Abstract: Rayleigh-Sommerfeld theory of planar screen diffraction is extended to spherical cases, related diffraction formula and its far field approximant within the spherical coordinate system are produced. On this basis, the statistic characters of far field speckle intensity are studied, the far field speckle intensity is theoreticaly verified to be spatial stable stachastic process. Lateral and longitudinal correlation radii are deduced, which are different from planar cases.