## Abstract

A pupil plane imaging system, consisting of a camera and optics that image the entrance pupil of a telescope, measures scintillation induced by atmospheric turbulence. Algorithms are developed to estimate the distribution of turbulence from scintillation assuming the well known relationship between scintillation scale size and the range of turbulence layer. The algorithms were exercised using a
$75\text{\hspace{0.17em} cm}$ pupil within a 1 meter telescope located at North Oscura Peak in New Mexico, based on light from a source
$\text{52 .6 \hspace{0.17em} km}$ away. Estimates of the
${{C}_{n}}^{2}$ profile over the path are derived using coarse range bins. From the
${{C}_{n}}^{2}$ profile, an estimate of Fried's transverse coherence length was computed and compared with that from other sensors. The algorithm is tested in several ways. Error sources are discussed, including the intrinsic insensitivity of the technique to turbulence near the pupil.

© 2007 Optical Society of America

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### Equations (8)

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(1)
$$\u3008{\mid \chi \left(k\right)\mid}^{2}\u3009={\sum}_{i=1\mathrm{,}N}{{C}_{n}}^{2}\left({z}_{i}\right)\Delta {z}_{i}\Phi \left(k\prime \right)S\left(k\prime ,{z}_{i}\right)\text{,}$$
(2)
$${\sum}_{k}\mid \u3008{\mid \chi \left(k\right)\mid}^{2}\u3009-{\sum}_{i}{{C}_{n}}^{2}\left({z}_{i}\right)\Delta {z}_{i}\Phi \left(k\prime \right)S{\left(k\prime ,{z}_{i}\right)\mid}^{2}\text{,}$$
(3)
$$\u3008{\sum}_{k}{\mid \u3008{\mid \chi \left(k\right)+\epsilon \left(k\right)\mid}^{2}\u3009-{\sum}_{i}{{C}_{n}}^{2}\left({z}_{i}\right)\Delta {z}_{i}\left[\Phi \left(k\prime \right)S\left(k\prime ,{z}_{i}\right)\text{\hspace{1em}}+{\epsilon}_{p}\left(k\prime ,{z}_{i}\right)\right]\mid}^{2}\u3009\text{,}$$
(4)
$${\sum}_{k}\left\{{\left(\u3008{\mid \chi \left(k\right)\mid}^{2}\u3009+{\sigma}^{2}\right)}^{2}-2\left(\u3008{\mid \chi \left(k\right)\mid}^{2}\u3009+{\sigma}^{2}\right){\sum}_{i}{\zeta}_{i}\Phi \left(k\prime \right)\times S\left(k\prime ,{z}_{i}\right)+{\sum}_{i}{\sum}_{j}{\zeta}_{i}{\zeta}_{j}\left[\Phi \left(k\prime \right)S\left(k\prime ,{z}_{i}\right)\Phi \left(k\prime \right)S\left(k\prime ,{z}_{j}\right)+{{\sigma}_{p}}^{2}\delta \left({z}_{i}-{z}_{j}\right)\right]\right\}\text{,}$$
(5)
$${\sum}_{k}{\u3008{\mid \chi \left(k\right)\mid}^{2}\u3009}_{M}\Phi \left(k\prime \right)S\left(k\prime ,{z}_{i}\right)={\sum}_{j}\left[{\sum}_{k}\Phi \left(k\prime \right)S\left(k\prime ,{z}_{i}\right)\times \Phi \left(k\prime \right)S\left(k\prime ,{z}_{j}\right)+{{\sigma}_{p}}^{2}\delta \left({z}_{i}-{z}_{j}\right)\right]{\zeta}_{j},\equiv {\sum}_{j}{M}_{ij}{\zeta}_{j},$$
(6)
$$\text{for \hspace{0.17em}}i=1\text{,\hspace{0.17em}\u2026\hspace{0.17em},\hspace{0.17em}}N.$$
(7)
$${r}_{0}={\left[0.424{{k}_{0}}^{2}{\sum}_{i}{\zeta}_{i}{\left(1-{z}_{i}/L\right)}^{5/3}\right]}^{-3/5},$$
(8)
$${P}_{1}=\left\{0.5,52.1\right\}\text{\hspace{0.17em} km ,}{P}_{2}=\left\{17.5,35.1\right\}\text{\hspace{0.17em} km .}$$