Statistical properties of focal plane speckle

The second order statistical properties of coherent radiation scattered from a rough surface in the focal plane of an optical system are analysed. Two types of motion of the scattering surface are considered: arbitrary movement in his own plane without velocity gradients across the illuminating laser spot and secondly for a rotational target movement.

The expressions for the space–time intensity correlation function and the corresponding power spectrum are derived and the characteristics of speckle motion are analysed. It is shown that for rotational motion of the target the speckle pattern will rotate in the focal plane about a displaced axis. It is shown also that the statistical properties of the scattered radiation on the axis of the incident beam under rotational movement conditions are identical to those under uniform motion of the scattering surface.

An experiment carried out with a He–Ne laser has confirmed the mathematical model suggested.