Displacement field gradient measurement using the speckle photography method

Discussion of the effect of relative displacements gradient on the Fourier halo of specklegram has ben conducted. It was predicted theoretically that the energy distribution of the Fourier halo obtained from the point-by-point analysis of a specklegram depends both on the type of basic speckle structure, and the Fourier transform of a diaphragm shape function for the optical Fourier processor applied. Scale factors of this transform are linear combinations of gradient tensor components. A type of the speckle structure is determined by the characteristic function, defined as a sum of double convolution of the speckle shape function. The theoretical results were verified experimentally for various configurations of translation, strain and rotation, respectively.