Numerical experiments are carried out for a plane wave propagating in atmospheric turbulence and reflected from a
rough surface under weak to strong fluctuation condition. The statistical characteristics of the scintillation index and the
number density of the phase singularity (or the optical vortex) are analyzed. The density of the phase singularity is
evaluated as a function of the Rytov index, the Fresnel length, the correlation scale and roughness of the surface.
Correlation and interaction between both types of phase singularity caused by rough surface and turbulence are analyzed.
Results could provide a theoretical basis for measurement of surface roughness under known turbulence condition or
measurement of atmospheric turbulence under known surface roughness condition.
"Statistics of phase singularity of a speckle field in atmospheric
turbulence", Proc. SPIE 7387, Speckle 2010: Optical Metrology, 73871H (13 September 2010); doi: 10.1117/12.868315; https://doi.org/10.1117/12.868315