TIME DELAY

If there is a time delay between when turbulence is measured and when a correction is applied to the deformable mirror, there is a degradation in performance.[#!7!#] This effect is not often thought of as an anisoplanatic effect; however, it can be treated as such. ...
d (z) = v(z)τ, (35)
d2 = 2.91 k02$\displaystyle \int\limits_{{\,\,\, 0}}^{{\,\,\,\,\,\, L}}$dz Cn2(z) v2(z) τ2 = $\displaystyle \left(\vphantom{ {\tau / \tau _2} }\right.$τ/τ2$\displaystyle \left.\vphantom{ {\tau / \tau _2} }\right)^{2}_{}$, (36)
E = $\displaystyle {{\tau ^2} \over {\tau _2^2D^{1/ 3}}}$, (37)
σ$\scriptstyle \varphi$2 = 2.91 k02$\displaystyle \int\limits_{{\,\,\, 0}}^{{\,\,\,\,\,\, L}}$dz Cn2(z) v5/3(z) τ5/3 = $\displaystyle \left(\vphantom{ {\tau / \tau _{5/ 3}} }\right.$τ/τ5/3$\displaystyle \left.\vphantom{ {\tau / \tau _{5/ 3}} }\right)^{{5/ 3}}_{}$, (38)

where the temporal moment is defined as
1/τm5/3 = 2.91 k02$\displaystyle \int\limits_{{\,\,\, 0}}^{{\,\,\,\,\,\, L}}$dz Cn2(z) vm(z).     (39)

...