## Abstract

Temporal fluctuations of the atmospheric piston are critical for interferometers as they determine their sensitivity. We characterize an instrumental setup,
termed the piston scope, that aims at measuring the atmospheric time constant, ${\tau}_{0}$, through the image motion in the focal plane of a Fizeau interferometer.
High-resolution piston scope measurements have been obtained at the observatory of Paranal, Chile in April 2006. The derived atmospheric parameters are shown to be consistent with data from the astronomical site monitor, provided that the atmospheric turbulence is displaced along a single direction.
The piston scope measurements of lower temporal and spatial resolution were recorded for what is believed to be the first time in February 2005 at the Antarctic site of Dome C. Their reanalysis in terms of the new data calibration sharpens the conclusions of a first qualitative examination [Appl. Opt. **45,** 5709 (2006)].

© 2007 Optical Society of America

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### Equations (11)

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(1)
$${W}_{\phi}\left(f\right)=0.00969{k}^{2}{\int}_{0}^{+\infty}{\displaystyle {f}^{-11/3}{{C}_{n}}^{2}}\mathrm{d}h,$$
(2)
$$\tilde{M}\left(f\right)=\lambda /\left(2\pi \right)A\left(f\right)\text{FT}\left[\left({\delta}_{B}-{\delta}_{\text{0}}\right)/B-\left({\delta}_{B}+{\delta}_{\text{0}}\right)/2\ast d/\mathrm{d}x\right]\left(f\right),$$
(3)
$$\tilde{M}\left(f\right)=\lambda /\left(2\pi \right)A\left(f\right)\left[2\text{\hspace{0.17em} sin}\left(\pi fB\right)-2\pi fB\text{\hspace{0.17em} cos}\left(\pi fB\right)\right]/B\text{,}$$
(4)
$${W}_{\varphi}\left(f\right)={\tilde{M}}^{2}\left(f\right){W}_{\phi}\left(f\right).$$
(5)
$${w}_{\varphi}\left(\nu \right)=\frac{1}{V}{\displaystyle {\int}_{-\infty}^{+\infty}{W}_{\varphi}}\left({f}_{x}\text{\hspace{0.17em} cos \hspace{0.17em}}\alpha +{f}_{y}\text{\hspace{0.17em} sin \hspace{0.17em}}\alpha ,{f}_{y}\text{\hspace{0.17em} cos \hspace{0.17em}}\alpha -{f}_{x}\text{\hspace{0.17em} sin \hspace{0.17em}}\alpha \right)\mathrm{d}{f}_{y}\text{.}$$
(6)
$${D}_{\varphi}\left(t\right)=2{\displaystyle {\int}_{-\infty}^{+\infty}\left(1-\text{cos}\left(\text{2}\pi \nu t\right)\right){w}_{\varphi}\left(\nu \right)}\mathrm{d}\nu ,$$
(7)
$$\text{\hspace{0.17em}}=2\times 0.00969{{C}_{n}}^{2}\mathrm{d}h/{B}^{2}{\displaystyle {\int}_{0}^{+\infty}{f}^{-8/3}{\left(2{J}_{1}\left(\pi fd\right)/\left(\pi fd\right)\right)}^{2}}\mathrm{d}f\times {\displaystyle {\int}_{0}^{2\pi}\left(1-\text{cos}\left(\text{2}\pi f\text{\hspace{0.17em} cos}\left(\theta +\alpha \right)Vt\right)\right){\left[2\text{\hspace{0.17em} sin}\left(\pi Bf\text{\hspace{0.17em} cos \hspace{0.17em}}\theta \right)-2\pi fB\text{\hspace{0.17em} cos \hspace{0.17em}}\theta \text{\hspace{0.17em} cos}\left(\pi fB\text{\hspace{0.17em} cos \hspace{0.17em}}\theta \right)\right]}^{2}}\mathrm{d}\theta .$$
(8)
$${D}_{\varphi}\left(t\gg {\tau}_{0}\right)\propto {{r}_{0}}^{-5/3}\propto {\displaystyle {\int}_{0}^{+\pi}{{C}_{n}}^{2}}\mathrm{d}h,$$
(9)
$${V}_{\text{ps}}\propto {\overline{V}}_{5/3}={\left[\frac{{\displaystyle {\int}_{0}^{+\infty}V{\left(h\right)}^{5/3}{{C}_{n}}^{2}\left(h\right)\mathrm{d}h}}{{\displaystyle {\int}_{0}^{+\infty}{{C}_{n}}^{2}\left(h\right)\mathrm{d}h}}\right]}^{3/5}.$$
(10)
$${\overline{V}}_{5/3}\approx \text{max}\left({V}_{g},0.4{V}_{200\text{\hspace{0.17em} mB}}\right).$$
(11)
$${D}_{\varphi}\left(t\right)={D}_{\varphi}\left(t\gg {t}_{c}\right)\times \left(1-\text{exp}\left(-{\left(t/{t}_{c}\right)}^{-5/3}\right)\right).\hspace{0.17em}$$