Statistical properties of the sum of partially-developed,correlated speckle patterns

General formulas for the average contrast and probability density function of the sum ofN partially-developed, correlated speckle patterns have been theoretically derived. These two parameters characterizing the statistical properties of added speckle patterns have been actually evaluated for the sum of two partially-developed, correlated speckle patterns and shown in figures as a function of the surface roughness of illuminated objects, the wavelength difference of two illuminating lights, and the number of scattering cells within the illuminated area of objects.