## Abstract

We present a novel angle-resolved low coherence interferometry scheme for rapid measurement of depth-resolved angular scattering distributions to enable determination of scatterer size via elastic scattering properties. Depth resolution is achieved using a superluminescent diode in a modified Mach-Zehnder interferometer with the mixed signal and reference fields dispersed by an imaging spectrograph. The spectrograph slit is located in a Fourier transform plane of the scattering sample, enabling angle-resolved measurements over a 0.21 radian range. The capabilities of the new technique are demonstrated by recording the distribution of light scattered by a sub-surface layer of polystyrene microspheres in 40 milliseconds. The data are used to determine the microsphere size with good accuracy. Future clinical application to measuring the size of cell nuclei in living epithelial tissues using backscattered light is discussed.

© 2004 Optical Society of America

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### Equations (7)

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(1)
$$I({\lambda}_{m},{y}_{n})=\u3008{\mid {E}_{r}({\lambda}_{m},{y}_{n})\mid}^{2}\u3009+\u3008{\mid {E}_{s}({\lambda}_{m},{y}_{n})\mid}^{2}\u3009+2\mathrm{Re}\u3008{E}_{s}({\lambda}_{m},{y}_{n}){E}_{r}^{*}({\lambda}_{m},{y}_{n})\u3009\mathrm{cos}\mathit{\varphi},$$
(2)
$${\Gamma}_{\mathit{SR}}(z,{y}_{n})=\int dk{e}^{ikz}\u3008{E}_{s}(k,{y}_{n}){E}_{r}^{*}(k,{y}_{n})\u3009\mathrm{cos}\varphi .$$
(3)
$${E}_{r}\left(k\right)={E}_{o}\mathrm{exp}\left[-{(\left(k-{k}_{o}\right)/\Delta k)}^{2}\right]\mathrm{exp}\left[-{(\left(y-{y}_{o}\right)/\Delta y)}^{2}\right]\mathrm{exp}\left[ik\Delta l\right]$$
(4)
$${E}_{s}(k,\theta )={\sum}_{j}{E}_{o}\mathrm{exp}\left[-{(\left(k-{k}_{o}\right)/\Delta k)}^{2}\right]\mathrm{exp}\left[ik{l}_{j}\right]{S}_{j}(k,\theta )$$
(5)
$${\Gamma}_{\mathit{SR}}(z,{y}_{n})=\sum _{j}\int \mathit{dk}{\mid {E}_{o}\mid}^{2}\mathrm{exp}\left[-2{(\left(k-{k}_{o}\right)/\Delta k)}^{2}\right]\mathrm{exp}\left[ik\left(z-\Delta l+{l}_{j}\right)\right]$$
(6)
$$\times {S}_{j}(k,{\theta}_{n}={y}_{n}/{f}_{4})\mathrm{cos}\varphi .$$
(7)
$${\Gamma}_{\mathit{SR}}(z,{y}_{n})={\mid {E}_{o}\mid}^{2}\mathrm{exp}[-{\left(\left(z-\Delta l+{l}_{j}\right)\Delta k\right)}^{2}/8]{S}_{j}({k}_{o},{\theta}_{n}={y}_{n}/{f}_{4})\mathrm{cos}\varphi .$$