Correlation function for speckle size in the right-half-space

For radiation from a diffuser illuminated by a monochromatic plane wave, we calculate the field correlation using the Rayleigh–Sommerfeld–Smythe integral formula. This provides expressions of spatial correlation function valid at any point in the hemisphere. The non-paraxial formulas for the speckle sizes are new and the other results are consistent with the well-known solutions in the literature.