Speckle dynamics for dual-beam optical illumination of a rotating structure

An out-of-plane rotating object is illuminated with two spatially separated coherent beams, giving rise to fully developed speckles, which will translate and gradually decorrelate in the observation plane, located in the far field. The speckle pattern is a compound structure, consisting of random speckles modulated by a smaller and repetitive structure. Generally, these two components of the compound speckle structure will move as rigid structures with individual velocities determined by the characteristics of the two illuminating beams. Closed-form analytical expressions are found for the space- and time-lagged covariance of irradiance and the corresponding power spectrum for the two spatially separated illuminating beams. The present analysis is valid for propagation through an arbitrary ABCD system, though the focus for the experimental evaluation is far-field observations using an optical Fourier transform system. It is shown that the compound speckle structures move as two individual structures with the same decorrelation length. The velocity of the random speckles is a combination of angular and peripheral velocity, where the peripheral velocity is inversely proportional to the radius of the wavefront curvature of the incident beams. The velocity of the repetitive structure is a combination of angular and peripheral velocity, where the peripheral velocity is proportional to the ratio of the angle to the distance between the beams in the object plane. Experimental data demonstrate good agreement between theory and measurements for selected combinations of beam separation, angle between beams, and radius of wavefront curvature at the object.