## Abstract

We present an effective approach to manage dispersion compensation for a fiber-optic optical coherence tomography (OCT) imaging system in which an electro-optic (EO) phase modulator or an acousto-optic (AO) frequency modulator is used. To balance both the second and third order dispersion caused by the modulator, two independent optical components would be needed. The approach reported here combines a grating-lens delay line and an extra length of a single-mode optical fiber, enabling full compensation of the dispersion caused by the modulator up to the third order. Theoretical analysis of the proposed dispersion management scheme is provided. Experimental results confirmed the theoretical prediction and an optimal OCT axial resolution offered by the light source was recovered. The proposed method can potentially incorporate dynamic dispersion compensation for the sample during depth scanning.

© 2004 Optical Society of America

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### Equations (10)

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(1)
$$l=2\mid OO\prime \mid +\mid NP\mid -\mid NP\prime \mid .$$
(2)
$$\varphi \left(\omega \right)=\frac{4\omega}{c}\{L\phantom{\rule{.2em}{0ex}}\mathrm{cos}\left(\Delta \theta \right)+\frac{f}{\mathrm{cos}\left(\Delta \theta \right)}+\left[f\phantom{\rule{.2em}{0ex}}\mathrm{tan}\left(\Delta \theta \right)-{x}_{o}\right]\mathrm{tan}\phantom{\rule{.2em}{0ex}}\mathit{\gamma}+{y}_{o}\mathrm{sin}\left(\Delta \theta \right)\},$$
(3)
$$\varphi \u2033=\frac{{\partial}^{2}\varphi \left(\omega \right)}{\partial {\omega}^{2}}=\frac{-16{\pi}^{2}c}{{\omega}^{3}}\frac{{m}^{2}}{{d}^{2}{\mathrm{cos}}^{2}{\theta}_{\lambda}}\left(L-f\right)\left(1-\Delta \theta \right),$$
(4)
$$\varphi \u2034=\frac{\partial {\varphi}^{3}\left(\omega \right)}{\partial {\omega}^{3}}=\frac{48{m}^{2}{\pi}^{2}c\left(L-f\right)}{{d}^{2}{\omega}^{4}{\mathrm{cos}}^{2}{\theta}_{\lambda}}\left[1+(\mathrm{tan}{\theta}_{\lambda}+\frac{1}{3}\Delta \theta )\left(\frac{2\pi mc}{\omega d\phantom{\rule{.2em}{0ex}}\mathrm{cos}{\theta}_{\lambda}}\right)\right]+\frac{192{\pi}^{3}{m}^{3}{c}^{2}f}{{d}^{3}{\omega}^{5}{\mathrm{cos}}^{3}{\theta}_{\lambda}}\Delta \theta .$$
(5)
$${\varphi}_{\gamma}^{\u2033}\frac{-16{\pi}^{2}c}{{\omega}^{3}}\frac{{m}^{2}f}{{d}^{2}{\mathrm{cos}}^{2}{\theta}_{\lambda}}\mathrm{tan}\gamma (\mathrm{tan}{\theta}_{\lambda}+2\Delta \theta ),$$
(6)
$${\varphi}_{\gamma}^{\u2034}=\frac{48{m}^{2}{\pi}^{2}\mathit{cf}}{{d}^{4}{\omega}^{4}{\mathrm{cos}}^{2}{\theta}_{\lambda}}\mathrm{tan}\phantom{\rule{.2em}{0ex}}\gamma [\mathrm{tan}\phantom{\rule{.2em}{0ex}}{\theta}_{\lambda}+2\Delta \theta +\frac{2\pi mc}{\omega d\phantom{\rule{.2em}{0ex}}\mathrm{cos}{\theta}_{\lambda}}(\frac{1}{{\mathrm{cos}}^{2}{\theta}_{\lambda}}+\frac{4}{3}\Delta \theta )].$$
(7)
$${C}_{R2}\left(L-f\right)+{\varphi}_{M}^{\u2033}={C}_{f2}l,$$
(8)
$${C}_{R3}\left(L-f\right)+{\varphi}_{M}^{\u2034}={C}_{f3}l.$$
(9)
$$L-f=\frac{{\varphi}_{M}^{\u2034}{C}_{f2}-{\varphi}_{M}^{\u2033}{C}_{f3}}{{C}_{R2}{C}_{f3}-{C}_{R3}{C}_{f2}},$$
(10)
$$l=\frac{{\varphi}_{M}^{\u2034}{C}_{R2}-{\varphi}_{M}^{\u2033}{C}_{R3}}{{C}_{R2}{C}_{f3}-{C}_{R3}{C}_{f2}}.$$