The amplitude of speckles which are in the extremely deep Fresnel diffraction region and generated by weak scattering screens is extracted. It is found that when scattering distance is fixed, the property of phase distribution varies with weak scattering screen roughness. For a weak scattering screen, the phase distribution property changes with scattering distance. The phase votex phenomenon does not appear until the surface of weak scattering screen is rough enough. It is interesting that there are phase vortices on scattering screen surface. The phase votex density will rise when scattering screen becomes rougher or scattering distance turns larger. Experimental results are helpful to realize that the phase and the phase votex distribution property vary with roughness of weak scattering screen and scattering distance which lies in the extremely deep Fresnel diffraction region. Moreover, the results contribute to the understanding of the speckle field evolution with scattering distance.