## Abstract

An efficient and fast simulation technique is presented to calculate characteristic features of confocal imaging through scattering media. The simulation can predict the time-resolved confocal response to pulsed illumination that allows optimizing of imaging contrast when time-gating techniques are applied. Modest computational effort is sufficient to obtain contrast predictions for arbitrary numerical aperture, focus depth, pinhole size, and scattering density, while the simulation accuracy is independent of scattering density and pinhole size. In the case of isotropic scattering, our results indicate that reflection-mode confocal imaging through scattering media is limited to $\mu d\approx 3.5$ optical thicknesses for continuous-wave illumination. If time-gating is applied, imaging through scattering densities of $\mu d\approx 8$ is theoretically possible.

© 2001 Optical Society of America

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### Equations (11)

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(1)
$$u=\frac{8\pi z}{\mathrm{\lambda}}{sin}^{2}\frac{\alpha}{2},$$
(2)
$$v=\frac{2\pi r}{\mathrm{\lambda}}sin\alpha ,$$
(3)
$$R(z)={r}_{0}+|d-z|tan\left(\mathrm{arcsin}\frac{\mathrm{NA}}{n}\right),$$
(4)
$${z}^{(1)}=-\frac{ln(1-{q}_{z})}{\mu}cos\left\{\mathrm{arctan}\left[{q}_{r}\left(tan\alpha -\frac{{r}_{0}}{d}\right)\right]\right\},$$
(5)
$${r}^{(1)}={q}_{r}\left[{r}_{0}+|d-{z}^{(1)}|\left(tan\alpha -\frac{{r}_{0}}{d}\right)\right],$$
(6)
$${p}_{\mathrm{esc}}({z}^{(1)})=\frac{1}{2}[exp(-\mu {z}^{(1)})-\mu {z}^{(1)}{E}_{1}(\mu {z}^{(1)})],$$
(7)
$${E}_{1}(x)\approx \left\{\begin{array}{cc}-(lnx+\gamma )+x-\frac{{x}^{2}}{4}+\frac{{x}^{3}}{18}& \hspace{1em}x1.618\\ \frac{exp(-x)}{x}\left(1-\frac{1}{x}+\frac{2}{{x}^{2}}\right)& \hspace{1em}x1.618\end{array}\right.$$
(8)
$$l=-\frac{ln(1-\mathit{Kq})}{\mu},$$
(9)
$$K=\left\{\begin{array}{ll}1-exp(-\mu z/sin\theta )& \hspace{1em}0\theta \u2a7d\pi /2\\ 1& \hspace{1em}0\u2a7e\theta \u2a7e-\pi /2\end{array}\right..$$
(10)
$$C=\frac{{\Sigma}_{\mathrm{signal}}}{{\Sigma}_{\mathrm{noise}}}.$$
(11)
$$C(g)\propto \frac{2\mathit{\mu}(1-g)}{sinh[2\mathit{\mu}(1-g)]}.$$