## Abstract

A pupil plane imaging (PPI) system has been designed and implemented to measure scintillation induced by atmospheric turbulence and to estimate key parameters of atmospheric turbulence. A high-speed, high-resolution camera images the pupil of a telescope. The process of estimating normalized intensity variance and the underlying rationale is discussed. Experimental results are presented for data taken at North Oscura Peak in southern New Mexico from light originating at Salinas Peak or an aircraft, over near-horizontal paths of
$\sim 50\text{\hspace{0.17em} km}$. Strong scintillation is often observed. The results are compared to those of other instruments operating in parallel, and systematic and random errors are discussed. The primary goal is to accurately estimate scintillation strength using PPI in order to assess adaptive optics performance as a function of such scintillation.

© 2007 Optical Society of America

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### Equations (10)

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(1)
$${r}_{0}={\left[0.424{k}_{o}^{2}{\displaystyle \underset{0}{\overset{L}{\int}}{C}_{n}^{2}\left(z\right){\left(1-z/L\right)}^{5/3}\left(\mathrm{d}z\right)}\right]}^{-3/5}\text{,}$$
(2)
$${\sigma}_{\chi}^{2}=0.561{k}_{o}^{7/6}{\displaystyle \underset{0}{\overset{L}{\int}}{C}_{n}^{2}\left(z\right){\left(1-z/L\right)}^{5/6}}{z}^{5/6}\mathrm{d}z\text{,}$$
(3)
$$C\left(m,n,i\right)=c{\displaystyle \underset{m\mathrm{\Delta}x}{\overset{\left(m+1\right)\mathrm{\Delta}x}{\int}}\mathrm{d}x}{\displaystyle \underset{n\mathrm{\Delta}y}{\overset{\left(n+1\right)\mathrm{\Delta}y}{\int}}\mathrm{d}y}{\displaystyle \underset{i\mathrm{\Delta}t}{\overset{\left(i+1\right)\mathrm{\Delta}t}{\int}}\mathrm{d}t}\text{\hspace{0.17em}}I\left(x,y,t\right)\text{,}$$
(4)
$${\text{NIV}}_{i}=\sum _{m\text{,}n}C{\left(m,n,i\right)}^{2}/{\left[\sum _{m\text{,}n}C\left(m,n,i\right)\right]}^{2}-1\text{,}\phantom{\rule[-0.0ex]{1.0em}{0.0ex}}\left(\text{frame \hspace{0.17em}}i\right)\text{.}$$
(5)
$${\sigma}_{\chi i}^{2}=\sum _{m\text{,}n}\mathrm{log}{\left[C\left(m,n,i\right)/\u3008C\u3009\right]}^{2}/M-{\left\{\sum _{m\text{,}n}\mathrm{log}[C\left(m,n,i\right)/\u3008C\u3009]/M\right\}}^{2}\text{,}\phantom{\rule[-0.0ex]{1.0em}{0.0ex}}\left(\text{frame \hspace{0.17em}}i\right)\text{,}$$
(6)
$$\text{NIV}=\mathrm{exp}\left(4{\sigma}_{\chi}^{2}\right)-1.$$
(7)
$${\text{NIV}}_{\text{sp}}=\sum _{i}{\text{NIV}}_{i}/N\text{,}$$
(8)
$${\text{NIV}}_{t}=\sum _{m\mathrm{,}n}\{\sum _{i}C{\left(m,n,i\right)}^{2}/{\left[\sum _{i}C\left(m,n,i\right)\right]}^{2}-1\}/M\text{,}$$
(9)
$${\text{NIV}}_{\text{blk}}=\sum _{m\mathrm{,}n}\left\{\sum _{{m}_{1}\mathrm{,}{n}_{1}\mathrm{,}i}C{\left(m+{m}_{1},n+{n}_{1},i\right)}^{2}/{\left[\sum _{i\mathrm{,}{m}_{1}\mathrm{,}{n}_{1}}C\left(m+{m}_{1},n+{n}_{1},i\right)\right]}^{2}-1\right\}/{M}_{b}\text{,}$$
(10)
$${\text{NIV}}_{h}=\mathrm{min}\left\{\left|H\left[C\left(m,n,i\right),{C}_{o}\right]-\mathrm{Pr}\left[\text{NIV}\right]\right|\right\}\text{.}$$