COMBINED DISPLACEMENT

If there are several anisoplanatic effects present, with each not decreasing the Strehl ratio much, it is a common practice to multiply the Strehl ratios for the individual effects to get a combined Strehl ratio. The validity of this assumption is now examined. The total displacement that is due to a translation, an angular offset, a time delay, and a chromatic offset is
dt(z) = d + $\displaystyle \bbox$θz + v(z)τ + dc(z),     (46)

where chromatic displacement is given in Eq. (50). The two terms necessary for calculating the Strehl ratio are
E = $\displaystyle {{d_{\,2}} \over {D^{1/ 3}}}$, (47)
σ$\scriptstyle \varphi$2 = d 5/3, (48)

where
dm = 2.91 k02$\displaystyle \int\limits_{{\,\,\, 0}}^{{\,\,\,\,\,\,\infty}}$dz Cn2(z) $\displaystyle \left\vert\vphantom{ {d_t(z)} }\right.$dt(z)$\displaystyle \left.\vphantom{ {d_t(z)} }\right\vert^{m}_{}$.     (49)

...

... Tyler et al.[#!18!#] took advantage of the vector nature of the displacement almost to eliminate the effect of chromatic anisoplanatism on an adaptive-optics system by choosing an optimal offset angle of a beacon from the propagation direction.