## Abstract

During strong scintillation, the number and location of branch points in a distorted optical field induced by atmospheric turbulence are closely related to the characteristic parameters of the turbulence effect, propagation distance, and wavelength. It is necessary to consider the effect of the beacon’s wavelength on the adaptive optics system that is used to compensate for atmospheric turbulence. Our analytical results show that the performance of adaptive optics can be improved by nearly a factor of 2 when the beacon’s wavelength is chosen slightly longer than the wavelength of the main laser in the branch points considered.

© 2004 Optical Society of America

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### Equations (7)

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(1)
$$\mathrm{\phi}\left(\mathbf{\text{r}}\right)={tan}^{-1}\left\{\frac{\mathrm{Im}\left[U\left(\mathbf{\text{r}}\right)\right]}{\mathrm{Re}\left[U\left(\mathbf{\text{r}}\right)\right]}\right\},$$
(2)
$$\mathrm{\Delta}{\mathrm{\phi}}_{x}\left(i,j\right)=\mathrm{arg}\left(exp\left\{j\left[\mathrm{\phi}\left(i+1,j\right)-\mathrm{\phi}\left(i,j\right)\right]\right\}\right),$$
(3)
$$\mathrm{\Delta}{\mathrm{\phi}}_{y}\left(i,j\right)=\mathrm{arg}\left(exp\left\{j\left[\mathrm{\phi}\left(i,j+1\right)-\mathrm{\phi}\left(i,j\right)\right]\right\}\right),$$
(4)
$$g\left(i,j\right)=-\mathrm{\Delta}{\mathrm{\phi}}_{x}\left(i,j\right)-\mathrm{\Delta}{\mathrm{\phi}}_{y}\left(i+1,j\right)+\mathrm{\Delta}{\mathrm{\phi}}_{x}\left(i,j+1\right)+\mathrm{\Delta}{\mathrm{\phi}}_{y}\left(i,j\right).$$
(5)
$$u_{j}{}^{1}=\sum _{k\mathrm{neighbor\; of}j}exp\left({\mathit{id}}_{j,k}\right)u_{k}{}^{0},$$
(6)
$$u_{j}{}^{11}=\sum _{k\mathrm{neighbor}\mathrm{of}j}exp\left(i\mathrm{\alpha}{d}_{j,k}\right)u_{k}{}^{0}.$$
(7)
$$\mathrm{SR}=\frac{\mathrm{Actual\; intensity\; in\; the\; Airy\; disk}}{\mathrm{Intensity\; in\; the\; Airy\; disk\; with\; no\; turbulence}}.$$