In laser beam propagation through the atmosphere under condition where strong scintillation is present, real zeros can appear in the beacon field. On these zero points the phases are undetermined, which are called branch points. The occurrence of branch points causes the conventional least squares phase estimation to fail.
The scintillation index is defined of wave front sensor. The relations between branch point number and index versus Rytov variance are simulated numerically. The number of branch point increases with Rytov variance and the index increases and saturates with Rytov variance. The branch point is not only related to Rytov variance but also Fresnel number. Under the given Rytov variance, the larger Fresnel has the more branch point number. The corrected Strehl ratios are compared with least square method and extended least square method for various turbulent conditions.