Statistical properties of phase difference for partially developed speckle fields in the diffraction region

According to the movement of an equiprobability density ellipse in the complex plane of the speckle amplitude, a phase angle is obtained to theoretically evaluate the so-called free statistical properties of the phase difference for partially developed Gaussian speckle fields. The statistical properties of the phase difference between two points in the partially developed speckle fields have been investigated in the diffraction region. The theoretical results have been discussed with respect to Kadono's experimental results (Opt. Quantum Electron. 19 (1987) 59). The validity of this theory has been discussed.