## Abstract

A full-field optical coherence tomography (FF-OCT) system utilizing a simple but novel image restoration method suitable for a high-speed system is demonstrated. An *en-face*
image is retrieved from only two phase-shifted interference fringe images through using the mathematical Hilbert transform. With a thermal light source, a high-resolution FF-OCT system having axial and transverse resolutions of 1 and
$2.2\text{\hspace{0.17em} \mu m}$, respectively, was implemented. The feasibility of the proposed scheme is confirmed by presenting the obtained *en-face* images of biological samples such as a piece of garlic and a gold beetle.
The proposed method is robust to the error in the amount of the phase shift and does not leave residual fringes. The use of just two interference images and the strong immunity to phase errors provide great advantages in the imaging speed and the system design flexibility of a high-speed high-resolution FF-OCT system.

© 2008 Optical Society of America

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### Equations (10)

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(1)
$${I}_{0}\left(x,y\right)={I}_{R}+{I}_{S}+A\left(x,y\right)\left[\mathrm{cos}\text{\hspace{0.17em}}\varphi \left(x,y\right)\right].$$
(2)
$${I}_{\alpha}\left(x,y\right)={I}_{R}+{I}_{S}+A\left(x,y\right)\left[\mathrm{cos}\left(\varphi \left(x,y\right)-\alpha \right)\right].$$
(3)
$${S}_{1}=2A\left(x,y\right)\mathrm{sin}\left(\frac{\alpha}{2}\right)\mathrm{sin}\left[\varphi \left(x,y\right)-\frac{\alpha}{2}\right].$$
(4)
$${S}_{1}=A\prime \left(x,y\right)\left[\mathrm{sin}\text{\hspace{0.17em}}\Phi \left(x,y\right)\right],$$
(5)
$$A\prime \left(x,y\right)\equiv 2A\left(x,y\right)\mathrm{sin}\left(\frac{\alpha}{2}\right),$$
(6)
$$\Phi \equiv \varphi \left(x,y\right)-\left(\frac{\alpha}{2}\right).$$
(7)
$${S}_{\text{2}}=H\left\{{S}_{1}\right\}=A\prime \left(x,y\right)\left[\mathrm{cos}\text{\hspace{0.17em}}\Phi \left(x,y\right)\right].$$
(8)
$$A\prime \left(x,y\right)=\sqrt{{{{\displaystyle S}}_{1}}^{2}+{{{\displaystyle S}}_{2}}^{2}}.$$
(9)
$$\Delta z=\frac{2\text{\hspace{0.17em}ln \hspace{0.17em}}2}{\pi}\left(\frac{{{\lambda}_{c}}^{2}}{\Delta \lambda}\right)$$
(10)
$${R}_{\mathrm{min}}=\frac{{\left({R}_{\text{ref}}+{R}_{\text{inc}}\right)}^{2}}{2N{\zeta}_{\text{sat}}{R}_{\text{ref}}},$$