By measuring the parameters of weak random screens with AFM and constructing a specially designed setup with gated integrator, the properties of autocorrelation functions of speckle fields produced by weak random screens on the focused and defocused image planes are studied experimentally. It is found that: 1) as the surface roughness increases, the average size of the speckle grains on the focused image plane decreases, and the spatial separation range of the secondary maximum of the autocorrelation functions is reduced while its fluctuation is increased; 2) as the defocus increases, the autocorrelation function of the speckle intensity on the defocused image plane decreases more smoothly and the first order minimum and the secondary maximum become indistinct or even disappear.