC}}\left[{k}_{m}\right]\right)+j\left({\hat{D}}_{i}^{90}\left[{k}_{m}\right]-{\hat{D}}_{i}^{\mathit{DC}}\left[{k}_{m}\right]\right),$$
(8)
$${i}_{\mathrm{Im}}=\frac{{i}_{n}\mathrm{cos}\left(\Delta {\varphi}_{\mathrm{mn}}\right)-{\beta}_{\mathrm{mn}}{i}_{m}}{\mathrm{sin}\left(\Delta {\varphi}_{\mathrm{mn}}\right)}.$$