## Abstract

We propose a new method for viewing through turbid or obstructing media. The medium is illuminated with a modulated cw laser and the amplitude and phase of the transmitted (or reflected) signal is measured. This process takes place for a set of wavelengths in a certain wide band. In this way we acquire the Fourier transform of the temporal output. With this information we can reconstruct the temporal shape of the transmitted signal by computing the inverse transform. The proposed method benefits from the advantages of the first-light technique: high resolution, simple algorithms, insensitivity to boundary condition, etc., without suffering from its main deficiencies: complex and expensive equipment.

© 2003 Optical Society of America

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### Equations (11)

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(1)
$${E}_{\mathrm{in}}(t,{\omega}_{j})\cong exp(i{\omega}_{j}t)(1+acos\mathrm{\Omega}t)=exp(i{\omega}_{j}t)\{1+(a/2)[exp(i\mathrm{\Omega}t)+exp(-i\mathrm{\Omega}t)]\},$$
(2)
$${I}_{\mathrm{in}}(t)\cong 1+2acos\mathrm{\Omega}t,$$
(3)
$${E}_{\mathrm{out}}(t,{\omega}_{j})=A({\omega}_{j})(1/2)exp(i{\omega}_{j}t)(exp(i{\varphi}_{j}^{0})+a/2\times \{exp[i(\mathrm{\Omega}t+{\varphi}_{j}^{(+)})]+exp[-i(\mathrm{\Omega}t-{\varphi}_{j}^{(-)})]\}).$$
(4)
$${I}_{\mathrm{out}}({\omega}_{j})\cong {A}^{2}({\omega}_{j})\{1+2\mathit{ac}cos[\mathrm{\Omega}t+\mathrm{\Delta}\varphi ({\omega}_{j})/2]\},$$
(5)
$$\mathrm{\Delta}\varphi ({\omega}_{j})\equiv ({\varphi}_{j}^{(-)}-{\varphi}_{j}^{(+)})/2$$
(6)
$$c\equiv cos[{\varphi}_{j}^{0}-({\varphi}_{j}^{(+)}+{\varphi}_{j}^{(-)})/2]\cong 1.$$
(7)
$$\delta \omega =2\mathrm{\Omega},$$
(8)
$$H({\omega}_{j})=A({\omega}_{j})exp(i\varphi {\omega}_{j}),$$
(9)
$$\varphi ({\omega}_{j})=\left[2\sum _{m=0}^{M}\mathrm{\Delta}\varphi ({\omega}_{m})-\mathrm{\Delta}\varphi ({\omega}_{1})-\mathrm{\Delta}\varphi ({\omega}_{M})\right]\frac{\delta \omega}{\mathrm{\Omega}}.$$
(10)
$$\delta \omega \approx \frac{2\pi}{{T}_{D}}\ll \frac{2\pi}{{T}_{B}}$$
(11)
$${T}_{D}\cong {L}^{2}/D\cong 3{\mu}_{s}^{\prime}{\mathit{nL}}^{2}/c$$