Table 1: Definitions of atmospheric time constants.

Quantity of interest		 Formula Time constant

Phase SF		 $D_\varphi(t) = (t/\tau_0)^{5/3}$ $\tau_0 = 0.314\; r_0/\overline{V}_{5/3}$

Piston SF, t< d/V $D_\phi(t) = (t/t_1)^{2}$ $t_1 = 0.273\; (r_0/\overline{V}_{2})(d/r_0)^{1/6}$

Piston SF, t> d/V $D_\phi(t) = (t/t_0)^{5/3}$ $t_0 = 0.66 \; \tau_0 $

Piston variance during an exposure t> d/V $\sigma^2_\phi (t)= (t/T_0)^{5/3}$ $ T_0 = 2.58\; \tau_0 $

Phase tracker error, $\nu_{\rm c}> 0.3 \; d/V$ $\sigma_{\rm c}^2 (\nu_{\rm c})= (2 \pi \nu_{\rm c} t_1)^{-2}$ t1


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