## Abstract

Doppler optical coherence tomography (DOCT) is a technique for simultaneous cross-sectional imaging of tissue structure and blood flow. We derive the fundamental uncertainty limits on frequency estimation precision in DOCT using the Cramer-Rao lower bound in the case of additive (e.g., thermal, shot) noise. Experimental results from a mirror and a scattering phantom are used to verify the theoretical limits. Our results demonstrate that the stochastic nature of frequency noise influences the precision of flow imaging, and that the noise model must be selected judiciously in order to estimate the frequency precision.

© 2005 Optical Society of America

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### Equations (10)

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(1)
$$s\left(t\right)=A\left(t\right)\mathrm{cos}\left[2\pi \left({f}_{r}-{f}_{s}\right)t+\beta \left(t\right)\right],$$
(2)
$$s\left(t\right)=A\left(t\right)\mathrm{cos}\left[2\pi {f}_{s}t+\beta \left(t\right)\right],0\le t\le {t}_{0}$$
(3)
$${f}_{s}^{min}=\frac{1}{{t}_{0}}$$
(4)
$$\mathit{Var}\left[\hat{\alpha}\left(\stackrel{\u20d1}{R}\right)-\alpha \right]\ge {\left(E\left\{{\left[\frac{\partial \phantom{\rule{.2em}{0ex}}\mathrm{ln}\phantom{\rule{.2em}{0ex}}p(\stackrel{\u20d1}{R}\mid \alpha )}{\partial \alpha}\right]}^{2}\right\}\right)}^{-1}$$
(5)
$$r\left(t\right)=s(t,\alpha )+n\left(t\right)$$
(6)
$${\sigma}_{\hat{\alpha}}^{2}\ge {\left(\frac{1}{{N}_{0}}\underset{0}{\overset{{t}_{0}}{\int}}{\left[\frac{\partial s(t,\alpha )}{\partial \alpha}\right]}^{2}dt\right)}^{-1}$$
(7)
$${\sigma}_{\hat{f}}^{2}\ge {\left(\frac{2{\pi}^{2}}{3}\frac{{A}^{2}}{{N}_{0}}{t}_{0}^{2}\right)}^{-1}$$
(8)
$${f}_{s}^{min}\approx \sigma \propto \frac{1}{{t}_{0}\sqrt{\mathit{SNR}}}$$
(9)
$$R\left(\tau \right)=\mid R\left(\tau \right)\mid \mathrm{exp}\left[-i\varphi \left(\tau \right)\right]\equiv \u3008{s}^{*}\left(t\right)s\left(t+\tau \right)\u3009$$
(10)
$$\Omega =16{(\pi \u2044{\lambda}_{0})}^{2}{D}_{T}\phantom{\rule{.4em}{0ex}}[\mathrm{rad}\u2044s]$$