## Abstract

A method for simulating conventional time gating in low-coherence
optical imaging processes in highly scattering media is given. The
method uses monochromatic instead of broadband light, and spatial
filtering is substituted for time gating. The process enables the
study of imaging techniques in scattering media to be carried out in an
easy and highly controllable way. Experimental results are
given.

© 1999 Optical Society of America

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### Equations (10)

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(1)
$$L=c\mathrm{\tau}=\left(d/2\right)\left(\mathrm{\theta}_{1}{}^{2}+\mathrm{\theta}_{2}{}^{2}\right)=\left(1/2d\right)\left[x_{1}{}^{2}+{\left({x}_{2}-{x}_{1}\right)}^{2}\right]$$
(2)
$$2c\mathrm{\tau}/{\mathrm{\lambda}}^{2}d=f_{1}{}^{2}+f_{2}{}^{2}.$$
(3)
$$f_{1}{}^{2}+f_{2}{}^{2}=2c{\mathrm{\tau}}_{1}/{\mathrm{\lambda}}^{2}d=f_{c}{}^{2}.$$
(4)
$${\mathrm{\theta}}_{c}={cos}^{-1}\left({f}_{c}/r\right)={cos}^{-1}\left[{\left(\frac{{\mathrm{\tau}}_{1}}{\mathrm{\tau}}\right)}^{1/2}\right],$$
(5)
$$\mathrm{\tau}=\left(1/2\mathit{cd}\right)\left[x_{1}{}^{2}+y_{1}{}^{2}+{\left({x}_{2}-{x}_{1}\right)}^{2}+{\left({y}_{2}-{y}_{1}\right)}^{2}\right],$$
(6)
$${\mathrm{\tau}}_{1}=\left({\mathrm{\lambda}}^{2}d/2c\right)\left({f}_{1}{x}^{2}+{f}_{1}{y}^{2}+{f}_{2}{x}^{2}+{f}_{2}{y}^{2}\right)=\left({\mathrm{\lambda}}^{2}d/2c\right)\left({f}_{1}{r}^{2}+{f}_{2}{r}^{2}\right),$$
(7)
$${f}_{c}{r}^{2}=2c{\mathrm{\tau}}_{1}/{\mathrm{\lambda}}^{2}d={f}_{1}{r}^{2}+{f}_{2}{r}^{2}.$$
(8)
$$T\left(\mathrm{\tau}\right)=\left\{\begin{array}{ll}1& \mathrm{for}0\le \mathrm{\tau}\le {\mathrm{\tau}}_{1}\\ cos\left\{2{cos}^{-1}\left[{\left(\frac{{\mathrm{\tau}}_{1}}{\mathrm{\tau}}\right)}^{1/2}\right]\right\}& \mathrm{for}{\mathrm{\tau}}_{1}\le \mathrm{\tau}\le 2{\mathrm{\tau}}_{1}\\ 0& \mathrm{for}{\mathrm{\tau}}_{1}\ge 2{\mathrm{\tau}}_{1}\end{array}\right\},$$
(9)
$${\mathrm{\tau}}_{1}={\left(x/F\right)}^{2}\left(d/2c\right),$$
(10)
$${\mathrm{\tau}}_{1}=0.7022{x}^{2},$$